First passage time of N excluded volume particles on a line

TL;DR

This paper investigates the first passage time of multiple particles sliding on a line, considering effects like adsorption, desorption, finite size, and interactions, with implications for protein-DNA dynamics.

Contribution

It introduces a comprehensive model for first passage times of multiple particles on a line, including adsorption, desorption, finite size effects, and interactions, extending previous simpler models.

Findings

Mean first passage time scales as 1/N^2 at low densities

Corrections to the mean first passage time are identified at higher concentrations

Finite size effects and particle interactions significantly influence the search dynamics

Abstract

Motivated by recent single molecule studies of proteins sliding on a DNA molecule, we explore the targeting dynamics of N particles ("proteins") sliding diffusively along a line ("DNA") in search of their target site (specific target sequence). At lower particle densities, one observes an expected reduction of the mean first passage time proportional to 1/N**2, with corrections at higher concentrations. We explicitly take adsorption and desorption effects, to and from the DNA, into account. For this general case, we also consider finite size effects, when the continuum approximation based on the number density of particles, breaks down. Moreover, we address the first passage time problem of a tagged particle diffusing among other particles.