Modeling antibiotic tolerance in biofilms by accounting for nutrient limitation

Abstract

A mathematical model of biofilm dynamics was used to investigate the protection from antibiotic killing that can be afforded to microorganisms in biofilms based on a mechanism of localized nutrient limitation and slow growth. The model assumed that the rate of killing by the antibiotic was directly proportional to the local growth rate. Growth rates in the biofilm were calculated by using the local concentration of a single growth-limiting substrate with Monod kinetics. The concentration profile of this metabolic substrate was calculated by solving a reaction-diffusion problem. The model predicted the following features: stratified patterns of growth with zones of no growth in the biofilm interior, slow killing of biofilm microorganisms that was further retarded as the initial biofilm thickness increased, nonuniform spatial patterns of killing inside the biofilm, biofilm killing rates that decrease in a nonlinear way as the concentration of the growth-limiting substrate feeding the biofilm is decreased, and heightened tolerance when external mass transfer resistance is manifested. This modeling study also provides motivation for further investigation of a hypothetical cell state in which damaged cells score as nonviable but continue to consume substrate. The existence of such a cell state can further retard biofilm killing, according to the simulations. The results support the important contributions of nutrient limitation and slow growth to the antibiotic tolerance of microorganisms in biofilms.