Discrete dynamic modeling of biological regulatory networks

Réka AlbertDepartment of Physics, Department of Biology and

Huck Institutes for the Life SciencesPennsylvania State University

Life at the cellular level

• Cellular functions rely on the coordinated action of interacting components.

• Proteins – provide structure to cells and tissues– work as molecular motors– sense chemicals in the environment– drive chemical reactions– regulate gene expression

• Interconnections between components are the essence of a living process. David Goodsell/ Science Photo Library

receptor proteins, enzymes, ribosomes, DNA

external signals

gene regulation

protein-protein interactions

GENOME

PROTEOME

Citrate Cycle

METABOLISM

Bio-chemical reactions

Many non-identical elements connected by diverse interactions

signal transduction

Cellular networks

Genome level~30,000 nodes

Module level30 nodes

Component level~3 nodes

Statistical mechanicsof networks

Functional modelingMolecular biology

Common features of biological systems • functionally diverse elements• time-varying abundances & activities for each element• diverse interactions that form networks• have functions that need to be performed

sensitive to some changes, insensitive/adaptable to othersevolvable, shaped by evolution and natural selection

Network = backbone of processNode states + transfer functions functional state of system

Hypothesis: the organization of the regulatory network is more importantthan the kinetic details of the individual interactions.

From dose-response curves to Boolean switches • X – mRNA

• Y – transcriptional activator

If ν is large, the dose-responsecurve becomes a switch

If Y>KY dX/dt>0 mRNA productionIf Y<KY dX/dt<0 mRNA decay

If activation is below threshold,mRNA can decay.

Boolean simplification:X* = YActivation: If Y=ON X*=ONDecay: If Y= OFF X*=OFF

* denotes the next state

Hill function

Implementing time in discrete models

1. Synchronous models• The state of each node is updated simultaneously at

multiples of a common time step.• Underlying assumption: the timescales of all synthesis and

decay processes are similar

2. Asynchronous modelsThe state of each node is updated individually

Implementation used here: • At each time step randomly select a permutation of the

nodes and update them in that order.

Synchronous models have deterministic state transitions,asynchronicity introduces stochasticity (update order dependence) in the dynamics.

Modeling drought signaling in plants

Phenomenon: abscisic acid induced closure of plant stomata

Hypotheses: network inference from indirect informationprotein activity is switch-like

Validation: reproduces known wild type and disrupted behavior.Explored: disruptions

changes in initial conditionschanges in timing

Insight: variability in timing and initial conditions does not matter65% of perturbations have no negative effectidentified critical perturbations

S. Li, S. Assmann and R. Albert, PLoS Biology 4, e312 (2006).

ABA

CO2 H2O

Stomatal sizes are determined by the turgor (fullness) of the guard cells.

During drought conditions plants synthesize a hormone called abscisic acid (ABA) that initiates a signal transduction network to close stomata.

How is this crucial process being orchestrated, and how is its sensitivity and reliability maintained?

The exchange of O2 and CO2 in plants occurs through stomata.

90% of the water taken up by a plant is lost in transpiration.

Stomata and guard cells

• Genetic & pharmacological perturbations of putative mediatorsCompare input - output (ABA- aperture change) relationships in normal and perturbed plants

• Scarce biochemical evidence for interaction

Experimental observations mainly indirect

ABA Closure

K+ effluxCa2+c

increase

membrane depolarizationNO, S1P, IP3

ABI1

Network construction from indirect evidence

– nodes: all proteins, molecules, ion channels implicated in the process– compress biological information into activation or inhibition– hypothesis: indirect causal relationships and processes correspond to

paths ABA ion flow, ABA Sph kinase activity

– activating or inhibiting effects on processes represented as intersection of two paths SphK (ABA closure)

Need to determine the closest regulator and target of each node

interaction Node/Process BNode A

Arabidopsispromotes SphKABA

Arabidopsispartially promotes ABA → AnionEMSphK

Commelinacommunispromotes ABA → closurePLC

species

Network reductionFind the most parsimonious (least redundant) network that incorporates allnodes and known processes. • Introduce intermediary nodes• Contract intermediary nodes• Review and revise

General algorithm: binary transitive reduction with critical edges, pseudo-vertex collapse, implemented as NET-SYNTHESIS

R. Albert, B. DasGupta et al, Journ. Comp Biology 14, 927 (2007).

enzymes, signal transduction proteins, transport, small molecules• intermediary nodes

Asynchronous Boolean model

States: 1 = active/high/open,0 = inactive/low/closed

NOT (inhibitors), AND (conditional activation), OR (independent activation)

Ca2+c* = (CaIM or CIS) and not Ca2+ ATPase

Closure* = (KOUT or KAP) and AnionEM and Actin and not Malate

10,000 replicate simulations with randomly selected initial condition (except for ABA), random update order at each timestep.

Output: frequency of closure=1 state

Signal transduction is resilient to perturbations

Normal response to ABA stimulus.

ABI1 knockout mutantsrespond faster.

Perturbations in Ca2+ leadto slower response.

Perturbations in pH lead to decreased sensitivity.

Surprising prediction: Ca2+ disruption has less severe effects than pHc disruption.

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Experimental validation

Normal: “open” and“closed” statedistinguishable

pHc disrupted: “open”and “closed” stateindistinguishable

Ca2+ disrupted: “open”and “closed” state

distinguishable

Aperture in µm

Per

cent

age

Discrete model of T cell survivalPhenomenon: survival of cytotoxic T cells in T-LGL leukemiaConstructed: survival signaling network inside T- LGL cellsHypotheses: discrete states, switch-like state changesValidation: reproduces known deregulations and known key mediators

Predicts: minimal initial condition necessary for T-LGL statemanipulations that ensure apoptosis of T-LGL cells additional deregulations

Predictions were validated experimentally

Implications: identifying therapeutic targets for T-LGL leukemiatumor and cancer vaccine development

J. R. Zhang, M. V. Shah, J. Yang, S. B. Nyland, X. Liu, J. K. Yun, R. Albert, T. P.Loughran, PNAS 105, 16308 (2008).

CTL activation induced cell death and LGL leukemia

• cytotoxic T lymphocytes (CTL) eliminate infected cells and tumor cells• The majority of activated CTL undergo activation induced cell death (AICD), mainly through Fas-induced apoptosis

• T-LGL: abnormal clonal expansion of antigen primed mature CTL• Activation of multiple survival pathways (MAPK; JAK-STAT)• Insensitive to Fas-induced apoptosis• No known curative therapy

Erika L. Pearce & Hao Shen, 2006, Immunological Reviews

Thierry Lamy & Thomas P. Loughran, Jr, 1998, Cancer Control

General CTL activation‐AICD 

network (extracted from 

literature)

General CTL activation‐AICD 

network (extracted from 

literature)

Augmented T‐LGL CTL survival network

Augmented T‐LGL CTL survival network

Known deregulated components in T‐LGL and related pathways

T‐LGL CTL survival network

T‐LGL CTL survival network

NET‐SYNTHESIS (a signaling network inference and simplification tool)

Discrete dynamic model

Discrete dynamic model

Reveal possible causes of the pathway abnormalities 

Reveal possible causes of the pathway abnormalities 

Identify key survival 

mediators

Identify key survival 

mediators

Strategy

T-LGL survival signaling network

Rectangle: intracellular; ellipse: extracellular; diamond: receptor.Upregulated, downregulated, deregulated node; Activation, inhibition edge

Asynchronous Boolean modelAims: reproduce an LGL-like state

determine minimal cause of an LGL-like statedetermine minimal intervention that reverses LGL-like state

Rules for state transitions: • Timestep: a round of updating during which all nodes are updated in a

randomly selected order• Simulation ends when apoptosis = 1 (cell death) is reached• Multiple (>300) simulations for each initial condition, 20~40 timesteps

• Output of the model: the frequency of node activation; representative of cells that are still alive

Determined the causal hierarchy within the known deregulations

Overexpression of IL15 and PDGF can cause all known deregulations.

Upregulated, downregulated in LGL Positive, negative causal effect

Reproduce a T-LGL-like state

Minimum condition: IL-15 constantly ON, PDGF intermittently ON, Stimuli initially ON.• Suggestive of inflammation during infection• Provision of IL-15 and PDGF may generate long-lived CTL for the virus and cancer vaccines.

C

Apoptosis stabilizes at OFF in a subsetof simulations, JAK upregulated, IL-2 and proliferation downregulated.

Identify key mediators of T-LGL survival• Identify nodes that stabilize when a T-LGL-like state is achieved• Alter the node state and track the change of apoptosis frequency• Key mediator: altering its state causes total apoptosis.• Identified: SPHK1, NFκB, S1P, SOCS, GAP, BID and IL2RB

Validation: NFκB constitutivelyactive in T-LGL

Validation: NFκB inhibition induces apoptosis in T-LGL

Model: NFκB stabilizes at ON,setting it OFF causes total apoptosis

Identify additional deregulations• Model: T-bet needs to be constitutively activated concurrently

with NFκB activation to reproduce the low IL-2 production phenotype in leukemic T-LGL

• Experimental validation: T-bet overexpressed and highly active in T-LGL

Lessons learned

• Network allows the logical organization of disparate information into a coherent whole

• Network-based discrete dynamic model • enables ranking of most important components and interactions• has predictive value - corrections to conventional wisdom • allows discovery of new strategies

• Methodology can be refined iteratively with experiments

• The topology of the network of interactions plays a determinant role in the system's behavior

Acknowledgements

Alfred P. Sloan FoundationNSF, NIHUS Dept. of Agriculture

Song LiRanran ZhangJuilee Thakar Assieh Saadatpour –MoghaddamColin CampbellZhongyao SunRuisheng WangSuann Yang

Collaborators:Sarah Assmann (PSU Biology)Eric Harvill (PSU Vet. Sci.) and his groupThomas Loughran (HMC) and his groupBhaskar DasGupta