Molecular Spiders with Memory

TL;DR

This paper models molecular spiders with memory, showing that slowing down at new sites can enhance exploration efficiency and increase diffusion, especially in multi-legged spiders, based on a one-dimensional movement model.

Contribution

It introduces a novel model of molecular spiders with memory effects, revealing how site-dependent slowdown influences their movement and exploration dynamics.

Findings

Slowing down at new sites creates an effective bias towards unvisited sites.

For one-leg spiders, slowdown does not affect long-term behavior.

For two-leg spiders, slowdown increases diffusion and exploration speed.

Abstract

Synthetic bio-molecular spiders with "legs" made of single-stranded segments of DNA can move on a surface which is also covered by single-stranded segments of DNA complementary to the leg DNA. In experimental realizations, when a leg detaches from a segment of the surface for the first time it alters that segment, and legs subsequently bound to these altered segments more weakly. Inspired by these experiments we investigate spiders moving along a one-dimensional substrate, whose legs leave newly visited sites at a slower rate than revisited sites. For a random walk (one-leg spider) the slowdown does not effect the long time behavior. For a bipedal spider, however, the slowdown generates an effective bias towards unvisited sites, and the spider behaves similarly to the excited walk. Surprisingly, the slowing down of the spider at new sites increases the diffusion coefficient and accelerates the growth of the number of visited sites.