Section: New Results

Analysis of metabolic coupling in gene regulatory networks

The regulation of gene expression is tightly interwoven with metabolism and signal transduction. A realistic view of genetic regulatory networks should therefore not only include direct interactions resulting from transcription regulation, but also indirect regulatory interactions mediated by metabolic effectors and signaling molecules. We coined the term metabolic coupling to denote these indirect interactions mediated by metabolism. Ignoring metabolic coupling during the analysis of the network dynamics may lead crucial feedback loops to be missed.

In previous work, published in PLoS Computational Biology in 2010, we showed how indirect interactions arising from metabolic coupling can be derived from a model of the underlying biochemical reaction network. We applied this approach to the carbon assimilation network in Escherichia coli investigating how the structural properties of the network are modified by the inclusion of metabolic interactions. Our results showed that the derived gene regulatory network is densely connected, contrary to what is usually assumed. Moreover, we found that the signs of the indirect interactions are largely fixed by the direction of metabolic fluxes, independently of specific parameter values and rate laws, and that a change in flux direction may invert the sign of indirect interactions. 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.

It remains an open question, however, to which extent the indirect interactions induced by metabolic coupling affect the dynamics of the system. This is a key issue for understanding the relative contributions of the regulation of gene expression and metabolism during the adaptation of the cell to changes in its environment. In collaboration with Valentina Baldazzi, formerly post-doctoral fellow in IBIS and now research scientist at INRA (Avignon), we have carried out a dynamic analysis by developing a qualitative PL model of the gene regulatory network, including both the direct and indirect interactions. We previously showed, in a paper published in the IEEE/ACM Transactions on Computational Biology and Bioinformatics this year, that PL models provide a good approximation of the direct and indirect interactions occurring in gene regulation [10] .

In order to obtain a clearer view of the dynamic role of metabolic coupling in the adaptation of gene expression, we developed several qualitative models corresponding to a network topology including all, some, or none of the indirect interactions. The dynamical properties of the models were analyzed and compared with available experimental data using the computer tool GNA (Section  5.1 ). In particular, we compared the steady-state concentrations of enzymes and transcription regulators during growth on glucose and acetate, as well as the dynamic response of gene expression to the exhaustion of glucose and the subsequent assimilation of acetate. We find significant differences between the dynamics of the system in the absence and presence of metabolic coupling. This confirms that indirect interactions are essential for correctly reproducing the observed adaptation of gene expression to a change in carbon source. Our work thus underlines the importance of metabolic coupling in gene regulatory networks, and shows that such indirect interactions cannot be neglected when studying the adaptation of an organism to changes in its environment. A short, preliminary paper on this work was presented at an invited session of the 18th IFAC World Congress held in Milano [12] and a long paper has been accepted for publication in the Journal of Theoretical Biology [2] .