Strong-coupling dynamics of a multi-cellular chemotactic system

Abstract

Chemical signaling is one of the ubiquitous mechanisms by which inter-cellular communication takes place at the microscopic level, particularly via chemotaxis. Such multi-cellular systems are popularly studied using continuum, mean-field equations. In this letter we study a stochastic model of chemotactic signaling. The Langevin formalism of the model makes it amenable to calculation via non-perturbative analysis, which enables a quantification of the effect of fluctuations on both the weak and strongly-coupled biological dynamics. In particular we show that the (i) self-localization due to auto-chemotaxis is impossible. (ii) when aggregation occurs, the aggregate performs a random walk with a renormalized diffusion coefficient $D_R \propto \epsilon^{-2} N^{-3}$. (iii) the stochastic model exhibits sharp transitions in cell motile behavior for negative chemotaxis, behavior which has no parallel in the mean-field Keller-Segel equations.