First Passage Properties of Molecular Spiders

TL;DR

This paper investigates the first passage times of molecular spiders, synthetic DNA walkers, on different lattice models, revealing how boundary conditions and site visit slowdown affect their efficiency in reaching targets.

Contribution

It introduces a comparative analysis of first passage times for molecular spiders on 1D and 2D lattices with various boundary conditions, highlighting the impact of catalysis-induced slowdown.

Findings

Performance gain is higher in 2D circular boundaries than in 1D with absorbing ends.

Slowdown on visited sites can significantly improve passage times.

Absorbing boundary shape influences the efficiency of molecular spiders.

Abstract

Molecular spiders are synthetic catalytic DNA-based nanoscale walkers. We study the mean first passage time for abstract models of spiders moving on a finite two-dimensional lattice with various boundary conditions, and compare it with the mean first passage time of spiders moving on a one-dimensional track. We evaluate by how much the slowdown on newly visited sites, owing to catalysis, can improve the mean first passage time of spiders and show that in one dimension, when both ends of the track are an absorbing boundary, the performance gain is lower than in two dimensions, when the absorbing boundary is a circle; this persists even when the absorbing boundary is a single site.