From Qualitative to Quantitative Models of Gene Regulatory Networks in Bacteria

The adaptation of bacteria to changes in their environment involves adjustments in the expression of genes coding for enzymes, regulators, membrane transporters, etc. [14], [26], [17]. These adjustments are controlled by gene regulatory networks ensuring the coordinated expression of clusters of functionally related genes. A realistic view of gene regulatory networks does not only include direct interactions resulting from transcription regulation, but also indirect regulatory interactions mediated by metabolic effectors and signaling molecules. The network controlling carbon uptake in the bacterium Escherichia coli is a case in point. Global regulators like Crp control expression of enzymes in carbon metabolism, while intermediates of the latter pathways control the expression of global regulators. For instance, the phosphorylation of EIIA activates adenylate cyclase (Cya) to produce cAMP which is required for the activation of Crp. Ignoring indirect interactions during the analysis of the network dynamics may lead crucial feedback loops to be missed. I will describe how indirect interactions between genes can be derived from a model of the underlying biochemical reaction network by combining quasi-steady-state approximations expressing weak assumptions on time-scale hierarchies in the system [23], [22], [27] with sensitivity criteria from metabolic control analysis [22], [24]. When applied to a model of the carbon assimilation network in E. coli, the derived gene regulatory network is shown to be densely connected, contrary to what is usually assumed. Moreover, the network is largely sign-determined, meaning that the signs of the indirect interactions are fixed by the flux directions of biochemical reactions, independently of specific parameter values and rate laws. An inversion of the fluxes following a change in growth conditions may affect the signs of the indirect interactions though. This leads to a feedback structure that is at the same time robust to changes in the kinetic properties of enzymes and that has the flexibility to accommodate radical changes in the environment [2]. In theory, it is possible to write down mathematical models of the gene regulatory networks, and study their dynamical properties by means of classical systems analysis tools. In practice, this is not easy to achieve though, as quantitative data on kinetic parameters are usually absent, the models have a large number of variables, and they are strongly nonlinear. This has motivated the interest in qualitative models which, from incomplete knowledge of the system, are