Molecular Spiders on the Plane

TL;DR

This paper models the movement of synthetic DNA-based molecular spiders on a surface, analyzing their diffusion, visited sites, and the counter-intuitive effect of slowed-down movement increasing motility.

Contribution

It provides analytical results for bipedal spiders and numerical analysis for multileg spiders, including non-Markovian effects due to substrate conversion.

Findings

Analytic results for bipedal spiders' diffusion

Numerical insights into multileg spider behavior

Counter-intuitive increase in motility with slower hopping rates

Abstract

Synthetic bio-molecular spiders with "legs" made of single-stranded segments of DNA can move on a surface covered by single-stranded segments of DNA called substrates when the substrate DNA is complementary to the leg DNA. If the motion of a spider does not affect the substrates, the spider behaves asymptotically as a random walk. We study the diffusion coefficient and the number of visited sites for spiders moving on the square lattice with a substrate in each lattice site. The spider's legs hop to nearest-neighbor sites with the constraint that the distance between any two legs cannot exceed a maximal span. We establish analytic results for bipedal spiders, and investigate multileg spiders numerically. In experimental realizations legs usually convert substrates into products (visited sites). The binding of legs to products is weaker, so the hopping rate from the substrates is smaller. This makes the problem non-Markovian and we investigate it numerically. We demonstrate the emergence of a counter-intuitive behavior - the more spiders are slowed down on unvisited sites, the more motile they become.