DNA confined in nanochannels: Hairpin tightening by entropic depletion

Organized states arising from compression of single semiflexible polymer chains in nanochannels

We use molecular dynamics simulation to probe the nonequilibrium physics of single nanochannel-confined semiflexible polymers in a homogeneous flow field. The flow field compresses the polymer against the end of the nanochannel, simulating an experiment of a nanochannel confined chain compressed against a slit barrier. The flow-based compression gives rise to a packing of the chain against the channel end that possesses a striking organization, consisting of interweaving of folds and circular coils. For stiff chains at low flow, we find that the organization is dominated by repeated hairpin folds. For stiff chains at higher flow, we observe that circular coils arise along with the folds, with folding and coiling domains becoming interwoven at the highest flow speeds. Chain organization is retained even when the chain persistence length is on order of the channel width. We show that the global polymer organization, consisting of a number of defined folds and coiled loops, arises from the minimization of the total chain free energy.

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.

Free energy of a knotted polymer confined to narrow cylindrical and conical channels

Monte Carlo simulations are used to study the conformational behavior of a semiflexible polymer confined to cylindrical and conical channels. The channels are sufficiently narrow that the conditions for the Odijk regime are marginally satisfied. For cylindrical confinement, we examine polymers with a single knot of topology 3_{1}, 4_{1}, or 5_{1}, as well as unknotted polymers that are capable of forming S loops. We measure the variation of the free energy F with the end-to-end polymer extension length X and examine the effect of varying the polymer topology, persistence length P, and cylinder diameter D on the free-energy functions. Similarly, we characterize the behavior of the knot span along the channel. We find that increasing the knot complexity increases the typical size of the knot. In the regime of low X, where the knot/S-loop size is large, the conformational behavior is independent of polymer topology. In addition, the scaling properties of the free energy and knot span are in agreement with predictions from a theoretical model constructed using known properties of interacting polymers in the Odijk regime. We also examine the variation of F with the position of a knot in conical channels for various values of the cone angle α. The free energy decreases as the knot moves in a direction where the cone widens, and it also decreases with increasing α and with increasing knot complexity. The behavior is in agreement with predictions from a theoretical model in which the dominant contribution to the change in F is the change in the size of the hairpins as the knot moves to the wider region of the channel.

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.

Stretching Wormlike Chains in Narrow Tubes of Arbitrary Cross-Sections

We considered the stretching of semiflexible polymer chains confined in narrow tubes with arbitrary cross-sections. Based on the wormlike chain model and technique of normal mode decomposition in statistical physics, we derived a compact analytical expression on the force-confinement-extension relation of the chains. This single formula was generalized to be valid for tube confinements with arbitrary cross-sections. In addition, we extended the generalized bead-rod model for Brownian dynamics simulations of confined polymer chains subjected to force stretching, so that the confinement effects to the chains applied by the tubes with arbitrary cross-sections can be quantitatively taken into account through numerical simulations. Extensive simulation examples on the wormlike chains confined in tubes of various shapes quantitatively justified the theoretically derived generalized formula on the force-confinement-extension relation of the chains.

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.

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.

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.

Nematic order in solutions of semiflexible polymers: Hairpins, elastic constants, and the nematic-smectic transition

Coarse-grained models of lyotropic solutions of semiflexible polymers are studied by both molecular dynamics simulations and density functional theory calculations, using an implicit solvent bead-spring model with a bond-angle potential. We systematically vary the monomer density, persistence length, and contour length over a wide range and explore the full range from the isotropic-nematic transition to the nematic-smectic transition. In the nematic regime, we span the entire regime from rigid-rod like polymers to thin wormlike chains, confined in effective straight tubes caused by the collective nematic effective ordering field. We show that the distribution of bond angles relative to the director is well described by a Gaussian, irrespective of whether the chains are rod-like or rather flexible. However, the related concept of "deflection length" is shown to make sense only in the latter case for rather dilute solutions since otherwise the deflection length is of the order of about two bond lengths only. When the solution is semi-dilute, a substantial renormalization of the persistence length occurs, while this effect is absent in the isotropic phase even at rather high monomer densities. The effective radii of the "tubes" confining the chains in the related description of orientational ordering are significantly larger than the distances between neighboring chains, providing evidence for a pronounced collective character of orientational fluctuations. Hairpins can be identified close to the isotropic-nematic transition, and their probability of occurrence agrees qualitatively with the Vroege-Odijk theory. The corresponding theoretical predictions for the elastic constants, however, are not in good agreement with the simulations. We attribute the shortcomings of the theories to their neglect of the coupling between local density and orientational fluctuations. Finally, we detected for this model a transition to a smectic phase for reduced monomer densities near 0.7.

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.

Splay-density coupling in semiflexible main-chain nematic polymers with hairpins

A main-chain nematic polymer melt/solution exhibits macroscopic orientational order of main polymer chains, i.e., a preferred (nematic) direction. It has long been known that in such polymeric liquid crystals spatial density/concentration variations and distortions of the nematic direction are coupled, obeying a vectorial continuity constraint whose rigidity increases with chain length. Its vectorial nature precludes the application to flexible chains, where backfolds (hairpins) are present and apolar nematic symmetry is manifest, which has been its puzzling feature from the beginning. We now establish a description of the splay-density coupling in the case of arbitrary backfolding, devising a continuity constraint for the "recovered" polar order of the chain tangents and introducing hairpins as its new type of sources. Performing detailed Monte Carlo simulations of nematic monodomain melts of "soft" worm-like chains with variable length and flexibility, we show via their structure factors that the weakening of the coupling due to the backfolding can be consistently quantified on the macroscopic level.

Adhesion of gram-negative rod-shaped bacteria on 1D nano-ripple glass pattern in weak magnetic fields

This research project has major applications in the healthcare and biomedical industries. Bacteria reside in human bodies and play an integral role in the mechanism of life. However, their excessive growth or the invasion of similar agents can be dangerous and may cause fatal or incurable diseases. On the other hand, increased exposure to electromagnetic radiation and its impact on health and safety is a common concern to medical science. Some nanostructure materials have interesting properties regarding facilitating or impeding cell growth. An understanding of these phenomena can be utilized to establish the optimum benefit of these structures in healthcare and medical research. We focus on the commonly found rod‐shaped, gram‐negative bacteria and their orientation and community development on the cellular level in the presence of weak magnetic fields on one dimensional nano‐ripple glass patterns to investigate the impact of nanostructures on the growth pattern of bacteria. The change in bacterial behavior on nanostructures and the impact of magnetic fields will open up new venues in the utilization of nanostructures. It is noticed that bacterial entrapment in nano‐grooves leads to the growth of larger colonies on the nanostructures, whereas magnetic fields reduce the size of colonies and suppress their growth.

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.

Tunable Confinement for Bridging Single-Cell Manipulation and Single-Molecule DNA Linearization

DNA linearization by nanoconfinement has offered a new avenue toward large-scale genome mapping. The ability to smoothly interface the widely different length scales from cell manipulation to DNA linearization is critical to the development of single-cell genomic mapping or sequencing technologies. Conventional nanochannel technologies for DNA analysis suffer from complex fabrication procedures, DNA stacking at the nanochannel entrance, and inefficient solution exchange. In this work, a dynamic and tunable confinement strategy is developed to manipulate and linearize genomic-length DNA molecules from a single cell. By leveraging pneumatic microvalve control and elastomeric collapse, an array of nanochannels with confining dimension down to 20 nm and length up to sub-millimeter is created and can be dynamically tuned in size. The curved edges of the microvalve form gradual transitions from microscale to nanoscale confinement, smoothly facilitating DNA entry into the nanochannels. A unified micro/nanofluidic device that integrates single-cell trapping and lysis, DNA extraction, purification, labeling, and linearization is developed based on dynamically controllable nanochannels. Mbp-long DNA molecules are extracted directly from a single cell and in situ linearized in the nanochannels. The device provides a facile and promising platform to achieve the ultimate goal of single-cell, single-genome analysis.

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.

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.

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.

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.

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.

Theory of Semiflexible Filaments and Networks

We briefly review the recent developments in the theory of individual semiflexible filaments, and of a crosslinked network of such filaments, both permanent and transient. Starting from the free energy of an individual semiflexible chain, models on its force-extension relation and other mechanical properties such as Euler buckling are discussed. For a permanently crosslinked network of filaments, theories on how the network responds to deformation are provided, with a focus on continuum approaches. Characteristic features of filament networks, such as nonlinear stress-strain relation, negative normal stress, tensegrity, and marginal stability are discussed. In the new area of transient filament network, where the crosslinks can be dynamically broken and re-formed, we show some recent attempts for understanding the dynamics of the crosslinks, and the related rheological properties, such as stress relaxation, yield stress and plasticity.

Thermoplastic nanofluidic devices for biomedical applications

Microfluidics is now moving into a developmental stage where basic discoveries are being transitioned into the commercial sector so that these discoveries can affect, for example, healthcare. Thus, high production rate microfabrication technologies, such as thermal embossing and/or injection molding, are being used to produce low-cost consumables appropriate for commercial applications. Based on recent reports, it is clear that nanofluidics offers some attractive process capabilities that may provide unique venues for biomolecular analyses that cannot be realized at the microscale. Thus, it would be attractive to consider early in the developmental cycle of nanofluidics production pipelines that can generate devices possessing sub-150 nm dimensions in a high production mode and at low-cost to accommodate the commercialization of this exciting technology. Recently, functional sub-150 nm thermoplastic nanofluidic devices have been reported that can provide high process yield rates, which can enable commercial translation of nanofluidics. This review presents an overview of recent advancements in the fabrication, assembly, surface modification and the characterization of thermoplastic nanofluidic devices. Also, several examples in which nanoscale phenomena have been exploited for the analysis of biomolecules are highlighted. Lastly, some general conclusions and future outlooks are presented.

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.

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.

Stretching a Semiflexible Polymer in a Tube

How the statistical behavior of semiflexible polymer chains may be affected by force stretching and tube confinement is a classical unsolved problem in polymer physics. Based on the Odijk deflection theory and normal mode decomposition in terms of Fourier expansion, we have derived a new compact formula for the extension of a wormlike chain of finite length strongly confined in a tube and simultaneously stretched by an external force. We have also suggested a new deflection length, which together with the force-extension relation is valid for a very extended range of the tube-diameter/persistence-length ratio comparing to the classic Odijk theory. The newly derived formula has no adjustable fitting parameters for the whole deflection regime; in contrast, the classic Odijk length needs different prefactors to fit the free energy and average extension, respectively. Brownian dynamics simulations based on the Generalized Bead-Rod (GBR) model were extensively performed, which justified the theoretical predictions.

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.

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.

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.

Interplay between chain stiffness and excluded volume of semiflexible polymers confined in nanochannels

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.

Modeling the relaxation time of DNA confined in a nanochannel

Using a mapping between a Rouse dumbbell model and fine-grained Monte Carlo simulations, we have computed the relaxation time of λ-DNA in a high ionic strength buffer confined in a nanochannel. The relaxation time thus obtained agrees quantitatively with experimental data [Reisner et al., Phys. Rev. Lett. 94, 196101 (2005)] using only a single O(1) fitting parameter to account for the uncertainty in model parameters. In addition to validating our mapping, this agreement supports our previous estimates of the friction coefficient of DNA confined in a nanochannel [Tree et al., Phys. Rev. Lett. 108, 228105 (2012)], which have been difficult to validate due to the lack of direct experimental data. Furthermore, the model calculation shows that as the channel size passes below approximately 100 nm (or roughly the Kuhn length of DNA) there is a dramatic drop in the relaxation time. Inasmuch as the chain friction rises with decreasing channel size, the reduction in the relaxation time can be solely attributed to the sharp decline in the fluctuations of the chain extension. Practically, the low variance in the observed DNA extension in such small channels has important implications for genome mapping.