Description

Stochastic kinetic methods are currently considered to be the most realistic and elegant means of representing and simulating the dynamics of biochemical and biological networks. Deterministic versus stochastic modelling in biochemistry and systems biology introduces and critically reviews the deterministic and stochastic foundations of biochemical kinetics, covering applied stochastic process theory for application in the field of modelling and simulation of biological processes at the molecular scale. Following an overview of deterministic chemical kinetics and the stochastic approach to biochemical kinetics, the book goes onto discuss the specifics of stochastic simulation algorithms, modelling in systems biology and the structure of biochemical models. Later chapters cover reaction-diffusion systems, and provide an analysis of the Kinfer and BlenX software systems. The final chapter looks at simulation of ecodynamics and food web dynamics.

Key Features

  • Introduces mathematical concepts and formalisms of deterministic and stochastic modelling through clear and simple examples
  • Presents recently developed discrete stochastic formalisms for modelling biological systems and processes
  • Describes and applies stochastic simulation algorithms to implement a stochastic formulation of biochemical and biological kinetics

Readership

Researchers and students studying and working in the field of modelling and simulation of biological processes at molecular scale

Table of Contents

List of figures

List of tables

Preface

About the Authors and Contributors

Chapter 1: Deterministic chemical kinetics

Abstract:

1.1 Determinism and Chemistry

1.2 The Material Balance

1.3 The Rate Law

1.4 Solving the Conservation Equations

1.5 Simple Reaction Mechanisms

1.6 The Law of Mass Action

1.7 Conclusions

Chapter 2: The stochastic approach to biochemical kinetics

Abstract:

2.1 Introduction

2.2 The chemical master equation

2.3 Solution of the Master Equation

The irreversible reaction A → B

The Irreversible Reaction A + B → C

Other Irreversible Bimolecular Reactions

The reversible reaction A + B C at equilibrium

Other reversible bimolecular reactions at equilibrium

2.4 The relationship between the deterministic and stochastic formalisms

Chapter 3: The exact stochastic simulation algorithms

Abstract.

3.1 Introduction

3.2 The reaction probability density function

3.3 The stochastic simulation algorithms

3.4 Case studies

3.5 Caveats regarding the modeling of living systems

Chapter 4: Modelling in systems biology

Abstract

4.1 What is biological modeling

4.2 System Biology

4.3 Complexity of a biological system

4.4 Stochastic modeling approach

4.5 Formalizing complexity

Chapter 5: The structure of biochemical models

Abstract

5.1 Classification of biological processes and mathematical formalism

5.2 Spatially Homogeneous Models

5.3 Variants of the SSA for non-Markovian and non-homogeneous processes

Chapter 6: Reaction-diffusion systems

Abstract

6.1 Introduction

6.2 A generalization of the Fick’s law

6.3 The optimal size

Details

No. of pages:
390
Language:
English
Copyright:
© 2013
Published:
Imprint:
Woodhead Publishing
Print ISBN:
9781907568626
Electronic ISBN:
9781908818218