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42 LS06 Abstracts

CP1

A One-Dimensional Model of Blood Flow in Arter-ies with Friction, Convection and Unsteady TaylorDiffusion Based on the Womersley Velocity Profile

We present a one-dimensional model for blood flow in ar-teries, without assuming an a priori shape for the velocityprofile across an artery. We combine the one-dimensionalequations for conservation of mass and momentum withthe Womersley model for the velocity profile. The veloc-ity profiles produced are used to evaluate the friction, tocorrect the nonlinear terms and in unsteady Taylor diffu-sion theory. We present flow simulations for numerical anddisease modeling purposes.

Charles S. PeskinCourant Institute of Mathematical SciencesNew York [email protected]

Karim AzerCourant Institute of Mathematical Sciecnes, NYUKarim [email protected]

CP1

Simplified Models of the Respiratory Control Sys-tem.

We have developed simplified mathematical models for thecontrol of respiration in mammals. One component con-sists of a model of the brainstem respiratory oscillatorthat incorporates regulation of frequency and amplitude ofbreathing in response to physiological control signals (oxy-gen and carbon dioxide). The neural model was coupledto simplified models of the lungs incorporating oxygen andcarbon dioxide transport. The models explain some exper-imental observations on open- and closed-loop regulationof breathing.

Alona Ben-TalMassey UniversityInstitute of Information & Mathematical [email protected]

Jeffrey C. SmithNINDS, [email protected]

Ilya RybakDrexel UniversitySchool of Biomedical [email protected]

CP1

An Evolutionary Hybrid Cellular AutomatonModel of Solid Tumour Growth

We propose a model of tumour growth, in which each cellis equipped with a micro-environment response network.This network determines the cellular behaviour, and is sub-ject to mutations and subsequently Darwinian evolution.Using this approach we have investigated the impact ofthe tissue oxygen concentration on the growth and evolu-tionary dynamics of the tumour. The results show that theoxygen concentration affects both the genetic diversity andmorphology of the tumour.

Philip GerleeUniveristy of Dundee

[email protected]

Alexander AndersonDepartment of MathematicsUniversity of [email protected]

CP1

Simulating Cardiac Blood-Muscle-Valve Mechanicsby An Adaptive Version of the Immersed BoundaryMethod

Cardiac mechanics can be modeled as the interaction ofa viscous incompressible fluid (the blood) and a (visco-)elastic structure (the walls and valves of the heart). Theimmersed boundary (IB) method is an approach to suchproblems. We shall present an adaptive version of theIB method and describe the application of this adaptivemethodology to the three-dimensional simulation of bloodflow in the heart. Computer animations of the beatingheart will be shown.


David M. McQueenCourant Institute for Mathematical SciencesNew York [email protected]

Richard HornungLawrence Livermore National [email protected]

Boyce E. GriffithCourant Institute of Mathematical SciencesNew York [email protected]

CP1

Finite Elements and Operator Splitting Methodfor the Numerical Simulation of Fluid Flow in De-formable Domains with Application to Blood Flow

The modeling of blood flow in human arteries involvesa Fluid-Structure Interaction problem (FSI) because theregion itself in which the fluid is confined changes as aconsequence of the fluid motion. Several approaches areavailable to simulate FSI. Our goal is to explore the ben-efits and the applicability of a numerical algorithm basedon finite elements method and operator splitting in orderto avoid iterative procedures for the location of the de-formable boundary.

Tsorng-Whay PanDepartment of MathematicsUniversity of [email protected]

Giovanna Guidoboni, Roland GlowinskiUniversity of HoustonDepartment of [email protected], [email protected]

LS06 Abstracts 43

CP1

An Arterial Blood Pressure Model

The arterial pulse pressure waveform analysis has impor-tant clinical applications. Some approximations of the flowdescribed by Navier-Stokes equations can be written asN-soliton solutions of a Korteweg-de Vries equation, com-pleted by a windkessel flow. Experiments show that N =2 or 3, leading to a model with a small number of parame-ters that can be useful in new diagnosis methods based onindexes of pulse pressure shape variability estimated fromnon-invasive measurements.

Michel [email protected]

Emmanuelle CrepeauLaboratoire de Mathematiques AppliqueesUniversite de Versailles [email protected]

Taous-Meriem LalegINRIA [email protected]

CP1

Deformation of a Circular Rod with Twist andBend in Fluids

The overwound or underwound double helix of DNA occursin DNA transcription, DNA replication, and formation ofDNA loops in protein-DNA interactions, which are essen-tial in biological processes. In particular, the deformationof circular DNA molecules occurs in many prokaryotic andviral DNAs and also occurs in the mitochondria of eukary-otic cells. We consider an elastic rod in a closed circularconfiguration with a uniform twist that adds up to an in-teger number of full turns so that the triad configurationis smoothly periodic. Moreover this rod is embedded inthe incompressible viscous fluid. The immersed boundarymethod is used to study the instability of a circular rodwith twist and bend. Without twist, a closed circular rodgives an equilibrium configuration; that is, there is no netforce or torque and it is stable. But with enough twist,the circular configuration becomes unstable, and the rodrelaxes to a stable coiled configuration.

Sookkyung LimMathematical Biosciences InstituteThe Ohio State [email protected]

CP1

The Open Nucleotide Pocket of the Profilin:actinX-Ray Structure Is Unstable and Closes in the Ab-sence of Profilin

The open nucleotide pocket conformation of actin in theprofilin:actinCaATP x-ray structure is hypothesized to bea crucial intermediate for nucleotide exchange during actindepolymerization/polymerization. The necessary modifi-cation of actin with profilin for crystallization leads to am-biguities in this interpretation. Molecular dynamics simu-lations of the open nucleotide pocket, profilin-free actinstructure show the structure is actually unstable, andcloses. Thus there is currently no thermodynamically sta-ble structure representing the open nucleotide pocket state

of actin.

Peter KollmanDepartment of Pharmaceutical [email protected]

Edward F. PateDepartment of MathematicsWashington State [email protected]

Roger CookeUniversity of California, San [email protected]

Todd MinehardtDepartment of Pharmaceutical [email protected]

CP2

Mathematical Model of Steroidogenesis to Pre-dict Intracellular Response to Endocrine Disrupt-ing Compounds

Exposure to endocrine disrupting compounds (EDC) caninduce adverse effects on reproduction mediated throughalterations in the enzymes involved in steroidogenesis. Weare developing a deterministic model of the intratesticularand intraovarian metabolic network in fish that mediatessteroidogenesis. This model allows for an improved under-standing of the source to outcome linkages necessary forrisk assessments with EDCs. This work was reviewed bythe U.S. EPA and approved for publication but does notnecessarily reflect Agency policy.

Daniel Villeneuve, Gerald AnkleyU.S. Environmental Protection [email protected], [email protected]

Michael S. Breen, Rory B. ConollyNational Center for Computational ToxicologyU.S. Environmental Protection [email protected], [email protected]

CP2

Combining BrdU-Labeling Experiments and Math-ematical Modeling to Understand Natural KillerCell Development and Homeostasis

Its unclear which role population dynamics play in thedistribution of NK cells over different maturation stagesand in shaping the receptor repertoire. Experimental datawere used to test different mathematical models and to op-timize population dynamical parameters. Similar studieswere performed on spleen cells, in order to elucidate matureNK cell homeostasis. Results will be discussed with respectto understanding the regulation of adaptive immunity andspecification of important stages in NK cell selection.

Marjet ElemansKarolinska [email protected]

Maria Johansson, Eleftheria RosmarakiKI-MTC

44 LS06 Abstracts

[email protected], [email protected]

Ramit MehrFaculty of Life SciencesBar-Ilan [email protected]

CP2

Large Scale Statistical Parameter Estimation forthe Dynamic Cardiac Metabolism During Ischemia

We propose a Bayesian methodology which integrates, viaa prior distribution, constraints and prior knowledge intothe parameter estimation process for a three-compartmentdynamic model for the cardiac metabolism. The severelyunderdetermined parameter estimation problem is thensolved by a combination of optimization methods and sta-tistical sampling techniques. A study of the stability ofsensitivity to serve as a basis for model reduction is alsoproposed.

Rachael S. HagemanCase Western Reserve UniversityDepartment of [email protected]

Daniela Calvetti, Rossana OcchipinitiCase Western Reserve University, Dept of MathematicsCenter for Integrated Metabolic [email protected], [email protected]

Erkki SomersaloHelsinki University of TechnologyLaboratory of [email protected]

CP2

Germline Codon Usage As An Indicator of ImmuneSelection Dynamics

The genetic code defines the relationship between genotypeand phenotype at the basis of all processes of evolution.Based on a network view of the genetic code, in whichevery codon is a node and every edge is a mutation, westudied the enclosed process of selection leading to affinitymaturation of immune receptors. We found that differentgermline receptor DNA prime different types of change ap-propriate to movement in affinity landscapes of differingroughness.

Uri Hershberg, Mark ShlomchikSection of Immunobiology, Department of LaboratoryMedicineYale University School of [email protected], [email protected]

CP2

Regulation Mechanisms in the Immune System

We model interactions among effector and regulatory Tcells during an immune response to two simultaneous tar-gets to show that the system discriminates based on targetbehavior and not only TCR affinity. The model affirmsthe necessity of regulatory cells for self-tolerance, but alsoshows that low amounts do not hinder, but enhance strongresponses by inducing T cell contraction and emigration

from the lymph node, leading to rapid target elimination.

Peter S. KimStanford [email protected]

Peter LeeStanford UniversitySchool of [email protected]

Doron LevyStanford [email protected]

CP2

Modeling Osteoporosis: Predicting HumanBiomarker Response to Parathyroid Hormone

Parathyroid hormone (PTH) is a potent bone formingagent that is used to treat severe osteoporosis. PTH-mediated signal transduction modulates the natural boneremodeling cycle and achieves net gain in bone mass withdaily dosing. A mathematical model for the human boneremodeling cycle has been developed that predicts the ef-fects of PTH on bone remodeling and related biomark-ers. Model simulations explore the effects on biomarkersof PTH dosing patterns and variability in PTH pharma-cokinetics.

Laura K. PotterGlaxoSmithKlineScientific Computing and Mathematical [email protected]

Frank TobinScientific Computing & Mathematical [email protected]

CP2

Vanguard Neural Crest Cells Colonize the Gut:Mathematical and Experimental Analyses

Neural crest cells (NCC) colonize the embryonic gut. Fail-ure of this colonization results in Hirschsprungs Disease(HD). A continuum model is developed to replicate NCCcolonization and predictions are compared with experimen-tal observations. NCC colonization is driven by vanguardproliferation. Accordingly, we examine the case where van-guard proliferation is artificially suppressed. Both experi-ments and modelling predict that colonization still occurs.These results explain why genes that influence NCC pop-ulation size cause HD when mutated.

Michael Mariani, Donald NewgreenThe Murdoch Childrens Research [email protected], [email protected]

Matthew J. SimpsonDepartment of Mathematics and StatisticsThe University of [email protected]

Kerry A. LandmanDepartment of Mathematics amd StatisticsUniversity of [email protected]

LS06 Abstracts 45

CP2

Modeling Extracellular Matrix Realignment Dur-ing Glioblastoma Invasion in An in Vitro Experi-ment

The outcome for patients with highly malignant brain tu-mors is extremely poor. One factor that makes GBM diffi-cult to treat is its high invasiveness. To better understandinvasion, we study a 3D assay for tumor spheroid inva-sion in collagen gel. Previous work indicates that invasivecells follow directed paths away from the tumor spheroidand we present a model that illustrates how the interac-tions between invasive cells and collagen fibrils can causedirected motility.

Andrew M. SteinUniversity of MichiganUniversity of [email protected]

CP3

Reduced Models of Networks of Electrically Cou-pled Neurons

Neurons in the brain are coupled both chemically(synapses) and electrically (gap junctions). In networksof chemically coupled neurons, the precise details of thevoltage spikes are often unimportant. It is therefore rea-sonable to model voltage spike shapes either in stereotyp-ical ways, or even not at all, as in the integrate-and-firemodel. By contrast, the speed at which signals propagatethrough networks of electrically coupled neurons can besensitive to the details of spike shapes. For reduced mod-els such as integrate-and-fire models, this raises accuracyissues. We demonstrate these issues computationally, anddiscuss ways of resolving them.

Christoph Borgers, Erin C. MunroTufts [email protected], [email protected]

CP3

A Stochastic Model for Neuronal Membrane Po-tential and Time-Varying Inputs

We propose a stochastic model for the firing activity of aneuronal unit, that is based on a suitable exponential trans-formation of a continuous-time stochastic process subjectto random jumps. Such a model includes the decay effectof the membrane potential in absence of stimuli, and theoccurrence of various types of tyme-varying inputs. Ananalysis of the probability distributions of the membranepotential and of the firing times is performed.

Antonio Di CrescenzoDipartimento di Matematica e InformaticaUniversita‘ di [email protected]

CP3

“Equation-Free” Modelling of Neural Systems

“Equation-free” modeling allows one to compute with theeffective equations governing the macroscopic dynamics ofa system even if they cannot be explicitly derived, pro-vided that the microscopic dynamics are known. Thesetechniques can be used to do bifurcation analysis of com-plex networks of neurons. We demonstrate these ideas forseveral types of networks, studying steady states and spa-

tiotemporal patterns such as bumps and waves.

Carlo R. LaingMassey [email protected]

CP3

Waves and Noise in Dendrites with Active Spines

Dendrites form the major components of neurons and manyare equipped with excitable channels located in spines.Computationally we obtain a quasi–analytic solution whichcan be used to study the neural response to spatio-temporalpatterns of synaptic input. We examine the robustness ofthe wave propagation to both space-time white and corre-lated noise that arise in the cable (eg electrical coupling)and spine-heads (eg stochastic gating) through weak andstrong approximations.

Gabriel J. LordHeriot-Watt [email protected]

Yulia TimofeevaThe University of [email protected]

Steve CoombesUniversity of NottinghamDivision of Applied Mathematics, School of [email protected]

CP3

Neural Timing in Highly Convergent Systems

In order to study how the convergence of many variableneurons on a single target can sharpen timing information,we investigate the limit as the number of input neurons andthe number of incoming spikes required to fire the targetboth get large with the ratio fixed. We use asymptoticforms of the density and the standard deviation near thelimit to understand the behavior of octopus cells in themammalian cochlear nucleus.

Michael C. ReedDuke [email protected]

Colleen C. MitchellUniversity of IowaDepartment of [email protected]

CP3

Inverse First Passage Time Methods and Their Ap-plications to Neuronal Modeling

We consider an Ornstein-Uhlenbeck diffusion process Xt

constrained by an unknown absorbing boundary S(t). Weassume known the distribution of the time T when theprocess crosses for the first time the boundary. The aimof our study is to determine the boundary shape. Twoalternative algorithms are proposed and their features arediscussed. Application of these methods to a classificationalgorithm and to detect non-stationarity in observed data

46 LS06 Abstracts

in a neuroscience context is presented.

Laura Sacerdote, Cristina ZuccaDept. MathematicsTorino [email protected], [email protected]

CP3

Wavelet Analysis of Neurophysiological Signals

Using wavelet analysis we have studied: (a) movement-related changes in the local field potentials recorded fromthe subthalamic nucleus of patients with Parkinsons dis-ease, (b) cortical control of hand movement in healthy sub-jects from functional MRI time series, and (c) seizure EEGin kindled epileptic rats. The mathematical framework andsome results of the analysis of these neurophysiological sig-nals will be discussed.

Moran Weinberger, Jonathan DostrovskyDepartment of PhysiologyUniversity of [email protected], [email protected]

Kristine MosierDepartment of RadiologyIndiana [email protected]

Michael KubekDepartment of Anatomy & Cell BiologyIndiana [email protected]

Harlan ShannonDivison of CNS ResearchEli Lilly Research [email protected]

Asok K. SenProfessor of Applied [email protected]

CP3

Modeling Excitatory Neurotransmitter TransportProcesses

Synapses in the central nervous system adapt to reflect thehistory of received action potentials on a molecular level,a phenomenon known as synaptic plasticity. Of recent in-terest is the question of “spill-over”, can neurotransmittersreleased at one presynaptic terminal escape that cleft andeventually trigger a response in neighboring synapses? Toaddress this question we are coordinating experiments onthe transport systems responsible for mediating the up-take and sequestration of the excitatory neurotransmitterglutamate (M. Kavanaugh, UM), with the analysis of com-putational models.

Emily F. StoneDept. of Mathematical SciencesThe University of [email protected]

CP4

Virus Competition at Multiple Scales

Viruses compete and are subject to natural selection

at multiple levels: within-cell, within-host and within-population (of hosts). We looked at how viruses can op-timally exploit their hosts and how this behaviour mayinfluence the most successful strategy at the between-host,or epidemiological level. I will present a fairly general wayto consistently combine models of disease process and dis-ease spread with the goal of understanding the net selectionpressure on a model virus. The method is illustrated usingtwo popular models at the within- and between-host levels.

Daniel CoombsUniversity of British [email protected]

Michael A. GilchristUniversity of TennesseeDept. of Ecology & Evolutionary [email protected]

Colleen BallUniversity of British [email protected]

CP4

The Role of IL-2 in CD4 T Cell Proliferation: In-sights from Modeling CFSE Data

We analyze the data on the dynamics of CFSE-labeled CD4T cells in vitro at suboptimal concentrations of IL-2 usingseveral mathematical models. We find that to adequatelydescribe the data, the death rate of divided cells needs toincrease with the number of divisions cells have undergone.Our results suggest that IL-2 regulates expansion of CD4T cell by increasing dependence of cell death rate on thedivision number, and not by speeding up cell division.

Dejan MilutinovicTheoretical BiologyUtrecht [email protected]

Rob De BoerDivision of Theoretical BiologyUtrecht [email protected]

Vitaly V. GanusovTheoretical BiologyUtrecht [email protected]

CP4

Influenza A Virus Infection Dynamics and its De-pendence on Antibody Response

We present a mathematical model of IAV infection in anindividual, explore the effect of initial viral load and per-form sensitivity analysis to explore which parameters in-fluence the onset, duration and severity of infection. Im-mune memory is modeled by a new variable that quantifiesthe antigenic distance between the virus and the existingantibodies. We find that if antibody response is low ornonexistent, chronic disease may develop.

Baris HanciogluUniversity of PittsburghDepartment of [email protected]

LS06 Abstracts 47

Gilles ClermontUniversity of PittsburghDepartment of Critical Care [email protected]

David SwigonDepartment of MathematicsUniversity of [email protected]

CP4

Ebv-Cimmsim: An Agent-Based Model of EpsteinBarr Virus

Epstein Barr virus (EBV) infects more than 90% of allhumans benignly for life but occasionally leads to onco-genic transformation in susceptible individuals. As EBVis a human pathogen, appropriate animal models do notexist. In this talk, I will present an agent-based model,EBV-CImmSim, which simulates both the acute and thechronic phases of EBV infection. The results of this modelcorrespond qualitatively to data relating to the infected B-cell dynamics derived from patients presenting with acuteinfectious mononucleosis (AIM). Furthermore, the modelsuggests that EBV persistence is maintained via exit of la-tently infected B cells into the circulation, which acts asa reservoir for continuous reactivation of the virus. In theabsence of this compartment, the infection is cleared.

Abdul Salam JarrahVirginia Bioinformatics InstituteVirginia [email protected]

F. CastiglioneIstituto Applicazioni del CalcoloRome, [email protected]

K. DucaVirginia Bioinformatics InstituteVirginia [email protected]

V. Hadinoto, D. Thorley-LawsonTufts U. Medical SchoolBoston, [email protected], [email protected]

R. LaubenbacherVirginia Bioinformatics InstituteVirginia [email protected]

CP4

A Dynamic Model for Induced Reactivation of La-tent Virus

We report on a deterministic mathematical model to de-scribe reactivation of latent Kaposi’s Sarcoma-associatedHerpese Virus (KSHV) in BCBL-1 cell cultures. Modelparameters are estimated from properties of uninducedcell cultures undergoing spontaneous reactivation. Addi-tional parameters that describe chemically-induced reacti-vation are determined, by fitting to experimental data andstandard errors are reported. This model provides goodagreement with experimental data and establishes a gen-eral framework for modeling of other inducers and latent

viral-cell systems.

Hoan NguyenCenter for Research in Scientific ComputationNorth Carolina State [email protected]

jennifer Webster-CyriaqueDepartment of Dental EcologySchool of Dentistry, [email protected]

ht Banks, Grace M. KeplerCenter for Research in Scientific ComputationNorth Carolina State [email protected], [email protected]

CP4

Continuous Model for the Rock - Scissors - PaperGame Between Bacteriocin Producing Bacteria

In this work, important aspects of bacteriocin produc-ing bacteria and their interplay are elucidated. Variousattempts to model the Resistant, Producer and Sensi-tive Escherichia coli strains in the so called RSP (Rock-Scissors-Paper) game have been made and the questionarose whether there is a continuous model that admits acyclic structure. The observations in experiments showeda cyclic dynamics of these three competing species. Thispaper gives a possible competitive Lotka-Volterra systemmodel and clarifies the underlying dynamics. A continu-ous, spatially homogeneous competitive model, describingthe interactions between these bacteria with an exact pa-rameter set for a robust coexistence, is established. Alsostatistical effects will be considered. There are medicalapplications in eukaryotic organisms such as Malaria andinfectious diseases.

Gunter F. NeumannFriedrich-Schiller-University, Jena.Chair of [email protected]

Stefan SchusterFriedrich-Schiller-University JenaDepartment of [email protected]

CP4

Mathematical Modeling of Hhv-6 Immune SystemDynamics

We propose a mathematical model for describing the im-mune system response to the Human Herpesvirus-6 in-fection. Our research is focused on the cellular responseof CD4/CD8 T-cells at infection. Starting with a simplemodel that can be applied to clinical data, we estimatevalues of important parameters. The predictions based onthis beginning model, and the future work for improve-ment of it to a realistic model through adapting to newexperimental data, will be discussed.

Jeong-Mi YoonDepartment of Computer & Mathematical Sciences,University of [email protected]

Mandri ObeyesekereUniversity of Texas M. D. Anderson Cancer Center

48 LS06 Abstracts

[email protected]

CP5

Effect of Space and Stochasticity on Two Compet-ing Plant System

The talk aims in studying the effect of space and stochas-ticity on two competing plant species, of which one is a su-perior competitor and the other, a superior disperser. Thesystem is modeled as a spatially structured Markov processand is analyzed using systematic perturbation expansion,based on the theory of distributions to account for spaceand the underlying stochastic differential equations to ac-count for stochasticity. Analytical results are compared tosimulations of the underlying Markov Processes.

Otso OvaskainenDepartment of Biological and Environmental SciencesUniversity of [email protected]

Sandip BanerjeeUniversity of [email protected]

CP5

The Impact of External Forcing on Invasion, Ex-tinction and Coexistence

External forcing can have a significant impact on ecologicaland epidemiological systems, not only through resonanceamplification and the generation of subharmonics but alsoin shifting the thresholds at which a species becomes ex-tinct or invades a community. This threshold phenomenonis clearly of great importance in wildlife management andmedical science. Conditions for threshold shift are deter-mined for many species differential equation systems andtheir dependence on subharmonic resonance established us-ing Lyapunov exponent analysis.

Jonathan V. GreenmanUniversity of [email protected]

CP5

Modeling Marine Phage Ecology

Marine phage infect bacteria, the largest biomass in theocean, and daily destroy about 25% of the marine bacteria,playing an important role in the carbon cycle of the oceans.Still little is known about phage ecology and population dy-namics. From shotgun sequencing, our mathematical mod-els based on a Lander-Waterman algorithm explain aboutspecies diversity and abundance of marine phage. A twocompartment model is developed, and parameters are fit todescribe phage/bacteria dynamics. Analysis of the modelgives stable and oscillatory regimes for this system thatmatch biological experiments.

Joseph M. MahaffySan Diego State UniversityDept of Mathematical [email protected]

CP5

Effects of Non-Reproductive Groups on Population

Growth

We describe several population models exposed to a mildand long standing infectious disease, i.e. without signifi-cant increased natural mortality rate among infected indi-viduals, and providing no immunity/recovery. We modifythese models to include non-reproductive groups, and ana-lyze their potential effects on the dynamics of the popula-tion. We are interested in how the non-reproductive classmay curb the growth of the infected group while keepingthe healthy population at acceptable levels.

Fabio A. MilnerPurdue UniversityDepartment of [email protected]

Daniel MaxinPurdue University, [email protected]

CP5

Interactions Between Dispersal, Competition andLandscape Heterogeneity

I describe and interpret results obtained from analysinga set of stochastic, spatially explicit models of populationdynamics. The analytical method employed a novel math-ematical technique that uses stochastic differential equa-tions. Spatial heterogeneity is generally found to have apositive effect on populations. With regards to both patchsize and dispersal scale, an intermediate level is found to beoptimal, due to a conflict between minimising endogenouscompetition and maximising the benefits of heterogeneity.

Ace R. NorthUniversity of [email protected]

CP5

Modelling the Spatio-Temporal Dynamics of Multi-Species Host-Parasitoid Interactions: AggregatedSearching, Heterogeneous Patterns and EcologicalImplications

A mathematical model of the spatio-temporal dynamics ofa two host, two parasitoid system is presented. There isa coupling of the four species through parasitism of bothhosts by one of the parasitoids. When searching for hosts,the parasitoids are observed to aggregate in response tochemical signalling cues emitted by the host plants dur-ing host feeding, a phenomenon which is widely reported.We model this aggregative parasitoid behaviour in a multi-species community using a reaction-diffusion-chemotaxismodel. The spatio-temporal dynamics of our system high-light behaviour of significant interest. In addition to inva-sive behaviour characterised by travelling waves, we ob-serve both quasi-chaotic dynamic heterogeneous spatio-temporal patterns and a destabilisation of the system toproduce quasi-stationary heterogeneous patterns. We showthat the destabilisation is due to chemotaxis. The dynam-ical behaviour of our system has significant ecological im-plications and the concepts of stability and coexistence,biological control and evolution of parasitoid searching be-haviour are discussed.

Mark Chaplain, Alexander R. A. AndersonDivision of MathematicsUniversity of Dundee

LS06 Abstracts 49


Peter G. [email protected]

Stephen F. HubbardDivision of Applied and Environmental BiologyUniversity of [email protected]

Ian G. PearceDivision of Mathematics, University of [email protected]

CP5

Invading Beetles in Nyc: Modeling a ContagionProcess with Timing Uncertainty

We present a model of the spread of a contagious process ona network of nodes that allows the incorporation of uncer-tainty about the timing of events. The model is appropriatefor analyzing real-world data on the spread of disease, orof an invasive species. We illustrate the model by applyingit to data on the spread of the invasive Asian LonghornedBeetle among the street trees of New York City.

Gareth J. RussellNew Jersey Institute of [email protected]

Jacqueline LuNew York City [email protected]

CP5

Nonlinear Dynamics of a Demographically andSpatially Structured Population under Perturba-tion

In some situations the management objective of a nuisancepopulation is to achieve a steady-state equilibrium signif-icantly below the carrying capacity. Achieving such anobjective through harvest may be complicated by the pres-ence of stage and spatial structure in the target population.In such cases, optimal harvest strategies must account fordifferences among classes of individuals in their relativecontribution to the population. We consider this hetero-geneity in the dynamics of density-dependent structuredpopulations.

Evan Cooch, Patrick SullivanCornell UniversityDepartment of Natural [email protected], [email protected]

Elise ZipkinCornell [email protected]

CP6

A Mechanism for Morphogen-Controlled DomainGrowth

Growth is a fundamental aspect of development: it re-sults from a tightly regulated combination of processes in-cluding cell differentiation, division and movement. Re-

cent experimental studies have highlighted the role of amorphogen (Dpp) in controlling domain growth in theDrosophila wing. We model this phenomenon using a sys-tem of reaction-diffusion equations with advection. Anal-ysis is carried out using a Lagrangian based approach andresults show how uniform growth across the wing may beachieved.

Ruth E. Baker, Philip K. MainiCentre for Mathematical BiologyUniversity of [email protected], [email protected]

CP6

Data Pooling and Robust Dynamic Prediction inPredictive Fermentation Microbiology

A desirable feature of mechanistic models of bacterial pop-ulation growth is that they describe the interaction be-tween a bacterium and its micro-environment in a frame-work that can be calibrated under relevant experimentalconditions. I present a two-phase modeling approach thatpermits validation the environmental dynamics prior to fullmodel validation. In this talk, I will discuss the approachand introduce a model building and database managementsoftware that facilitates collaboration among multiple re-search groups via the internet.

Daniel P. DoughertyLyman Briggs School of ScienceDepartment of Statistics and Probability, [email protected]

CP6

Hyperbolic Models for Chemosensitive Movementin Interacting Cell Systems

In the talk, we present two hyperbolic models in interact-ing cell systems. The first model describes chemotacticcell movement driven by a diffusive external signal whilethe second model in addition includes intracellular signaltransduction mechanism to the cell dynamics. Macroscopicbehavior in biological systems can be explained in terms ofmicroscopic parameters of the hyperbolic models. The con-ditions for global existence are also investigated in termsof the properties of signal transduction network .

Radek ErbanUniversity of OxfordMathematical [email protected]

Kyungkeun KangSungkyunkwan [email protected]

Angela StevensMax-Planck-Institute for Mathematics in the Sciencesin [email protected]

Hyung Ju HwangDepartment of Mathematics, Trinity College [email protected]

CP6

Better Triple-Drug Regimen for Hiv: Evaluating

50 LS06 Abstracts

Clinically Feasible Strategies

Current HIV drug therapy, although highly effective, maycause severe side effects making adherence to the prescribedregimen difficult. We weigh the positive results of treat-ment, such as higher helper T-cell levels, against such neg-ative consequences; the appropriate weights can be esti-mated by considering clinical determinants of when to ini-tiate therapy. We then systematically compare clinicallyfeasible triple-drug strategies based on expected treatmentoutcome, including the possibility that therapy will fail dueto emergent drug resistance.

Olga KrakovskaDepartment of Applied MathematicsThe University of Western [email protected]

Lindi M. WahlDept of applied mathematicsUniversity of Western [email protected]

CP6

Emergent Bursting in Small Networks of Condi-tional Square-wave Bursting Cells

Consider a population of neurons that are all capable ofsquare-wave bursting when given appropriate inputs, buttuned such that some cells are silent, some are bursting,and some are tonically active. When synaptic coupling isintroduced, how will the population behave? In this talk,I will discuss ways in which synaptic coupling promotesemergent bursting in the network. In particular, I will ex-plain a mechanism that can lead to network bursting, evenwhen none of the cells in the network burst in isolation. Iwill use models for conditional respiratory pacemaker cellsin the pre-Botzinger complex to illustrate this mechanism.

Jonathan E. RubinUniversity of PittsburghDepartment of [email protected]

CP6

Reaction Diffusion and Density Dependent Chemo-taxis

A system of reaction-diffusion equations with volume fillingchemosensitivity is considered. Questions of existence anduniqueness ansas well as qulitative behaviour of solutions isdiscussed. Applications to morphogenesis and angiogenesisare outlined.

Brian SleemanLeeds [email protected]

CP6

Analyzing Morphogen Interpretation Mechanismsin the Developing Brain

The mechanism of morphogen interpretation ”[Ashe HL,Briscoe J. The interpretation of morphogen gradients. De-velopment. 2006 Feb;133(3):385-94. ]” at the cellular levelis important in understanding the role of morphogen gra-dients in cell fate specification, proliferation, and furthersignalling cascades. Models of morphogen interpretation

mechanisms involve complex biological networks, whichcan be analyzed with computational tools such as logi-cal and ODE-based methods ”[ THOMAS, R. and KAUF-MAN, M., ”Multistationarity, the basis of cell differentia-tion and memory. II. Logical analysis of regulatory net-works in terms of feedback circuits.”, Chaos 11, (2001)180-195.]”,”[ THOMAS, R. and KAUFMAN, M., ”Multi-stationarity, the basis of cell differentiation and memory. I.Structural conditions of multistationarity and other non-trivial behavior.”, Chaos, 11 (2001) 165-179.]”. We usethese tools in conjunction with experimental data to iden-tify morphogens and interpretation mechanisms, which in-duce bistable behavior in the developing brain ”[MonukiES, Porter FD, Walsh CA. Patterning of the dorsal telen-cephalon and cerebral cortex by a roof plate-Lhx2 pathway.Neuron. 2001 Nov 20;32(4):591-604. ]”. We also discussimplications for biological phenomena such as robustness.

Wayne Hayes, Edwin Monuki, Shyam SrinivasanUniversity of California, [email protected], [email protected], [email protected]

CP6

The Role of Wnt Signaling in Colorectal Cancer: aTheoretical Study

Wnt signaling regulates gene expression in development,stem cells and colorectal cancer by controlling β-cateninlevels. As β-catenin is also a primary component of ad-herens junctions, we developed an ODE model to investi-gate how transcription and adhesion interact. Some exper-imentalists hypothesise that the system is purely compet-itive, whereas others propose the presence of two forms ofβ-catenin. Our model allows us to discriminate betweenthese theories on the basis of their response to specific sys-tem perturbations.

Ingeborg Van LeeuwenUniversity of NottinghamCentre for Mathematical [email protected]

Oliver JensenApplied MathematicsUniversity of [email protected]

John KingUniversity of NottinghamSchool of Mathematical [email protected]

Helen ByrneUniversity of NottinghamCentre for Mathematical [email protected]

CP7

Biological Control Through Intraguild Predation:a Case Study In

Rusty crayfish are aggressive invaders of the Great Lakesecosystem. They interact with indigenous smallmouth bassthrough intraguild predation. Mature bass are predatorsof rusty crayfish, but predation is gape-limited, the largestcrayfish escaping predation. These individuals are the mostfecund and compete with juvenile bass, causing a “juvenilecompetitive bottleneck.” We used a stage-structured modelto investigate the biological control of rusty crayfish by

LS06 Abstracts 51

smallmouth bass and suggest methods for effective control.

Mark LewisUniversity of Alberta, [email protected]

Caroline J. BampfyldeDepartment of Mathematical & Statistical SciencesUniversity of [email protected]

CP7

Stochastic Stable Population Growth in IntegralProjection Models: Theory and Application

Integral projection models generalize classical matrix pro-jection models by allowing individuals to be cross-classifiedby multiple attributes, discrete or continuous. We showthat stochastic integral models share the qualitative prop-erties of stochastic matrix models that are essential for ap-plications: existence of a long-term growth rate, ergodicityof population structure, and asymptotic lognormality oftotal population. Case-studies demonstrate model param-eterization from empirical data, and applications in situa-tions that pose difficulties for conventional matrix models.

Stephen P. EllnerCornell UniversityDept. of Ecology and evolutionary [email protected]

Mark ReesUniversity of SheffieldDepartment of Plant and Animal [email protected]

CP7

Diet Selection As An Asynchronous DifferentialForaging Game

An important issue addressed by Behavioural Ecology isthat of the evolutionary relevancy of foraging strategiesadopted by animals in quest of a patchily distributed re-source, both in terms of diet selection and patch-leavingdecisions under competition. Solving the correspondingasynchronous non-zero sum differential game, which in-volves discontinuous state feedback strategies constructedvia a regular synthesis technique, requires a careful anal-ysis of the induced discontinuities of the adjoint variables.Partial preferences arise in several fashions.

Frederic HamelinCNRS and University of Nice - Sophia Antipolis – I3SINRA Sophia [email protected]

Pierre Bernhard, aj ShaijuCNRS and University of Nice - Sophia Antipolis – [email protected], [email protected]

eric WajnbergINRA Sophia [email protected]

CP7

Modelling P.HERMAPHRODITA Nematode Dis-

persal in Homogeneous Environments

We consider a correlated random walk in two dimensionsfor simulating the movement of the slug parasitic nema-tode P.hermaphrodita in order to quantify its dispersal inhomogeneous environments. The correlated random walkleads to anomalous diffusion, more precisely to a fractionalsub-diffusion equation. The stochastic process associatedis characterized by strong memory effects on the level ofthe probability distribution function, i.e., unlike a Markovprocess, the now-state of the system depends on the entirehistory of its preparation.

Simona M. HapcaSIMBIOS Centre, University of Abertay, Dundee, UKDD1 1HG, [email protected]

John Crawford, Iain YoungSIMBIOS Centre,University of Abertay, Dundee, [email protected], [email protected]

CP7

Effects of Genetic and Phenotypic Diversity onPredator-Prey Cycles

We examine characteristics of limit cycles in a simplepredator-prey system which allows phenotypic diversityand rapid evolution in the prey species. Level of de-fense against predation and the community compositionof the prey species determine whether the system exhibitsshort-duration classical predator-prey oscillations, longer“evolutionary cycles” or exists at equilibrium. Distinc-tive phenomena resulting from rapid prey evolution includepredator-trait cycles in which prey density remains nearlyconstant while predator density and prey traits cycle.


Laura JonesCornell UniversityDepartment of Ecology and Evolutionary [email protected]

CP7

Modeling Wolf Movement in a Heterogeneous En-vironment

The effect of linear features (e.g. roads) on animal move-ment is not well understood. We derive an advection-diffusion model with variable coefficients for the mean tran-sit time, which describes the expected time for a wolf tointeract with environment features, including prey items.This formulation is the adjoint of the forward Kolmogorovequation. By analyzing the model under various linear fea-ture configurations and densities, we demonstrate the effectof linear features on predator-prey interactions.


Hannah Mckenzie, Evelyn MerrillUniversity of [email protected], [email protected]

52 LS06 Abstracts

CP7

Does Transient Spatiotemporal Chaos Apply toEcological Systems?

A sudden, system-intrinsic collapse of spatiotemporal chaosto regular dynamics is a striking phenomenon; it was sug-gested as a source for species extinction. The Gray-Scottsystem captures fundamental ecological mechanisms likedensity dependent species reproduction, food competition,species decay, and dispersal. Numerical studies show thatthe transient time increases exponentially with mediumsize. The collapse process is robust to noise, but the av-erage transient lifetime can be influenced drastically. Wealso find that few nonlocal connections in the network canprevent the collapse phenomenon.

Renate A. WackerbauerUniversity of Alaska FairbanksDepartment of [email protected]

Sumire KobayashiDartmouth CollegeDept of [email protected]

Safia G. YonkerUniversity of Alaska, FairbanksPhysics [email protected]

CP7

Modelling Dispersal in Highly Fragmented Land-scapes

We model dispersal in highly fragmented landscapes as acorrelated random walk incorporating edge-mediated be-havior, and employ its diffusion approximation to deriveclosed expressions for various characteristics of the disper-sal process, e.g. average time of an individual spendingin current patch i before hitting patch j, conditional thatit will hit patch j before hitting any of the other patchesor dying. Our results can be used to construct individual-based simulation models of movement.

Otso Ovaskainen, Chaozhi ZhengDepartment of Biological and Environmental SciencesUniversity of [email protected], [email protected]

CP8

Adaptive Control of Abnormal Rhythms in a Patchof Cardiac Tissue

Suppressing cardiac arrhythmias via implantable pace-maker devices is of obvious clinical importance. Stimuliapplied by the artificial pacemaker are constrained in thatthey must preempt the stimuli applied by the heart’s nat-ural pacemaker cells. Using a mapping model of pacedcardiac dynamics, we analyze a feedback control schemeknown as extended time-delay autosynchronization (ET-DAS) which operates successfully under the above con-straint. We discuss optimal choice of the feedback gainand minimization of noise sensitivity.

Carolyn BergerDepartment of PhysicsDuke [email protected]

John W. CainDepartment of MathematicsVirginia Commonwealth [email protected]

Daniel GauthierDepartments of Physics and Biomedical EngineeringDuke [email protected]

CP8

A Mathematical Model for the Pulsatile Secretionof Gnrh Hormone by Synchronized Gnrh Neurons

Based on recently observed autocrine effects of GnRH onits own release, we develop a mathematical model for pul-satile GnRH release in which GnRH plays the roles of afeedback regulator and a diffusible synchronizing agent.Results on both the single-cell and population models ofGnRH neurons suggest that the positive and negative ef-fects of GnRH regulation through the G-proteins is suffi-cient and robust in generating GnRH pulses.

Anmar KhadraDepartment of MathematicsUniversity of British [email protected]

Yue-Xian LiUniversity of British ColumbiaDepartment of [email protected]

CP8

Traveling Pulses in a One-dimensional Neural Net-work Model with Long-range Horizontal Connec-tions

We investigate existence and stability of traveling pulsesin a one-dimensional neural network with recurrent excita-tion. The network model uses non-local integro-differentialequations whose integral kernel represents spatial distribu-tion of synaptic weights. The latter is decomposed intoan exponential representing local connections and a set ofdelta functions representing long-range patchy connections.Solving for pulse solutions of the system, we determinewave-speeds relation to threshold. Stability is determinedby zeroes of the associated Evans function.

Paul Bressloff, Zachary KilpatrickUniversity of [email protected], [email protected]

CP8

Spatially Explicit Resource Competition Modelingof Florida Plant Scrub Species

We simulated demographic consequences of resource com-petitive interactions for two indigenous Florida scrubspecies in contrasting spatial scenarios. We used data ondemography, spatial distribution, and competitive interac-tions between Ceratiola ericoides, a dominant shrub andHypericum cumulicola, an endemic scrub species to pa-rameterize mathematical functions. We assessed the con-sequences of alternative spatial configurations on the per-sistence of the endemic plant as a potential management

LS06 Abstracts 53

strategy for the restoration of endangered species.

Jessica LarsonDept. of MathematicsUniversity of Central [email protected]

Pedro Quintana-AscencioDept. of BiologyUniversity of Central [email protected]

David J. KaupInstitute for Training and Simulation & Dept. ofMathematicsUniversity of Central [email protected]

CP8

Waves of Spreading Cortical Depression

Waves of spreading cortical depression (SD) occur in ex-periments on various brain structures in different animalsand have been implicated in classic migraine with aura.Mechanisms that are believed to be important for SD in-clude ion diffusion, membrane ionic currents, osmotic ef-fects, the spatial buffer mechanism, neurotransmitter sub-stances, gap junctions, metabolic pumps, and synaptic con-nections. In this talk, continuum models of SD, consistingof coupled nonlinear diffusion equations for the ion concen-trations, will be described.

Anisha PandaDepartment of Mathematical SciencesNew Jersey Institute of [email protected]

Huaxiong HuangDepartment of Mathematics and StatisticsYork [email protected]

Robert M. MiuraDepartment of Mathematical SciencesNew Jersey Institute of [email protected]

CP8

Spatial Patterns Produced by Neural Field Equa-tions

We study spatially patterned stationary solutions of anintegro-differential equation introduced by Wilson andCowan and proposed by Amari as a model of neural ac-tivity on a layer of interconnected neurons:

∂u(x, t)

∂t= −u(x, t) +

∫R

ω(x− y)f(u(y, t))dy + h.

In particular, we investigate the existence of N -bump sta-tionary solutions, or solutions positive on a region that canbe decomposed into a disjoint union of N finite intervals.Our focus is to extend existing results for the symmetriccase, establish the linear stability of those solutions, andcharacterize a class of Mexican-hat coupling functions thatallow N -bump solutions.

J. Angela H. MurdockUniversity of Memphis

[email protected]

CP8

Analysis of the Paradoxical (excitatory) Effect ofPotassium Currents on Hormone Secretion

Lactotrophs are excitable cells. Electrical activity trans-lates into calcium entry, provoking secretion of the hor-mone prolactin. Dopamine inhibits prolactin release by in-creasing potassium currents, which hyperpolarize the cells,preventing Ca entry. Surprisingly, low concentrations ofdopamine can increase prolactin secretion. How can anincrease in inhibitory currents strengthen hormone secre-tion? We show how a small increase in fast K+ currentscould convert a spiking pattern into bursting and increaseCa2+ influx, increasing prolactin release.

Joel TabakDept of Biological SciencesFlorida State [email protected]

CP8

Stable and Metastable States in Visual Cortex

A large-scale, biophysically realistic model of turtle visualcortex is being used to study the spatiotemporal dynam-ics of cortical responses to visual stimuli. This presenta-tion uses a system of linear non-autonomous ordinary dif-ferential equations to model the system. The stability ofthe system is then studied using the theory of Lyapunovfunctions for non-autonomous systems. The analysis indi-cates the system has a single stable fixed point and multiplemetastable states.

Philip UlinskiThe University of Chicago, ChicagoDepartment of Organismal Biology and [email protected]

CP9

Coupling PDE-Based Intracellular Signaling withMembrane-Bound Monte Carlo Simulations

Microscopy evidence suggests that the spatial heterogene-ity of signaling biomolecules is important in signaling path-ways. Yet, most mathematical models assume a uniformdistribution of signaling molecules. The work presentedhere couples kinetic Monte Carlo simulations, describingthe spatial heterogeneity of membrane-bound ErbB re-ceptors, with a reaction-diffusion-advection PDE systemgoverning downstream intracellular signaling. The resultsshow that spatial heterogeneity is important for ErbB reg-ulation.

Erik AndriesDepartment of PathologyUniversity of New [email protected]

CP9

Modeling and Computation of Signal Transduc-tion of olfactory Cilia with Non-Uniform CNG andCl(Ca) Channels Distributions

Olfactory cilia contain the known components of olfac-tory signal transduction, including key aspects, cyclic-nucleotide-gated (CNG) channels and Ca2+-gated Cl-

54 LS06 Abstracts

channels (Cl(Ca)). These two channels produce primarycurrents that are induced by signal transduction eventswithin the cilia of olfactory receptor neuron. We use an-alytical and computational methods to study mathemati-cal models of certain aspects of signal transduction in frogolfactory cilia in conjunction with known experimental re-sults. Predictions on properties of the cilia are desired and,in particular, information on the distribution of the CNGand Cl(Ca) channels. We develop two group of mathemat-ical models for two different experiments, one is involvinginterplay between CNG and Cl(Ca) channels and other oneis involving the diffusion of Ca2+ into cilia and the result-ing electrical activity. All models consisting of two differ-ential equations describing Ca2+ concentration, membranepotential and some cases it is analytically solvable. Usingforward problems with matching experimental data we ob-tain estimates of spatial distribution of Cl(Ca) channelsalong the length of a cilium.

Dorjsuren BadamdorjUniversity of [email protected]

CP9

Dynamic Regulation of Interferon-Stat1 Signaling

We developed a detailed kinetic model of the Interferon-Stat1 signal transduction pathway. The model reproducesthe dynamic behavior of the pathway in a quantitativemanner for wildtype Stat1 and different mutant proteins.We analyzed the control exerted on interferon signaling bythe individual reaction and transport steps. The numericaland analytical results show that two little understood pro-cesses, nuclear dephosphorylation and nucleo-cytoplasmicshuttling of unphosphorylated Stat1, control the amplitudeand duration of Stat1 activation.

Stephan BeirerTheoretical Biophysics DepartmentHumboldt University Berlin, [email protected]

Thomas Meyer, Uwe VinkemeierAbteilung Zellulare SignalverarbeitungForschungsinstitut fur Molekulare Pharmakologie, [email protected], [email protected]

Thomas HoferTheoretical Biophysics DepartmentHumboldt University Berlin, [email protected]

CP9

Control of Cellular Apoptosis in Ovarian Follicles

In each ovarian cycle, only a definite number of folli-cles ovulate, the others degenerate through an apoptosis-mediated process. We have designed a multi-scalemathematical model where degeneration results from thehormonally-controlled confinement of follicular cells withina zone of vulnerability towards apoptosis. We study howthe control operates and how to control apoptosis by con-sidering the characteristics of the 2D-conservation law de-scribing the age and maturity structuration of the follicularcell population.

Frederique ClementINRIA [email protected]

Michel [email protected]

Nki [email protected]

CP9

Multi-Scale Models for Gene Network Engineering

Armed with increasingly fast supercomputers and greaterknowledge of the molecular mechanisms of gene expres-sion, it is now practical to numerically simulate complexnetworks of regulated biological reactions, or gene circuits.It is also becoming feasible to calculate the free energy ofnoncovalent binding of regulatory proteins to specific DNAtarget sites. We developed a hybrid stochastic-discrete andstochastic-continuous simulation algorithm, with which weobtain an accurate time-evolution of the behavior of com-plex gene circuits, including a clear picture on the role ofhighly dilute, but significant, regulatory proteins. Theseregulatory proteins are responsible for the non-linear con-trol used by biological organisms to regulate their mostimportant processes. The network simulations provide in-sight, which can guide rational engineering of regulatoryproteins and DNA operator sequences using molecular me-chanics simulations. In this presentation we examine twoimportant gene circuits, the bistable switch and the oscilla-tor. We study the role of specific biomolecular interactionphenomena on the dynamics of these gene circuits. Us-ing models that span multiple time and space scales, fromatomistic, to molecular, to interaction networks we developdesign principles for high quality bistable switch and oscil-lator circuits.

Yiannis N. KaznessisDept. of Chemical Engineering and Materials ScienceUniversity of [email protected]

Howard SalisUniversity of [email protected]

CP9

Quasi-Equilibrium Approximation of BiochemicalReaction Networks

We consider a biochemical reaction system in which reac-tions between various molecular species occur on differenttime scales. With a graph-theoretical approach, a pertur-bation method and an invariant theory we eliminate fastkinetics and reduce the system on a slow time scale. Underquasi-equilibrium assumption on deterministic descriptionof models, we explore a reduction method on a slow timescale and present conditions for a complete separation ofslow and fast kinetics for the governing equation. On thestochastic description, we reduce the system on a slow timescale by utilizing a perturbation analysis on Markov pro-cesses and quasi-equilibrium approximation on fast sub-system. We make a connection between quasi-equilibriumapproximation as applied to deterministic and stochasticdescription. We present an efficient stochastic simulationalgorithm on slow time scale based on analytic results andillustrate the numerical accuracy of the approximation bysimulating motivating examples.

Chang Hyeong Lee

LS06 Abstracts 55

Department of Mathematics, University of [email protected]

CP9

A Dissimilarity Parameterized Approach to theEmbedding Problem in Molecularbiology

We discuss an approach to the embedding problem in struc-tural molecular biology that treats interatomic distances(dissimilarities) as independent variables. Using distancegeometry we can steer the set of dissimilarities to one cor-responding to the interpoint distances of an actual config-uration of atoms. Our formulation leads to a large-scale,bound constrained, nonconvex spectral optimization prob-lem that seems less plagued by nonmeaningful local mini-mizers than coordinate parameterized formulations. More-over, as we discuss, computational costs are tractable.

Michael W. TrossetCollege of William & [email protected]

Robert M. LewisCollege of William and [email protected]

CP9

Stochastic Simulation for Mod-eling Highly-Branched Protein-Protein InteractionNetworks: Attacking Combinatorial Complexity

Automated generation of biochemical reaction networkswith rule-based graphic rewriting scheme and ”on-the-fly”technique have been used to model and simulate protein-protein interactions. However, complex and highly-branched networks, where number of reactions exponen-tially grows as higher-ordered molecular complexes beingformed, still remain computationally intractable. We pro-pose a discrete event simulation method which computesdynamics of a system without pre-generating a biochemicalreaction network. This method provides a modeling andcomputational technique which greatly reduces the com-binatorial complexity observed in most protein-protein in-teraction systems and present a viable way to study largemolecular systems.

William HlavacekTheoretical Biology and Biophysics GroupLos Alamos National [email protected]

Jin YangTheoretical Biology and BiophysicsLos Alamos National [email protected]

CP10

Using Contact Network Models for the Spread andControl of Influenza

The threat of avian influenza and the 2004-2005 influenzavaccine supply shortage in the United States has sparkeda debate about optimal vaccination strategies to reducethe burden of morbidity and mortality caused by the in-fluenza virus. I will discuss a comparative analysis of twoclasses of suggested vaccination strategies: mortality-basedstrategies that target high risk populations and morbidity-based that target high prevalence populations. We have

used the methods of contact network epidemiology to eval-uate the efficacy of these strategies across a wide range ofviral transmission rates and for two different age-specificmortality distributions. We have found that the optimalstrategy depends critically on the viral transmission level(reproductive rate) of the virus: morbidity-based strate-gies outperform mortality-based strategies for moderatelytransmissible strains, while the reverse is true for highlytransmissible strains. If time permits, I will also discussthe ramifications of mutating pathogens to the spread ofdisease.

Lauren A. MeyersThe University of Texas at AustinSection of Integrative [email protected]

Shweta A. BansalUniversity of Texas, [email protected]

CP10

Pair-Level Approximations to the Spatio-TemporalDynamics of Epidemics on Asymmetric ContactNetworks

Existing pair approximations to the spatio-temporal dy-namics of epidemics assume that the contact matrix is sym-metric. There are circumstances where this is unlikely to betrue for example transmission between fish farms via rivernetworks or more generally spread by transport links. Weextend the formalism to asymmetric networks and comparethe results of a naive application of the symmetric model,of a partially asymmetric model, of our fully asymmetricmodel and of stochastic simulation.

Kieran Sharkey, Roger G. BowersThe University of [email protected], [email protected]

CP10

Evolution of Metabolic Network Functions

From the reaction content of the metabolic networks ofover 200 organisms which have been retrieved from theKEGG database, we derive scenarios for networks of com-mon ancestors as defined in the NCBI taxonomy tree. Astructural analysis using the recently developed techniqueof network expansion allows to investigate at which stageduring evolution particular network functions are discov-ered or lost. We further identify structural features whichare responsible for the emergence of these functions.

Daniel KahnUniversite Lyon [email protected]

Oliver EbenhohHumboldt University [email protected]

CP10

Comparing Evolutionary Markov Processes

Molecular evolution is often modeled as a homogeneous,positive-recurrent, irreducible Markov process. Evolutionis studied using the process’ infinitesimal generator, oth-erwise known as its “substitution matrix.” Over eighty

56 LS06 Abstracts

substitution matrices have been proposed, but rigorousquantitative comparisons are lacking between them. Us-ing composition and latent-variable analyses, we proposeHilbert-space and statistical metrics to quantify the “dif-ference” between different substitution matrices, and byimplication, different evolutionary Markov processes.

Andrew D. FernandesBioinformatics ProgramNorth Carolina State [email protected]

William AtchleyNorth Carolina State [email protected]

CP10

Optimal Disease Control - the Importance of Eco-nomics and Time-Scales for Control

Using a contact-process model for the spread of crop dis-ease over a regional scale, we examine the importance ofthe time-scale for control with respect to the cost of the epi-demic. We analytically derive economically optimal treat-ment regimes using methods from control theory to showthat there are significant qualitative differences betweenlong and short-term control. We also emphasise the im-portance of economic constraints by deriving a critical re-lationship between the epidemiological and economic pa-rameters.

Graeme A. Forster, Christopher GilliganUniversity of [email protected], [email protected]

CP10

The Adaptive Dynamics of the Evolution of HostResistance to Indirectly Transmitted Micropara-sites

We use adaptive dynamics and pairwise invadability plotsto examine the evolutionary dynamics of host resistanceto microparasitic infection transmitted indirectly via freestages. We investigate trade-offs between pathogen trans-mission rate and intrinsic growth rate. Adaptive dynam-ics distinguishes various evolutionary outcomes associatedwith repellors, attractors or branching points. We find cri-teria corresponding to these and demonstrate that a majorfactor deciding the evolutionary outcome is whether trade-offs are acceleratingly or deceleratingly costly.

Angela E. Giafis, Roger G. BowersThe University of [email protected], [email protected]

CP10

Simulations As a Mathematical Tool

Simulations based on a collection of physical and socialaction-at-a-distance forces can be used to describe inter-acting organisms. Examples of these will be given for botha panicking crowd and a classical biological phenomenon:niche partitioning by salamanders along a streambank-forest floor ecotone. The simulations are found to pro-duce realistic salamander behavior, including the non-overlapping territories and interspecific niche partitioning.Furthermore, the simulations validate the functional forms

used for social forces.

Tom ClarkeInsitute for Simulation and TrainingUniversity of Central [email protected]

Linda MaloneIndustrial Engineering and Mangement SystemsUniversity of Central [email protected]

Linda Walters, John FauthDept. of BiologyUniversity of Central [email protected], [email protected]

Rex OlesonInsitute for Simulation and TrainingUniversity of Central [email protected]

David J. KaupInstitute for Training and Simulation & Dept. ofMathematicsUniversity of Central [email protected]

CP10

On the Role of Cross-Immunity and Vaccines onthe Survival of Less Fit Flu-Strains

A pathogen’s route to survival involves various mechanismsincluding their ability to invade (host’s susceptibility) andtheir reproductive success within an invaded host (“infec-tiousness”). The immunological history of an individual of-ten plays an important role in reducing host’s susceptibilityor it helps the host mount a faster immunological responsede facto reducing infectiousness. The cross-immunity gen-erated by prior infections to influenza A strains from thesame subtype provide a significant example. In this paper,we study the role of invasion mediated cross-immunity ina population where a precursor related strain (within thesame subtype) has already become established. An uncer-tainty and sensitivity analysis is carried out on the abilityof the invading strain to survive for given cross-immunitylevels. Our findings indicate that it is possible (for relativelow levels of cross-immunity) to increase the likelihood ofstrain coexistence even in the case when invading strainsare “unfit”, that is, when the basic reproductive numberof the invading strain is less than one. The development of“flu” vaccines that minimally enhance herd cross-immunitylevels may, by increasing genotype diversity, help facilitatethe generation and survival of novel “virulent” strains, thatis strains that have high levels of reproduction within thehost.

Miriam NunoHarvard School of Public [email protected]

Xiaohong WangArizona State UniversityDepartment of Mathematics and [email protected]

Gerardo ChowellMathematical Modeling and AnalysisLos Alamos National Laboratory

LS06 Abstracts 57

[email protected]

Carlos Castillo-ChavezDepartment of Mathematics andArizona State [email protected]

CP11

Hepatitis A: The Us and Canada As a CoupledEpidemiological System

Vaccination against Hepatitis A has been widespread inthe US since 1996, and more limited in Canada, thoughfew epidemic models of Hepatitis A have been developed.Evidence suggests correlated epidemics in the two coun-tries. Here we analyze an epidemic model which treats thecountries as coupled populations, using dynamical systemsmethods, in order to study the impact of vaccination inthe US, and how disease dynamics in the US affect diseasedynamics in Canada.

Raluca AmarieiUniversity of GuelphDepartment of Mathematics and [email protected]

CP11

Implications of Universal Hepatitis A Vaccina-tion in Canada: Predictions of An Age-StructuredCompartmental Model

Vaccination against Hepatitis A became widespread in the1990s, however few transmission models have been devel-oped. Here we develop an age-structured compartmentalmodel to predict the impact of universal vaccination inCanada. Peculiarities of HAV transmission such as a co-hort effect and travel-related incidence are addressed. Themodel shows that transmissibility has declined by a factor2.8 over the past century. The model also predicts thatvaccinating 4-year-olds achieves the best gains.

Arni RaoUniversity of [email protected]

Ba’ PhamGlaxoSmithKline [email protected]

Murray KrahnUniversity of [email protected]

Vladimir Gilca, Bernard DuvalInstitut national de sante publique [email protected],[email protected]

Maggie ChenToronto General [email protected]

Andrea TriccoGlaxoSmithKline [email protected]

Chris T. BauchDepartment of Mathematics and Statistics

University of [email protected]

CP11

Estimation and Identification of Klebsiella Pneu-moniae Aggregation Dynamics

The bacterial pathogen Klebsiella pneumoniae is a causeof community- and hospital- acquired lung, urinary tract,and blood stream infections. A common contaminant of in-dwelling cathethers, it is theorized that a common infectionpathway for this gram-negative organism is via shedding offof biofilm colonies. In an effort to better understand bac-terial proliferation in the host bloodstream, we develop asize-structured PDE for the aggregation dynamics of thebacteria in an agitated suspension. We will present resultsof an investigation of the fragmentation properties of theviscoelastic biofilm emboli.

David M. BortzUniversity of MichiganDepartment of [email protected]

CP11

Multi-Strain Disease Dynamics Due to Stochasticand Periodic Forcing

We consider the coupled-system dynamics of multi-straindiseases such as the flu, malaria and dengue fever. Whenthe probability of reinfection to a second strain is weak,the global coupling between the strains leads to a manifoldof steady endemic states. We show that the manifold isglobally attracting but that stochastic noise results in mo-tion on the manifold. We then investigate the oscillatoryepidemics that result from seasonal forcing and latentcyperiods.

Thomas W. CarrSouthern Methodist UniversityDepartment of [email protected]

Michael TaylorDepartment of MathematicsSouthern Methodist [email protected]

CP11

Maximum Likelihood Estimation in Nonlinear Dy-namical Models of Hiv

The study of dynamical models of HIV, based on system ofnonlinear ordinary differential equations (ODE), has con-siderably improved the knowledge on the pathogenesis ofthe infection. Complexity of those models leads to greatdifficulties for inference and classical sofwares for nonlinearmixed effects models cannot be used. We develop an al-gorithm for direct likelihood maximization adapted to thecontext of ODE. Based on simulated and real data, weshow that it provides efficient estimations of parameters.

Rodolphe ThiebautInserm [email protected]

Daniel Commenges, Jeremie GuedjINSERM E0338

58 LS06 Abstracts


CP11

Disease Modeling to Assess Outbreak Detectionand Response

Bioterrorism is a serious threat that has become widely rec-ognized since the anthrax mailings of 2001. In response,one national research activity has been the developmentof biosensors and networks thereof. A driving factor be-hind biosensor development is the potential to provideearly detection of a biological attack, enabling timely treat-ment. This presentation introduces a disease progressionand treatment model to quantify the potential benefit ofearly detection. To date the model has been used to assessresponses to inhalation anthrax and smallpox outbreaks.

Diane C. Jamrog, Adam SzpiroLincoln LaboratoryMassachusetts Institute of [email protected], [email protected]

CP11

Effects of Contact Tracing and Removal on theSpread of New Emerging Diseases

This study presents a framework for studying the effectsof contact tracing, quarantine and isolation on the spreadof emerging infectious diseases, using SARS outbreak datafrom Hong Kong as an illustration. We consider three dif-ferent contact tracing functions and their effects on the dis-eases reproduction number, including sensitivity and un-certainty analysis. Tracing and quarantining contacts ofdiagnosed cases can reduce transmission greatly, but mayalso be cost-prohibitive on the large scale needed for erad-ication.


Christopher M. Kribs ZaletaUniversity of Texas at [email protected]

Maia MartchevaDepartment of MathematicsUniversity of [email protected]

Anuj MubayiArizona State [email protected]

CP11

An Sir Epidemic Model with Partial TemporaryImmunity

The SIR-epidemic model considers that recovered individ-uals are permanently immune, while the SIS model consid-ers recovered individuals to be immediately re-susceptible.We study the case of temporary immunity in an SIR basedmodel with delayed coupling between the susceptible andremoved classes. We perform a numerical and analyticalbifurcation analysis of the resulting DDEs and describehow temporary immunity leads to recurrent outbreaks andhow model parameters affect the severity and period of the

outbreaks.

Thomas W. CarrSouthern Methodist UniversityDepartment of [email protected]

Michael TaylorDepartment of MathematicsSouthern Methodist [email protected]

CP12

Polymer Coating of Biological Surfaces

Many drug delivery systems suffer from undesirable inter-actions with the host immune system. It has been exper-imentally established that covalent attachment of suitablepolymers to the surface of the drug carrier can reduce suchundesirable interactions. In this talk we present and anal-yse mathematical and computational models of the poly-mer coating of biological surfaces. In particular, we applyour models to the coating of virus particles by hydrophilicpolymers (such as pHPMA) which are currently used insome gene therapy systems.

Radek ErbanUniversity of OxfordMathematical [email protected]

Kerry Fisher, Leonard SeymourUniversity of OxfordDepartment of Clinical [email protected],[email protected]

Jonathan ChapmanMathematical InstituteUniversity of [email protected]

CP12

A Penalty Func-tion Method for Distance-Constrained MolecularDynamics Simulation

MD simulation can be used to study various dynamic prop-erties of proteins, but a long sequence of iterations has to becarried out even for small protein motions due to the smalltime step (10e-15sec) required. The bonding forces areamong those causing fast protein vibrations that requiresmall time steps to integrate, but they may be replaced bya set of bond length constraints, to increase the step sizeand hence the simulation speed. Lagrange multiplier meth-ods have been developed for constrained dynamics simula-tion. However, the multipliers have to be determined inevery step to satisfy the constraints through the solutionof a nonlinear system of equations. Here we propose apenalty-function method for constrained dynamics by con-sidering the least action problem with the bond-length con-straints as a constrained optimization problem and defininga quadratic penalty function for the constraints. The sim-ulation with the penalty function method can be done byusing a conventional unconstrained solver such as Verlet,only with the penalty parameter increased in an appropri-ate manner as the simulation proceeds. More specifically,we scale the constraints with their force constants whenforming the penalty terms. The resulting force function

LS06 Abstracts 59

can then be viewed as a smooth continuation of the originalforce field as the penalty parameter increases. The penaltyfunction method is easy to implement and costs less than aLagrange multiplier method, which requires the solution ofa nonlinear system of equations in every time step. We im-plemented the penalty function method in CHARMM andapplied it to protein Bovine Pancreatic Trypsin Inhibitor(BPTI). We compared the simulation results with Verletand Shake, and found that the penalty function methodhad high correlations with Shake and outperformed Ver-let. In particular, the RMSD fluctuations of backbone andnon-backbone atoms and the velocity auto correlations ofC atoms of the protein calculated by the penalty functionmethod agreed well with those by Shake. We describe thepenalty function method and its implementation details,discuss our results and the issues to be resolved, show theadvantages as well as the disadvantages of the method, anddemonstrate the potential of using the method for generalconstrained molecular dynamics and energy minimization.

Ajith GunaratneIowa State UniversityDepartment of [email protected]

Zhijun WuIowa State UniversityDept of [email protected]

CP12

Swelling Dynamics of Weakly Acidic Polyelec-trolyte

The behavior of polyelectrolytes plays an important rolein many biological processes, e.g. vesicle exocytosis. Weexplore a simple model of polyelectrolyte swelling, featur-ing flows that are driven by gradients in electro-chemicalpotential and that conserve volume. The mean-field po-tentials derive from a statistical thermodynamics modelof Gibbs free energy and include pressure, electro-staticpotential, short-range interaction energies and entropicterms. We explore the interplay of corresponding forcecomponents during swelling.

Viktoria HsuUniversity of [email protected]

CP12

The Firing of an Excitable Neuron in the Presenceof Stochastic Trains of Strong Synaptic Inputs

We consider a fast-slow excitable system subject to astochastic excitatory input train, and show that under gen-eral conditions its long term behavior is captured by anirreducible Markov chain. In particular, the firing prob-ability to each input, expected number of response fail-ures between firings, and distribution of slow variable val-ues between firings can be obtained analytically from thedistribution of interexcitation intervals. The approach wepresent immediately generalizes to any pair of input trains,excitatory or inhibitory and synaptic or not, with distinctswitching frequencies. We also discuss how the method canbe extended to other models, such as integrate-and-fire,that feature a single variable that builds up to a thresholdwhere an instantaneous spike and reset occur. The Markovchain analysis guarantees the existence of a limiting distri-

bution and allows for the identification of different bifur-cation events, and thus has clear advantages over directMonte Carlo simulations. We illustrate this analysis on amodel thalamocortical (TC) cell subject to two exampledistributions of excitatory synaptic inputs, in the cases ofconstant and rhythmic inhibition. The analysis shows thatthere is a drastic drop in the likelihood of firing just afterinhibitory onset in the case of rhythmic inhibition, relativeeven to the case of elevated but constant inhibition. Thisobservation provides support for a possible mechanism forthe induction of motor symptoms in Parkinson’s disease.

Jonathan E. RubinUniversity of PittsburghDepartment of [email protected]

Kresimir JosicUniversity of HoustonDepartment of [email protected]

CP12

Support Vector Regression Approach for Predic-tion of Relative Lipid Accessibility in MembraneProteins

Membrane proteins constitute a significant fraction of atypical proteome and they play a number of critical func-tions, e.g., enabling signaling and transport through themembranes. Computational studies of membrane proteinsare an important complement of (often facing serious lim-itations) experimental efforts in that regard. Here wepresent a novel protocol for prediction of relative lipid ac-cessibility in membrane domains. The new method is basedon a linear, Support Vector Regression-based model thatcan be used to efficiently and reliably estimate the param-eters in the model from a limited number of experimen-tally validated examples. The new method will be avail-able to the community through the MINNOU web server(http://minnou.cchmc.org).

Michael WagnerCincinnati Children’s Research [email protected]

Baoqiang CaoUniversity of [email protected]

Jarek MellerChildren’s Hospital Research FoundationUniversity of Cincinnati, Cincinnati, [email protected]

CP12

A Chemical Kinetic Model for RNA PolymeraseTranslocation During Transcriptional Elongation ofthe Nascent Rna Chain

A chemical kinetic model of the elongation dynamics ofRNA polymerase along a DNA strand is introduced. Un-like previous models that attempt to explain the motion ofRNA polymerase using internal strain and stresses, we pro-pose a chemical kinetic model which governs the discretemovement of the RNA polymerase along a DNA tether,with no consideration given to elastic effects. The model’snovel feature includes a ’look-ahead’ feature in which nu-cleotides bind reversibly to the DNA prior to being incor-

60 LS06 Abstracts

porated covalently into the nascent RNA chain. Results arepresented for a random DNA sequence, and also with spe-cific DNA sequences that have been used in single-moleculeexperiments of the random walk of RNA polymerase alongDNA. We also discuss preliminary parameter fitting resultsof our model to the experimental data.

Richard YamadaCenter for Applied MathematicsCornell [email protected]


CP12

Building Molecular Surfaces Using Surface TensionModels

An important tool in the analysis of biological macro-molecules is the solvent-accessible surface, a ”wrapper”for the molecule which defines the boundary between thethe solvent and the molecular interior. These surfaces aretypically generated geometrically, through the action of arolling probe meant to represent a single water molecule.We are exploring new, finite-element-based approaches togenerate surfaces via energy minimization, under the as-sumption of constant solvent pressure and surface tension.

Randy ZauharDepartment of Chemistry & BiocUniversity of the Sciences in [email protected]

LiFeng TianDept. Chem & BiochemUniversity of the [email protected]

MS1

Correlation Approaches for Extracting Process In-formation from Spatial Data

Small-scale spatial patterns in ecosystems (e.g. plantspecies distributions, epidemic patterns) are driven by en-vironmental variation and demographic stochasticity, mod-ified by movement and spatial interactions among species.Defining these spatial dynamics in terms of spatial correla-tion functions provides a natural connection to data. HereI demonstrate how, given that we know which spatial pro-cesses are operating, one can invert Fourier-transformedversions of correlation models to estimate the parametersof spatial processes.

Ben BolkerDepartment of ZoologyUniversity of Florida, [email protected]

MS1

Perturbative Approach to Transient Dynamics inSpatial Ecology

The coexistance or exclusion of interacting species is offundamental importance in ecology. If an individual’s in-teractions extend beyond its nearest neighbours, there is

a natural small parameter for developing a perturbationtheory around the infinite-range, mean-field limit. Thispermits an asymptotically exact calculation of the contri-bution of space and stochasticity. I apply this to the eigen-values describing approach to equilibrium, showing how theinteraction and dispersal kernels determine the stability ofspatially extended populations.

Stephen J. CornellInstitute of Integrative and Comparative BiologyUniversity of [email protected]

Otso OvaskainenDepartment of Biological and Environmental SciencesUniversity of [email protected]

MS1

Conditional Dispersal in Ecological Models

Traditional spatial models in ecology assume that organ-isms disperse randomly by simple diffusion or similar pro-cesses. In some cases, however, organisms may disperse inresponse to their surroundings or other organisms. McPeekand Holt introduced the term “conditional” to describethat type of dispersal. This talk will describe some modelswith conditional dispersal. The models are partial differ-ential equations similar to reaction-diffusion equations, butincorporating advection or density dependent diffusion orboundary conditions.

Chris CosnerUniversity of MiamiDepartment of [email protected]

Robert CantrellDepartment of MathematicsUniversity of [email protected]

Yuan LouOhio State UniversityDepartment of [email protected]

MS1

Spatial Stochastic Host-symbiont Models

Optimal foraging and habitat selection theories that arebased on non-spatial, deterministic models predict evolu-tion towards generalist strategies in fine-grained habitatsand towards specialization in coarse-grained habitats. Inaddition, coevolutionary processes appear to favor extremespecialization among parasites. We introduce a spatiallyexplicit, stochastic model that confirms the effect of habi-tat coarseness on specialization in the absence of coevo-lutionary processes. To understand the effects of coevo-lutionary processes, we introduce feedback between hostsand their symbionts into our spatially explicit, stochasticmodel. This is joint work with Nicolas Lanchier, Universityof Minnesota.

Claudia NeuhauserUniversity of [email protected]

LS06 Abstracts 61

MS2

The Criticality Hypothesis: How Local CorticalNetworks Might Optimize Information Processing

Several models suggest that neural networks should oper-ate near a critical point to optimize information transmis-sion, information storage, computational power, and sta-bility. To test this, we recorded cortical slices and cultureson 60-channel multielectrode arrays. Networks producedavalanches of neural activity whose sizes were distributedaccording to a power law, reminiscent of critical phenom-ena. Moreover, avalanches occurred in repeating patternsthat could be used to store information. These data areconsistent with the criticality hypothesis.

John BeggsIndiana UniversityDept. of [email protected]

MS2

Reverse-Correlation Techniques and Cortical Ar-chitecture

Reverse-time correlation measurements give the averageorientation dynamics of individual neurons within a highlyexcited visual cortical neuronal network. The resulting ori-entation tuning curves provide specific information aboutthe nature of cortico-cortical connections, in particular, thestrength and extent of cortical inhibition. We present a setof models that uncover and explain the connection betweenthe experimentally observed tuning curves and the relevantcortical architecture.

Louis TaoDepartment of Mathematical SciencesNew Jersey Institute of [email protected]

Michael J. ShelleyNew York UniversityCourant Inst of Math [email protected]

Gregor KovacicRensselaer Polytechnic InstDept of Mathematical [email protected]

David CaiCourant instituteNew York [email protected]

MS2

Statistical Modeling of Multi-neuron Responses inPrimate Retina

Neural circuits are well known to exhibit correlated spikingactivity, whose origin and significance is a topic of muchcurrent interest. We show that a generalized linear model,fit using maximum likelihood, can account for the stimulus-dependence, history-dependence, and correlation structurein the spike responses of a group of nearby neurons in pri-mate retina. We will discuss implications for the multi-neuronal coding of visual information.

Jonathan W. PillowUniversity College London

Gatsby [email protected]

MS2

Detecting Weak Ratiometric Signals from Geneti-cally Encoded FRET Indicators

Genetically encoded ratiometric indicators have become animportant part of the neural imaging toolkit. Voltage-sensitive and calcium-sensitive indicators have been usedto study neurons as well as other tissues such as the heartand liver. We present a simple, new multivariate methodfor teasing out small ratiometric signals from FRET- orStokes’ shift-based fluorescence data. We will present themethod and show an application to sensory neurons in ze-brafish.

Andrew SornborgerUniversity of GeorgiaDept. of [email protected]

MS3

A Mathematical Model of Tumor Lymphangiogen-esis

The lymphatic system provides a much more favorable en-vironment for tumor invasion and metastasis than does theblood vasculature. As more specific markers for lymphan-giogenesis are emerging, a modeling of this process is be-coming more feasible. In this talk I shall present such amodel, in terms of PDEs for the densities of lymphatic en-dothelial and cancer cells, concentrations of urikinase, plas-minogen and extracellular matrix, and VEGF-C growth-factor. joint work with Georgios Lolas.

Avner FriedmanMathematical Biosciences Institute, Ohio State [email protected]

MS3

Modeling the Tumor-vasculature Interaction Sug-gests Time-dense Antiangiogenic Schedulings

Clinical inferences can be derived from the simple ODEmodel of antiangiogenic therapy proposed by Hahnfeldtet al. (1999) and its generalizations. We compared con-stant continuous-infusion and periodic boli-based thera-pies, showing by analytical conditions and simulations thatschedulings which guarantee the same mean drug concen-tration may exhibit different efficacy, with the profiles thatapproach the constant one being more effective. This be-havior appears to depend on the functional form of thenonlinear tumor-vasculature relationship.

Alberto d’OnofrioEuropean Institute of Oncology- Milan, Italyalberto.d’[email protected]

Andrea RoccaEuropean Institute of Oncology,Milan, [email protected]

Alberto GandolfiIst. Analisi SistemiInformatica - CNR, Roma, Italy

62 LS06 Abstracts

[email protected]

MS3

A New Cancer Drug Regimen Based on the Inter-play Between Tumor Growth and Angiogenesis -Prediction of a Mathematical Model

We mathematically modeled the interplay between key bio-logical, pathological and pharmacological processes under-lying drug-patient interactions, from the molecular level tothat of the whole organism. Simulating a large numberof treatment options, we showed that unlike the recom-mended regimen, applying large doses every three weeks,the optimal treatment schedule for common anticancerdrugs, such as docetaxel and doxorubicin, is one of rela-tively small doses, the dosing interval being one week.

Levon Arakelyan, Yifat MerblOptimata Ltd., Ramat Gan, [email protected], [email protected]

Vladimir VainsteinInstitute for Medical Biomathematics,Bene Ataroth, [email protected]

Zvia AgurInstitute for Medical Biomathematics and Optimata Ltd.,andBene Ataroth, [email protected]

Yuri KheifetzThe Institute for Medical BioMathematics, [email protected]

MS3

Stochastic Geometrical Methods for the StatisticalAnalysis of Tumor-induced Angiogenesis

Tumor-induced angiogenesis may be modelled as a birth-and-growth stochastic process, which is composed ofbranching and subsequent growth of vessel networks. Thegrowth of vessels (and possibly the inhibition of growth, viadrugs) is coupled with interacting underlying fields, so thatthe geometric structure of vessels becomes spatially hetero-geneous. Here we provide methods of statistical analysisfor the estimation of geometric densities that characterizethe morphology of a real system.

Elena VillaDepartment of Mathematics and ADAMSS Centre,Universita’ degli Studi di Milano, Milan, [email protected]

Alessandra MichelettiDepartment of Mathematics and ADAMSS Centre,Universita’ degli Studi di Milano, Milano, [email protected]

Vincenzo CapassoDepartment of Mathematics and ADAMSS Centre,Universita’ degli studi di Milano, Milan, [email protected]

Daniela MoraleDepartment of Mathematics and ADAMSS Centre,DepartUniversita’ degli Studi di Milano, Milan, [email protected]

MS4

Parameter Estimation in PBPK Models

A physiologically based pharmacokinetic (PBPK) modelfor TCDD was used as the framework for models of TCDD,PCB126, PeCDF, and a mixture of these three chemicals.A goal was to assess how a model developed specificallyfor TCDD would serve as a general Ah receptor modelfor individual dioxin-like chemicals as well as a mixture ofdioxin-like chemicals. I’ll discuss the mixture model andefforts on variance estimates for the model parameters andpredictions.

Michael EasterlingConstella Health [email protected]

MS4

Development of an Air-Tissue Computational FluidDynamics Model to Describe Extraction of Hydro-gen Sulfide in Rat Nasal Passages

Rats exposed to hydrogen sulfide (H2S) develop olfac-tory neuronal loss (ONL). A computational fluid dynamicsmodel was developed to simulate H2S uptake in the ratnasal cavity. Wall mass flux was governed by H2S reactionkinetics in nasal tissue with kinetic parameters estimatedfrom a pharmacokinetic model. Regions with predictedhigh H2S flux were associated with sites that develop ONL,indicating that airflow patterns play an important role inthe distribution of H2S-induced lesions.

Jeffry Schroeter, Melvin Andersen, David Dorman, JuliaKimbellCIIT Centers for Health [email protected], [email protected],[email protected], [email protected]

MS4

One of the Applications of Physiologically BasedPharmacokinetic Modeling: Interpretation ofBiomonitoring Data

Physiologically based pharmacokinetic (PBPK) modelinghas been applied broadly for a wide variety of compoundsto describe the relationship between external and internalmeasures of exposure. As a measure of internal exposure,biomonitoring data reveal the presence of chemicals in hu-man populations. To interpret the health implications ofsuch data, however, requires knowledge of dosimetry thatcan be provided by PBPK modeling.

Yu-Mei TanCIIT Centers for Health [email protected]

MS4

Modeling Sensory Irritation Response in Rats

A model describing the decrease in respiration from inhaledgases that irritate nasal cavity nerves in rats is presented.The model is optimized to describe respiratory responsedata and evaluated through sensitivity analysis. The modelpredicts data well and reasonably describes the physiologi-cal system of sensory irritant response. (This abstract doesnot reflect EPA policy.)

Karen A. YokleyUniversity of North Carolina-Chapel Hill

LS06 Abstracts 63

Curriculum in [email protected]

MS5

Some Lessons in Math and Biology Education

I summarize experiences from a project that coupled mathand biology undergraduates in field and laboratory re-search projects. This encouraged the students to jointlydevelop hypotheses and appropriate experimental systemsto address them, in conjunction with development of math-ematical models. I’ll also present educational survey re-sults of attendees at the 2005 SMB/ESMTB meeting. Thesurvey allows differences to be determined based upon ed-ucation background of the respondent, their gender andcountry of origin.

Louis J. GrossDepartments of Ecology and MathematicsUniversity of [email protected]

MS5

CoMBiNe- A Computational and MathematicalBiology Network

I will present an overview of a new project supported bythe Shodor Education Foundation to help make integratingmathematics, computation, and biology in the classroomeasier. We are developing an electronic resource in coordi-nation with the National Science Digital Library throughthe Shodor Foundation’s CSERD website for easy access tobasic introduction, interactive activities, laboratory ideas,and references of mathematical and computational topicsin biology. The project will make use of existing materialsand provide a searchable, indexed interface to help facultymake the discovery and integration of those materials rou-tine and seamless.

Eric Marland, Rene SalinasAppalachian State [email protected], [email protected]

MS5

Computational Science Education and Research forUndergraduate Biology Majors

From ecology to spread of disease to metabolism, biologyoffers a wealth of interesting applications for undergrad-uates in computational science. Moreover, with a foun-dation in mathematics and computer science, biology ma-jors can perform meaningful interdisciplinary research ininternships, graduate school, and post-graduate positions.This talk covers some of the applications, materials, andopportunities that have evolved through Wofford College’sEmphasis in Computational Science.

Angela B. ShifletMathematics and Computer ScienceWofford [email protected]

MS5

Creating a Mathematical Biology Course for Biol-ogy Majors

In spite of the surge in applications of mathematics in biol-ogy, biology majors often take only the minimum number of

mathematics courses. We discuss efforts to create a math-ematical biology course targeted at biology majors withminimal prerequisites (1 semester of calculus). Course em-phasis is in the modeling process, particularly as it relatesto the scientific method. Communication and interpreta-tion is stressed, thereby giving this course a novel aspect tomathematics majors as well. Higher level mathematics areintroduced in a way that might motivate biology studentsto take further mathematics courses.

Brian WaltonJames Madison [email protected]

MS6

Functional Analysis of Biochemical Signaling Path-ways Mediating the Acute Inflammatory Response

Acute inflammation in the skin is mediated by IL-1 sig-naling. We have used CellDesigner software to developa detailed, visual representation of this signaling. Func-tional modules are abstracted from the visual representa-tion. Quantitative description of the modules and their keyinteractions allows essential behaviors of the IL 1 pathwayto be captured while omitting many of the molecule-to-molecule interactions depicted in the visual model. (Thispresentation does not necessarily reflect policies of theU.S.EPA.)

Rory B. ConollyNational Center for Computational ToxicologyU.S. Environmental Protection [email protected]

James n. McDougalBoonshoft School of MedicineWright State [email protected]

MS6

The Challenge of in Vivo Experiments in Supportof Systems Biology Models

Systems biology models have specific biologically-basedstructures and parameters. After structure is decided, alarge number of diverse parameters must be determined fora model to accurately predict behavior. Theoretically, pa-rameters from intact organisms are more appropriate thanparameters from cell lines. Estimation of parameters usingan intact in vivo system can bring a wide variety of chal-lenges. Examples of various types of model parameters andtheir estimation using in vivo methods will be discussed.

James n. McDougalBoonshoft School of MedicineWright State [email protected]

MS6

Statistical Issues in the Development of SystemsBiology Models

Abstract not available at press time.

Chris PortierNational Toxicology [email protected]

64 LS06 Abstracts

MS6

Application of Functional Genomics Technologiesto Understand the Topology of Signaling Networks

Over the past decade, the focus on genomic sequencing andgene discovery has provided a virtual parts list that com-prise the molecular machinery of the cell. Today, the focushas shifted towards obtaining a broader understanding ofgene function and how the various genes are contextuallyorganized into signaling modules. In this presentation, wewill discuss the application of high-coverage functional ge-nomic screens together with bioinformatic tools for dissect-ing cell signaling modules.

Russell S. ThomasCIIT Centers for Health [email protected]

MS7

Modeling and Computation of Signal Transduc-tion in Olfactory Cilia with Non-Uniform CNG andCl(Ca) Channels Distributions

Signal transduction in olfactory cilia is produced primar-ily by the cyclic-nucleotide-gated (CNG) and Ca2+-gatedCl (Cl(Ca)) ion channels.We use analytical and computa-tional methods to study mathematical models in conjunc-tion with known experimental results. We develop differ-ential equation models for two different experiments, oneinvolves the interplay between CNG and Cl(Ca) channelsand the other, the diffusion of Ca2+ into cilia and resultingelectrical activity. The Ca2+ concentration and membranepotential are simulated in our study. We obtain predictionson the distribution of the Cl(Ca) ion channels and place-ment of the channel types in order to optimize the electricalsignal.

Dorjsuren BadamdorjUniversity of [email protected]

MS7

Methods to Estimate Distributed Parameters inNeuronal Cable Theory Models

Spatially distributed ionic channel densities in a nervecell determine the type of excitable responses of the cell.These densities are typically represented by constant pa-rameters, but it is known that channels are non-uniformlydistributed. We will discuss two numerical approachesto identifying a non-constant conductance, one being amarching method based on overspecified boundary data,the other a pde-constrained optimization method. Thesewill be applied to linear and nonlinear cable models.

Jonathan BellUniversity of Maryland, Baltimore CountyDepartment of [email protected]

MS7

Channel Localization Via Calcium Imaging

Calcium, the most important of the second messengers, lo-cally modulates the excitability of nerve and muscle. Weexploit the ability to monitor cytosolic calcium, through-out intact cells, with sub-millisecond temporal resolutionand sub-micron spatial resolution in the construction ofa map of channel density. In the process we pose and

solve two inverse problems: (1) Infer from the change incytosolic calcium Fluorescence the associated membranecalcium current in space and time, and (2) Infer from thecalcium current the nonuniform distribution of all partici-pating channels.

Steven CoxDept. of Computational & Applied MathematicsRice [email protected]

MS7

Ion Channel Distributions in Olfactory Neurons:Asymptotic Analysis

Transduction of an odor into an electrical signal to thebrain involves the activation of cyclic-nucleotide-gated(CNG) channels in olfactory cilia. An inverse problem ispresented which uses experimental measurements of electri-cal activity to determine the distribution of CNG channelsalong the cilium. The model, which consists of two nonlin-ear partial differential equations, is studied using pertur-bation techniques. A one-dimensional computer minimiza-tion and special delay iteration are used with the perturba-tion formulas to obtain solutions in the cases of simulatedand experimental data.

Donald A. FrenchUniversity of [email protected]

David A. EdwardsUniversity of DelawareNewark, [email protected]

MS7

Identification of Ion Channel Distributions in Ol-factory

Recent discoveries are revealing that cilia, which are smallhairlike cellular projections, play a fundamental role inmany diseases. In our lab we have focused on olfactory ciliaand the determination of the distributions of their variousion channel types. Transduction of an odorant moleculeinto an electrical signal begins in these olfactory cilia. Ourresearch findings suggest that the profile of their channeldistributions is quite different than the shapes previouslyconsidered. This diversity of shapes appears to have asignificant impact on the strength of the transmitted sig-nal. Although fully experimental procedures (immunocy-tochemistry) appear to be feasible for some (but currentlynot all) of the channel types they are very difficult andhave not been successful to date. As an alternative, we haveformed sets of data which measure the current response dueto specific ion channels during the diffusion of a ligand intoa cilium. This data, in conjunction with the computationalsolution of an inverse problem arising in our mathematicalmodel of this ciliary diffusion process, has led to estimatesof ion channel distributions. These inverse problems are ar-gueably more difficult than, but related to, a well-studied(though apparently not well-understood) class of such in-verse problems. In this talk we provide an overview of ourwork on this problem and its context. We also formulate aparticular integral equation problem that arises in the so-lution of the inverse problem and describe some theoreticaland computational results.

Donald A. French

LS06 Abstracts 65

University of [email protected]

Rick FlanneryDepartment of Cell Biology, Neurobiology, and AnatomyUniversity of [email protected]

Chuck GroetschMathematical SciencesUniversity of [email protected]

Steve KleeneCollege of MedicineUniversity of [email protected]

MS8

Some Spatial Aspects of Control and Managementin Disease Ecology

Recent approaches on spatial spread of wildlife diseasesand infestations provide assessments of control methods.Little work has been done to determine optimal spatio-temporal controls, allowing choice of objective functionsfor economic costs of control and associated disease costs.We describe case studies using a mixture of analytic andcomputational methods to derive optimal spatial controls.Linking these methods to geographic information systemsprovides managers and epidemiologists with efficient toolsto manage disease spread.

Suzanne M. LenhartUniversity of TennesseeDepartment of [email protected]

Louis J. GrossDepartments of Ecology and MathematicsUniversity of [email protected]

MS8

Host Extinction Dynamics in Epidemiology Models

We present a SI model formulated through birth and deathprocesses. This model reveals and corrects errors in similarexisitng models. Complete mathematical investigation ofthis simple model shows that the host extinction dynamicscan happen and the outcomes may depend on the initialconditions. We also present some extensions of this modelto structured SI models, including delay differential equa-tion SI models. We show that host extinction dynamics isubiquitous to many well formulated epidemiology models.

Yang KuangArizona State UniversityDepartment of [email protected]

MS8

Evolutionary Suicide by Hypertumor: a Novel Hy-pothesis for the Cause of Necrosis in MalignantNeoplasia.

Tumor necrosis is a common feature of malignancy. Re-cent mathematical models suggest that necrosis may be

caused by hypertumors—tumors growing on a tumor. Hy-pertumors arise when a cell strain trades away the abilityto secrete tumor angiogenesis factors to gain growth po-tential. What results is an area of tissue characterized byaggressive histology and hypoxia, ultimately causing thedefinitive ecological collapse of necrosis. Here I elucidateconditions under which natural selection favors the hyper-tumor.

John D. NagyScottsdale Community CollegeArizona State [email protected]

MS8

Introduction to Disease Ecology with a Case Study

Rabies, the most important viral zoonotic disease world-wide, has been undergoing epidemic expansion along theeastern seaboard of the United States since the mid-1970sfollowing an accidental introduction of rabid raccoons froma source of endemic infection in the southeastern US. Us-ing data submitted from US States to the Centers for Dis-ease Control and Prevention, we have constructed stochas-tic simulations of the spatial dynamics of rabies as it hasspread into new geographic region. The simulation wasconstructed as an interaction network with nodes of thenetwork defined by township and county centroids. Inter-action strengths along specific connections were sensitiveto local geographic conditions and parameterized againstreported data on the time and spatial location of detectedrabid animals. The parameterized model has proven to be avaluable model for strategic planning for disease emergenceand to direct the development of spatial control strategies.

Les RealDept Biology, Center for Disease EcologyEmory [email protected]

MS8

Case Study of Disease Ecology: Avian Flu

Avian Influenza or bird flu has recently been the subjectof much media attention and public interest. Opinions onits potential to spawn a global pandemic range from thealarmist to the cautiously skeptical. In this talk deter-ministic models are presented for both the temporal tra-jectories of the bird flu both in avian as well as humanpopulations. Of particular interest is the propensity of aninfection of an avian population to induce a human pan-demic.

Paul J. TianMathematical Biosciencs InstituteThe Ohio State [email protected]

MS9

New Multiscale Approaches for Examining theStructure and Dynamics of Membrane Bound Pro-teins

Some new approaches for simulating membrane bound pro-teins in lipid bilayers will be presented. Specifically, someaspects of Multiscale Coupling will be elaborated on, whereatomistic-level simulations of membrane bound proteins(such as the influenza A virus M2 proton channel) are di-rectly coupled to corresponding field theory-based meso-

66 LS06 Abstracts

scopic bilayer/viscous solvent simulations. The protein isobserved to couple to the long-wavelength stress fields aris-ing at the mesoscopic level, and small structural changesare indicated.

Gary Ayton, Gregory VothDepartment of Chemistry, University of [email protected], [email protected]

MS9

Boundary Layer Analysis of the Shape of Two-phase Lipid Vesicles

We present approximate analytical solutions of the shapeequations of giant unilameller vesicles with fluid phase co-existence using a boundary layer calculation. We show thatthe boundary layer calculation agrees well with the numer-ical solution for a variety of parameter values. We demon-strate, using the best fit parameter values of our earlierwork, that the shape obtained from the boundary layer cal-culation matches well with the experimental shapes. Theapproximate calculation eliminates the laborious and timeconsuming iterative task of manually tuning parameters toobtain a suitable numerical shape. It also facilitates thedetermination and influence on shape of material parame-ters associated with the resistance to changes in mean andGaussian curvature and with any distributed or localizedspontaneous curvature.

Tobias BaumgartDepartment of ChemistryUniversity of [email protected]

S. DasTheoretical and Applied Mechanics,Cornell University,[email protected]

James JenkinsCornell [email protected]

MS9

Forces and Geometry in 3-D Membrane Mechanics


William KlugMechanical and Aerospace EngineeringUniversity of California, Los [email protected]

MS9

Simulation of Multicomponent Vesicle Membranesand Membranes with Open Edges

We will present numerical algorithms to simulate the recentexperimental observations of multicomponent vesicle mem-branes based on a variational phase field approach. Theapproach can also be used to simulate membranes withfree edges. The effectiveness of our simulation approachwill be demonstrated.

Xiaoqiang WangInstitute for Mathematics and ApplicationsUniversity of [email protected]

MS9

Adaptive Algorithms for the Simulation of VesicleMembranes


Jian ZhangDepartment of MathematicsPenn State Universityzhang [email protected]

Qiang DuPenn State UniversityDepartment of [email protected]

MS10

Individualized Response-guided Monitoring ofCancer Therapy: A Simulation-based Approach


Dean BottinoNovartis [email protected]

MS10

FromTissue Sample to Cancer Prognosis: Data Quan-tification and Application for Protein Biomarkers


Ned HaubeinThe BioAnalytics Group [email protected]

MS10

Insights from Data Driven Modeling and ModelDriven Drug Design


Birgit SchoeberlMerrimack [email protected]

MS11

Numerical Analysis of a Degenerate Biofilm Model

Recently, a doubly degenerated diffusion-reaction mod-elling framework was proposed that is able to describe theformation of spatially heterogeneous biofilm morphologies,such as cluster-and-channel or ”mushroom” biofilm archi-tectures. In this presentation we review the basics of themodel, its application to mixed culture biofilms, and dis-cuss numerical strategies how to solve it.

Hermann J. EberlDept. Mathematics and StatisticsUniversity of [email protected]

LS06 Abstracts 67

MS11

Thin-film Modelling of Biofilm Growth



MS11

Biofilms and the Plasmid Maintenance Question


Hal L. SmithArizona state [email protected]

MS11

Drug Delivery in Bacterial Biofilms

A continuum modelling approach is used to describebiofilm growth based on fluid dynamics and conservationlaws. The modelling considers the role of nutrient andbacterial cell-cell signalling, both important factors in thenormal development of biofilms. The model is extended toinvestigate the effects of an externally applied anti-biotictreatments (that directly kill bacteria) and cell-signallingtargeting drugs. A number of key results are establishedbased on asymptotic and numeric analysis of the model.

John P. WardLoughborough University, [email protected]

MS12

The Effect of Luminal Depletion on the Dynamicsof Ca-regulated Ca Channels

We analyze how the dynamics of depletion and refillingof a restricted volume of endoplasmic reticulum associatedwith an intracellular Ca-regulated Ca channel influencesit’s stochastic gating and equilibrium properties. We em-phasize numerical solutions of advection-reaction equationsdescribing probability densities representing cytosolic [Ca]and lumenal [Ca] conditioned on the channel’s state. Ex-tensions of this approach can give insight into the effectof luminal depletion on the characteristics of Ca puffs andsparks.

Marco A. Huertas, Gregory D. SmithCollege of William and [email protected], [email protected]

MS12

Analysis of the Effect of Residual Calcium on theGating of Calcium-regulated Calcium Channels

We study the effect of ‘residual calcium’ on the stochasticgating of several inositol-4,5-triphosphate receptor mod-els coupled to a differential equation describing a dynamiccalcium domain. Using Monte-Carlo simulations, numer-ical solution of a system of Fokker-Planck-type equationsand analytical methods, we show how the equilibrium openprobability of such models depends on the time constantfor calcium domain formation and collapse compared to

the characteristic time scale for calcium channel gating.

Bori MazzagHumboldt State [email protected]

Christopher Tignanelli, Gregory D. SmithCollege of William and [email protected], [email protected]

MS12

Calcium Waves as a Signal for Late Long Term Po-tentiation

As a coincidence of synaptic stimulation and back propa-gating action potentials, the initiation of calcium waves indendrites of hippocampal pyramidal cells has been shownexperimentally. It is also known that calcium is a criticalsecond messenger for gene regulation within the nucleus.We construct and analyze a model which incorporates anappropriate spatial mechanism of calcium signaling to ac-count for protein production leading to synaptic strength-ening indicative of late long term potentiation.

Bradford E. PeercyRice [email protected]

MS12

A Model of the Roles of Essential Kinases in theInduction and Expression of Late Long-Term Po-tentiation

The induction of late long-term potentiation (L-LTP) re-lies on several key second messengers and kinases. We de-veloped a model representing synaptic actions of proteinkinase A, MAP kinase, and CaM kinase II, and activa-tion of transcription by CaM kinase IV and MAP kinase.The model simulates electrical and chemical L-LTP, in-hibitor effects, and synaptic tagging. Supralinear stimulus-response relationships are essential to translate brief stim-uli into long-lasting synaptic strengthening. The modelsuggests experimental tests and clarifies relationships ofhippocampal L-LTP with synaptic strengthening in otherorganisms.

Douglas BaxterUniversity of TexasMedical School at [email protected]

John H. ByrneDept. Neurobiology and AnatomyUniv Texas-Houston Med [email protected]

Paul D. SmolenDepartment of Neurobiology and Anatomy,University of Texas Medical School at [email protected]

MS13

Mathematical Modeling of Cancer Virotherapy

Cancer therapy with replicating viruses may have variousoutcomes which can be best understood by mathematicalmodeling. We propose a model which includes most salientfeatures of virotherapy: kinetics of untreated tumor, infec-

68 LS06 Abstracts

tion of tumor cells, replication of viruses, elimination of in-fected tumor cells and effects of immune response on virusby cytotoxic T-cells. The model is validated by availabledata on virotherapy for multiple myeloma in SCID mice.Relevant equilibrium points are evaluated, and by usingsimulations we analyze the influence of model parameterson the outcome of the therapy. We also propose a modelfor virotherapy enhanced by radiation. Viruses engineeredto express thyroid sodium iodide symporter make infectedcells targets for radioactive idodide. The effects of radia-tion upon administration of radioactive iodide may lead toelimination of tumor cells, when virotherapy alone is notsufficient. We evaluate various therapeutic scenarios anddiscuss therapy optimization.

David DingliProgram in Evolutionary DynamicsHarvard [email protected]

Zeljko BajzerMayo ClinicBiomathematics [email protected]

MS13

A Model for Antimitotic Chemotherapy: The Im-portance of the Proliferation Ratio

A model for antimitotic chemotherapy is presented whichsuggests the limits of such therapy and explores the efficacyof different therapy regimes. The proliferation ratio and sothe tumor age on therapy commencement will be shown tobe a key factor in these efficacies.

Michele BourdeauRisk ManagementLehman [email protected]

MS13

Modeling Gompertzian Tumor Growth throughCell Dynamics

A model for Gompertzian tumor growth based on cell dy-namics and cell quiescence is presented. The model pre-dicts that tumors of the same carrying capacity may havesignificantly different proliferation profiles which depend onquiescent cell death rate. The model is applied to specificexamples of multiple myeloma, parathyroid and testiculartumors.

Frank P. KozuskoDepartment of MathematicsHampton [email protected]

MS13

Optimizing Topotecan Therapy in Pediatric Neu-roblastoma

Topotecan (TPT) has activity in a dose/schedule depen-dent manner against neuroblastoma. Mathematical mod-els are described that incorporate the growth of neuroblas-toma along with the antitumor and toxic effects of TPT.In addition, optimal control methods are used to aid indesigning effective treatment strategies. The goal of thisanalysis is to combine the various known pharmacokinetic

and pharmacodynamic results of TPT in a formal mathe-matical framework to design more effective treatment ap-proaches in pediatric neuroblastoma.

Carl PanettaDepartment of Pharmaceutical SciencesSt. Jude Children’s Research [email protected]

MS14

Mechanics Explains the Structures of Coiled Poly-mers in Bacteria


Steven AndrewsPhysical Biosciences DivisionLawrence Berkeley National [email protected]

MS14

A Stochastic Immersed Boundary Method Incor-porating Fluctuations : Toward Modeling Cell Mi-cromechanics

The mechanics of many cellular systems involve elasticstructures which interact with a fluid, for example the outercell membrane deforms during protrusions generated dur-ing motility and cell organelles such as the Golgi Appa-ratus and Mitochondria involve membranes which deformand bud vesicular and tubular structures during biologicalprocesses. Modeling, analyzing, and simulating the me-chanics of such systems presents many mathematical chal-lenges. The immersed boundary method is one modelingapproach for such systems, and has been applied to manymacroscopic biological problems, such as blood flow in theheart and lift generation in insect flight. At the lengthscales of cells and cell organelles, thermal fluctuations alsobecome significant and must be taken into account. Inthis talk we discuss an extension of the immersed bound-ary method framework which incorporates thermal fluctu-ations through appropriate stochastic forcing terms in thefluid equations. This gives a system of stiff SPDE’s forwhich standard numerical approaches perform poorly. Wediscuss a novel stochastic numerical method which exploitsstochastic calculus to handle stiff features of the equations.We further show how this numerical method can be ap-plied in practice to model the basic microscopic mechanicsof polymers, polymer knots, membrane sheets, and vesi-cles. We also discuss preliminary work on modeling thedynamics of cell organelle structures.

Paul AtzbergerRensselaer Polytechnic [email protected]

MS14

T-Cell Receptor Signaling Model Predicts MultipleActivation Levels and Switching Mechanisms

A properly functioning immune system requires ligand-appropriate T-cell responses. Theoretically, T-cell re-sponses (viral, self, and partial) to antigens are biologicallycontrolled by two parameters: receptor to peptide ratio(μ) and specific peptide affinity (κ). An experimentally-verified mass-action ODE model describing this signalingprocess is derived with minimal rate constant fitting. Simu-lations varying μ) and κ suggest existence of multiple quasi-stable states corresponding with appropriate immune re-

LS06 Abstracts 69

sponses, implying possible switching mechanisms control-ling T-cell receptor activation.

John M. BurkeMassachusetts Institute of TechnologyBiological Engineering [email protected]

Douglas LauffenburgerDivision of Biological Engineering, Dept. of Chem. [email protected]

Melissa KempBiological Engineering DivisionMassachusetts Institute of [email protected]

Lucia WilleDepartment of BiologyMassachusetts Institute of [email protected]

Emily MiraldiDepartment of ChemistryOberlin [email protected]

MS14

Finding Gene Regulatory Sites: Protein Localiza-tion


Samual IsaacsonDepartment of MathematicsThe University of [email protected]

MS14

Stochasticity in Gene Regulatory Networks andCell Signaling Pathways

First a model of a synthetic gene regulatory networks willbe presented. This stochastic model quantitatively cap-tured the means and distributions of the expression fromthis modular system and accurately predict the in vivobehavior of an expanded network that included positivefeedback. The model also revealed the counterintuitiveprediction that noise in protein expression levels can in-crease upon arrest of cell division, which was confirmedexperimentally. Then a stochastic model of the biochem-ical steps that regulate activation of the MAPK in yeastsignaling pathway will be used to demonstrate the use ofequation free method to quickly compute the steady statedistribution of activated MAPK.

Xiao WangDepartment of Statistics and Operations ResearchUniversity of North Carolina at Chapel [email protected]

MS15

Modeling Chemotaxis in Escherichia coli: FromSingle Receptors to Strongly-coupled Clusters

The chemotaxis network in E. coli is remarkable for itssensitivity to small relative changes in the concentrations

of multiple chemical signals. We present a model for sig-nal integration by mixed clusters of interacting two-statechemoreceptors. Our model results compare favorably tothe results obtained by Sourjik and Berg using in vivo flu-orescence resonance energy transfer (FRET). Importantly,we identify two distinct regimes of behavior, dependingon the relative energies of the two states of the receptors.In regime I, coupling of receptors leads to high sensitivity,while in regime II, coupling of receptors leads to high coop-erativity, i.e. high Hill coefficient. For homogeneous recep-tors, we predict an observable transition between regimeI and regime II with increasing receptor methylation oramidation. Furthermore, we address the question of adap-tation within our model.

Roberts EndresDepartment of Molecular BiologyPrinceton [email protected]

MS15

From Signal Transduction to Spatial Pattern For-mation in E. coli

Appropriate responses to signals in the environment areessential for the survival of any organism, and thus so-phisticated means of detecting external signals, transduc-ing them into internal signals, and altering behavioral pat-terns appropriately have evolved. Many organisms usea random-walk search strategy to search for food whenthe signals are spatially uniform, and bias movement ap-propriately when a suitable change in signal is detected.The collective behavior of bacterial populations providesan example of how cell-level decision-making translatesinto population-level behavior, and illustrates the math-ematical problem of incorporating individual-level behav-ior into population-level models. In this talk we focus onthe flagellated bacterium E. coli, for which a great deal isknown about signal detection, transduction and cell-levelswimming behavior. We review the biological backgroundon individual and population-level processes and discussthe velocity-jump approach used for describing population-level behavior based on individual-level intracellular pro-cesses. We also show how aspects of the signal transduc-tion and response enter into the macroscopic equations,and discuss computational issues that arise in the bacte-rial pattern formation problem.

Hans G. OthmerUniversity of MinnesotaDepartment of [email protected]

MS15

Diversity in Bacterial Chemotaxis

The chemotaxis pathways in Escherichia coliand Bacillussubtilisboth regulate the same task, namely excitation andadaptation to environmental signals. Both pathways em-ploy orthologous genes that genetically complement be-tween the two species (i.e. can function in the heterologoushost). Yet how these orthologs contribute to network func-tion in each organism is different due to differences in thepathway topologies. Bacterial chemotaxis, therefore, pro-vides an excellent system for studying the structure andevolution of biological networks using comparative anal-ysis. We present mathematical models for the pathwaysregulating chemotaxis in E. coli and B. subtilis. By ana-lyzing the two models, we identify a common regulatory

70 LS06 Abstracts

strategy in both organisms. These results demonstrate thelimitations of pathway inferences based solely on proteinhomology and indicate the need for a theoretical metricto analyze functionally similar pathways. We then demon-strate how comparative analysis can be used to reconstructpathways in species with limited experimental data such asHelicobacter pylori, illustrating the power of comparativenetwork analysis as a tool for analyzing, dissecting, andreconstructing complex biological networks.

Chris RaoDepartment of Chemical EngineeringUniveristy of [email protected]

MS15

Modelling Bacterial Chemotaxis: From MolecularInteraction to Cellular Behavior

I will first review some of the recent progress made in mod-elling various aspects of the bacterial chemotaxis pathway.I will then focus on describing our works on understandingmolecular level cooperativity, which is responsible for largesignal amplification sustained in a wide dynamic range inbacterial chemotaxis.

Yuhai TuIBM [email protected]

MS16

Epidemiological Approaches in the Study of SocialDynamics: Drinking Dynamics at US colleges



MS16

Estimating the Reproductive Number and the Ef-fect of Hypothetical Interventions for the SpanishFlu Pandemic in Geneva, Switzerland

Recurrent outbreaks of the avian H5N1 influenza virus inseveral regions of the world pose a global pandemic threat.I will present an analysis of historical hospital notificationdata of the 1918 influenza pandemic in Geneva, Switzer-land. We estimated the number of secondary cases gen-erated by a primary case during its period of infectious-ness during the first two waves of infection. We then usedthese estimates to evaluate the single and combined effectof reductions in the overall influenza transmission rate viaeffective isolation strategies in hospitals or via reductionsin the susceptibility of the general population through, forexample, increasing hygiene and protective measures (e.g.,increase hand washing, use of face masks), prophylactic an-tiviral use, and vaccination. Some model parameters areestimated by fitting an epidemic model to the data and oth-ers are obtained from published literature. We estimatedthe reproductive number for the spring wave R1 +1.49 (95% CI: 1.45 − 1.53) and the fall wave R2 = 3.75 (95 % CI:3.57 − 3.93). We found that the implementation of single-component interventions is unlikely to achieve containmentwhile control through their combined effect is feasible.

Gerardo Chowell

Mathematical Modeling and AnalysisLos Alamos National [email protected]

Catherine AmmonInstitute of Social and Preventive MedicineFaculty of Medicine, CMU, PoBox 1211, Geneva 4,[email protected]

Mac HymanMathematical Modeling and AnalysisLos Alamos National [email protected]

Nick HengartnerStatistical Science GroupLos Alamos National [email protected]

MS16

Comparing Rubella Vaccination Strategies inChina - Modeling and Simulation

Computer simulations of a deterministic model are usedto predict the effect of the changing age distribution inChina on the dynamics of rubella epidemiology and theincidence of congenital rubella syndrome (CRS). In com-paring rubella vaccination strategies for China using simu-lations, our results predict some severe consequences of thecurrent policy and suggest better alternatives for reducingand eliminating the incidence of CRS.

Herbert HethcoteUniversity of [email protected]

Linda GaoNorth Central [email protected]

MS16

Disease Emergence in Multi-host, Multi-patch Epi-demic Models

Most pathogens are capable of infecting multiple hosts.These multiple hosts provide many avenues for the dis-ease to emerge. In this investigation, we formulate andanalyze multi-host and multi-patch epidemic models anddetermine conditions under which the disease can emerge.In particular, SIS and SIR epidemic models are formulatedfor a pathogen that can infect n different hosts. The basicreproduction number is computed and shown to increasewith n, the number of hosts that can be infected. TheSIS model for two hosts is studied in detail. Necessaryand sufficient conditions are derived for the global stabilityof an endemic equilibrium. Numerical examples illustratethe dynamics of the two- and three-host epidemic models.The models have applications to hantavirus in rodents andother zoonotic diseases with multiple hosts.

Robert McCormackDepartment of Mathematics and StatisticsTexas Tech [email protected]

Linda AllenDepartment of mathematics and Statistics

LS06 Abstracts 71

Texas Tech [email protected]

MS16

Could Low-efficacy Malaria Vaccines Increase Sec-ondary Infections in Endemic Areas?

Recent breakthroughs in malaria vaccines have given newhope that a safe, effective malaria vaccine may be found.The following epidemiological question is addressed: couldthe introduction of a low or medium efficacy malaria vac-cine lead to an increase in the number of secondary in-fections and what characteristics of such a vaccine willhave the greatest effect on the outcome? A mathemati-cal model is developed for a malaria vaccine that is givenonce prior to infection which accounts for separate malariainfection events. There is a threshold depending on therelative transmission probability, the recovery rate and theacquired immunity rate. If the recovery rate decreases,then there will always be fewer secondary infections. How-ever, if the recovery rate increases, then there is a “shoul-der” within which the number of secondary infections willdecrease. Beyond this, the number of secondary infectionswill increase unless the transmission probability is suffi-ciently lowered. This effect is lessened as the acquiredimmunity rate increases. If the transmission probabilityis not sufficiently lowered, then vaccinated individuals willalways cause more secondary infections than unprotectedindividuals. For low efficacy vaccines, this will be corre-lated to an increase in the overall severity of the disease inendemic areas.

Robert J. SmithThe University of Illinois at [email protected]

MS16

Mathematical Models of Tuberculosis Re-infectionsand Multiple Strains

The reemerge of tuberculosis (TB), the TB co-infectionswith HIV and the fast growing of multiple-drug resistanttuberculosis (MDR-TB) have brought new challenges forcontrolling and eliminating this old disease. In this talk,the transmission dynamics of tuberculosis is studied bya mathematical model that incorporates re-infections andmultiple strains. The model presents several distinct bifur-cations and multiple stable nontrivial steady states for boththe basic reproductive number less than one and greaterthan one. It shows that a single tipping point cannottotally determine the transmission dynamics and the fullpicture of the dynamics are determined not only by pa-rameters but also by the initial data. It also shows thatMDR-TB can survival independent of drug-sensitive TB.

Baojun SongMontclair State UniversityDepartment of Mathematical [email protected]

MS17

Oscillation Mechanism of Intracellular CalciumDynamics


Martin FalckeHahn Meitner [email protected]

MS17

Calcium Signaling Differentiation in the MaturingXenopus oocyte: A Modeling Approach

The calcium signaling apparatus undergoes significantchanges during oocyte maturation. Brief, local simula-tion through caged IP3 or calcium gives rise to sweap-ing and long-lasting intracellular Ca2+ elevations in themature egg, while the reponse in the occyte is local andshort. To the contrary, Ca2+ puffs, spatially and tempo-rally limited release events through single clusters of releasechannels, are shorter in the mature egg. We use mathe-matical modeling in conjunction with experimental anal-ysis (Klaled Machaca, U of Arkansas, Med. Sciences) toidentify changes in the Ca2+ signaling machinery duringoocyte maturation consistent with the experimental find-ings. We hypothesize that incraesed IP3 affinity of theIP3 receptors in the mature egg causes the long-lastingCa2+ elevation in the mature egg. We further hypothesizethat clustering of release channel clusters to larger super-clusters gives rise to the shortening of the Ca2+ puffs inthe mature egg.

Peter JungOhio [email protected]

MS17

Messages Diffuse Faster than Messengers


John PearsonLos Alamos National LaboratoryComputational Science Methods, (X-8)[email protected]

MS17

Stochastic Gating of Instantaneously CoupledCalcium-regulated Calcium Channels

Although there is consensus that calcium puffs and sparksarise from the cooperative action of multiple intracellularcalcium channels, the precise relationship between single-channel kinetics and the collective phenomena of stochas-tic calcium excitability is not well understood. Here wepresent and analyze several stochastic automata networkmodels of calcium release sites that include calcium acti-vation, calcium inactivation, or both.

Gregory D. SmithCollege of William and [email protected]

MS18

Beads in Mucus, Generalized Langevin Equations,and State Space Models


John FricksDept of StatisticsPenn State [email protected]

MS18

Cholera Population Dynamics - Inference for Par-

72 LS06 Abstracts

tially Observed Systems

A population model for cholera in Bangladesh is investi-gated as a case study in inferring infectious disease dy-namics from data. Inference for nonlinear state space mod-els can be a challenging step in developing stochastic dy-namical models appropriate for infectious diseases. Thismotivates the introduction of a new method for likelihoodbased inference, which we call MAPLE (Maximum A Pos-terori Limit Likelihood Estimation). The MAPLE algo-rithm computes a maximum likelihood estimator as thelimit of an average of Bayesian posterior mean estimators.The new methodology has computational advantages anda theoretical justification.

Edward IonidesDept of StatisticsUniversity of [email protected]

MS18

Stochastic Challenges in Single-molecule Bio-physics

Recent advances in nanotechnology allow scientists for thefirst time to follow a biological process on a single moleculebasis. These advances also raise many challenging stochas-tic inference and modeling problems. First, by zooming inon single molecules, recent single-molecule experiments re-vealed that many classical models derived from oversimpli-fied assumptions are no longer valid. Second, the stochas-tic nature of the experimental data and the presence oflatent processes much complicate the inference. In thistalk we will use the modeling of subdiffusion phenomenonin protein conformational fluctuations and the modeling ofenzyme reaction pathways to illustrate the stochastic chal-lenges in single-molecule biophysics.

Samuel KouDept of StatisticsHarvard [email protected]

MS18

Multiscale Approximations to Reaction Networks

A reaction network is a chemical system involving multiplereactions and chemical species. Stochastic models of suchnetworks treat the system as a continuous time Markovchain on the number of molecules of each species with re-actions as possible transitions of the chain. In many casesof biological interest some of the chemical species in thenetwork are present in much greater abundance than oth-ers and reaction rate constants can vary over several ordersof magnitude. We consider approaches to approximationof such models that take the multiscale nature of the sys-tem into account. Our primary example is a model of acell’s viral infection for which we apply a combination ofaveraging and law of large number arguments to show thatthe “slow” component of the model can be approximatedby a deterministic equation and to characterize the asymp-totic distribution of the “fast” components. The main goalis to illustrate techniques that can be used to reduce thedimensionality of much more complex models.

Lea PopovicDept of MathematicsCornell [email protected]

MS19

Mathematical Models of Cancer

In this talk we will present an overview of recent develop-ments in the mathematical modelling of cancer growth. Wewill focus specifically on partial differential equation anddiscrete models of tumour-induced angiogenesis (includingblood flow and drug delivery) and cancer cell invasion oftissue (the role of the urokinase plasminogen activation sys-tem). Mathematical and clinical/therapeutic implicationsof the model results will be discussed.

Mark ChaplainDivision of MathematicsUniversity of [email protected]

MS19

Evolutionary Models of Carcinogenesis


Robert GatenbyDepartment of RadiologyUniversity of [email protected]

MS19

Mathematics-driven Experimental Oncology


Vito QuarantaDepartment of Cancer BiologyVanderbuilt [email protected]

MS19

Mathematical Modeling in Clinical Oncology


Kristin R. SwansonUniversity of WashingtonDept of [email protected]

MS20

Title not available at press time


Jeff HastyDepartment of BioengineeringUniversity of California, San [email protected]

MS20

New Approaches to Studying Stochastic ChemicalKinetics in Biochemical Reaction Networks

We used various analytic and numerical methods to eluci-date complex dynamics in stochastic signal transduction.We demonstrate that the commonly used linear noise ap-proximation to solving the chemical master equation failswhen the number of proteins becomes too low. Conse-quently, we developed a new analytical approximation to

LS06 Abstracts 73

the solution of the master equation, based on the generat-ing function approach, which works in a much wider rangeof protein number fluctuations. We show that in a lin-ear signaling pathway, a reaction rate at a node could betuned so the node acts either as a noise amplifier or as anoise filter. For more complex cascades, we mapped the thestochastic chemical kinetics master equation into a quan-tum field theoretical problem, which we solved using thevariational principle.

Garegin A. PapoianDepartment of ChemistryUniversity of North Carolina at Chapel [email protected]

Yueheng LanUniversity of North Carolina at Chapel [email protected]

MS20

The Role of Population Dynamics in PhenotypicVariability

A population of genetically identical cells is known to ex-hibit a substantial phenotypic variability. This variabil-ity originates from both intrinsic and extrinsic sources.We concentrate on the role of population dynamics as anunavoidable source of variations. A clonal population ismodeled as an ensemble of nearly identical genetic circuitswhose dynamics is altered by the growth and division ofcells. The predictions of theoretical analysis is comparedwith experimental measurements at the single-cell level.

Dmitri VolfsonDept of BioengineeringUniversity of California, San [email protected]

Jeff HastyDepartment of BioengineeringUniversity of California, San [email protected]

Lev S. TsimringInstitute for Nonlinear ScienceUniversity of California San Diego, La Jolla, CA [email protected]

MS20

Control of Cell Cycle Entry by a BistableMyc/Rb/E2F Switch

The entry of mammalian cell cycle is associated with a dis-tinct time point, the restriction point (R-point), at whichcells are committed to proliferation. Removal of growthfactors before the R-point rejects cells back to the quies-cence. Removal of growth factors after the R-point, how-ever, does not prevent completion of the cell cycle. De-spite its importance in maintaining normal cell physiology,the molecular nature of the R-point remains elusive due tolack of integrated understanding of the underlying regula-tory network. Here we combined mathematical modelingwith detailed experimentation in a mammalian cell culturesystem to gain insight into the R-point control. Our re-sults suggest that the Myc-Rb-E2F pathway functions as abistable switch that separates quiescence and proliferation.Once turned-on, as characterized by activation of E2F, theswitch can trigger S-phase in a digital all-or-none man-ner. Furthermore, E2F activation is dependant on both

the duration and the level of input growth stimuli. Corre-spondingly, the cell cycle entry is governed by a restrictioncurve (R-curve), at which each point represents the mini-mum duration required for growth stimuli at a given levelto activate E2F expression. Genetic and biochemical mod-ifications of the R-curve may contribute to development ofcancer and terminal quiescence.

Lingchong YouDuke UniversityDepartment of Biomedical Engineering &[email protected]

MS21

Introduce Undergrad Research Presentations 3 and4



MS21

Introduce 2 Undergrad Research Presentations 5and 6


Aloysius HelminckNorth Carolina State [email protected]

MS21

Introduce 2 Undergrad Research Presentations 1and 2


Charles E. SmithNorth carolina state [email protected]

MS22

Validation and Applications of a Non-linear One-dimensional Model of Pulse

We present a non-linear 1D model of blood pressure andvelocity pulse wave propagation in the larger arteries tounderstand the performance of the system in healthy con-ditions and how anatomic variations and cardiovascularpathologies, such as atherosclerosis, affect the pattern ofpulse waves. We validate our 1D model by comparisonagainst a well-defined laboratory model with 35 arteries.Our numerical model is able to capture the main wavepropagation features measured in the experiment.

Jordi Alastruey ArimonDept of AeronauticsImperial College, [email protected]

MS22

Sensitivity Analysis and Parameter Estimation for

74 LS06 Abstracts

a Model of the Cardiovascular


Ben FitzpatrickDepartment of MathematicsLoyola Marymount [email protected]

MS22

Sensitivity Analysis and Parameter Estimation fora Model of the Cardiovascular


Franz KappelDepartment of MathematicsUniversity of [email protected]

MS22

Autonomic and Vascular Regulation in Aging

Human aging is associated with changes in the autonomiccontrol that may affect interactions among multiple organsystems. Regulatory changes in the cardiovascular andcerebrovascular systems may have broad impact on cere-bral perfusion and adaptation to activities of daily living,namely to the orthostatic stress. Genetic, environmentaland behavioral risk factors, however, may have additivenonlinear effects on systemic regulation that may acceler-ate aging process and functional decline.

Vera NovakBeth Israel Deaconess Medical Center andHarvard Medical [email protected]

MS22

Blood Flow Changes Caused by Respiratory Me-chanical Effects

Changing pressure in the trunk due to respiration alterspressure for arteries and veins in the chest and stomachregion in humans. This talk presents 1D models of thecardiovascular system and the respiratory pump. Thesemodels serve as tools for understanding the physiology andallow variations from normal resting conditions to exer-cise. We show how to evaluate physiological conditions inresponse to CPR. Results raised a spectrum of problemsthat require clarification related to the role of pumps, thedifferences between flows and pressures, and the functionof valves.

Johnny OttesenInst for mathematics and physicsRoskilde University, [email protected]

MS23

A Hybrid Model of Tumour Invasion: Evolutionand the Microenvironment

The importance of tumour cell/microenvironment itera-tions is currently of great interest to the biological commu-nity. In particular, both the immediate microenvironment(cell-cell or cell-matrix interactions) and the extended mi-croenvironment (e.g. vascular bed) are thought to play

crucial roles in both tumour progression and suppression.In this talk we present a hybrid discrete/continuum math-ematical model which describes the invasion of host tissueby tumour cells and examines how mutations in cell phe-notypic attributes (e.g. P53 mutation, cell-cell adhesion,invasiveness) affect both tumour morpholgy and geneticmakeup. In the model, we focus on four key variables im-plicated in the invasion process, namely, tumour cells, hosttissue (extracellular matrix, ECM), matrix-degradative en-zymes (MDE) associated with the tumour cells and oxygensupplied by the angiogenic network. In particular we willdiscuss the evolutionary implications of tumours growth ineither harsh/mild microenvironmental conditions.

Sandy AndersonUniversity of [email protected]

MS23

Mathematical Modeling of Cellular Signaling:Lipid Signaling Kinetics

Our goal is the construction of a comprehensive mathemat-ical model for the uridine 5-diphosphate signaling path-way in the macrophage, a type of white blood cell. Themathematical model currently includes a system of nonlin-ear ODEs that describe the major pathway components,with an emphasis on the production and degradation ofdiacylglycerol, a cellular second messenger molecule whichplays an important role in initiating various changes incell behavior. Modeling techniques, challenges, and com-putational simulations will be presented. (Joint work withH. Alex Brown, Jeffrey Forrester, Mark Byrne and othermembers of the Brown lab.)

Hannah Callender, Mary Ann HornDepartment of MathematicsVanderbilt [email protected],[email protected]

MS23

Nonlinear Simulation of Tumor Growth

In this talk, I will focus on recent efforts to study solidtumor progression. Here we focus on a continuum-scaledescription and pose the problem in terms of conservationlaws for nutrients, chemical factors and tumor cell popu-lations. We develop a multiscale mixture model that ac-counts for cell-to-cell adhesion. We analyze the equationsand develop accurate, adaptive numerical schemes. We re-late the model to more classical single-phase models and wedemonstrate the predictive capability of the model throughcomparisons with experimental studies of tumor growth.We then discuss extensions to include the effect of residualstress.

John LowengrubDepartment of MathematicsUniversity of California at [email protected]

MS23

Drug Delivery to Solid Tumors

Physiological transport barriers limit the distribution ofsystemically administered chemotherapeutics in solid tu-mors. Intratumoral delivery is a promising technique thatcan improve the efficacy of existing chemotherapeutics by

LS06 Abstracts 75

circumventing physiological barriers. I will present a con-tinuum reaction diffusion model of intratumoral deliveryof paclitaxel loaded microspheres and illustrate how simu-lations augmented by analytical approximations can helpto elucidate the impact of cell pharmacokinetics, tumormorphology, microsphere release kinetics and spatial dis-tribution on intratumoral drug distribution.

Rami TzafririHarvard-MIT Biomedical Engineering [email protected]

MS24

Wavelets in Medical Sciences-Case Studies


Faouzi KheneResearch Institute,KFUPMDhahran,Saudi Arabiamfkhene

MS24

Multifractal Analysis of Pollution of Delhi andBombay


Pamm ManchandaGNDU, Department ofMathematicsAmritsar,[email protected]

MS24

New Fractal Methods for Time Series Analysis


Fahim NekkaFaculty of Pharmacy& Research Inst.MathMontreal University,[email protected]

MS24

Multifractal Analysis of ECG


Abul Hasan SiddiqiMathematical Sciences DepartmentKing Fahd University of Petroleum & [email protected]

MS25

Air-Mucus Transport in the Lung


Roberto CamassaMathematicsUniversity of North [email protected]

MS25

Exact and Asymptotic Hydrodynamics Solutions

for Low Reynolds Number Spinning Rods


Terry Jo LeitermanMathUNC Chapel [email protected]

MS25

Bio Fluids Experiments: Nanoscale-Macro Scale


Richard McLaughlinUNC Chapel [email protected]

MS25

Nanoscale Biological Manipulation


Richard SuperfinePhysicsUNC Chapel [email protected]

MS26

A Novel Algorithm for MALDI-TOF MS Data Pre-processing Using Wavelets

Mass Spectrometry, especially matrix assisted laser desorp-tion/ionization (MALDI) time of flight (TOF), is emergingas a leading technique in the proteomics revolution. It canbe used to find disease-related protein patterns in mixturesof proteins derived from easily obtained samples. In thispaper, a novel algorithm for MALDI-TOF MS data prepro-cessing is developed. A MatLab implementation shows thepreprocessing steps consecutively including step-intervalunification, adaptive stationary discrete wavelet denoising,baseline correction using splines, normalization, and peakdetection, a newly designed peak alignment method usingclustering techniques.

Don HongMiddle Tennessee State [email protected]

MS26

Incorporating Covariates in Survival Analysis Us-ing Artificial Neural Networks

In survival analysis, the Cox proportional hazards modelis widely used to incorporate covariates. However, it hasstrong assumptions and requires knowledge of all covari-ates under consideration at every failure time. We considertime-dependent covariates and propose a method based onartificial neural networks. This method relaxes the as-sumptions and allows us to perform inference using theobserved covariates values. We illustrate its use throughsimulations and apply it to a study of lung cancer.

Yali LiuEast Tennessee State [email protected]

76 LS06 Abstracts

MS26

Simulation of Solid Tumor Growth

We develop and check the accuracy a mathematical modelfor solid tumor growth. The model uses a set of partial dif-ferential equations describing the spatio-temperal changesin cell concentrations based on reaction-diffusion dynamicsand the law of mass conservation. Unlike existing models,this model takes into account higher dimensions and ar-bitrary geometries, and incorporates random mitotic rateand nutrient supply. Furthermore, the model incorporatethe dependence of cell proliferation rate on the growth in-hibiting factors secreted by necrotic cells. The model issolved using B-spline collocation method. The results arecompared with the published experimental data. The bio-logical and clinical implications are discussed.

Zach SinkalaMiddle Tennessee State [email protected]

MS26

Stochastic and State Space Models of Carcinogen-esis

In this lecture, I will summarize the most recent develop-ment of cancer biology from the past 5-10 years. By artic-ulating these biological studies, I will then propose somestochastic and state space models for carcinogenesis. I willdevelop stochastic differential equations for the state vari-ables. Using these stochastic equations as the stochasticsystem model, I will then propose some state space mod-els with the stochastic observation model being based oncancer incidence data available from SEER or other stud-ies. A general Bayesian procedure using multi-level Gibbssampling and predictive inferences to estimate the param-eters and to predict the state variables will be developed.The models and the methods are illustrated by using theBritish physician data and some environmental data.

Waiyuan TanUniversity of [email protected]

MS27

Modelling Multi-stage Breast Cancer Develop-ment, Treatment and Recurrence

Models of the step-wise development of cancer help in theunderstanding of how the disease develops and lead to moreefficient treatment strategies that prevent local recurrence.In breast cancer, about 10-30 percent of patients develop arecurrent tumour within a few years of the primary treat-ment. We present a model of the multi-stage developmentof breast tumours with respect to clonal breast formation,examine radiation treatment strategies, and discuss therisks of local recurrence.

Jayant VaidyaDepartment of Surgery and Molecular OncologyUniversity of [email protected]

Mark ChaplainDivision of MathematicsUniversity of [email protected]

Heiko Enderling

University of DundeeDivision of [email protected]

Alexander AndersonDepartment of MathematicsUniversity of [email protected]

MS27

Derivation of the Tumor Control Probability(TCP) for Radiation Treatment

The Tumour Control Probability (TCP) is used as an in-dicator of the effectiveness of radiation treatment of can-cer. Standard TCP models do not include the cell cycle ofcancer cells. In my talk, I will derive a cell cycle cancergrowth model from physical principles. This model can beextended to a nonlinear birth-death process, which thengives an explicit formula for the TCP. This TCP formulais an extension of the model of Zaider and Minerbo (jointwork with A. Dawson). This talk related to G. de Vries’talk in the Minisymposium on ”Mathematical Models ofInteractions in Biological Rythms”.

Thomas J. HillenUniversity of AlbertaDepartment of Mathematical and Statistical [email protected]

MS27

Anti Bcl-2 Therapy Inhibits Tumoral Angiogenesis

Recent experiments show that vascular endothelial growthfactor (VEGF) is the crucial mediator of downstreamevents that ultimately lead to enhanced endothelial cellsurvival and increased vascular density within many tu-mours. The newly discovered pathway involves up-regulation of the anti-apoptotic protein Bcl-2, which inturn leads to increased production of interleukin-8 (IL-8).The VEGF - Bcl-2 - IL-8 pathway suggests new targetsfor the development of anti-angiogenic strategies. In thistalk, I present and validate a mathematical model designedto predict the effect of the therapeutic blockage of VEGF,IL-8, and Bcl-2 at different stages of tumour progression.

Harsh JainDepartment of MathematicsUniversity of [email protected]

MS27

Metamodeling the Tumor-immune System Interac-tion

Tumoral dynamics and antitumor immunotherapies arelikely to be influenced by the modalities of interaction be-tween tumor cells and immune system effectors, and by theinter-effectors interactions. In the framework of the the-ory of competing populations, we study here the influenceof the proliferation response of effectors to tumor burden,and of cooperation and/or competition between immunesystem effectors, by means of a meta-modeling approach.

Alberto d’OnofrioEuropean Institute of Oncology- Milan, Italyalberto.d’[email protected]

LS06 Abstracts 77

MS28

Resolving the Bursting Mechanisms in a Two-compartment Pyloric Dilator Cell Model

The role of electrical coupling between neurons with widelydifferent intrinsic properties is not well understood. Wesystematically reduce a multi-compartment conductance-based model of electrically coupled neurons in the crus-tacean pyloric network that exhibits multi-stable modes ofoscillation. We determine the low-dimensional organizingstructure behind its multi-stability in a “critical regime” ofthe dynamics, and thus study the dependence of the sys-tems selection of network oscillation on initial conditionsand parameters such as the electrical coupling strength.

Cristina Soto-TrevinoDepartment of Mathematical [email protected]

Farzan NadimNJIT & Rutgers [email protected]

Robert ClewleyCornell UniversityDepartment of [email protected]

MS28

Multistability of Half-center Bursting in a Two-cellInhibitory Network with T-currents Analyzed viaa Poincare Return Map

We explore the dynamics of a network of two type-I modelneurons endowed with T-currents and coupled by recip-rocal inhibition. The post-inhibitory rebound due to theT-current deinactivation allows the network to maintain astable antiphase (half-center) periodic bursting, wherebya burst in one cell causes a rebound burst in the partnercell. We show that the existence and stability of burstingsolutions is captured by a 1D Poincare return map, andfind that multiple bursting states with different numbersof spikes per burst can be co-stable for a range of parame-ter values.

Victor MatveevNew Jersey Institute of [email protected]

Amit BoseDept of Mathematical [email protected]


MS28

The Role of Feedback to Descending ProjectionNeurons in Rhythmic Motor Pattern Generation

Pattern-generating networks are generally studied assum-ing feed-forward architecture from descending projectionneurons that initiate, terminate or modify the network out-put. Yet, in all complex systems, feedback to descendinginputs is pervasive and mostly not understood. We model

the interaction between the gastric mill motor network andtwo identified descending projection neurons in the crab.Using reduced mathematical models, we demonstrate thatrhythmic feedback to descending neurons moves the locusof pattern-generation from a half-center oscillator to anexcitation-feedback circuit.

Michael NusbaumUniv. of Pennsylvania School of [email protected]

Nickolas [email protected]

Amit BoseDept of Mathematical [email protected]


MS28

Exploring a Mammalian Locomotor CPG Networkvia Analysis of Reduced Subnetworks

We examine a detailed conductance-based model of a neu-ronal network in the neonatal rodent spinal cord that servesas a central pattern generator for coordinated locomotion.The size of the full model precludes detailed analysis; sym-metry and functionality considerations are used to isolatereduced subnetworks that are building blocks or schemat-ics of the full network. The phase-response and synchro-nization properties of the subnetworks illuminate the cor-responding properties of the larger system.

Erik SherwoodCenter for Applied MathematicsCornell [email protected]

John GuckenheimerCornell [email protected]

Robert ClewleyCornell UniversityDepartment of [email protected]

MS29

Structural Monotonicity of Chemical ReactionNetworks

New results linking the structural and dynamical proper-ties of certain chemical reaction networks will be presented.The key idea is to find appropriate coordinates in whichthe system is monotone, so that convergence results canbe applied to prove that solutions converge. An importantfeature of our results is that they are independent of theprecise form of the reaction kinetics. For instance, we donot require that they are of mass action type. The maintools used in the proofs come from graph theory and dy-namical systems theory. This is joint work with David An-geli (University of Firenze) and Eduardo Sontag (Rutgers

78 LS06 Abstracts

University).

Patrick DeLeenheerDepartment of MathematicsUniversity of [email protected]

MS29

Convex and Toric Geometry for the Dynamics ofReaction Networks

The stability problem of complex reaction networks withnonlinear kinetics can be addressed by reformulation inconvex coordinates and by using the properties of cer-tain algebraic structures defined on the reaction monomi-als. The procedure is exemplified using a Hopf bifurcation,showing which features in a network can give rise to chem-ical oscillations.

Markus EiswirthFritz-Haber-Institute, [email protected]

MS29

Graph-theoretic Approach to Oscillations in Bio-chemical Networks with Multiple Delays

In chemical modeling, delays represent subsystems of un-known intermediates and delay system models capture theessential properties of a chemical mechanism when only afew details are available. We use a bipartite graph to rep-resent the chemical mechanism, and show that if certainsubgraphs are present in the graph then the correspond-ing delay model can admit oscillations for some values ofthe system’s parameters. Our subgraph condition for os-cillations generalizes the condition of a negative (feedback)cycle which is usually used in the biochemical literature.

Maya MinchevaDepartment of ChemistryUniversity of Lethbridge, [email protected]

MS29

What is the Origin of Cell Diversity?

Complexity of interactive gene regulation is considered tobe responsible for generating diversity of distinct cell typesin developmental process. I studied diversity of cell typesby analyzing the number of steady states (or attractors)of gene activity using network models. The results werecontrary to the previous arguments. Neither gene numbernor connectivity between genes increases number of steadystates. Number of loops in gene regulation rather increasesnumber of steady states.

Atsushi MochizukiDivision of Theoretical BiologyNational Institute for Basic Biology, Okazaki, [email protected]

MS30

Dynamics of Polymer Veils

This project focuses on the formation and dynamics of pat-terns created by the interaction between swimming bacte-ria, thin polymeric gels, and fluid motion. Here motilemarine bacteria chemotactically aggregate to a layer over

marine sediment and begin producing polymer which even-tually forms a loose hydrogel. Bacteria are transientlyattached to this gel by stalks. Bacteria attached to theveil rotate their flagella, which produces a small fluid flowthat draws nutrient rich water across the veil. Meanwhilebacteria continuously detach and re-attach from the veil.Detached bacteria actively swim and are also advected bythe fluid flow, coupling the bacterial concentration to thefluid flow. The bacteria tend to attach at the boundarybetween regions of relatively high and low polymer concen-tration evidently because of fluid effects. This aggregationis reinforced by the evolving fluid dynamics which tends topush bacteria away from voids and towards the edges. Vi-sual observation of the veil shows regular hexagonal arraysor rolls depending on the experimental parameters. Wedescribe the pattern formation that occurs in this systemusing both analytic and numerical techniques. BoundaryIntegral Methods will be used to simulate the fluid flowthat is generated by attached bacteria; a reaction-diffusion-advection model will be formulated to describe the translo-cation of and nutrient consumption by the attached anddetached bacteria and the nutrient concentration. We willalso use gel mechanics to explore the effects of viscoelas-tic properties of the veil. These systems will be coupledtogether to create a full model for pattern formation insystems of sulfur-oxidizing bacteria.

Nick CoganFlorida State [email protected]

MS30

Flow Through Flowing Structures: A MulitphaseModel of True Slime Mold

The true slime mold physarum polycephalum is a singlecell organism reaching up to meters in size. The cyto-plasm shows periodic shuttle streaming through a networkof tublar structures reaching velocities up to 1 mm/s. Themotion is driven by the periodic contraction of an actin-myosin gel and is necessary to transmit chemical signalsand organize structures over large distances. We present amechanochemical mulitfluid model of the sol/gel that de-scribes the initiation of streaming.

Toshiyuki NakagakiResearch Institute for Electronic ScienceHokkaido [email protected]

Robert D. GuyMathematics DepartmentUniversity of [email protected]

MS30

Transport Along A Contracting Tube

In addition to passing kidney stones, the peristaltic con-tractions of the ureter also propel urine toward the bladderin boluses. Thus, flow in CDs is very different from flow ina pipe with fixed diameter, because the linear velocity ofthe boluses is determined, not by urine flow rates, but bythe velocity of the peristaltic waves, whereas the lengthsof the boluses, and thus the contact time with the CD ep-ithelium, vary with urine flow rates. We model solute andfluid transport along an actively contracting tube as animmersed boundary problem, in axisymmetric cylindricalcoordinates. The model equations embody the principal of

LS06 Abstracts 79

mass conservation of solute and water, and represent single-barrier transport processes. Model solutions are computedusing a second-order immersed interface-type method. Themodel can be used to assess the effective tubular transportproperties of the CD undergoing peristalsis.

Anita T. LaytonDuke UniversityDepartment of [email protected]

MS30

The Endothelial Glycocalyx: Flow, Permeability,and Stress

Fluid mechanical forces from blood are transmitted acrossthe membrane of endothelial cells via the glycocalyx, adense matrix of membrane-bound macromolecules whosestructure is not well understood. Using mathematical mod-els we explore the effect of matrix permeability on flowthrough the matrix and the resulting fluid stresses exertedon the matrix. We also use physical models to measureflow as a function of the size and spatial distribution of‘macromolecules’.

Aaron L. FogelsonUniversity of [email protected]

Laura A. MillerDepartment of MathematicsUniversity of [email protected]

Karin LeidermanMathematics DepartmentUniversity of [email protected]

MS31

The UBM Program at NJIT

The Undergraduate Biology and Mathematics TrainingProgram seeks to train undergraduates at the interface ofbiology and mathematics through a combination of curric-ular activities and research project based activities. In thistalk, we will provide an overview of our program describingstudent cohort activities in the Spring, Summer and Fallsemesters. We will also describe the two main researchprojects conducted by the 2005 cohort of students. Oneproject involved quantifying the formation of plant bor-ders, the other focused on determining the location of gapjunctions in neuronal networks.

Jorge GolowaschDivision of Biological SciencesNew Jersey Institute of [email protected]


Amitabha K. BoseNew Jersey Inst of TechnologyDepartment of Mathematical [email protected]

MS31

The UBM Program at Truman State

At Truman, faculty and undergraduates in the biology andthe mathematical sciences are engaged in multi-semestercollaborative interdisciplinary research experiences. Theoutcomes of this NSF UBM supported program include fos-tering sustained cross-disciplinary collaborative relation-ships between faculty and preparing our undergraduatesto work in an interdisciplinary fashion. These ends areachieved through research activities and a year-long pro-gram of seminars and workshops. Preliminary assessmentdata will be used to illuminate successes

Jeffrey OsbornTruman State UniversityDepartment of [email protected]

Jon BeckTruman State UniversityDepartment of Computer [email protected]

Michael KelrickTruman State UniversityDepartment of [email protected]

Jason MillerTruman State UniversityDepartment of [email protected]

MS31

Interdisciplinary Training for Undergraduates inBiological and Mathematical Sciences at ArizonaState University

The UBM program at ASU intimately combines new cross-disciplinary courses and summer research programs. Theformer are constructed to allow maximal participationamong undergraduate cadres, and facilitate life sciencemajors to achieve a minor in mathematics, and, likewise,mathematics majors to enrich their education with a minorin bioscience. Research projects span modeling of ecologi-cal and evolutionary processes through the lens of stoichio-metric constraints, bio-economics, chemostat theory, andmodeling of visual perception. The program’s holistic ap-proach in mathematical biology training can also verticallyintegrate all the relevant components in the ASU educationsystem. The program has already trained 17 students.

John D. NagyScottsdale Community CollegeArizona State [email protected]

Yang KuangArizona State UniversityDepartment of [email protected]

MS31

REUs on DEEP Problems

In the past few years, I have the privilege to mentor overa dozen research experiences for undergraduates (REUs)

80 LS06 Abstracts

on problems concerning the dynamics of ecology and evo-lutionary processes (DEEP). These research experienceshave varied in mathematical content (ranging from provingtheorems to empirically testing predictions in mesocosms),group size (ranging from one student in isolation to threestudents as part of a larger REU program), duration (fromone month to two years), final outcomes and degree of in-terdisciplinary involvement. In this talk, I will give anoverview of these experiences and share stories of success,failure, and unexpected surprises.

Sebastian SchreiberCollege of William and [email protected]

MS32

Adaptive Multiscale Stochastic Simulation of Bio-chemical Systems

Biochemical systems are inherently multiscale and stochas-tic. In microscopic systems formed by living cells, the smallnumbers of reactant molecules can result in dynamical be-havior that is discrete and stochastic rather than continu-ous and deterministic. An analysis tool that respects thesedynamical characteristics is the stochastic simulation al-gorithm (SSA), a numerical simulation procedure that isessentially exact for chemical systems that are spatially ho-mogeneous or well stirred. Despite recent improvements,as a procedure that simulates every reaction event, the SSAis necessarily inefficient for most realistic problems. Thereare two main reasons for this, both arising from the mul-tiscale nature of the underlying problem: (1) stiffness, i.e.the presence of multiple timescales, the fastest of which arestable; and (2) the need to include in the simulation bothspecies that are present in relatively small quantities andshould be modeled by a discrete stochastic process, andspecies that are present in larger quantities and are moreefficiently modeled by a deterministic differential equation(or at some scale in between). Discrete stochastic simu-lation algorithms that can efficiently solve the multiscaleproblem are highly desired. This talk will introduce our re-cent work in multiscale stochastic simulation methods forbiochemical systems.

Yang CaoDept. of Computer ScienceVirginia [email protected]

MS32

STOCHKIT: Software Tools for Discrete Stochas-tic and Multiscale Simulation of Biochemical Sys-tems

Traditional ordi-nary differential equation-based approaches to simulationof chemical reacting systems fail to capture the randomnessinherent in such systems at scales common in intracellularbiochemical processes. We present StochKit, an efficient,extensible stochastic simulation framework that aims tomake stochastic simulation accessible to practicing biolo-gists and chemists, while remaining open to extension vianew stochastic and multiscale algorithms.

Linda R. PetzoldUniversity of California, Santa [email protected]

MS32

Moment Approach for Computing Discrete-stochastic Biological Systems

It has now been demonstrated that the behavior of lowmolecular number reaction systems encountered in biolog-ical settings frequently requires a discrete-stochastic de-scription via the chemical master equation (CME). How-ever, solving this differential-difference equation for theprobability distributions of most biochemical systems typ-ically presents substantial computational challenges. Weconsider an alternative, but equivalent representation ofCME probability in terms of its factorial moments. Thisf-moment approach results in a formulation, which exhibitssignificant advantages for computing certain CME systemproperties.

Michael SamoilovCenter for Synthetic BiologyLawrence Berkeley National [email protected]

MS32

Stochastic Modeling of the Eukaryotic Cell Cycle

Events of the eukaryotic cell cycle (DNA synthesis, mitosisand cell division) are regulated by a complicated networkof interacting protein kinases, phosphatases, transcriptionfactors and proteases. Deterministic models (nonlinearODEs) have proved very useful in accounting for averageproperties of populations of growing-dividing cells, for un-derstanding how the control system works in normal cells(and why it fails when certain genes are mutated), and forpredicting counterintuitive outcomes of novel experiments.But deterministic models are insufficient to deal with agrowing body of experimental results on the variability ofthe cell cycle control system within single cells. To accountfor such variability will require a careful accounting of allsources of stochastic fluctuations in the control system, in-cluding molecular noise at the level of gene expression,protein synthesis and degradation, protein-protein inter-actions, and random events in the division process and thedistribution of molecular components to the two daugh-ter cells. I will present some preliminary results on myresearch group’s attempts, to date, to convert phenomeno-logical deterministic ODE models into elementary reactionmechanisms suitable for exact stochastic simulations.

John J. TysonVirginia Poly Inst & St UnivDepartment of [email protected]

MS33

Mathematical Analysis of Effector Caspase Ampli-fication in the Death Receptor Network in Single-cells

A proposed mechanism of ligand-induced single-cell rapidall-or-none death is positive feedback in the apoptotic net-work. However, this hypothesis is not supported experi-mentally in HeLa cells. Apoptosis is described by an ex-perimentally verified, mass-action ODE model, which in-dicates that in single HeLa cells, the mitochondrial deathpathway is responsible for rapid, all-or-none apoptosis. Asa corollary of Singular Perturbation model reduction, athreshold parameter is identified that when crossed, ini-

LS06 Abstracts 81

tiates fast, all-or-none mitochondrial cell death.

Peter SorgerDepartment of Biology, Division of Biological [email protected]

Douglas LauffenburgerDivision of Biological Engineering, Dept. of Chem. [email protected]

John AlbeckDepartment of [email protected]

John M. BurkeMassachusetts Institute of TechnologyBiological Engineering [email protected]

MS33

Monotonicity and the Stability of Biochemical Sys-tems

We use the concept of monotone dynamical systems tostudy certain biochemical networks and predict their longtime behavior. We show that under certain qualitative andquantitative conditions, the systems in question presentglobal attractivity towards one or several equilibria. Cru-cially, the system itself is not necessarily required to bemonotone in some important cases. Some results can begeneralized to systems with delays or reaction terms.

German A. EncisoRutgers UniversityDepartment of [email protected]

Eduardo SontagRutgers [email protected]

MS33

Rule-based Modeling of Biochemical Networks

The modular structure of signaling proteins gives rise tocomplex networks that are challenging to model. The con-ventional approach to specifying these networks is error-prone and fraught with hidden assumptions that are dif-ficult to justify. As an alternative, we have developed amodeling language that allows a rule-based description ofsignaling biochemistry based on protein modularity. Wediscuss various approaches to simulating rule-based modelsand the insights that can be gained about the underlyingbiology.

Michael Blinov, William Hlavacek, Byron GoldsteinTheoretical Biology and Biophysics GroupLos Alamos National [email protected], [email protected], [email protected]

G. Matthew FrickeGo Figure [email protected]

Richard Posner, Josh Colvin

Department of Biological SciencesNorthern Arizona [email protected], [email protected]

James FaederTheoretical DivisionLos Alamos National [email protected]

MS33

Signal Transduction at Point-blank Range: Brow-nian Dynamics Simulations of Receptor-mediatedRas/PI 3-kinase Crosstalk

We have developed an efficient Brownian dynamics modelfor stochastic simulation and computational analysis of sig-nal transduction reactions on cell membranes. For a rela-tively simple system, the collision coupling mechanism, thesimulations are in quantitative agreement with continuumtheory. We have used this validated approach to studythe spatial interplay and crosstalk between two receptor-mediated signal transduction pathways, involving activa-tion of Ras and phosphoinositide (PI) 3-kinase, at the sin-gle molecule level.

Michael MonineDepartment of Chemical & Biomolecular EngineeringNorth Carolina State [email protected]

Jason HaughNorth Carolina State UniversityDepartment of Chemical & Biomolecular Engineeringjason [email protected]

MS34

A Model of the Epithelial-Mesenchymal Transition(EMT) Regulatory Network

EMT, a fundamental process governing embryonic devel-opment in multicellular organisms, has recently been im-plicated in the early stages of cancer metastasis. Dur-ing this transition, epithelial cells lose adhesive propertiesand acquire a motile mesenchymal phenotype. EMT is di-rectly correlated with the downregulation of E-cadherin,a protein involved in adherens junctions holding epithelialcells together. Several oncogenic pathways are now knownto induce E-cadherin downregulation. We will present amodel EMT regulatory network involving the TGF-beta,Ras and Wnt signaling pathways. Our computer simu-lations demonstrate how a reduction in E-cadherin levelscorrelate with the induction of EMT and, in parallel, howthe mesenchymal marker, vimentin, is upregulated.

Baltazar D. Aguda, Felicia NgBioinformatics [email protected], [email protected]

MS34

A Mathematical Model of the G2 to M Transition

A mathematical model of the cell cycle transion from G2phase into Mitosis has been developed. The purpose ofthis model is to ascertain (in collaboration with experimen-talists) the biochemical mechanisms involved in the DNAdamage G2 checkpoint response and to model the effectof disruption of checkpoint response pathways on cellular

82 LS06 Abstracts

outcomes.

Kevin J. KesselerLineberger Cancer CenterUNC - Chapel [email protected]

MS34

Cellular Identity, Microenvironment, and GenomicIntegrity

In development, a balance between cellular proliferation,differentiation, and death emerges in collective genetic re-sponse to naturally varied intrinsic and extrinsic factors.Highthroughput efforts to ”interrogate” systems have ledto putative causal relationships, on a molecular level; i.e.,databases of pathways of interacting gene products. Ofnote, it seems that cell-type and experimental-preparationspecificity is of paramount importance. I will present workon top-down modelling that addresses genomic integrity,microenvironment, and lineage commitment during neuro-genesis.

Hugh R. MacmillanDept. of Mathematical SciencesClemson [email protected]

MS34

A Mathematical Model of Haemopoiesis as Exem-plified by CD34 Cell Mobilization into the Periph-eral Blood

We propose to simulate the kinetics of haemopoietic cells,including CD34+cells, with a mathematical model con-sisting of nonlinear, coupled, ordinary differential equa-tions. This minimal model mimics the known kinetics ofhaemopoietic progenitor cells in the bone marrow and theCD34+ cells, white blood cells, and platelets from the pe-ripheral blood in the presence of the granulocyte colony-stimulating factor. Perturbations within this system, sub-jected to granulocyte colony-stimulating factor treatmentand apheresis of peripheral blood progenitor cells (CD34+cells) in healthy individuals, are reproduced. With thismodel, we make predictions for reducing the length of timewith neutropenia after high-dose chemotherapy. Resultsbased on this model indicate that myelosuppressive treat-ment combined with infusion of CD34+ peripheral bloodprogenitor cells provides a faster recovery of the haemopoi-etic system than does treatment with the granulocytecolony-stimulating factor alone. Additionally, this modelpredicts that infusion of white blood cells and plateletscan relieve the symptoms of neutropenia and thrombo-cytopenia, respectively, without drastically hindering thehaemopoietic recovery period after high-dose chemother-apy.

Mandri ObeyesekereUniversity of Texas M. D. Anderson Cancer [email protected]

MS35

Systems Approaches to Understanding Robustnessand Performance in Circadian Rhythm

The regulatory architecture responsible for robust mainte-nance of 24 hour cycles is analyzed as a control system.Circadian rhythms possess the ability to entrain their in-ternal phase to that of the environment. This ability re-

lies on the phase response of circadian gene regulation todfferent environmental cues, of which light is the most ob-vious and important. Dynamic analysis of oscillatory sys-tems necessitate the development of methods specific forthese systems’ attributes, such as the period and phase.Investigation of the phase behavior of Drosophila circa-dian rhythm gives experimentally testable predictions forthe control mechanisms of circadian phase and period re-sponses.

Francis J. DoyleDept. of Chemical EngineeringUniversity of California, Santa [email protected]

MS35

Incorporating Mechanisms for Fatigue into a Cog-nitive Architecture

This research uses outputs from mathematical models thatcharacterize how circadian rhythms and sleep-wake home-ostasis influence overall human cognitive functioning. Themathematical models are used to represent fatigue by driv-ing parameter changes in a cognitive architecture, whichuses a common set of mechanisms to produce psychologi-cally valid performance predictions across a range of tasks.With mechanisms to represent fatigue, quantitative, a pri-ori predictions can be made about the impact of sleep lossin particular tasks.

Glenn GunzelmannAir Force Research LaboratoryAFRL/[email protected]

MS35

Frontiers in Modeling Circadian Rhythms, its In-puts and Outputs

Complementary experimental and modeling efforts have al-lowed determination of key features of the human circadiansystem and its effects on performance. Limit cycle oscil-lators are used model the 2-dimensional state circadiansystem. Current efforts include incorporating the effectof wavelength of light and non-photic effects on the inputpathway, and circadian control of melatonin rhythms. Theuse of analysis and modeling of data to understand thephysiology will be discussed.

Richard KronauerHarvard UniversityBrigham and Women’s [email protected]

MS35

Modeling Individual Differences

Reducing or displacing sleep consistently leads to neu-robehavioral impairment, although the magnitude of im-pairment varies considerably among individuals. Sleep-dependent changes in neurobehavioral performance acrosstime of day and over days have been captured in biomath-ematical models. However, these models do not deal withinter-individual differences. Novel approaches to biomath-ematical prediction of performance in the face of inter-individual differences, and the physiologic implicationsthereof, will be discussed.

Hans Van Dongen

LS06 Abstracts 83

Sleep and Performance Research CenterWashington State University [email protected]

MS36

Can We Discern Cause-and-effect in PolycysticOvarian Syndrome (PCOS) and Diabetes?

Soon after PCOS was defined as Amenorrhea associatedwith bilateral polycystic ovaries, obesity (up to 50%) andandrogen excess (up to 80+ %) were recognized as com-mon features. Hormonal studies confirmed both excess an-drogen (ovarian and adrenal) and insulin resistance (IR)and/or type 2 diabetes (up to 80+ %). Since effective ther-apies treat either IR or androgen excess, a positive feedbackmechanism involving insulin and androgen signaling mustbe central to the causal pathway in PCOS.

Claude HughesQuintiles, Inc.Morrisville, NC [email protected]

MS36

BK Channel Diversity: Consequences for CellularExcitability

BK channels are expressed in many tissues throughout thebody, where they play diverse roles in the control of cellu-lar excitability. This diversity arises from different cellularcontexts, as well as alternative splice variants, accessorysubunits, and modulation by circulating steroids on mul-tiple time scales. To capture the diversity and its conse-quences, we model whole cell excitability using stochasticsimulation of a BK channel gating model.

David McCobbDept. of Neurobiology and BehaviorCornell [email protected]

Danielle LylesCenter for Applied MathCornell Universitydanielle [email protected]

MS36

Glucose Sensing by Combined Metabolic and IonicOscillations in Pancreatic Islets

Pancreatic beta-cells secrete insulin to maintain blood glu-cose within a narrow range. We have proposed that se-cretion is mediated by a combination of fast electrical andslow metabolic oscillations. The fast and slow oscillationsboth follow the typical pattern of relaxation oscillators -off, oscillating, saturated - but may differ in the thresh-olds for the transitions. The nine resulting combinationsaccount for most of the oscillatory patterns observed, in-cluding pure fast and pure slow.

Krasimira Tsaneva-AtanasovaNational Institutes of HealthBethesda, MD [email protected]

Richard BertramDepartment of MathematicsFlorida State University

[email protected]

Arthur ShermanNational Institute of HealthBethesda, MD [email protected]

MS36

Improving Clinical Outcomes Through Data Min-ing

With the advent of electronic medical records, opportuni-ties are emerging to apply advance mathematical modelingand data mining methods to improve the quality of health-care. Practice management software is being developed tosuggest the most favorable treatment plans to physiciansgiven the complex array of diagnostic information avail-able. Medical arenas with fee-for-services or where compe-tition for patients is acute (eg. assisted reproduction) areparticularly interested in modeling approaches to improveresults and revenue.

James TrimarchiBrown [email protected]

MS37

Odor Identity and Concentration Coding in aModel Olfactory System

Using realistic computational model of the locust olfac-tory system we studied its response properties for differentodor concentrations. A dimension reduction analysis re-vealed that projection neurons activities for different odorsdiverged quickly in the response space while the activi-ties corresponding to different concentrations of a particu-lar odor evolved along neighboring trajectories. Both theidentity and the concentration of odors, therefore, can beencoded in the spatiotemporal firing patterns of projectionneurons activity.

Maxim BazhenovSalk Institute for Biological [email protected]

MS37

Dynamic Clustering in a Model of the Insect’s An-tennal Lobe


Alla BorisyukUniversity of UtahDept of [email protected]

MS37

Neural Dynamics in the Antennal Lobe: SensoryCoding and Memory Traces in an Insects Brain

I will present a detailed analysis of the neural dynam-ics in the antennal lobe of the honeybee, as recordedwith calcium-imaging. The analysis yields three impor-tant results: 1) the neural dynamics possess odor specific-attractors; 2) the perceptron provides a realistic model forodor recognition and odor discrimination; 3) the sponta-neous activity of this network contains memory traces thatare stored following the Hebbian learning rule, and they

84 LS06 Abstracts

can be retrieved through a principal component analysis.

Roberto Fernandez GalanCarnegie Mellon [email protected]

MS37

Encoding a Temporally Structured Sensory Stim-ulus with a Temporally Structured Neural Repre-sentation

Can the temporal structure of a stimulus interfere withthe spatio-temporal structure of the neural representation?We investigated this in the locust olfactory system. Whenodors were presented in trains of nearly overlapping pulses,responses of first-order interneurons changed reliably andoften greatly with pulse position, as responses to one pulseinterfered with subsequent responses. However, ensem-ble based spatio-temporal coding could disambiguate thesepatterns, providing an invariant response to the stimulusin second-order interneurons.

Mark Stopfer

NIH/[email protected]

MS38

Effect of Antibiotic on Heterogeneous BacterialPopulations

We consider a mathematical model of two microbial strainscompeting for a common nutrient while exposed to periodicdosing of an antibiotic or growth inhibitor. One strain isassumed to be more resistant to the drug but slower grow-ing than its competitor. The focus of our work is on ob-taining sufficient conditions for successful drug treatment,i.e., eradication of the bacteria, and on finding conditionsimplying persistence of one or more of the strains. Thisamounts to a stability analysis of the periodic solutions ofthe model.

Mudassar ImranArizona State [email protected]

MS38

Competition for Multiple Resources

We discuss a standard chemostat model of three speciescompeting for three essential resources. We show thatthe model can have at least two limit cycles, or an un-stable limit cycle. The results suggest that this standardmodel can exhibit both equilibrium dynamics and non-equilibrium dynamics for a given set of parameter values.(Joint work with Hal L. Smith and Steven M. Baer)

Steven BaerDepartment of Mathematics and StatisticsArizona State [email protected]


Bingtuan LiDepartment of MathematicsUniversity of Louisville

[email protected]

MS38

Stoichiometric Model that Links Cellular Machin-ery with Global Nutrient Ratios

Redfield ratios are one of the largest-scale patterns found inthe Biosphere. First identified by Harvard oceanographerAlfred Redfield in 1930s, the pattern refers to the remark-able similarity of carbon(C) : Nitrogen (N) : Phosphorus(P) ratios in open ocean and phytoplankton. In particular,Redfield ratios state that for every P atom there are about16 N atoms in both oceanic water and phytoplankton. Dueto the importance of Redfield ratio to biogeochemical cy-cles, carbon balance and, hence, global climate, numerousattempts have been made to explain it. Here, we deriveRedfield ratios by linking molecular processes on cell levelwith competition among species and global nutrient feed-backs. First, we show that N:P=16 can stem from fun-damental molecular constants such as N content in aminoacids, and N and P content in nucleotides to manifest itselfin a biochemically optimal RNA:Protein ratio. Next, weincorporate this biochemical optimum into the ODE modelof competition between phytoplankton species to show howthe pattern found on molecular scale can propagate itselfto global Redfield ratio. The necessary condition for thisto happen is nutrient feedbacks that indeed exist in oceans.

Simon LevinEcology and Evolutionary BiologyPrinceton [email protected]

James ElserArizona State [email protected]

Irakli LoladzeDepartment of MathematicsUniversity of Nebraska - [email protected]

MS38

A Resource-based Model of Microbial Quiescence

The implications of microbial quiescence are analyzedthrough a model that involves ”wake-up” and ”sleep” ratesfor cell transition between a quiescent and an active state.These rates depend on resource levels, turning on and off atthresholds which may not coincide. The population is ei-ther washed out or a single ”survival” steady state exists.Proportional nutrient enrichment is used to analyticallyand numerically explore the steady state bifurcating fromthe washout state.


Tufail M. MalikDepartment of Mathematics and StatisticsArizona State [email protected]

MS39

Mechanisms of Chromosome Segregation in Bud-

LS06 Abstracts 85

ding Yeast

We have used quantitative fluorescence microscopy tocount the number of proteins that comprise the micro-tubule binding site at the kinetochore. These measure-ments represent the minimal molecular requirements forassembling one kinetochore-MT attachment. We proposethat the core centromere nucleosome (120 bp wrappedaround a Cse4 containing nucleosome) and flanking chro-matin adopts a cruciform configuration in metaphase. Thisestablishes the geometry for the microtubule attachmentsite.

Kerry BloomUniversity of North Carolinakerry [email protected]

MS39

Modeling Polymer Dynamics in Bacterial Cell Di-vision

In order to correctly divide into two daughter cells, E. coliuses a remarkable dynamic process whereby it alternatelyassembles and disassembles a linear polymer at each of itsends which suppresses the formation of the division ringeverywhere but at the midpoint of the cell. By model-ing this process, we replicate much of the experimentallyobserved behaviour and thereby generate a set of mecha-nistic constraints and experimentally testable quantitativepredictions.

Eric N. CytrynbaumUniversity of British ColumbiaDepartment of [email protected]

MS39

FtsZ Self-Assembly Dynamics and Bacterial CellDivision

FtsZ, a bacterial tubulin homolog, forms a ring that con-stricts to divide the cell. The ring is constructed fromsingle-stranded protofilaments, which have been visualizedby EM in vitro. Protofilaments are turning over veryrapidly, with a half time of 8 sec both in vitro and in vivo.The protofilaments transit from a straight to a curved con-formation, and we propose that this is the basis for theconstriction force.

Harold EricksonDuke [email protected]

MS39

Modeling the Stochastic Mechanics of the BuddingYeast Mitotic Spindle

Proper segregation of chromosomes is one of the most fun-damental cellular processes. The physical movement andseparation that occurs during each round of division in eu-karyotes is mediated largely by microtubules in a complexknown as the mitotic spindle. We have developed stochas-tic models for microtubule assembly that describe the phys-ical and chemical forces that influence the dynamics. Wehave focussed our modeling efforts on budding yeast, be-cause it has the simplest mitotic spindle and therefore islikely the most tractable.

David J. Odde

University of MinnesotaDepartment of Biomedical [email protected]

MS40

Modeling Shear Wave Propagation in Biotissue:An Internal Variable Approach to Dissipation

In this presentation, we examine the propagation of dis-turbances consisting primarily of shear waves through bi-otissue. We develop a model based on specific physicalgeometries in polar coordinates, using the well known equa-tions of motion and a set of constitutive equations based onthe internal variable method outlined in [H.T Banks, J.H.Barnes, A.Eberhardt, H.Tran, and S.Wynne,Modeling andcomputation of propagating waves from coronary stenoses,Computational and Applied Mathematics,Vol 21, N.3, 2002]. Computational results first for a viscoelastic homoge-neous medium are presented and compared to previousfindings. We then consider a more complex geometry byintroducing heterogeneities into the medium. The resultingsimulations are discussed.

Nicholas Luke, Shannon Wynne, H.T. BanksNorth Carolina State [email protected], [email protected], [email protected]

MS40

Multiphasic Models for Chondron Deformation un-der Micropipette Aspiration

The chondron of articular cartilage consists of a cell and itsencapsulating pericellular matrix (PCM). Previous appli-cation of a single phase layered elastic contact solution formicropipette aspiration demonstrated a considerable de-crease in apparent PCM stiffness of isolated human chon-drons with osteoarthritis. We extend this layered elasticsolution by treating the chondron as a multiphasic (solid-fluid, or solid-fluid-ion) material to quantify the relativecontributions of collagen and proteoglycan fixed chargedensity to apparent PCM stiffness.

Mansoor A. HaiderNorth Carolina State UniversityDepartment of Mathematicsm [email protected]

Farshid GuilakDuke University Medical [email protected]

Brandy A. BenedictNorth Carolina State [email protected]

MS40

Modeling Auricular Chondrocytes for Lining ofVascular Stents

Stents are tube-like meshes used in the treatment of coro-nary artery diseases. They serve to prop the diseased arter-ies open and to secure normal blood flow. Although stentshave revolutionized the treatement of coronary artery dis-eases, there are various clinical complications in patientfollow-ups.The major one is re-stenosis or re-narrowing ofcoronary arteries which might lead to a heart attack. Re-stenosis is largely related to the development of scar tissue

86 LS06 Abstracts

(neo-intimal hyperplasia) that occurs within an artery af-ter it has been treated with a foreign device with poor bio-compatibility. To improve the biocompatibility of stents,a team of cardiologists around Dr. Rosenstrauch at theTexas Heart Institute is investigating the use of geneticallyengineered auricular chondrocytes for lining a stent. Stentslined with geneticaly engineered chondrocytes might lowerthe re-stenosis reates and provide a long-lasting biocompat-ible prothesis. The speaker will talk about a mathematicalmodel describing the growth of auricular chondrocytes on astent in the novel environment: exposed to controlled flowconditions for enhanced growth.

Suncica CanicDepartment of MathematicsUniversity of [email protected]

MS40

Modeling Scanning Microphotolysis to MeasureMolecular Diffusion in Articular Cartilage

Diffusion is the primary mode of transport of solutesthrough articular cartilage. We developed a mathemati-cal model of scanning microphotolysis (SCAMP) to mea-sure macromolecular diffusion in subcellular-size volumesof cartilage. SCAMP is a rapid, single-line photobleach-ing procedure that accounts for out-of-plane bleaching athigh magnification. Data was analyzed by best-fit compar-ison to simulations generated using alternating directionimplicit discretization of the diffusion-reaction equation inconjunction with the 3-D bleaching (excitation) and point-spread (detection) profiles.

Farshid Guilak, Susan Christensen, Holly LeddyDuke University Medical [email protected], [email protected], [email protected]

MS40

Biphasic Modeling and Optimization of MouseCartilage in Compression for Material PropertyDeterminations

Cartilage mechanical properties are important measures oftissue function. Mouse models of cartilage degeneration areimportant for studying a role for genetic background in thisprocess. A micro-indentation testing system was used todetermine the compressive and biphasic mechanical prop-erties of cartilage in the small joints of the mouse. A non-linear optimization program employing a genetic algorithmfor parameter estimation, combined with a biphasic finiteelement model of the micro-indentation test, was developedto obtain the biphasic, compressive material properties ofarticular cartilage.

Farshid GuilakDuke University Medical [email protected]

Li CaoDepartment of Biomedical EngineeringDuke [email protected]

Inchan YounDepartment of SurgeryDuke [email protected]

Lori SettonDept. of Biomedical EngineeringDuke [email protected]

MS41

How and Why Cells Make Networks within the Pi-tuitary Gland

Pituitary cells that secrete growth hormone (GH) are dis-tributed according to a 3D-network. The architecture ofthis network is robust across lifespan and displays modular-ity correlated with pituitary GH content and body growth.Importantly, this anatomical network supports functionalconnectivity revealed by spatially stereotyped motifs ofcell synchronization after stimulation by GH-releasing hor-mone. This type of network may be a critical determinantfor coordinated secretory pulses by the pituitary gland andother endocrine tissues.

Patrice MollardCNRS UMR5203 INSERM U661University Montpellier 1 & [email protected]

Xavier BonnefontCNRS UMR5203 INSERM U661Universities Montpellier 1 & [email protected]

MS41

A Model for the Switch Between the Pulse andSurge Pattern of GnRH Secretion

We propose a mathematical model allowing for the alter-nating pulse and surge pattern of GnRH (GonadotropinReleasing Hormone) secretion. The model is based on thecoupling between two FitzHugh-Nagumo systems runningon different time scales. The analysis of the slow/fast dy-namics allows to explain different secretion patterns (slowoscillations, fast oscillations and periodical surge). Spec-ifications on the parameter values are derived from phys-iological knowledge in terms of amplitude, frequency andplateau length of oscillations.

Frederique ClementINRIA [email protected]

MS41

An Electrophysiological Approach to GatheringData Needed to Model the Gonadotropin-releasingHormone Neural Network

Gonadotropin-releasing hormone (GnRH) secreting neu-rons form the final common pathway for the central regula-tion of fertility. This is accomplished by releasing GnRH ina frequency-modulated pattern to code downstream repro-ductive activity. We use electrophysiological approaches tounderstand how individual GnRH neurons initiate, main-tain and terminate action potential firing, how these cellscoordinate activity to produce distinct hormone pulses andhow this activity is modulated by homeostatic and non-homeostatic feedback.

Suzanne MoenterDivision of Endocrinology and MetabolismUniversity of Virginia

LS06 Abstracts 87

[email protected]

MS41

Catastrophe Theory Model of Hyperthyroidism


Sir Christopher ZeemanWarwick Mathematics [email protected]

MS42

Progress in Sleep Studies and Modeling

Recent studies at the molecular, cellular, and systems leveloffer several candidate mechanisms by which sleep statesmay enhance learning, thereby serving an important cog-nitive function. We will outline the scope of these hypoth-esized effects and some approaches to modeling them. Wewill also describe efforts to understand the dynamics ofsleep-wake cyclicity, focusing on modeling and quantita-tive analysis, especially dynamical systems and stochasticmodeling approaches.

Janet A. BestMathematical Biosciences InstituteOhio State [email protected]

MS42

Modeling Learning and Forgetting in REM Sleep

In a computational modeling study, we investigate the re-versal of hippocampal cell activity in REM sleep from a fir-ing pattern that promotes synaptic strengthening (or learn-ing) to a pattern more consistent with synaptic weakening(or forgetting) during the course of memory consolidation.Numerical simulations using a biophysically accurate neu-ron model support our hypothesis that changes in the rel-ative strengths or efficacies of the two synaptic pathwaystargeting hippocampal cells cause this reversal.

Victoria BoothUniversity of MichiganDepts of Mathematics and [email protected]

MS42

Network Dynamics and Mechanisms of Transitionin the Mouse Sleep-Wake Network

Behavioral states (wake, NREM sleep, and REM sleep)and transitions between them are regulated by a net-work of neurons in the brainstem and hypothalamus. Wemodel network dynamics with a system of coupled Morris-Lecar-type relaxation oscillators. The fast-slow nature ofthe equations captures network behavior on multiple timescales. We study mechanisms of transition in reduced mod-els obtained using combinations of fast-slow and dominantscale techniques. We also discuss canard-like behavior inthe equations.

Emery BrownHarvard Univ/ [email protected]

Nancy J. KopellBoston University

Department of [email protected]

Thomas ScammellDepartment of NeurologyBeth Israel Deaconess Medical [email protected]

Cecilia Diniz BehnDept of MathematicsBoston [email protected]

MS42

The Function of Sleep for Learning and Memory

Experimental recordings show that hippocampal cells firein the same manner during REM sleep as during wakinglearning, supporting a strengthening of LTP, the buildingblock for learning. Once the memory is consolidated, re-activation firing during REM reverses in a manner thatsupports depotentiation, or weakening of those hippocam-pal synapses encoding the memory. This finding is consis-tent with the idea that the hippocampus is an assemblywarehouse rather than permanent repository of complexassociative memories.

Gina PoeUniversity of MichiganDept of [email protected]

MS43

Support-vector Regression Approach for Predic-tion of Relative Lipid Accessibility in MembraneProteins

Computational prediction of relative solvent accessibilityfor amino acid residues in soluble proteins plays an im-portant role in folding simulations, protein structure pre-diction and functional annotations. Here, we present anovel protocol for prediction of relative lipid accessibilityin membrane domains. The new method is based on alinear, Support Vector Regression-based model that canbe used to efficiently and reliably estimate the parame-ters in the model from a limited number of experimen-tally validated examples. The new method will be avail-able to the community through the MINNOU web server(http://minnou.cchmc.org).


Jarek MellerChildren’s Hospital Research FoundationUniversity of Cincinnati, Cincinnati, [email protected]

MS43

A Prototype of the Human-virus Interactome Re-source

The large amounts of information generated by researchin systems biology makes it necessary for biologists to em-ploy literature mining tools in their work. We describe theprototype of a digital library containing interactions be-tween human and viral proteins, which provides virologists

88 LS06 Abstracts

a tool to rapidly identify protein interactions responsiblefor infection. The data is obtained by text mining the lit-erature and searching proteomic databases, and needs tobe updated frequently.

Kurt MalyDepartment of Computer ScienceOld Dominion [email protected]

Alex PothenOld Dominion UniversityDept of Computer [email protected]

M ZubairDepartment of Computer ScienceOld Dominion [email protected]

Chris OsgoodDepartment of Biological SciencesOld Dominion [email protected]

John SemmesMolecular and Cell BiologyEastern Virginia Medical [email protected]

MS43

A Two-level Architecture for Proteomic Networks

We describe an approach to clustering protein-protein in-teraction networks in order to identify functional modules.Our algorithm accounts for the small-world nature of thenetwork by dissecting the protein interaction network intoa global subnetwork of hub proteins (connected to severalclusters), and a local network consisting of cluster proteins.

Emad RamadanDepartment of Computer ScienceOld Dominion [email protected]

Alex PothenOld Dominion UniversityDept of Computer [email protected]

Chris OsgoodDepartment of Biological SciencesOld Dominion [email protected]

MS43

Peptide Mass Fingerprinting Via Machine Learn-ing: New Algorithms and Applications

Peptide Mass Fingerprinting is a process by which the iden-tity of a protein is determined by measuring the masses ofits tryptic peptides (its fingerprint) via mass spectrome-try. The process requires a database search, whereby theexperimentally determined spectrum is compared againsttheoretical spectra, which requires an appropriate metric.We propose new algorithms to design metrics to increasethe specificity and sensitivity of the process. Early compu-

tational results are promising.

Rachana JainBiomedical EngineeringUniversity of [email protected]


MS44

A Stochastic Model of the Tubuloglomerular Feed-back Mechanism in a Rat Nephron

Experimental studies have demonstrated the presence ofself-sustained oscillations in proximal tubular pressure inthe nephrons of rats. The oscillations are regular in nor-motensive Sprague-Dawley rats, and highly irregular inspontaneously hypertensive rats. A dynamic model ofthe renal autoregulation has been extended to include astochastic differential equations model of one of the mainparameters that determines feedback gain. The model re-produces fluctuations and irregularities in both period andamplitude that the former deterministic models failed todescribe. This approach assumes that the gain exhibitsspontaneous erratic variations, which can be explained bya variety of influences, which change over time (blood pres-sure, hormone levels etc). Estimation of key parametersof the model reveals important differences in the autoreg-ulation mechanisms between the two strains of rats. Thisinsight was achieved by directly modeling the dynamic fea-tures of the feedback gain, normally modeled with a con-stant that is not capable of capturing time variations.

Niels-Henrik Holstein-RathlouDepartment of Medical PhysiologyUniversity of [email protected]

Kay-Pong YipUniversity of South [email protected]

Susanne DitlevsenUniversity of CopenhagenDepartment of [email protected]

Donald MarshBrown UniversityDonald [email protected]

MS44

Theoretical Effects of Convection and EpithelialNO Production on NO Distribution in the RenalMedullary Microcirculation

The objective of this study is to develop a three-dimensional mathematical model of nitric oxide (NO)transport in the renal medulla in order to investigate howNO affects blood distribution in the medulla. Using a one-unit model, that is, a single vasa recta embedded in intersti-tium and surrounded by nephron loops, we have found thatconvection (i.e., blood flow per se) has negligible effects onNO concentration in pericytes, i.e., the smooth muscle-like cells that impart contractile properties to descendingvasa recta (DVR). However, the shear stress-mediated ef-

LS06 Abstracts 89

fects of blood flow on NO generation rates, and thereforeon NO concentrations, are predicted to be significant. Weare expanding the model to include all vessels and tubularsegments based on one vascular bundle and surroundingtubules, to examine whether the heterogeneous structureof the medulla and the tubular production of NO result inNO concentration differences between short and long vasarecta, respectively, thereby affecting blood flow distribu-tion between the outer medullary vascular bundles and theperipheral capillaries.

Aurelie EdwardsTufts [email protected]

MS44

Dynamics in Coupled Nephrons may Contribute toIrregular Flow Oscillations in Spontaneously Hy-pertensive Rats

We used a bifurcation analysis of a mathematical modelof two nephrons, coupled through their tubuloglomerularfeedback (TGF) systems, to investigate the role of cou-pling in the emergence of irregular tubular flow oscilla-tions in spontaneously hypertensive rats (SHR). We an-alyzed a characteristic equation for a model of couplednephrons having NaCl backleak; that characteristic equa-tion revealed a number of parameter regions having thepotential for differing stable dynamic states. Numericalsimulations using the full model equations exhibit a num-ber of differing dynamic behaviors in these regions. Somebehaviors show marked irregularity and exhibit a degreeof spectral complexity that is consistent with physiologicexperiments in SHR.

Anita T. LaytonDuke UniversityDepartment of [email protected]

Leon MooreSUNY at Stony [email protected]

Harold LaytonDUKE [email protected]

MS44

Estimation of Parameters for Maximum UrineConcentrating Capability in a Mathematical Modelof the Rat Inner Medulla

A nonlinear optimization technique was used to estimateparameter sets that maximize the ratio of the urine osmo-lality to the total NaCl active transport rate in a mathe-matical model of the urine concentrating mechanism. Theparameters were allowed to vary within ranges suggested byphysiologic experiments. A set of parameters that yieldedresults close to reported experimental values was identi-fied. Research supported by NIH grants DK-42091 andS06GM08102, and NSF grant DMS-0340654.

Mariano MarcanoUniversity of Puerto [email protected]

Anita T. LaytonDuke University

Department of [email protected]

Harold LaytonDUKE [email protected]

MS44

Nephron Initiated Interactions in a Renal VascularNetwork

Blood flow to single nephrons is governed by two nonlinearregulators that operate in each nephron, and by nonlin-ear interactions between the two. One mechanism, tubu-loglomerular feedback (TGF), senses NaCl concentrationin tubular fluid, and the other senses intravascular pres-sure. Both mechanisms are nonlinear, and each generatesa characteristic limit cycle oscillation. The two oscillationsinteract in each nephron. In addition, TGF initiates asignal that is propagated retrograde down the nephron’safferent arteriole, and the excitation spreads to adjacentnephrons, inducing synchronization of the TGF oscilla-tions. Approximately 20 nephrons derive their blood sup-plies from a single cortical radial artery, and all are withinrange of signal propagation from each of the others. Wehave modeled this interaction, and have also included jux-tamedullary nephrons, whose longer length produces TGFoscillations with longer periods than those of the corticalnephrons. There are two initial conclusions: 1) increasingcoupling strength increases the amplitude of the TGF oscil-lation in individual nephrons, and 2) although the activityof the longer nephrons can influence even the most distantcortical nephrons, the entire nephron ensemble does not be-come fully synchronized at a single frequency at any levelof coupling strength. The cortical nephrons can becomesyncrhonized at a single frequency even at fairly low cou-pling strength, and the juxtamedullary nephrons can be-come synchronized at high coupling strength, and the twogroups show evidence of interaction, but a single frequencyis not achieved. Supported by NIH Grant EB003508.

Donald MarshBrown UniversityDonald [email protected]

MS44

A Mathematical Model of Distal ConvolutedTubule (DCT): Determinants of Potassium Secre-tion

This simulation of rat DCT includes luminal and peritubu-lar cell membrane transporters responsible for Na reabsorp-tion in exchange for K secretion. Early tubule conditionsare conducive to maximal K fluxes, while late conditions re-quire K transport against an electrochemical gradient; themodel identifies the transporters that optimize K secretionunder each condition. Tubule inlet volume flow and Naconcentration both enhance K secretion; the model tubuleidentifies the relative importance of each factor.

Alan M. WeinsteinCornell [email protected]

MS45

Modeling Influenza Vaccination Using Minority

90 LS06 Abstracts

Games

Seasonal epidemics of influenza remain a major globalhealth concern and a pandemic of influenza is expectedimminently. One of the national health objectives of theUnited States is to increase the influenza vaccination cov-erage in order to prevent or substantially reduce influenzaepidemics. Vaccination is voluntary and the vaccine is ef-fective for one season only; thus an individual needs todecide every year whether to vaccinate or not. Gener-ally, individuals are selfish as their sole interest is to avoidgetting infected, preferably without having to vaccinate.Here we address the question of whether selfish individu-als can adapt their vaccination behavior to prevent severeinfluenza epidemics or whether public health programs arenecessary. Inspired by Minority Games, we construct anindividual-level model and we analyze the adaptive dynam-ics of vaccination behavior for influenza in a population ofnon-communicating selfish individuals. We find that mostof the time influenza epidemics cannot be prevented byvaccination, and occasionally severe epidemics occur evenwithout the introduction of pandemic strains.

Sally BlowerSemel Institute of Neuroschience and Human [email protected]

Raffaele Vardavas, Romulus BrebanSemel Institute for Neuroscience and Human [email protected], [email protected]

MS45

Game Theory and the Developing World

The principles of social justice and health as a human rightin the developing world have been advocated as the mainjustification for health assistance from rich to poor coun-tries. While we do not disagree with this, we argue thata strategy that emphasizes the shared benefit to rich andpoor countries would facilitate this process. We proposethat the accomplishment of these challenging tasks shouldbe viewed from the perspective of game theory, where theinterests of the parties (in this case rich and poor countries)overlap. As the world becomes increasingly integratedwith globalization, economic development in resource-poorcountries will increase the opportunities for richer countriesto profit from investment in the developing world. Globalhealth has political and international security implicationsfor the developed world, as well.

Carlos Franco-ParedesDivision of Infectious DiseasesEmory University School of [email protected]

MS45

Modeling Social Conflicts of Public Health

Public health strategies that are optimal for the communityare not necessarily optimal for the individual. For example,if most of the community is vaccinated, it can be best foran individual to refuse vaccination. This way they receivethe benefits of reduced disease prevalence while avoidinganticipated adverse effects of the vaccine. Such conflictscan undermine public health programs, and their mathe-matical analysis involves an interesting application of game

theory.

Alison GalvaniDepartment of Epidemiology and Public HealthYale University School of [email protected]

MS45

Controlling Influenza Epidemics via Public HealthVaccination Incentives

Using a Minority Game model that describes the adaptivedynamics of vaccination coverage for influenza in a pop-ulation of non-communicating selfish individuals, we askif certain public health incentives could be used to helpprevent influenza epidemics. Specifically, we evaluate thepotential effects of the two following incentives: 1) If thehead of the family pays to get vaccinated then their fam-ily gets vaccinated for free; 2) If an individual pays to getvaccinated then that individual will get free vaccinationsfor a certain number of successive years. Vaccinating fam-ilies would increase: the average prevalence, the variabilityin prevalence and the frequency of epidemics. However,we show that certain public health incentives that offerfree vaccination could ameliorate influenza epidemics. Weshow that it is possible to construct public health incentivesthat help the vaccination coverage to remain very close tothe critical vaccination coverage with only small variability.We discuss public health implications.

Sally BlowerSemel Institute of Neuroschience and Human [email protected]

Raffaele VardavasSemel Institute for Neuroscience and Human [email protected]

Romulus BrebanSemel Institute of Neuroschience and Human [email protected]

MS46

Walking on Water

We present the results of a combined experimental andtheoretical investigation of the hydrodynamics of water-walking creatures. We enumerate the many styles of hydro-dynamic propulsion at the free surface, and the resultingdistinctions form the basis of a dynamic classification ofall water-walkers. We consider creatures spanning a broadrange of scales, from millimetric insects reliant on surfacetension, to tail-walking dolphins. Accompanying adven-tures in biorobotics are described.

David HuCourant Institute, [email protected]

John BushDepartment of MathematicsMassachusetts Institute of [email protected]

LS06 Abstracts 91

MS46

The Role of Bristled Wings in Tiny Insect Flight

The smallest flying insects often use ’clap and fling’ to aug-ment lift forces generated during flight. There is, however,an aerodynamic cost for this behavior. For low Reynoldsnumber flight, very large drag forces are generated duringclap and fling. Another feature common to most tiny flyinginsects is wing ciliation. Using a porous media version ofthe immersed boundary method, the effect of wing ciliation(i.e. wing bristles) on flight aerodynamics will be explored.

Laura A. MillerDepartment of MathematicsUniversity of [email protected]

MS46

Computational Simulation of Metachronal Wavesin Cilia

A simulation of the formation of metachronal waves incarpets of pulmonary cilia is presented. The cilia movein a two-layer fluid model. The fluid layer adjacent tothe cilia base is purely viscous while the tips of the ciliamove through a viscoelastic fluid. An overlapping fixed-moving grid formulation is employed to capture the effectof the cilia on the surrounding fluid. The 9+2 internalmicrotubule structure of an individual cilium is modeledusing large-deflection, curved, finite-element beams. Real-istic models of the forces exerted by dynein molecules areextracted from measurements of observed cilia shapes. Thepossibility of formation of metachronal waves under differ-ent assumptions of boundary conditions is investigated andshown to be dependent on the surrounding geometry.

Sorin M. MitranDept. of Mathematics, Applied Math Prog.University of North [email protected]

MS46

A Model of Force Generation in Motile Cells

Directed migration of amoeboid cells is involved in pro-cesses such as embryonic development, wound healing, andthe metastasis of cancer. Migration entails force generationwithin cells, and understanding how this force generationis controlled in space and time to produce cellular motil-ity is a major challenge. I present a continuum model ofcell motility in which the active deformation of the cell re-sults from spatially-controlled remodeling of the cytoskele-ton, and force is transmitted to the substrate via controlledadhesion sites. The passive cellular response is viscoelas-tic. Finite element simulations of this model reproduce celltraction patterns that are observed experimentally.

Magdalena A. StolarskaUniversity of Minnesota - [email protected]

MS47

Mechanistic Temperature Compensation of theCircadian Clock

One of the key features of the molecular mechanism un-derlying the circadian clock is its ability to robustly com-pensate for changes in temperature over a range of 10 Cor more, a feature that isnt typical of models of the clock

mechanism. Here we discuss alternate ways of achieving ro-bust temperature compensation and explore the idea thatevolution has optimized the interaction of several feedbackloops to produce an oscillator whose period is tightly reg-ulated.

Emery ConradVirginia Polytechnic Institute and State [email protected]

MS47

Controlling the Period of Intracellular Clocks

The basic function of circadian ( 24-hour) clocks withincells is to provide 24-hour timing of biological events. Theperiod of the clocks is affected by genetic mutations, butis remarkably robust to changes in temperature. Severalmathematical models and techniques will be presented todetermine the period of cellular circadian clocks. Thesemathematical theories of period regulations will be vali-dated against experimental data.

Daniel ForgerUniversity of [email protected]

MS47

Modeling Circadian Rhythms: Deterministic andStochastic Approaches

In most organisms the detailed molecular mechanism ofthe circadian clock involves interlocked positive and neg-ative feedback loops. We studied deterministic models ofincreasing complexity for the occurrence of autonomouscircadian oscillations, for their entrainment by light-darkcycles, and their phase shifting by light pulses. Stochas-tic versions of these models indicate that the robustnessof circadian rhythms with respect to molecular noise is af-fected upon entrainment by light-dark cycles, by the co-operativity in repression, the proximity from a bifurcationpoint, the rate of association of the inhibitory protein tothe promoter of the clock gene, and the coupling betweenoscillating cells.

Didier GonzeUnite de Chronobiologie Theorique, Universite Libre [email protected]

MS47

System Biology Reveals an Opposite Role for Tauin Circadian Rhythms

Circadian rhythms are stable 24 hour physiologic cyclesregulated by negative feedback loops. The tau mutationin casein kinase I (CKI?tau) causes a four hour shortingof rhythms and a decrease of kinase activity in vitro. Itis difficult to reconcile this loss of function with the cur-rent model of circadian clock function. The Forger-Peskinmodel, a detailed quantitative model of the mammalian cir-cadian clock, predicts the opposite, that CKI?tau must bea gain of function mutation. We have verified this counter-intuitive modeling prediction and find that CKI?tau pro-duces a gain of function in cells These findings experimen-tally validate the systems biology approach and provide aremarkable example of how a specific mutation can be botha loss and a gain of function depending on the substrate.

David Virshup

92 LS06 Abstracts

Huntsman Cancer InstituteUniversity of [email protected]

MS48

Problem-Based Learning: A Way to Motivate Un-dergraduates at the Math/Bio Interface

Mathematics and statistics are essential to properly de-scribe dynamical phenomena, to construct experimentalplans, and to predict general rules in the life sciences.With this in mind, I teach a course in France taken bymore than 800 students annually. Students are dividedinto small groups and special interactive exercises are builtto introduce them to the modeling process. I will presentsome of the activities we have developed and how studentsmotivation has increased significantly.

Sandrine CharlesUniversite Claude Bernard Lyon 1Laboratory of Biometry and Evolutive [email protected]

MS48

The State of Mathematical Biology Training in theUK

With researchers across the world showing a growing inter-est in the education of mathematical biologists, in this talkI examine and compare the training offered by institutionsacross the UK. In particular, I will discuss the mathemat-ical biology education at the undergraduate and postgrad-uate level in both mathematics and biology departments.I will look at the final career destination of these studentsand investigate how the training prepares students for acareer in mathematical biology research.

Christina CobboldDepartment of MathematicsUniversity of [email protected]

MS48

Computational Tools for a Two-Course CalculusSequence for Biology Majors

The Department of Mathematics at Benedictine Univer-sity has begun to offer a rigorous two-semester calculussequence for biology students. Two important course goalsare the integration of mathematical and biological reason-ing through the understanding of biological models andthe development of skills to use appropriate computationalsoftware to analyze and solve biological problems. We dis-cuss how and why we use Excel, Derive, Berkeley Madonna,and MATLAB to achieve these goals.

Timothy D. ComarBenedictine [email protected]

MS48

BIO SIGMAA

A new special interest group in the MAA. This talk willdiscuss the new SIGMAA, its direction, and a few upcom-ing inaugural events. We will also have an open discussionon how the new SIGMAA can work with SMB to promote

and support mathematical and computational biology.

Eric Marland, Rene SalinasAppalachian State [email protected], [email protected]

MS49

Mitigating Immunodominance in Multi-EpitopeTumor Vaccines by Polytopic Vaccination

The refractory nature of cancer to many standard thera-pies has led to substantial efforts to achieve immune con-trol. We describe a theory that elucidates the mechanismby which polytopic, or multi-site, vaccination mitigates im-munodominance in therapeutic T-cell vaccines for cancer.By inducing a T-cell response to each cancer-associated epi-tope in a distinct lymph node, vaccine efficacy is increasedand immunodominance is reduced. Our approach capturesthe dynamic characteristics between the T-cell receptorsand tumor.

Michael DeemRice UnversityDept. of Biomedical [email protected]

MS49

Prediction of Treatment Outcome for LaserSurgery of Prostate Cancer

Temperature is usually used as the control variable in lasertherapy, it is however not an effective measure of treatmentoutcomes. We proposed models that predict cell damageand heat shock protein in the prostate tumor to charac-terize effectiveness of the treatment and likelihood of can-cer recurrence. These models can optimize the therapyoutcome by mitigating tumor recurrence and resistance tofollow-up chemotherapy and radiation therapy due to HSPexpression and insufficient injury.

Yusheng FengThe University of Texas at [email protected]

Jon Bass, M. Nichole Rylander, Kenneth Diller, J.Tinsley OdenUniversity of Texas at [email protected], [email protected],[email protected], [email protected]

MS49

Protein Wrapping as a Selectivity Switch in thePharmacological Oncokinome

Kinases are central targets for drug-based treatments ofcancer. Progress in drug development faces challenges dueto undesirable cross-reactivity and difficulties in modulat-ing selectivity. We present a structure-based predictor ofcross reactivity and validate it against affinity fingerprint-ing of the kinases and our own drug re-design geared atsharpening the inhibitory impact. The predictor comparespatterns of packing defects and introduces a packing dis-tance between kinases shown to be equivalent to the phar-macological distance.

Ariel FernandesRice [email protected]

LS06 Abstracts 93

MS49

Mathematical Modeling of Angiogenesis in CancerResearch

Angiogenesis is critical for tumor growth. To understandmechanisms of angiogenesis, we have developed a mathe-matical model to simulate two-dimensional angiogenesis inthe cornea, a commonly used tissue for testing efficaciesof angiogenic and antiangiogenic agents. One of the ad-vantages of the model is that results from numerical simu-lations can be compared directly with experimental data.Specifically, the dose responses to bFGF, an angiogenicfactor, predicted by the model are consistent with experi-mental observations.

Fan YuanDept. of BioengineeringDuke [email protected]

MS50

Randomized Approximation Algorithms for SetMulticover Problems with Applications to ReverseEngineering of Protein and Gene Networks

In this paper we investigate the computational complexi-ties of a combinatorial problem that arises in the reverseengineering of protein and gene networks. Our contribu-tions are as follows:

• We abstract a combinatorial version of the problemand observe that this is “equivalent” to the set multi-cover problem when the “coverage” factor k is a func-tion of the number of elements n of the universe. Animportant special case for our application is the casein which k = n− 1.

• We observe that the standard greedy algorithm pro-duces an approximation ratio of Ω(log n) even if k is“large”, i.e., k = n− c for some constant c > 0.

• Let 1 < a < n denotes the maximum number of el-ements in any given set in our set multicover prob-lem. Then, we show that a non-trivial analysis ofa simple randomized polynomial-time approximationalgorithm for this problem yields an expected approx-imation ratio E[r(a, k)] that is an increasing func-tion of a/k. The behavior of E[r(a, k)] is “roughly”as follows: it is about ln(a/k) when a/k is at leastabout e2 ≈ 7.39, and for smaller values of a/k it de-

creases towards 1 as a linear function of√

a/k withlima/k→0 E[r(a, k)] = 1. Our randomized algorithm isa cascade of a deterministic and a randomized round-ing step parameterized by a quantity β followed bya greedy solution for the remaining problem. Wealso comment about the impossibility of a significantlyfaster convergence of E[r(a, k)] towards 1 for any ran-domized approximation algorithm.

Bhaskar DasGuptaDepartment of Computer ScienceUniversity of Illinois at [email protected]

Eduardo SontagRutgers [email protected]

Piotr BermanPennsylvania State [email protected]

MS50

Identifying Functional Constraints on the Quanti-tative Evolutionary Design of a Metabolic Circuit

We address the following questions for the well-characterized coupled redox cycles of NADPH and glu-tathione in human erythrocytes. Suppose that networktopology and kinetic mechanisms are conserved, that muta-tions can alter the values of any enzyme kinetic parameterover broad ranges, but only circuits that fulfill the perfor-mance specifications of the wild type are selected. Do theselected circuits share a well-defined design? What specificfunctional requirements evolutionarily constrain the valuesof each parameter?

Armindo J. SalvadorCentre for Neuroscience and Cell BiologyThe University of [email protected]

Michael SavageauDepartment of Biomedical EngineeringThe University of California, [email protected]

MS50

The Apparent First-order Kinetics of the SubstrateDisappearance in Enzyme Digestion: A TheoreticalInvestigation

We theoretically investigate the kinetics for protein diges-tion by mathematically formulating rate equations for twoproposed mechanisms namely the one by one and zippermechanisms. Our analysis shows that the kinetics of di-gestion follows apparent first-order kinetics irrespective ofthe mechanism for low initial substrate concentration withrespect to the initial enzyme concentration. Also our re-sults suggest new experimental protocol that could revealinformation on the mechanism of digestion.

Santiago Schnell, J SrividhyaIndiana UniversitySchool of [email protected], [email protected]

MS50

On the Distinguishability of Growth Factor Traf-ficking Kinetics

We analyze a model of EGF receptor trafficking understeady state sorting conditions and derive uniformly validanalytical approximations for constitutively trafficking re-ceptors. Interestingly, these approximations take on thesame functional form under a wide range of conditions thatincludes the extremes of perfectly stable and unstable en-dosomal complexes. This illustrates that it is possible tofit experimental data to a model that assumes a stable en-dosomal complex even when this premise is invalid.

Rami Tzafriri, Elazer EdelmanHarvard-MIT Biomedical Engineering [email protected], [email protected]

MS51

The Emerging Role of Modeling and Simulation atAll Stages of Drug Development

Recent estimates by FDA have projected that of all new

94 LS06 Abstracts

drugs initially tested in human subjects, only 8 percenteventually make it to the bedside. The primary cause ofdrug failure in the clinic is the selection of an inappropri-ate dose and schedule. Modeling mathematically describeswhat the body does to administered drug (Pharmacoki-netics) and what the drug does to the body (Pharmacody-namics) to guide and provide rational/quantitative basisfor dose regimen selection throughout drug development.

Nelson L. JumbeGenentech [email protected]

MS51

Case Studies of Innovative Problem Solving inTherapeutic Protein Development

Therapeutic proteins (MW ¿1000 Da), have unique phar-macokinetic (PK) and pharmacodynamic (PD) propertiescompared to small molecules. Different approaches cur-rently being applied for the optimization of dosing in clin-ical development of therapeutic proteins include, (i) mech-anistic PK/PD modeling to predict drug effects; (ii) non-linear mixed effect modeling to assess variability and iden-tify covariate effect on drug disposition; and (iii) usingMonte Carlo simulation to guide strategic decision mak-ing on fixed dosing-vs.-weight-based dosing for monoclonalantibodies.

Jian-Feng Lu, Amita Joshi, Bert Lum, SaraKenkare-MitraGenentech, IncSSF, [email protected], [email protected],[email protected], [email protected]

Nelson L. JumbeGenentech [email protected]

MS51

Quantitative Structure-Pharmacokinetic Relation-ships (QSPKR) using Bayesian Neural Networks

Where the number of molecular descriptors is typicallygreater than the number of tested compounds, Bayesianneural networks may provide predicted time-series datathat allow for PK modeling, data characterization, and pri-mary parameter estimation, without the significant limita-tions that accompany most other methods of in silico mod-eling. Such capabilities hold the promise of reducing thefailure rate of compounds in development, while providingkey insights into the molecular, physiological, and pharma-cological factors controlling drug dose-exposure-responserelationships.

Donald E. MagerSUNY BuffaloBuffalo, [email protected]

MS51

Improving Clinical Trial Designs using ClinicalTrial Simulation (CTS)

The failure of a clinical trial to provide successful outcomesis a significant problem in drug development because failedtrials must be repeated at a considerable expense to a com-

pany. Using simulation-based design optimization (SBDO)methods, information gained from Clinical Trial Simulation(CTS) is expanded to not only identify the best design butalso the robustness of the design. Thus, more than onedesign is proposed that will provide a successful trial out-come.

Jonathan MonteleoneDOV Pharmaceutical, IncSomerset, [email protected]

MS52

Interaction of Biological rhythms : Its Relevance,by Means of Examples, for Physiology


Jacques BelairUniversity of MontrealDepartment of [email protected]

MS52

Chronotherapy Strategies in Cancer: It’s AboutTime

Cancer chemotherapy causes major cytotoxic stress on nor-mal tissues. Chronotherapy takes advantage of the exis-tence of optimal treatment times; fast renewing tissues,both normal and tumoral, display a circadian rhythmicityin drug susceptibility. With a cell cycle model, we devisethe best strategies for colorectal cancer treatment, takinginto account toxicity on the hematopoietic system. Weshow how the best schedule depends on the interplay be-tween the cell cycle kinetics, the circadian amplitude ofdrug susceptibility and the treatment itself.

Samuel Bernard, Branka Cajavec, Hanspeter HerzelHumboldt UniversityBerlin [email protected], [email protected], [email protected]

MS52

Effect of Noise on Cardiac Arrhythmias Associatedwith Long-QT Syndrome

Early afterdepolarizations (EADs) can induce cardiac ar-rhythmias. In a mathematical model of ventricular cells,we show that fluctuations generated by additive Gaussianwhite current noise or the stochastic opening and closingof ionic channels influence the genesis of EADs. Prolongedrepolarization was simulated by partially blocking a potas-sium current (IKs). The stochastic fluctuations inducedEADs with patterns that depend on the noise amplitude.The relevance to arrhythmias in patients with Long-QTsyndrome will be discussed.

Michael GuevaraMcGill UniversityMontreal Quebec [email protected]

Claudia LermaMcGill UiversityMontreal Quebec [email protected]

LS06 Abstracts 95

Trine Krogh-MadsenMcGill [email protected]

Leon GlassMcGill UniversityDepartment of [email protected]

MS52

Interactions of the Cell Cycle and Radiation Treat-ment of Cancer

The determination of cancer treatment schedules with ra-diotherapy is highly dependent on mathematical models ofproliferation and the effect of radiation on cells. Althoughmuch is known about the cell cycle, few models used inthe study of radiotherapy take the cell cycle into account.We construct a model describing the dynamics of prolif-erating cells (highly sensitive to radiotherapy) and restingcells (less sensitive to radiotherapy), and examine the sig-nificance of the cell cycle and its regulation on the effec-tiveness of radiotherapy. We find that the subpopulationof resting cells may contribute to failure in radiotherapy.This presentation relates to the talk given by T. Hillenin the minisymposium ”Mathematical Modeling of CancerTreatment”.

Ozden YurtsevenUniversity of AlbertaEdmonton [email protected]

Gerda de VriesUniversity of AlbertaDepartment of Mathematical & Statistical [email protected]


MS53

Finding the Center - How to Solve Simple Geome-try Problems at the Cellular Scale

Fragments of fish pigment cells can form and center aggre-gates of pigment granules by dynein-motor-driven trans-port along a self-organized radial array of microtubules(MTs). I will present a quantitative model that de-scribes pigment aggregation, MT-aster self-organizationand the subsequent centering of both structures. I willpresent analysis and simulations of a set of partial integro-differential equations describing the coupled granule-MTinteraction that successfully explains much of the observedbeahviour and sheds light on role of polymer dynamics andpolymer-motor interactions in cytoskeletal organization.

Eric N. CytrynbaumUniversity of British ColumbiaDepartment of [email protected]

MS53

A Divergent Mechanism of Spatial Gradient Sens-ing Revealed through Quantitative Imaging and

Modeling

Directed migration of eukaryotic cells often relies on theirability to distinguish receptor-mediated signaling at dif-ferent subcellular locations, a phenomenon known as spa-tial sensing. We have analyzed, using mathematical mod-els and live-cell imaging experiments, the sensitivity ofplatelet-derived growth factor (PDGF) gradient sensing infibroblasts. We demonstrate that PDGF detection is gov-erned by mechanisms that are fundamentally distinct fromthose characterized in other chemotactic cells, with impli-cations for fibroblast chemotaxis during wound invasion.

Jason HaughNorth Carolina State UniversityDepartment of Chemical & Biomolecular Engineeringjason [email protected]

MS53

Intracellular Gradients and Microtubule Chemo-taxis

Microtubules are linear filaments of the intracellular cy-toskeleton that serve to organize cytoplasmic components.A major question in understanding cytoplasmic organiza-tion is how the self-assembly of microtubules is controlledspatially and temporally. We have found that intracellularchemical gradients could potentially play a significant rolein microtubule organization and would be affected by thesize and shape of the cell itself.

David J. OddeUniversity of MinnesotaDepartment of Biomedical [email protected]

MS53

Dynamics of Cell Adhesion: Mass-action Kineticsin the Presence of Long-range Interactions

A model is presented that explains why focal adhesions instationary or slowly moving cells tend to concentrate at cellperiphery in high curvature regions. According to the the-ory, adhesions move in the direction opposite to contractileforces exerted on them by stress fibers. This translocationto the periphery occurs by treadmilling with the speed pro-portional to the diffusion coefficient of integrins, the keysurface receptors mediating adhesion assembly.

Boris M. SlepchenkoUniversity of Connecticut Health CenterCenter for Cell Analysis and [email protected]

MS54

Biocalculus in the Community College: Transfer,Workforce, and Continuing Education

A majority of students who successfully complete under-graduate life science degrees fulfill their math requirementsat community colleges. To fully implement the national re-forms called for in recent reports, two-year colleges must beincluded. In this talk, a successful biocalculus course devel-oped for the community college population will be detailed.The course audience includes those going directly into in-dustry, those transferring to baccalaureate programs, andthose already in research working to obtain a quantitative

96 LS06 Abstracts

perspective.

Mike MartinJohnson County Community [email protected]

MS54

Biocalculus: Reflecting the Needs of the Students

There are three basic paths to teaching calculus to studentsof biology. The first is the course that emphasizes the stan-dard calculus topics and minimizes the special backgroundand interests of the students. The second is the coursethat emphasizes those aspects of calculus that mathemati-cians have found useful when doing biomathematics. Thethird is the course that emphasizes the needs of the stu-dents and minimizes some standard topics usually found ina calculus course. Here, the third path is described throughexamples and test material developed over 25 years at Mar-quette University. In general, spreadsheets replace algebra,and data is the primary object of study, instead of func-tion and equation. This approach allows the developmentof all standard results while also providing a clear path tocourses in statistics.

Stephen J. MerrillMarquette UniversityDept of Math, Stats & Comp [email protected]

MS54

Calculus and Beyond

Calculus is an important tool for the biological sciences,and the development of targeted textbooks is a key ingre-dient to motivating freshmen biology majors and demon-strate to them the importance of acquiring the means toexpress biological processes in a formal and precise lan-guage. Beyond calculus, modeling, stochastic processes,and statistical tools are important quantitative skills everybiology student must acquire. This talk will present effortsin this direction by the author.

Claudia NeuhauserUniversity of [email protected]

MS54

Biocalculus and Beyond: Getting Biology Majorsat William and Mary Hooked on Mathematics andReeling Them In

Like many campuses throughout the United States,William and Mary has bought hook, line, and sinker intobuilding curricular bridges between mathematics and biol-ogy. As part of this initiative, I developed a two semestercalculus sequence for the life sciences whose goals includesubstitutability for the regular calculus sequence and in-troducing biology majors to the excitement of modeling. Iwill share some of my harrowing tales of trying to navigatebetween this interdisciplinary Sylla and Charybdis and mysuccesses and failures of enticing students into higher levelmathematics courses. These higher level courses, in addi-tion to the regular mathematical fare, include several at theinterface of mathematics and biology. I will compare andcontrast my experiences in teaching two of these courses, asophomore introduction to mathematical biology and a ju-nior/senior co-taught seminar on metapopulation ecology,

that differ drastically in size, structure, and content.

Sebastian SchreiberCollege of William and [email protected]

MS55

The Evolution of Defence Portfolios in Integro-difference Models of

Some organisms maintain a battery of defensive strategiesagainst their exploiters, while others fail to employ a de-fence that seems obvious. We investigate the evolution ofdefence portfolios in a discrete-time model with a mutationkernel, resulting in a system of integro-difference equations.We introduce the concept of strategy-blocking, where onestrategy prevents the appearance of another that wouldbe adaptive in its absence, and discuss why reed warblersreject cuckoo eggs but not cuckoo chicks.

Nicholas BrittonDepartment of Mathematical SciencesUniversity of [email protected]

MS55

Adaptive Speciation: Theory and Evolutionary Ex-periments

Understanding the origin of diversity is a fundamentalproblem in biology. According to traditional evolution-ary theory, the process of diversification is a by-product ofgeographical separation. However, I will show that diversi-fication as an adaptive response to biological interactions isalso a plausible evolutionary process. I will describe mod-els for evolutionary branching based on the mathematicalframework of adaptive dynamics as well as ongoing effortsto test our theory in evolving Escherichia coli populations.

Michael DoebeliDepartments of Mathematics and [email protected]

MS55

The Evolution of Microbial Diversity in SpatiallyHomogeneous Environments Containing a SingleResource

According to the competitive exclusion principle a simplehabitat, defined to be a spatially homogeneous environ-ment that contains a single resource, can only ever supportone competitor. Contrary to this theoretical prediction anumber of laboratory experiments of microbial evolutionhave found that diversity can evolve in simple habitats.Using a system of non-local PDEs we test a hypothesisthat biochemical trade-offs of microbial metabolism playan important role in the evolution of microbial diversity

Ivana GudeljDepartment of Mathematical SciencesUniversity of [email protected]

MS55

Evolution of Developmental Timing – Warming

LS06 Abstracts 97

Climate and Phenological Change

Cold blooded organisms develop nonlinearly with respectto temperatures; with seasonal swings tend synchroniz-ing developmental timing and conveying higher fitness.Persistence of species depends on whether adaptation ofphenology can track rates of climate change. Our ap-proach couples existing models of phenology and quantita-tive genetic theory to predict how phenological parametersmay evolve. Evolutionary trajectories are characterizedby rapid changes to create synchrony, followed by gradualadaptation to parameters with marginal dynamic proper-ties.

James PowellDepartment of Mathematics and StatisticsUtah State [email protected]

Christina CobboldDepartment of MathematicsUniversity of [email protected]

MS56

Gates and Oscillators: A Network Model of theMammalian Circadian Clock

The mammalian circadian clock, in the suprachiasmaticnucleus has at least two anatomically and functionally dis-tinct cellular constituents. Some cells respond rapidly uponreceipt of direct retinal input but are not electrically rhyth-mic while others have endogenous molecular oscillations,but do not immediately respond to photic input. Us-ing these two phenotypes, we have modeled maintenanceof phase coherence among autonomous cellular oscillators,showing that a common mechanism can account for bothfree-running rhythms and entrainment.

Nicholas Foley, Rae SilverColumbia [email protected], [email protected]

Michael AntleDepartment of Psychology, University of CalgaryHotchkiss Brain Institute, University of [email protected]

MS56

Synchrony Among Daily Oscillators in the Brain

Specific brain areas act as circadian pacemakers requiredfor daily rhythms in behavior and physiology. In vivo andin vitro, multiple circadian oscillators synchronize to eachother to sustain near 24-h rhythms. Using long-durationrecording methods, we have begun to study signals re-quired for coordinated activity. We find that a neuropep-tide (vasoactive intestinal polypeptide) plays a critical rolein entrainment among neurons within one pacemaker, thesuprachiasmatic nucleus, which regulates daily rhythms inlocomotion.

Erik HerzogDepartment of BiologyWashington [email protected]

MS56

Design Principles for Phase Splitting Behavior ofCoupled Cellular Oscillators

Hamsters housed in constant light exhibit a phenomenonknown as splitting, in which an animal’s single daily boutof locomotor activity dissociates into two components thatare about 12hr apart. Recent data show that this phe-nomenon is due to reorganization of the cellular oscillatorsin the SCN with its right and left halves oscillating in an-tiphase. To better understand the splitting, we have ap-plied mathematical reasoning to infer the essential designprinciples of this phenomenon

Premananda IndicDepartment of NeurologyUniversity of Massachusetts Medical [email protected]

MS56

Suprachiasmatic Nucleus: A Primer for Mathe-maticians

The suprachiasmatic nucleus (SCN) in the anterior hy-pothalamus is a paired nucleus straddling the midline andcomposed of 16,000 heterogeneous, densely-packed neu-rons. A wealth of data indicates that it is the site of themaster circadian clock in mammals. Now we need to under-stand how multiple single-cell circadian oscillators withinthe SCN synchronize to each other and the environmen-tal light schedule to create an integrated tissue pacemakerwith coherent molecular and electrical rhythmicity

William SchwartzDepartment of NeurologyUniversity of Massachusetts Medical [email protected]

MS57

Cyton Theory: A Framework for Evaluating theCellular Calculus of Signal Integration

How receptor-mediated signals are integrated simultane-ously by lymphocytes to control rates of both growth anddeath is a complex problem. We are developing a model ofthe lymphocyte built on an internal mechanical unit calledthe cyton and show how it can explain and resolve signalintegration problems using a cellular calculus. The devel-opment of a numerical solver allows the interplay betweenproliferation and survival to be extracted from CFSE andBrDU incorporation data.

Marian TurnerThe alter and Eliza Hall Institute of Medical [email protected]

Carel van GendBioinformatics and Computational Biochemistry GroupEuropean Media [email protected]

Philip D. HodgkinNHMRC Principal Research FellowWalter and Eliza Hall Institute for Medical [email protected]

Edwin HawkinsThe Walter and Eliza Hall Institute of Medical [email protected]

98 LS06 Abstracts

MS57

The Impact of Affinity on Proliferation and Deathin the Immune Response

High affinity B-lymphocytes are critical for protection fromextracellular pathogens, such as bacteria and parasites. Tounderstand the basis for positive selection of these cells, wehave investigated transgenic mice expressing B cell recep-tors of varying affinity. Proliferation and death rates areestimated through a model-based analysis of time-series la-beling data (e.g., BrdU and Casp). These methods haveenabled us to elucidate how B cell fate is governed by itsability to bind antigen.

Ashraf KhalilDepartment of Laboratory MedicineYale University School of [email protected]

Uri Hershberg, Mark ShlomchikSection of Immunobiology, Department of LaboratoryMedicineYale University School of [email protected], [email protected]

Shannon M. AndersonSection of ImmunobiologyYale University School of [email protected]

Ann M. HabermanDepartment of Laboratory MedicineYale University School of [email protected]

Steven H. KleinsteinDepartement of Computer SciencePrinceton [email protected]

Yoram LouzounDepartment of mathematicsBar Ilan [email protected]

MS57

Elucidating Lymphocyte Development Using BrdULabeling

Immune responses involve many cell types, including B, Tand NK lymphocytes expressing a diversity of receptors forforeign antigens and self-molecules. The dynamics of im-mune cell repertoires, in particular their development, arehighly complex and non-linear. Understanding the popu-lation dynamics which underlie lymphocyte developmentis essential for elucidating the causes of various immunedysfunctions and cancers. The results of our studies com-bining combine modeling with BrdU data to address thisissue will be reported.

Ramit Mehr, Gitit ShahafFaculty of Life SciencesBar-Ilan [email protected], [email protected]

MS57

Quantifying Cell Turnover Using CFSE Data

The CFSE dilution assay is used to estimate the param-eters determining cell division and death in vitro/in vivo.For homogeneous cell populations, we consider the “Smith-Martin” model of cell turnover and analyze different tech-niques for estimating its parameters. The CFSE data aloneallows to estimate only the duration of the division phase,and in some cases the average division time can be deter-mined using Gett-Hodgkin method. Additional measure-ments are required to estimate all model parameters.

Sergei S. PilyuginDepartment of MathematicsUniversity of [email protected]

Vitaly V. GanusovTheoretical BiologyUtrecht [email protected]

Kaja Murali-KrishnaDepartment of ImmunologyUniversity of [email protected]

Rafi AhmedMicrobiology and ImmunologyEmory [email protected]

Rustom AntiaDepartment of BiologyEmory [email protected]

Rob De BoerDivision of Theoretical BiologyUtrecht [email protected]

MS58

Optimum Scheduling of Countermeasures

The use of mathematical models to automatically gener-ate optimal circadian adjustment schedules (CAS) includescomputational challenges. CAS are necessary for individ-uals working night shifts or traveling rapidly across timezones. CAS are used by NASA to help shuttle crew adaptto shifts in the sleep wake cycle. An iterative techniquedeveloped to design CAS will be presented and comparedto other methods, including model based predictive controland the calculus of variation.

Dennis Dean IIDivision of Sleep MedicineBrigham and Women’s [email protected]

Elizabeth B. KlermanBrigam and Women’s HospitalHarvard Medical Schoolebklerman@rics. bwh. harvard. edu

Daniel B. Forger IIIUniversity of [email protected]

LS06 Abstracts 99

MS58

The Use of Biomathematical Models Within Oper-ational Fatigue Risk Management Systems

Biomathematical models of work-related fatigue are be-coming widely used in industrial, emergency response, andmilitary operations. The inputs available for modelingvary in these different settings, as does the information re-quired by managers and commanders for decision-making.In addition, biomathematical models are being rapidly in-tegrated into broader systems of operational risk manage-ment. The practical components, considerations and com-plexities of different fatigue risk management systems willbe detailed.

Adam FletcherDepartment of Behavioral BiologyWalter Reed Army Institute of [email protected]

Katie J. KandelaarsCentre for Sleep Research, The University of [email protected]

MS58

Applications of a Fatigue Model for Predictingand Managing the Consequences of Fatigue in theTransportation Industry


Steve HurshIstitutes for Behavior Resources andScience Applications International [email protected]

MS58

Identifying Two-process Performance Models usingLimited Data


Peter ThompsonSystems Technology, [email protected]@systemstech.com

MS59

Stocastic Modeling of Experiments on Virus-stimulated Interferon Beta Induction in Single Hu-man Dendritic Cells


Jay JayaprakashDept. of PhysicsOhio State [email protected]

MS59

Microsimulation Modeling of Spatial Reorganiza-tion in Immunity


Tom KeplerDept of Biostats and Bioinf

Duke [email protected]

MS59

Modeling Immunity in the Lung to Bacterial andViral Pathogens


Simeone MarinoDept of Micro/ImmunoUniversity of [email protected]

Denise E. KirschnerUniv of Michigan Med SchoolDept of Micro/[email protected]

MS59

: Parameter Identifiability and Statistical InverseProblems in


Hulin WuUniversity of RochesterDepartment of Biostatistics and Computational [email protected]

MS60

Models for Directed Cell Movement in Fibre Net-works

Mesenchymal motion is a form of cellular movement thatoccurs in three-dimensions through tissues formed from fi-bre networks, for example the invasion of tumor metas-tases through collagen networks. The movement of cells isguided by the directionality of the network and in addition,the network is degraded by proteases. I derive mathemat-ical models for mesenchymal motion in a timely varyingnetwork tissue. The models are based on transport equa-tions and their drift-diffusion limits. It turns out that themean drift velocity is given by the mean orientation of thetissue and the diffusion tensor is given by the variance-covariance matrix of the tissue orientations. I will discussrelations to existing models and future applications.


MS60

In Silico Mathematical Model of the Atherogenesis,and its Stability Analyzes

We construct a mathematical model of the early forma-tion of an atherosclerotic lesion based on a simplificationof Russell Ross paradigm. Study centres on the interplaybetween chemical and cellular species we employ a modelof chemotaxis first given by E. F. Keller and Lee Segel andpresent our model as a coupled system of non-linear reac-tion diffusion equations. We perform numerical simulationsdemonstrating that our model captures certain observedfeatures of CVD.

Jay R. Walton

100 LS06 Abstracts

Department of MathematicsTexas A&[email protected]

Laura RitterTexas A & M [email protected]

Akif IbragimovDepartment of Mathematics and Statistics.Texas Tech [email protected]

Catherine McNealDepartment of Internal Medicine, Division of CardiologyScott & White, Temple, TX 76508, [email protected]

MS60

Chemotaxis Models and their Application to An-giogenesis

In the current talk the author will present some recent workon chemotaxis models and their application to angiogene-sis, and possibly morphogenesis.

Brian SleemanLeeds [email protected]

MS60

Modeling the Role of Environmental Cues duringAngiogenesis

Angiogenesis is the growth of new capillaries and bloodvessels from the existing vascular network. It is importantfor wound healing and is a means by which tumors becomevascularized. During angiogenesis endothelial cells prolif-erate and migrate to form new capillaries, a process that isorchestrated by environmental cues such a growth factors.Approaches for modeling the role of environmental cuesduring angiogenesis will presented, along with numericalmethods that preserve fundamental features (eg. mass) ofthe biological system.

Howard LevineIowa State [email protected]

Michael SmileyIowa State UniversityDepartment of [email protected]

MS60

Traveling Wave Phenomena for System ModelingHypertrophy and Hyperplasia in Soft Tissue

The growth of soft tissue in vivo often involves a com-plex interplay between various biochemical, genetic andmechanical processes. An important example of this inter-play is provided by growth and remodeling of the smoothmuscle cells (SMCs) within the medial layer of a large di-ameter human artery. Growth of SMCs is accomplishedvia two different processes: growth in size of individualcells (hypertrophy) and growth in the number of cells (hy-perplasia). Through genetic expression, SMCs enter into

distinct phases to accomplish hypertrophy and hyperplasiain which they exhibit differing mechanical (stress/strain)and transport (diffusion) processes. We describe a model-ing frame for capturing these effects and discuss analyticaland simulation results for an example model.

Jay R. WaltonDepartment of MathematicsTexas A&[email protected]

Akif IbragimovDepartment of Mathematics and Statistics.Texas Tech [email protected]

PP1

Transmembrane Protein Structure DeterminationUsing Solid State NMR

Nuclear Magnetic Resonance (NMR) is a technique for thestudy of molecular structures. Solid state NMR (ssNMR)uses orientational constraints to build an atomic model ofthe molecule, and has been successful in determining thestructures of membrane proteins such as ion channels. Wediscuss mathematical problems that arise when building amodel with ssNMR data. As an illustration, we build amodel of the M2 transmembrane protein that is a protonchannel in the Influenza A Virus.

Richard BertramDepartment of MathematicsFlorida State [email protected]

Jack QuineDepartment of Mathematics, Florida State [email protected]

Srisairam AchuthanDept. of Mathematics, Florida State [email protected]

Tom AsburyInstitute of Molecular Biology (IMB),Florida State [email protected]

Jun HuNIDDK, [email protected]

Tim CrossDept. of Chemistry & NHMFLFlorida State [email protected]

PP1

Compound Selection in Toxicological Studies UsingPrincipal Component Analysis.

Several basic schemes and methods using simple statisticsand Principal component analysis are used in compound se-lection for toxicological studies. To illustrate the method, 5biophysical properties are used for 71 compounds relevantfor hydrocarbon disposition and toxicity. A comparison be-tween (1) a sample using the simple statistics and assess-ment by principal component analysis, and (2) sampling

LS06 Abstracts 101

based on uniformity in the space of the first few principalcomponents is examined.

Charles Smith, Gyoungjin Ahn, Jim Riviere

Biomathematics(Dept. of Statistics)N.C. State [email protected], [email protected],jim [email protected]

PP1

Bacteria-Phage Co-Evolution As a Cause of Bacte-rial Diversity

Parasites are believed to play a significant role in host di-versification, and there is an increasing body of experi-mental evidence supporting this hypothesis. In particular,experimental studies of bacterial evolution in spatially ho-mogeneous environments have shown that the introductionof a bacterial parasite (phage) into the system significantlyincreases bacterial diversity. We use systems of non-localPDEs describing bacteria-phage co-evolution in order toidentify ecological mechanisms that could be responsiblefor this increase in diversity.

Sinan S. ArkinDepartment of MathematicsImperial College [email protected]

Ivana GudeljDepartment of Mathematical SciencesUniversity of [email protected]

Robert BeardmoreDepartment of MathematicsImperial College [email protected]

PP1

Pipath: An Algorithm For Generating α-HelicalAtomic Structures From Solid-State Nmr Data

Solid-state NMR PISEMA experiments generate orienta-tion constraints which can be used to determine a mem-brane protein’s atomic structure. We present a new al-gorithm, PIPATH, that finds the most α-helical structurein agreement with the PISEMA data. PIPATH uses tech-niques from graph theory to find an optimal assignmentand structure. The structure generated is typically quiteclose to the target structure and is a useful initial modelfor subsequent refinement



Thomas M. AsburyInstitute of Molecular BiophysicsFlorida State [email protected]

micheal Chapman

Dept. of Chemistry and BiochemiNIDDK, Nat. Inst. ofHealthBethesda [email protected]




PP1

Pipath: An Optimized Algorithm for GeneratingAlpha-Helical Structures from Pisema Data

Solid-state NMR PISEMA experiments generate orienta-tion constraints which can be used to dervice a membraneprotein’s atomic structure. We present here a new algo-rithm PIPATH that finds the most α-helical structure inagreement with the PISEMA data. PIPATH uses tech-niques from graph theory to find an optimal assignmentand structure. The structure generated is typically quiteclose to the target structure and is a useful initial modelfor subsequent refinement.




Tom Asbury

Institute of Molecular Biology (IMB),Florida State [email protected]



PP1

Computational Study of Spatial Localization Ef-fects on Signaling Cascades Dynamics

Transport phenomena and protein localization details areoften left aside in the design of quantitative models of cellu-lar signaling pathways. However, there is increasing exper-imental evidence showing that complex intracellular traffic

102 LS06 Abstracts

and differential spatial localization of members of a sig-naling cascade occur in response to many signals. Modelsneglecting these processes could miss significant featuresand lead to an incomplete understanding of the live sys-tem. In this study we used computer models to analyzehow spatial localization could affect the behavior in Sac-charomyces cerevisiae signaling pathways, with special em-phasis put on the effects on stimuli response’s dynamics.The models show that spatial localization and transportrates could play a determinant role controlling signalingresponse profiles.

Marcelo BeharUniversity of North [email protected]

PP1

Extravascular Burden of Carbon Monoxide (CO)During CO Exposure and Washout

The extent of extravascular uptake of CO in CO poison-ing has been debated. We developed a model of CO uptakeand distribution which includes diffusion of CO from bloodinto tissues and binding of CO to myoglobin. After vali-dation against data from both short and long-term humanCO exposures, additional experimental studies were simu-lated and extravascular distributions of CO predicted. Ex-travascular CO levels can change independently of bloodcarboxyhemoglobin level, and can transiently rise duringoxygen therapy.

Eugene Bruce, Kinnera Erupaka, Margaret BruceUniversity of [email protected], [email protected], [email protected]

PP1

The High-Throughput Development of High Affin-ity Nucleic Acid Molecules for Targets: ComplexSelex: A Mathematical Model and Computer Sim-ulation Study

SELEX (Systematic Evolution of Ligands by EXponential)is an experimental protocol to enrich target-binding ligandsfrom a highly complex nucleic acid library by iterative ex-traction and amplification of target-bound ligands. In thistalk, we present mathematical model and computer algo-rithm for simulating SELEX experiments against complextarget mixtures (the complex SELEX). We also presentsimulation results such as the discovery of optimal exper-imental conditions under which the target-binding ligandsare developed in high efficiency.

Chi-Kan ChenApplied Math DepartmentNational Chung-Hsing University, [email protected]

PP1

Prediction of Polyadenylation Sites of Mrna UsingSupport Vector Machine

Messenger RNA polyadenylation is important in cellularprocesses, such as mRNA stability. Many human andmouse genes have multiple polyadenylation sites (poly(A)sites) that lead to different functional transcripts. Biasedalternative polyadenylation in human tissue suggests thatthe coordinates of similar poly(A) sites can be regulated.In this poster, the Support Vector Machine is used to pre-dict the poly(A) sites based on the gene sequence. Our

objective is to characterize the alternative polyadenylationby mathematical modeling.

Bin TianDepartment of BiochemistryUniversity of Medicine & Dentistry of New [email protected]

Robert MiuraDepartment of Mathematical SciencesNew Jersey Institute of [email protected]

Yiming ChengNew Jersey Institute of [email protected]

PP1

A System Equivalence Related To Dulac’s Exten-sion of Bendixson’s Negative Theorem For PlanarDynamical Systems

Bendixson’s Theorem [1] is useful in proving non-existenceof periodic orbits for planar systems

dx

dt= F (x, y),

dy

dt= G(x, y) (1)

in simply connected domain D, where F,G are continu-ously differentiable. From the work of Dulac [2] one sus-pects that system (1) has periodic solutions if and only ifthe more general system

dx

dτ= B(x, y)F (x, y),

dy

dτ= B(x, y)G(x, y) (2)

does, which makes subcase (1) more tractable, when suit-able non-zero B(x, y) which are can be found. Thus,Bendixson’s Theorem can be applied to system (2), whereotherwise it is unfruitful in establishing non-existence ofperiodic solutions for system (1). The object of this noteis to give a simple proof justifying this Dulac-related pos-tulate of the equivalence of systems (1) and (2).

Charlie H. CookeOld Dominion UniversityDepartment of [email protected]

PP1

Mathematical Modelling of Take-All Decline inWinter Wheat

Take-all disease of wheat is caused by the soil-borne fun-gus Gaeumannomyces graminis var. tritici (Ggt), whichinfects the roots, crown, and basal stem of plants. Thehighest risk of take-all occurs when wheat is planted inconsecutive years. Disease severity and yield loss can besubstantial in second, third, and fourth wheat crops, withthe worst take-all usually occurring in the third consecu-tive crop. Take-all becomes less severe, and yields usuallyincrease, with the fifth or sixth successive wheat crop. Itis postulated that this occurs because of a natural increasein soil microorganisms antagonistic to the pathogen–a phe-nomenon known as ”take-all decline,” which persists onlyso long as wheat is grown continuously. Using mathemati-cal modelling we test hypotheses about the mode of actionof the antagonist microorganisms.

Nik J. Cunniffe

LS06 Abstracts 103

Department of Plant SciencesUniversity of [email protected]

PP1

Modeling Plasma Membrane Recruitment of Cy-tosolic Signaling Proteins

We visualize the stimulated translocation of cytosolic sig-naling proteins to the plasma membrane in live B lym-phocytes with multicolor confocal fluorescence microscopy.We use previously developed image processing algorithmsto systematically quantify the time course of recruitmentand the spatial colocalization of signaling proteins withcrosslinked receptor. We describe these events with areaction-diffusion model and estimate relevant kinetic pa-rameters for the translocation and the spatially localizedinteraction between signaling proteins and crosslinked re-ceptor complexes.

Raibatak DasUniversity of British ColumbiaDepartment of [email protected]

Daniel CoombsUniversity of British [email protected]

PP1

A Secondary Mechanism for Cardiac ExcitationPropagation

It is well known that cardiac action potential propagationis possible due to intracellular coupling by gap junctionchannels. However, recent studies involving gap junctiondeficient myocytes illustrate a complicated relationship be-tween propagation velocity and the degree of gap junctionalcoupling. This suggests that there might be a secondarymechanism to ensure propagation success. Here, we ex-plore a mechanism in which propagation is supported vianegative electric potentials in the narrow junctional cleftspaces between neighboring cells.

Elizabeth DomanUniversity of [email protected]

PP1

Rapid Evolution and Predator-Prey Dynamicswith Variable Costs of Defense

Predation may be a selective pressure that drives adap-tation. We investigate the effects of genetic variability inpredator search efficiency and anti-predator defense on thestability of a predator-prey system. In particular, we ex-amine the impact of varied versus fixed costs of defenseon population dynamics. We assume that the trade-off forinvestment in defense is a decrease in fecundity and that,at low prey density, defense is without cost.


Rebecca DoreDepartment of Ecology and Evolutionary Biology

Cornell [email protected]

Laura JonesCornell UniversityDepartment of Ecology and Evolutionary [email protected]

PP1

The Combined Effect of Synaptic and Cellular Res-onance

We derive a mathematical theory to explain the subthresh-old behavior of a resonant cell when it is stimulated bya presynaptic cell via a resonant synapse. We demon-strate how a cell combines the information contained inthe frequency dependant synaptic response with its ownfrequency dependant behavior. Our results show that themaximal response in the postsynaptic cell occurs at a fre-quency located between the preferred frequencies of thesynapse and cell. We show how one can tune the locationof the maximal response by changing the steepness of thesynaptic response - frequency profile.



Jonathan DroverNew Jersey Institute of [email protected]

Vahid TohidiRutgers - NewarkDept of Biological [email protected]

PP1

Modeling Immunological Synapse Formation andRepolarization

T cells form an immunological synapse (IS) with antigenpresenting cells (APC) bearing appropriate antigenic stim-uli. Experiments have shown that the IS can repolarizeto another APC having a higher antigenic load. We willpresent FRAP experiments and extract the relevant bio-physical parameters governing important processes of re-ceptor diffusion and binding. Mechanisms of IS formationand repolarization are discussed in the context of these pa-rameter estimates.

Daniel Coombs, Omer DushekUniversity of British [email protected], [email protected]

PP1

A Diffusive Model of Ampa Receptor Trafficking inthe Postsynaptic Membrane

AMPA receptor diffusion in the postsynaptic membrane isan essential mechanism for maintaining steady-state con-centrations and affecting changes in AMPA receptor num-ber during LTP/LTD. We propose a model of AMPA re-

104 LS06 Abstracts

ceptor trafficking that includes diffusion. We find that dif-fusion is critical in maintaining constituitive receptor recy-cling and a characteristic steady-state concentration pro-file. Our model provides the rate of relaxation to newsteady-states set by the induction of LTP/LTD, whichcould be used for testing the model’s validity.

Berton A. Earnshaw, Paul BressloffUniversity of [email protected], [email protected]

PP1

Modeling and Simulation of Circadian Rhythm ofCyanobacteria by Phosphorylation of the Proteins

We are interested in the mechanism of circadian rhythmof Cyanobacteria. We make a model by use of phosphory-lation of Kai C, which is surpressed or accelerated by KaiA and Kai B. By use of it, we investigate some importantproperties of it theoretically.

Isamu OhnishiHiroshima Universityisamu [email protected]

Kazumi Ebisu, Tatsuo ShibataDept. of Math. and Life Sci.,Hiroshima [email protected],[email protected]

PP1

The Role of Gap Junctions in a Neural Field Model

Recent research has shown a high density of gap junctionsin areas of the brain that experience epileptic events. Gapjunctions allow direct electrical connections between neu-rons and cause a diffusive-type effect on neuronal voltagebetween surrounding cells. We extend an Amari-type neu-ral field model by including a diffusion-like term to modelgap junctions and investigate how this changes the dynam-ics of spatially localised solutions. Numerical work showsfamilies of solutions are destroyed as the strength of theterm modelling gap junctions increases. By placing restric-tive assumptions upon the firing rate function, analyticalsolutions are explored.

Amanda J. ElvinMassey [email protected]

PP1

Ubm at Murray State University: Biomaps

The poster will provide insight into the format of the Bi-ology and Mathematics of Population Studies (BioMaPS)program started in January 2006. The mathematics andbiology students work in teams with all involved in labora-tory experience and mathematical modeling studies. Re-search questions, schedule of the program, successes andchallenges will be addressed.

K. Renee Fister, Maeve L. McCarthy, Nicole Gerlanc,Chris Mecklin, Terry Derting, Howard WhitemanMurray State [email protected],[email protected],[email protected],[email protected],

[email protected],[email protected]

PP1

Mathematical Improbability of Using Animals AsCams for Toxicology and Medical Research

Because of differences in gene regulation, gene networksand molecular mechanisms that have been revealed by evo-lutionary biology and molecular biology we now under-stand why even two very similar complex biological systemsmay respond differently to the same stimuli, and hence whyone such complex system (for example, inbred strains of ro-dents) cannot reliably predict response for a different com-plex system (for example, humans). Current biomedicalresearch is studying disease and drug response at the levelwhere known differences between complex systems becomemanifest, hence using nonhuman animals as causal analog-ical models for human disease and drug testing is a scien-tifically invalid paradigm. This has profound implicationsfor using animals in toxicology testing and as models forhuman disease.

Ray GreekAmericans For Medical [email protected]

Niall ShanksWichita State [email protected]

PP1

Household Epidemiological Models With ClusteredResistant Individuals

The spatial structure of a population can have profoundeffects on the spread of epidemics. We are studying mod-els of populations partitioned into households, where infec-tion attempts occur both within and between households.Fixed spatially clustered resistant individuals are intro-duced into the population, which may actually increase therate of spread of an epidemic, although this may then becounteracted by clustering of infectious individuals withinhouseholds as well, depending on their mobility.

Amanda Criner, David E. HiebelerDept of Mathematics and StatisticsUniversity of Maineamanda [email protected],[email protected]

PP1

Multi-Host and Multi-Patch Models of ZoonoticDiseases


Robert K. McCormackDepartment of mathematics and StatisticsTexas Tech [email protected]

PP1

Predator-Prey Equations with Prey Taxis: Discon-tinuous Travelling Waves

Diffusion processes have been widely used to incorporatespatial effects into predator–prey models. However, obser-

LS06 Abstracts 105

vations report that predators tend to move towards prey.Here we consider prey taxis as a primary spatial processes.Without diffusion process we show analytically that dis-continuous wave solutions occur due to the singular bar-rier. Introduced diffusion process is shown to make thesediscontinuous solutions smoothly. Fractional step meth-ods are used to demonstrate the nature of discontinuoustravelling wave solutions.



Jungmin Leeuniversity of [email protected]

PP1

Kinetic Analysis of the Mechanism of the Cell Di-vision Cycle in Caulobacter Crescentus

Progress in understanding cell cycle regulation in bacteriahas lagged behind eukaryotes. Recently, however, the dis-covery of two master regulator proteins, CtrA and GcrAin Caulobacter crescentus, allows us to propose a realis-tic molecular mechanism for cell cycle control in this bac-terium. The mechanism is cast in a quantitative modelrevealing the temporal dynamics of the genes and proteinsregulating the cell cycle in Caulobacter wild type cells aswell as in several mutants.


Shenghua LiDepartment of Biological SciencesVirginia Polytechnic Institute and State [email protected]

Bruno SobralVirginia Bioinformatics InstituteVirginia Polytechnic Institute and State [email protected]

Paul BrazhnikVirginia Polytechnic Institute and State [email protected]

PP1

A Realistic Mathematical Model of the Canine Pul-monary Veins Sleeves

Pulmonary veins (PV) are the great vessels connected be-tween lung and left atrium and transport oxygenated bloodto the heart. There are 4 pulmonary veins in human be-ings. At the intersection between pulmonary veins andleft atrium, there is a short segment covered with stri-ated cardiac muscle and called pulmonary vein sleeve. Dueto the complex intermingled muscle bundles, pulmonaryvein sleeves display characteristic electrical behavior. Thecellular electrophysiological properties of pulmonary vein

sleeves were reported few decades ago. However, the clini-cal significance of pulmonary vein was not found until re-cently. In patients with atrial fibrillation, it was foundthat ectopic foci existed in the pulmonary veins. There-fore, electrophysiological studies on pulmonary veins havedrawn a lot of attention recently. For example, in the ex-periments of dogs and rabbits, besides the fast responsetype of action potential, various pacemaker-like automatic-ities and triggered activities, e.g., early afterdepolariza-tions (EAD), delayed afterdepolarizations (DAD), havebeen demonstrated in the pulmonary veins sleeves underphysiological or pathophysiological situations (see [Hociniet al., 2002], [Ehrlich et al., 2003], [Hojo et al., 2003],[Wang et al., 2003, 2005], [Po et al., 2005], [Chen et al.,2000, 2001, 2002-a, 2002-b, 2002-c, 2003-a, 2003-b, 2003-c, 2004-a, 2004-b]). In this study, we have developed amathematical model which fits well the experiments forthe canine PV. Using this model, we have successfully re-produced the experimentally observed frequency responses,ischemia/hyperkalemia phenomena, pacemaker-like auto-maticities, and triggered activities of PV sleeves. Also, asin the experimental results of [Po et al., 2005], our modelAPD restitution curve, an important index for the breakupof reentry, was very flat, which supports the hypothesisthat reentrant PV tachycardia is a potential mechanism ininitiating atrial fibrillation.

Juan-Ming Yuan, Chu-Pin LoDepartment of Applied MathematicsProvidence [email protected], [email protected]

Tzyy-Leng HorngDepartment of Applied Mathematics, Feng ChiaUniversity,Taichung, [email protected]

Hsiang-Ning LukDepartment of Anesthesiology, Taichung Veterans GeneralHospital, Taichung, [email protected]

Tsu-Juey WuCardiovascular Center, Taichung Veterans GeneralHospital,Taichung, [email protected]

Hui-Chun TienDepartment of Applied Mathematics, ProvidenceUniversity,Taichung, [email protected]

PP1

Maximizing Cell Free Ethanol Production

Ethanol production by yeast is limited by the toxic effectof ethanol on the yeast and other factors. Removing themicroorganisms from the ethanol production process (cellfree) has a number of advantages including greater processflexibility, more freedom to manipulate enzymes, and theability to easily optimize the production process by alteringenzyme levels. Models of the twelve enzymatic reactionsinvolved in the production of ethanol from glucose indicatethe potential to increase ethanol production.

Eric Marland, Andrew Madison

106 LS06 Abstracts

Appalachian State [email protected], [email protected]

Eric AllainDepartment of ChemistryAppalachian State [email protected]

Diana Dardugno, Rene SalinasAppalachian State [email protected], [email protected]

PP1

Multistability in a Two-Cell Inhibitory Networkwith Synaptic Facilitation and T-Currents

We explore the dynamics of two type-I neurons with T-like currents coupled by reciprocal inhibition.This net-work exhibits low-frequency tonic firing and chaotic fir-ing states, and transitions to antiphase bursting at suf-ficient coupling strength, due to deinactivation of the T-currents. We show that synaptic facilitation promotesbistability between bursting and tonic activity states, andmay regularize chaotic firing. In addition, we analyze themulti-stability between distinct bursting states using a one-dimensional Poincare map.



Victor MatveevDept. of Mathematical SciencesNew Jersey Institute of [email protected]

PP1

Stochastic Modeling of Periodic Mass AntibioticTreatments for Blinding Trachoma

We develop a stochastic mathematical model to simu-late ocular chlamydial infection in communities undergo-ing biannual mass antibiotic treatments. Model param-eters were fit using maximum likelihood estimation anddata collected by our group from approximately 5000 chil-dren in Ethiopia. Simulations show infection is eliminatedin more villages with each subsequent treatment. However,in villages that still harbor infection, it returns to the same,quasi-stationary distribution. Overall, local elimination isfeasible; subsequent Ethiopian data confirm these results.

Kathryn J. MaxeyF.I. Proctor FoundationUniversity of California San [email protected]

Dr. Tom LietmanF.I. Proctor FoundationUniversity of California, San [email protected]

PP1

Diffusion of High Energy Metabolites in MdckCells and Myocytes

Effective diffusion of high energy metabolites in cells is dif-ficult to quantify. We describe mathematical models thatuse data for various experimental conditions (e.g., control,stress) to assess diffusion barriers and cell function require-ments. We test the hypothesis that local changes modulatefunction without significant changes in global cytosolic con-centrations of ATP, ADP and inorganic phosphate. Themodel is described by a diffusion equation in two space di-mensions and time; namely, C′ = �·D�C+S, where C, Dand S are vectors of concentrations, diffusion coefficients,and sources and sinks, respectively.

Raymond MejiaLaboratory of Cardiac EnergeticsNHLBI, [email protected]

Ronald LynchDepartments of Physiology and PharmacologyUniversity of [email protected]

PP1

Analysis of a Simple Model of Circadian Rhythmof Arabidopsis Thaliana

We are basically interested in circadian rhythm of Ara-bidopsis thaliana. We consider about a simple model equa-tion of two main components of mRNA’s and its productiveproteins. Under some simple conditions, it has a periodicsolution. We investigate properties of the system by use ofthe numerical simulation and stability analysis.

Isamu OhnishiHiroshima Universityisamu [email protected]

Kazumi EbisuDept. of Math. and Life Sci.,Hiroshima [email protected]

PP1

Perspectives on the Drift-Paradox Problem

Plankton are often considered passive tracers, but indi-vidual plankton behavior may dominate at smaller scales.Using a hydrodynamic model to create various flows inan idealized channel with and without rooted plants, wemodel plankton behavior with an individual-based modeland explore the extent to which vertical migration can af-fect biological residence time in the channel. We gain ad-ditional insight into simulation results by studying a two-dimensional advection-diffusion equation representing thesystem.


Virginia B. PasourCornell University, Center for Applied [email protected]

LS06 Abstracts 107

Todd CowenCornell University, Civil and Environmental [email protected]

PP1

Random Networks Applied to Axon Growth

Many biological situations involve nanoscale fibers havingdirections and shapes that appear random. We proposeand study models at the microscale (fiber growth) and atthe macroscale (network scale) for the probability distri-bution of position and direction for curves in space. Themodel is applied in two space dimensions, where the di-rection variable is an angle. Simulations are performedto apply the theory to axonal growth, and the results arecompared to data.

Donald A. DrewRensselaer Polytech InstituteDept of Mathematical [email protected]

Yanthe E. PearsonRensselaer Polytechnic [email protected]

PP1

A Dynamic Mechanism for Episodic Bursting

Episodic bursting is a behavior found in pancreatic beta-cells as well as in hypothalamic GnRH neurons. One mech-anism that has been proposed for beta-cells is based uponoscillations in glycolysis. Here we describe an alterna-tive method for episodic bursting based on the interactionof two activity-dependant slow variables. The dynamicsof this episodic bursting mechanism can be understoodthough an analysis of the fast subsystem, and its modu-lation by one or the other slow variable.


Joseph A. RhoadsFlorida State UniversityDepartment of [email protected]

PP1

Confined Animal Feeding Operations As Amplifiersof Influenza

A pandemic could occur if a strain of influenza such as theH5N1 avian influenza virus evolves so that it is transmis-sible among humans. Domestic species such as poultry orswine could serve as local amplifiers for such a new strain ofinfluenza. This amplification could be particularly strongif the transmission among the birds or pigs is high becausethey have very close contacts with each other in confinedanimal feeding operations (CAFOs). CAFO-workers forma bridging population between the CAFO species and thegeneral population. In order to assess the magnitude ofthis amplification, we formulate and analyze a mathemat-ical model for the transmission dynamics of a novel in-fluenza virus with three sequentially linked populations:the CAFO species, the CAFO workers and the rest of thelocal population. We show that for a given percentage of

CAFO workers in the community, an influenza epidemic isamplified significantly when the infectivity of the virus islow, so that the basic reproduction number in humans isjust above 1.

Roberto A. SaenzUniversity of IowaDept of [email protected]

Herbert HethcoteUniversity of [email protected]

Greg GrayCenter for Emerging Infectious DiseasesUniversity of [email protected]

PP1

The Throughput of the Transitional 3 B Cell PoolAccounts for Losses Between Transitional and Ma-ture B Cells

Our study aimed to examine the hypothesis that the tran-sitional 3 (T3) peripheral B lymphocytes subset containscells undergoing negative selection derived from both theemerging and mature B cells pools. To address these issues,we used mathematical models of population dynamics, andfit it to existing in vivo BrdU labeling data. We suggestthat the throughput of the T3 B cells pool can account formost of the losses in B cells maturation.

David AllmanPathology and Laboratory Medicine, University [email protected]

Gitit Shahaf, Ramit MehrFaculty of Life SciencesBar-Ilan [email protected], [email protected]

Michael CancroPathology and Laboratory Medicine, University [email protected]

PP1

A Model for Auxin Response in Arabidopsis

Auxin is a ubiquitous plant hormone, involved duringnearly all growth stages and processes. Recently reportedresults have elucidated the intracellular interactions thatunderlie observed responses to auxin. We have developeda differential equation model for auxin response in leaf cellsof Arabidopsis thaliana. Simulation runs produce concen-tration profiles consistent with experimental results. Themodelled cells can be coupled by auxin transport terms toallow simulations of canalization in a field of cells.

Marc R. RousselUniversity of Lethbridge, CanadaDepartment of [email protected]

Martin J. SlingerlandUniversity of Lethbridge

108 LS06 Abstracts

[email protected]

PP1

Probability Density Approaches to Modeling Localand Global Intracellular Calcium Dynamics

Deterministic ODE models of intracellular calcium (Ca)dynamics traditionally neglect the stochastic gating of Cachannels and important aspects of local Ca signaling. Herewe present a novel probability density approach to model-ing Ca dynamics in cells that involves coupling ODEs forthe bulk cytosolic and ER [Ca] to advection-reaction equa-tions for the probability density of the [Ca] in cytosolic andlumenal domains associated with each channel and condi-tioned on channel state.

Blair Williams, Marco A. Huertas, Gregory D. SmithCollege of William and [email protected], [email protected], [email protected]

PP1

A Model for the Actin Polymer Brownian Ratchet

Actin forms the cytoskeleton polymer allowing cells tomaintain their shape and plays a role in motility. We ex-tend models for polymer growth and decay in response todiffusion of monomers in the cytoplasm. The model in-cludes the interaction of the cell membrane with the lead-ing edge of polymer growth, providing a model for theBrownian Ratchet. We also discuss the distribution of actinchain length consistent with the distribution of barbed andpointed ends.

Donald A. DrewRensselaer Polytech InstituteDept of Mathematical [email protected]

Csilla SzaboRensselaer Polytechnic [email protected]

PP1

Cancer Growth Model by Ecology with Mass Ad-vantage, Stability and Complete Deletion Condi-tions Using Mass Shape Information

This cancer growth model consists of the proliferation rateλ+ of cancer cells and with a weaker inhibition rate λ−

in ina cancer mass than λ−

out outside it by like immune. Thismeans mass advantage. λ+−λ−

in > 1 λ+−λ−out < 1 Results

(1)A higher λ+ gives more irregular mass shapes althoughλ+ can not be easily evaluated because of other nonlineareffects. (2)The situation means the existence of stabilitynot to make a small mass. (3)The conditions to initiate acancer mass and its complete deletion can be calculated.

Mitsuo TakaseLINFOPS [email protected]

PP1

How Deeply Memory Compression Can Be Con-cerned with the Knowledge Structure in GenesLike Hierarchical Neural Networks

In genes memory compression caused by the mixing of

near DNA sequences through unequal crossover, gene con-version, etc. and orthogonalization through translocationand duplication can exist and speed up evolution as inthe brain it is caused by Hebb rule and mutual inhibitionby inhibitory cells building hierarchical knowledge struc-tures with common characters. Here how wide range ofcomponents like not only gap genes, pair rule genes andsegment polarity genes in Drosophila but also alpha helix,beta sheet, domains, motifs and modules can be concernedwith memory compression is shown.

Mitsuo Takase, Michiko TakaseLINFOPS [email protected], [email protected]

PP1

A Spiny Branched Dendritic Tree and its Spatio-temporal Filtering Properties

The dendrites of many nerve cells are complex branchingstructures that receive and process thousands of synapticinputs from other neurons. Dendritic spines can be presentin large densities on the dendrites. They are equippedwith excitable channels and loci for receiving excitatorysynaptic input. Here we introduce a mathematical modelof a branched dendritic tree based upon a generalisation ofthe analytically tractable Spike-Diffuse-Spike model. Theactive membrane dynamics of spines are modelled by anintegrate-and-fire process. The spines are assumed to bediscretely distributed along a passive branched dendriticstructure. We obtain a quasi-analytical solution usingthe sum-over-paths approach formulated by Abbott et al.(Biol. Cybern., 1991, vol.66, pp. 49-60). The model sup-ports saltatory travelling wave propagation and wave scat-tering amongst branched dendritic trees. It is ideally suitedfor the study of spatio-temporal filtering properties andneural responses to different patterns of synaptic input.

Gabriel J. LordHeriot-Watt [email protected]

Stephen CoombesUniversity of [email protected]

Yulia TimofeevaThe University of [email protected]

PP1

Bursting Without a Slow Variable in a LactotrophModel.

We describe a model of the pituitary lactotroph. Low con-centration of dopamine activates an A-type K+ current.In the model this converts continuous spiking into a burst-ing pattern. Even though inactivation of this current isnecessary for bursting it is not a slow process.


Natalia ToporikovaDepartment of Mathematics, Florida State [email protected]

LS06 Abstracts 109

Joel Tabak, Marc FreemanDept of Biological SciencesFlorida State [email protected], [email protected]

PP1

Multiscale Modeling to Combat Colorectal Cancer

The Integrative Biology consortium brings together com-puter scientists, modelers and experimentalists to build avirtual tumour. We focus on colorectal cancer because ofits social impact and the biological information available.The model, a hybrid cellular automaton, integrates pro-cesses at the subcellular, cellular and tissue levels. Thismultiscale approach enables us to investigate interactionsbetween such processes, to combine single-level experimen-tal data, and to test the system’s overall response to dif-ferent treatments.http://www.integrativebiology.ox.ac.uk/


Helen ByrneUniversity of NottinghamCentre for Mathematical [email protected]

Philip K. MainiCentre for Mathematical BiologyUniversity of [email protected]


Oliver JensenApplied MathematicsUniversity of [email protected]

Carina EdwardsUniversity of OxfordMathematical [email protected]

Ingeborg Van LeeuwenUniversity of NottinghamCentre for Mathematical [email protected]

PP1

Mathematical Modeling of Cancer Progression:Understanding the Role of the RhoC Gtpase on-offSwitch in Aggressive Phenotypes of Breast Cancer

The most damaging change during cancer progression isthe growth of metastases. RhoC GTPase was found to becrucial in that process in different cancers, particularly, ina highly aggressive form of breast cancer. RhoC is a molec-ular switch cycling between inactive (GDP-bound) and ac-tive (GTP-bound) states, tightly regulated by several reg-ulatory proteins. We have developed a dual mathematical-experimental approach to understand this cycle and its

deregulation in cancer cells in comparison with normalones.

Alejandra C. Ventura

Int. Med.-Hematology/OncologyMedical School, University of [email protected]

PP1

Synchronization of Circadian Oscillators

Living beings adjust to the environment via synchro-nization of their biological clocks to external drives likethe light-dark cycle and food availability patterns. Ex-perimental entrainment patterns in activity recordings ofhouse mice under light- and food- restriction are analyzed.Generic nonlinear entrainment behavior like phase locking,phase slipping, or free running behavior are found in thisreal biological circadian system. A model of coupled Vander Pol oscillators gives insight into the interaction of light-and food- entrainable biological clocks in these mice.

Jon KlaasUniversity of Alaska FairbanksDept of [email protected]

Abel Bult-ItoUniversity of Alaska FairbanksDept of [email protected]

Renate A. WackerbauerUniversity of Alaska FairbanksDepartment of [email protected]

PP1

Graphical Causal Reasoning Tool for Systems Bi-ology: C-Map

Abstract available on-site at the conference. Supportedby NIH Cell Migration Consortium GM64346 (KJ) andGM073180 (TE, KJ, GW)

Gabriel WeinrebUniversity of North Carolina at Chapel [email protected]

PP1

Reciprocity Relations Between Stokes Flows of Vis-cous and Viscoelastic Fluids

Linear response theory of thermal fluctuations or drivenmotion of tracers provides a basis for exploring viscous,elastic and compressible properties of condensed matter.Applications range from atomic physics where the methodswere first developed, to recent applications in microrheol-ogy. The emphasis here is on hydrodynamics and defor-mations of incompressible viscoelastic materials for vari-ous geometries and driving conditions, as determined fromknown viscous behavior by straightforward prescriptions,called reciprocity relations. Linear response theory canbe formulated to yield an explicit correspondence in thegoverning equations of Stokes flow between a viscous fluidand any linear viscoelastic material, valid for an arbitraryprescribed source: of force, flow, displacement or stress;local or nonlocal; steady or oscillatory. Upon specification

110 LS06 Abstracts

of the geometry and source, non-inertial and inertial vis-cous Stokes solutions (known as Stokes singularities) trans-fer to exact solutions for linear viscoelastic fluids. Reci-procity relations inform elasticity-induced contrasts in flowor displacement fields for prescribed forces or stresses; con-versely, one may infer sources necessary to achieve identicalresponses in viscous and viscoelastic materials. Two spe-cial Stokes singularities form the basis of microrheologyexperiments and their interpretation: a prescribed veloc-ity on a translating sphere and a stationary point sourceof force. We revisit and amplify these examples as an il-lustration of the reciprocity relations, focusing on measur-able non-inertial and inertial features. Next, we illustratethe generality in source type and geometry of this corre-spondence principle by analyzing the linear response for anonlocal, planar source of unsteady stress.

Ke XuUniversity of North Carolina at Chapel [email protected]

PP1

Modeling Pattern Formation in Proteus MirabilisColonies

When inoculated on a hard medium, a colony of the bac-terium Proteus mirabilis can form concentric ring patternsof cell density. These patterns have been described as theresult of periodic colony expansion due to collective move-ment of swarmer cells differentiated from short-rod swim-mer cells. However, recent experiments show that swimmercells can stream inward towards the center of the colonyand suggest intercellular communication between cells. Wedevelop a new model incorporating chemotaxis of swim-mers, and we present preliminary results on modeling ra-dial spoke-like patterns.

Chuan XueUniversity of [email protected]

PP1

Dual feedback mechanisms for p53 response toDNA damage

Recent experiments indicate that p53 responds to DNAdamage by series of pulses of constant amplitude and pe-riod. The mechanism and function of these pulses are notyet fully understood. We explore the pulse-generating po-tentials of several dual-feedback schemes (containing posi-tive and negative feedback loops) and propose a mechanismwhereby p53 pulses might coordinate cell cycle arrest andapoptosis after DNA damages.


Paul BrazhnikVirginia Polytechnic Institute and State [email protected]

Tongli ZhangVirginia Polytechnic Institute & State [email protected]

PP1

Pet: Parameter Estimation Toolkit

PET provides computational biologists with a graphicaluser interface for performing simulations and estimatingparameters of mathematical models of reaction networksdescribing gene, protein and metabolic interactions. PETis designed 1) to manage the potentially complicated rela-tionships between a model and simulations of a large col-lection of experimental observations, 2) to assist the userin manual exploration of parameter space, and 3) to pro-vide support for automatic parameter estimation based onboth global and local optimization algorithms.


Jason ZwolakVirginia [email protected]

Tom PanningVirginia Polytechnic Institute and State [email protected]

Layne WatsonDepartments of Mathematics and Computer ScienceVirginia [email protected]

PP2

Modeling Aspects of Wound Closure: The Effectsof Tgf-β and Wound Geometry

Several aspects of dermal wound healing such as the role oftransforming growth factor beta (TGF-β) and the effects ofwound geometry are still not completely understood. Usinga diffusion equation and a linear parameter, we reproducesome of the known features of the temporal evolution of theconcentration of TGF-β and predict how the concentrationof TGF-β and the geometry of a wound influence the timerequired for healing.

Anthony Y. Aidoo, Kim WardEastern Connecticut State [email protected], [email protected]

Joseph MantheySaint Joseph [email protected]

PP2

Nonequilbrium Ising Bloch Transition in ForcedNonlocally Coupled Oscillators

We study phase and amplitude models for 2:1 resonant os-cillators with nonlocal coupling and show that Ising-Blochtransition is dimmed by a regime with drifting frontal os-cillators causing fluctuations of propagation direction. Weshow that strong nonvariational effects leading to patternformation impede the oscillators drifting and enforce tran-sition to a Bloch front

Dorjsuren Battogtokhtokyo [email protected]

LS06 Abstracts 111

PP2

How Do the Basic Reproduction Ratio (R0) andBasic Depression Ratio (D0) Determine the Dy-namics of a System with Many Host and ManyDirectly Transmitted Pathogen Strains?

For an individual host strain, the pathogen strain withmaximum R0 out-competes all others and survives alonewith the host at a point equilibrium. For an individualpathogen strain, the host strain with minimum D0 behavessimilarly. With many host and pathogen strains how dothese criteria interact and is multi-strain co-existence pos-sible? Furthermore, can stable cycles occur? We answerthese questions using a combination of algebraic and nu-merical studies.

Rachel E. BennettUniversity of [email protected]

Roger G. BowersThe University of [email protected]

PP2

The Evolution of Parasites in Spatially StructureHost Populations: An Approximate Analytical Ap-proach

We use approximation techniques and simulation to exam-ine the evolution of parasites in spatially structured pop-ulations. Trade-off shapes have important implications tothe evolutionary outcome and we demonstrate that there isan ES non-maximal dispersal rate. When parasite disper-sal and life-history evolves, we find that transmission andvirulence are maximised. We contrast the results of the ap-proximations and simulations and highlight the problemsthat small selection gradients in spatially explicit popula-tions may cause.

Mike BootsSheffeld [email protected]

PP2

Modeling Bacterial Populations Undergoing AcidStress

Recent outbreaks of acid resistant bacterial pathogens haveraised safety concerns about a wide variety of acidified foodproducts. A model was developed to aid in understandingacid sensitivity of bacterial cells within a bacterial cell cul-ture. Culture growth generating subpopulations of cellswith varying acid resistance was simulated using Matlabsoftware. Data from the model may be used to developmethods that ensure the safe production of a variety ofacid and acidified foods.

Fred BreidtUSDA/ARSNorth Carolina State [email protected]

PP2

Synchronization and Multistability: Predictionsfrom Phase Models

We consider a model for a network of hippocampal in-

terneurons based on the work of Wang and Buzsaki [J.Neurosci. 16:6402-6413, 1996]. We construct a phasemodel representation of the network, and show that thismodel can give reasonably accurate quantitative informa-tion, such as the size of basins of attraction and the maxi-mum heterogeneity permissible in the inherent frequenciesof the neurons before synchrony is lost. We show that pre-dictions of existence and stability of phase-locked solutionsfrom the two cell network carry over to N-cell networks,either exactly or in the limit of large N.

Hojjat BazazziBioengineeringUniversity of [email protected]

Jeff ChadwickApplied MathematicsUniversity of [email protected]

Sue Ann CampbellDepartment of Applied MathematicsUniversity of Waterloo, Waterloo Ontario, [email protected]

PP2

Using Integral Projection Models to Explore Evo-lution in Complex Environments: Soay Sheep As aCase Study

The selection pressures an organism experiences over itslifetime vary as a consequence of changes in its environ-ment (both biotic and abiotic) and its own physiology. In-corporating these complexities into models is necessary inorder to make accurate predictions about the life historydecisions an organism makes. Using the long term indi-vidually structured Soay Sheep dataset; we show how therecently developed integral projection model may be usedto develop such life history analyses.

Dylan ChildsSheffeld [email protected]

PP2

Phase-LikeTransition in Escaping Behaviors ofPrey Flock Induced by a Predator’s Attack

A prey flock escaping from a predator was investigatedby using molecular dynamics (MD) simulations in a two-dimensional model. A phase-like transition was observedat a critical attack angle in the state of the flock moving inresponse to predator’s attack. Contribution of the variablessuch as attack speed and angle of the predator was furtherdiscussed with regard to tactics for efficient prey capturein the prey-predator relationships.

Tae-Soo ChonDiv. of Biological SciencesPusan National University, Busan (Pusan), Republic [email protected]

Sang Hee LeeDepartment of Entomology and NematologyUniversity of Florida, Ft. [email protected]

112 LS06 Abstracts

PP2

Determining Environmental Conditions for theSuccessful in-Vitro Maturation of MammalianOocytes

Harvesting of immature oocytes (eggs) and successful mat-uration in the laboratory would be a significant break-through in the field of assisted reproduction. Success isbelieved to depend on the ability to mimic the nutritionalenvironment that pertains within the body in the ovarianfollicle surrounding the oocyte, which is difficult to deter-mine experimentally. We describe mathematical modellingusing experimental data that is aimed at increasing ourunderstanding of the in-vivo and in-vitro oocyte environ-ments.

Yvonne StokesSchool of Mathematical SciencesThe University of [email protected]

Michelle LaneDepartment of Obstetrics and GynaecologyThe University of [email protected]

Alys Clark, Stephen CoxSchool of Mathematical SciencesThe University of [email protected], [email protected]

Jeremy ThompsonDepartment of Obstetrics and GynaecologyThe University of [email protected]

PP2

Patterns on Growing Square Domains Via ModeInteractions

We consider reaction-diffusion systems on growing squaredomains with Neumann boundary conditions (NBC). Westudy transitions between two types of squares and tran-sitions between squares and stripes using mode interac-tions for bifurcation problems with D4+T 2 symmetry (hid-den symmetries) and the symmetry constraint imposed byNBC. We obtained surprising results: the transition fromsquares to stripes in NBC can go through time periodicstates, and there are differences between periodic bound-ary conditions and NBC problems.

Martin Golubitsky, Adela ComaniciUniversity of [email protected], [email protected]

PP2

Biocalculus: Interdisciplinary Course Developmentand Validation

Benedictine University now offers a two-semester calculussequence for majors in the biological sciences. A new text-book and lab manual for this course is currently being de-veloped by a team of mathematicians and biologists fromBenedictine University. We will discuss the content choicesand how this interdisciplinary team functions. We willalso present preliminary data indicating that the biocal-culus students demonstrate at least the same conceptualunderstanding and computational skills as the traditional

calculus students.

Timothy D. ComarBenedictine [email protected]

PP2

Mathematical Models of Glucose, Insulin and FreeFatty Acid Metabolism in Juveniles Having Irreg-ular Exercise Regimens

Hepatic glucose regulation has been notoriously difficultto study in vivo due to the liver’s role in hundreds of si-multaneous metabolic processes. A theoretical mathemat-ical model is proposed examining insulin secretion, insulinsensitivity, endogenous glucose, free fatty acids and aero-bic exercise in the early development of visceral adiposity.Employing deterministic, dynamic and stochastic elements,the model elucidates metabolic syndrome pathogenesis lon-gitudinally. Model results are validated using U.S. juvenileand adult obesity and diabetes prevalence results.

Charles H. DarbyNorth Carolina State [email protected]

Jim RiviereBiomathematics(Dept. of Statistics)N.C. State Universityjim [email protected]

Charles E. SmithNorth carolina state [email protected]

PP2

Net Reproductive Value and Graph Reductionwith Applications to Control of Invasive Species

Matrix models are widely used tool for demographic anal-ysis of age and stage structured biological populations.Dynamic properties of the model can be summarized bythe net reproductive value (R0). Here we introduce a newmethod to calculate and analyze R0 directly from the lifecycle graph. We show, with examples, how our method ofanalysis of the R0 can be used in the design of strategiesfor invasive species and conservation.

Tomas De-Camino-BeckUniversity of [email protected]


PP2

The Effect of Life-Stage Breakdown on Basins ofAttraction

A stage-structured model of two competing species hasbeen shown to exhibit multiple attractors for a varietyof parameter values. Previous work has been done oncomputing the basins of attraction using initial conditionswhere only the oldest life-stage of each species is present.Here we consider the impact on these basins of attraction ofsplitting the initial conditions between multiple life-stages,

LS06 Abstracts 113

while keeping the total population size fixed.

Jeff EdmundsUniversity of Mary [email protected]

PP2

Biomechanical Modelling of Colonic Crypt Fission

Colorectal cancer is initiated by unregulated cell division inthe epithelium of the small pits (crypts) that line the colon.The crypt then deforms and divides a number of timesleading to a polyp or adenoma. We examine the initiationof crypt fission using a biomechanical model incorporatingboth intercellular forces and the forces generated by cellattachment to and movement along the basal lamina.

Carina EdwardsUniversity of OxfordMathematical [email protected]


PP2

Do Albatrosses Really Perform Levy Flights WhenForaging?

We examine the hypothesis that wandering albatrosses(Diomedea exulans) undergo Levy flights when searchingfor food. Levy flights are random walks whose step lengthscome from probability distributions that have infinite vari-ance. Levy flights have no typical scale, and so have beeninterpreted as comprising an efficient foraging strategy. Were-analyse the original temporal flying/floating data thatwere used to infer Levy flights, and use state-space mod-els to examine recent spatio-temporal data from satellite-tracked birds.

Nick Watkins, Mervyn Freeman, Richard Phillips,Andrew M. EdwardsBritish Antarctic [email protected], [email protected], [email protected],[email protected]

PP2

A Hyperbolic Model for Animal Group Formationand Activity Patterns

The social interactions between organisms that formgroups are governed by three types of forces: attraction,repulsion and alignment. I will present a nonlocal hyper-bolic model that takes into consideration all these socialforces to study group formation. Linear analysis and nu-merical simulations are used to explore the behavior of themodel, and reveal a wide range of spatial patterns. Thesepatterns can be related to the daily activities of animalgroups, such as foraging and traveling.

Frithjof LutscherUniversity of [email protected]

Mark LewisUniversity of Alberta, Canada

[email protected]

Raluca EftimieUniversity of Alberta, Edmonton, [email protected]

Gerda de VriesUniversity of AlbertaDepartment of Mathematical & Statistical [email protected]

PP2

Towards a General Stability Theory of PopulationDynamical Models

We propose a generalized model for foodchains of arbitrarylength and foodwebs to study the stability properties of theequilibrium state where all species coexist. Sudden changesin the dynamics (bifurcations) can occur when parametersare varied. The main advantage of the generalized modelis that its stability can be analysed without specifying theinteraction functions between species. We discuss the im-pact of the specific shape of the functional response on thestability properties.

Wolfgang EbenhoehICBM, University of Oldenburg, [email protected]

Thilo GrossFachbreich PhysikUniversitat [email protected]

Ulrike FeudelUniversity of OldenburgICBM, Theoretical Physics/Complex [email protected]

PP2

Predicting Protein Production from Codon UsagePatterns: Merging Population Genetics & ProteinTranslation

I demonstrate how the pattern of codon usage within a genecan be used to predict protein production rates. Usinga population genetics model, I formalize the relationshipbetween the adaptation of a sequence to nonsense errors,its expression level, and its probability of fixation. I vali-date the approach using several hundred yeast genes. Mypredictions are probabilistic in nature and coincide withindependently measured values.

Michael A. GilchristUniversity of TennesseeDept. of Ecology & Evolutionary [email protected]

PP2

Effect of Spatial Inhomogeneities on the Tubu-loglomerular Feedback System

We use a simple mathematical model of rat thick ascend-ing limb (TAL) to investigate the effects of tubular non-constant transport rate of chloride and inner radius onTGF-mediated oscillations. Mathematical models have in-dicated that these regular oscillations arise from a bifurca-tion: if feedback loop gain is sufficiently large and if the

114 LS06 Abstracts

delay in TGF signal transmission is sufficiently long, thenthe stable state of the system is a regular oscillation andnot a time-independent steady state. In addition, exper-iments have shown that the TGF system in hypertensiverats may exhibit irregular oscillations. These oscillationsappear to have characteristic of deterministic chaos. Themathematical model previously devised by the group haspredicted that irregular oscillations may arise from cou-pling of nephrons with sufficiently different bifurcation pa-rameters. As a consequence of the new mathematical re-sults, TAL inhomogeneities may have an remarkable im-pact on the TGF-mediated oscillations. In particular ir-regular oscillations resembling those reported by experi-mentalists, may arise from a bifurcation, not necessarilythrough nephrons coupling. This research was supportedin part by NIH grant DK-42091, and by National ScienceFoundation under Agreement No. 0112050. Co-authors:Leon Moore, Harold Layton

Paula GrajdeanuMathematical Biosciences [email protected]

PP2

Mathematical Modeling of Plastron Respiration inTicks (Acari: Ixodidae)

Ticks are blood-feeding arthropods that are well knownfor their survivability. Although ticks are terrestrial or-ganisms, they can survive extended periods of submergenceunder water as for example after heavy rainfall or flooding.A plastron is a physical gill consisting of a thin layer of airtrapped by hydrophobic hairs or other cuticular projec-tions. Hence a plastron is an alternate respiration systemthat can absorb oxygen from water. The complex spirac-ular plates of ticks have been postulated to serve as plas-trons but until now, this has not been verified. In thisstudy, we confirm the existence of plastron respiration inthe dog tick Dermacentor variabilis. Adult dog ticks cansurvive submergence in water for over two weeks. Wettingthe spiracular plate with alcohol, thereby debilitating anypotential plastron function lowered survival to less thanthree days. Biomathematical studies currently in progressare modeling the efficiency of the spiracular plate as a plas-tron. We have developed a mathematical model to predictsurvivability of submerged ticks under water. This modelrequires determination of a suite of physical and biologi-cal parameters including volume of the air film containedwithin the spiracular plate, the plastron air/water inter-face area and the oxygen consumption and biomass of thesubmerged tick. It is hoped that this model can be success-fully used in the future to predict underwater survivabil-ity of other species of ticks which show both interspecificand intergeneric morphological variation in spiracular platestructure. This study provides the first example of plastronrespiration in the Ixodidae.

Matt Heimann, Bach Q. HaTruman State [email protected], [email protected]

PP2

Ecological Interference and the Persistence of Ver-tically Transmitted Parasites

A model that allows a virulent vertically transmitted para-site (VTP) to be maintained in a system containing a hostand a horizontally transmitted parasite (HTP) is analysed.The method of persistence relies on the VTP offering the

host a level of protection through reduced transmission ofthe HTP. The model raises questions about persistence ofdiseases through interactions with others, and also the sta-bilising effects of VTPs on dynamical systems in a biolog-ical control context.

Ed JonesSheffield [email protected]

PP2

A Function to Predict Sleep and Wake PatternsUsing Social and Circadian Factors

Recent literature suggests bio-mathematical models ofwork-related fatigue could be improved by accounting forsocial factors impacting on sleep and recovery. Currently,accuracy of existing models in operational environmentsis limited in certain applications. An alternate model ac-counting for such factors has been developed. Initial vali-dations have been performed using operational data. Pa-rameter stability has also been investigated using MonteCarlo simulation analysis. The development and initialvalidations of this model will be discussed.

Jillian DorrianCentre for Sleep ResearchUniversity of South [email protected]

Adam FletcherDepartment of Behavioral BiologyWalter Reed Army Institute of [email protected]

Katie J. KandelaarsCentre for Sleep Research, The University of [email protected]

PP2

Einstein Relation Approach to Protein Folding Dy-namics

We propose a protein folding simulation approach basedon energy type partition and Einstein Relations for con-strained movements as the important key for understand-ing of protein shape change dynamics. Lagrange methodsensure that the simultaneous minimization of two or moreenergy forms is describable in terms of the free energies,gradients or forces. Interesting point is that a structuralfree energy gradient exactly balances an electrical ensemblegradient leading to an infinite mobility.

Yeona KangDept. of Applied mathematics and StatisticsStonybrook [email protected]

Charles FortmannStonyBrook University at New yorkApplied mathematics and [email protected]

PP2

A Reduced Differential Model for Cardiac Action

LS06 Abstracts 115

Potentials

A differential model for cardiac action potentials with onlyten state variables is proposed for 0D or 3D electromechan-ical simulations of the heart. Three variables describe themembrane potential, the main ionic currents and two oth-ers, the Na+/Ca2+ exchangers and Na+/K+ pumps. Theremaining seven variables describe the subcellular Ca2+

dynamics. Simulations of action potentials of pacemaker,atrial, ventricular and Purkinje fiber cells are similar tothose obtained with more complex models.

Sorine [email protected]

Djabella KarimaINRIA Rocquencourt. BP 105. 78153 Le Chesnay [email protected]

PP2

Network Environ Analysis

Network environ analysis (NEA) uses network representa-tion of ecological systems to identify and quantify impor-tant ecosystem properties such as dominance of indirect ef-fects, network amplification, network homogenization andnetwork synergism. These properties provide new insightsinto system level behavior of ecological networks. UsingNEA, objects can be studied as part of a connected sys-tem which is a fundamentally different way of investigat-ing ecosystems. This gives a quantitative foundation to thewidely held perception of the interconnectedness of nature.

Caner KazanciDepartment of Mathematics and Faculty of EngineeringUniversity of [email protected]

Bernard Patten, Stuart WhippleInstitute of EcologyUniversity of [email protected], [email protected]

PP2

Mathematical Modeling of Tumor SpheroidGrowth

Multicellular tumor spheroids are made of three layers withdifferent mechanical properties, i.e. proliferating outerlayer, quiescent middle zone, and necrotic zone. Helm-linger et al (1997)’s experiment showed that tumor growthcan be regulated by stress and that mechanical proper-ties of the outer gel, such as stiffness, can inhibit tumorgrowth in vitro. Using the cell-based model on the pro-liferating zone, continuum model on other regions, andreaction-diffusion model for nutrients on whole domain, Iinvestigate the stress effect on tumor growth.

Yangjin KimSchool of MathematicsUniversity of [email protected]

Hans G. OthmerUniversity of MinnesotaDepartment of Mathematics

[email protected]

PP2

Graph-theoretic Models of the Human Hsp70 AT-Pase Domain

In this work we represent the Human Hsp70 ATPase do-main by mathematical graphs. Graphical invariants arecalculated for each model generating corresponding numer-ical data. The graph-theoretic models coupled with datamining tools inherently combine primary sequential infor-mation, structural information and amino acid motif recog-nition. Previous work by the author shows that graphicalinvariants such as those associated with efficient computernetwork designs can also be indicative of protein and nu-cleic acid structures. These findings initiate a similar studyof the HSp70 molecular chaperone.

Celia McIntoshBiological SciencesEast Tennessee State [email protected]

Daniel LambMathematicsEast Tennessee State [email protected]

Rhydon JacksonInformation and Computer ScienceEast Tennessee State [email protected]

Debra J. KnisleyEast Tennessee State [email protected]

PP2

Does Cannibalism Stabilize a Population?

Cannibalism occurs in a variety of taxa in nature. Forms ofcannibalism can include consumption of eggs by larvae oradults and predation on smaller individuals by larger ones.Sometimes cannibalism occurs without discrimination ofkin. Whatever competitive advantage this confers mustbe visible at the population level. We consider settings inwhich cannibalism is beneficial to a population.

Glenn W. LedderUniversity of NebraskaDept of [email protected]

PP2

Dynamics of a Multistage Circadian System

Tissues throughout the body exhibit circadian rhythms,forming a multi-oscillatory system whose disruption resultsin jet lag. Our simulations of a multistage circadian systemreveal the flexibility and stability inherent in a multistagesystem, as well as potential pitfalls. The modeling predictsthat jet lag is most severe following an eastward change of5-8 time zones due to prolonged desynchrony of the systemcaused by the antidromic reentrainment of some but notall components.

Hava SiegelmannUniversity of Massachusetts Amherst

116 LS06 Abstracts

[email protected]

Tanya LeiseAmherst [email protected]

PP2

Networks of Three-Identical Coupled Systems

We consider networks of three-identical coupled systems ofODE’s, where which system has at most two couplings. Weshow that there are 34 distinct networks of three-identicalsystems, at most double coupled, as opposed to only twosuch two-identical coupled systems of ODE’s. We also showthat, remarkably, transitions from a synchonous equilib-rium that can occur are determined by the coupling struc-ture of the network.

Martin GolubitskyUniversity of [email protected]

Maria LeitePurdue UniversityDepartment of [email protected]

PP2

Invasions, Range Limits, and Coexistence in Rivers

Spatial patterns of community composition and species re-placement in rivers emerge from complex interplays of hy-drological, geochemical, biological, and ecological factors.While these processes are well understood locally, a mecha-nistic basis for large-scale emerging patterns is lacking. Westudy invasion speeds, range limits, and spatially-mediatedcoexistence in reaction-advection-diffusion equations fortwo competitors in heterogeneous environments. We showthat emergent patterns have plausible spatial scales, givenparameter estimates for certain algae (periphyton).

Frithjof LutscherUniversity of [email protected]

Edward McCauleyUniversity of [email protected]


PP2

Protecting Mobile Fish: Results from DiffusionModels

Persistence of fish populations is a key goal of many marineprotected areas. I introduce a PDE model of a populationwhich has all ages of fish moving and which has a partiallyprotected habitat. The minimum reserve size necessary forspecies to persist is found for a variety of parameters andboundary conditions (including periodic). These resultsare compared to models where only the juveniles disperse.

Urmila MalvadkarDepartment of Mathematics, Statistics, and ComputerScience

St. Olaf [email protected]

Alan M. HastingsUC [email protected]

PP2

Modeling Functional Consequences of Amino AcidReplacements in Proteins

A computational mutagenesis methodology based on dataobtained from a multibody statistical contact potentialgenerates both scalar residual score and vector residualprofile characterizations for every single-site mutant of aprotein. With a focus on mutants for which experimen-tal activity data is available, the residual scores enable aclear elucidation of the structure-function relationship in aprotein. Additionally, the residual profiles lead to accurateinferential models of mutant protein biochemical activityrelative to wild type.

Majid Masso, Iosif VaismanGeorge Mason [email protected], [email protected]

PP2

A Note on Science, Mathematics, and AppliedMathematics

Science is that human activity devoted to the search forthe very explanation for (i.e., for the truth about) someparticular naturally occurring phenomenon. The Scien-tific Method is a six-stage model-building process, onewhich mimes the biological process by which first genetic,then neuronal, systems have been used to construct intra-corporeal models for ensuring survival. We investigatewhether mathematics (pure; then applied) is either nec-essary or sufficient for Science, but must answer negativelyeach question.

G Arthur Mihram, Danielle MihramUniv of Southern California, [email protected]

PP2

Linked Selected and Neutral Loci in a Heteroge-neous Environment

We analyze a system of ODEs modeling allele frequenciesat two linked genomic loci, one selected and one neutral,in an environment consisting of two habitats with diver-gent selection. We use geometric singular perturbationtheory and formal expansions to describe the dynamics andasymptotic behavior of the system. One conclusion is thatmarker-selected locus associations will not generally per-sist long enough to allow inference of dynamics and recenthistory at the selected locus from the state of the markerlocus.

Bryan WoodGeorgetown [email protected]

Judith R. MillerGeorgetown UniversityDepartment of [email protected]

LS06 Abstracts 117

PP2

Chemotaxis in Fluid Flows

We study the distribution of microorganisms representedas self-propelled particles, in a fluid medium. The particlesare transported by the flow and, in addition, they swim inthe direction of the gradient of an external (chemical) field.We show that the combined effect of chaotic mixing andchemotaxis leads to aggregation of particles on a complexmanifold. We discuss the properties of the aggregates andefficiency of chemotaxis in flows with fluctuating chemicalconcentrations.

Zoltan NeufeldUniversity College [email protected]

PP2

Three New R’s: Random Walks, Riordan Arrays,and RNA

We use an algebraic and combinatorial technique to counttwo classes of random walks. It is interesting that cer-tain subsets of the walks are counted by the numbers1,1,1,2,4,8,17,37, .... These numbers are commonly calledthe RNA numbers and they also count RNA secondarystructures of a specified length. A bijection is constructedbetween the set of RNA structures of a given length and asubset of random walks of a given length and height.

Asamoah NkwantaMorgan State [email protected]

PP2

Inferring Causal Subnetworks Using Point ProcessModels

If one could measure simultaneously and individually thespiking activity of all neurons in a neural network, fitting anetwork model to the data might reveal causal connectionsamong the neurons. However, connections from unmea-sured neurons could create the illusion of causal influenceamong the measured neurons. We have developed a frame-work that addresses effects from unmeasured neurons inorder to reveal causal influence among the measured neu-rons. The approach exploits predictions from a point pro-cess model of the relationship between neuron spikes andexternal variables such as a stimulus. The resulting anal-ysis can be potentially applied to a large range of exper-iments where the spikes of multiple neurons are recordedsimultaneously.

Duane NykampUniversity of MinnesotaSchool of [email protected]

PP2

On Using Wavelets for Transient Feature Selectionin Odor Detection

The performance of electronic olfaction devices is highlydependent on the quality of input signals that representthe sensors response. These units collect information aboutthe odors they are assessing using an array of 15 or moregas sensors. Consequently, these devices have a high-dimensional input feature space which makes odor clas-sification difficult. Here a multiresolutional approximation

technique called the Discrete Wavelet Transform is em-ployed to capture only the relevant features of the sensorarray dynamics. Three families of wavelets are evaluatedusing three statistical and neural network classifiers (K-nearest neighbor, backpropagation, and RBF neural net-works) for three odor samples (bacteria , coffee and co-las). The experimental results show promising classifica-tion improvements when compared to conventional steady-state classification. Thus, higher classification accuracyand speed are obtained by using transient-feature compres-sion with Wavelet decomposition.

Ekachai PhaisangittisagulNorth Carolina State UniversityAke [email protected]

PP2

A New Approache to Identify Binding Sites

We have developed a novel approach to identify proteinbinding sites by analyzing triangulated protein surface rep-resentation. Atom-atom interactions are derived based oninteractions of neighboring surface elements using line-of-sight intersection test. Atoms are, then, converted intonodes in a edge-weighted graph. The nodes are further an-alyzed using a cluster algorithm. Current implementationcan identify the ion binding site of calix-4-arene and thenucleotide binding site of human Ras.

Randy ZauharDepartment of Chemistry & BiocUniversity of the Sciences in [email protected]

Michael BruistDepartment of Chemistry & BiochemistryUniversity of the Sciences in [email protected]

Niny RaoDepartment of Chemistry & BiocUniveristy of the Sciences in [email protected]

PP2

Intra-Genomic Conflict and Evolution of Gene Si-lencing

Using a model of early genome evolution, we investigatethe hypothesis that gene silencing originally evolved as amechanism to protect genomes from transposable elements(TEs). We show that pressure from TE replication createsweak selection in favor of TE silencers and we explore vari-ous aspects of the selective dynamics. We show that cyclesof TE activity readily develop if TEs occasionally escapefrom silencing, due to an “arms race” between TEs and TEsilencers.

John McDonaldSchool of BiologyGeorgia Institute of [email protected]

Paul SchliekelmanDepartment of StatisticsUniversity of [email protected]

118 LS06 Abstracts

PP2

Single-Occupancy Binding In Simple Bounded andUnbounded Systems

The number of substrate molecules that can bind to theactive site of an enzyme at one time is constrained. Thisposter presents boundary conditions corresponding to theconstraint of single occupancy binding. Two simple mod-els of substrate molecules diffusing to a single occupancysite are considered. When the diffusive time scale is muchshorter than the time scale for entering the single occu-pancy site, the dynamics of binding are accurately de-scribed by simple approximations.

Mark F. SchumakerDepartment of MathematicsWashington State [email protected]

PP2

Haart and the Epidemic of Hiv+ End Stage RenalDisease

The number of patients with HIV infection and end stagerenal disease (ESRD) continues to rise. To assess the im-pact of antiretroviral therapy on the progression of patientswith AIDS to the development of end stage renal disease,we developed a mathematical model of HIV infection inthe ESRD population using available population data. Themodel was then used to evaluate recent data and to projectthe prevalence of HIV ESRD through 2020.

Elissa J. SchwartzDepartment of MathematicsHarvey Mudd [email protected]

Lynda SzczechDivision of NephrologyDuke University Medical [email protected]

Michael RossDivision of NephrologyMount Sinai Medical [email protected]

Mary KlotmanDivision of Infectious DiseasesMount Sinai Medical [email protected]

Jonathan Winston, Paul KlotmanDivision of NephrologyMount Sinai Medical [email protected], [email protected]

PP2

Mechanistic Model of Escherichia Coli Cell Deathunder Acidic Conditions

By processing acidified vegetable products, e.g. pickles,there is risk of contamination by microbial pathogen suchas Escherichia coli. We have developed a mechanisticmathematical model which can be used to understand themechanism behind the killing of these deadly bacteria. Ourmodel predicts that killing of E. coli is due to the low lev-els of intracellular pH. The continued development of this

model will aid in enhancing safety for acidified food pro-duction.

Althea M. SmithNorth Carolina State [email protected]

Fred BreidtUSDA/ARSNorth Carolina State [email protected]

Sharon R. LubkinNorth Carolina State UnivDepartment of [email protected]

PP2

Reverse Correlation and Network Architecture

Reverse-time Correlation (RTC) measurements gives theaverage response dynamics of individual neurons within arecurrent neuronal network. The resulting RTC functionprovides specific information about the nature of the recur-rent network connections, and in particular, the strength ofinhibition. We present a set of models that uncover and ex-plain the connection between RTC functions and networkarchitecture.

Louis TaoDepartment of Mathematical SciencesNew Jersey Institute of [email protected]

PP2

Distributed and Parallel Algorithms in the Life Sci-ences

This presentation discusses the mathematical frameworkto allow distributed or parallel simulation of biological sys-tems. Both stocastic and deterministic cases are outlined.It is expected that large-scale/ high detail computationalsimulation of cells, tissues and organs of the human bodywill speed up the development of new medical devices andtreatment protocols. The lung-heart system is used as anexample of how distributed/parallel simulation algorithmscan be successfully deployed.

Yosef G. Tirat-GefenSenior Member IEEE Computer Societyand IEEE Engineering in Medicine and Biology [email protected]

PP2

A Computational Model for Motor Pattern Switch-ing Between Taste-Induced Ingestion and RejectionOromotor Behaviors

We present a computational model for activity patternssimilar to taste-induced ingestion (licking) and rejection(gaping) generated in the brainstem. Single-compartment,conductance-based models are used for individual neurons;cells within the network are coupled through mutual inhi-bition. Using geometric dynamical systems methods, wedescribe conditions under which a single network config-uration can produce both activity patterns. The analysispredicts that prolonged inhibition of some neurons may be

LS06 Abstracts 119

an important component responsible for this switch.

David TermanDept. of Math/MBIOhio State [email protected]

Joseph TraversDept. of Oral BiologyOhio State [email protected]

Sharmila VenugopalNeuroscience Graduate ProgramOhio State [email protected]

PP2

Numerical Simulation Methods for Tissue Morpho-genesis

Morphogenesis is concerned with shape formations of tis-sues, organs and bodies and is of fundamental importanceto developmental biology and tissue engineering research.To study the mechanisms of epithelial-mesenchymal tissueinteractions (e.g. branching morphogenesis) in terms of ge-ometry and mechanical force, a two-phase Newtonian fluidmodel is proposed and solved numerically using the im-mersed interface method (IIM). Jump conditions are nec-essary to employ the second-order accurate finite differ-ence scheme in the immersed interface method. Interfa-cial jump conditions for kinematic variables (velocity andpressure) are derived for the case where the two phasesmay have unequal viscosity coefficients. Our results of thejump conditions match well with existing results in theliterature where the viscosity coefficients are equal acrossthe interface. I will illustrate the local Cartesian coordi-nates transformation techniques used in the derivations ofboth the jump conditions for the fluid equations and thefinite difference scheme for the IIM. The interface betweenthe two phases is chosen to be represented implicitly usingzero level sets. The implementation of the two-phase fluidsolver in both 2D and 3D geometry coupled with the levelset method for moving interface problems is not trivial. Iwill show some preliminary simulation results for modelingtissue morphogenesis using our efficient numerical solver.

Zhilin LiDepartment of MathematicsNorth Carolina State [email protected]

Xiaohai WanNorth Carolina State [email protected]

Sharon R. LubkinNorth Carolina State UnivDepartment of [email protected]

PP2

When Does Spatial Structure Matter? Sir ModelsBetween the Local and Mean Field

We extend pair-wise spatial SI models to elucidate the ef-fects of recovery and waning immunity. We demonstrate aloss of limit cycle behaviour, and an increase in the critical

transmissibility and extinction thresholds, when recover isincluded. We then extend the reproduction processes ofhosts and infection to include proportions of global inter-actions. Thus, providing intermediate structures betweenthe local and mean-field. The evolutionary dynamics ofhost-parasite interactions within this intermediate case isthen discussed.

Steven D. WebbSheffield [email protected]

PP2

A Mathematical Model of U Wave in Electrocar-diogram

U wave was first observed by Einthoven and defined asthe waveform occurred immediately after T wave and be-fore P wave. With more clinic implications, U wave canbe observed in various pathological conditions, such as hy-pokalemia, cardiac ischemia etc. Interestingly, the originof the U wave in ECG is still not certain. Previously, wedemonstrated volatile anesthetics could suppress delayedafter depolarizations and triggered activity in canine ven-tricular preparations. Recently, we have documented thatvolatile anesthetics reversibly suppress U wave in clinicalpatients. A mathematical model of U wave will be pre-sented.

J.-J CaoDept. of Applied Math.Providence [email protected]

Hsiang-Ning LukDepartment of Anesthesiology, Taichung Veterans GeneralHospital, Taichung, [email protected]

Chu-Pin LoDepartment of Applied MathematicsProvidence [email protected]

H.-C. TienDept. of Applied Math.Providence [email protected]

Juan-Ming YuanDepartment of Applied MathematicsProvidence [email protected]

PP2

Computer Modeling of Perlecan Regulation onGrowth Factor Binding to Vascular Surface

Certain molecules in blood circulation such as per-lecan/heparan sulfate play an important role in regulatingcancer growth and cardiovascular disease development, thereal mechanism, however, is still under investigation. Wepropose a convection-diffusion-reaction model for simulat-ing the process of perlecan regulation. An explicit-implicitsplitting technique is applied to solve the coupled nonlin-ear system of equations, where the chemical reaction ishandled by the explicit Runge-Kutta method, while the

120 LS06 Abstracts

convection-diffusion process is treated implicitly.

Wensheng Shen, Jun ZhangUniversity of KentuckyDepartment of Computer [email protected], [email protected]

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