Simulation of DNA Extension in Nanochannels

Unraveling the Influence of Topology and Spatial Confinement on Equilibrium and Relaxation Properties of Interlocked Ring Polymers

We use Langevin dynamics simulations to study linked ring polymers in channel confinement. We address the in- and out-of-equilibrium behavior of the systems for varying degrees of confinement and increasing topological and geometrical complexity of the interlocking. The main findings are three. First, metric observables of different link topologies collapse onto the same master curve when plotted against the crossing number, revealing a universal response to confinement. Second, the relaxation process from initially stretched states is faster for more complex links. We ascribe these properties to the interplay of several effects, including the dependence of topological friction on the link complexity. Finally, we show that transient forms of geometrical entanglement purposely added to the initial stressed state can leave distinctive signatures in force-spectroscopy curves. The insight provided by the findings could be leveraged in single-molecule nanochannel experiments to identify geometric entanglement within topologically linked rings.

Prediction and Control in DNA Nanotechnology

DNA nanotechnology is a rapidly developing field that uses DNA as a building material for nanoscale structures. Key to the field's development has been the ability to accurately describe the behavior of DNA nanostructures using simulations and other modeling techniques. In this Review, we present various aspects of prediction and control in DNA nanotechnology, including the various scales of molecular simulation, statistical mechanics, kinetic modeling, continuum mechanics, and other prediction methods. We also address the current uses of artificial intelligence and machine learning in DNA nanotechnology. We discuss how experiments and modeling are synergistically combined to provide control over device behavior, allowing scientists to design molecular structures and dynamic devices with confidence that they will function as intended. Finally, we identify processes and scenarios where DNA nanotechnology lacks sufficient prediction ability and suggest possible solutions to these weak areas.

Scaling regimes for wormlike chains confined to cylindrical surfaces under tension

We compute the free energy of confinement [Formula: see text] for a wormlike chain (WLC), with persistence length [Formula: see text], that is confined to the surface of a cylinder of radius R under an external tension f using a mean field variational approach. For long chains, we analytically determine the behavior of the chain in a variety of regimes, which are demarcated by the interplay of [Formula: see text], the Odijk deflection length ([Formula: see text]), and the Pincus length ([Formula: see text], with [Formula: see text] being the thermal energy). The theory accurately reproduces the Odijk scaling for strongly confined chains at [Formula: see text], with [Formula: see text]. For moderate values of f, the Odijk scaling is discernible only when [Formula: see text] for strongly confined chains. Confinement does not significantly alter the scaling of the mean extension for sufficiently high tension. The theory is used to estimate unwrapping forces for DNA from nucleosomes.

Compression of a confined semiflexible polymer under direct and oscillating fields

The folding transition of biopolymers from the coil to compact structures has attracted wide research interest in the past and is well studied in polymer physics. Recent seminal works on DNA in confined devices have shown that these long biopolymers tend to collapse under an external field, which is contrary to the previously reported stretching of the chain. In this work, we capture the compression of a confined semiflexible polymer under direct and oscillating fields using a coarse-grained computer simulation model in the presence of long-range hydrodynamics. In the case of a semiflexible polymer chain, the inhomogeneous hydrodynamic drag from the center to the periphery of the coil couples with the chain bending to cause a swirling movement of the chain segments, leading to structural intertwining and compaction. Contrarily, a flexible chain of the same length lacks such structural deformation and forms a well-established tadpole structure. While bending rigidity profoundly influences the chain's folding favorability, we also found that subject to the direct field, chains in stronger confinements exhibit substantial compaction, contrary to the one in moderate confinements or bulk where such compaction is absent. However, an alternating field within an optimum frequency can effectuate this compression even in moderate or no confinement. This field-induced collapse is a quintessential hydrodynamic phenomenon, resulting in intertwined knotted structures even for shorter chains, unlike other spontaneous knotting experiments where it happens exclusively for longer chains.

Knot Factories with Helical Geometry Enhance Knotting and Induce Handedness to Knots

We performed molecular dynamics simulations of DNA polymer chains confined in helical nano-channels under compression in order to explore the potential of knot-factories with helical geometry to produce knots with a preferred handedness. In our simulations, we explore mutual effect of the confinement strength and compressive forces in a range covering weak, intermediate and strong confinement together with weak and strong compressive forces. The results find that while the common metrics of polymer chain in cylindrical and helical channels are very similar, the DNA in helical channels exhibits greatly different topology in terms of chain knottedness, writhe and handedness of knots. The results show that knots with a preferred chirality in terms of average writhe can be produced by using channels with a chosen handedness.

Modulation of DNA conformation in electrolytic nanodroplets

The behavior of deoxyribonucleic acid (DNA) molecules in confinement is of profound importance in various bioengineering and medical applications. In the present study, all-atom molecular dynamics simulation is utilized to investigate the transition of the double-strand DNA (dsDNA) conformation in the electrolytic nanodroplet. Three typical conformations, i.e., C-shaped, folded S-shaped, and double C-shaped, are observed for different droplet sizes and ionic concentrations. To reveal the physics underlying this phenomenon, the characteristics of the dsDNA molecules, such as the overcharging intensity, the end-to-end distance, the radius of gyration, etc. are analyzed in detail based on the numerical results. It is found that the transition can be ascribed to the buckling of the polymer molecules under the compression due to the confinement of the nanodroplet, and it can be modulated by the ionic concentration in the electrolyte. Generally, nanoscale confinement dominates dsDNA behavior over the electrostatic effects in smaller nanodroplets, while the latter becomes more important for larger nanodroplets. This competition results in the persistence length increasing with the nanodroplet radii. Based on these discussions, a non-dimensional elasto-capillary number μ is proposed to classify the dsDNA conformations into three regions.

Quantifying the effects of slit confinement on polymer knots using the tube model

Knots can spontaneously form in DNA, proteins, and other polymers and affect their properties. These knots often experience spatial confinement in biological systems and experiments. While confinement dramatically affects the knot behavior, the physical mechanisms underlying the confinement effects are not fully understood. In this work, we provide a simple physical picture of the polymer knots in slit confinement using the tube model. In the tube model, the polymer segments in the knot core are assumed to be confined in a virtual tube due to the topological restriction. We first perform Monte Carlo simulation of a flexible knotted chain confined in a slit. We find that with the decrease of the slit height from H=+∞ (the 3D case) to H=2a (the 2D case), the most probable knot size L_{knot}^{*} dramatically shrinks from (L_{knot}^{*})_{3D}≈140a to (L_{knot}^{*})_{2D}≈26a, where a is the monomer diameter of the flexible chain. Then we quantitatively explain the confinement-induced knot shrinking and knot deformation using the tube model. Our results for H=2a can be applied to a polymer knot on a surface, which resembles DNA knots measured by atomic force microscopy under the conditions that DNA molecules are weakly absorbed on the surface and reach equilibrium 2D conformations. This work demonstrates the effectiveness of the tube model in understanding polymer knots.

Topological Friction and Relaxation Dynamics of Spatially Confined Catenated Polymers

We study catenated ring polymers confined inside channels and slits with Langevin dynamics simulations and address how the contour position and size of the interlocked or physically linked region evolve with time. We show that the catenation constraints generate a drag, or topological friction, that couples the contour motion of the interlocked regions. Notably, the coupling strength decreases as the interlocking is made tighter, but also shorter, by confinement. Though the coupling strength differs for channel and slit confinement, the data outline a single universal curve when plotted against the size of the linked region. Finally, we study how the relaxation kinetics changes after one of the rings is cut open and conclude that considering interlocked circular polymers is key for isolating the manifestations of topological friction. The results ought to be relevant for linked biomolecules in experimental or biological confining conditions.

Crowding-induced polymer trapping in a channel

In this work, we report an intriguing phenomenon: crowding-induced polymer trapping in a channel. Using Langevin dynamics simulations and analytical calculations, we find that for a polymer confined in a channel, crowding particles can push a polymer into the channel corner through inducing an effective polymer-corner attraction due to the depletion effect. This phenomenon is referred to as polymer trapping. The occurrence of polymer trapping requires a minimum volume fraction of crowders, ϕ^{*}, which scales as ϕ^{*}∼(a_{c}/L_{p})^{1/3} for a_{c}≫a_{m} and ϕ^{*}∼(a_{c}/L_{p})^{1/3}(a_{c}/a_{m})^{1/2} for a_{c}≪a_{m}, where a_{c} is the crowder diameter, a_{m} is the monomer diameter, and L_{p} is the polymer persistence length. For DNA, ϕ^{*} is estimated to be around 0.25 for crowders with a_{c}=2nm. We find that ϕ^{*} also strongly depends on the shape of the channel cross section, and ϕ^{*} is much smaller for a triangle channel than a square channel. The polymer trapping leads to a nearly fully stretched polymer conformation along a channel corner, which may have practical applications, such as full stretching of DNA for the nanochannel-based genome mapping technology.

Intrinsic structure and dynamics of monolayer ring polymer melts

We present the general structural and dynamical characteristics of flexible ring polymers in narrowly confined two-dimensional (2D) melt systems using atomistic molecular dynamics simulations. The results are further analyzed via direct comparison with the 2D linear analogue as well as the three-dimensional (3D) ring and linear melt systems. It is observed that dimensional restriction in 2D confined systems results in an increase in the intrinsic chain stiffness of the ring polymer. Fundamentally, this arises from an entropic penalty on polymer chains along with a reduction in the available chain configuration states in phase space and spatial choices for individual segmental walks. This feature in combination with the intermolecular interactions between neighboring ring chains leads to an overall extended interpenetrated chain configuration for the 2D ring melt. In contrast to the generally large differences in structural and dynamical properties between ring and linear polymers in 3D melt systems, relatively similar local-to-global chain structures and dynamics are observed for the 2D ring and linear melts. This is attributed to the general structural similarity (i.e., extended double-stranded chain conformations), the less effective role of the chain ends, and the absence of complex topological constraints between chains (i.e., interchain entanglement and mutual ring threading) in the 2D confined systems compared with the corresponding 3D bulk systems.

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.

Equilibrium Conformation of Catenated DNA Networks in Slitlike Confinement

A kinetoplast is a planar network of catenated DNA rings with topology that resembles that of chain mail armor. In this work, we use single-molecule experiments to probe the conformation of kinetoplasts confined to slits. We find that the in-plane size of kinetoplasts increases with degree of confinement, akin to the slitlike confinement of linear DNA. The change in kinetoplast size with channel height is consistent with the scaling prediction from a Flory-type approach for a 2D polymer. With an increase in extent of confinement, the kinetoplasts appear to unfold and take on more uniform circular shapes, in contrast to the broad range of conformations observed for kinetoplasts in bulk.

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.

Confinement and Processing Can Alter the Morphology and Periodicity of Bottlebrush Block Copolymers in Thin Films

Bottlebrush block copolymers (BBCPs) are intriguing architectural variations on linear BCPs with highly tunable structure. Confinement can have a significant impact on polymer assembly, giving rise to changes in morphology, assembly kinetics, and properties like the glass transition. Given that confinement leads to significant changes in the persistence length of bottlebrush homopolymers, it is reasonable to expect that BBCPs will see significant changes in their structure and periodicity relative to the bulk morphology. Understanding how confinement influences assembly will be important for designing BBCPs for thin film applications including membranes, integrated photonic structures, and potentially BCP lithography. In order to study the effects of confinement on BBCP conformation and morphology, a blade coating was used to prepare films with continuous variation in film thickness. Unlike thin films of linear BCPs, islands/holes were not observed, and instead mixtures of parallel and perpendicular morphologies emerge after annealing. The lamellar periodicity (L₀) of the morphologies is found to be thickness dependent, increasing L₀ with decreasing film thickness for blade coated films. Films coated out of tetrahydrofuran (THF) resulted in a single well-defined lamellar periodicity, verified through atomic force microscopy (AFM) and grazing incidence small-angle X-ray scattering (GISAXS), which increases dramatically from the bulk value (30.6 nm) and continues to increase as the film thickness decreases. The largest observed L₀ was 65.5 nm, and this closely approaches the estimated upper limit of 67 nm corresponding to a fully extended backbone in a bilayer arrangement. Films coated out of propylene glycol methyl ether acetate (PGMEA) resulted in a mixture of perpendicular lamellae and a smaller, likely cylindrical morphology. The lamellar portion of the film shows the same thickness dependence as the lamellae observed in the THF coated films. The scaling of the lamellar L₀ with respect to film thickness follows predictions for confined semiflexible polymers with weak excluded volume interactions and can be related to models for confinement of DNA. Spin coated films shows the same reduction in periodicity, although at very different film thicknesses. This result suggests that the material has shallow free-energy barriers to transitioning between different L₀ and morphologies, a property that could be taken advantage of for patterning diverse structures with a single material.

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.

Conformation of Flexible and Semiflexible Chains Confined in Nanoposts Array of Various Geometries

The conformation and distribution of a flexible and semiflexible chain confined in an array of nanoposts arranged in parallel way in a square-lattice projection of their cross-section was investigated using coarse-grained molecular dynamics simulations. The geometry of the nanopost array was varied at the constant post diameter dp and the ensuing modifications of the chain conformation were compared with the structural behavior of the chain in the series of nanopost arrays with the constant post separation Sp as well as with the constant distance between two adjacent post walls (passage width) wp. The free energy arguments based on an approximation of the array of nanopost to a composite of quasi-channels of diameter dc and quasi-slits of height wp provide semiqualitative explanations for the observed structural behavior of both chains. At constant post separation and passage width, the occupation number displays a monotonic decrease with the increasing geometry ratio dc/wp or volume fraction of posts, while a maximum is observed at constant post diameter. The latter finding is attributed to a relaxed conformation of the chains at small dc/wp ratio, which results from a combination of wide interstitial volumes and wide passage apertures. This maximum is approximately positioned at the same dc/wp value for both flexible and semiflexible chains. The chain expansion from a single interstitial volume into more interstitial volumes also starts at the same value of dc/wp ratio for both chains. The dependence of the axial chain extension on the dc/wp ratio turns out to be controlled by the diameter of the interstitial space and by the number of monomers in the individual interstitial volumes. If these two factors act in the same way on the axial extension of chain fragments in interstitial volumes the monotonic increase of the axial chain extension with the dc/wp in the nanopost arrays is observed. At constant wp, however, these two factors act in opposite way and the axial chain extension plotted against the dc/wp ratio exhibits a maximum. In the case of constant post diameter, the characteristic hump in the single chain structure factor whose position correlates with the post separation is found only in the structure factor of the flexible chain confined in the nanopost array of certain value of Sp. The structure factor of the flexible chain contains more information on the monomer organization and mutual correlations than the structure factor of the semiflexible chain. The stiffer chain confined in the nanopost array is composed of low number of statistical segments important for the presence of respective hierarchical regimes in the structure factor.

Ionizing Radiation and Complex DNA Damage: Quantifying the Radiobiological Damage Using Monte Carlo Simulations

Ionizing radiation is a common tool in medical procedures. Monte Carlo (MC) techniques are widely used when dosimetry is the matter of investigation. The scientific community has invested, over the last 20 years, a lot of effort into improving the knowledge of radiation biology. The present article aims to summarize the understanding of the field of DNA damage response (DDR) to ionizing radiation by providing an overview on MC simulation studies that try to explain several aspects of radiation biology. The need for accurate techniques for the quantification of DNA damage is crucial, as it becomes a clinical need to evaluate the outcome of various applications including both low- and high-energy radiation medical procedures. Understanding DNA repair processes would improve radiation therapy procedures. Monte Carlo simulations are a promising tool in radiobiology studies, as there are clear prospects for more advanced tools that could be used in multidisciplinary studies, in the fields of physics, medicine, biology and chemistry. Still, lot of effort is needed to evolve MC simulation tools and apply them in multiscale studies starting from small DNA segments and reaching a population of cells.

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.

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.

Bacterial chromosome organization. II. Few special cross-links, cell confinement, and molecular crowders play the pivotal roles

Using a coarse-grained bead-spring model of bacterial chromosomes of Caulobacter crescentus and Escherichia coli, we show that just 33 and 38 effective cross-links in 4017 and 4642 monomer chains at special positions along the chain contour can lead to the large-scale organization of the DNA polymer, where confinement effects of the cell walls play a key role in the organization. The positions of the 33/38 cross-links along the chain contour are chosen from the Hi-C contact map of bacteria C. crescentus and E. coli. We represent 1000 base pairs as a coarse-grained monomer in our bead-spring flexible ring polymer model of the DNA polymer. Thus, 4017/4642 beads on a flexible ring polymer represent the C. crescentus/E. coli DNA polymer with 4017/4642 kilo-base pairs. Choosing suitable parameters from Paper I, we also incorporate the role of compaction of the polymer coil due to the presence of molecular crowders and the ability of the chain to release topological constraints. We validate our prediction of the organization of the bacterial chromosomes with available experimental data and also give a prediction of the approximate positions of different segments within the cell. In the absence of confinement, the minimal number of effective cross-links required to organize the DNA chains of 4017/4642 monomers was 60/82 [Agarwal et al., Europhys. Lett. 121, 18004 (2018) and Agarwal et al., J. Phys.: Condens. Matter 30, 034003 (2018)].

Bacterial chromosome organization. I. Crucial role of release of topological constraints and molecular crowders

We showed in our previous studies that just 3% cross-links (CLs), at special points along the contour of the bacterial DNA, help the DNA-polymer to get organized at micron length scales [T. Agarwal et al., J. Phys.: Condens. Matter 30, 034003 (2018) and T. Agarwal et al., EPL (Europhys. Lett.) 121, 18004 (2018)]. In this work, we investigate how does the release of topological constraints help in the "organization" of the DNA-polymer. Furthermore, we show that the chain compaction induced by the crowded environment in the bacterial cytoplasm contributes to the organization of the DNA-polymer. We model the DNA chain as a flexible bead-spring ring polymer, where each bead represents 1000 base pairs. The specific positions of the CLs have been taken from the experimental contact maps of the bacteria Caulobacter crescentus and Escherichia coli. We introduce different extents of ease of release of topological constraints in our model by systematically changing the diameter of the monomer bead. It varies from the value where chain crossing can occur freely to the value where chain crossing is disallowed. We also study the role of compaction of the chain due to molecular crowders by introducing an "effective" weak Lennard-Jones attraction between the monomers. Using Monte Carlo simulations, we show that the release of topological constraints and the crowding environment play a crucial role to obtain a unique organization of the polymer.

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.

Confinement induces helical organization of chromosome-like polymers

Helical organization is commonly observed for a variety of biopolymers. Here we study the helical organization of two types of biopolymers, i.e., DNA-like semiflexible and bottle-brush polymers, in a cell-like confined space. A bottle-brush polymer consists of a backbone and side chains emanating from the backbone, resembling a supercoiled bacterial chromosome. Using computer simulations, we calculate 'writhe' distributions of confined biopolymers for a wide range of parameters. Our effort clarifies the conditions under which biopolymers are helically organized. While helical organization is not easily realized for DNA-like biomolecules, cylindrical confinement can induce spiral patterns in a bottle brush, similarly to what was observed with bacterial chromosomes. They also suggest that ring-shape bottle brushes have a stronger tendency for helical organization. We discuss how our results can be used to interpret chromosome experiments. For instance, they suggest that experimental resolution has unexpected consequences on writhe measurements (e.g., narrowing of the writhe distribution and kinetic separation of opposite helical states).

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

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

Nanoplumbing with 2D Metamaterials

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

Measuring the wall depletion length of nanoconfined DNA

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

Monte Carlo simulation algorithm for B-DNA

Understanding the structure-function relationship of biomolecules containing DNA has motivated experiments aimed at determining molecular structure using methods such as small-angle X-ray and neutron scattering (SAXS and SANS). SAXS and SANS are useful for determining macromolecular shape in solution, a process which benefits by using atomistic models that reproduce the scattering data. The variety of algorithms available for creating and modifying model DNA structures lack the ability to rapidly modify all-atom models to generate structure ensembles. This article describes a Monte Carlo algorithm for simulating DNA, not with the goal of predicting an equilibrium structure, but rather to generate an ensemble of plausible structures which can be filtered using experimental results to identify a sub-ensemble of conformations that reproduce the solution scattering of DNA macromolecules. The algorithm generates an ensemble of atomic structures through an iterative cycle in which B-DNA is represented using a wormlike bead-rod model, new configurations are generated by sampling bend and twist moves, then atomic detail is recovered by back mapping from the final coarse-grained configuration. Using this algorithm on commodity computing hardware, one can rapidly generate an ensemble of atomic level models, each model representing a physically realistic configuration that could be further studied using molecular dynamics. © 2016 Wiley Periodicals, Inc.

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

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

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

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

Distribution of label spacings for genome mapping in nanochannels

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

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.