Search Results (16)

Quite often polymers exhibit different elastic behavior depending on the statistical ensemble (Gibbs vs. Helmholtz). This is an effect of strong fluctuations. In particular, two-state polymers, which locally or globally fluctuate between two classes of microstates, can exhibit strong ensemble inequivalence with negative elastic moduli (extensibility or compressibility) in the Helmholtz ensemble. Two-state polymers consisting of flexible beads and springs have been studied extensively. Recently, similar behavior was predicted in a strongly stretched wormlike chain consisting of a sequence of reversible blocks, fluctuating between two values of the bending stiffness (the so called reversible wormlike chain, rWLC). In this article, we theoretically analyse the elasticity of a grafted rod-like semiflexible filament which fluctuates between two states of bending stiffness. We consider the response to a point force at the fluctuating tip in both the Gibbs and the Helmholtz ensemble. We also calculate the entropic force exerted by the filament on a confining wall. This is done in the Helmholtz ensemble and, under certain conditions, it yields negative compressibility. We consider a two-state homopolymer and a two-block copolymer with two-state blocks. Possible physical realizations of such a system would be grafted DNA or carbon nanorods undergoing hybridization, or grafted F-actin bundles undergoing collective reversible unbinding. Full article

Kinks can appear along the contour of semiflexible polymers (biopolymers or synthetic ones), and they affect their elasticity and function. A regular sequence of alternating kink defects can form a semiflexible nanospring. In this article, we theoretically analyze the elastic behavior of such a nanospring with a point magnetic dipole attached to one end while the other end is assumed to be grafted to a rigid substrate. The rod-like segments of the nanospring are treated as weakly bending wormlike chains, and the propagator (Green’s function) method is used in order to calculate the conformational and elastic properties of this system. We analytically calculate the distribution of orientational and positional fluctuations of the free end, the force-extension relation, as well as the compressional force that such a spring can exert on a planar wall. Our results show how the magnetic interaction affects the elasticity of the semiflexible nanospring. This sensitivity, which is based on the interplay of positional and orientational degrees of freedom, may prove useful in magnetometry or other applications. Full article

Reversible adsorption of a single stiff wormlike macromolecule to flat membranes with various permeabilities is considered theoretically. It is shown that the adsorbed layer microstructure is significantly different from either a flexible chain or a stiff chain adsorption at a solid surface. Close to the critical point, the adsorbing wormlike chain forms a strongly anisotropic proximal layer near the membrane in addition to a nearly isotropic distal layer. The proximal layer is characterized by the algebraic monomer concentration profile, $c\left(x\right)\propto {\left|x\right|}^{-\beta }$, due to the self-similar distribution of aligned polymer loops. For a perfectly penetrable membrane, $\beta =1$ which is different from $\beta =4/3$ obtained for semiflexible chain adsorption at a solid surface. Moreover, we establish that the critical exponent for a partially permeable membrane depends on its properties (porosity w) and propose an asymptotically exact theory (based on the generalized Edwards equation) predicting this dependence, $\beta =\beta \left(w\right)$. We also develop a scaling theory elucidating, in particular, an intricate competition of loops and tails in both proximal and distal sublayers. Full article

Actin filament’s polyelectrolyte and hydrodynamic properties, their interactions with the biological environment, and external force fields play an essential role in their biological activities in eukaryotic cellular processes. In this article, we introduce a unique approach that combines dynamics and electrophoresis light-scattering experiments, an extended semiflexible worm-like chain model, and an asymmetric polymer length distribution theory to characterize the polyelectrolyte and hydrodynamic properties of actin filaments in aqueous electrolyte solutions. A fitting approach was used to optimize the theories and filament models for hydrodynamic conditions. We used the same sample and experimental conditions and considered several g-actin and polymerization buffers to elucidate the impact of their chemical composition, reducing agents, pH values, and ionic strengths on the filament translational diffusion coefficient, electrophoretic mobility, structure factor, asymmetric length distribution, effective filament diameter, electric charge, zeta potential, and semiflexibility. Compared to those values obtained from molecular structure models, our results revealed a lower value of the effective G-actin charge and a more significant value of the effective filament diameter due to the formation of the double layer of the electrolyte surrounding the filaments. Contrary to the data usually reported from electron micrographs, the lower values of our results for the persistence length and average contour filament length agree with the significant difference in the association rates at the filament ends that shift to sub-micro lengths, which is the maximum of the length distribution. Full article

Semiflexible nunchucks are block copolymers consisting of two long blocks with high bending rigidity jointed by a short block of lower bending stiffness. Recently, the DNA nanotube nunchuck was introduced as a simple nanoinstrument that mechanically magnifies the bending angle of short double-stranded (ds) DNA and allows its measurement in a straightforward way [Fygenson et al., Nano Lett. 2020, 20, 2, 1388–1395]. It comprises two long DNA nanotubes linked by a dsDNA segment, which acts as a hinge. The semiflexible nunchuck geometry also appears in dsDNA with a hinge defect (e.g., a quenched denaturation bubble or a nick), and in end-linked stiff filaments. In this article, we theoretically investigate various aspects of the conformations and the tensile elasticity of semiflexible nunchucks. We analytically calculate the distribution of bending fluctuations of a wormlike chain (WLC) consisting of three blocks with different bending stiffness. For a system of two weakly bending WLCs end-jointed by a rigid kink, with one end grafted, we calculate the distribution of positional fluctuations of the free end. For a system of two weakly bending WLCs end-jointed by a hinge modeled as harmonic bending spring, with one end grafted, we calculate the positional fluctuations of the free end. We show that, under certain conditions, there is a pronounced bimodality in the transverse fluctuations of the free end. For a semiflexible nunchuck under tension, under certain conditions, there is bimodality in the extension as a function of the hinge position. We also show how steric repulsion affects the bending fluctuations of a rigid-rod nunchuck. Full article

The application of single chain mean-field theory (SCMFT) on semiflexible chain brushes is reviewed. The worm-like chain (WLC) model is the best mode of semiflexible chain that can continuously recover to the rigid rod model and Gaussian chain (GC) model in rigid and flexible limits, respectively. Compared with the commonly used GC model, SCMFT is more applicable to the WLC model because the algorithmic complexity of the WLC model is much higher than that of the GC model in self-consistent field theory (SCFT). On the contrary, the algorithmic complexity of both models in SCMFT are comparable. In SCMFT, the ensemble average of quantities is obtained by sampling the conformations of a single chain or multi-chains in the external auxiliary field instead of solving the modified diffuse equation (MDE) in SCFT. The precision of this calculation is controlled by the number of bonds $N_m$ used to discretize the chain contour length L and the number of conformations M used in the ensemble average. The latter factor can be well controlled by metropolis Monte Carlo simulation. This approach can be easily generalized to solve problems with complex boundary conditions or in high-dimensional systems, which were once nightmares when solving MDEs in SCFT. Moreover, the calculations in SCMFT mainly relate to the assemble averages of chain conformations, for which a portion of conformations can be performed parallel on different computing cores using a message-passing interface (MPI). Full article

Semiflexible polymers bound to planar substrates by a short-range surface potential are studied by Molecular Dynamics simulations to clarify the extent to which these chain molecules can be considered as strictly two-dimensional. Applying a coarse-grained bead-spring model, the chain length N and stiffness $\kappa$ as well as the strength of the adsorption potential ${ϵ}_{wall}$ are varied over a wide range. The excluded-volume (EV) interactions inherent in this model can also be “switched off” to provide a discretized version of the Kratky–Porod wormlike chain model. We study both local order parameters (fraction f of monomers within the range of the potential, bond-orientational order parameter $\eta$ ) and the mean square gyration radius parallel, ${⟨R_g^2⟩}_{\left|\right|}$ , and perpendicular, ${⟨R_g^2⟩}_{\perp }$ , to the wall. While for strongly adsorbed chains EV has negligible effect on f and $\eta$ , we find that ${⟨R_g^2⟩}_{\left|\right|}$ is strongly affected when the chain contour length exceeds the persistence length. Monomer coordinates in perpendicular (⊥) direction are correlated over the scale of the deflection length which is estimated. It is found that $f,\eta$ , and ${⟨R_g^2⟩}_{\perp }$ converge to their asymptotic values with $1/N$ corrections. For both weakly and strongly adsorbed chains, the distribution functions of “loops”, “trains”, and “tails” are analyzed. Some consequences pertaining to the analysis of experiments on adsorbed semiflexible polymers are pointed out. Full article

We consider semiflexible chains governed by preferred curvature and twist and their flexural and twist moduli. These filaments possess a helical rather than straight three-dimensional (3D) ground state and we call them helical filaments (H-filament). Depending on the moduli, the helical shape may be smeared by thermal fluctuations. Secondary superhelical structures are expected to form on top of the specific local structure of biofilaments, as is documented for vimentin. We study confinement and adsorption of helical filaments utilizing both a combination of numerical simulations and analytical theory. We investigate overall chain shapes, transverse chain fluctuations, loop and tail distributions, and energy distributions along the chain together with the mean square average height of the monomers $⟨z^2⟩$ . The number fraction of adsorbed monomers serves as an order parameter for adsorption. Signatures of adsorbed helical polymers are the occurrence of 3D helical loops/tails and spiral or wavy quasi-flat shapes. None of these arise for the Worm-Like-Chain, whose straight ground state can be embedded in a plane. Full article

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. Full article

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. Full article

Bundled actin structures play an essential role in the mechanical response of the actin cytoskeleton in eukaryotic cells. Although responsible for crucial cellular processes, they are rarely investigated in comparison to single filaments and isotropic networks. Presenting a highly anisotropic structure, the determination of the mechanical properties of individual bundles was previously achieved through passive approaches observing bending deformations induced by thermal fluctuations. We present a new method to determine the bending stiffness of individual bundles, by measuring the decay of an actively induced oscillation. This approach allows us to systematically test anisotropic, bundled structures. Our experiments revealed that thin, depletion force-induced bundles behave as semiflexible polymers and obey the theoretical predictions determined by the wormlike chain model. Thickening an individual bundle by merging it with other bundles enabled us to study effects that are solely based on the number of involved filaments. These thicker bundles showed a frequency-dependent bending stiffness, a behavior that is inconsistent with the predictions of the wormlike chain model. We attribute this effect to internal processes and give a possible explanation with regard to the wormlike bundle theory. Full article

Instability and structural transitions arise in many important problems involving dynamics at molecular length scales. Buckling of an elastic rod under a compressive load offers a useful general picture of such a transition. However, the existing theoretical description of buckling is applicable in the load response of macroscopic structures, only when fluctuations can be neglected, whereas membranes, polymer brushes, filaments, and macromolecular chains undergo considerable Brownian fluctuations. We analyze here the buckling of a fluctuating semiflexible polymer experiencing a compressive load. Previous works rely on approximations to the polymer statistics, resulting in a range of predictions for the buckling transition that disagree on whether fluctuations elevate or depress the critical buckling force. In contrast, our theory exploits exact results for the statistical behavior of the worm-like chain model yielding unambiguous predictions about the buckling conditions and nature of the buckling transition. We find that a fluctuating polymer under compressive load requires a larger force to buckle than an elastic rod in the absence of fluctuations. The nature of the buckling transition exhibits a marked change from being distinctly second order in the absence of fluctuations to being a more gradual, compliant transition in the presence of fluctuations. We analyze the thermodynamic contributions throughout the buckling transition to demonstrate that the chain entropy favors the extended state over the buckled state, providing a thermodynamic justification of the elevated buckling force. Full article

This paper presents a theoretical formalism for describing systems of semiflexible polymers, which can have density variations due to finite compressibility and exhibit an isotropic-nematic transition. The molecular architecture of the semiflexible polymers is described by a continuum wormlike-chain model. The non-bonded interactions are described through a functional of two collective variables, the local density and local segmental orientation tensor. In particular, the functional depends quadratically on local density-variations and includes a Maier–Saupe-type term to deal with the orientational ordering. The specified density-dependence stems from a free energy expansion, where the free energy of an isotropic and homogeneous homopolymer melt at some fixed density serves as a reference state. Using this framework, a self-consistent field theory is developed, which produces a Helmholtz free energy that can be used for the calculation of the thermodynamics of the system. The thermodynamic properties are analysed as functions of the compressibility of the model, for values of the compressibility realizable in mesoscopic simulations with soft interactions and in actual polymeric materials. Full article

The worm-like chain is one of the best theoretical models of the semiflexible polymer. The structure factor, which can be obtained by scattering experiment, characterizes the density correlation in different length scales. In the present review, the numerical method to compute the static structure factor of the worm-like chain model and its general properties are demonstrated. Especially, the chain length and persistence length involved multi-scale nature of the worm-like chain model are well discussed. Using the numerical structure factor, Gaussian fluctuation theory of the worm-like chain model can be developed, which is a powerful tool to analyze the structure stability and to predict the spinodal line of the system. The microphase separation of the worm-like diblock copolymer is considered as an example to demonstrate the usage of Gaussian fluctuation theory. Full article

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