Reaction Kinetic Models of Antibiotic Heteroresistance.

Antal Martinecz,Pia Abel Zur Wiesch,Fabrizio Clarelli,Sören Abel

doi:10.3390/ijms20163965

Antal Martinecz, Pia Abel Zur Wiesch + Show 2 more

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https://doi.org/10.3390/ijms20163965

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Abstract

Bacterial heteroresistance (i.e., the co-existence of several subpopulations with different antibiotic susceptibilities) can delay the clearance of bacteria even with long antibiotic exposure. Some proposed mechanisms have been successfully described with mathematical models of drug-target binding where the mechanism’s downstream of drug-target binding are not explicitly modeled and subsumed in an empirical function, connecting target occupancy to antibiotic action. However, with current approaches it is difficult to model mechanisms that involve multi-step reactions that lead to bacterial killing. Here, we have a dual aim: first, to establish pharmacodynamic models that include multi-step reaction pathways, and second, to model heteroresistance and investigate which molecular heterogeneities can lead to delayed bacterial killing. We show that simulations based on Gillespie algorithms, which have been employed to model reaction kinetics for decades, can be useful tools to model antibiotic action via multi-step reactions. We highlight the strengths and weaknesses of current models and Gillespie simulations. Finally, we show that in our models, slight normally distributed variances in the rates of any event leading to bacterial death can (depending on parameter choices) lead to delayed bacterial killing (i.e., heteroresistance). This means that a slowly declining residual bacterial population due to heteroresistance is most likely the default scenario and should be taken into account when planning treatment length.

Highlights

When bacteria are exposed to antibiotics in vitro or in vivo, the elimination rate often changes dramatically over time
We assess whether hypothetical variations in the parameters of the multistep processes involved in bacterial drug-susceptibility can result in bi- or multiphasic time-kill curves
The aim of this paper is to extend the toolbox for modeling the intracellular processes that kill bacteria and to illustrate how these tools can be used to describe bacterial heteroresistance

Summary

Introduction

When bacteria are exposed to antibiotics in vitro or in vivo, the elimination rate often changes dramatically over time. An initial phase of rapid decline is followed by a phase where bacterial killing is very slow or even absent. The bacteria that survive the rapid decline are not genetically different from those that were killed. When the bacteria are recultured from the surviving population and exposed to antibiotics at the same concentration again, they exhibit the same bi- or multiphasic killing as in the first experiment. This sets delayed bacterial killing apart from stable resistance mutations (antibiotic resistance). Multiphasic bacterial killing has clinical implications: it is thought to complicate treatments, as it allows fractions of bacterial populations to survive extended exposure to antibiotics [1,2]

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