Theoretical Investigation of the Role of Protein-DNA Search in Quorum Sensing Cells

Abstract

Quorum sensing (QS) is a cellular interaction mechanism in bacteria that regulates gene expression. The search and binding of the AHL-bound LuxR-type proteins to specific sites on DNA in QS cells of Gram-negative bacteria is a complex process and we have theoretically investigated it using a simple discrete-state model. We have shown that several factors such as the rate of formation of the AHL-bound LuxR protein within the cells and its dissociation to freely diffusing autoinducer molecule (AHL), the diffusion of the latter in and out of the cells, the presence of a feedback loop and the cell population density is very important in the protein target search and can control the gene regulation processes. We also explain these observations physically. We have also performed stochastic simulations to validate our theoretical results. We have also looked at a different problem where we calculated transit time distributions in inertial active particles. Transition path times are defined as the time taken by a particle to make a transition between two stable molecular conformers. Typically, active forces cause enhanced diffusion, superdiffusion. ATP dependent forces present in a cell disrupt the equilibrium in the environment, thereby causing active forces. We have obtained an analytical expression of the transit times for such systems and have also performed simulations to validate our analytical results. We have also found approximate expressions in the short and the long time limits. In addition to this, we have derived approximately the mean transition path time