Mobility of a semiflexible chain confined in a nanochannel

Abstract

The classic results of de Gennes and Odijk describe the mobility of a semiflexible chain confined in a nanochannel only in the limits of very weak and very strong confinement, respectively. Using Monte Carlo sampling of the Kirkwood diffusivity with full hydrodynamic interactions, we show that the mobility of a semiflexible chain exhibits a broad plateau as a function of extension before transitioning to an Odijk regime, and that the width of the plateau depends on the anisotropy of the monomers. For the particular case of DNA in a high ionic strength buffer, which has highly anisotropic monomers, we predict that this Rouse-like behavior will be observed over most of the measurable chain extensions seen in experiments.

FIG. 1

(color online) Averaged extension of a flexible (l_p = 5.3 nm, blue squares) and a semiflexible (l_p = 53 nm, red circles) chain containing 2048 touching beads of width w = 4.6 nm as a function of the effective channel width, D – w, available to the chain. To aid the eye, lines corresponding to the Odijk regime (solid), transition regime (dotted), and extended de Gennes/de Gennes regimes (long dashed) are shown.

FIG. 2

(color online) Mobility versus extension. All simulations correspond to w = 4.6 nm and a = 1.38 nm. (a) Results for five different chain lengths for l_p = 53 nm. The shaded region corresponds to the extensions seen in DNA experiments [8]. (b) Results for three different persistence lengths for L = 9:42 μm (N_b = 2048 beads). The dotted line is the scaling of eq. (4) and the dashed line shows the scaling of eq. (5). The solid lines are the approximation in eq. (6). The vertical lines are the values for the onset of the scaling 〈X〉/L ~ D^–1 for the 53 nm chain (red, 〈X〉/L = 0.15) and the 23 nm chain (green, 〈X〉/L = 0.2).