Semiflexible Filaments Research Articles

First-contact time to a patch in a multidimensional potential well

The escape of a diffusing particle from a potential well is an important aspect of many dynamic processes in chemistry, physics, and biology, and such an escape process often involves finding a restricted region or patch in a multidimensional potential well. We study an idealized model of this process via simulation and analytic theory. By combining results from special cases having either high symmetry or zero potential, we obtain a simple formula for the first-contact time for a particle moving to a boundary patch in an arbitrary number of dimensions. We apply this formula in two, three, and six dimensions. The predicted dependences of the first-contact time on the well depth and patch size are compared to results from simulations, and close agreement is found. We extend the theory to calculate the first-contact time between two particles in separate harmonic potential wells. As an application of this extended theory, we calculate the first-contact time for two parallel semiflexible biopolymer filaments and compare these results to previous simulations.

Brownian dynamics algorithm for entangled wormlike threads

The authors present a hybrid Brownian dynamics/Monte Carlo algorithm for simulating solutions of highly entangled semiflexible polymers or filaments. The algorithm combines a Brownian dynamics time-stepping approach with an efficient scheme for rejecting moves that cause chains to cross or that lead to excluded volume overlaps. The algorithm allows simulation of the limit of infinitely thin but uncrossable threads, and is suitable for simulating the conditions obtained in experiments on solutions of long actin protein filaments.

Reversible stress softening of actin networks

The mechanical properties of cells play an essential role in numerous physiological processes. Organized networks of semiflexible actin filaments determine cell stiffness and transmit force during mechanotransduction, cytokinesis, cell motility and other cellular shape changes. Although numerous actin-binding proteins have been identified that organize networks, the mechanical properties of actin networks with physiological architectures and concentrations have been difficult to measure quantitatively. Studies of mechanical properties in vitro have found that crosslinked networks of actin filaments formed in solution exhibit stress stiffening arising from the entropic elasticity of individual filaments or crosslinkers resisting extension. Here we report reversible stress-softening behaviour in actin networks reconstituted in vitro that suggests a critical role for filaments resisting compression. Using a modified atomic force microscope to probe dendritic actin networks (like those formed in the lamellipodia of motile cells), we observe stress stiffening followed by a regime of reversible stress softening at higher loads. This softening behaviour can be explained by elastic buckling of individual filaments under compression that avoids catastrophic fracture of the network. The observation of both stress stiffening and softening suggests a complex interplay between entropic and enthalpic elasticity in determining the mechanical properties of actin networks.

Active gels: where polymer physics meets cytoskeletal dynamics

The cytoskeleton provides eukaryotic cells with mechanical support and helps them to perform their biological functions. It is predominantly composed of a network of semiflexible polar protein filaments. In addition, there are many accessory proteins that bind to these filaments, regulate their assembly, link them to organelles and provide the motors that either move the organelles along the filaments or move the filaments themselves. A natural approach to such a multiple particle system is the study of its collective excitations. I review some recent work on the theoretical description of the emergence of a number of particular collective motile behaviours from the interactions between different elements of the cytoskeleton. In order to do this, close analogies have been made to the study of driven soft condensed matter systems. However, it emerges naturally that a description of these soft active motile systems gives rise to new types of collective phenomena not seen in conventional soft systems. I discuss the implications of these results and perspectives for the future.

Energetics and Dynamics of Constrained Actin Filament Bundling

The formation of filopodia-like bundles from a dendritic actin network has been observed to occur in vitro as a result of branching induced by Arp2/3 complex. We study both the energetics and dynamics of actin filament bundling in such a network to evaluate their relative importance in bundle formation processes. Our model considers two semiflexible actin filaments fixed at one end and free at the other, described using a normal-mode approximation. This model is studied by both Brownian dynamics and free-energy minimization methods. Remarkably, even short filaments can bundle at separations comparable to their lengths. In the dynamic simulations, we evaluate the time required for the filaments to interact and bind, and examine the dependence of this bundling time on the filament length, the distance between the filament bases, and the cross-linking energy. In most cases, bundling occurs in a second or less. Beyond a certain critical distance, we find that the bundling time increases very rapidly with increasing interfilament separation and/or decreasing filament length. For most of the cases we have studied, the energetics results for this critical distance are similar to those obtained from dynamics simulations run for 10 s, suggesting that beyond this timescale, energetics, rather than kinetic constraints, determine whether or not bundling occurs. Over a broad range of conditions, we find that the times required for bundling from a network are compatible with experimental observations.

Nonlinear dynamics of semiflexible magnetic filaments in an ac magnetic field

Flexible spontaneously magnetized filaments exist in the living world (magnetotactic bacteria) and arise in magnetic colloids with large magnetodipolar interaction parameter. We demonstrate that these filaments possess variety of novel nonlinear phenomena in an ac magnetic field: orientation of the filament in the direction perpendicular to the field and the development of the oscillating U-like shapes, which presumably can lead to the formation of rings of magnetic filaments. It is found that these phenomena are determined by the development of the localized boundary modes of the filament deformation. We have illustrated by qualitative estimates that the phenomena found may be useful for insight into the complex pattern formation phenomena in ensembles of magnetic particles under the action of an ac magnetic field.

A Master Relation Defines the Nonlinear Viscoelasticity of Single Fibroblasts

Cell mechanical functions such as locomotion, contraction, and division are controlled by the cytoskeleton, a dynamic biopolymer network whose mechanical properties remain poorly understood. We perform single-cell uniaxial stretching experiments on 3T3 fibroblasts. By superimposing small amplitude oscillations on a mechanically prestressed cell, we find a transition from linear viscoelastic behavior to power law stress stiffening. Data from different cells over several stress decades can be uniquely scaled to obtain a master relation between the viscoelastic moduli and the average force. Remarkably, this relation holds independently of deformation history, adhesion biochemistry, and intensity of active contraction. In particular, it is irrelevant whether force is actively generated by the cell or externally imposed by stretching. We propose that the master relation reflects the mechanical behavior of the force-bearing actin cytoskeleton, in agreement with stress stiffening known from semiflexible filament networks.

Pumping Fluids with Periodically Beating Grafted Elastic Filaments

Using Brownian dynamics simulations, we investigate the pumping efficiency of an array of periodically beating semiflexible filaments that are grafted to a surface. Full hydrodynamic interactions among and within filaments and no slip at the surface are considered. Optimal pumping is obtained for a characteristic ratio of applied forward-backward torques and filament persistence length. For independently driven filaments, phase locking between neighboring filaments occurs autonomously via hydrodynamic coupling, giving rise to significantly enhanced pumping efficiency.

Dynamic fluctuations of dipolar semiflexible filaments

On the basis of the model of a flexible magnetic filament, the characteristics of their thermal fluctuations are considered. The crossover of the time dependence of the mean quadratic displacement from t(3/4) to t(1/2) at the magnetic field increase is found. Two characteristic mechanisms of the magnetization relaxation time distribution--straightening of the thermal undulations and excitation of the bending modes of the free ends under the action of an ac magnetic field--are described. In both cases, the characteristic scaling law omega(-3/4) of the magnetic susceptibility in a high-frequency range is found.

Alternative Explanation of Stiffening in Cross-Linked Semiflexible Networks

Strain stiffening of filamentous protein networks is explored by means of a finite strain analysis of a two-dimensional network model of cross-linked semiflexible filaments. The results show that stiffening is caused by nonaffine network rearrangements that govern a transition from a bending-dominated response at small strains to a stretching-dominated response at large strains. Filament undulations, which are key in the existing explanation of stiffening, merely postpone the transition.

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

Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Korea, Materials Research Laboratory and Department of Materials, Physics, Molecular, Cellular, and Developmental Biology, University of CaliforniasSanta Barbara, Santa Barbara, California 93106, Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19010, College of Optoelectronic Engineering, Chongqing University, Chongqing, China, and Temperature-Humidity Group, Korea Research Institute of Standards and Science, Daejeon, Korea

Dynamics of inextensible semiflexible filaments

We address the problem of the fluctuating dynamics of an isolated inextensible and semiflexible filament of length L . By focusing explicitly on two key properties of the filaments--their connectivity and inextensibility--we obtain insights into their dynamics. We calculate the dynamics, and we calculate the correlation functions for chains of finite length taking into account the boundary conditions at the chain ends. We obtain closed-form expressions that separate the internal bending modes from the global rotation modes.

Single-Filament Dynamics and Long-Range Ordering of Semiflexible Biopolymers under Flow and Confinement

We report the collective and single-filament dynamics of long semiflexible actin filaments flowing in an evaporating droplet adhering on glass and accumulating along the physical barrier constituted by the droplet triple line. The observation of fluorescent reporter filaments embedded in the entangled network enables us to relate the final collective organization of the accumulated filaments to the individual filament dynamics. Three areas corresponding to distinct filament organizations are observed in the region of the initial triple line pinning, after complete evaporation of the droplet. A nematic liquid-crystal-like alignment of the filaments is observed at the edge of the droplet because of the dynamic filament alignment, whereas a less-ordered packing is generated because of the bending and folding of most of the filaments. The latter unconventional dynamics is analyzed in terms of the amplification of undulation modes typical of semiflexible polymers. The receding regime of the droplet triple line leads finally to a remaining film of actin filaments showing random organization.

On the Origin of Stiffening in Biopolymers

AbstractStrain stiffening of protein networks is explored by means of a finite strain analysis of a two-dimensional network model of cross-linked semiflexible filaments. The results show that stiffening is caused by non-affine network rearrangements that govern a transition from a bending dominated response at small strains to a stretching dominated response at large strains. Thermally-induced filament undulations only have a minor effect; they merely postpone the transition.

Scaling of F-Actin Network Rheology to Probe Single Filament Elasticity and Dynamics

The linear and nonlinear viscoelastic response of networks of cross-linked and bundled cytoskeletal filaments demonstrates remarkable scaling with both frequency and applied prestress, which helps elucidate the origins of the viscoelasticity. The frequency dependence of the shear modulus reflects the underlying single-filament relaxation dynamics for 0.1-10 rad/sec. Moreover, the nonlinear strain stiffening of such networks exhibits a universal form as a function of prestress; this is quantitatively explained by the full force-extension relation of single semiflexible filaments.

Stretching of semiflexible polymers with elastic bonds.

A semiflexible harmonic chain model with extensible bonds is introduced and applied to the stretching of semiflexible polymers or filaments. The semiflexible harmonic chain model allows to study effects from bending rigidity, bond extension, discrete chain structure, and finite length of a semiflexible polymer in a unified manner. The interplay between bond extension and external force can be described by an effective inextensible chain with increased stretching force, which leads to apparently reduced persistence lengths in force-extension relations. We obtain force-extension relations for strong- and weak-stretching regimes which include the effects of extensible bonds, discrete chain structure, and finite polymer length. We discuss the associated characteristic force scales and calculate the crossover behaviour of the force-extension curves. Strong stretching is governed by the discrete chain structure and the bond extensibility. The linear response for weak stretching depends on the relative size of the contour length and the persistence length which affects the behaviour of very rigid filaments such as F-actin. The results for the force-extension relations are corroborated by transfer matrix and variational calculations.

Anomalous fluctuations of active polar filaments.

Using a simple model, we study the fluctuating dynamics of inextensible, semiflexible polar filaments interacting with active and directed force generating centers such as molecular motors. Taking into account the fact that the activity occurs on time scales comparable to the filament relaxation time, we obtain some unexpected differences between both the steady-state and dynamical behaviors of active as compared to passive filaments. For the statics, the filaments have a length-scale-dependent rigidity. Dynamically, we find strongly enhanced anomalous diffusion.

Tracer studies on f-actin fluctuations.

We present a study on the fluctuations of semiflexible actin filaments using fluorescence videomicroscopy, focusing on the end-to-end fluctuations of single filaments. In order to specifically measure the position of the polymer's ends, we developed a novel noninvasive method that consists of annealing short end tags to the filaments. This allows us to probe polymer fluctuations to a very high accuracy. We compared the distribution of the end-to-end distance with recent theoretical results, and found excellent agreement. We also studied the dynamics of the mean-square end-to-end distance deltaR2(t) and orientation of the ends, deltaTheta(2)(t), finding power laws t(3/4) and t(1/4), respectively. Scaling behavior for deltaR2(t) is observed over several decades in relaxation time in agreement with theoretical results.

Dynamics of a semiflexible filament under external force

We investigate the dynamics of a single semiflexible filament under the action of external forces. We show that unlike in stiff elastic rods in the thermally activated semiflexible filaments external forces applied at one extremity of the filament do not propagate to the other end till the filament is fully stretched. This asymmetric tension profile is shown to be the reason for qualitatively different behavior exhibited by semiflexible filaments under external tension.

Dynamics of folding in semiflexible filaments.

The dynamics of a single semiflexible filament under the action of a compressing force is simulated. We find that the filament folds asymmetrically with a folding length which depends only on the bending stiffness kappa and the applied force f. It is shown that this behavior can be attributed to the exponentially falling tension profile in the filament. While the folding time tau(0) depends on the initial configuration, the distance moved by the terminal point of the filament and the length of the fold scales as tau(1/2) at tau>>tau(0) and is independent of the initial configuration.