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. Analysing the dynamics of some of these 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 [13], 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.

In another paper published in BMC Systems Biology [14], Delphine Ropers and BIOCORE members Stefano Casagranda, Jean-Luc Gouzé, and Suzanne Touzeau, have developed a new approach to deal with model complexity. The approach, named Principle Process Analysis, allows to identify processes playing a key role in the model dynamics and to reduce the complex dynamics to these core processes, omitting processes that are inactive. In particular, it has allowed the reduction of a well-known model of circadian rhythms in mammals into a succession of simpler submodels. Their analysis has resulted in the identification of the source of circadian oscillations, the main oscillator being the negative feedback loop involving proteins PER, CRY, CLOCK-BMAL1, in agreement with previous modelling and experimental studies.

Recent work has shown that coarse-grained models of resource allocation can account for a number of empirical regularities relating the the macromolecular composition of the cell to the growth rate. Some of these models hypothesize control strategies enabling microorganisms to optimize growth. While these studies focus on steady-state growth, such conditions are rarely found in natural habitats, where microorganisms are continually challenged by environmental fluctuations. In recent years, in the framework of the PhD thesis of Nils Giordano, we extended the study of microbial growth strategies to dynamical environments, using a self-replicator model. In collaboration with the BIOCORE project-team, we formulated dynamical growth maximization as an optimal control problem that can be solved using Pontryagin’s Maximum Principle and we compared the theoretical results thus obtained with different possible implementations of growth control in bacterial cells [5]. The extension and experimental validation of some of these results are currently being carried out by Antrea Pavlou in the framework of her PhD project, funded by the ANR project Maximic (Section 7.2).