  In response to a concentration gradient of nutrient, E. coli bacterium
modulates the rotational bias of flagellar motors which control its
run-and-tumble motion, to migrate towards regions of high nutrient
concentration. Presence of stochastic noise in the biochemical pathway of the
cell has important consequence on the switching mechanism of motor bias, which
in turn affects the runs and tumbles of the cell. We model the intra-cellular
reaction network in terms of coupled time-evolution of three stochastic
variables, kinase activity, methylation level and CheY-P protein level, and
study the effect of methylation noise on the chemotactic performance of the
cell. In presence of a spatially varying nutrient concentration profile, a good
chemotactic performance allows the cell to climb up the concentration gradient
fast and localize in the nutrient-rich regions in the long time limit. Our
simulations show that the best performance is obtained at an optimal noise
strength. While it is expected that chemotaxis will be weaker for very large
noise, it is counter-intuitive that the performance worsens even when noise
level falls below a certain value. We explain this striking result by detailed
analysis of CheY-P protein level statistics for different noise strengths. We
show that when the CheY-P level falls below a certain (noise-dependent)
threshold, the cell tends to move down the concentration gradient of the
nutrient, which has a detrimental effect on its chemotactic response. This
threshold value decreases as noise is increased, and this effect is responsible
for noise-induced enhancement of chemotactic performance. In a harsh chemical
environment, when the nutrient degrades with time, the amount of nutrient
intercepted by the cell trajectory, is an effective performance criterion. In
this case also, we find an optimum noise strength, depending on the nutrient
lifetime.
