Tethered single-legged molecular spiders on independent 1D tracks

TL;DR

This paper models the motion of tethered single-legged molecular spiders on independent 1D tracks, revealing that a team of such walkers exhibits superdiffusive transient behavior due to boundary interactions, unlike individual walkers.

Contribution

It introduces a model of tethered single-legged molecular spiders on parallel tracks and demonstrates superdiffusive motion in teams, contrasting with single walkers.

Findings

Team of tethered walkers exhibits superdiffusive transient behavior.

Single-legged walkers on their own do not show superdiffusion.

Tethered teams diffuse faster and have longer boundary periods than two-legged walkers.

Abstract

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.