Population Dynamics Approach for the Study of Synergetic Coupling between Antibiotic and Helper Compounds

Abstract

Non-antibiotics affect bacterial susceptibility towards antibiotics in a multifactorial manner, including perturbation of membrane energetic and a possibly direct interaction with drug efflux transporters themselves. Thus, efflux inhibiting compounds affect susceptibilities to antibiotics that act either intracellular or at the bacterial wall. Therefore they may be applied as helper compounds to conventional antibiotic treatments. A valid definition of the effect of these compounds is crucial. Conventional microbiological quotations such as checkerboard or MIC definition do not discriminate the complexity of a system where several compounds interact with several targets both on the bacterial membrane and soma. We presume the fact, that certain resistance mechanisms, such as efflux, are neither adequately nor precisely monitored, utilizing the established microbiologic screening tools, such as agar- or microdilution techniques. In this context this paper may contribute as an innovative step, utilizing mathematic modeling in order to describe interactions on the surface of microorganisms. Thus, mathematical modeling might be a tool which can be adopted to optimize the description of certain forms of bacterial resistance, as well as the influence of antibacterial drugs on such targets which interact with bacterial outer-membrane transport mechanisms. This paper presents modeling of bacterial population dynamics as an attempt to precise complex compound target interaction. Furthermore, the importance of a synergetic coupling term in the model is exemplified by comparison with experimental data of Kumar et al. [1]. A specific procedure for extraction of model coefficients is devised for further experimental studies of the coupling between an antibiotics and a helper compound. In particular, it is found that the scarce experimental data of Kumar et al. [1] can be fitted to the mathematical model demonstrating synergetic effects of non-antibiotics.