We have used a realistic model for double stranded DNA and Monte Carlo simulations to compute the extension (mean span) of a DNA molecule confined in a nanochannel over the full range of confinement in a high ionic strength buffer. The simulation data for square nanochannels resolve the apparent contradiction between prior simulation studies and the predictions from Flory theory, demonstrating the existence of two transition regimes between weak confinement (the de Gennes regime) and strong confinement (the Odijk regime). The simulation data for rectangular nanochannels support the use of the geometric mean for mapping data obtained in rectangular channels onto models developed for cylinders. The comparison of our results with experimental data illuminates the challenges in applying models for confined, neutral polymers to polyelectrolytes. Using a Flory-type approach, we also provide an improved scaling result for the relaxation time in the transition regime close to that found in experiments.

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.

DNA confinement in nanochannels is emerging as an important tool for genomics and an excellent platform for testing the theories of confined wormlike polymers. Using cutting-edge, large scale Monte Carlo simulations of asymptotically long wormlike chains, we show that, in analogy to the rod-to-coil transition for free wormlike polymers, there exists a universal, Gauss-de Gennes regime that connects the classic Odijk and de Gennes regimes of channel-confined chains. For DNA in a nanochannel, this Gauss-de Gennes regime spans practically the entire experimentally relevant range of channel sizes, including the nanochannels used in an incipient genome mapping technology.