A macroscopic asymmetric diffusion equation to model the responses of microbial populations to chemical attractants and repellents is derived from a biased random walk model for the motion of individual cells. The equation is different from the well-known Keller-Segel equation which contains a Fickian diffusion term. The implications of this difference for selected problems of biological interest are considered. In particular the aggregation of a population of microorganisms in a region of high concentration of attractant is discussed. Some similarities and limitations of both models are noted. © 1981.
Lapidus, I. R. (1981). Chemosensory responses of microorganisms: Asymmetric diffusion as the limit of a biased random walk. Journal of Theoretical Biology, 92(4), 345–358. https://doi.org/10.1016/0022-5193(81)90251-4