One-Parameter Scaling Theory for DNA Extension in a Nanochannel

Probing protein-DNA interactions and compaction in nanochannels

DNA confined to nanofluidic channels with a cross-section from tens to hundreds of nm wide and hundreds of microns long stretches in an equilibrium process free of flow or end tethering. Because DNA is free to move along the channel axis, its extension is exquisitely sensitive to DNA-DNA interactions and the DNA persistence length, as well as the contour length. We discuss how this sensitivity has been used to probe DNA-protein interactions at physiological concentrations of both DNA and proteins.

Escape dynamics of active ring polymers in a cylindrical nanochannel

We explore the escape dynamics of active ring polymers confined in a cylindrical nanochannel using Brownian dynamics. Our simulation results show that the escape time decreases with the increase of the Péclet number, which is not noticeable between the two stages of the escape process, based on whether the center of mass of the polymer is inside or outside the nanochannel. However, the monomer motion trajectory of the active polymer is very different from that of the passive polymer, similar to the snake-like motion with uniform velocity. The passive polymer, however, is in constant fugitive motion with increased velocity at the tail end of the escape. Our work is vital for understanding the escape dynamics of active ring polymers in the confined nanochannel, which provides new perspectives on their characterization and analysis.

Ejection dynamics of a semiflexible polymer from a nanosphere

Polymer ejection has been of interest due to its relation to the viral genome ejection. However, the ejection dynamics of a semiflexible polymer from a nanosphere is not yet understood. Here, a theory is developed for the ejection dynamics of a polymer with total length L_{0} and persistence length l from a sphere of diameter D. These length scales define different confinement regimes to study the polymer dynamics. The polymer sometimes undergoes between two to three regimes during its ejection. The rate of change of the free energy of confinement is balanced by the rate of energy dissipation, in each regime. The polymer experiences a final stage in which the free energy of polymer attachment to the sphere governs the ejection. The total ejection time τ depends on the polymer dynamics in the various regimes that it passes through in the phase space. Dependence of the ejection time on the polymer length, the persistence length, and the sphere diameter τ∝L_{0}^{α}D^{β}l^{γ} is obtained from the theory. It is shown that α changes between 1 and 1.7, β between 3 and 5, and γ takes a zero or positive value often smaller than 1. Agreement of these exponents with other theory and simulations are discussed.

Entropic force of cone-tethered polymers interacting with a planar surface

Computer simulations are used to characterize the entropic force of one or more polymers tethered to the tip of a hard conical object that interact with a nearby hard flat surface. Pruned-enriched Rosenbluth method Monte Carlo simulations are used to calculate the variation of the conformational free energy F of a hard-sphere polymer with respect to the cone-tip-to-surface distance h from which the variation of the entropic force f≡|dF/dh| with h is determined. We consider the following cases: a single freely jointed tethered chain, a single semiflexible tethered chain, and several freely jointed chains of equal length each tethered to the cone tip. The simulation results are used to test the validity of a prediction by Maghrebi et al. [Maghrebi et al., Europhys. Lett. 96, 66002 (2011)0295-507510.1209/0295-5075/96/66002; Phys. Rev. E 86, 061801 (2012)1539-375510.1103/PhysRevE.86.061801] that f∝(γ_{∞}-γ_{0})h^{-1}, where γ_{0} and γ_{∞} are universal scaling exponents for the partition function of the tethered polymer for h=0 and h=∞, respectively. The measured functions f(h) are generally consistent with the predictions, with small quantitative discrepancies arising from the approximations employed in the theory. In the case of multiple tethered polymers, the entropic force per polymer is roughly constant, which is qualitatively inconsistent with the predictions.

Compression and Stretching of Single DNA Molecules under Channel Confinement

We study the compression and extension response of single dsDNA (double-stranded DNA) molecules confined in cylindrical channels by means of Monte Carlo simulations. The elastic response of micrometer-sized DNA to the external force acting through the chain ends or through the piston is markedly affected by the size of the channel. The interpretation of the force (f)-displacement (R) functions under quasi-one-dimensional confinement is facilitated by resolving the overall change of displacement ΔR into the confinement contribution ΔR_D and the force contribution ΔR_f. The external stretching of confined DNA results in a characteristic pattern of f-R functions involving their shift to the larger extensions due to the channel-induced pre-stretching ΔR_D. A smooth end-chain compression into loop-like conformations observed in moderately confined DNA can be accounted for by the relationship valid for a Gaussian chain in bulk. In narrow channels, the considerably pre-stretched DNA molecules abruptly buckle on compression by the backfolding into hairpins. On the contrary, the piston compression of DNA is characterized by a gradual reduction of the chain span S and by smooth f-S functions in the whole spatial range from the 3d near to 1d limits. The observed discrepancy between the shape of the f-R and f-S functions from two compression methods can be important for designing nanopiston experiments of compaction and knotting of single DNA in nanochannels.

Limitations of the equivalent neutral polymer assumption for theories describing nanochannel-confined DNA

The prevailing theories describing DNA confinement in a nanochannel are predicated on the assumption that wall-DNA electrostatic interactions are sufficiently short-ranged such that the problem can be mapped to an equivalent neutral polymer confined by hard walls with an appropriately reduced effective channel size. To determine when this hypothesis is valid, we leveraged a recently reported experimental data set for the fractional extension of DNA molecules in a 250-nm-wide poly(dimethyl siloxane) (PDMS) nanochannel with buffer ionic strengths between 0.075 and 48 mM. Evaluating these data in the context of the weakly correlated telegraph model of DNA confinement reveals that, at ionic strengths greater than 0.3 mM, the average fractional extension of the DNA molecules agree with theoretical predictions with a mean absolute error of 0.04. In contrast, experiments at ionic strengths below 0.3 mM produce average fractional extensions that are systematically smaller than the theoretical predictions with a larger mean absolute error of 0.15. The deviations between experiment and theory display a correlation coefficient of 0.82 with the decay length for the DNA-wall electrostatics, linking the deviations with a breakdown in approximating the DNA with an equivalent neutral polymer.

Extension distribution for DNA confined in a nanochannel near the Odijk regime

DNA confinement in a nanochannel typically is understood via mapping to the confinement of an equivalent neutral polymer by hard walls. This model has proven to be effective for confinement in relatively large channels where hairpin formation is frequent. An analysis of existing experimental data for Escherichia coli DNA extension in channels smaller than the persistence length, combined with an additional dataset for λ-DNA confined in a 34 nm wide channel, reveals a breakdown in this approach as the channel size approaches the Odijk regime of strong confinement. In particular, the predicted extension distribution obtained from the asymptotic solution to the weakly correlated telegraph model for a confined wormlike chain deviates significantly from the experimental distribution obtained for DNA confinement in the 34 nm channel, and the discrepancy cannot be resolved by treating the alignment fluctuations or the effective channel size as fitting parameters. We posit that the DNA-wall electrostatic interactions, which are sensible throughout a significant fraction of the channel cross section in the Odijk regime, are the source of the disagreement between theory and experiment. Dimensional analysis of the wormlike chain propagator in channel confinement reveals the importance of a dimensionless parameter, reflecting the magnitude of the DNA-wall electrostatic interactions relative to thermal energy, which has not been considered explicitly in the prevailing theories for DNA confinement in a nanochannel.

Direct observation of confinement-induced diffusophoresis

Nanofluidic devices have channel dimensions which come to within one order of magnitude of the Debye length of common aqueous solutions. Conventionally, external driving is used to create concentration polarization of ions and biomolecules in nanofluidic devices. Here we show that long-range ionic strength gradients intrinsic to all nanofluidic devices, even at equilibrium, also drive a drift of macromolecules. To demonstrate the effect, we confine long DNA to straight nanochannels of constant, rectangular cross-section (100 × 100 nm²) which are connected to large microfluidic reservoirs. The motion of DNA is observed in absence of any driving. We find that at low ionic strengths, molecules in nanochannels migrate toward the nano-micro interface, while they are undergoing purely diffusive motion in high salt. Using numerical models, we demonstrate that the motion is consistent with the ionic strength gradient at the micro-nano interface even at equilibrium, and that the dominant cause of the drift is diffusophoresis.

Simulations corroborate telegraph model predictions for the extension distributions of nanochannel confined DNA

Hairpins in the conformation of DNA confined in nanochannels close to their persistence length cause the distribution of their fractional extensions to be heavily left skewed. A recent theory rationalizes these skewed distributions using a correlated telegraph process, which can be solved exactly in the asymptotic limit of small but frequent hairpin formation. Pruned-enriched Rosenbluth method simulations of the fractional extension distribution for a channel-confined wormlike chain confirm the predictions of the telegraph model. Remarkably, the asymptotic result of the telegraph model remains robust well outside the asymptotic limit. As a result, the approximations in the theory required to map it to the polymer model and solve it in the asymptotic limit are not the source of discrepancies between the predictions of the telegraph model and experimental distributions of the extensions of DNA during genome mapping. The agreement between theory and simulations motivates future work to determine the source of the remaining discrepancies between the predictions of the telegraph model and experimental distributions of the extensions of DNA in nanochannels used for genome mapping.

Topologically Linked Chains in Confinement

We examine how channel confinement affects the equilibrium properties of topologically linked ring polymers and, by contrast, of equivalent unlinked rings, too. By performing extensive simulations of semiflexible rings of different chain length, N, and channel diameter, D, we discover three notable properties purely due to linking. First, upon entering the weak confinement regime, the length of the physically linked portion, lLKThe, becomes independent of chain length. Next, even when confinement is strong enough to pull apart and segregate unlinked rings, lLK stays much larger than in the highly stretched limit. Finally, at fixed N, lLK varies approximately as D^0.5, and we provide a simple scaling argument for this power-law behavior. These properties, which may hold for different link topologies, can be tested by current experimental setups on DNA rings confined in microchannels. Moreover, they could be relevant for the efficient in vivo unlinking of newly replicated bacterial chromosomes.

Stochastic unfolding of nanoconfined DNA: Experiments, model and Bayesian analysis

Nanochannels provide a means for detailed experiments on the effect of confinement on biomacromolecules, such as DNA. Here we introduce a model for the complete unfolding of DNA from the circular to linear configuration. Two main ingredients are the entropic unfolding force and the friction coefficient for the unfolding process, and we describe the associated dynamics by a non-linear Langevin equation. By analyzing experimental data where DNA molecules are photo-cut and unfolded inside a nanochannel, our model allows us to extract values for the unfolding force as well as the friction coefficient for the first time. In order to extract numerical values for these physical quantities, we employ a recently introduced Bayesian inference framework. We find that the determined unfolding force is in agreement with estimates from a simple Flory-type argument. The estimated friction coefficient is in agreement with theoretical estimates for motion of a cylinder in a channel. We further validate the estimated friction constant by extracting this parameter from DNA's center-of-mass motion before and after unfolding, yielding decent agreement. We provide publically available software for performing the required image and Bayesian analysis.

Nanoplumbing with 2D Metamaterials

Complex manipulations of DNA in a nanofluidic device require channels with branches and junctions. However, the dynamic response of DNA in such nanofluidic networks is relatively unexplored. Here, the transport of DNA in a 2D metamaterial made by arrays of nanochannel junctions is investigated. The mechanism of transport is explained as Brownian motion through an energy landscape formed by the combination of the confinement free energy of DNA and the effective potential of hydrodynamic flow, which both can be tuned independently within the device. For the quantitative understanding of DNA transport, a dynamic mean-field model of DNA at a nanochannel junction is proposed. It is shown that the dynamics of DNA in a nanofluidic device with branched channels and junctions is well described by the model.

Nanochannel-Confined TAMRA-Polypyrrole Stained DNA Stretching by Varying the Ionic Strength from Micromolar to Millimolar Concentrations

Large DNA molecules have been utilized as a model system to investigate polymer physics. However, DNA visualization via intercalating dyes has generated equivocal results due to dye-induced structural deformation, particularly unwanted unwinding of the double helix. Thus, the contour length increases and the persistence length changes so unpredictably that there has been a controversy. In this paper, we used TAMRA-polypyrrole to stain single DNA molecules. Since this staining did not change the contour length of B-form DNA, we utilized TAMRA-polypyrrole stained DNA as a tool to measure the persistence length by changing the ionic strength. Then, we investigated DNA stretching in nanochannels by varying the ionic strength from 0.06 mM to 47 mM to evaluate several polymer physics theories proposed by Odijk, de Gennes and recent papers to deal with these regimes.

Alpha-Synuclein Modulates the Physical Properties of DNA

Fundamental research on Parkinson's disease (PD) most often focuses on the ability of α-synuclein (aS) to form oligomers and amyloids, and how such species promote brain cell death. However, there are indications that aS also plays a gene-regulatory role in the cell nucleus. Here, the interaction between monomeric aS and DNA in vitro has been investigated with single-molecule techniques. Using a nanofluidic channel system, it was discovered that aS binds to DNA and by studying the DNA-protein complexes at different confinements we determined that aS binding increases the persistence length of DNA from 70 to 90 nm at high coverage. By atomic force microscopy it was revealed that at low protein-to-DNA ratio, the aS binding occurs as small protein clusters scattered along the DNA; at high protein-to-DNA ratio, the DNA is fully covered by protein. As DNA-aS interactions may play roles in PD, it is of importance to characterize biophysical properties of such complexes in detail.

Measuring the wall depletion length of nanoconfined DNA

Efforts to study the polymer physics of DNA confined in nanochannels have been stymied by a lack of consensus regarding its wall depletion length. We have measured this quantity in 38 nm wide, square silicon dioxide nanochannels for five different ionic strengths between 15 mM and 75 mM. Experiments used the Bionano Genomics Irys platform for massively parallel data acquisition, attenuating the effect of the sequence-dependent persistence length and finite-length effects by using nick-labeled E. coli genomic DNA with contour length separations of at least 30 µm (88 325 base pairs) between nick pairs. Over 5 × 106 measurements of the fractional extension were obtained from 39 291 labeled DNA molecules. Analyzing the stretching via Odijk's theory for a strongly confined wormlike chain yielded a linear relationship between the depletion length and the Debye length. This simple linear fit to the experimental data exhibits the same qualitative trend as previously defined analytical models for the depletion length but now quantitatively captures the experimental data.

Correlation anisotropy and stiffness of DNA molecules confined in nanochannels

The anisotropy of orientational correlations in DNA molecules confined in cylindrical channels is explored by Monte Carlo simulations using a coarse-grained model of double-stranded (ds) DNA. We find that the correlation function ⟨C(s)⟩_⊥ in the transverse (confined) dimension exhibits a region of negative values in the whole range of channel sizes. Such a clear-cut sign of the opposite orientation of chain segments represents a microscopic validation of the Odijk deflection mechanism in narrow channels. At moderate-to-weak confinement, the negative ⟨C(s)⟩_⊥ correlations imply a preference of DNA segments for transverse looping. The inclination for looping can explain a reduction of stiffness as well as the enhanced knotting of confined DNA relative to that detected earlier in bulk at some channel sizes. Furthermore, it is shown that the orientational persistence length P_or fails to convey the apparent stiffness of DNA molecules in channels. Instead, correlation lengths P_∥ and P_⊥ in the axial and transverse directions, respectively, encompass the channel-induced modifications of DNA stiffness.

Self-Avoiding Wormlike Chain Confined in a Cylindrical Tube: Scaling Behavior

Within a confining tube section, the multithreads of a strongly confined, backfolding polymer exert the excluded-volume repulsions on each other and produce physical properties that are very different from those of a confined ideal chain. The conformational properties of a such confined wormlike chain are of fundamental interest and are also practically useful in understanding the DNA confinement problems. Here, the excluded-volume effects are added to the standard wormlike-chain model by a self-consistent field theory. The numerical solutions are examined in light of their scaling properties.

Compressing a confined DNA: from nano-channel to nano-cavity

We analyze the behavior of a semiflexible polymer confined in nanochannel under compression in axial direction. Key to our discussion is the identification of two length scales; the correlation length ξ of concentration fluctuation and what we call the segregation length [Formula: see text]. These length scales, while degenerate in uncompressed state in nanochannel, generally split as [Formula: see text] upon compression, and the way they compete with the system size during the compression determines the crossover from quasi-1D nanochannel to quasi-0D nanocavity behaviors. For a flexible polymer, the story becomes very simple, which corresponds to a special limit of our description, but a much richer behavior is expected for a semiflexible polymer relevant to DNA in confined spaces. We also briefly discuss the dynamical properties of the compressed polymer.

Distribution of label spacings for genome mapping in nanochannels

In genome mapping experiments, long DNA molecules are stretched by confining them to very narrow channels, so that the locations of sequence-specific fluorescent labels along the channel axis provide large-scale genomic information. It is difficult, however, to make the channels narrow enough so that the DNA molecule is fully stretched. In practice, its conformations may form hairpins that change the spacings between internal segments of the DNA molecule, and thus the label locations along the channel axis. Here, we describe a theory for the distribution of label spacings that explains the heavy tails observed in distributions of label spacings in genome mapping experiments.

Evaluation of Blob Theory for the Diffusion of DNA in Nanochannels

We have measured the diffusivity of λ-DNA molecules in approximately square nanochannels with effective sizes ranging from 117 nm to 260 nm at moderate ionic strength. The experimental results do not agree with the non-draining scaling predicted by blob theory. Rather, the data are consistent with the predictions of previous simulations of the Kirkwood diffusivity of a discrete wormlike chain model, without the need for any fitting parameters.

Odijk excluded volume interactions during the unfolding of DNA confined in a nanochannel

We report experimental data on the unfolding of human and E. coli genomic DNA molecules shortly after injection into a 45 nm nanochannel. The unfolding dynamics are deterministic, consistent with previous experiments and modeling in larger channels, and do not depend on the biological origin of the DNA. The measured entropic unfolding force per friction per unit contour length agrees with that predicted by combining the Odijk excluded volume with numerical calculations of the Kirkwood diffusivity of confined DNA. The time scale emerging from our analysis has implications for genome mapping in nanochannels, especially as the technology moves towards longer DNA, by setting a lower bound for the delay time before making a measurement.