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We provide a detailed stochastic description of the swimming motion of anE.coli bacterium in two dimension, where we resolve tumble events in time. Forthis purpose, we set up two Langevin equations for the orientation angle andspeed dynamics. Calculating moments, distribution and autocorrelation functionsfrom both Langevin equations and matching them to the same quantitiesdetermined from data recorded in experiments, we infer the swimming parametersof E.coli . They are the tumble rate ${\lambda}$, the tumble time $r^{-1}$ ,the swimming speed $v_0$ , the strength of speed fluctuations ${\sigma}$, therelative height of speed jumps ${\eta}$, the thermal value for the rotationaldiffusion coefficient $D_0$ , and the enhanced rotational diffusivity duringtumbling $D_T$ . Conditioning the observables on the swimming directionrelative to the gradient of a chemoattractant, we infer the chemotaxisstrategies of E.coli . We confirm the classical strategy of a lower tumble ratefor 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 diffusivereorientation. We also find that speed fluctuations are increased by about 30%when swimming up the gradient compared to the reversed direction.

Statistical parameter inference of bacterial swimming strategies