The growth of microorganisms involves the conversion of nutrients in the environment into biomass, mostly proteins and other macromolecules. This conversion is accomplished by networks of biochemical reactions cutting across cellular functions, such as metabolism, gene expression, transport and signalling. Mathematical modelling is a powerful tool for gaining an understanding of the functioning of this large and complex system and the role played by individual constituents and mechanisms. This requires models of microbial growth that provide an integrated view of the reaction networks and bridge the scale from individual reactions to the growth of a population. In this review, we derive a general framework for the kinetic modelling of microbial growth from basic hypotheses about the underlying reaction systems. Moreover, we show that several families of approximate models presented in the literature, notably flux balance models and coarse-grained whole-cell models, can be derived with the help of additional simplifying hypotheses. This perspective clearly brings out how apparently quite different modelling approaches are related on a deeper level, and suggests directions for further research.

International audienceWe present a simple method that allows to analyze the biological processes of a dynamical model and classify them. Along the system trajectories, we decompose the model into biological meaningful processes and then study their activity or inactivity during the time evolution of the system. The structure of the model is then reduced to the core mechanisms involving only the active processes. The initial conditions are supposed to lie in some rectangle, that could represent one order of magnitude for the variables. Keeping only the active processes, we obtain the principal processes in the rectangle and then in the adjacent rectangles where the trajectories may have a transition. Finally we obtain a partition of the space with a reduced model within each rectangle. We apply these techniques to a classical model of gene expression with protein and messenger RNA

International audienceUnderstanding the dynamical behavior of biological networks is complicated due to their large number of components and interactions. We present a method to analyse key processes for the system behavior, based on the a priori knowledge of the system trajectory and the simplification of mathematical models of these networks. The method consists of the model decomposition into biologically meaningful processes, whose activity or inactivity is evaluated during the time evolution of the system. The structure of the model is reduced to the core mechanisms involving active processes only. We assess the quality of the reduction by means of global relative errors and apply our method to two models of the circadian rhythm in Drosophila and the influence of RKIP on the ERK signaling pathway