Abstract:
Quorum sensing (QS) is a bacterial communication process in which cells detect the local environment and collectively activate gene expression. The transcriptional activator (LuxR) for these genes has a specific allosteric site where the autoinducer (AHL) can bind and turn the activator on. At the single-cell level, the response to gene activation is poorly coordinated among the QS population which leads to heterogeneity in an isogenic population. The paper presents a theoretical framework that uses a discrete-state stochastic approach to address the issue of heterogeneity in the context of DNA target search processes in QS cells and takes into account the relevant physical–chemical processes. This minimal model allows us to understand the molecular mechanisms of the protein target search in the context of cell heterogeneity, and evaluate the analytical expression of the protein search times for the targets on DNA. Specifically, it is shown that the variations in AHL and LuxR binding rates, arising from the asymmetric distribution of LuxR proteins in the cell population, can cause significant variations in the target search on the DNA. It is also found that the intrinsic heterogeneity in the cell population can affect the average search time and this in turn depends on the AHL and LuxR binding rates. Proposed theoretical results have been validated by Monte Carlo simulations.