Modelling protection from antimicrobial agents in biofilms through the formation of persister cells

Abstract

A mathematical model of biofilm dynamics was used to investigate the protection from antimicrobial killing that could be afforded to micro-organisms in biofilms based on a mechanism of ‘persister’ cell or phenotypic variant formation. The persister state is a hypothetical, highly protected state adopted by a small fraction of the cells in a biofilm. Persisters were assumed to be generated at a fixed rate, independent of the presence of substrate or antimicrobial agent. Cells were assumed to revert from the persister state when exposed to the growth substrate. Persister cells were assumed to be incapable of growth. The model predicted that persister cells increased in numbers in the biofilm, even though they were unable to grow, accumulating in regions of substrate limitation. In these regions, normal cells failed to grow, but did slowly convert to the persister state. Calculations of persister formation in planktonic cultures predicted that persisters would be present in low numbers in growing cultures, but should accumulate under conditions of slow growth, e.g. very low dilution rates in continuous culture or stationary phase in batch culture. When antibiotic treatment was simulated, bacteria near the biofilm surface were killed, but persisters in the depth of the biofilm were poorly killed. After antibiotic treatment ceased, surviving persister cells quickly reverted and allowed the biofilm to regrow. This modelling study provides motivation for further investigation of the hypothetical persister cell state as an explanation for biofilm resistance to antimicrobial agents.