Introduction to Modeling for Biosciences / Edition 1

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Overview

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, shastic modeling techniques, differential equations and Gillespie’s shastic 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 shastic and differential equation based modeling.

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Editorial Reviews

From the Publisher
From the reviews:

“The intersection of biological and computational sciences is well served by this clear, well-written, and interesting guide to the variety of methods currently being used to formulate computational models for biological systems. … the book very accessible to a wide range of readers—from students to experienced researchers—from a variety of backgrounds. … Thus, this volume is very timely. … Overall, this book is an excellent and approachable introduction to biological modeling.” (Sara Kalvala, ACM Computing Reviews, May, 2011)

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Product Details

  • ISBN-13: 9781849963251
  • Publisher: Springer London
  • Publication date: 8/11/2010
  • Edition description: 2010
  • Edition number: 1
  • Pages: 322
  • Product dimensions: 6.40 (w) x 9.30 (h) x 1.10 (d)

Table of Contents

1 Foundations of Modeling 1

1.1 Simulation vs. Analytic Results 3

1.2 Stochastic vs. Deterministic Models 5

1.3 Fundamentals of Modeling 6

1.4 Validity and Purpose of Models 11

2 Agent-Based Modeling 15

2.1 Mathematical and Computational Modeling 15

2.1.1 Limits to Modeling 17

2.2 Agent-Based Models 21

2.2.1 The Structure of ABMs 22

2.2.2 Algorithms 25

2.2.3 Time-Driven Algorithms 26

2.2.4 Event-Driven Models 28

2.3 Game of Life 30

2.4 Malaria 34

2.4.1 A Digression 37

2.4.2 Stochastic Systems 39

2.4.3 Immobile Agents 43

2.5 General Consideration when Analyzing a Model 46

2.5.1 How to Test ABMs? 47

2.6 Case Study: The Evolution of Fimbriation 48

2.6.1 Group Selection 49

2.6.2 The Model 51

3 ABMs Using Repast and Java 79

3.1 The Basics of Agent-Based Modeling 80

3.2 An Outline of Repast Concepts 83

3.2.1 Contexts and Projections 84

3.2.2 Model Parameterization 86

3.3 The Game of Life in Repast S 87

3.3.1 The model.score File 88

3.3.2 The Agent Class 89

3.3.3 The Model Initializer 103

3.3.4 Summary of Model Creation 104

3.3.5 Running the Model 105

3.3.6 Creating a Display 106

3.3.7 Creating an Agent Style Class 107

3.3.8 Inspecting Agents at Runtime 109

3.3.9 Review 109

3.4 Malaria Model in Repast Using Java 110

3.4.1 The Malaria Model 110

3.4.2 The model.score File 111

3.4.3 Commonalities in the Agent Types 112

3.4.4 Building the Root Context 112

3.4.5 Accessing Runtime Parameter Values 113

3.4.6 Creating a Projection 114

3.4.7 Implementing the Common Elements of the Agents 115

3.4.8 Completing the Mosquito Agent 118

3.4.9 Scheduling the Actions 119

3.4.10 Visualizing the Model 120

3.4.11 Charts 121

3.4.12 Outputting Data 124

3.4.13 A Statistics-Gathering Agent 124

3.4.14 Summary of Concepts Relating to the Malaria Model 127

3.4.15 Running Repast Models Outside Eclipse 128

3.4.16 Going Further with Repast S 130

4 Differential Equations 131

4.1 Differentiation 131

4.1.1 A Mathematical Example 136

4.1.2 Digression 139

4.2 Integration 141

4.3 Differential Equations 144

4.3.1 Limits to Growth 147

4.3.2 Steady State 150

4.3.3 Bacterial Growth Revisited 152

4.4 Case Study: Malaria 154

4.4.1 A Brief Note on Stability 161

4.5 Chemical Reactions 166

4.5.1 Michaelis-Menten and Hill Kinetics 168

4.5.2 Modeling Gene Expression 173

4.6 Case Study: Cherry and Adler's Bistable Switch 177

4.7 Summary 182

5 Mathematical Tools 183

5.1 A Word of Warning: Pitfalls of CAS 183

5.2 Existing Tools and Types of Systems 185

5.3 Maxima: Preliminaries 187

5.4 Maxima: Simple Sample Sessions 189

5.4.1 The Basics 189

5.4.2 Saving and Recalling Sessions 194

5.5 Maxima: Beyond Preliminaries 195

5.5.1 Solving Equations 196

5.5.2 Matrices and Eigenvalues 198

5.5.3 Graphics and Plotting 200

5.5.4 Integrating and Differentiating 205

5.6 Maxima: Case Studies 209

5.6.1 Gene Expression 209

5.6.2 Malaria 210

5.6.3 Cherry and Adler's Bistable Switch 212

5.7 Summary 214

6 Other Stochastic Methods and Prism 215

6.1 The Master Equation 217

6.2 Partition Functions 225

6.2.1 Preferences 227

6.2.2 Binding to DNA 231

6.2.3 Codon Bias in Proteins 235

6.3 Markov Chains 236

6.3.1 Absorbing Markov Chains 240

6.3.2 Continuous Time Markov Chains 242

6.3.3 An Example from Gene Activation 244

6.4 Analyzing Markov Chains: Sample Paths 246

6.5 Analyzing Markov Chains: Using PRISM 248

6.5.1 The PRISM Modeling Language 249

6.5.2 Running PRISM 251

6.5.3 Rewards 257

6.5.4 Simulation in PRISM 261

6.5.5 The PRISM GUI 263

6.6 Examples 264

6.6.1 Fim Switching 265

6.6.2 Stochastic Versions of a Differential Equation 268

6.6.3 Tricks for PRISM Models 270

7 Simulating Biochemical Systems 273

7.1 The Gillespie Algorithms 273

7.1.1 Gillespie's Direct Method 274

7.1.2 Gillespie's First Reaction Method 275

7.1.3 Java Implementation of the Direct Method 276

7.1.4 A Single Reaction 278

7.1.5 Multiple Reactions 279

7.1.6 The Lotka-Volterra Equation 281

7.2 The Gibson-Bruck Algorithm 284

7.2.1 The Dependency Graph 285

7.2.2 The Indexed Priority Queue 285

7.2.3 Updating the τ Values 286

7.2.4 Analysis 288

7.3 A Constant Time Method 289

7.3.1 Selection Procedure 290

7.3.2 Reaction Selection 292

7.4 Practical Implementation Considerations 293

7.4.1 Data Structures-The Dependency Tree 294

7.4.2 Programming Techniques-Tree Updating 295

7.4.3 Runtime Environment 296

7.5 The Tau-Leap Method 297

7.6 Dizzy 297

7.7 Delayed Stochastic Models 301

7.8 The Stochastic Genetic Networks Simulator 303

7.9 Summary 305

A Reference Material 307

A.1 Repast Batch Running 307

A.2 Some Common Rules of Differentiation and Integration 307

A.2.1 Common Differentials 307

A.2.2 Common Integrals 308

A.3 Maxima Notation 309

A.4 PRISM Notation Summary 310

A.5 Some Mathematical Concepts 310

A.5.1 Vectors and Matrices 310

A.5.2 Probability 313

A.5.3 Probability Distributions 314

A.5.4 Taylor Expansion 315

References 317

Index 319

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