Pathway Based Mean Field Models for E. Coli Chemotaxis
Professor Xu Yang
Department of Mathematics
UC Santa Barbara
In this talk, we give a mathematical derivation of a pathway- based
mean-field model for E. coli chemotaxis based on the moment closure in
kinetic theory. The pathway based model incorporate the most recent
intracellular chemical dynamics. The derived moment system, under some
assumptions, gets to the chemotaxis model pro- posed in [G. Si, T. Wu,
Q. Quyang and Y. Tu, Phys. Rev. Lett., 109 (2012), 048101], especially
an important physical assumption made in which can be understood
explicitly in this new moment system. We obtain the Keller-Segal limit
by considering the moment system in the regime of long time and strong
tumbling rate. Numerical experiments are presented to show the agreement
of the moment system with (individual based) signaling pathway- based E.
coli chemotaxis simulator ([L. Jiang, Q. Ouyang and Y. Tu, PLoS Comput.
Biol., 6 (2010), e1000735]).