arXiv subjects

Panayotis Benetatos

Publications and source records attributed to Panayotis Benetatos.

At least 19 recordsLinked to original sources

arXiv2026

The elasticity of semiflexible polymers with reversible spontaneous curvature in two dimensions

Many semiflexible filaments exhibit structural asymmetries that lead to a curved ground state (curvature in the absence of thermal fluctuations, external forces, or torques). This property is known as spontaneous curvature. Many semiflexible polymers can reversibly develop spontaneous curvature through internal conformational transitions or through transient interactions with their molecular environment. In this article, we show that such reversible spontaneous curvature, even in the absence of transitions in the value of the bending stiffness, provides a minimal mechanism for ensemble-dependent elasticity. We formulate an analytically tractable two-state modified wormlike-chain model in two dimensions, in which an uncurved state (without spontaneous curvature) competes with a curved state (possessing spontaneous curvature). The transition is controlled by an activation energy. Within the weak-bending approximation, we obtain the Gibbs and Helmholtz partition functions for a stretched filament with reversible constant (uniform along the backbone) or sinusoidal spontaneous curvature and for a grafted bistable filament driven either by an end torque or a bending force. Stretching or bending induces a crossover from spontaneous-curvature-dominated to entropic elasticity. We show how the elastic response differs in the two ensembles (Gibbs vs Helmholtz). In addition, we consider the case where the curved state is also characterized by a higher value of the bending stiffness. In that case, a reentrant transition is possible as we stretch the bistable filament.

cond-mat.soft↗

arXiv2025

Cross-linked pair of polymer chains under strong tension

We study two cross-linked polymer systems in the strong stretching regime. The first consists of two polymers sharing one endpoint, with the other two endpoints coupled by a harmonic potential. Within the weakly bending approximation, we analyze the tensile elastic response for freely jointed or wormlike chains; for the latter, the approximation applies either at large tension or at moderate tension with large persistence length (rodlike limit). We obtain analytic expressions for the force--extension relation and for the longitudinal and transverse mismatch of the cross-linked endpoints. In the thermodynamic limit, the cross-link does not affect the tensile elasticity, but it significantly suppresses transverse fluctuations, effectively forming a loop structure. The second system is a polymer necklace in the thermodynamic limit, composed of two strongly stretched polymers interconnected by a regular sequence of reversible cross-links. Using an analogy with a two-dimensional system of concatenated Gaussian loops ("Gaussian slinky"), we calculate the mean fraction of cross-linked sites as a function of the tensile force and find weak and strong binding regimes connected by a crossover. For shallow binding potential wells (compared with $k_{\rm{B}}T$), we employ a continuum description and exploit the mapping between directed polymers and a two-dimensional quantum particle to determine the crossover behavior and the mean transverse separation between the two polymer chains.

cond-mat.soft↗

arXiv2025

Elasticity of a Freely Jointed Chain with Quenched Disorder

We introduce a simple theoretical model, the Freely Jointed Chain with quenched hinges (qFJC), which captures the quenched disorder in the local bending stiffness of the polymer. In this article, we analyze the tensile elasticity of the qFJC in the Gibbs (fixed-force) ensemble. For finite-size systems, we obtain a recurrence relation of the exact free energy, which allows us to calculate the exact force-extension relation numerically for an arbitrary size of the system. In the thermodynamic limit, when $L({\rm contour \;length})\gg L_p({\rm persistence \;length})$, we obtain a framework to deal with quenched disorder in the polymer configuration. This allows us to obtain the response function for the discrete and continuous qFJC in the thermodynamic limit. It turns out that the extension of the continuous qFJC can be cast in a simple form. Furthermore, we have applied our analysis to rod-coil multiblock copolymers.

cond-mat.soft↗

arXiv2024

Bending Elasticity of the reversible Freely Jointed Chain

The freely jointed chain model with reversible hinges (rFJC) is the simplest theoretical model that captures reversible transitions of the local bending stiffness along the polymer chain backbone, e.g. helix-coil-type of local conformational changes or changes due to the binding/unbinding of ligands). In this work, we analyze the bending fluctuations and the bending response of a grafted rFJC in the Gibbs (fixed-force) ensemble. We obtain a recursion relation for the partition function of the grafted rFJC under bending force, which allows, in principle, exact-numerical calculation of the behavior of a rFJC of arbitrary size. In contrast to stretching, we show that under sufficiently stiff conditions, the differential bending compliance and the mean fraction of closed hinges are non-monotonic functions of the force. We also obtain the persistence length $L_p$ of the rFJC, the moments $\langle R^2 \rangle$ (mean-square end-to-end distance), and $\langle z^2 \rangle$ (mean-square transverse deflection) for the discrete chain and take the continuum limit. The tangent vector auto-correlation decays exponentially, as in the wormlike chain model (WLC). Remarkably, the expression of $\langle R^2 \rangle$ as a function of the contour length $L$ becomes the same as that in the WLC. In the thermodynamic limit, we have calculated the exact bending response analytically. As expected, for $L\gg L_p$, the boundary conditions do not matter, and the bending becomes equivalent to stretching. In contrast, for $L_p\gg L$, we have shown the non-monotonicity of the bending response (the compliance and mean fraction of closed hinges).

cond-mat.soft↗

arXiv2018

Inequivalence of fixed-force and fixed-extension statistical ensembles for a flexible polymer tethered to a planar substrate

Recent advances in single macromolecule experiments have sparked interest in the ensemble dependence of force-extension relations. The thermodynamic limit may not be attainable for such systems, that leads to inequivalence of the fixed-force and the fixed-extension ensemble. We consider an ideal Gaussian chain described by the Edwards Hamiltonian with one end tethered to a rigid planar substrate. We analytically calculate the force-extension relation in the two ensembles and we show their inequivalence which is caused by the confinement of the polymer to half space. The inequivalence is quite remarkable for strong compressional forces. We also perform Monte-Carlo simulations of a tethered wormlike chain with contour length 20 times its persistence length which corresponds to experiments measuring the conformations of DNA tethered to a wall. The simulations confirm the ensemble inequivalence and qualitatively agree with the analytical predictions of the Gaussian model. Our analysis shows that confinement due to tethering causes ensemble inequivalence, irrespective of the polymer model.

cond-mat.soft↗

arXiv2017

Tensile elasticity of semiflexible polymers with hinge defects

It has become clear in recent years that the simple uniform wormlike chain model needs to be modified in order to account for more complex behavior which has been observed experimentally in some important biopolymers. For example, the large flexibility of short ds-DNA has been attributed to kink or hinge defects. In this paper, we calculate analytically, within the weak bending approximation, the force-extension relation of a wormlike chain with a permanent hinge defect along its contour. The defect is characterized by its bending energy (which can be zero, in the completely flexible case) and its position along the polymer contour. Besides the bending rigidity of the chain, these are the only parameters which describe our model. We show that a hinge defect causes a significant increase in the differential tensile compliance of a pre-stressed chain. In the small force limit, a hinge defect significantly increases the entropic elasticity. Our results apply to any pair of semiflexible segments connected by a hinge. As such, they may also be relevant to cytoskeletal filaments (F-actin, microtubules), where one may treat the cross-link connecting two filaments as a hinge defect.

cond-mat.soft↗

arXiv2016

Elasticity of a semiflexible filament with a discontinuous tension due to a cross-link or a molecular motor

We analyze the stretching elasticity of a wormlike chain with a tension discontinuity resulting from a Hookean spring connecting its backbone to a fixed point. The elasticity of isolated semiflexible filaments has been the subject in a significant body of literature, primarily because of its relevance to the mechanics of biological matter. In real systems, however, these filaments are usually part of supramolecular structures involving cross-linkers or molecular motors which cause tension discontinuities. Our model is intended as a minimal structural element incorporating such a discontinuity. We obtain analytical results in the weakly bending limit of the filament, concerning its force-extension relation and the response of the two parts in which the filament is divided by the spring. For a small tension discontinuity, the linear response of the filament extension to this discontinuity strongly depends on the external tension. For large external tension $f$, the spring force contributes a subdominant correction $\sim 1/f^{3/2}$ to the well known $\sim 1/\sqrt{f}$ dependence of the end-to-end extension.

physics.bio-ph↗

arXiv2015

Mechanical properties of branched actin filaments

Cells moving on a two dimensional substrate generate motion by polymerizing actin filament networks inside a flat membrane protrusion. New filaments are generated by branching off existing ones, giving rise to branched network structures. We investigate the force-extension relation of branched filaments, grafted on an elastic structure at one end and pushing with the free ends against the leading edge cell membrane. Single filaments are modeled as worm-like chains, whose thermal bending fluctuations are restricted by the leading edge cell membrane, resulting in an effective force. Branching can increase the stiffness considerably; however the effect depends on branch point position and filament orientation, being most pronounced for intermediate tilt angles and intermediate branch point positions. We describe filament networks without cross-linkers to focus on the effect of branching. We use randomly positioned branch points, as generated in the process of treadmilling, and orientation distributions as measured in lamellipodia. These networks reproduce both the weak and strong force response of lamellipodia as measured in force-velocity experiments. We compare properties of branched and unbranched networks. The ratio of the network average of the force per branched filament to the average force per unbranched filament depends on the orientation distribution of the filaments. The ratio exhibits compression dependence and may go up to about 4.5 in networks with a narrow orientation distribution. With orientation distributions measured in lamellipodia, it is about two and essentially independent from network compression, graft elasticity and filament persistence length.

physics.bio-ph↗

arXiv2014

Tension-induced binding of semiflexible biopolymers

We investigate theoretically the effect of polymer tension on the collective behavior of reversibly binding cross-links. For this purpose, we employ a model of two weakly bending wormlike chains aligned in parallel by a tensile force, with a sequence of inter-chain binding sites regularly spaced along the contours. Reversible cross-links attach and detach at the sites with an affinity controlled by a chemical potential. In a mean-field approach, we calculate the free energy of the system and find the emergence of a free-energy barrier which controls the reversible (un)binding. The tension affects the conformational entropy of the chains which competes with the binding energy of the cross-links. This competition gives rise to a sudden increase in the fraction of bound sites as the tension increases. We show that this transition is related to the cross-over between weak and strong localization of a directed polymer in a pinning potential. The cross-over to the strongly bound state can be interpreted as a mechanism for force-stiffening of cross-linked polymers -- beyond the elasticity of a single wormlike chain.

physics.bio-ph↗

arXiv2014

Cross-link induced shrinkage of grafted Gaussian chains

The statistical mechanics of polymers grafted on surfaces has been the subject of intense research activity because of many potential applications. In this paper, we analytically investigate the conformational changes caused by a single cross-link on two ideal (Gaussian) chains grafted on a rigid planar surface. Both the cross-link and the surface reduce the number of allowed configurations. In the absence of the hard substrate, the sole effect of the cross-link is a reduction in the effective Kuhn length of a tethered chain. The cross-link induced shrinkage (collapse) of the grafted chains (mushrooms) turns out to be a reduction in the variance of the distribution of the height of the chain rather than a reduction of the height itself.

cond-mat.soft↗

arXiv2013

Bundling in brushes of directed and semiflexible polymers

We explore the effect of an attractive interaction between parallel-aligned polymers, which are perpendicularly grafted on a substrate. Such an attractive interaction could be due to, e.g., reversible cross-links. The competition between permanent grafting favoring a homogeneous state of the polymer brush and the attraction, which tends to induce in-plane collapse of the aligned polymers, gives rise to an instability of the homogeneous phase to a bundled state. In this latter state the in-plane translational symmetry is spontaneously broken and the density is modulated with a finite wavelength, which is set by the length scale of transverse fluctuations of the grafted polymers. We analyze the instability for two models of aligned polymers: directed polymers with a line tension and weakly bending chains with a bending stiffness.

cond-mat.soft↗

arXiv2013

Elasticity of cross-linked semiflexible biopolymers under tension

Aiming at the mechanical properties of cross-linked biopolymers, we set up and analyze a model of two weakly bending wormlike chains subjected to a tensile force, with regularly spaced inter-chain bonds (cross-links) represented by harmonic springs. Within this model, we compute the force-extension curve and the differential stiffness exactly and discuss several limiting cases. Cross-links effectively stiffen the chain pair by reducing thermal fluctuations transverse to the force and alignment direction. The extra alignment due to cross-links increases both with growing number and with growing strength of the cross-links, and is most prominent for small force f. For large f, the additional, cross-link-induced extension is subdominant except for the case of linking the chains rigidly and continuously along their contour. In this combined limit, we recover asymptotically the elasticity of a weakly bending wormlike chain without constraints, stiffened by a factor four. The increase in differential stiffness can be as large as 100% for small f or large numbers of cross-links.

physics.bio-ph↗

arXiv2012

Force-extension relation of cross-linked anisotropic polymer networks

Cross-linked polymer networks with orientational order constitute a wide class of soft materials and are relevant to biological systems (e.g., F-actin bundles). We analytically study the nonlinear force-extension relation of an array of parallel-aligned, strongly stretched semiflexible polymers with random cross-links. In the strong stretching limit, the effect of the cross-links is purely entropic, independent of the bending rigidity of the chains. Cross-links enhance the differential stretching stiffness of the bundle. For hard cross-links, the cross-link contribution to the force-extension relation scales inversely proportional to the force. Its dependence on the cross-link density, close to the gelation transition, is the same as that of the shear modulus. The qualitative behavior is captured by a toy model of two chains with a single cross-link in the middle.

cond-mat.dis-nn↗

arXiv2011

A constrained random-force model for weakly bending semiflexible polymers

The random-force (Larkin) model of a directed elastic string subject to quenched random forces in the transverse directions has been a paradigm in the statistical physics of disordered systems. In this brief note, we investigate a modified version of the above model where the total transverse force along the polymer contour and the related total torque, in each realization of disorder, vanish. We discuss the merits of adding these constraints and show that they leave the qualitative behavior in the strong stretching regime unchanged, but they reduce the effects of the random force by significant numerical prefactors. We also show that a transverse random force effectively makes the filament softer to compression by inducing undulations. We calculate the related linear compression coefficient in both the usual and the constrained random force model.

cond-mat.soft↗

arXiv2011

Orientational order and glassy states in networks of semiflexible polymers

Motivated by the structure of networks of cross-linked cytoskeletal biopolymers, we study the orientationally ordered phases in two-dimensional networks of randomly cross-linked semiflexible polymers. We consider permanent cross-links which prescribe a finite angle and treat them as quenched disorder in a semi-microscopic replica field theory. Starting from a fluid of un-cross-linked polymers and small polymer clusters (sol) and increasing the cross-link density, a continuous gelation transition occurs. In the resulting gel, the semiflexible chains either display long range orientational order or are frozen in random directions depending on the value of the crossing angle, the crosslink concentration and the stiffness of the polymers. A crossing angle $θ\sim 2π/M$ leads to long range $M$-fold orientational order, e.g., "hexatic" or "tetratic" for $θ=60^{\circ}$ or $90^{\circ}$, respectively. The transition is discontinuous and the critical cross-link density depends on the bending stiffness of the polymers and the cross-link geometry: the higher the stiffness and the lower $M$, the lower the critical number of cross-links. In between the sol and the long range ordered state, we always observe a gel which is a statistically isotropic amorphous solid (SIAS) with random positional and random orientational localization of the participating polymers.

cond-mat.soft↗

arXiv2010

Stretching semiflexible filaments with quenched disorder

We study the effect of quenched randomness in the arc-length dependent spontaneous curvature of a wormlike chain under tension. In the weakly bending approximation in two dimensions, we obtain analytic results for the force-elongation curve and the width of transverse fluctuations. We compare quenched and annealed disorder and conclude that the former cannot always be reduced to a simple change in the stiffness of the pure system. We also discuss the effect of a random transverse force on the stretching response of a wormlike chain without spontaneous curvature.

cond-mat.soft↗

arXiv2010

Stretching weakly bending filaments with spontaneous curvature in two dimensions

Some important biomolecules (for instance, bacterial FtsZ and eukaryotic DNA) are known to posses spontaneous (intrinsic) curvature. Using a simple extension of the wormlike chain model, we study the response of a weakly bending filament in two dimensions to a pulling force applied at its ends (a configuration common in classical in-vitro experiments and relevant to several in-vivo cell cases). The spontaneous curvature of such a chain or filament can in general be arc-length dependent and we study a case of sinusoidal variation, from which an arbitrary case can be reconstructed via Fourier transformation. We obtain analytic results for the force-extension relationship and the width of transverse fluctuations. We show that spontaneous-curvature undulations can affect the force-extension behavior even in relatively flexible filaments with a persistence length smaller than the contour length.

cond-mat.soft↗

arXiv2010

Random networks of cross-linked directed polymers

We explore the effect of random permanent cross-links on a system of directed polymers confined between two planes with their end-points free to slide on them. We treat the cross-links as quenched disorder and we use a semimicroscopic replica field theory to study the structure and elasticity of this system. Upon increasing the cross-link density, we get a continuous gelation transition signaled by the emergence of a finite in-plane localization length. The distribution of localization length turns out to depend on the height along the preferred direction of the directed polymers. The gelation transition also gives rise to a finite in-plane shear modulus which we calculate and turns out to be universal, i.e., independent of the energy and length scales of the polymers and the cross-links. Using a symmetry argument, we show that cross-links of negligible extent along the preferred axis of the directed polymers do not cause any renormalization to the tilt modulus of the uncross-linked system.

cond-mat.soft↗