A stochastic model of starvation-survival of Escherichia coli

Abstract

In most natural environments, bacteria experience frequent phases of starvation in between growth periods \cite{Barcina97, Hoehler13, Kjelleberg93, Moriarty93, Morita93, Reese18, Siegele92}. While the kinetics of starvation can vary depending on the species and nutrients involved, bacteria that do not form spores in harsh environments generally undergo loss of viability after several days in starvation \cite{Morita93}. The causes of loss of viability under such circumstances are not widely known. \textit{Escherichia coli} under carbon starvation have often been used as a model system for studying bacterial starvation. In a recent paper, Schink et al. propose that the limiting nutrient cost for carbon-starved \textit{E. coli} is the maintenance of ion homeostasis across the inner membrane and find that starving \textit{E. coli} cells in an osmo-balanced medium results in a significantly reduced death rate \cite{Schink21}. To test if this hypothesis is sufficient to explain the observed kinetics of \textit{E. coli} starvation, we developed a mathematical model of ion homeostasis and membrane permeability. We then conducted both an analytical consideration of the model and numerical MATLAB simulations to compare the expected behavior of the system under the model to experimentally observed phenomena. We found that the model suggests a mathematical basis for many of the important characteristics of starvation-survival kinetics. Additionally, the model was largely successful at replicating the numerical dynamics observed experimentally, with minor discrepancies. These results suggest that understanding the requirements of maintaining ion homeostasis and membrane integrity as a limiting nutrient cost for survival is a viable explanation for the kinetics of \textit{E. coli} survival in under starvation, and indicate that this model should be tested further.