The ErTo model: A dynamical model of optimal protein allocation in E. coli

Abstract

In order to adapt to its environment, E. coli regulates large groups of proteins in cohort using a surprisingly small number of regulators. Despite this, the regulation of protein allocation in E. coli often results in optimal growth rates. Previous studies have illuminated how E. coli distributes its resources between the various groups of resources, and what the resultant growth rates are. This has been done for wildtype E. coli, and for a mutant in which regulation of the group of catabolic proteins is broken. Most studies of protein allocation in E. coli have focused on the steady state regime. However, regulation also happens dynamically, during transitions between steady states. A recent study was able to successfully describe the dynamics of protein sectors and the growth rate under variation of the nutrient source. We derive a model of protein allocation which can potentially describe steady-state and dynamical behaviour of groups of protein and the growth rate, both in wildtype E. coli and the non-regulating mutant. The central assumption is that E. coli maximises its growth rate. Our model is able to capture steady state behaviour well, but fails in the dynam- ical regime. We reveal the paradoxical role of product inhibition of catabolic proteins, which within our framework is both required to predict steady state be- haviour, but prevents accurate prediction of the dynamics of protein allocation. In the future our framework could shed light on the link between production inhibition and regulation in E. coli.