  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
multi-legged spider 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 single-legged walkers, each on its own one-dimensional track,
connected by a "leash", i.e., a kinematic constraint that no two spiders can be
more than a certain distance apart. Even though a single one-legged walker does
not at all exhibit directional, superdiffusive motion, we find that a team of
one-legged walkers on parallel tracks, connected by a flexible tether, does
enjoy a superdiffusive transient. Furthermore, the one-legged walker teams
exhibit a greater expected number of steps per boundary period and are able to
diffuse more quickly through the product sea than two-legged walkers, which
leads to longer periods of superdiffusion.
