Modeling the relaxation time of DNA confined in a nanochannel

Abstract

Using a mapping between a Rouse dumbbell model and fine-grained Monte Carlo simulations, we have computed the relaxation time of λ-DNA in a high ionic strength buffer confined in a nanochannel. The relaxation time thus obtained agrees quantitatively with experimental data [Reisner et al., Phys. Rev. Lett. 94, 196101 (2005)] using only a single O(1) fitting parameter to account for the uncertainty in model parameters. In addition to validating our mapping, this agreement supports our previous estimates of the friction coefficient of DNA confined in a nanochannel [Tree et al., Phys. Rev. Lett. 108, 228105 (2012)], which have been difficult to validate due to the lack of direct experimental data. Furthermore, the model calculation shows that as the channel size passes below approximately 100 nm (or roughly the Kuhn length of DNA) there is a dramatic drop in the relaxation time. Inasmuch as the chain friction rises with decreasing channel size, the reduction in the relaxation time can be solely attributed to the sharp decline in the fluctuations of the chain extension. Practically, the low variance in the observed DNA extension in such small channels has important implications for genome mapping.

Figure 1

Relaxation time (purple diamonds) obtained from Eq. 5 with $c=1.2$ and the WOSM compared to the experimental data of Reisner et al. (black triangles).

Figure 2

(a) Fractional extension of DNA in a square nanochannel of size D from Monte Carlo simulations (red circles) and from Reisner et al. (black triangles). Error bars for the simulation data are the standard error, and when not explicitly shown, the error is of order of the symbol size. Simulation parameters: $l_p=50\hspace{0.17em}\text{nm},\hspace{0.17em}w=10\hspace{0.17em}\text{nm},\hspace{0.17em}L=18.63\hspace{0.17em}\mu \mathrm{m}$ (i.e., 1863 spheres). The same set of parameters is used throughout this work. (b) Same data plotted in dimensionless log-log form. The solid blue line is the prediction for the Odijk regime with no free parameters. The dashed line is the predicted slope for the proposed Gauss-de Gennes regime, and the solid green line is the scaling $D^{1-1/\nu }$ with $\nu =0.5876$.

Figure 3

Normalized chain friction (left panel, orange triangles) and normalized fluctuations in the mean span (right panel, blue squares) of the WOSM as a function of channel size.

Figure 4

(a) Probability density function for the chain extension $\psi (X)$ in the WOSM for different channel sizes as a function of fractional extension. The channel sizes shown are (from right to left in nm): 30, 36, 43, 52, 62, 74, 89, 106, 127, 152, 183, 219, 262, 314, 376, 450. (b) Normal probability plot of the 16 distributions. The solid black line indicates a normal distribution. The color scheme in both panels is the same.