Transport Models for Collective Dynamics in Biological Systems

Kinetic models of chemotaxis and traveling bands

Benoît Perthame

Université Pierre et Marie Curie


Explaining patterns in cell colonies is an old and still continuing subject sometimes called 'socio-micro-biology'. Cells, as bacteria E. coli, communicate through chemicals they emit in their surrounding and to which they also react. Many PDE models have been proposed in this field, in particular the Keller-Segel system is well adpated to describe the phenomena at the colony scale.

Kinetic models of chemotaxis have been used since the 80s, based on experimental observation of the run and tumble movement of bacteria. They are useful to include informations at the individual level through the modulation of run-tumbling frequency. They also allow, through asymptotic analysis, to recover the transport coefficients at the population scale (Keller-Segel system).

We will explain how the microscopic behavior of E. coli and its way to modulate the runs, gives rise to the Flux Limited Keller-Segel equation in the diffusion limit. In opposition to the traditional Keller-Segel system, this new model can sustain robust traveling bands as observed in the famous experiment of Adler.

This work is a collaboration with V. Calvez (ENS Lyon), N. Bournaveas (Univ. Edinburgh), A. Buguin, J. Saragosti and P. Silberzan (Curie Institute, Paris).