Section: New Results

Modelling bacterial growth

Various mathematical approaches have been used in the literature to describe the networks of biochemical reactions involved in microbial growth. With various levels of detail, the resulting models provide an integrated view of these reaction networks, including the transport of nutrients from the environment and the metabolism and gene expression allowing the conversion of these nutrients into biomass. The models hence bridge the scale between individual reactions to the growth of cell populations. In a review article published in the Journal of the Royal Society Interface [18], several IBIS members as well as colleagues from the BIOCORE project-team, discuss various models of microbial growth that are, at first sight, quite diverse. They have a different scope and granularity, make different simplifications, use different approaches to obtain predictions from the model structure and have their origin in different fields. In the review we derive a general framework for the kinetic modelling of microbial growth from a few basic hypotheses on the systems of biochemical reactions underlying microbial growth. Additional simplifying assumptions lead to the several families of approximate models of microbial growth found in the literature, including self-replicator models of bacterial growth developed by Nils Giordano in his PhD thesis and published in PLoS Computational Biology last year [5]. This reveals how the models are related on a deeper level and provides a sound basis for further modelling studies.

Analysing the dynamics of some of the network models mentioned above becomes quickly intractable, when mathematical functions are for instance given by complex algebraic expressions resulting from the mass balance of biochemical reactions. In a paper published in the Bulletin of Mathematical Biology [16], Edith Grac, former post-doc in Ibis, Delphine Ropers, and Stefano Casagranda and Jean-Luc Gouzé from the BIOCORE project-team, have studied how monotone system theory and time-scale arguments can be used to reduce high-dimension models based on the mass-action law. Applying the approach to an important positive feedback loop regulating the expression of RNA polymerase in E. coli, made it possible to study the stability of the system steady states and relate the dynamical behaviour of the system to observations on the physiology of the bacterium E. coli.