Douglas R. Tree

Interplay between chain stiffness and excluded volume of semiflexible polymers confined in nanochannels.

The properties of channel-confined semiflexible polymers are determined by a complicated interplay of chain stiffness and excluded volume effects. Using Pruned-Enriched Rosenbluth Method (PERM) simulations, we study the equilibrium properties of channel-confined polymers by systematically controlling chain stiffness and excluded volume. Our calculations of chain extension and confinement free energy for freely jointed chains with and without excluded volume show excellent agreement with theoretical predictions. For ideal wormlike chains, the extension is seen to crossover from Odijk behavior in strong confinement to zero-stretching, bulk-like behavior in weak confinement. In contrast, for self-avoiding wormlike chains, we always observe that the linear scaling of the extension with the contour length is valid in the long-chain limit irrespective of the regime of confinement, owing to the coexistence of stiffness and excluded volume effects. We further propose that the long-chain limit for the extension corresponds to chain lengths wherein the projection of the end-to-end distance along the axis of the channel is nearly equal to the mean span parallel to the axis. For DNA in nanochannels, this limit was identified using PERM simulations out to molecular weights of more than 1 megabase pairs; the molecular weight of λ-DNA is found to exhibit nearly asymptotic fractional extension for channels sizes used commonly in experiments.

Modeling the relaxation time of DNA confined in a nanochannel

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.

Resolution limit for DNA barcodes in the Odijk regime

We develop an approximation for the probability of optically resolving two fluorescent labels on the backbone of a DNA molecule confined in a nanochannel in the Odijk regime as a function of the fluorescence wavelength, channel size, and the properties of the DNA (persistence length and effective width). The theoretical predictions agree well with equivalent data produced by Monte Carlo simulations of a touching wormlike bead model of DNA in a high ionic strength buffer. Although the theory is only strictly valid in the limit where the effective width of the nanochannel is small compared with the persistence length of the DNA, simulations indicate that the theoretical predictions are reasonably accurate for channel widths up to two-thirds of the persistence length. Our results quantify the conjecture that DNA barcoding has kilobase pair resolution-provided the nanochannel lies in the Odijk regime.

Entropic depletion of DNA in triangular nanochannels

Using Monte Carlo simulations of a touching-bead model of double-stranded DNA, we show that DNA extension is enhanced in isosceles triangular nanochannels (relative to a circular nanochannel of the same effective size) due to entropic depletion in the channel corners. The extent of the enhanced extension depends non-monotonically on both the accessible area of the nanochannel and the apex angle of the triangle. We also develop a metric to quantify the extent of entropic depletion, thereby collapsing the extension data for circular, square, and various triangular nanochannels onto a single master curve for channel sizes in the transition between the Odijk and de Gennes regimes.