Dimensionality-dependent crossover in motility of polyvalent burnt-bridges ratchets

TL;DR

This study explores how the movement of polyvalent burnt-bridges ratchets varies with track width, revealing a transition from ballistic to diffusive motion and providing a model to optimize their design for targeted applications.

Contribution

It introduces a kinetic analysis of polyvalent BBRs on tracks of varying width and develops an analytical model to predict their motion, aiding in design optimization.

Findings

BBRs remain nearly ballistic on narrow to moderate tracks

Transition to diffusive motion occurs on wider tracks

A tradeoff exists between track association time and superdiffusivity

Abstract

The burnt-bridges ratchet (BBR) mechanism is a model for biased molecular motion whereby the construct destroys track binding sites as it progresses, and therefore acts as a diffusing forager, seeking new substrate sites. Using Monte Carlo simulations that implement the Gillespie algorithm, we investigate the kinetic characteristics of simple polyvalent BBRs as they move on tracks of increasing width. We find that as the track width is increased the BBRs remain nearly ballistic for considerable track widths proportional to the span (leg length) of the polyvalent walker, before transitioning to near-conventional diffusion on two-dimensional tracks. We find there exists a tradeoff in BBR track association time and superdiffusivity in the BBR design parameter space of span, polyvalency and track width. Furthermore, we develop an analytical model to describe the ensembleaverage motion on the track and find it is in good agreement with our Gillespie simulation results. This work offers insights into design criteria for de novo BBRs and their associated tracks, where experimentalists seek to optimize directionality and track association time.