Modeling the relaxation time of DNA confined in a nanochannel

Structural behavior of monomer of SARS-CoV-2 spike protein during initial stage of adsorption on graphene

Spike glycoprotein of the SARS-CoV-2 virus and its structure play a crucial role in the infections of cells containing angiotensin-converting enzyme 2 (ACE2) as well as in the interactions of this virus with surfaces. Protection against viruses and often even their deactivation is one of the great varieties of graphene applications. The structural changes of the non-glycosylated monomer of the spike glycoprotein trimer (denoted as S-protein in this work) triggered by its adsorption onto graphene at the initial stage are investigated by means of atomistic molecular dynamics simulations. The adsorption of the S-protein happens readily during the first 10 ns. The shape of the S-protein becomes more prolate during the adsorption, but this trend, albeit less pronounced, is observed also for the freely relaxing S-protein in water. The receptor-binding domain (RBD) of the free and adsorbed S-protein manifests itself as the most rigid fragment of the whole S-protein. The adsorption even enhances the rigidity of the whole S-protein as well as its subunits. Only one residue of the RBD involved in the specific interactions with ACE2 during the cell infection is involved in the direct contact of the adsorbed S-protein with the graphene. The new intramolecular hydrogen bonds formed during the S-protein adsorption replace the S-protein-water hydrogen bonds; this trend, although less apparent, is observed also during the relaxation of the free S-protein in water. In the initial phase, the secondary structure of the RBD fragment specifically interacting with ACE2 receptor is not affected during the S-protein adsorption onto the graphene.

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.

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.

Relaxation of surface-tethered polymers under moderate confinement

We study the relaxation of surface-tethered polymers in microchannels under moderate confinement (i.e. h ∼ Rg, where h is the channel height and Rg is the radius of gyration of the polymer) by experiments with fluorescence-marked DNA molecules and coupled lattice-Boltzmann/molecular dynamics simulations. The determined scaling exponent suggests that the relaxation is dominated by Zimm-dynamics with significant intra-chain hydrodynamic interactions. The relaxation of the DNA molecules is slower in shallower channels, indicating a pronounced effect of confinement on the longest relaxation time. An experimental correlation is obtained for the longest relaxation time as a function of the molecular contour length and the channel height. Good agreement between the experimental and the simulation results is found.

A nanofluidic knot factory based on compression of single DNA in nanochannels

Knots form when polymers self-entangle, a process enhanced by compaction with important implications in biological and artificial systems involving chain confinement. In particular, new experimental tools are needed to assess the impact of multiple variables influencing knotting probability. Here, we introduce a nanofluidic knot factory for efficient knot formation and detection. Knots are produced during hydrodynamic compression of single DNA molecules against barriers in a nanochannel; subsequent extension of the chain enables direct assessment of the number of independently evolving knots. Knotting probability increases with chain compression as well as with waiting time in the compressed state. Using a free energy derived from scaling arguments, we develop a knot-formation model that can quantify the effect of interactions and the breakdown of Poisson statistics at high compression. Our model suggests that highly compressed knotted states are stabilized by a decreased free energy as knotted contour contributes a lower self-exclusion derived free energy.

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.

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.

Dynamic simulations show repeated narrowing maximizes DNA linearization in elastomeric nanochannels

This paper uses computer simulations to reveal unprecedented details about linearization of deoxyribonucleic acid (DNA) inside dynamic nanochannels that can be repeatedly widened and narrowed. We first analyze the effect of rate of channel narrowing on DNA linearization dynamics. Quick (∼0.1 s) narrowing of nanoscale channels results in rapid overstretching of the semi-flexible chain followed by a slower (∼0.1-10 s) relaxation to an equilibrium extension. Two phenomena that induce linearization during channel narrowing, namely, elongational-flow and confinement, occur simultaneously, regardless of narrowing speed. Interestingly, although elongational flow is a minimum at the mid-point of the channel and increases towards the two ends, neither the linearization dynamics nor the degree of DNA extension varies significantly with the center-of-mass of the polymer projected on the channel axis. We also noticed that there was a significant difference in time to reach the equilibrium length, as well as the degree of DNA linearization at short times, depending on the initial conformation of the biopolymer. Based on these observations, we tested a novel linearization protocol where the channels are narrowed and widened repeatedly, allowing DNA to explore multiple conformations. Repeated narrowing and widening, something uniquely enabled by the elastomeric nanochannels, significantly decrease the time to reach the equilibrium-level of stretch when performed within periods comparable to the chain relaxation time and more effectively untangle chains into more linearized biopolymers.

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.

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.

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

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

Knotting dynamics of DNA chains of different length confined in nanochannels

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

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.

Force-Extension for DNA in a Nanoslit: Mapping between the 3D and 2D Limits

The force-extension relation for a semiflexible polymer confined in a nanoslit is investigated. Both the effective correlation length and force-extension relation change as the chain goes from 3D (large slit heights) to 2D (tight confinement). At low forces, correlations along the polymer give an effective dimensionality. The strong force limit can be interpolated with the weak force limit for two regimes: when confinement dominates over extensile force and vice versa. These interpolations give good agreement with simulations for all slit heights and forces. We thus generalize the Marko-Siggia force-extension relation for DNA and other semiflexible biopolymers in nanoconfinement.

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.

Stripe to slab confinement for the linearization of macromolecules in nanochannels

We investigated the recently suggested advantageous analysis of chain linearization experiments with macromolecules confined in a stripe-like channel (Huang and Battacharya, EPL, 2014, 106, 18004) using Monte Carlo simulations. The enhanced chain extension in a stripe, which is due to the significant excluded volume interactions between the monomers in two dimensions, weakens considerably on transition to an experimentally feasible slit-like channel. Based on the chain extension-confinement strength dependence and the structure factor behavior for a chain in a stripe, we infer the excluded volume regime (de Gennes regime) typical for two-dimensional systems. On widening of the stripe in a direction perpendicular to the stripe plane, i.e. on the transition to the slab geometry, the advantageous chain extension decreases and a Gaussian regime is observed for not very long semiflexible chains. The evidence for pseudo-ideality in confined chains is based on four indicators: the extension curves, variation of the extension with the persistence length P, estimated limits for the regimes in the investigated systems, and the structure factor behavior. The slab behavior can be observed when the two-dimensional stripe (originally of a one-monomer thickness) reaches a reduced thickness D larger than approximately D/P ≈ 0.2 in the third dimension. This maximum height of a slab at which the advantage of a stripe is retained is very low and has implications for DNA linearization experiments.

Evaluation of the Kirkwood approximation for the diffusivity of channel-confined DNA chains in the de Gennes regime

We use Brownian dynamics with hydrodynamic interactions to calculate both the Kirkwood (short-time) diffusivity and the long-time diffusivity of DNA chains from free solution down to channel confinement in the de Gennes regime. The Kirkwood diffusivity in confinement is always higher than the diffusivity obtained from the mean-squared displacement of the center-of-mass, as is the case in free solution. Moreover, the divergence of the local diffusion tensor, which is non-zero in confinement, makes a negligible contribution to the latter diffusivity in confinement. The maximum error in the Kirkwood approximation in our simulations is about 2% for experimentally relevant simulation times. The error decreases with increasing confinement, consistent with arguments from blob theory and the molecular-weight dependence of the error in free solution. In light of the typical experimental errors in measuring the properties of channel-confined DNA, our results suggest that the Kirkwood approximation is sufficiently accurate to model experimental data.

Hydrodynamics of DNA confined in nanoslits and nanochannels

Modeling the dynamics of a confined, semi exible polymer is a challenging problem, owing to the complicated interplay between the configurations of the chain, which are strongly affected by the length scale for the confinement relative to the persistence length of the chain, and the polymer-wall hydrodynamic interactions. At the same time, understanding these dynamics are crucial to the advancement of emerging genomic technologies that use confinement to stretch out DNA and "read" a genomic signature. In this mini-review, we begin by considering what is known experimentally and theoretically about the friction of a wormlike chain such as DNA confined in a slit or a channel. We then discuss how to estimate the friction coefficient of such a chain, either with dynamic simulations or via Monte Carlo sampling and the Kirk-wood pre-averaging approximation. We then review our recent work on computing the diffusivity of DNA in nanoslits and nanochannels, and conclude with some promising avenues for future work and caveats about our approach.

Knotting and Unknotting Dynamics of DNA Strands in Nanochannels

The self-knotting dynamics of DNA strands confined in nanochannels is studied with Brownian simulations. The model DNA chains are several microns long and placed inside channels that are 50-300 nm wide. This width range covers the transition between different metric scaling regimes and the concomitant drop of DNA knotting probability for channel widths below ∼75 nm. We find that knots typically originate from deep looping and backfoldings of the chain ends. Upon lowering the channel width, backfoldings become shallower and rarer and the lifetime of knots decreases while that of unknots increases. This lifetimes interplay causes the dramatic reduction of knots incidence for increasing confinement. The results can aid the design of nanochannels capable of harnessing the self-knotting dynamics to quench or relax the DNA topological state as desired.

Mixed confinement regimes during equilibrium confinement spectroscopy of DNA

We have used a combination of fluorescence microscopy experiments and Pruned Enriched Rosenbluth Method simulations of a discrete wormlike chain model to measure the mean extension and the variance in the mean extension of λ-DNA in 100 nm deep nanochannels with widths ranging from 100 nm to 1000 nm in discrete 100 nm steps. The mean extension is only weakly affected by the channel aspect ratio. In contrast, the fluctuations of the chain extension qualitatively differ between rectangular channels and square channels with the same cross-sectional area, owing to the "mixing" of different confinement regimes in the rectangular channels. The agreement between experiment and simulation is very good, using the extension due to intercalation as the only adjustable parameter.

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.

Simulations of DNA stretching by flow field in microchannels with complex geometry

Recently, we have reported the experimental results of DNA stretching by flow field in three microchannels (C. H. Lee and C. C. Hsieh, Biomicrofluidics 7(1), 014109 (2013)) designed specifically for the purpose of preconditioning DNA conformation for easier stretching. The experimental results do not only demonstrate the superiority of the new devices but also provides detailed observation of DNA behavior in complex flow field that was not available before. In this study, we use Brownian dynamics-finite element method (BD-FEM) to simulate DNA behavior in these microchannels, and compare the results against the experiments. Although the hydrodynamic interaction (HI) between DNA segments and between DNA and the device boundaries was not included in the simulations, the simulation results are in fairly good agreement with the experimental data from either the aspect of the single molecule behavior or from the aspect of ensemble averaged properties. The discrepancy between the simulation and the experimental results can be explained by the neglect of HI effect in the simulations. Considering the huge savings on the computational cost from neglecting HI, we conclude that BD-FEM can be used as an efficient and economic designing tool for developing new microfluidic device for DNA manipulation.

Electro-entropic excluded volume effects on DNA looping and relaxation in nanochannels

We investigate the fluctuation-relaxation dynamics of entropically restricted DNA molecules in square nanochannels ranging from 0.09 to 19.9 times the persistence length. In nanochannels smaller than the persistence length, the chain relaxation time is found to have cubic dependence on the channel size. It is found that the effective polymer width significantly alter the chain conformation and relaxation time in strong confinement. For thinner chains, looped chain configurations are found in channels with height comparable to the persistence length, with very slow relaxation compared to un-looped chains. Larger effective chain widths inhibit the formation of hairpin loops.