Quantitative analysis of extension-torsion coupling of actin filaments

Actin filaments have a double-helix structure consisting of globular actin molecules. In many mechanical cellular activities, such as cell movement, division, and shape control, modulation of the extensional and torsional dynamics of the filament has been linked to regulatory actin-binding protein functions. Therefore, it is important to quantitatively evaluate extension-torsion coupling of filament to better understand the actin filament dynamics. In the present study, the extension-torsion coupling was investigated using molecular dynamics simulations. We constructed a model for the actin filament consisting of 14 actin subunits in an ionic solvent as a minimal functional unit, and analyzed longitudinal and twisting Brownian motions of the filament. We then derived the expected value of energy associated with extension and torsion at equilibrium, and evaluated the extension-torsion stiffness of the filament from the thermal fluctuations obtained from the MD simulations. The results demonstrated that as the analyzed sampling-window duration was increased, the extension-torsion coupling stiffness evaluated on a nanosecond scale tended to converge to a value of 7.6×10(-11) N. The results obtained from this study will contribute to the understanding of biomechanical events, under mechanical tension and torque, involving extension-torsion coupling of filaments.     

The Antiparallel Dimerization of Myosin X Imparts Bundle Selectivity for Processive Motility

Myosin X is an unconventional actin-based molecular motor involved in filopodial formation, microtubule-actin filament interaction, and cell migration. Myosin X is an important component of filopodia regulation, localizing to tips of growing filopodia by an unclear targeting mechanism. The native α-helical dimerization domain of myosin X is thought to associate with antiparallel polarity of the two amino acid chains, making myosin X the only myosin that is currently considered to form antiparallel dimers. This study aims to determine if antiparallel dimerization of myosin X imparts selectivity toward actin bundles by comparing the motility of parallel and antiparallel dimers of myosin X on single and fascin-bundled actin filaments. Antiparallel myosin X dimers exhibit selective processivity on fascin-bundled actin and are only weakly processive on single actin filaments below saturating [ATP]. Artificial forced parallel dimers of myosin X are robustly processive on both single and bundled actin, exhibiting no selectivity. To determine the relationship between gating of the reaction steps and observed differences in motility, a mathematical model was developed to correlate the parameters of motility with the biochemical and mechanical kinetics of the dimer. Results from the model, constrained by experimental data, suggest that the probability of binding forward, toward the barbed end of the actin filament, is lower in antiparallel myosin X on single actin filaments compared to fascin-actin bundles and compared to constructs of myosin X with parallel dimerization.     

Emergence and maintenance of variable-length actin filaments in a limiting pool of building blocks

Actin is one of the key structural components of the eukaryotic cytoskeleton that regulates cellular architecture and mechanical properties. Dynamic regulation of actin filament length and organization is essential for the control of many physiological processes including cell adhesion, motility and division. While previous studies have mostly focused on the mechanisms controlling the length of single actin filaments, it remains poorly understood how distinct actin filament populations in cells maintain different lengths using the same set of molecular building blocks. Here, we develop a theoretical model for the length regulation of multiple actin filaments by nucleation and growth-rate modulation by actin-binding proteins in a limiting pool of monomers. We first show that spontaneous nucleation of actin filaments naturally leads to heterogeneities in filament length distribution. We then investigate the effects of filament growth inhibition by capping proteins and growth promotion by formin proteins on filament length distribution. We find that filament length heterogeneity can be increased by growth inhibition, whereas growth promoters do not significantly affect length heterogeneity. Interestingly, a competition between filament growth inhibitors and growth promoters can give rise to bimodal filament length distribution as well as a highly heterogeneous length distribution with large statistical dispersion. We quantitatively predict how heterogeneity in actin filament length can be modulated by tuning filamentous actin nucleation and growth rates in order to create distinct filament subpopulations with different lengths.     

Measurement of the persistence length of cytoskeletal filaments using curvature distributions

Cytoskeletal filaments, such as microtubules and actin filaments, play important roles in the mechanical integrity of cells and the ability of cells to respond to their environment. Measuring the mechanical properties of cytoskeletal structures is crucial for gaining insight into intracellular mechanical stresses and their role in regulating cellular processes. One of the ways to characterize these mechanical properties is by measuring their persistence length, the average length over which filaments stay straight. There are several approaches in the literature for measuring filament deformations, such as Fourier analysis of images obtained using fluorescence microscopy. Here, we show how curvature distributions can be used as an alternative tool to quantify biofilament deformations, and investigate how the apparent stiffness of filaments depends on the resolution and noise of the imaging system. We present analytical calculations of the scaling curvature distributions as a function of filament discretization, and test our predictions by comparing Monte Carlo simulations with results from existing techniques. We also apply our approach to microtubules and actin filaments obtained from in vitro gliding assay experiments with high densities of nonfunctional motors, and calculate the persistence length of these filaments. The presented curvature analysis is significantly more accurate compared with existing approaches for small data sets, and can be readily applied to both in vitro and in vivo filament data through the use of the open-source codes we provide.     

Polymerization and depolymerization of actin with nucleotide states at filament ends

Polymerization induces hydrolysis of ATP bound to actin, followed by γ-phosphate release, which helps advance the disassembly of actin filaments into ADP-G-actin. Mechanical understanding of this correlation between actin assembly and ATP hydrolysis has been an object of intensive studies in biochemistry and structural biology for many decades. Although actin polymerization and depolymerization occur only at either the barbed or pointed ends and the kinetic and equilibrium properties are substantially different from each other, characterizing their properties is difficult to do by bulk assays, as these assays report the average of all actin filaments in solution and are therefore not able to discern the properties of individual actin filaments. Biochemical studies of actin polymerization and hydrolysis were hampered by these inherent properties of actin filaments. Total internal reflection fluorescence (TIRF) microscopy overcame this problem by observing single actin filaments. With TIRF, we now know not only that each end has distinct properties, but also that the rate of γ-phosphate release is much faster from the terminals than from the interior of actin filaments. The rate of γ-phosphate release from actin filament ends is even more accelerated when latrunculin A is bound. These findings highlight the importance of resolving structural differences between actin molecules in the interior of the filament and those at either filament end. This review provides a history of observing actin filaments under light microscopy, an overview of dynamic properties of ATP hydrolysis at the end of actin filament, and structural views of γ-phosphate release.     

Actin filaments function as a tension sensor by tension-dependent binding of cofilin to the filament

Intracellular and extracellular mechanical forces affect the structure and dynamics of the actin cytoskeleton. However, the underlying molecular and biophysical mechanisms, including how mechanical forces are sensed, are largely unknown. Actin-depolymerizing factor/cofilin proteins are actin-modulating proteins that are ubiquitously distributed in eukaryotes, and they are the most likely candidate as proteins to drive stress fiber disassembly in response to changes in tension in the fiber. In this study, we propose a novel hypothesis that tension in an actin filament prevents the filament from being severed by cofilin. To test this, we placed single actin filaments under tension using optical tweezers. When a fiber was tensed, it was severed after the application of cofilin with a significantly larger delay in comparison with control filaments suspended in solution. The binding rate of cofilin to an actin bundle decreased when the bundle was tensed. These results suggest that tension in an actin filament reduces the cofilin binding, resulting in a decrease in its effective severing activity.     

A Prestressed Cable Network Model of the Adherent Cell Cytoskeleton

A prestressed cable network is used to model the deformability of the adherent cell actin cytoskeleton. The overall and microstructural model geometries and cable mechanical properties were assigned values based on observations from living cells and mechanical measurements on isolated actin filaments, respectively. The models were deformed to mimic cell poking (CP), magnetic twisting cytometry (MTC) and magnetic bead microrheometry (MBM) measurements on living adherent cells. The models qualitatively and quantitatively captured the fibroblast cell response to the deformation imposed by CP while exhibiting only some qualitative features of the cell response to MTC and MBM. The model for CP revealed that the tensed peripheral actin filaments provide the key resistance to indentation. The actin filament tension that provides mechanical integrity to the network was estimated at ~158 pN, and the nonlinear mechanical response during CP originates from filament kinematics. The MTC and MBM simulations revealed that the model is incomplete, however, these simulations show cable tension as a key determinant of the model response.     

The Stepping Pattern of Myosin X Is Adapted for Processive Motility on Bundled Actin

Myosin X is a molecular motor that is adapted to select bundled actin filaments over single actin filaments for processive motility. Its unique form of motility suggests that myosin X's stepping mechanism takes advantage of the arrangement of actin filaments and the additional target binding sites found within a bundle. Here we use fluorescence imaging with one-nanometer accuracy to show that myosin X takes steps of ∼18 nm along a fascin-actin bundle. This step-size is well short of the 36-nm step-size observed in myosin V and myosin VI that corresponds to the actin pseudohelical repeat distance. Myosin X is able to walk along bundles with this step-size if it straddles two actin filaments, but would be quickly forced to spiral into the constrained interior of the bundle if it were to use only a single actin filament. We also demonstrate that myosin X takes many sideways steps as it walks along a bundle, suggesting that it can switch actin filament pairs within the bundle as it walks. Sideways steps to the left or the right occur on bundles with equal frequency, suggesting a degree of lateral flexibility such that the motor's working stroke does not bias it to the left or to the right. On single actin filaments, we find a broad mixture of 10-20-nm steps, which again falls short of the 36-nm actin repeat. Moreover, the motor leans to the right as it walks along single filaments, which may require myosin X to adopt strained configurations. As a control, we also tracked myosin V stepping along actin filaments and fascin-actin bundles. We find that myosin V follows a narrower path on both structures, walking primarily along one surface of an actin filament and following a single filament within a bundle while occasionally switching to neighboring filaments. Together, these results delineate some of the structural features of the motor and the track that allow myosin X to recognize actin filament bundles.     

Origin of Twist-Bend Coupling in Actin Filaments

Actin filaments are semiflexible polymers that display large-scale conformational twisting and bending motions. Modulation of filament bending and twisting dynamics has been linked to regulatory actin-binding protein function, filament assembly and fragmentation, and overall cell motility. The relationship between actin filament bending and twisting dynamics has not been evaluated. The numerical and analytical experiments presented here reveal that actin filaments have a strong intrinsic twist-bend coupling that obligates the reciprocal interconversion of bending energy and twisting stress. We developed a mesoscopic model of actin filaments that captures key documented features, including the subunit dimensions, interaction energies, helicity, and geometrical constraints coming from the double-stranded structure. The filament bending and torsional rigidities predicted by the model are comparable to experimental values, demonstrating the capacity of the model to assess the mechanical properties of actin filaments, including the coupling between twisting and bending motions. The predicted actin filament twist-bend coupling is strong, with a persistence length of 0.15-0.4 μm depending on the actin-bound nucleotide. Twist-bend coupling is an emergent property that introduces local asymmetry to actin filaments and contributes to their overall elasticity. Up to 60% of the filament subunit elastic free energy originates from twist-bend coupling, with the largest contributions resulting under relatively small deformations. A comparison of filaments with different architectures indicates that twist-bend coupling in actin filaments originates from their double protofilament and helical structure.     

Mechanical Heterogeneity Favors Fragmentation of Strained Actin Filaments

We present a general model of actin filament deformation and fragmentation in response to compressive forces. The elastic free energy density along filaments is determined by their shape and mechanical properties, which were modeled in terms of bending, twisting, and twist-bend coupling elasticities. The elastic energy stored in filament deformation (i.e., strain) tilts the fragmentation-annealing reaction free-energy profile to favor fragmentation. The energy gradient introduces a local shear force that accelerates filament intersubunit bond rupture. The severing protein, cofilin, renders filaments more compliant in bending and twisting. As a result, filaments that are partially decorated with cofilin are mechanically heterogeneous (i.e., nonuniform) and display asymmetric shape deformations and energy profiles distinct from mechanically homogenous (i.e., uniform), bare actin, or saturated cofilactin filaments. The local buckling strain depends on the relative size of the compliant segment as well as the bending and twisting rigidities of flanking regions. Filaments with a single bare/cofilin-decorated boundary localize energy and force adjacent to the boundary, within the compliant cofilactin segment. Filaments with small cofilin clusters were predicted to fragment within the compliant cofilactin rather than at boundaries. Neglecting contributions from twist-bend coupling elasticity underestimates the energy density and gradients along filaments, and thus the net effects of filament strain to fragmentation. Spatial confinement causes compliant cofilactin segments and filaments to adopt higher deformation modes and store more elastic energy, thereby promoting fragmentation. The theory and simulations presented here establish a quantitative relationship between actin filament fragmentation thermodynamics and elasticity, and reveal how local discontinuities in filament mechanical properties introduced by regulatory proteins can modulate both the severing efficiency and location along filaments. The emergent behavior of mechanically heterogeneous filaments, particularly under confinement, emphasizes that severing in cells is likely to be influenced by multiple physical and chemical factors.     

Arabidopsis actin depolymerizing factor4 modulates the stochastic dynamic behavior of actin filaments in the cortical array of epidermal cells

Actin filament arrays are constantly remodeled as the needs of cells change as well as during responses to biotic and abiotic stimuli. Previous studies demonstrate that many single actin filaments in the cortical array of living Arabidopsis thaliana epidermal cells undergo stochastic dynamics, a combination of rapid growth balanced by disassembly from prolific severing activity. Filament turnover and dynamics are well understood from in vitro biochemical analyses and simple reconstituted systems. However, the identification in living cells of the molecular players involved in controlling actin dynamics awaits the use of model systems, especially ones where the power of genetics can be combined with imaging of individual actin filaments at high spatial and temporal resolution. Here, we test the hypothesis that actin depolymerizing factor (ADF)/cofilin contributes to stochastic filament severing and facilitates actin turnover. A knockout mutant for Arabidopsis ADF4 has longer hypocotyls and epidermal cells when compared with wild-type seedlings. This correlates with a change in actin filament architecture; cytoskeletal arrays in adf4 cells are significantly more bundled and less dense than in wild-type cells. Several parameters of single actin filament turnover are also altered. Notably, adf4 mutant cells have a 2.5-fold reduced severing frequency as well as significantly increased actin filament lengths and lifetimes. Thus, we provide evidence that ADF4 contributes to the stochastic dynamic turnover of actin filaments in plant cells.     

Effect of tensile force on the mechanical behavior of actin filaments

Actin filaments are the most abundant components of the cellular cytoskeleton, and play critical roles in various cellular functions such as migration, division and shape control. In these activities, mechanical tension causes structural changes in the double-helical structure of the actin filament, which is a key modulator of cytoskeletal reorganization. This study performed large-scale molecular dynamics (MD) and steered MD simulations to quantitatively analyze the effects of tensile force on the mechanical behavior of actin filaments. The results revealed that when a tensile force of 200pN was applied to a filament consisting of 14 actin subunits, the twist angle of the filament decreased by approximately 20°, corresponding to a rotation of approximately -2° per subunit, representing a critical structural change in actin filaments. Based on these structural changes, the variance in filament length and twist angle was found to decrease, leading to increases in extensional and torsional stiffness. Torsional stiffness increased significantly under the tensile condition, and the ratio of filament stiffness under tensile force to that under no external force increased significantly on longer temporal scales. The results obtained from this study contribute to the understanding of mechano-chemical interactions concerning actin dynamics, showing that increased tensile force in the filament prevents actin regulatory proteins from binding to the filament.     

Role of ATP-Hydrolysis in the Dynamics of a Single Actin Filament

We study the stochastic dynamics of growth and shrinkage of single actin filaments taking into account insertion, removal, and ATP hydrolysis of subunits either according to the vectorial mechanism or to the random mechanism. In a previous work, we developed a model for a single actin or microtubule filament where hydrolysis occurred according to the vectorial mechanism: the filament could grow only from one end, and was in contact with a reservoir of monomers. Here we extend this approach in two ways—by including the dynamics of both ends and by comparing two possible mechanisms of ATP hydrolysis. Our emphasis is mainly on two possible limiting models for the mechanism of hydrolysis within a single filament, namely the vectorial or the random model. We propose a set of experiments to test the nature of the precise mechanism of hydrolysis within actin filaments.     

Geometrical and Mechanical Properties Control Actin Filament Organization

The different actin structures governing eukaryotic cell shape and movement are not only determined by the properties of the actin filaments and associated proteins, but also by geometrical constraints. We recently demonstrated that limiting nucleation to specific regions was sufficient to obtain actin networks with different organization. To further investigate how spatially constrained actin nucleation determines the emergent actin organization, we performed detailed simulations of the actin filament system using Cytosim. We first calibrated the steric interaction between filaments, by matching, in simulations and experiments, the bundled actin organization observed with a rectangular bar of nucleating factor. We then studied the overall organization of actin filaments generated by more complex pattern geometries used experimentally. We found that the fraction of parallel versus antiparallel bundles is determined by the mechanical properties of actin filament or bundles and the efficiency of nucleation. Thus nucleation geometry, actin filaments local interactions, bundle rigidity, and nucleation efficiency are the key parameters controlling the emergent actin architecture. We finally simulated more complex nucleation patterns and performed the corresponding experiments to confirm the predictive capabilities of the model.     

Free vibration analysis of microtubules based on the molecular mechanics and continuum beam theory

A molecular structural mechanics (MSM) method has been implemented to investigate the free vibration of microtubules (MTs). The emphasis is placed on the effects of the configuration and the imperfect boundaries of MTs. It is shown that the influence of protofilament number on the fundamental frequency is strong, while the effect of helix-start number is almost negligible. The fundamental frequency is also found to decrease as the number of the blocked filaments at boundaries decreases. Subsequently, the Euler–Bernoulli beam theory is employed to reveal the physics behind the simulation results. Fitting the Euler–Bernoulli beam into the MSM data leads to an explicit formula for the fundamental frequency of MTs with various configurations and identifies a possible correlation between the imperfect boundary conditions and the length-dependent bending stiffness of MTs reported in experiments.     

Structure and Dynamics of the Actin Filament

We used all-atom molecular dynamics simulations to investigate the structure and properties of the actin filament, starting with either the recent Oda model or the older Holmes model. Simulations of monomeric and polymerized actin show that polymerization changes the nucleotide-binding cleft, bringing together the Q137 side chain and bound ATP in a way that may enhance the ATP hydrolysis rate in the filament. Simulations with different bound nucleotides and conformations of the DNase I binding loop show that the persistence length of the filament depends only on loop conformation. Computational modeling reveals how bound phalloidin stiffens actin filaments and inhibits the release of γ-phosphate from ADP-P_i actin.     

Strain field in actin filament network in lamellipodia of migrating cells: Implication for network reorganization

Cell motility is spatiotemporally regulated by interactions among mechanical and biochemical factors involved in the regulation of cytoskeletal actin structure reorganization. Although the molecular mechanisms underlying cell motility have been well investigated, the contributions of mechanical factors such as strain in the network reorganization remain unclear. In this study, we have quantitatively evaluated the strain field in the actin filament network forming the lamellipodia of migrating fish keratocytes to elucidate the mechanism by which actin filament network reorganization is regulated by biomechanical factors. The results highlight the existence of a negative (compressive) strain in the lamellipodia whose direction is parallel to that of cell movement. A close correlation was found between the distributions of the strain and the actin filament density in the lamellipodia, suggesting that negative strain may be involved in filament depolymerization. Based on this result, we propose a selective depolymerization model which suggests that negative strain may couple with biomechanical factors such as ADF/cofilin to promote selective depolymerization of filaments oriented in the direction of the deformation because such filaments experience relatively higher levels of the deformation. This model, in conjunction with others, may explain the observed reduction in filament density and the reorganization of actin filament network at the back of the lamellipodia of migrating fish keratocytes. Thus, we suggest that by coupling with biochemical factors, mechanical factors are involved in the regulation of actin filament depolymerization, thereby contributing to the regulation of cell motility.     

Spatial distribution of filament elasticity determines the migratory behaviors of a cell

Any cellular response leading to morphological changes is highly tuned to balance the force generated from structural reorganization, provided by actin cytoskeleton. Actin filaments serve as the backbone of intracellular force, and transduce external mechanical signal via focal adhesion complex into the cell. During migration, cells not only undergo molecular changes but also rapid mechanical modulation. Here we focus on determining, the role of spatial distribution of mechanical changes of actin filaments in epithelial, mesenchymal, fibrotic and cancer cells with non-migration, directional migration, and non-directional migration behaviors using the atomic force microscopy. We found 1) non-migratory cells only generated one type of filament elasticity, 2) cells generating spatially distributed two types of filament elasticity showed directional migration, and 3) pathologic cells that autonomously generated two types of filament elasticity without spatial distribution were actively migrating non-directionally. The demonstration of spatial regulation of filament elasticity of different cell types at the nano-scale highlights the coupling of cytoskeletal function with physical characters at the sub-cellular level, and provides new research directions for migration related disease.     

Effect of Age and Cytoskeletal Elements on the Indentation-Dependent Mechanical Properties of Chondrocytes

Articular cartilage chondrocytes are responsible for the synthesis, maintenance, and turnover of the extracellular matrix, metabolic processes that contribute to the mechanical properties of these cells. Here, we systematically evaluated the effect of age and cytoskeletal disruptors on the mechanical properties of chondrocytes as a function of deformation. We quantified the indentation-dependent mechanical properties of chondrocytes isolated from neonatal (1-day), adult (5-year) and geriatric (12-year) bovine knees using atomic force microscopy (AFM). We also measured the contribution of the actin and intermediate filaments to the indentation-dependent mechanical properties of chondrocytes. By integrating AFM with confocal fluorescent microscopy, we monitored cytoskeletal and biomechanical deformation in transgenic cells (GFP-vimentin and mCherry-actin) under compression. We found that the elastic modulus of chondrocytes in all age groups decreased with increased indentation (15–2000 nm). The elastic modulus of adult chondrocytes was significantly greater than neonatal cells at indentations greater than 500 nm. Viscoelastic moduli (instantaneous and equilibrium) were comparable in all age groups examined; however, the intrinsic viscosity was lower in geriatric chondrocytes than neonatal. Disrupting the actin or the intermediate filament structures altered the mechanical properties of chondrocytes by decreasing the elastic modulus and viscoelastic properties, resulting in a dramatic loss of indentation-dependent response with treatment. Actin and vimentin cytoskeletal structures were monitored using confocal fluorescent microscopy in transgenic cells treated with disruptors, and both treatments had a profound disruptive effect on the actin filaments. Here we show that disrupting the structure of intermediate filaments indirectly altered the configuration of the actin cytoskeleton. These findings underscore the importance of the cytoskeletal elements in the overall mechanical response of chondrocytes, indicating that intermediate filament integrity is key to the non-linear elastic properties of chondrocytes. This study improves our understanding of the mechanical properties of articular cartilage at the single cell level.     

Coarse-Graining Provides Insights on the Essential Nature of Heterogeneity in Actin Filaments

Experiments have shown that actin is structurally polymorphic, but knowledge of the details of molecular level heterogeneity in both the dynamics of a single subunit and the interactions between subunits is still lacking. Here, using atomistic molecular dynamics simulations of the actin filament, we identify domains of atoms that move in a correlated fashion, quantify interactions between these domains using coarse-grained (CG) analysis methods, and perform CG simulations to explore the importance of filament heterogeneity. The persistence length and torsional stiffness calculated from molecular dynamics simulation data agree with experimental values. We additionally observe that distinct actin conformations coexist in actin filaments. The filaments also exhibit random twist angles that are broadly distributed. CG analysis reveals that interactions between equivalent CG pairs vary from one subunit to another. To explore the importance of heterogeneity on filament dynamics, we perform CG simulations using different methods of parameterization to show that only by including heterogeneous interactions can we reproduce the twist angles and related properties. Free energy calculations further suggest that in general the actin filament is best represented as a set of subunits with differing CG sites and interactions, and the incorporating heterogeneity into the CG interactions is more important than including that in the CG sites. Our work therefore presents a systematic method to explore molecular level detail in this large and complex biopolymer.