Models and Languages for Computational Systems Biology ...deterministic. Stochastic Simulation:...
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Introduction Models and Languages Challenges Models and Languages for Computational Systems Biology – Lecture 1 Jane Hillston. LFCS and CSBE, University of Edinburgh 13th January 2011
Transcript of Models and Languages for Computational Systems Biology ...deterministic. Stochastic Simulation:...
Introduction Models and Languages Challenges
Models and Languages for ComputationalSystems Biology – Lecture 1
Jane Hillston.LFCS and CSBE, University of Edinburgh
13th January 2011
Introduction Models and Languages Challenges
Outline
IntroductionMotivationMeasurement, Observation and Induction
Models and LanguagesCase Study
Challenges
Introduction Models and Languages Challenges
Systems Biology
• Biological advances mean that much more is now knownabout the components of cells and the interactions betweenthem.
• Systems biology aims to develop a better understanding ofthe processes involved.
• It involves taking a systems theoretic view of biologicalprocesses — analysing inputs and outputs and therelationships between them.
• A radical shift from earlier reductionist approaches, systemsbiology aims to provide a conceptual basis and amethodology for reasoning about biological phenomena.
Introduction Models and Languages Challenges
Relation to Computer Science
Formalisms from theoretical computer science have found a newrole in developing models for systems biology, allowing biologiststo test hypotheses and prioritise experiments.
Perhaps more than any other discipline computer scientists have atrack record of developing languages and formal reasoningtechniques to support them.
Introduction Models and Languages Challenges
What is Systems Biology?
“The principal aim of systems biology is to provide both aconceptual basis and working methodologies for the scientificexplanation of biological phenomena” – Olaf Wolkenhauer
Introduction Models and Languages Challenges
Systems Biology Methodology
ExplanationExplanationInterpretationInterpretation
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Natural SystemNatural System
Systems AnalysisSystems Analysis?
InductionInductionModellingModelling
Formal SystemFormal System
Biological PhenomenaBiological Phenomena-MeasurementMeasurementObservationObservation
� DeductionDeductionInferenceInference
Introduction Models and Languages Challenges
Biological Phenomena
• As an approach systems biology can be applied to manydifferent biological systems at different scales.
• For example, from gene regulation within the nucleus of a cell,to whole organs, or even complete organisms.
• The biological phenomena to be studied will clearly dependon the type of system being investigated.
• A grand challenge for systems biology is to developmulti-scale models which seek to account for high-levelbehaviour (at the level of the whole organisms) at all levelsdown to the intra-cellular processes.
Introduction Models and Languages Challenges
Biochemical Pathways
At the intra-cellular level we can distinguish three distinct types ofpathways or networks
Gene networks: Genes control the production of proteins but arethemselves regulated by the same or differentproteins.
Signal transduction networks: External stimuli initiate messagesthat are carried through a cell via a cascade ofbiochemical reactions.
Metabolic pathways: The survival of the cell depends on its abilityto transform nutrients into energy.
But these distinctions are to some extent arbitrary as models mayinclude elements of more than one pathway type.
Introduction Models and Languages Challenges
Signal transduction pathways
• All signalling is biochemical:
• Increasing protein concentrationbroadcasts the information aboutan event.
• The message is “received” by aconcentration dependent responseat the protein signal’s site of action.
• This stimulates a response at thesignalling protein’s site of action.
• Signals propagate through a seriesof protein accumulations.
Introduction Models and Languages Challenges
Systems Biology Methodology
ExplanationInterpretation
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Natural System
Systems Analysis?
InductionModelling
Formal System
Biological Phenomena-MeasurementObservation
� DeductionInference
Introduction Models and Languages Challenges
Measurement, Observation and Induction
• Robot Scientist project — Kell, King, Muggleton et al.
• Combination of machine learning for hypothesis generationand genetic algorithms for automatic experimental tuning.
• Experiments are carried out by a robot.
• Data is generated at rates which exceed what is possiblewhen there are humans in the loop.
• Moreover the intelligent experiment selection strategy iscompetitive with (good) human strategies, and significantlyoutperforms cheapest and random selection strategies.
Introduction Models and Languages Challenges
The Robot Scientist
BackgroundKnowledge
Machine learning
Experimentselection
Final Hypothesis
ExperimentsRobot
Consistenthypotheses
Analysis
Results
• No human intellectual input in the design of experiments orthe interpretation of data.
• Integrates scientific discovery software with laboratoryrobotics.
Introduction Models and Languages Challenges
The Robot Scientist
The initial robot, Adam, solveda problem related to identifyingthe gene in yeast responsiblefor an enzyme crucial to theproduction of the amino acidlysine.
A successor robot, Eve, is nowin operation at AberystwythUniversity.
See press report at http://www.timesonline.co.uk/tol/news/science/article6024880.ece
Introduction Models and Languages Challenges
Systems Biology Methodology
ExplanationInterpretation
6
Natural System
Systems Analysis?
InductionModelling
Formal System
Biological Phenomena-MeasurementObservation
� DeductionInference
Introduction Models and Languages Challenges
Formal Systems
There are two alternative approaches to constructing dynamicmodels of biochemical pathways commonly used by biologists:• Ordinary Differential Equations:
• continuous time,• continuous behaviour (concentrations),• deterministic.
• Stochastic Simulation:• continuous time,• discrete behaviour (no. of molecules),• stochastic.
Introduction Models and Languages Challenges
The objective of modelling
“The principal aim of systems biology is to provide both a conceptualbasis and working methodologies for the scientific explanation ofbiological phenomena” – Olaf Wolkenhauer
The key word here is explanation.
The role of modelling is to explore possible explanations moreabstractly and more efficiently than might be done with wet labexperiments.
Introduction Models and Languages Challenges
Case Study: Circadian Rhythms – Overview
The study by Locke et al. ( Extension of a genetic network modelby iterative experimentation and mathematical analysis. MolecularSystems Biology) focuses on the circadian rhythms in plants,combining mathematical models and molecular biology.
Their objective is to identify the genes (and proteins) responsiblefor maintaining the daily rhythms observed in the plants.
The research exploits an interplay between mathematical models,experiments in the laboratory and literature search.
It is held up as an exemplar of what systems biology is trying toachieve, and the breakthroughs that it can bring about when it issuccessful.
Introduction Models and Languages Challenges
Case Study: Circadian Rhythms – Initial Model
From initial experiments Locke et al. identified a two genes and twoproteins which appeared to operate in a simple loop:
TOC1 LHY
LHY
TOC1
An initial mathematical model (ODEs) was constructed to capturethis model.
Introduction Models and Languages Challenges
Case Study: Circadian Rhythms – Role of Mathematics
Initial simulations with the mathematical model showed goodagreement with the experimental data for some of the observedphenomena but significant discrepancies for others.
Experiments were then undertaken with the mathematical model tofind an alternative model which was biologically plausible butproduced a better fit.
These mathematical experiments conjectured a network with twointeracting loops.
Introduction Models and Languages Challenges
Case Study: Circadian Rhythms – Elaborated Model
LHY
TOC1
Y
TOC1
X
Y
X
LHY
Two “new” genes wereintroduced to the modelwhich now hasinterlocking loops andmore complex feedback.
The simulation resultsfrom this model showedmuch better agreementwith the observed data.
Introduction Models and Languages Challenges
Case Study: Circadian Rhythms – Validating the Model
The researchers then sought to identify the “new” genes X and Y .
Searching the literature elicited several candidate genes whichprevious experimental studies had suggested were implicated inthe circadian rhythm.
In particular, “knockout” data for one, GIGANTEA (GI), coincidedwith the pattern from simulation experiments of the original modelwith a single loop.
Subsequent wet lab experiments have reinforced this impressionthat GI is gene Y .
Introduction Models and Languages Challenges
Formal Systems Revisited
• The case study used mathematics (i.e. a set of ODEs) directlyas the formal system.
• Previous experience in other application domains has shownthat there can be benefits to interposing a formal modelbetween the system and the underlying mathematical model.
• Using such an intermediary can aid is model construction andmodel understanding, it can reduce errors and provide accessto logic-based analysis techniques such as model checking.
• Moreover taking this “high-level programming” style approachoffers the possibility of different “compilations” to differentmathematical models.
Introduction Models and Languages Challenges
Integrated Analysis
System
MathematicalModel
e.g ODE or SSA
ODE
System
Stochastic Process Algebra
Model
SSAModel Checking
ODE
Stochastic Process Algebra
Model
Analysis
SSAModel Checking
Introduction Models and Languages Challenges
Challenges
• Individual vs. Population
• Noise vs. Determinism
• Modularity vs. Infinite Regress
• Dealing with the Unknown
Introduction Models and Languages Challenges
Individual vs. Population behaviour
• Biochemistry is concerned with the reactions betweenindividual molecules and so it is often more natural to modelat this level.
• However experimental data is usually more readily available interms of populations rather than individual moleculescf. average reaction rates rather than the forces at play on anindividual molecule in a particular physical context.
• These should be regarded as alternatives, each beingappropriate for some models. The challenge then becomeswhen to use which approach.
• Note that given a large enough number of molecules an“individuals” model will (in many circumstances) beindistinguishable from the a “population” level model.
Introduction Models and Languages Challenges
Noise vs. Determinism
• With perfect knowledge the behaviour of a biochemicalreaction would be deterministic.
• However, in general, we do not have the requisite knowledgeof thermodynamic forces, exact relative positions,temperature, velocity etc.
• Thus a reaction appears to display stochastic behaviour.
• When a large number of such reactions occur, therandomness of the individual reactions can cancel each otherout and the apparent behaviour exhibits less variability.
• However, in some systems the variability in the stochasticbehaviour plays a crucial role in the dynamics of the system.
Introduction Models and Languages Challenges
Comparing stochastic simulation and ODEs
Consider a Michaelis Menten reaction in which a substrate S istransformed to a product S via a complex C formed with anenzyme E.
b/u C c S
E
S
It is relatively straightforward to contrast the results of the twomethods. We compare the results of 2000 runs of the stochasticalgorithm simulating a system with initial molecular populationsS0 = 100,E0 = 10,C0 = 0,S0 = 0 and a volume of 1000 units.
Introduction Models and Languages Challenges
Results for S0 = 100,E0 = 10,C0 = 0,S0 = 0 (vol 1000)
Introduction Models and Languages Challenges
Results for S0 = 100,E0 = 10,C0 = 0,S0 = 0 (vol 1000)
Introduction Models and Languages Challenges
In vivo behaviour compared with model behaviour
However, it is worth bearing in mind that an actual in vivobiochemical reaction would follow just one of the many randomcurves that average together producing the closely fitting mean.This curve may deviate significantly from that of the deterministicapproach, and thus call into question its validity.
But this does not mean that the randomness exhibited by aparticular stochastic simulation trajectory will be the same as therandomness of a particular in vivo reaction. Indeed, a set ofstochastic simulation trajectories (ensemble) is usually averagedbefore any conclusions are drawn.
Introduction Models and Languages Challenges
Comparing results at lower population sizes
S0 = 10,E0 = 1,C0 = 0,S0 = 0 (vol 100)
Introduction Models and Languages Challenges
Mean results for 11, 110 and 1100 molecules
Introduction Models and Languages Challenges
Vliar-Kueh-Barkai-Leibler Circadian clock (cartoon)
Introduction Models and Languages Challenges
Circadian clock (deterministically . . . )
Introduction Models and Languages Challenges
Circadian clock (. . . and stochastically)
Introduction Models and Languages Challenges
Modularity vs. Infinite Regress
As computer scientists we are firm believers in modularity andcompositionality. When it comes to biochemical pathways opinionamongst biologists is divided about whether is makes sense totake a modular view of cellular pathways.
Some biologists (e.g. Leibler) argue that there is modularity,naturally occuring, where they define a module relative to abiological function.
Others such as Cornish-Bowden are much more skeptical and citethe problem of infinite regress as being insurmountable.
Introduction Models and Languages Challenges
The problem of Infinite Regress
Introduction Models and Languages Challenges
Dealing with the Unknown
There is a fundamental challenge when modelling cellularpathways that little is known about some aspects of cellularprocesses.
In some cases this is because no experimental data is available, orthat the experimental data that is available is inconsistent.
In other cases the data is unknowable because experimentaltechniques do not yet exist to collect the data, or those that doinvolve modification to the system.
Even when data exists the quality is often very poor.
Introduction Models and Languages Challenges
References
R.D. King, K.E. Whelan, F.M. Jones, P.J.K. Reiser, C.H. Bryant,S. Muggleton, D.B. Kell, S. OliverFunctional Genomic Hypothesis Generation and Experimentation by aRobot ScientistNature, 427, pp 247–252, 2004.
J.C.W. Locke, M.M. Southern, L. Kozma-Bognar, V. Hibberd, P.E. Brown,M.S. Turner and A.J. Millar.Extension of a genetic network model by iterative experimentation andmathematical analysis.Molecular Systems Biology, msb4100018-E2, 2005.
D. Forger, M. Drapeau, B. Collins and J. Blau.A new model for circadian clock research?Molecular Systems Biology, msb4100019-E1, 2005.
Introduction Models and Languages Challenges
References
A. Cornish-Bowden and M.L. CardenasSystems biology may work when we learn to understand the parts interms of the wholeBiochemical Society Transactions, 33, pp 516–519, 2005.
L.H. Hartwell, J.J. Hopfield, S. Leibler and A.W. Murray,From molecular to modular cell biologyNature, 402, pp C47–C50, 1999.
J. Fisher and T.A. Henzinger,Executable Cell BiologyNature Biotechnology, 25(11), 1239–1249, 2007.
