Introduction to Modeling for Biosciences

by Barnes, David J.; Chu, Dominique

• ISBN13: 9781849963251
• ISBN10: 1849963258
• Format: Hardcover
• Copyright: 2010-08-17
• Publisher: Springer-Verlag New York Inc

Summary

Mathematical modeling can be a useful tool for researchers in the biological scientists. Yet in biological modeling there is no one modeling technique that is suitable for all problems. Instead, different problems call for different approaches. Furthermore, it can be helpful to analyze the same system using a variety of approaches, to be able to exploit the advantages and drawbacks of each. In practice, it is often unclear which modeling approaches will be most suitable for a particular biological question, a problem which requires researchers to know a reasonable amount about a number of techniques, rather than become experts on a single one."Introduction to Modeling for Biosciences" addresses this issue by presenting a broad overview of the most important techniques used to model biological systems. In addition to providing an introduction into the use of a wide range of software tools and modeling environments, this helpful text/reference describes the constraints and difficulties that each modeling technique presents in practice, enabling the researcher to quickly determine which software package would be most useful for their particular problem.Topics and features: introduces a basic array of techniques to formulate models of biological systems, and to solve them; intersperses the text with exercises throughout the book; includes practical introductions to the Maxima computer algebra system, the PRISM model checker, and the Repast Simphony agent modeling environment; discusses agent-based models, stochastic modeling techniques, differential equations and Gillespie's stochastic simulation algorithm; contains appendices on Repast batch running, rules of differentiation and integration, Maxima and PRISM notation, and some additional mathematical concepts; supplies source code for many of the example models discussed, at the associated website http://www.cs.kent.ac.uk/imb/.This unique and practical guide leads the novice modeler through realistic and concrete modeling projects, highlighting and commenting on the process of abstracting the real system into a model. Students and active researchers in the biosciences will also benefit from the discussions of the high-quality, tried-and-tested modeling tools described in the book.Dr. David J. Barnes is a lecturer in computer science at the University of Kent, UK, with a strong background in the teaching of programming. Dr. Dominique Chu is a lecturer in computer science at the University of Kent, UK. He is an internationally recognized expert in agent-based modeling, and has also in-depth research experience in stochastic and differential equation based modeling.

Author Biography

David J. Barnes is a lecturer in computer science at the University of Kent, UK, with a strong background in the teaching of programming.

Table of Contents

Foundations of Modeling	p. 1
Simulation vs. Analytic Results	p. 3
Stochastic vs. Deterministic Models	p. 5
Fundamentals of Modeling	p. 6
Validity and Purpose of Models	p. 11
Agent-Based Modeling	p. 15
Mathematical and Computational Modeling	p. 15
Limits to Modeling	p. 17
Agent-Based Models	p. 21
The Structure of ABMs	p. 22
Algorithms	p. 25
Time-Driven Algorithms	p. 26
Event-Driven Models	p. 28
Game of Life	p. 30
Malaria	p. 34
A Digression	p. 37
Stochastic Systems	p. 39
Immobile Agents	p. 43
General Consideration when Analyzing a Model	p. 46
How to Test ABMs?	p. 47
Case Study: The Evolution of Fimbriation	p. 48
Group Selection	p. 49
The Model	p. 51
ABMs Using Repast and Java	p. 79
The Basics of Agent-Based Modeling	p. 80
An Outline of Repast Concepts	p. 83
Contexts and Projections	p. 84
Model Parameterization	p. 86
The Game of Life in Repast S	p. 87
The model.score File	p. 88
The Agent Class	p. 89
The Model Initializer	p. 103
Summary of Model Creation	p. 104
Running the Model	p. 105
Creating a Display	p. 106
Creating an Agent Style Class	p. 107
Inspecting Agents at Runtime	p. 109
Review	p. 109
Malaria Model in Repast Using Java	p. 110
The Malaria Model	p. 110
The model.score File	p. 111
Commonalities in the Agent Types	p. 112
Building the Root Context	p. 112
Accessing Runtime Parameter Values	p. 113
Creating a Projection	p. 114
Implementing the Common Elements of the Agents	p. 115
Completing the Mosquito Agent	p. 118
Scheduling the Actions	p. 119
Visualizing the Model	p. 120
Charts	p. 121
Outputting Data	p. 124
A Statistics-Gathering Agent	p. 124
Summary of Concepts Relating to the Malaria Model	p. 127
Running Repast Models Outside Eclipse	p. 128
Going Further with Repast S	p. 130
Differential Equations	p. 131
Differentiation	p. 131
A Mathematical Example	p. 136
Digression	p. 139
Integration	p. 141
Differential Equations	p. 144
Limits to Growth	p. 147
Steady State	p. 150
Bacterial Growth Revisited	p. 152
Case Study: Malaria	p. 154
A Brief Note on Stability	p. 161
Chemical Reactions	p. 166
Michaelis-Menten and Hill Kinetics	p. 168
Modeling Gene Expression	p. 173
Case Study: Cherry and Adler's Bistable Switch	p. 177
Summary	p. 182
Mathematical Tools	p. 183
A Word of Warning: Pitfalls of CAS	p. 183
Existing Tools and Types of Systems	p. 185
Maxima: Preliminaries	p. 187
Maxima: Simple Sample Sessions	p. 189
The Basics	p. 189
Saving and Recalling Sessions	p. 194
Maxima: Beyond Preliminaries	p. 195
Solving Equations	p. 196
Matrices and Eigenvalues	p. 198
Graphics and Plotting	p. 200
Integrating and Differentiating	p. 205
Maxima: Case Studies	p. 209
Gene Expression	p. 209
Malaria	p. 210
Cherry and Adler's Bistable Switch	p. 212
Summary	p. 214
Other Stochastic Methods and Prism	p. 215
The Master Equation	p. 217
Partition Functions	p. 225
Preferences	p. 227
Binding to DNA	p. 231
Codon Bias in Proteins	p. 235
Markov Chains	p. 236
Absorbing Markov Chains	p. 240
Continuous Time Markov Chains	p. 242
An Example from Gene Activation	p. 244
Analyzing Markov Chains: Sample Paths	p. 246
Analyzing Markov Chains: Using PRISM	p. 248
The PRISM Modeling Language	p. 249
Running PRISM	p. 251
Rewards	p. 257
Simulation in PRISM	p. 261
The PRISM GUI	p. 263
Examples	p. 264
Fim Switching	p. 265
Stochastic Versions of a Differential Equation	p. 268
Tricks for PRISM Models	p. 270
Simulating Biochemical Systems	p. 273
The Gillespie Algorithms	p. 273
Gillespie's Direct Method	p. 274
Gillespie's First Reaction Method	p. 275
Java Implementation of the Direct Method	p. 276
A Single Reaction	p. 278
Multiple Reactions	p. 279
The Lotka-Volterra Equation	p. 281
The Gibson-Bruck Algorithm	p. 284
The Dependency Graph	p. 285
The Indexed Priority Queue	p. 285
Updating the ¿ Values	p. 286
Analysis	p. 288
A Constant Time Method	p. 289
Selection Procedure	p. 290
Reaction Selection	p. 292
Practical Implementation Considerations	p. 293
Data Structures-The Dependency Tree	p. 294
Programming Techniques-Tree Updating	p. 295
Runtime Environment	p. 296
The Tau-Leap Method	p. 297
Dizzy	p. 297
Delayed Stochastic Models	p. 301
The Stochastic Genetic Networks Simulator	p. 303
Summary	p. 305
Reference Material	p. 307
Repast Batch Running	p. 307
Some Common Rules of Differentiation and Integration	p. 307
Common Differentials	p. 307
Common Integrals	p. 308
Maxima Notation	p. 309
PRISM Notation Summary	p. 310
Some Mathematical Concepts	p. 310
Vectors and Matrices	p. 310
Probability	p. 313
Probability Distributions	p. 314
Taylor Expansion	p. 315
References	p. 317
Index	p. 319
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