Stiff-response-induced instability for chemotactic bacteria and flux-limited Keller-Segel equation

Abstract

Collective motion of chemotactic bacteria as E. Coli relies, at the individual level, on a continuous reorientation by runs and tumbles. It has been established that the length of run is decided by a stiff response to a temporal sensingof chemical cues along the pathway.We describe a novel mechanism for pattern formation stemming from the stiffness of chemotactic response relying on a kinetic chemotaxis model which includes a recently discovered formalism for the bacterial chemotaxis. We prove instability both for amicroscopic description in the space-velocity space and for the macroscopic equation, a flux-limited Keller-Segel equation, which has attracted much attention recently.A remarkable property is that the unstable frequencies remain bounded, as it is the case in Turing instability. Numerical illustrations based on a powerful Monte Carlo method show that the stationary homogeneous state of population density isdestabilized and periodic patterns are generated in realistic ranges of parameters. These theoretical developments are in accordance with several biological observations.

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Cited by in corpus (8)

• Traveling Wave and Aggregation in a Flux-Limited Keller-Segel Model
• Kinetic theory for a simple modeling of phase transition: Dynamics out of local equilibrium
• Multiple asymptotics of Kinetic Equations with Internal States
• A critical blow-up exponent for flux limitation in a Keller-Segel system
• Effects of internal dynamics on chemotactic aggregation of bacteria
• Kinetic chemotaxis tumbling kernel determined from macroscopic quantities
• Numerical study of the volcano e ect in chemotactic aggregation based on a kinetic transport equation with non-instantaneous tumbling
• Motility switching and front-back synchronisation in polarized cells