Steady state running rate sets the speed and accuracy of accumulation of swimming bacterial populations

We study the chemotaxis of a population of genetically identical swimming bacteria undergoing run and tumble dynamics driven by stochastic switching between clockwise and counterclockwise rotation of the flagellar rotary system. Understanding chemotaxis quantitatively requires that one links the switching rate of the rotary system in a gradient of chemoattractant/repellant to experimental measures of the efficiency of a population of bacteria in moving up/down the gradient. Here we achieve this by using a probabilistic model and show that the response of a population to the gradient is complex. We find the changes to a phenotype (the steady state switching rate in the absence of gradients) affects the average speed of the response as well as the width of the distribution and both must be taken into account to optimise the overall response of the population in complex environments. This is due to the behaviour of individuals in the 'tails' of the distribution. Hence we show that for chemotaxis, the behaviour of atypical individuals can have a significant impact on the fitness of a population.