Backfolding of Wormlike Chains Confined in Nanochannels

Trapping, entrainment and synchronization of semiflexible polymers in narrow, asymmetric confinements

The physical properties of polymeric actin facilitate many mechanical processes within the cell, including cellular deformation and locomotion, whereby the polymers can be confined to a range of different geometries. As actin polymers often form entangled solutions in the cell, we have investigated the effect of confinement on the evolution of entangled semiflexible polymer solutions. Using a microfluidic platform, we examined the physical dynamics of actin polymers confined within narrow (2-4 μm) rectangular channels. Focusing on the entanglement process of two actin polymers, we found that their prolonged entrainment leads to synchronized horizontal undulations and decreased translational diffusion. In the absence of cross-linking molecules or proteins, the long-range entrainment interactions are predominantly controlled by the geometric boundaries. We directly measure the deflection length Λ for an individual polymer, either solitarily confined within a channel or confined in the presence of a second filament, enabling the determination of the change in free energy associated with polymer entanglement. Our results indicate that geometrical confinement can serve as a solitary variable influencing the physical dynamics of entangled semiflexible polymers.

Finite-size corrections for confined polymers in the extended de Gennes regime

Theoretical results for the extension of a polymer confined to a channel are usually derived in the limit of infinite contour length. But experimental studies and simulations of DNA molecules confined to nanochannels are not necessarily in this asymptotic limit. We calculate the statistics of the span and the end-to-end distance of a semiflexible polymer of finite length in the extended de Gennes regime, exploiting the fact that the problem can be mapped to a one-dimensional weakly self-avoiding random walk. The results thus obtained compare favorably with pruned-enriched Rosenbluth method (PERM) simulations of a three-dimensional discrete wormlike chain model of DNA confined in a nanochannel. We discuss the implications for experimental studies of linear λ-DNA confined to nanochannels at the high ionic strengths used in many experiments.

Extension of nanoconfined DNA: Quantitative comparison between experiment and theory

The extension of DNA confined to nanochannels has been studied intensively and in detail. However, quantitative comparisons between experiments and model calculations are difficult because most theoretical predictions involve undetermined prefactors, and because the model parameters (contour length, Kuhn length, effective width) are difficult to compute reliably, leading to substantial uncertainties. Here we use a recent asymptotically exact theory for the DNA extension in the "extended de Gennes regime" that allows us to compare experimental results with theory. For this purpose, we performed experiments measuring the mean DNA extension and its standard deviation while varying the channel geometry, dye intercalation ratio, and ionic strength of the buffer. The experimental results agree very well with theory at high ionic strengths, indicating that the model parameters are reliable. At low ionic strengths, the agreement is less good. We discuss possible reasons. In principle, our approach allows us to measure the Kuhn length and the effective width of a single DNA molecule and more generally of semiflexible polymers in solution.

Measurements of DNA barcode label separations in nanochannels from time-series data

We analyzed time-series data for fluctuations of intramolecular segments of barcoded E. coli genomic DNA molecules confined in nanochannels with sizes near the persistence length of DNA. These dynamic data allowed us to measure the probability distribution governing the distance between labels on the DNA backbone, which is a key input into the alignment methods used for genome mapping in nanochannels. Importantly, this dynamic method does not require alignment of the barcode to the reference genome, thereby removing a source of potential systematic error in a previous study of this type. The results thus obtained support previous evidence for a left-skewed probability density for the distance between labels, albeit at a lower magnitude of skewness. We further show that the majority of large fluctuations between labels are short-lived events, which sheds further light upon the success of the linearized DNA genome mapping technique. This time-resolved data analysis will improve existing genome map alignment algorithms, and the overall idea of using dynamic data could potentially improve the accuracy of genome mapping, especially for complex heterogeneous samples such as cancer cells.

Knotting dynamics of DNA chains of different length confined in nanochannels

Langevin dynamics simulations are used to characterize the typical mechanisms governing the spontaneous tying, untying and the dynamical evolution of knots in coarse-grained models of DNA chains confined in nanochannels. In particular we focus on how these mechanisms depend on the chain contour length, Lc, at a fixed channel width D = 56 nm corresponding to the onset of the Odijk scaling regime where chain backfoldings and hence knots are disfavoured but not suppressed altogether. We find that the lifetime of knots grows significantly with Lc, while that of unknots varies to a lesser extent. The underlying kinetic mechanisms are clarified by analysing the evolution of the knot position along the chain. At the considered confinement, in fact, knots are typically tied by local backfoldings of the chain termini where they are eventually untied after a stochastic motion along the chain. Consequently, the lifetime of unknots is mostly controlled by backfoldings events at the chain ends, which is largely independent of Lc. The lifetime of knots, instead, increases significantly with Lc because knots can, on average, travel farther along the chain before being untied. The observed interplay of knots and unknots lifetimes underpins the growth of the equilibrium knotting probability of longer and longer chains at fixed channel confinement.

Modeling the stretching of wormlike chains in the presence of excluded volume

We propose an interpolation formula (the EV-WLC relation) for the force-extension behavior of wormlike chains in the presence of hard-core excluded volume interactions, analogous to the classic interpolation formula from Marko and Siggia for ideal wormlike chains. Using pruned-enriched Rosenbluth method (PERM) simulations of asymptotically long, discrete wormlike chains in an external force, we show that the error in the EV-WLC interpolation formula to describe discrete wormlike chains is systematically smaller than the error in the Marko-Siggia interpolation formula, except for the saturation region in which both formulas have the same limiting behavior. We anticipate that the EV-WLC interpolation formula will prove useful in the coarse-graining of wormlike chain models for dynamic simulations. Related results for the excess free energy due to excluded volume provide strong support for the physical basis of the Pincus regime.

Experimental evidence of weak excluded volume effects for nanochannel confined DNA

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.

Scaling regimes of a semiflexible polymer in a rectangular channel

We derive scaling relations for the extension statistics and the confinement free energy for a semiflexible polymer confined to a channel with a rectangular cross section. Our motivation is recent numerical results [Gupta et al., J. Chem. Phys. 140, 214901 (2014)] indicating that extensional fluctuations are quite different in rectangular channels compared to square channels. Our results are of direct relevance for interpreting current experiments on DNA molecules confined to nanochannels, as many experiments are performed for rectangular channels with large aspect ratios, while theoretical and simulation results are usually obtained for square channels.

Kirkwood diffusivity of long semiflexible chains in nanochannel confinement

We compute the axial diffusivity of asymptotically long semiflexible polymers confined in square channels. Our calculations employ the Kirkwood approximation of the mobility tensor by combining computational fluid dynamics (CFD) calculations of the hydrodynamic tensor in channel confinement with pruned-enriched Rosenbluth method (PERM) simulations of a discrete wormlike chain model. Three key results emerge from our study. First, for the classic de Gennes regime, we confirm that Brochard and de Gennes' blob theory correctly predicts the scaling of the axial diffusivity, contrary to the conclusions of previous analyses. Second, for the extended de Gennes regime, we show that a modified blob theory, which has been used to incorporate the effect of local stiffness on DNA diffusion in nanoslits, explains the deviation from the prediction of classic blob theory for diffusion in nanochannels. Third, we provide a calculation similar to the modified blob theory to explain the relative insensitivity of the diffusivity to channel size for channels between the extended de Gennes regime and the Odijk regime, which is the most relevant regime for experiments and technological applications of DNA confinement in nanochannels. Our results are not only relevant to the dynamics of confined semiflexible polymers such as DNA, but also reveal interesting analogies between confinement in channels and slits.

Distribution of distances between DNA barcode labels in nanochannels close to the persistence length

We obtained experimental extension data for barcoded E. coli genomic DNA molecules confined in nanochannels from 40 nm to 51 nm in width. The resulting data set consists of 1 627 779 measurements of the distance between fluorescent probes on 25 407 individual molecules. The probability density for the extension between labels is negatively skewed, and the magnitude of the skewness is relatively insensitive to the distance between labels. The two Odijk theories for DNA confinement bracket the mean extension and its variance, consistent with the scaling arguments underlying the theories. We also find that a harmonic approximation to the free energy, obtained directly from the probability density for the distance between barcode labels, leads to substantial quantitative error in the variance of the extension data. These results suggest that a theory for DNA confinement in such channels must account for the anharmonic nature of the free energy as a function of chain extension.