Shepherd Model for Knot-Limited Polymer Ejection from a Capsid

TL;DR

This paper introduces a mathematical model for the ejection of knotted polymers from a capsid, capturing the effects of knot reptation and internal pressure, and provides exact and continuum solutions.

Contribution

It develops a tractable, exact discrete model and a continuum approximation for polymer ejection involving knots, highlighting the scaling behavior with the number of knots.

Findings

Ejection speed scales as 1/L with the number of knots.

Exact solutions for finite knots are derived.

Continuum theory matches discrete results for large L.

Abstract

We construct a tractable model to describe the rate at which a knotted polymer is ejected from a spherical capsid via a small pore. Knots are too large to fit through the pore and must reptate to the end of the polymer for ejection to occur. The reptation of knots is described by symmetric exclusion on the line, with the internal capsid pressure represented by an additional biased particle that drives knots to the end of the chain. We compute the exact ejection speed for a finite number of knots L and find that it scales as 1/L. We also construct a continuum theory for many knots that matches the exact discrete theory for large L.