Methods : Analysis and simulation of bacterial regulatory networks
Computer simulation is a powerful tool for explaining the capability of bacteria to adapt to sudden changes in their environment in terms of structural features of the underlying regulatory network, such as interlocked positive and negative feedback loops. Moreover, computer simulation allows the prediction of unexpected or otherwise interesting phenomena that call for experimental verification. The use of simplified models of the stress response networks makes simulation easier in two respects. In the first place, model reduction restricts the class of models to a form that is usually easier to treat mathematically, in particular when quantitative information on the model parameters is absent or unreliable. Second, in situations where quantitative precision is necessary, the estimation of parameter values from available experimental data is easier to achieve when using models with a reduced number of parameters.
Over the past few years, we have developed a qualitative simulation method adapted to a class of piecewise-linear (PL) differential equation models of genetic regulatory networks. The PL models, originally introduced by Leon Glass and Stuart Kauffman, and related to the logical models of René Thomas, provide a coarse-grained picture of the dynamics of genetic regulatory networks. They associate a protein or mRNA concentration variable to each of the genes in the network, and capture the switch-like character of gene regulation by means of step functions that change their value at a threshold concentration of the proteins. The advantage of using PL models is that the qualitative dynamics of the high-dimensional systems are relatively simple to analyze, using inequality constraints on the parameters rather than exact numerical values. The qualitative dynamics of genetic regulatory networks can be conveniently analyzed by means of discrete abstractions that transform the PL model into so-called state transition graphs.
Left : Example of a genetic regulatory network of two genes (a and b), each coding for a regulatory protein (A and B). Protein B inhibits the expression of gene a, while protein A inhibits the expression of gene b and its own gene. Right : PL model with step functions describing this genetic regulatory network.
Source : Batt et al. (2008), Automatica, 44(4):982-989.
The development and analysis of PL models of genetic regulatory network has been implemented in the qualitative simulation tool Genetic Network Analyzer (GNA). GNA has been used for the analysis of several bacterial regulatory networks, such as the initiation of sporulation in B. subtilis, quorum sensing in P. aeruginosa, the carbon starvation response in E. coli, and the onset of virulence in E. chrysanthemi. GNA is currently distributed by the Genostar company, but remains freely available for academic research. The analysis of realistic models of bacterial regulatory networks by means of GNA leads to large state transition graphs, which makes manual verification of properties of interest practically infeasible. This has motivated the coupling of GNA to formal verification tools, in particular model checkers that allow properties formulated in temporal logic to be verified on state transition graphs.