Effect of polyvalency on tethered molecular walkers on independent one-dimensional tracks

We study the motion of random walkers with residence time bias between first and subsequent visits to a site, as a model for synthetic molecular walkers composed of coupled DNAzyme legs known as molecular spiders. The mechanism of the transient superdiffusion has been explained via the emergence of a boundary between the new and the previously visited sites, and the tendency of the multilegged walker to cling to this boundary, provided residence time for a first visit to a site is longer than for subsequent visits. Using both kinetic Monte Carlo simulation and an analytical approach, we model a system that consists of unipedal walkers, each on its own one-dimensional track, connected by a tether, i.e., a kinematic constraint that no two walkers can be more than a certain distance apart. Even though a single unipedal walker does not at all exhibit directional, superdiffusive motion, we find that a team of unipedal walkers on parallel tracks, connected by a flexible tether, does enjoy a superdiffusive transient. Furthermore, unipedal walker teams exhibit a greater expected number of steps per boundary period and are able to diffuse more quickly than bipedal walker teams, which leads to longer periods of superdiffusion.