Modeling H + and K + transport across cell membranes

Abstract

This paper presents and analyzes a model for the kinetic behavior of certain ion transport mechanisms known to exist on bacterial cell membranes. Such models are crucial in understanding and predicting microbiological processes and have many important applications. In particular this work may be regarded as an initial step in the development of a more complex model relating to the effects of certain organic acids on homeostasis and osmoregulation in bacteria—these have far-reaching implications in the area of novel food preservation techniques. A model for the transport of hydrogen, H +, and potassium, K +, ions across membranes of Escherichia coli cells is first proposed. A special case of this general model, which takes the form of two coupled, nonlinear, ordinary differential equations, is chosen and studied analytically using simple phase-plane analysis. This not only demonstrates (by reference to existing experimental results) the viability of the model, but also provides information on appropriate magnitudes of many of the parameters appearing in the model. The work also suggests further experimental and theoretical study.