Transport Models for Collective Dynamics in Biological Systems

Derivation of macroscopic models from the kinetic chemotaxi model incorporating E.coli chemo-sensory system

Min Tang

Shanghai Jiao Tong University

Starting from a kinetic model that incorporate the most recent progresses of the molecular mechanism of the E. coli chemo-sensory system, we derive a momentum system and find its parabolic limit. The original motivation of incorporating the methylation level into the kinetic model is to explain the recent observed "frequency dependent behavior" in spatial-temporal varying environments and the "volcano effect", which can not be explained by the classical Keller-Segal model. In these spatial-temporal fast varying environments, the moment closure used by Othmer et al. in their pioneer work in 2004 is no longer applicable. We introduce in this presentation a different closure strategy based on the fact that the methylation level is locally concentrated. The locally concentrated assumption is verified both analytically and numerically by looking at the individual based monte carlo simulations. We can derive the parabolic limit of this new moment system which has the same form as the Keller-Segal equation. Moreover, this new momentum system can fit the individual based simulations and explain the "frequency dependent behavior" experimental data well.