Monte Carlo simulation for kinetic chemotaxis model: An application to the traveling population wave

Abstract A Monte Carlo simulation of chemotactic bacteria is developed on the basis of the kinetic modeling, i.e., the Boltzmann transport equation, and is applied to a one-dimensional traveling population wave in a microchannel. In this simulation, the Monte Carlo method, which calculates the run-and-tumble motions of bacteria, is coupled with a finite volume method to calculate the macroscopic transport of the chemical cues in the field. The simulation method can successfully reproduce the traveling population wave of bacteria that was observed experimentally. The microscopic dynamics of bacteria, e.g., the velocity autocorrelation function and velocity distribution function of bacteria, is also investigated. The bacteria that form the traveling population wave create quasi-periodic motions along with the traveling population wave. Simulations are also performed with variations in the sensitivity and modulation parameters of the response function of bacteria. The sensitivity significantly affects both the wave profile and the microscopic motions of bacteria, whereas the modulation amplitude is linearly related to the traveling speed of the population wave but does not have a significant relationship to the wave profile or the microscopic motions of bacteria.