Extended Keller-Segel model of chemotactic migration in heterogeneous porous media

How bacteria move in heterogeneous porous media like tissues and soil underlies processes like infection and bioremediation. However, existing models of bacteria transport fail to describe collective migration in porous media. To address this gap in knowledge, we use direct observation of bacteria populations inside transparent porous media that form traveling fronts following self-generated nutrient gradients. Unlike similar population scale behavior in liquid media, the front speed and shape are also strongly regulated by the structure of the porous medium itself. We show that the classic Keller-Segel model of chemotaxis can describe this behavior, but only when two revisions to the motility parameters are incorporated: (i) they are reduced in a confinement-dependent manner, and (ii) they are corrected to incorporate cell-cell collisions that are promoted by confinement. Using this revised model, we elucidate how nutrient consumption, cellular growth, and confinement-dependent motility together shape the dynamics and morphology of these traveling fronts. Taken together, our work provides a quantitative description of chemotactic migration of bacteria, and active matter in general, in heterogeneous environments.