Using pruned-enriched Rosenbluth method (PERM) simulations of a discrete wormlike chain model, we provide compelling evidence in support of Odijk's prediction of two distinct Odijk regimes for a long wormlike chain confined in a nanochannel. In both cases, the chain of persistence length l p is renormalized into a series of deflection segments of characteristic length D 2/3 l p 1/3 , where D is the channel size. In the first (classic) Odijk regime, these deflection segments are linearly ordered. In the second Odijk regime, thin, long wormlike chains can backfold at a length scale quantified by the global persistence length. We have measured this quantity by simulations and modified Odijk's global persistence length theory to account for thermal fluctuations. The global persistence length, which is defined to be independent of the effect of excluded volume, provides the requisite closure to Odijk's scaling theory for the second regime and thus allows us to resolve much of the confusion surrounding the so-called "transition" regime for DNA confined in a nanochannel. We show that Odijk's theory for the backfolded regime correctly describes both the average chain extension and the variance about this extension for wormlike chains in channel sizes between the classic Odijk regime and the de Gennes blob regimes, with our data spanning several decades in terms of Odijk's scaling parameter ξ. Although the backfolded Odijk regime occupies a very narrow range of D/l p , it is indeed a regime when viewed in terms of ξ and grows in size with increasing monomer anisotropy.

The details surrounding the cross-over from wormlike-specific to universal polymeric behavior has been the subject of debate and confusion even for the simple case of a dilute, unconfined wormlike chain. We have directly computed the polymer size, form factor, free energy and Kirkwood diffusivity for unconfined wormlike chains as a function of molecular weight, focusing on persistence lengths and effective widths that represent single-stranded and double-stranded DNA in a high ionic strength buffer. To do so, we use a chain-growth Monte Carlo algorithm, the Pruned-Enriched Rosenbluth Method (PERM), which allows us to estimate equilibrium and near-equilibrium dynamic properties of wormlike chains over an extremely large range of contour lengths. From our calculations, we find that very large DNA chains (≈ 1,000,000 base pairs depending on the choice of size metric) are required to reach flexible, swollen non-draining coils. Furthermore, our results indicate that the commonly used model polymer λ-DNA (48,500 base pairs) does not exhibit “ideal” scaling, but exists in the middle of the transition to long-chain behavior. We subsequently conclude that typical DNA used in experiments are too short to serve as an accurate model of long-chain, universal polymer behavior.

We have used a combination of fluorescence microscopy experiments and Pruned Enriched Rosenbluth Method simulations of a discrete wormlike chain model to measure the mean extension and the variance in the mean extension of λ-DNA in 100 nm deep nanochannels with widths ranging from 100 nm to 1000 nm in discrete 100 nm steps. The mean extension is only weakly affected by the channel aspect ratio. In contrast, the fluctuations of the chain extension qualitatively differ between rectangular channels and square channels with the same cross-sectional area, owing to the "mixing" of different confinement regimes in the rectangular channels. The agreement between experiment and simulation is very good, using the extension due to intercalation as the only adjustable parameter.

We present experimental demonstration that weak excluded volume effects arise in DNA nanochannel confinement. In particular, by performing measurements of the variance in chain extension as a function of nanochannel dimension for effective channel size ranging from 305 nm to 453 nm, we show that the scaling of the variance in extension with channel size rejects the de Gennes scaling δ2X ~ D1/3 in favor of δ2X ~ D0 using uncertainty at the 95% confidence level. We also show how simulations and confinement spectroscopy can be combined to reduce molecular weight dispersity effects arising from shearing, photocleavage, and nonuniform staining of DNA.

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.