The volcano effect in bacterial chemotaxis

A population-level model of bacterial chemotaxis is derived from a simple bacterial-level model of behavior. This model, to be contrasted with the Keller-Segel equations, exhibits behavior we refer to as the "volcano effect": steady-state bacterial aggregation forming a ring of higher density some distance away from an optimal environment. The model is derived, as in Erban and Othmer (2004) [1], from a transport equation in a state space including the internal biochemical variables of the bacteria and then simplified with a truncation at low moments with respect to these variables. We compare the solutions of the model to stochastic simulations of many bacteria, as well as the classic Keller-Segel model. This model captures behavior that the Keller-Segel model is unable to resolve, and sheds light on two different mechanisms that can cause a volcano effect.