PIMS - CSC Seminar: Min Tang

Recently, the biochemical pathways regulating the flagellar motors were uncovered. This knowledge gave rise to a class of kinetic-transport equations, that takes into account an intra-cellular molecular content and which relates the tumbling frequency to this information. It turns out that the tumbling frequency depends on the chemotactic signal, and not on its gradient. We first derive the standard Kinetic-transport model which heuristically includes tumbling frequencies depending on the path-wise gradient of chemotactic signal, after appropriate rescaling. The main difficulty is to explain why the path-wise gradient of chemotactic signal can arise in this asymptotic process. And then build a new kinetic system of PBMFT under the assumption that the methylation level is locally concentrated, whose turning operator takes into account the dynamical intracellular pathway.

We recover the PBMFT proposed by Si et al. as the hyperbolic limit and connect to the Keller-Segel equation as the parabolic limit of this new model. An augmented Keller-Segel equation with macroscopic intercellular signaling pathway dynamics, which can explain the experimental observation in fast varying environment is proposed.