  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 move
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).
