Transition path properties of a run and tumble particle subjected to an external potential

Run-and-tumble particle (RTP) motion is a key model for certain bacteria and other actively moving microscopic particles, combining phases of directed motion with ‘tumbles’, stationary phases during which the particle reorients itself. We here continue previous studies of unconstrained RTP motion and consider the transition path properties of an RTP subjected to an external potential. Exact expressions are derived for the RTP transition path properties, supported by results from Monte Carlo simulations. We explore the effects of particle velocity, tumble rate and the external potential on the splitting probability, transition path time, coefficient of variation, transition path shape, unsuccessful transition path distribution and duration, based on forward and backward master equations. Counterintuitively, the presence of the potential may accelerate the escape of RTPs. Moreover, we show that the external potential gives rise to the appearance of an asymmetry of the transition path properties which increases with the steepness of the potential. While the potential does not affect the forward and reverse transition paths of the RTP, these are affected by the particle velocity, in contrast with free RTPs.