Behavioral dynamic modelling of fast responses: the Escherichia coli SOS system as a case study

The mathematical description of gene expression time profiles is generally a very hard task, given the overwhelming complexity of the underlying molecular components and their interaction network. In this paper we approach this problem from a different perspective: in the presence of very stringent requirements (time, energy consumption,...) the behaviour of a biological entity may be forced to follow a stereotyped pattern amenable, as such, of formal mathematical description. For example, the crowd behavior induced by panic is well described by mathematical models able to accurately simulate group decisions. Here, we discuss the peculiar features of a generic "fast" response at the mRNA level and translate them in a straightforward mathematical model characterized by tunable parameters each having a precise biological meaning. The example of the SOS system in Escherichia coli will be considered together with experimental data provided by our laboratory.