Longitudinal dispersion of DNA in nanochannels

TL;DR

This paper develops a theoretical model for the longitudinal dispersion of confined DNA in nanochannels, highlighting the role of orientational fluctuations and deriving a diffusion equation with a dispersion coefficient.

Contribution

It introduces a Green function approach to model DNA dispersion in nanochannels, incorporating orientational fluctuations and extending Taylor's method to this context.

Findings

Dispersion proportional to the sixth power of segment angle.

Model underestimates dispersion compared to experiments.

Harmonic approximation may limit accuracy.

Abstract

A theory is presented of the longitudinal dispersion of DNA under equilibrium confined in a nanochannel. Orientational fluctuations of the DNA chain build up to give rise to substantial fluctuations of the coil in the longitudinal direction of the channel. The translational and orientational degrees of freedom of the polymer are described by the Green function satisfying the usual Fokker-Planck equation. It is argued that this is analogous to the transport equation occurring in the theory of convective diffusion of particles in pipe flow. Moreover, Taylor's method may be used to reduce the Fokker-Planck equation to a diffusion equation for long DNA although subtleties arise connected with the orientational distribution of segments within the channel. The longitudinal "step length" turns out to be proportional to the typical angle of a DNA segment to the sixth power. The dispersion is underestimated compared to experiment, probably because the harmonic approximation is used to describe the polymer confinement.