Mathematical Modelling of Bacterial Quorum Sensing: A Review

Abstract

Bacterial quorum sensing (QS) refers to the process of cell-to-cell bacterial communication enabled through the production and sensing of the local concentration of small molecules called autoinducers to regulate the production of gene products (e.g. enzymes or virulence factors). Through autoinducers, bacteria interact with individuals of the same species, other bacterial species, and with their host. Among QS-regulated processes mediated through autoinducers are aggregation, biofilm formation, bioluminescence, and sporulation. Autoinducers are therefore "master" regulators of bacterial lifestyles. For over 10 years, mathematical modelling of QS has sought, in parallel to experimental discoveries, to elucidate the mechanisms regulating this process. In this review, we present the progress in mathematical modelling of QS, highlighting the various theoretical approaches that have been used and discussing some of the insights that have emerged. Modelling of QS has benefited almost from the onset of the involvement of experimentalists, with many of the papers which we review, published in non-mathematical journals. This review therefore attempts to give a broad overview of the topic to the mathematical biology community, as well as the current modelling efforts and future challenges.B Judith Pérez-Velázquez

Ecological feedback in quorum-sensing microbial populations can induce heterogeneous production of autoinducers

“…Thus, stochastic gene expression explains the coexistence of different phenotypic states in one population in many experimental situations [76][77][78][79][80][81][82]. In the context of quorum sensing, the level of autoinducers in the population is the environmental cue that triggers the stochastic switch between 'on' and 'off' state explaining heterogeneous autoinducer production when the response function is bistable [22][23][24][25]. In other words, bistable regulation together with stochastic gene expression can explain a bimodal autoinducer synthesis in the population.…”

“…For the mean production, that is for the expectation value of the production distribution, it holds that p = M 1 = C 1 and the variance is given by Var(p) = p 2 − p 2 = M 2 − M 2 1 = C 2 . By applying transformations (23,24) to the mean-field equation (1) and plugging in the form of the fitness function in equation (4), one obtains:…”

“…From an experimental point of view it is often not known, however, whether autoinducer synthesis is up-regulated for all autoinducer levels or only above a threshold level. To explain phenotypic heterogeneity of autoinducer production, currently favored threshold models of quorum sensing typically assume a bistable gene regulation function [22][23][24][25]. For bistable regulation, cellular autoinducer synthesis is up-regulated above a threshold value of the autoinducer concentration in the population, whereas it is down-regulated below the threshold ("all-or-none" expression); see Fig.…”

Front-propagation in bacterial inter-colony communication

“…Research on the processes involved in quorum sensing has long been reinforced by theoretical studies, taking into account factors like flow, diffusion, adhesion, decay or degradation of the signaling molecules, or growth of the signal-producing population (reviewed in [16]). However, these studies often focus on processes in single cells, or cells in well-mixed liquid systems.…”

Computational Exploration of Putative LuxR Solos in Archaea and Their Functional Implications in Quorum Sensing

“…During the process, QSSMs are synthesized and secreted out from the cells, which further sensed by it or other cells to continue the cascade (Parsek and Greenberg, 2000; Kim et al, 2005). These QSSMs help microbial world to establish diverse vital processes propelled by QS like biofilm formation, secretion of various virulence factors, sporulation, motility, bioluminescence, and many more (Nealson et al, 1970; Henrichsen, 1972; Costerton et al, 1978; Rumbaugh et al, 1999; Yarwood and Schlievert, 2003; Parsek and Greenberg, 2005; Li et al, 2011; Perez-Velazquez et al, 2016). …”