Dynamic optimisation of resource allocation in microorganisms

Bacterial growth is a fundamental process in which cells sustain and reproduce themselves from available matter and energy. Optimisation principles have been widely used to explain and predict the growth behaviour of microor-ganisms, assumed to be optimized by evolution. This has given rise, among other things, to bacterial growth laws describing how the abundance of components of the gene expression machinery increases with the growth rate. These studies have mainly focused on the situation where the system is in balanced growth, a steady state in which all cell components grow at the same rate. Balanced-growth conditions, however, are far from natural growth conditions in which the environment is continually changing. We focus on the optimal allocation of resources between the gene expression machinery and other subsystems during growth-phase transitions. We describe an abstract model of the biochemical reaction processes occur-ring in the cell, based on first principles and articulated around two subsystems: the gene expression machinery and the uptake of nutrients from the environment. Using this so-called self-replicator model, we investigate the optimal dynamic reallocation of resources following a rapid change in the environment. We formulate our question as an optimal control problem that can be solved using Pontryagin's maximum principle. Preliminary results have shown the predominance of bang-singular control of resource allocation following abrupt environmental transitions.