Bacterial Chemotactic Tumble Angles Reduce Backtracking And Maximize Information Gathering

Chemotaxing bacteria gather information from the environment and use that to control the balance between runs and tumbles in order achieve a biased motion toward the source of a chemoattractant. We have examined the role of the tumble angle on how effectively gradients are coupled into a bacteriumu0027s trajectory. Chemotaxis was simulated using the ZBP program, and the average tumble angle varied from 0 to 180 degrees in the presence and absence of the normal angle variance and/or rotational diffusion. 100,000 step (0.1 µm/step) trajectories from these simulations where analysed using the k-space information metric to quantify how much information was reflected in the paths. For wild-type bacteria the information in the trajectories is essentially constant across all tumble angles (and several gradients). However, if either the angle variance or the rotational diffusion is set to zero, distinct minima appear in the trajectory information appear at 0, 90, and 180 degrees - and there are broad maxima around 70 and 110 degrees. In simulations where both the angle variance and the rotational diffusion are set to zero, the trajectory information exhibits several more prominent minima, notably at 135, 60, and 45 degrees. We suggest that these minima arise because angles that are small integer fractions of 180 or 540 degrees increase the likelihood of backtracking - thus reducing the new space explored by the bacterium. When a bacterium does tumble, it should do so in a way as to explore as much new space as possible in order to optimize information gathering. Notably that is not 90 degrees, but one maximum is close to the normal tumble angle of 68 degrees for E. coli.