Table Of ContentSimulation Foundations, Methods and Applications
David J. Barnes
Dominique Chu
Guide to
Simulation and
Modeling for
Biosciences
Second Edition
Simulation Foundations, Methods
and Applications
Series editor
Louis G. Birta, University of Ottawa, Canada
Advisory Board
Roy E. Crosbie, California State University, Chico, USA
Tony Jakeman, Australian National University, Australia
Axel Lehmann, Universität der Bundeswehr München, Germany
Stewart Robinson, Loughborough University, UK
Andreas Tolk, Old Dominion University, USA
Bernard P. Zeigler, University of Arizona, USA
More information about this series at http://www.springer.com/series/10128
David J. Barnes Dominique Chu
(cid:129)
Guide to Simulation
and Modeling
for Biosciences
Second Edition
123
DavidJ. Barnes DominiqueChu
University of Kent University of Kent
Canterbury, Kent Canterbury, Kent
UK UK
ISSN 2195-2817 ISSN 2195-2825 (electronic)
Simulation Foundations,Methods andApplications
ISBN978-1-4471-6761-7 ISBN978-1-4471-6762-4 (eBook)
DOI 10.1007/978-1-4471-6762-4
LibraryofCongressControlNumber:2015947120
SpringerLondonHeidelbergNewYorkDordrecht
©Springer-VerlagLondon2010,2015
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David dedicates this book to Ruby
Preface
Inthisbookweseektoprovideadetailedintroductiontoarangeofsimulationand
modeling techniques that are appropriate for use in the biosciences. The book is
primarilyintendedforbioscientists,butwillbeequallyusefulforanybodywishing
to start simulation and modeling in related fields. The topics we discuss include
agent-based models, stochastic modeling techniques, differential equations, and
Gillespie’sstochasticsimulationalgorithm.Throughout,wepayparticularattention
to the needs of the novice modeler. We recognize that simulation and modeling in
science in general (and in biology, in particular) require both skills (i.e., pro-
gramming, developing algorithms, and solving equations) and techniques (i.e., the
abilitytorecognizewhatisimportantandneedstoberepresentedinthemodel,and
what can and should be left out). In our experience with novice modelers we have
noticed that: (i) both skill and technique are equally important; and (ii) both are
normally lacking to some degree.
Thephilosophyofthisbook,therefore,istodiscussbothaspects—thetechnical
sideandthesidethatconcernsbeingabletoidentifytherightdegreeofabstraction.
Asfarasthelatterareaisconcerned,wedonotbelievethatthereisasetofrulesthat,
iffollowed,willnecessarilyleadtoasuccessfulmodelingresult.Therefore,wehave
not provided a list of such rules. Instead, we adopt a practical approach which
involves walking the reader through realistic and concrete modeling projects. In
doingso,wehighlightandcommentontheprocessofabstractingtherealsysteminto
amodel.Themotivationforthisapproachisthatitisakintoapprenticeship,allowing
thereaderbothtoobservepracticalexpertiseandtogeneratepersonalunderstanding
andintuition,whichwillultimatelyhelpthemtoformulatetheirownmodels.
Includedinthebookarepracticalintroductionstoanumberofusefultools,such
as the Maxima computer algebra system, the PRISM model checker, the Repast
Simphony agent modeling environment, and the Smoldyn cellular modeling envi-
ronment. Some of the chapters also include exercises to help the reader sharpen
their understandingof thetopics. Thebook issupportedbya website, http://www.
cs.kent.ac.uk/imb/,whichincludessourcecodeofmanyoftheexamplemodelswe
discuss.
Canterbury, UK David J. Barnes
July 2015 Dominique Chu
vii
Contents
1 Foundations of Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Simulation Versus Analytic Results . . . . . . . . . . . . . . . . . . . . . 3
1.2 Stochastic Versus Deterministic Models . . . . . . . . . . . . . . . . . . 5
1.3 Fundamentals of Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4 Validity and Purpose of Models. . . . . . . . . . . . . . . . . . . . . . . . 11
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2 Agent-Based Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1 Mathematical and Computational Modeling. . . . . . . . . . . . . . . . 16
2.1.1 Limits to Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2 Agent-Based Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2.1 The Structure of ABMs . . . . . . . . . . . . . . . . . . . . . . . . 23
2.2.2 Algorithms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.2.3 Time-Driven Algorithms . . . . . . . . . . . . . . . . . . . . . . . 27
2.2.4 Event-Driven Models. . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.3 Game of Life . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.4 Malaria. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.4.1 A Digression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.4.2 Stochastic Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.4.3 Immobile Agents. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.5 General Considerations When Analyzing a Model . . . . . . . . . . . 46
2.5.1 Testing ABMs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.6 Case Study: The Evolution of Fimbriation . . . . . . . . . . . . . . . . 49
2.6.1 Group Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.6.2 A Model of Martian Mice . . . . . . . . . . . . . . . . . . . . . . 52
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
3 ABMs Using Repast Simphony. . . . . . . . . . . . . . . . . . . . . . . . . . . 79
3.1 Mapping Agent Concepts to Object-Oriented Languages. . . . . . . 80
3.1.1 Hand-Coding an Agent in Java. . . . . . . . . . . . . . . . . . . 81
3.2 The Repast Suite. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
3.2.1 Repast Simphony and ReLogo . . . . . . . . . . . . . . . . . . . 84
3.3 The Game of Life Using ReLogo and Groovy. . . . . . . . . . . . . . 85
ix
x Contents
3.3.1 Creating a New Model. . . . . . . . . . . . . . . . . . . . . . . . . 86
3.3.2 The UserPatch Class . . . . . . . . . . . . . . . . . . . . . . . . . . 87
3.3.3 The UserObserver Class. . . . . . . . . . . . . . . . . . . . . . . . 89
3.3.4 Visualizing the Model . . . . . . . . . . . . . . . . . . . . . . . . . 90
3.3.5 Implementing Cell State. . . . . . . . . . . . . . . . . . . . . . . . 92
3.4 Malaria Model in Repast Using ReLogo. . . . . . . . . . . . . . . . . . 96
3.4.1 The Malaria Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
3.4.2 Creating the Malaria Model . . . . . . . . . . . . . . . . . . . . . 97
3.4.3 A Basic Human Turtle Agent. . . . . . . . . . . . . . . . . . . . 97
3.4.4 Model Parameterization . . . . . . . . . . . . . . . . . . . . . . . . 100
3.4.5 The UserGlobalsAndPanelFactory Class. . . . . . . 101
3.4.6 The @ScheduledMethod Annotation. . . . . . . . . . . . . 102
3.4.7 The Human Agent. . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
3.4.8 parameters.xml and the SimBuilder Class. . . . . . 107
3.4.9 The Mosquito Agent . . . . . . . . . . . . . . . . . . . . . . . . . . 109
3.4.10 Runtime Memory Configuration for Large Models . . . . . 111
3.4.11 Recognizing the Common Elements of the Agents. . . . . . 112
3.4.12 Data Sets and Chart. . . . . . . . . . . . . . . . . . . . . . . . . . . 113
3.4.13 Outputting Data with Text Sinks. . . . . . . . . . . . . . . . . . 114
3.4.14 Batch Runs with Varying Parameter Values . . . . . . . . . . 116
3.4.15 Summary of Concepts Relating to the Malaria Model . . . 118
3.4.16 Going Further with Repast Simphony . . . . . . . . . . . . . . 118
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
4 Differential Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
4.1 Differentiation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
4.1.1 A Mathematical Example. . . . . . . . . . . . . . . . . . . . . . . 126
4.1.2 A Small Digression. . . . . . . . . . . . . . . . . . . . . . . . . . . 129
4.2 Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
4.3 Differential Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
4.3.1 Limits to Growth. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
4.3.2 Steady State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
4.3.3 Bacterial Growth Revisited. . . . . . . . . . . . . . . . . . . . . . 143
4.4 Case Study: Malaria. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
4.4.1 A Brief Note on Stability. . . . . . . . . . . . . . . . . . . . . . . 152
4.5 Chemical Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
4.5.1 Michaelis–Menten and Hill Kinetics . . . . . . . . . . . . . . . 159
4.5.2 Modeling Gene Expression. . . . . . . . . . . . . . . . . . . . . . 165
4.6 Case Study: Cherry and Adler’s Bistable Switch . . . . . . . . . . . . 168
4.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
Contents xi
5 Mathematical Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
5.1 A Word of Warning: Pitfalls of CAS. . . . . . . . . . . . . . . . . . . . 175
5.2 Existing Tools and Types of System . . . . . . . . . . . . . . . . . . . . 177
5.3 Maxima: Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
5.4 Maxima: Simple Sample Sessions . . . . . . . . . . . . . . . . . . . . . . 180
5.4.1 The Basics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
5.4.2 Saving and Recalling Sessions . . . . . . . . . . . . . . . . . . . 185
5.5 Maxima: Beyond Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . 186
5.5.1 Solving Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
5.5.2 Matrices and Eigenvalues. . . . . . . . . . . . . . . . . . . . . . . 189
5.5.3 Graphics and Plotting . . . . . . . . . . . . . . . . . . . . . . . . . 191
5.5.4 Integrating and Differentiating. . . . . . . . . . . . . . . . . . . . 197
5.6 Maxima: Case Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
5.6.1 Gene Expression. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
5.6.2 Malaria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
5.6.3 Cherry and Adler’s Bistable Switch. . . . . . . . . . . . . . . . 203
5.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206
6 Other Stochastic Methods and Prism . . . . . . . . . . . . . . . . . . . . . . 207
6.1 The Master Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
6.2 Partition Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
6.2.1 Weighted Configurations . . . . . . . . . . . . . . . . . . . . . . . 219
6.2.2 Binding to DNA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
6.2.3 Codon Bias in Proteins . . . . . . . . . . . . . . . . . . . . . . . . 226
6.3 Markov Chains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227
6.3.1 Absorbing Markov Chains . . . . . . . . . . . . . . . . . . . . . . 232
6.3.2 Continuous-Time Markov Chains . . . . . . . . . . . . . . . . . 233
6.3.3 An Example from Gene Activation . . . . . . . . . . . . . . . . 235
6.4 Analyzing Markov Chains: Sample Paths . . . . . . . . . . . . . . . . . 237
6.5 Analyzing Markov Chains: Using PRISM. . . . . . . . . . . . . . . . . 239
6.5.1 The PRISM Modeling Language. . . . . . . . . . . . . . . . . . 240
6.5.2 Running PRISM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
6.5.3 Rewards. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248
6.5.4 Simulation in PRISM. . . . . . . . . . . . . . . . . . . . . . . . . . 252
6.5.5 The PRISM GUI. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254
6.6 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256
6.6.1 Fim Switching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256
6.6.2 Stochastic Versions of a Differential Equation. . . . . . . . . 260
6.6.3 Tricks for PRISM Models . . . . . . . . . . . . . . . . . . . . . . 263
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264
