Mathematical investigation of microbial quorum sensing under various flow conditions

Abstract Microorganisms efficiently coordinate phenotype expressions through a decision-making process known as quorum sensing (QS). We investigated QS amongst heterogeneously distributed microbial aggregates under various flow conditions using a process-driven numerical model. Model simulations assess the conditions suitable for QS induction and quantify the importance of advective transport of signaling molecules. In addition, advection dilutes signaling molecules so that faster flow conditions require higher microbial densities, faster signal production rates, or higher sensitivities to signaling molecules to induce QS. However, autoinduction of signal production can substantially increase the transport distance of signaling molecules in both upstream and downstream directions. We present approximate analytical solutions of the advection-diffusion-reaction equation that describe the concentration profiles of signaling molecules for a wide range of flow and reaction rates. These empirical relationships, which predict the distribution of dissolved solutes following zero-order production kinetics along pore channels, allow to quantitatively estimate the effective communication distances amongst multiple microbial aggregates without further numerical simulations. Author Summary Microbes can interact with their surrounding environments by producing and sensing small signaling molecules. When the microbes experience a high enough concentration of the signaling molecules, they express certain phenotypes which is often energetically expensive. This microbial decision-making process known as quorum sensing (QS) has been understood to confer evolutionary benefits. However, it is still not completely understood how transport of the produced signaling molecules affects QS. Using a mathematical approach investigating QS across a range of environmentally relevant flow conditions, we find that advective transport promotes QS downstream yet also dilutes the concentration of signaling molecules. We quantify the importance of microbial cell location with respect to both other microbes and flow direction. By analyzing complex numerical simulation results, we provide analytical approximations to assess the distribution of signaling molecules in pore channels across a range of flow and reaction conditions.