Multiscale models of taxis-driven patterning in bacterial populations

Abstract. Spatially distributed populations of various types of bacteria often display intricate spatial patterns that are thought to result from the cellular response to gradients of nutrients or other attractants. In the past decade a great deal has been learned about signal transduction, metabolism, and movement in E. coli and other bacteria, but translating the individual-level behavior into population-level dynamics is still a challenging problem. However, this is a necessary step because it is computationally impractical to use a strictly cell-based model to understand patterning in growing populations, since the total number of cells may reach 1012 â1014 in some experiments. In the past phenomenological equations such as the PatlakâKellerâSegel equations have been used in modeling the cell movement that is involved in the formation of such patterns, but the question remains as to how the microscopic behavior can be correctly described by a macroscopic equation. Significant progress has been made for bacterial species that employ a ârun-and-tumble â strategy of movement, in that macroscopic equations based on simplified schemes for signal transduction and turning behavior have been derived [R. Erban and H. G. Othmer, SIAM J. Appl. Math., 65 (2004), pp. 361â391; R. Erban and H. G. Othmer, Multiscale Model. Simul., 3 (2005), pp. 362â394]. Here we extend previous work in a number of directions: (i) we allow for time-dependent signals,