A Mathematical Description of Bacterial Chemotaxis in Response to Two Stimuli

Bacteria are often exposed to multiple stimuli in complex environments, and their efficient chemotactic decisions are critical to survive and grow in their native environments. Bacterial responses to the environmental stimuli depend on the ratio of their corresponding chemoreceptors. By incorporating the signaling machinery of individual cells, we analyze the collective motion of a population of Escherichia coli bacteria in response to two stimuli, mainly serine and methyl-aspartate (MeAsp), in a one-dimensional and a two-dimensional environment, which is inspired by experimental results in Y. Kalinin et al., J. Bacteriol. 192(7):1796-1800, 2010. Under suitable conditions, we show that if the ratio of the main chemoreceptors of individual cells, namely Tar/Tsr, is less than a specific threshold, the bacteria move to the gradient of serine, and if the ratio is greater than the threshold, the group of bacteria moves toward the gradient of MeAsp. Finally, we examine the theory with Monte Carlo agent-based simulations and verify that our results qualitatively agree well with the experimental results in Y. Kalinin et al. (2010).