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 temporal sensing of chemical cues along the pathway.We analyze consequences on URLanized pattern formation resulting from modulation of tumbling frequency with stiff response . Thanks to both analytical arguments and numerical simulations, we show that the stationary homogeneous state of population density is destabilized in realistic ranges of parameters. A remarkable property is that the unstable frequencies remain bounded, as it is the case in Turing instability  . These theoretical developments are in accordance with several biological observations.
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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temporal sensing of
a temporal sensingof
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analyze consequences on URLanized pattern formation resulting from modulation of tumbling frequency with stiff response
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
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Thanks to both analytical arguments and numerical simulations, we show that the stationary homogeneous state of population density is destabilized in realistic ranges of parameters.
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. 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