Holling Type I versus Holling Type II functional responses in Gram-negative bacteria

Abstract

We consider how the double-membrane structure of the cell envelope of Gram-negative bacteria affects its functional response, which is the mathematical relationship that expresses how the nutrient uptake flux depends on environmental conditions. We show that, under suitable conditions, the Holling Type I functional response is a plausible model, as opposed to the Holling Type II (rectangular hyperbolic, ‘Michaelis–Menten’) response that is the default model in much of the literature. We investigate both diffusion-limited and capacity-limited regimes. Furthermore, we reconcile our findings with the preponderance in the established literature of hyperbolic models for the growth response, which are generally assumed to be valid, for both Gram-negative and Gram-positive bacteria. Finally, we consider the phenomenon of dynamic adjustment of investment of molecular building blocks in cellular components, and show how this will affect the functional response as observed by the experimenter.