Self-organized traveling wave in a kinetic transport equation for run-and-tumble chemotactic bacteria

Collective motion of chemotactic bacteria, such as E. Coli, relies, at individual level, on a continuous reorientation by alternating runs and tumbles. It has been established that the bacteria modulate the length of run according to a temporal sensing of extracellular chemical cues via an intracellular signal transduction. This chemotactic behavior can be described by a kinetic transport equation with a scattering kernel describing the velocity jump process in the run-and-tumble motions.

We have recently developed the Monte Carlo (MC) code of the kinetic transport equation which takes into account an adaptation dynamics of the intracellular signal transduction and a non-instantaneous tumbling duration. In this talk, we show our recent numerical results for the self-organized pattern formation based on the MC code. Especially, we put forcus on the bimodal aggregation (i.e., the volcano effect) , which is obverved in a micro-scale aggregation of chemtoactic bacteria. We investigated the microscopic and macroscopic mechanism of the volcano effect and clarified the parameter regime for the volcano effect to take place. In addition, we derived a continum-limit model (i.e., an extended Keller-Segel equation), which can reproduce the volcano effect at the appropriate parameter regime, by the asymptotic analysis of the kinetic transport equation.