Molecular Spiders in One Dimension

TL;DR

This paper models the movement of molecular spiders with DNA-based legs on a surface, analyzing their diffusion and velocity through mappings to exclusion processes, providing insights into their dynamics.

Contribution

It introduces a mathematical framework linking molecular spider models to exclusion processes and computes key movement parameters.

Findings

Diffusion coefficient for spiders with simple gait and varying legs

Velocity calculations for biased hopping spiders

Establishment of mappings between spider models and exclusion processes

Abstract

Molecular spiders are synthetic bio-molecular systems which have "legs" made of short single-stranded segments of DNA. Spiders move on a surface covered with single-stranded DNA segments complementary to legs. Different mappings are established between various models of spiders and simple exclusion processes. For spiders with simple gait and varying number of legs we compute the diffusion coefficient; when the hopping is biased we also compute their velocity.