Chiral run-and-tumble walker: Transport and optimizing search

We study the statistical properties of a non-Markovian chiral run-and-tumble particle (CRTP) in two dimensions in continuous space and time. In our model, the possible orientations of the particle correspond to the four cardinal directions. The particle can reorient by turning left, right or reversing its direction of motion at different rates. We show how chirality manifests itself in the transport properties like the spatial moments of the marginal position distribution and the first-passage properties of a CRTP. Interestingly, we find that the chirality leads to enhanced diffusion and a looping tendency in the trajectory space. Our results show that chirality plays a pivotal role in the improvement of the search strategy — notably, there exists an optimal bias in tumbling that minimizes the mean search time. We determine an analytical expression for this optimal bias. Furthermore, we find that there exists a critical rate for the reversal of direction beyond which the optimal bias becomes constant. This behavioural drift is in stark contrast to that of the simple non-chiral particle. We believe that these key observations can play a crucial role in determining how living systems efficiently search under non-equilibrium conditions.