Direct Observation of Biaxial Confinement of a Semiflexible Filament in a Channel

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.

Statistical Behaviors of Semiflexible Polymer Chains Stretched in Rectangular Tubes

We investigated the statistical behaviors of semiflexible polymer chains, which were simultaneously subjected to force stretching and rectangular tube confinement. Based on the wormlike chain model and Odijk deflection theory, we derived a new deflection length, by using which new compact formulas were obtained for the confinement free energy and force⁻confinement⁻extension relations. These newly derived formulas were justified by numerical solutions of the eigenvalue problem associated with the Fokker⁻Planck governing equation and extensive Brownian dynamics simulations based on the so-called generalized bead-rod (GBR) model. We found that, compared to classical deflection theory, these new formulas were valid for a much more extended range of the confinement size/persistence length ratio and had no adjustable fitting parameters for sufficiently long semiflexible chains in the whole deflection regime.

Elastic behavior of a semiflexible polymer in 3D subject to compression and stretching forces

We elucidate the elastic behavior of a wormlike chain in 3D under compression and provide exact solutions for the experimentally accessible force-extension relation in terms of generalized spheroidal wave functions. In striking contrast to the classical Euler buckling instability, the force-extension relation of a clamped semiflexible polymer exhibits a smooth crossover from an almost stretched to a buckled configuration. In particular, the associated susceptibility, which measures the strength of the response of the polymer to the applied force, displays a prominent peak in the vicinity of the critical Euler buckling force. For increasing persistence length, the force-extension relation and the susceptibility of semiflexible polymers approach the behavior of a classical rod, whereas thermal fluctuations permit more flexible polymers to resist the applied force. Furthermore, we find that semiflexible polymers confined to 2D can oppose the applied force more strongly than in 3D.

Correlation anisotropy and stiffness of DNA molecules confined in nanochannels

The anisotropy of orientational correlations in DNA molecules confined in cylindrical channels is explored by Monte Carlo simulations using a coarse-grained model of double-stranded (ds) DNA. We find that the correlation function ⟨C(s)⟩_⊥ in the transverse (confined) dimension exhibits a region of negative values in the whole range of channel sizes. Such a clear-cut sign of the opposite orientation of chain segments represents a microscopic validation of the Odijk deflection mechanism in narrow channels. At moderate-to-weak confinement, the negative ⟨C(s)⟩_⊥ correlations imply a preference of DNA segments for transverse looping. The inclination for looping can explain a reduction of stiffness as well as the enhanced knotting of confined DNA relative to that detected earlier in bulk at some channel sizes. Furthermore, it is shown that the orientational persistence length P_or fails to convey the apparent stiffness of DNA molecules in channels. Instead, correlation lengths P_∥ and P_⊥ in the axial and transverse directions, respectively, encompass the channel-induced modifications of DNA stiffness.

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.

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.

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.

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.

Alignment of nematic and bundled semiflexible polymers in cell-sized confinement

The finite size of cells poses severe spatial constraints on the network of semiflexible filaments called the cytoskeleton, a main determinant of cell shape. At the same time, the high packing density of cytoskeletal filaments poses mutual packing constraints. Here we investigate the competition between excluded volume interactions in the bulk and surface packing constraints on the orientational ordering of confined actin filaments as a function of filament density and the presence of crosslinks. We grow fluorescently labeled actin filaments in shallow (thickness dz 3 μm), rectangular microchambers with a systematically varied length (dy between 5 and 100 μm) and in-plane aspect ratio (dx/dy between 1 and 10). We determine the nematic director field by image analysis of fluorescence confocal images. We find that high-density (nematic) solutions respond sensitively to changes in the size and aspect ratio of the chambers. In small chambers (dy ≤ 20 μm), filaments align parallel to the long walls as soon as the aspect ratio is ≥1.5, indicating that surface-induced ordering dominates. In larger chambers, the filaments instead align along the chamber diagonal, indicating that bulk packing constraints dominate. The nematic order parameter is maximal in small and highly anisometric chambers. In contrast to the nematic solutions, low-density (isotropic) solutions are rather insensitive to confinement. Bundled actin solutions behave similarly to nematic solutions, but are less well-ordered. Our observations imply that the orientational order of actin filaments in flat confining geometries is primarily determined by a balance between bulk and surface packing constraints with a minimal effect of the enthalpic cost of filament bending. Our assay provides an interesting platform for the future reconstitution of more complex, active cytoskeletal systems with actively treadmilling filaments or molecular motors.

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.

Orientational correlations in confined DNA

We study how the orientational correlations of DNA confined to nanochannels depend on the channel diameter D by means of Monte Carlo simulations and a mean-field theory. This theory describes DNA conformations in the experimentally relevant regime where the Flory-de Gennes theory does not apply. We show how local correlations determine the dependence of the end-to-end distance of the DNA molecule upon D. Tapered nanochannels provide the necessary resolution in D to study experimentally how the extension of confined DNA molecules depends upon D. Our experimental and theoretical results are in qualitative agreement.

Longitudinal response of confined semiflexible polymers

The longitudinal response of single semiflexible polymers to sudden changes in externally applied forces is known to be controlled by the propagation and relaxation of backbone tension. Under many experimental circumstances, realized, for example, in nanofluidic devices or in polymeric networks or solutions, these polymers are effectively confined in a channel- or tubelike geometry. By means of heuristic scaling laws and rigorous analytical theory, we analyze the tension dynamics of confined semiflexible polymers for various generic experimental setups. It turns out that in contrast to the well-known linear response, the influence of confinement on the nonlinear dynamics can largely be described as that of an effective prestress. We also study the free relaxation of an initially confined chain, finding a surprising superlinear ~t(9/8) growth law for the change in end-to-end distance at short times.

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.

Buckling of stiff polymer rings in weak spherical confinement

Confinement is a versatile and well-established tool to study the properties of polymers either to understand biological processes or to develop new nanobiomaterials. We investigate the conformations of a semiflexible polymer ring in weak spherical confinement imposed by an impenetrable shell. We develop an analytic argument for the dominating polymer trajectory depending on polymer flexibility considering elastic and entropic contributions. Monte Carlo simulations are performed to assess polymer ring conformations in probability densities and by the shape measures asphericity and nature of asphericity. Comparison of the analytic argument with the mean asphericity and the mean nature of asphericity confirm our reasoning to explain polymer ring conformations in the stiff regime, where elastic response prevails.

Drift and diffusion of a confined semiflexible chain

We study the transverse and longitudinal linear response function of rigid chains subjected to an external force. Our main concern are stiff polymers confined in narrow pores with diameter less than their persistence length. We explicitly consider confinement in a transverse harmonic potential and generalize results by scaling arguments. Our results describe the drift of the filament under an external force, time evolution of the filament shape, and filament diffusion. Diffusion of a confined filament resembles the celebrated reptation process for flexible chains, albeit with distinct kinetic exponents. The limiting case of stiff free filaments is also mentioned.

Dynamics of a self-avoiding polymer chain in slit, tube, and cube confinements

Monte Carlo simulations are presented for the observation of the dynamics of a self-avoiding polymer in three types of confinement: slit, tube, and cube. We pay special attention to the parameter regime where the characteristic confinement dimension is smaller than the radius of gyration of the unconfined polymer. On the basis of the bond-fluctuation model, we measured the rotation time of the end-to-end vector of the polymer, the diffusion time for the center of the polymer to move a distance comparable to the root mean square end-to-end distance, and the looping time for the ends of the polymer to approach each other from an open position. As functions of the confinement width and polymer length, these three time scales are discussed in light of scaling theories.

Characterization of single semiflexible filaments under geometric constraints

Confinement effects on single semiflexible macromolecules are of central importance for a fundamental understanding of cellular processes involving biomacromolecules. To analyze the influence of confinement on the fluctuations of semiflexible macromolecules we study individual actin filaments in straight and curved microchannels. We experimentally characterize the segment distributions for fluctuating semiflexible filaments in microchannels as a function of the channel width. Moreover, the effect of channel curvature on the filament fluctuations is investigated. We find quantitative agreement between experimental results, Monte Carlo simulations, and the analytical description. This allows for determination of the persistence length of actin filaments, the deflection length, which characterizes the confinement effects, and the scaling exponents for the segment distribution of semiflexible macromolecules.

Swollen-to-globular transition of a self-avoiding polymer confined in a soft tube

Monte Carlo simulations are presented for the structural transition of a self-avoiding polymer confined in an elastic soft tube, within the Helfrich energy model for the description of a fluctuating surface. Based on the simulation data of the maximum extension of the confined polymer in the tube and of the tube radius, a swollen-to-globular transition is identified where the confined polymer undergoes an abrupt transition from a shape elongated along the tube axis to a globule that is of much smaller dimensions than that of an unperturbed polymer. An extended regime in the parameter space has been explored where various scaling properties can be viewed.

DNA confined in nanochannels: Hairpin tightening by entropic depletion

A theory is presented of the elongation of double-stranded DNA confined in a nanochannel based on a study of the formation of hairpins. A hairpin becomes constrained as it approaches the wall of a channel which leads to an entropic force causing the hairpin to tighten. The DNA in the hairpin remains double-stranded. The free energy of the hairpin is significantly larger than what one would expect if this entropic effect were unimportant. As a result, the distance between hairpins or the global persistence length is often tens of micrometer long and may even reach millimeter sizes for 10 nm thin channels. The hairpin shape and size and the DNA elongation are computed for nanoslits and circular and square nanochannels. A comparison with experiment is given.