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System Modeling in Cellular BiologyFrom Concepts to Nuts and Bolts$
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Zoltan Szallasi, Jorg Stelling, and Vipul Periwal

Print publication date: 2006

Print ISBN-13: 9780262195485

Published to MIT Press Scholarship Online: August 2013

DOI: 10.7551/mitpress/9780262195485.001.0001

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Kinetics in Spatially Extended Systems

Kinetics in Spatially Extended Systems

Chapter:
(p.177) 9 Kinetics in Spatially Extended Systems
Source:
System Modeling in Cellular Biology
Author(s):

Karsten Kruse

Johan Elf

Publisher:
The MIT Press
DOI:10.7551/mitpress/9780262195485.003.0009

This chapter presents theoretical approaches for describing the dynamics of biological systems. The first part discusses continuum descriptions in terms of partial differential equations. Such a description is appropriate if one is interested in the dynamics on scales that are large compared to molecular length scales as, for example, interaction distances of single molecules. The second part provides stochastic description in terms of the reaction-diffusion master equation. It is a generalization of techniques presented in Chapter 8 to account for inhomogeneous particle distributions. It shows that in the limit of many reactants within the diffusion range, the reaction-diffusion master equation is well approximated by a continuum description. The different approaches are illustrated by application to the Min-system of the bacterium Escherichia coli as well as other subcellular systems.

Keywords:   biological systems, continuum descriptions, stochastic description, partial differential equations, reaction-diffusion master equation, Min-system, Escherichia coli

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