Extension of DNA in a nanochannel as a rod-to-coil transition

Confinement free energy for a polymer chain: Corrections to scaling

Spatial confinement of a polymer chain results in a reduction of conformational entropy. For confinement of a flexible N-mer chain in a planar slit or cylindrical pore (confining dimension D), a blob model analysis predicts the asymptotic scaling behavior ΔF/N ∼ D^-γ with γ ≈ 1.70, where ΔF is the free energy increase due to confinement. Here, we extend this scaling analysis to include the variation of local monomer density upon confinement giving ΔF/N ∼ D^-γ(1 - h(N, D)), where the correction-to-scaling term has the form h ∼ D^y/N^Δ with exponents y = 3 - γ ≈ 1.30 and Δ = 3/γ - 1 ≈ 0.76. To test these scaling predictions, we carry out Wang-Landau simulations of confined and unconfined tangent-hard-sphere chains (bead diameter σ) in the presence of a square-well trapping potential. The fully trapped chain provides a common reference state, allowing for an absolute determination of the confinement free energy. Our simulation results for 32 ≤ N ≤ 1024 and 3 ≤ D/σ ≤ 14 are well-described by the extended scaling relation giving exponents of γ = 1.69(1), y = 1.25(2), and Δ = 0.75(6).

Bistability of a helical filament confined on a cylinder

The natural configuration of an intrinsically curved and twisted filament is uniquely a helix so that it can be referred to as a helical filament. We find that confining a helical filament on a cylinder can create a bistable state. When c_{0}R=0.5, where c_{0} is the intrinsic curvature of filament and R is the radius of cylinder, the phase diagram for the stability of a helix contains three regimes. Regime I has a small intrinsic twisting rate (ITR) and exhibits a bistable state which consists of two isoenergic helices. In regime II, the filament has a moderate ITR and the bistable state consists of a metastable low-pitch helix and a stable nonhelix. In regime III, the helix is unstable, owing to a large ITR. A similar phenomenon occurs when c_{0}R∼0.5. Monte Carlo simulation confirms these conclusions and indicates further that there are bistable nonhelices in regime III. This bistable system offers a prospective green material since the wide range of parameters and distinctive configurations for bistable states favor its realization and application.

Topological and physical links in soft matter systems

Linking, or multicomponent topological entanglement, is ubiquitous in soft matter systems, from mixtures of polymers and DNA filaments packedin vivoto interlocked line defects in liquid crystals and intertwined synthetic molecules. Yet, it is only relatively recently that theoretical and experimental advancements have made it possible to probe such entanglements and elucidate their impact on the physical properties of the systems. Here, we review the state-of-the-art of this rapidly expanding subject and organize it as follows. First, we present the main concepts and notions, from topological linking to physical linking and then consider the salient manifestations of molecular linking, from synthetic to biological ones. We next cover the main physical models addressing mutual entanglements in mixtures of polymers, both linear and circular. Finally, we consider liquid crystals, fluids and other non-filamentous systems where topological or physical entanglements are observed in defect or flux lines. We conclude with a perspective on open challenges.

Adsorption of Semiflexible Polymers in Cylindrical Tubes

Conformations of wormlike chains in cylindrical pores with attractive walls are explored for varying pore radius and strength of the attractive wall potential by molecular dynamics simulations of a coarse-grained model. Local quantities such as the fraction of monomeric units bound to the surface and the bond-orientational order parameter as well as the radial density distribution are studied, as well as the global chain extensions parallel to the cylinder axis and perpendicular to the cylinder surface. A nonmonotonic convergence of these properties to their counterparts for adsorption on a planar substrate is observed due to the conflict between pore surface curvature and chain stiffness. Also the interpretation of partially adsorbed chains in terms of trains, loops, and tails is discussed.

Cylindrical confinement of solutions containing semiflexible macromolecules: surface-induced nematic order versus phase separation

Solutions of semiflexible polymers confined in cylindrical pores with repulsive walls are studied by Molecular Dynamics simulations for a wide range of polymer concentrations. Both the case where both lengths are of the same order and the case when the persistence length by far exceeds the contour length are considered, and the enhancement of nematic order along the cylinder axis is characterized. With increasing density the character of the surface effect changes from depletion to the formation of a layered structure. For binary 50 : 50 mixtures of the two types of polymers an interplay between surface enrichment of the stiffer component and the isotropic-nematic transition is found, and a phase separated structure with cylindrical symmetry occurs, with the isotropic phase located around the cylinder axis. For melt densities the mixed nematic phase forms at the wall a layer with a screw-like structure of a tilted smectic phase. The observed behavior is tentatively interpreted in terms of the competition of the chain orientational entropy with entropy of mixing and excluded volume due to the wall.

Systematic Approach toward Accurate and Efficient DNA Sequencing via Nanoconfinement

Coarse-grained modeling tools are employed to simulate the mechanics of DNA loading within a nanoscale confinement and predict semiflexible polymer conformations within the confinement, providing design recommendations for DNA-sequencing devices. A workflow is developed to quantify competing requirements of efficiency and accuracy and extract metrics that guide design optimization. The mean first-passage time for DNA loading is calculated as a function of the nanochannel geometry and the applied electric field. We analyze the interplay between the free energy of confinement and the electric potential energy in achieving high-throughput, base-pair detection. The single-read probability is investigated as informative metrics for sequencing accuracy and for sensing-strategy design. High cost, low throughput, and low accuracy have so far limited the adoption of nanochannel analysis and other long-read technologies. Our work directly addresses these limitations with a systematic approach that is scalable to long molecules and complex geometries.

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.

Rod-like transition first or chain aggregation first? ordered aggregation of rod-like poly(p-phenyleneethynylene) chains in solution

The rod-like configuration of conjugated polymer chains with its low energetic disorder is the key to utilizing the backbone as a highly electrically-conductive wire. An energetic disorder that is higher than 0.1 eV, coupled with vibronic modes of the chains, leads to the localization of charges. Herein, we have tracked precisely the rod-like transition of poly(p-phenyleneethynylene) (PPE) chains as a function of temperature in diluted solutions, and shown a steep increase in persistence length at 230 K. The resulting rod-like configuration of the PPE chains with its extended electronic conjugation exhibited an extremely small energetic disorder of ∼70 meV, and was stabilized by subsequent polymer aggregate formation.

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.

Spontaneous ssDNA stretching on graphene and hexagonal boron nitride in plane heterostructures

Single-stranded DNA (ssDNA) molecules in solution typically form coiled structures, therefore stretching ssDNA is extremely crucial before applying any nanotechnology for ssDNA analysis. Recent advances in material fabrication enable the deployment of nanochannels to manipulate, stretch, sort and map double-stranded DNA (dsDNA) molecules, however nanochannels fail to stretch ssDNA molecules due to the ultra-short persistence length and the potential nonspecific-interaction-induced clogging. Given the significance of ssDNA stretching in genome analysis, here we report an ssDNA stretching platform: two dimensional in-plane heterostructure comprising graphene and hexagonal boron nitride (h-BN), and show that ssDNA can be stretched on a h-BN nanostripe sandwiched between two adjacent graphene domains (“nanochannel”). We further show that with a biasing voltage the stretched ssDNA can be electrophoretically transported along the “nanochannel”, allowing easy controls/manipulations. When being conveniently integrated with existing atomic resolution sensors, the heterostructure platform paves the way for sequencing DNA on a planar surface.

Single stranded DNA analysis is of interest for a range of applications; however, natural folding of DNA can cause problems with this. Here, the authors report on the in silico analysis of graphene and hexagonal-boron-nitride structures for the stretching and unfolding of DNA to allow for analysis.

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.

The Persistence Length of Semiflexible Polymers in Lattice Monte Carlo Simulations

While applying computer simulations to study semiflexible polymers, it is a primary task to determine the persistence length that characterizes the chain stiffness. One frequently asked question concerns the relationship between persistence length and the bending constant of applied bending potential. In this paper, theoretical persistence lengths of polymers with two different bending potentials were analyzed and examined by using lattice Monte Carlo simulations. We found that the persistence length was consistent with theoretical predictions only in bond fluctuation model with cosine squared angle potential. The reason for this is that the theoretical persistence length is calculated according to a continuous bond angle, which is discrete in lattice simulations. In lattice simulations, the theoretical persistence length is larger than that in continuous simulations.

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.

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.

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.

Hairpins in the conformations of a confined polymer

If a semiflexible polymer confined to a narrow channel bends around by 180°, the polymer is said to exhibit a hairpin. The equilibrium extension statistics of the confined polymer are well understood when hairpins are vanishingly rare or when they are plentiful. Here, we analyze the extension statistics in the intermediate situation via experiments with DNA coated by the protein RecA, which enhances the stiffness of the DNA molecule by approximately one order of magnitude. We find that the extension distribution is highly non-Gaussian, in good agreement with Monte-Carlo simulations of confined discrete wormlike chains. We develop a simple model that qualitatively explains the form of the extension distribution. The model shows that the tail of the distribution at short extensions is determined by conformations with one hairpin.

Stretching and compression of DNA by external forces under nanochannel confinement

Mechanical deformation of dsDNA molecules inside square nanochannels is investigated using simulations based on a coarse-grained model of DNA. The combined action of confinement and weak external forces is explored in a variety of confinement regimes, including the transition zone relevant to nanofluidic experiments. The computed free energy and force profiles are markedly affected by the channel size. Effective elastic softening of confined DNA molecules relative to the bulk DNA is observed in the channels of intermediate widths. The extension of DNA from its bulk equilibrium length in nanofluidic devices is resolved into contributions from the passive extension due to confinement and from the active stretching induced by force. Potential implications of the very different energy costs computed for the two extension modes (extension by confinement takes much more free energy than stretching by force) for behavior of DNA in nanofluidic chips are indicated.

Evidence for the extended de Gennes regime of a semiflexible polymer in slit confinement

We use off-lattice, pruned-enriched Rosenbluth method (PERM) simulations to compute the confinement free energy of a real wormlike chain of effective width w and persistence length lp in a slit of height H. For slit heights much larger than the persistence length of the polymer and much smaller than the thermal blob size, the excess free energy of the confined chain is consistent with a modified version of the scaling theory for the extended de Gennes regime in a channel that reflects the blob statistics in slit confinement. Explicitly, for channel sizes [Formula: see text], the difference between the confinement free energy of the real chain and that of an ideal chain scales like w/H.

The Statistical Segment Length of DNA: Opportunities for Biomechanical Modeling in Polymer Physics and Next-Generation Genomics

The development of bright bisintercalating dyes for deoxyribonucleic acid (DNA) in the 1990s, most notably YOYO-1, revolutionized the field of polymer physics in the ensuing years. These dyes, in conjunction with modern molecular biology techniques, permit the facile observation of polymer dynamics via fluorescence microscopy and thus direct tests of different theories of polymer dynamics. At the same time, they have played a key role in advancing an emerging next-generation method known as genome mapping in nanochannels. The effect of intercalation on the bending energy of DNA as embodied by a change in its statistical segment length (or, alternatively, its persistence length) has been the subject of significant controversy. The precise value of the statistical segment length is critical for the proper interpretation of polymer physics experiments and controls the phenomena underlying the aforementioned genomics technology. In this perspective, we briefly review the model of DNA as a wormlike chain and a trio of methods (light scattering, optical or magnetic tweezers, and atomic force microscopy (AFM)) that have been used to determine the statistical segment length of DNA. We then outline the disagreement in the literature over the role of bisintercalation on the bending energy of DNA, and how a multiscale biomechanical approach could provide an important model for this scientifically and technologically relevant problem.

One-Parameter Scaling Theory for DNA Extension in a Nanochannel

Experiments measuring DNA extension in nanochannels are at odds with even the most basic predictions of current scaling arguments for the conformations of confined semiflexible polymers such as DNA. We show that a theory based on a weakly self-avoiding, one-dimensional "telegraph" process collapses experimental data and simulation results onto a single master curve throughout the experimentally relevant region of parameter space and explains the mechanisms at play.

Structural Behavior of a Semiflexible Polymer Chain in an Array of Nanoposts

The structural properties of a flexible and semiflexible circular chain confined in an array of parallel nanoposts with a square lattice cross-sectional projection were studied using coarse-grained molecular dynamics simulations. To address the effect of the circular topology, a comparison with linear analogs was also carried out. In the interpretation of the chain structural properties, the geometry of the post array is considered as a combination of a channel approximating the interstitial volume with the diameter dc and a slit approximating the passage aperture with the width wp. The number of interstitial volumes occupied by a chain monotonically increases with the decreasing ratio dc/wp regardless of the way the geometry of the post array is varied. However, depending on how the array geometry is modified, the chain span along the posts displays a monotonic (constant post separation) or a non-monotonic behavior (constant passage width) when plotted as a function of the post diameter. In the case of monotonic trend, the width of interstitial spaces increases with the increasing chain occupation number, while, in the case of non-monotonic trend, the width of interstitial spaces decreases with the increasing chain occupation number. In comparison with linear topology, for circular topology, the stiffness affects more significantly the relative chain extension along the posts and less significantly the occupation number. The geometrical parameters of the post arrays are stored in the single-chain structure factors. The characteristic humps are recognized in the structure factor which ensue from the local increase in the density of segments in the circular chains presented in an interstitial volume or from the correlation of parallel chain fragments separated by a row of posts. Although the orientation correlations provide qualitative information about the chain topology and the character of confinement within a single interstitial volume, information about the array periodicity is missing.

Conformational Properties of a Back-Folding Wormlike Chain Confined in a Cylindrical Tube

When a semiflexible chain is confined in a narrow cylindrical tube, the formation of a polymer hairpin is a geometrical conformation that accompanies an exponentially large local free energy and, hence, is a relatively rare event. Numerical solutions of the hairpin distribution functions for persistence-length-to-tube-radius ratios over a wide range are obtained in high precision, by using the Green's function approach for the wormlike-chain model. The crossover region between the narrow and moderately narrow tubes is critically investigated in terms of the hairpin free energy, global persistence length, mean hairpin-tip distance from the tube axis, and hairpin-plane orientational properties. Accurate representations of the solutions by simple interpolation formulae are suggested.

Confinement-driven organization of a histone-complexed DNA molecule in a dense array of nanoposts

The first step in the controlled storage of lengthy DNA molecules is to keep DNA molecules separated while integrated in micrometer-sized space. Herein, we present hybrid Monte Carlo simulations of a histone-complexed DNA (hcDNA) molecule confined in a dense array of nanoposts. Depending on the nanopost dimension, a single, 8.7 kilobase pair hcDNA molecule was either localized and elongated in a single inter-post space surrounded by four nanoposts or spread over several inter-post spaces through passages between two neighboring nanoposts. The conformational change of a hcDNA molecule is interpreted in terms of competitive effects of confinements in the inter-post and passage spaces. We propose that, by elaborately designing nanopost arrays, the competitive confinement effects can be adjusted such that each hcDNA molecule is localized in a single inter-post space, and thereby multiple hcDNA molecules can be physically separated from each other while stored together in the nanopost array.

Simulations of knotting of DNA during genome mapping

Genome mapping involves the confinement of long DNA molecules, in excess of 150 kilobase pairs, in nanochannels near the circa 50 nm persistence length of DNA. The fidelity of the map relies on the assumption that the DNA is linearized by channel confinement, which assumes the absence of knots. We have computed the probability of forming different knot types and the size of these knots for long chains (approximately 164 kilobase pairs) via pruned-enriched Rosenbluth method simulations of a discrete wormlike chain model of DNA in channel sizes ranging from 35 nm to 60 nm. Compared to prior simulations of short DNA in similar confinement, these long molecules exhibit both complex knots, with up to seven crossings, and multiple knots per chain. The knotting probability is a very strong function of channel size, ranging from 0.3% to 60%, and rationalized in the context of Odijk's theory for confined semiflexible chains. Overall, the knotting probability and knot size obtained from these equilibrium measurements are not consistent with experimental measurements of the properties of anomalously bright regions along the DNA backbone during genome mapping experiments. This result suggests that these events in experiments are either knots formed during the processing of the DNA prior to injection into the nanochannel or regions of locally high DNA concentration without a topological constraint. If so, knots during genome mapping are not an intrinsic problem for genome mapping technology.

Wall depletion length of a channel-confined polymer

Numerous experiments have taken advantage of DNA as a model system to test theories for a channel-confined polymer. A tacit assumption in analyzing these data is the existence of a well-defined depletion length characterizing DNA-wall interactions such that the experimental system (a polyelectrolyte in a channel with charged walls) can be mapped to the theoretical model (a neutral polymer with hard walls). We test this assumption using pruned-enriched Rosenbluth method (PERM) simulations of a DNA-like semiflexible polymer confined in a tube. The polymer-wall interactions are modeled by augmenting a hard wall interaction with an exponentially decaying, repulsive soft potential. The free energy, mean span, and variance in the mean span obtained in the presence of a soft wall potential are compared to equivalent simulations in the absence of the soft wall potential to determine the depletion length. We find that the mean span and variance about the mean span have the same depletion length for all soft potentials we tested. In contrast, the depletion length for the confinement free energy approaches that for the mean span only when depletion length no longer depends on channel size. The results have implications for the interpretation of DNA confinement experiments under low ionic strengths.

Comparison of a stripe and slab confinement for ring and linear macromolecules in nanochannel

The combined effects of the channel asymmetry and the closed chain topology on the chain extension, structure factor, and the orientation correlations were studied using coarse-grained molecular dynamics simulations for moderate chain lengths. These effects are related to applications in linearization experiments with a DNA molecule in nanofluidic devices. According to the aspect ratio, the channels are classified as a stripe or slabs. The chain segments do not have any freedom to move in the direction of the narrowest stripe size, being approximately the same size as the segment size. The chains of both ring and linear topologies are extended more in a stripe than in a slab; this effect is strengthened for a ring. For a ring in a stripe, the extension-confinement strength dependence leads to effective Flory exponents even larger than 3/4, which is characteristic for a self-avoiding two-dimensional chain. While the chain extension-confinement strength dependence for both topologies conforms to the de Gennes regime in a stripe, a linear chain undergoes gradual transition to the pseudoideal regime as the slab height increases in the slab-like confinement. For a confined circle, the onset of the pseudoideal regime is shifted to larger slab heights. The structure factor confirms the absence of the pseudoideal and extended de Gennes regime in a stripe and the transition from the extended to the pseudoideal regime of a circular and linear chain upon increasing the slab heights.

Dynamics of DNA Squeezed Inside a Nanochannel via a Sliding Gasket

We use Brownian dynamics (BD) simulation of a coarse-grained (CG) bead-spring model of DNA to study the nonequilibrim dynamics of a single DNA molecule confined inside a rectangular nanochannel being squeezed with a sliding gasket piston or "nanodozer". From our simulations we extract the nonequilibrim density profile c ( x , t ) of the squeezed molecule along the channel axis (x-coordinate) and then analyze the non-equilibrium profile using a recently introduced phenomenological Nonlinear Partial Differential Equation (NPDE) model. Since the NPDE approach also fits the experimental results well and is numerically efficient to implement, the combined BD + NPDE methods can be a powerful approach to analyze details of the confined molecular dynamics. In particular, the overall excellent agreement between the two complementary sets of data provides a strategy for carrying out large scale simulation on semi-flexible biopolymers in confinement at biologically relevant length scales.

Semiflexible macromolecules in quasi-one-dimensional confinement: Discrete versus continuous bond angles

The conformations of semiflexible polymers in two dimensions confined in a strip of width D are studied by computer simulations, investigating two different models for the mechanism by which chain stiffness is realized. One model (studied by molecular dynamics) is a bead-spring model in the continuum, where stiffness is controlled by a bond angle potential allowing for arbitrary bond angles. The other model (studied by Monte Carlo) is a self-avoiding walk chain on the square lattice, where only discrete bond angles (0° and ±90°) are possible, and the bond angle potential then controls the density of kinks along the chain contour. The first model is a crude description of DNA-like biopolymers, while the second model (roughly) describes synthetic polymers like alkane chains. It is first demonstrated that in the bulk the crossover from rods to self-avoiding walks for both models is very similar, when one studies average chain linear dimensions, transverse fluctuations, etc., despite their differences in local conformations. However, in quasi-one-dimensional confinement two significant differences between both models occur: (i) The persistence length (extracted from the average cosine of the bond angle) gets renormalized for the lattice model when D gets less than the bulk persistence length, while in the continuum model it stays unchanged. (ii) The monomer density near the repulsive walls for semiflexible polymers is compatible with a power law predicted for the Kratky-Porod model in the case of the bead-spring model, while for the lattice case it tends to a nonzero constant across the strip. However, for the density of chain ends, such a constant behavior seems to occur for both models, unlike the power law observed for flexible polymers. In the regime where the bulk persistence length ℓp is comparable to D, hairpin conformations are detected, and the chain linear dimensions are discussed in terms of a crossover from the Daoud/De Gennes "string of blobs"-picture to the flexible rod picture when D decreases and/or the chain stiffness increases. Introducing a suitable further coarse-graining of the chain contours of the continuum model, direct estimates for the deflection length and its distribution could be obtained.

Modeling the relaxation of internal DNA segments during genome mapping in nanochannels

We have developed a multi-scale model describing the dynamics of internal segments of DNA in nanochannels used for genome mapping. In addition to the channel geometry, the model takes as its inputs the DNA properties in free solution (persistence length, effective width, molecular weight, and segmental hydrodynamic radius) and buffer properties (temperature and viscosity). Using pruned-enriched Rosenbluth simulations of a discrete wormlike chain model with circa 10 base pair resolution and a numerical solution for the hydrodynamic interactions in confinement, we convert these experimentally available inputs into the necessary parameters for a one-dimensional, Rouse-like model of the confined chain. The resulting coarse-grained model resolves the DNA at a length scale of approximately 6 kilobase pairs in the absence of any global hairpin folds, and is readily studied using a normal-mode analysis or Brownian dynamics simulations. The Rouse-like model successfully reproduces both the trends and order of magnitude of the relaxation time of the distance between labeled segments of DNA obtained in experiments. The model also provides insights that are not readily accessible from experiments, such as the role of the molecular weight of the DNA and location of the labeled segments that impact the statistical models used to construct genome maps from data acquired in nanochannels. The multi-scale approach used here, while focused towards a technologically relevant scenario, is readily adapted to other channel sizes and polymers.

Spontaneous Insertion, Helix Formation, and Hydration of Polyethylene Oxide in Carbon Nanotubes

Hydration strongly affects macromolecular conformation in solution and under nanoconfinement as encountered in nature and nanomaterials. Using atomistic molecular dynamics simulations we demonstrate that polyethylene oxide spontaneously enters single wall carbon nanotubes (CNTs) from aqueous solutions and forms rodlike, helix, and wrapped chain conformations depending on the CNT diameter. We show that water organization and the stability of the polyethylene oxide hydration shell under confinement is responsible for the helix formation, which can have significant implications for nanomaterial design.

The polymer physics of single DNA confined in nanochannels

In recent years, applications and experimental studies of DNA in nanochannels have stimulated the investigation of the polymer physics of DNA in confinement. Recent advances in the physics of confined polymers, using DNA as a model polymer, have moved beyond the classic Odijk theory for the strong confinement, and the classic blob theory for the weak confinement. In this review, we present the current understanding of the behaviors of confined polymers while briefly reviewing classic theories. Three aspects of confined DNA are presented: static, dynamic, and topological properties. The relevant simulation methods are also summarized. In addition, comparisons of confined DNA with DNA under tension and DNA in semidilute solution are made to emphasize universal behaviors. Finally, an outlook of the possible future research for confined DNA is given.

Effect of excluded volume on the force-extension of wormlike chains in slit confinement

We use pruned-enriched Rosenbluth method simulations to develop a quantitative phase diagram for the stretching of a real wormlike chain confined in a slit. Our simulations confirm the existence of a "confined Pincus" regime in slit confinement, analogous to the Pincus regime in free solution, where excluded volume effects are sensible. The lower bound for the confined Pincus regime in the force-molecular weight plane, as well as the scaling of the extension with force and slit size, agree with an existing scaling theory for this regime. The upper bound of the confined Pincus regime depends on the strength of the confinement. For strong confinement, the confined Pincus regime ends when the contour length in the Pincus blob is too short to have intrablob excluded volume. As a result, the chain statistics become ideal and the confined Pincus regime at low forces is connected directly to ideal chain stretching at large forces. In contrast, for weak confinement, the confined Pincus regime ends when the Pincus blobs no longer fit inside the slit, even though there is sufficient contour length to have excluded volume inside the Pincus blob. As a result, weak confinement leads to a free-solution Pincus regime intervening between the confined Pincus regime for weak forces and ideal chain stretching at strong forces. Our results highlight shortcomings in existing models for the stretching of wormlike chains in slits.

The Backfolded Odijk Regime for Wormlike Chains Confined in Rectangular Nanochannels

We confirm Odijk's scaling laws for (i) the average chain extension; (ii) the variance about the average extension; and (iii) the confinement free energy of a wormlike chain confined in a rectangular nanochannel smaller than its chain persistence length through pruned-enriched Rosenbluth method (PERM) simulations of asymptotically long, discrete wormlike chains. In the course of this analysis, we also computed the global persistence length of ideal wormlike chains for the modestly rectangular channels that are used in many experimental systems. The results are relevant to genomic mapping systems that confine DNA in channel sizes around 50 nm, since fabrication constraints generally lead to rectangular cross-sections.

Transition state theory demonstrated at the micron scale with out-of-equilibrium transport in a confined environment

Transition state theory (TST) provides a simple interpretation of many thermally activated processes. It applies successfully on timescales and length scales that differ several orders of magnitude: to chemical reactions, breaking of chemical bonds, unfolding of proteins and RNA structures and polymers crossing entropic barriers. Here we apply TST to out-of-equilibrium transport through confined environments: the thermally activated translocation of single DNA molecules over an entropic barrier helped by an external force field. Reaction pathways are effectively one dimensional and so long that they are observable in a microscope. Reaction rates are so slow that transitions are recorded on video. We find sharp transition states that are independent of the applied force, similar to chemical bond rupture, as well as transition states that change location on the reaction pathway with the strength of the applied force. The states of equilibrium and transition are separated by micrometres as compared with angstroms/nanometres for chemical bonds.

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.

Confinement and partitioning of a single polymer chain in a dense array of nanoposts

We present a Brownian dynamics simulation study on the confinement and partitioning of a single, flexible polymer chain in a dense array of nanoposts with different sizes and separations, especially, when the volume of an interstitial space formed among four nanoposts is less than the volume of the polymer chain. As the interstitial volume decreases by either increasing the nanopost diameter or decreasing the separation between nanoposts, the chain conformation becomes elongated in the direction parallel to the nanoposts. Interestingly, however, the degree of chain elongation varies in a non-monotonic fashion as the interstitial volume decreases while keeping the passage width between two nanoposts constant at a small value. We calculate the free energy of chain partitioning over several interstitial spaces from the partitioning probability, and find that the non-monotonic dependence of the chain elongation results from an interplay between the confinement-driven chain elongation along the direction parallel to the nanoposts and the chain spreading perpendicular to the nanoposts by partitioning chain segments over several interstitial spaces. These results present the possibility of utilizing a dense array of nanoposts as a template to control polymer conformations.

Fabrication and characterization of nanopore-interfaced nanochannel devices

Nanofluidic devices combining nanochannels and nanopores may enable a range of novel applications in the field of single-molecule biosensing and manipulation. Here we combine classic lithographically based fabrication and electron beam milling to construct a device that integrates sealed transverse features, such as nanocavities and nanochannels, with embedded pores vertically intersecting the nanochannels. Using fluorescent microscopy, we demonstrate that DNA molecules can be introduced into the nanochannels and translated transversely across the embedded pore in an extended-conformation without undergoing cross-pore translocation. Upon application of a trans-pore voltage drop, the molecules will undergo cross-pore translocation into an adjoining macroscopic reservoir.

DNA Brushing Shoulders: Targeted Looping and Scanning of Large DNA Strands

We present a nanofluidic device for targeted manipulations in the quarternary structure of single DNA molecules. We demonstrate the folding and unfolding of hairpin-shaped regions, similar to chromatin loops. These loops are stable for minutes at nanochannel junctions. We demonstrate continuous scanning of two DNA segments that occupy a common nanovolume. We present a model governing the stability of loop folds and discuss how the system achieves specific DNA configurations without operator intervention.

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.

Rigorous study of molecular dynamics of a single dsDNA confined in a nanochannel: Introduction of a critical mobility behaviour

The essential and effective characteristics of a double-stranded DNA (dsDNA) confined in a nanochannel is revisited by employing the rigorous full numerical approach of Molecular Dynamics (MD). The deformation of dsDNA and wall-biomolecule interaction which is critical in highly confined regime has been precisely imposed in numerical simulations. The numerical approach has been justified against available theoretical outcomes. A new and general expression for DNA electrophoretic mobility versus DNA length is extracted from numerical simulation which is out of reach of experimental methods due to practical shortcomings. The newly derived expression suggests an essential correction in the previously proposed expression for the critical case of small DNA molecules and reveals an astonishingly unbeknown trend of small DNA's mobility. Sub-molecular phenomenon of dsDNA melting under the condition of large external force is also studied. Assuming strong electric field exertion, the MD approach aptly demonstrates the elaborate melting phenomenon for dsDNA in sub-molecular scale.

Topological events in single molecules of E. coli DNA confined in nanochannels

We present experimental data concerning potential topological events such as folds, internal backfolds, and/or knots within long molecules of double-stranded DNA when they are stretched by confinement in a nanochannel. Genomic DNA from E. coli was labeled near the 'GCTCTTC' sequence with a fluorescently labeled dUTP analog and stained with the DNA intercalator YOYO. Individual long molecules of DNA were then linearized and imaged using methods based on the NanoChannel Array technology (Irys® System) available from BioNano Genomics. Data were collected on 189 153 molecules of length greater than 50 kilobases. A custom code was developed to search for abnormal intensity spikes in the YOYO backbone profile along the length of individual molecules. By correlating the YOYO intensity spikes with the aligned barcode pattern to the reference, we were able to correlate the bright intensity regions of YOYO with abnormal stretching in the molecule, which suggests these events were either a knot or a region of internal backfolding within the DNA. We interpret the results of our experiments involving molecules exceeding 50 kilobases in the context of existing simulation data for relatively short DNA, typically several kilobases. The frequency of these events is lower than the predictions from simulations, while the size of the events is larger than simulation predictions and often exceeds the molecular weight of the simulated molecules. We also identified DNA molecules that exhibit large, single folds as they enter the nanochannels. Overall, topological events occur at a low frequency (∼7% of all molecules) and pose an easily surmountable obstacle for the practice of genome mapping in nanochannels.

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.