Statistics of single cell trajectories in a bacterial swarm

In our work, we analyse the microscopic characteristics of the motion of individual bacterial cells in an advancing bacterial swarm consisting of over 10 million individuals. Statistical analysis of single cell trajectories in the swarm reveals a correlated random walk with a mean growth direction. The trajectory length of the random walk was found to obey a log-normal distribution. The distribution of turning angles revealed an interesting situation with a Gaussian hump centred around zero over a uniform background. The peak in the distribution of turning angles could be reasonably fitted to a truncated normal distribution. The background (angles from [-180,-100] and its mirror [100, 180]) displayed a uniform distribution. Such a distribution can be thought of as arising from a weakly biased random walk where the bias provides the global mean direction of the swarm while the overall uniform background arises from the Brownian (unbiased) portion. The bias results in finite correlation of the current direction with the previous direction resulting in the Gaussian hump centred around zero. The observed statistics of motion at the microscopic level can thus predict the mean directed swarm motion.