Morphological Stability of Chemotactic Fronts

Fronts – propagating interfaces that allow one spatial domain to invade another – are ubiquitous in nature. One of the most fundamental characteristics of a front is its morphological stability: Do shape perturbations decay or grow over time? While this question is well-studied for diverse classes of fronts, the conditions for the stability of chemotactic fronts – in which active agents collectively migrate in response to a self-generated chemical gradient – remain unknown, despite the prevalence of such fronts in biological and active matter. Here, we combine experiments, simulations, and theory to examine the stability of chemotactic fronts formed by migrating populations of E. coli. We identify two distinct modes in which chemotaxis influences the morphology of the population: cells in different locations along a front migrate at different velocities due to spatial variations in (i) the local nutrient gradient and in (ii) the ability of individual cells to sense and respond to the local nutrient gradient. The competition between these two modes regulates the overall stability of the front. Guided by these findings, we suggest that the cells' sensory machinery might have evolved to ensure stable front propagation. Moreover, as sensing of any stimuli is necessarily limited in living and active matter in general, the link between sensing by individuals and the morphological stability of an entire population revealed by our work may operate in other types of directed migration such as durotaxis, electrotaxis, and phototaxis.