Energy/entropy partition of force at DNA stretching.

We compute by molecular simulation the energy/entropic partition of the force in a stretched double-stranded (ds)DNA molecule that is not yet available from the single-molecule measurements. Simulation using the coarse-grained wormlike chain (WLC) model predicts a gradual decrease in the internal (bending) energy of DNA at stretching. The ensuing negative energy contribution to force fU is outweighed by the positive entropy contribution fS . The ratio fU /f, used to assess the polymer elasticity, is about -1 at the moderate extension of DNA. At the high extension, the extra energy expenses due to the contour length elongation make the ratio fU /f less negative. The simulation findings of the hybrid energy/entropy nature of DNA elasticity at weak and moderate forces are supported by computations using the thermoelastic method mimicking the polymer experiments in bulk. It is contended that the observation of the negative energy elasticity in DNA can be generalized to other semiflexible polymers described by the WLC model.

Force-displacement relations at compression of dsDNA macromolecules.

The elasticity of dsDNA molecules is investigated by Monte Carlo simulations based on a coarse-grained model of DNA. The force-displacement (f-r) curves are computed under the constraints of the constant force (Gibbs) or the constant length (Helmholtz) ensemble. Particular attention was paid to the compressional (negative) and weak tensile forces. It was confirmed that simulations using the vector Gibbs ensemble fail to represent the compression behavior of polymers. Simulations using the scalar Gibbs protocol resulted in a qualitatively correct compressional response of DNA provided that the quadratic averages of displacements were employed. Furthermore, a well-known shortcoming of the popular Marko-Siggia relation for DNA elasticity at weak tensile forces is elucidated. Conversely, the function f-r from the simulation at the constant length constraint, as well as the new closed-form expressions, provides a realistic depiction of the DNA elasticity over the wide range of negative and positive forces. Merely a qualitative resemblance of the compression functions f-r predicted by the employed approaches supports the notion that the elastic response of DNA molecules may be greatly affected by the specifics of the experimental setups and the kind of averaging of the measured variable.

Stretching and compression of DNA by external forces under nanochannel confinement.

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

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 Por 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.

Effect of chain stiffness for semiflexible macromolecules in array of cylindrical nanoposts.

Equilibrium conformation of a semiflexible macromolecule in an array of nanoposts exhibits a non-monotonic behavior both at variation of the chain stiffness and increased crowding imposed by nanoposts. This is a result of the competition between the axial chain extension in channel-like interstitial volumes between nanoposts and the chain partitioning among these volumes. The approximation of a nanopost array as a combination of a quasi-channel and a quasi-slit like geometry semi-qualitatively explains the behavior of a chain in the array. In this approximation, the interstitial spaces are viewed as being of the channel geometry, while the passages between two adjacent posts are viewed as being of the slit geometry. Interestingly, the stiffer chains tend to penetrate more readily through the passage apertures, in the direction perpendicular to the post axes, and thus to occupy more interstitial volumes. This is consistent with the prediction of the free-energy penalty that is lower for a stiffer chain at strong slit-like confinement. These findings can find applications in the control of macromolecular conformations in recent nanotechnological techniques with bio-macromolecules such as a DNA.

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.

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.

Structural transformation between long and short-chain form of liquid sulfur from ab initio molecular dynamics.

We present results of ab initio molecular dynamics study of the structural transformation occurring in hot liquid sulfur under high pressure, which corresponds to the recently observed chain-breakage phenomenon and to the electronic transition reported earlier. The transformation is temperature-induced and separates two distinct polymeric forms of liquid sulfur: high-temperature form composed of short chain-like fragments with open endings and low-temperature form with very long chains. We offer a structural description of the two liquid forms in terms of chain lengths, cross-linking, and chain geometry and investigate several physical properties. We conclude that the transformation is accompanied by changes in energy (but not density) as well as in diffusion coefficient and electronic properties­semiconductor-metal transition. We also describe the analogy of the investigated process to similar phenomena that take place in two other chalcogens selenium and tellurium. Finally, we remark that the behavior of heated liquid sulfur at ambient pressure might indicate a possible existence of a critical point in the low-pressure region of sulfur phase diagram.

Effective stiffening of DNA due to nematic ordering causes DNA molecules packed in phage capsids to preferentially form torus knots.

Observation that DNA molecules in bacteriophage capsids preferentially form torus type of knots provided a sensitive gauge to evaluate various models of DNA arrangement in phage heads. Only models resulting in a preponderance of torus knots could be considered as close to reality. Recent studies revealed that experimentally observed enrichment of torus knots can be qualitatively reproduced in numerical simulations that include a potential inducing nematic arrangement of tightly packed DNA molecules within phage capsids. Here, we investigate what aspects of the nematic arrangement are crucial for inducing formation of torus knots. Our results indicate that the effective stiffening of DNA by the nematic arrangement not only promotes knotting in general but is also the decisive factor in promoting formation of DNA torus knots in phage capsids.

Comparison of linear and ring DNA macromolecules moderately and strongly confined in nanochannels.

Understanding the mechanism of DNA extension in nanochannels is necessary for interpretation of experiments in nanofluidic channel devices that have been conducted recently with both linear and ring chains. The present article reviews the situation with linear chains and analyses the experimental results and simulations for channel-induced extension (linearization) of ring chains. Results for confined rings indicate a transition between moderate and strong confinement similar to that of linear chains. Owing to stronger self-avoidance in confined rings, the transition and chain extension is shifted relative to linear DNA. We suggest that a relationship similar to that used for the extension of linear chains may also be used for circular DNA.

Segregation of semiflexible macromolecules in nanochannel.

Investigation of segregation of polymer coils in open channel was extended relative to previous studies from flexible chains to semiflexible chains. Our results are based on simulation of confinement free energy of a chain in channel and on direct simulation of coil segregation process. For confinement free energy, we confirm the predicted opposite trend with increasing chain stiffness for the weak and for strong confinement regimes. Results of two different approaches are consistent, in agreement with theoretical analysis and indicate a stronger segregation tendency of flexible chains in channel relative to semiflexible chains both in its extent and dynamics.

Pressure of Linear and Ring Polymers Confined in a Cavity.

Nanoscale confinement of polymers in a cavity is central to a variety of biological and nanotechnology processes. Using the discrete WLC model we simulate the compression of flexible and semiflexible polymers of linear and ring topology in a closed cavity. Simulation reveals that polymer pressure inside the cavity increases with the chain stiffness but is practically unaffected by the chain topology. For flexible polymers, the computed dependence of pressure on the cavity size and polymer concentration is consistent with the scaling behavior expected for bulk polymers in a good solvent. However, the scaling behavior of semiflexible polymers is only in partial agreement with the theory prediction, with discrepancies arising from a continuous transition between regimes in chains of moderate lengths. The computed segment density profiles endorse the propensity of semiflexible polymers to concentrate beneath the cavity surface and thus elevate the pressure. The compaction of polymers by compression into the disordered globule or growing toroidal structure is documented.

Weak-to-strong confinement transition of semi-flexible macromolecules in slit and in channel.

We compare confinement of stiff macromolecule in channel and in slit. Whereas in the channel a distinct and established transition exists, we elucidate here an ongoing controversy reported from previous experiment and simulation on existence of such transition in the slit. Our extensive molecular simulations in both geometries show only a very weak conformational crossover between moderate and strong confinements in slit in the same range of confinements where the distinct transition in channel is observed. In contrast to situation in channels relatively stable hairpin-like structures are not indicated around this weak transition in the slit. Observed difference from the prediction on behavior in blob regime under moderate confinement is explained by a crossover between dimensionalities in the slit and the extent of ideal conformation statistics to which the stiffer chains are prone. The strong confinement regime of stiff chain in slit characterized here has not been interpreted yet and it differs from the respective saturation-like Odijk regime in the channel.

Persistence length of DNA molecules confined in nanochannels.

The influence of confinement on the persistence length of dsDNA molecules under a high ionic strength environment was explored by coarse-grained Monte Carlo simulations in channels of different profiles. It was found that under confinement three definitions of the persistence length of DNA molecules were not equivalent and represented different properties. In case of the global quantities, the projection and the WLC persistence lengths, the apparent values up to several hundred nanometres are observed for DNA confined in narrow channels. The orientational correlation function cos theta(s) of confined DNA shows a complex pattern, distinctive for semiflexible polymers. At weak and moderate confinements the function cos theta(s) suggests an unexpected increase in the apparent DNA flexibility. The orientational persistence length computed from the initial slope of the function cos theta(s) mirrors only short-scale correlations and gives the value close to the intrinsic persistence length of DNA. The simulation data of direct relevance to experimental studies of DNA in microfluidic devices are compared with analytical theories for stiff chains.

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 ΔRD and the force contribution ΔRf. 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 ΔRD. 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.

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.

Chain extension of DNA confined in channels.

The mechanism of DNA elongation in nanochannels was explored by Monte Carlo simulations as a function of the channel dimension D, DNA length, and stiffness. Simulations were based on the bead-spring model, representing double-stranded DNA chains of moderate length at a high salt concentration. As a rule, the channel-induced elongation profiles of R( parallel) vs D from the simulations were in qualitative agreement with those from microfluidic measurements of DNA. The longitudinal chain elongation in narrow channels was found to be correctly predicted by the Odijk relation for the deflection regime. The scaling relation of R( parallel) vs D(-1), based on the statistics of ideal-chain blobs, was used to explain the simulation data at the intermediate channel widths. Contrary to the blob-theory presumption, the nonlinear dependence of DNA elongation R( parallel) on the chain length N was observed in simulations at moderate confinement. It was suggested that discrepancies found between the simulations and the blob theory arose from the formation of various DNA hairpin structures within channels.

Channel confinement of flexible and semiflexible macromolecules.

We compare in detail the channel confinement of flexible and semiflexible chains over a broad range of confinements and chain lengths using molecular simulations. Flexible and semiflexible chains differ over the regimes involved under confinement. For the stiff chain we confirm a transition between strong and weak confinement at the tube diameter approximately equal to the chain persistence length. Deviations from the predicted behavior for confined semiflexible macromolecules in the tubelike channel under the weak confinement are explained by a tendency of chains toward ideal chain behavior. There are several indicators of this ideality based on the shape of chain extension R-confinement D curves, on the scaling of R with the chain length, on the structure factor of coil in the range of individual blobs in the channel, on ambiguity in introduction of excluded volume for confined stiff chains in theoretical treatments as well as on the reported experimental observation.

Persistence lengths and structure factors of wormlike polymers under confinement.

The behavior of semiflexible chains modeling wormlike polymers such as DNA and actin in confined spaces was explored by coarse-grained Monte Carlo simulations. The persistence length P, mean end-to-end distance R2, mean radius of gyration Rg2, and the size ratio R2/Rg2 were computed for chains in slits, cylinders, and spheres. It was found that the intrinsic persistence length of a free chain undergoes on confinement substantial alteration into the apparent persistence length. The qualitative differences were found in trends of the apparent persistence lengths between slits and cylinders on one side and spheres on the other side. The quantities P, R2, Rg2, and R2/Rg2 display similar dependences upon squeezing the chains in nanopores. The above quantities change nonmonotonically with confinement in slits and cylinders, whereas they drop smoothly with decreasing radius of a sphere. For elongation of a chain in a cylinder, two regimes corresponding to strong and moderate confinements were found and compared to experiments and predictions of the blob and Odijk theories. In a spherical cavity, the toroidal chain structure with a hole in the center was detected under strong confinements. The scattering form factor S(q) computed for semiflexible confined chains revealed three regimes of behavior in a slit and a cylinder that matched up well with the scaling theory. The complex form of the function S(q) computed for a sphere was interpreted as a sign of the toroidal structure. A reasonable agreement was found between the simulations and measurements of DNA and actin filaments, confined in nano- and microfluidic channels and spherical droplets, pertaining to the changes of the persistence lengths, chain elongation, and toroidal structure formation.

Energy-driven asymmetric partitioning of a semiflexible polymer between interconnected cavities.

The distribution of a semiflexible chain in the volume of two interconnected spherical cavities of equal size has been investigated by using Monte Carlo simulations. The chain possessed an extension exceeding that of the cavity, leading to large probabilities of translocated states despite the entropic penalty of passing the narrow passage. Furthermore, an asymmetric state with unequal subchain lengths in the two cavities was more favorable than the symmetric state. The preference for the asymmetric state is driven by the bending energy. Basically, in the symmetric state both subchains are forced to be bent, whereas in the asymmetric case only one of the subchains must bend, leading to an overall smaller bending penalty and overall smaller free energy of the asymmetric state. These results are in contrast to the entropy-controlled partitioning of polymers into confinement and the symmetric translocation state appearing for flexible polymers.