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Evaluation of bacterial motility from non-Gaussianity of finite-sample trajectories using the large deviation principle

Motility of bacteria is usually recognized in the trajectory data and compared with Brownian motion, but the diffusion coefficient is insufficient to evaluate it. In this paper, we propose a method based on the large deviation principle. We show that it can be used to evaluate the non-Gaussian characteristics of model Escherichia coli motions and to distinguish combinations of the mean running duration and running speed that lead to the same diffusion coefficient. Our proposed method does not require chemical stimuli to induce the chemotaxis in a specific direction, and it is applicable to various types of self-propelling motions for which no a priori information of, for example, threshold parameters for run and tumble or head/tail direction is available. We also address the issue of the finite-sample effect on the large deviation quantities, but we propose to make use of it to characterize the nature of motility.