Longitudinal dispersion of DNA in nanochannels

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 FokkerPlanck 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.