Non-Poissonian run-and-turn motions

Swimming bacteria exhibit a variety of motion patterns, in which persistent runs are punctuated by turning events. A simple yet fundamental question is to establish the properties of these random walks. While a complete answer is available when turning events follow a Poisson process, much less is known outside this particular case. We present a generic framework for such non-Poissonian run-and-turn motions. Extending the formalism of continuous time random walks, we obtain the generating function of moments in terms of noncommuting operators. We characterize analytically a bimodal model of persistent motion, which describes all types of swimming pattern, and is also relevant for cell motility.