Dynamic modeling of cooperative protein secretion in microorganism populations

Interactions between microorganisms can have a crucial effect on their population dynamics. Typically, interactions are mediated through the environment by molecules and proteins that are products of cell metabolism and physiology; they therefore reflect the internal dynamics of the single cell. In this work we aim to integrate single-cell properties of gene expression that affect indirect interactions between microorganisms under challenging conditions, into a quantitative model of population dynamics. Specifically we address the problem of a microbial population secreting a protein that can actively extract a growth-limiting resource, such as a simple sugar or iron, from the environment. The genes coding for the protein can undergo random epigenetic transitions between active and silenced states, and can be repressed by the product of their reaction. We model cooperative and competitive interactions between protein producing and non-producing phenotypes by nonlinear dynamical systems and analyze them both in terms of asymptotic states and of transient dynamics. Our model shows that phenotypic transitions allow a stable coexistence of the two phenotypes, and enables us to make predictions regarding the conditions required for such coexistence and the typical timescales of transient dynamics. It also shows how repression by the reaction product induces a feedback at the population-environment level that can result in limit cycle dynamics. The relation of these results to experiments are discussed.