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We provide a detailed stochastic description of the swimming motion of an E. coli bacterium in two dimension, where we resolve tumble events in time. For this purpose, we set up two Langevin equations for the orientation angle and speed dynamics. Calculating moments, distribution and autocorrelation functions from both Langevin equations and matching them to the same quantities determined from data recorded in experiments, we infer the swimming parameters of E. coli. They are the tumble rate lambda, the tumble time r(-1), the swimming speed v(0), the strength of speed fluctuations sigma, the relative height of speed jumps eta, the thermal value for the rotational diffusion coefficient D-0, and the enhanced rotational diffusivity during tumbling D-T. Conditioning the observables on the swimming direction relative to the gradient of a chemoattractant, we infer the chemotaxis strategies of E. coli. We confirm the classical strategy of a lower tumble rate for swimming up the gradient but also a smaller mean tumble angle (angle bias). The latter is realized by shorter tumbles as well as a slower diffusive reorientation. We also find that speed fluctuations are increased by about 30% when swimming up the gradient compared to the reversed direction.
We recorded large data sets of swimming trajectories of the soil bacterium Pseudomonas putida. Like other prokaryotic swimmers, P. putida exhibits a motion pattern dominated by persistent runs that are interrupted by turning events. An in-depth analysis of their swimming trajectories revealed that the majority of the turning events is characterized by an angle of phi(1) = 180 degrees (reversals). To a lesser extent, turning angles of phi(2 Sigma Sigma Sigma Sigma) = 00 are also found. Remarkably, we observed that, upon a reversal, the swimming speed changes by a factor of two on average a prominent feature of the motion pattern that, to our knowledge, has not been reported before. A theoretical model, based on the experimental values for the average run time and the rotational diffusion, recovers the mean-square displacement of P. putida if the two distinct swimming speeds are taken into account. Compared to a swimmer that moves with a constant intermediate speed, the mean-square displacement is strongly enhanced. We furthermore observed a negative dip in the directional autocorrelation at intermediate times, a feature that is only recovered in an extended model, where the nonexponential shape of the run-time distribution is taken into account.