Deterministic Versus Stochastic Modelling in Biochemistry and Systems Biology - 1st Edition - ISBN: 9781907568626, 9781908818218

Deterministic Versus Stochastic Modelling in Biochemistry and Systems Biology

1st Edition

Authors: Paulo Lecca Ian Laurenzi Ferenc Jordan
eBook ISBN: 9781908818218
Hardcover ISBN: 9781907568626
Imprint: Woodhead Publishing
Published Date: 9th April 2013
Page Count: 390
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Table of Contents

List of figures

List of tables


About the Authors and Contributors

Chapter 1: Deterministic chemical kinetics


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


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


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


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


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


6.1 Introduction

6.2 A generalization of the Fick’s law

6.3 The optimal size of the system’s subvolumes

6.4 The algorithm and data structure

6.5 Case study 1: chaperone-assisted folding

6.6 Case study 2: modeling the formation of Bicoid gradient

6.7 Conclusions and future directions

Chapter 7: KInfer: a tool for model calibration


7.1 Introduction

7.2 The model for inference

7.3 Synthetic case study: buffering SERCA pump

7.4 Real case studies

7.5 Glucose metabolisms of Lactococcus lactis

7.6 Discussion

Chapter 8: Modelling living systems with BlenX


8.1 Deterministic vs stochastic approach in systems biology

8.2 The BlenX language

8.3 The ubiquitin-proteasome system

8.4 A predator-prey model

8.5 Conclusions

Chapter 9: Simulation of ecodynamics: key nodes in food webs


9.1 Systems ecology

9.2 Ecological interaction networks

9.3 Pattern and process

9.4 Food web dynamics: simulation and sensitivity analysis




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


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


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© Woodhead Publishing 2013
Woodhead Publishing
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About the Authors

Paulo Lecca Author

Paola Lecca is a researcher at The Microsoft Research, University of Trento, Centre for Computational and Systems Biology, Italy. Her principal research interests include biochemical system identification and model calibration, stochastic chemical kinetics and reaction-diffusion system.

Affiliations and Expertise

The Microsoft Research – University of Trento, COSBI, Italy

Ian Laurenzi Author

Ian J. Laurenzi is a Senior Researcher at ExxonMobil. He is an expert in the areas of stochastic processes, statistics, computational biology and receptor-mediated adhesion of human blood platelets, and has investigated the genome-level dynamics of gene networks and the effect of sex upon mammalian gene expression.

Affiliations and Expertise

ExxonMobil, USA

Ferenc Jordan Author

Affiliations and Expertise

The Microsoft Research – University of Trento, Center for Computational and Systems Biology, Trento, Italy