Mathematical modeling of genetic regulatory networks : Stress responses in Escherichia coli
D. Ropers, H. de Jong, J. Geiselmann
P. Fu, M. Latterich, S. Panke (eds), Systems Biology and Synthetic Biology, John Wiley & Sons, Hoboken, NJ, 2009, 235-271.
Genetic regulatory networks control the expression of the genes of an organism and thus play a key role in its adaptation to the environment. Although genetic regulatory networks have been shaped by evolutionary processes, many aspects of their structure and dynamics can be fruitfully compared with the principles governing man-made systems. This motivates the use of traditional engineering methods based on mathematical modelling and computer simulation to address such questions as the modularity of a regulatory network, the response of the system to perturbations arising from its environment, and the robustness of its behaviour in the presence of noise. In this chapter, we review three approaches towards the modelling of genetic regulatory networks, based on graphs, differential equations, and stochastic master equations, respectively. We discuss examples of modelling studies to see what these approaches have taught us about the capacity of one particular organism, the enterobacterium Escherichia coli, to respond to a variety of environmental stresses. More generally, these examples illustrate the obvious, but often forgotten point that there is no one ’best’ modelling approach, but that different formalisms allow us to address different types of questions.