Filament Compliance Research Articles

Modeling spatial inhomogeneities in a crossbridge ensemble reveals where mean-field estimates of sarcomere stiffness break down.

How actomyosin crossbridges share and transmit loads between the thick and thin filaments in a sarcomere underlies the emergence of muscle's stimulus-dependent material properties. In particular, stiffness, the resistance to external length perturbations, is of interest because of its importance to muscle's in vivo function. Following A.F. Huxley's original work, many sarcomere models treat the thick and thin filaments as rigid and lump their compliance into a single series elastic element. Under this approximation, the crossbridges act as parallel elastic force generators. So their stiffnesses are thought to add linearly and their collective dynamics are captured by the ensemble mean. In this work, we investigate the accuracy of this approximation by exactly deriving the stiffness of a spring network that accounts for the spatially distributed filament and crossbridge compliances. We show that even the small degree of measured filament compliance in a sarcomere leads to a profound deviation of the mechanical behavior from the ensemble mean. Unlike the lumped compliance approximation, the exact accounting finds that the emergent stiffness depends on the spatial distribution of crossbridges; a property that cannot be captured by a mean model. Moreover, under physiologically relevant crossbridge numbers, the lumped compliance approximation underestimates the net stiffness of a pair of filaments by over two-fold. Further analyses show that crossbridge clusters may be thermodynamically favored because they lower the total system strain energy that arises from externally applied loads at the filament boundaries and the internal forces applied by the myosin powerstroke. We speculate that the dependence of stiffness and strain energy on the spatial inhomogeneity of crossbridges has mechanochemical consequences that affect the development and cycling of crossbridges in actomyosin networks.

The Compliance-induced Slowdown of Stress Relaxation in Active Sarcomeres

Muscle contracts when stimulated but also generates transient stress in response to externally imposed length changes. The stress-relaxation timescale of the perturbation-induced stress is vital for the everyday use of muscle. If stresses are long-lived, muscle is stiff like an elastic solid and useful for behaviors such as maintaining posture. But if stresses are rapidly dissipated, muscle yields like a liquid and enables rapid postural changes. Although common experience suggests that muscle routinely transitions between a solid-like and liquid-like response, current sarcomere models cannot account for large changes in the stress-relaxation time. We show by modeling muscles as half-sarcomeres with cycling crossbridges on a compliant filament backbone that filament compliance leads to a many-fold increase in the stress-relaxation time compared with a rigid backbone. The slowdown depends on a single dimensionless ratio l/p of the filament overlap l to an emergent length scale p that depends on how strain is shared between the filament backbone and crossbridges. This parameter depends on the mean number of attached crossbridges such that greater activation implies a greater value of l/p. We find that the stress-relaxation time is nearly constant for l/p ≪ 1, but increases as (l/p)2 when l/p ≫ 1. We estimate l/p > 5 for mammalian sarcomeres, which leads to a 10x slowdown of stress relaxation relative to having a rigid backbone. The physical basis is that in a compliant filament model, the attachment of one crossbridge distorts neighboring crossbridges and induces changes in its kinetics. Our predicted effect of filament compliance hypothesizes a new mechanism for muscle’s ability to maintain an elastic behavior on timescales much longer than crossbridge cycling. These effects may scale up to the whole fiber based on titin that mediates inter-sarcomeric interactions.

The force and stiffness of myosin motors in the isometric twitch of a cardiac trabecula and the effect of the extracellular calcium concentration.

Fast sarcomere-level mechanics in intact trabeculae, which allows the definition of the mechano-kinetic properties of cardiac myosin in situ, is a fundamental tool not only for understanding the molecular mechanisms of heart performance and regulation, but also for investigating the mechanisms of the cardiomyopathy-causing mutations in the myosin and testing small molecules for therapeutic interventions. The approach has been applied to measure the stiffness and force of the myosin motor and the fraction of motors attached during isometric twitches of electrically paced trabeculae under different extracellular Ca2+ concentrations. Although the average force of the cardiac myosin motor (∼6pN) is similar to that of the fast myosin isoform of skeletal muscle, the stiffness (1.07pNnm-1 ) is 2- to 3-fold smaller. The increase in the twitch force developed in the presence of larger extracellular Ca2+ concentrations is fully accounted for by a proportional increase in the number of attached motors. The mechano-kinetic properties of the cardiac myosin were studied in situ, in trabeculae dissected from the right ventricle of the rat heart, by measuring the stiffness of the half-sarcomere both at the twitch force peak (Tp ) of an electrically paced intact trabecula at different extracellular Ca2+ concentrations ([Ca2+ ]o ), and in the same trabecula after skinning and induction of rigor. Taking into account the contribution of filament compliance to half-sarcomere compliance and the lattice geometry, we found that the stiffness of the cardiac myosin motor is 1.07±0.09pNnm-1 , which is slightly larger than that of the slow myosin isoform of skeletal muscle (0.6-0.8pNnm-1 ) and 2- to 3-fold smaller than that of the fast skeletal muscle isoform. The increase in Tp from 61±4kPa to 93±9kPa, induced by raising [Ca2+ ]o from 1 to 2.5mm at sarcomere length ∼2.2μm, is accompanied by an increase of the half-sarcomere stiffness that is explained by an increase of the fraction of actin-attached motors from 0.08±0.01 to 0.12±0.02, proportional to Tp . Consequently, each myosin motor bears an average force of 6.14±0.52pN independently of Tp and [Ca2+ ]o . The application of fast sarcomere-level mechanics to intact trabeculae to define the mechano-kinetic properties of the cardiac myosin in situ represents a powerful tool for investigating cardiomyopathy-causing mutations in the myosin motor and testing specific therapeutic interventions.

An In-Situ Study of the Modulation of the Mechano-Kinetic Parameters of the Slow Isoform of Muscle Myosin II by the Heart Drug Omecamtiv Mecarbil

Omecamtiv Mecarbil (OM), a small molecule that binds to the catalytic domain of the myosin isoforms of both cardiac and slow muscles, increases actin affinity and promotes Pi release and, in myocells, increases Ca2+-sensitivity of force production (Malik et al. Science 331:1439, 2011; Nagy et al. Br J Pharmacol 172:4506, 2015). Despite the interest for OM as an activator of the myosin motor to understand motor-related myopathies and devise therapies (Spudich Biophys J 106:1236, 2014), the details of OM effects on force generation are unclear. We used fast sarcomere-level mechanics in demembranated rabbit soleus fibers to define the effect of OM (1 µM) on the force and stiffness of the half-sarcomere (hs) following Ca2+-activation. The hs-stiffness was analysed with a model that accounts for the contribution of the filament compliance and provides the estimate of the stiffness of the motors (e, which depends on the number of actin-attached motors). At saturating [Ca2+], OM depresses the isometric force by ∼50% by reducing the strain in the motors, without effects on e. Both the force-pCa and e-pCa relations are shifted to the left in OM with respect to the control (pCa50 is increased by 0.4 units) and their steepness is reduced by 50%. Thus the effect of OM on the force-pCa relation is fully accounted for by that on the e-pCa relation. We conclude that OM has a dual effect: it increases the Ca2+-sensitivity of the motor binding to actin, while it reduces the structural change associated to force generation. In the heart the internal [Ca2+] is below saturation and OM acts as a potentiator by increasing the number of motors. Supported by ECRF and Telethon.

Mechanical parameters of the molecular motor myosin II determined in permeabilised fibres from slow and fast skeletal muscles of the rabbit.

The different performance of slow and fast muscles is mainly attributed to diversity of the myosin heavy chain (MHC) isoform expressed within them. In this study fast sarcomere-level mechanics has been applied to Ca2+ -activated single permeabilised fibres isolated from soleus (containing the slow myosin isoform) and psoas (containing the fast myosin isoform) muscles of rabbit for a comparative definition of the mechano-kinetics of force generation by slow and fast myosin isoforms in situ. The stiffness and the force of the slow myosin isoform are three times smaller than those of the fast isoform, suggesting that the stiffness of the myosin motor is a determinant of the isoform-dependent functional diversity between skeletal muscles. These results open the question of the mechanism that can reconcile the reduced performance of the slow MHC with the higher efficiency of the slow muscle. The skeletal muscle exhibits large functional differences depending on the myosin heavy chain (MHC) isoform expressed in its molecular motor, myosin II. The differences in the mechanical features of force generation by myosin isoforms were investigated in situ by using fast sarcomere-level mechanical methods in permeabilised fibres (sarcomere length 2.4μm, temperature 12°C, 4% dextran T-500) from slow (soleus, containing the MHC-1 isoform) and fast (psoas, containing the MHC-2X isoform) skeletal muscle of the rabbit. The stiffness of the half-sarcomere was determined at the plateau of Ca2+ -activated isometric contractions and in rigor and analysed with a model that accounted for the filament compliance to estimate the stiffness of the myosin motor (ε). ε was 0.56±0.04 and 1.70±0.37pNnm-1 for the slow and fast isoform, respectively, while the average strain per attached motor (s0 ) was similar (∼3.3nm) in both isoforms. Consequently the force per motor (F0 =εs0 ) was three times smaller in the slow isoform than in the fast isoform (1.89±0.43 versus 5.35±1.51pN). The fraction of actin-attached motors responsible for maximum isometric force at saturating Ca2+ (T0,4.5 ) was 0.47±0.09 in soleus fibres, 70% larger than that in psoas fibres (0.29±0.08), so that F0 in slow fibres was decreased by only 53%. The lower stiffness and force of the slow myosin isoform open the question of the molecular basis of the higher efficiency of slow muscle with respect to fast muscle.

Filament turnover tunes both force generation and dissipation to control long-range flows in a model actomyosin cortex.

Actomyosin-based cortical flow is a fundamental engine for cellular morphogenesis. Cortical flows are generated by cross-linked networks of actin filaments and myosin motors, in which active stress produced by motor activity is opposed by passive resistance to network deformation. Continuous flow requires local remodeling through crosslink unbinding and and/or filament disassembly. But how local remodeling tunes stress production and dissipation, and how this in turn shapes long range flow, remains poorly understood. Here, we study a computational model for a cross-linked network with active motors based on minimal requirements for production and dissipation of contractile stress: Asymmetric filament compliance, spatial heterogeneity of motor activity, reversible cross-links and filament turnover. We characterize how the production and dissipation of network stress depend, individually, on cross-link dynamics and filament turnover, and how these dependencies combine to determine overall rates of cortical flow. Our analysis predicts that filament turnover is required to maintain active stress against external resistance and steady state flow in response to external stress. Steady state stress increases with filament lifetime up to a characteristic time τm, then decreases with lifetime above τm. Effective viscosity increases with filament lifetime up to a characteristic time τc, and then becomes independent of filament lifetime and sharply dependent on crosslink dynamics. These individual dependencies of active stress and effective viscosity define multiple regimes of steady state flow. In particular our model predicts that when filament lifetimes are shorter than both τc and τm, the dependencies of effective viscosity and steady state stress on filament turnover cancel one another, such that flow speed is insensitive to filament turnover, and shows a simple dependence on motor activity and crosslink dynamics. These results provide a framework for understanding how animal cells tune cortical flow through local control of network remodeling.

Actin Filament Strain Promotes Severing and Cofilin Dissociation

Computational and structural studies have been indispensable in investigating the molecular origins of actin filament mechanical properties and modulation by the regulatory severing protein cofilin. All-atom molecular dynamics simulations of cofilactin filament structures determined by electron cryomicroscopy reveal how cofilin enhances the bending and twisting compliance of actin filaments. Continuum mechanics models suggest that buckled cofilactin filaments localize elastic energy at boundaries between bare and cofilin-decorated segments because of their nonuniform elasticity, thereby accelerating filament severing. Here, we develop mesoscopic length-scale (cofil)actin filament models and evaluate the effects of compressive and twisting loads on strain energy distribution at specific interprotein interfaces. The models reliably capture the filament bending and torsional rigidities and intersubunit torsional flexibility measured experimentally with purified protein components. Buckling is predicted to enhance cofilactin filament severing with minimal effects on cofilin occupancy, whereas filament twisting enhances cofilin dissociation without compromising filament integrity. Preferential severing at actin-cofilactin boundaries of buckled filaments is more prominent than predicted by continuum models because of the enhanced spatial resolution. The models developed here will be valuable for evaluating the effects of filament shape deformations on filament stability and interactions with regulatory proteins, and analysis of single filament manipulation assays.

Thick Filament Compliance in Passively Stretched Skeletal Muscle

Titin is a giant sarcomeric protein (∼2.9MDa to 4.0MDa) that spans half of the sarcomere from the Z disc to the M band. Titin closely interacts with the thick filament inside the A band, and plays important roles in sarcomere development and force generation. In vertebrate muscle, multiple titin isoforms with different molecular weights exist resulting from alternative splicing of a single titin gene. Different sizes of titin lead to different overall stiffnesses of the muscle having multiple effects on muscle function. Titin with different sizes would expect to have different effects on myofilament properties. Here we used the Rbm20 mouse model to study how titins of different sizes, and hence, compliance can affect sarcomere structure with increasing sarcomere length in skeletal muscle using small angle X-ray diffraction. In this Rbm20 mouse model, homozygous mice (KO) expresses the largest titin, and heterozygous mice (HET) expresses an intermediate molecular weight titin compared to titin expressed in wild type mice. The results showed that titin-based passive tension strains thick filaments, and the titin isoform in Rbm20 KO muscle strains the thick filament the least. Our results also showed that the thick filament extensibility, and hence, compliance, in passively stretched muscle is non-linear. Meridional X-ray reflections attributed to myosin binding protein C (MyBP-C) decrease in intensity with increasing sarcomere length, consistent with the notion that MyBP-C interacts with actin and that this interaction is lost when thin filaments are pulled out of the C-zone. Our results also showed that KO muscle with most compliant titin isoform had the largest inter-filament spacing and lowest equatorial intensity ratio at slack length. Supported by R01AR060697 and P41GM103622 from the National Institutes of Health.

The contributions of filaments and cross‐bridges to sarcomere compliance in skeletal muscle

Force generation in the muscle sarcomere is driven by the head domain of the myosin molecule extending from the thick filament to form cross-bridges with the actin-containing thin filament. Following attachment, a structural working stroke in the head pulls the thin filament towards the centre of the sarcomere, producing, under unloaded conditions, a filament sliding of ∼ 11 nm. The mechanism of force generation by the myosin head depends on the relationship between cross-bridge force and movement, which is determined by compliances of the cross-bridge (C(cb)) and filaments. By measuring the force dependence of the spacing of the high-order myosin- and actin-based X-ray reflections from sartorius muscles of Rana esculenta we find a combined filament compliance (Cf) of 13.1 ± 1.2 nm MPa(-1), close to recent estimates from single fibre mechanics (12.8 ± 0.5 nm MPa(-1)). C(cb) calculated using these estimates is 0.37 ± 0.12 nm pN(-1), a value fully accounted for by the compliance of the myosin head domain, 0.38 ± 0.06 nm pN(-1), obtained from the intensity changes of the 14.5 nm myosin-based X-ray reflection in response to 3 kHz oscillations imposed on single muscle fibres in rigor. Thus, a significant contribution to C(cb) from the myosin tail that joins the head to the thick filament is excluded. The low C(cb) value indicates that the myosin head generates isometric force by a small sub-step of the 11 nm stroke that drives filament sliding at low load. The implications of these results for the mechanism of force generation by myosins have general relevance for cardiac and non-muscle myosins as well as for skeletal muscle.

The non‐linear elasticity of the muscle sarcomere and the compliance of myosin motors

Force in striated muscle is due to attachment of the heads of the myosin, the molecular motors extending from the myosin filament, to the actin filament in each half-sarcomere, the functional unit where myosin motors act in parallel. Mechanical and X-ray structural evidence indicates that at the plateau of isometric contraction (force T0), less than half of the elastic strain of the half-sarcomere is due to the strain in the array of myosin motors (s), with the remainder being accounted for by the compliance of filaments acting as linear elastic elements in series with the motor array. Early during the development of isometric force, however, the half-sarcomere compliance has been found to be less than that expected from the linear elastic model assumed above, and this non-linearity may affect the estimate of s. This question is investigated here by applying nanometre-microsecond-resolution mechanics to single intact fibres from frog skeletal muscle at 4 °C, to record the mechanical properties of the half-sarcomere throughout the development of force in isometric contraction. The results are interpreted with mechanical models to estimate the compliance of the myosin motors. Our conclusions are as follows: (i) early during the development of an isometric tetanus, an elastic element is present in parallel with the myosin motors, with a compliance of ∼200 nm MPa(-1) (∼20 times larger than the compliance of the motor array at T0); and (ii) during isometric contraction, s is 1.66 ± 0.05 nm, which is not significantly different from the value estimated with the linear elastic model.

Optical Trapping Shows a 3-Fold Increase in Myosin Head Stiffness by the FHC-Mutation R723G in the β-Cardiac Myosin Heavy Chain

Missense mutations in the β-cardiac myosin heavy chain (β-MyHC) are the most frequent cause of Familial Hypertrophic Cardiomyopathy (FHC). For these mutations mutant and wildtype β-MyHC are co-incorporated in the contractile apparatus, and direct functional effects of such mutations presumably trigger development of the FHC-phenotype. In M. soleus biopsies of affected patients we previously found increased isometric force generation for the converter mutation R723G, most likely due to increased stiffness of the myosin head domain. Quantification of the increase in head stiffness from fiber studies, however, was complicated by filament compliance, as well as non-equal and variable co-expression of mutant and wildtype protein in the tissue samples.In the present work we directly determined stiffness of individual myosin heads isolated from M. soleus tissue samples of affected patients using the three-bead optical trapping assay. Since each assay contained mutant and wildtype head domains, stiffness of individual heads with and without the R723G mutation could directly be compared. We determined head stiffness by imposing triangular stage displacements and recording bead displacements during binding events, taking into account compliance of the actin-bead link determined by the variance-Hidden-Markov method (Smith et al., BJ 2001). We found two populations of head domains, one with a head stiffness of 0.39 ± 0.24 pN/nm the other with an about 3-fold higher stiffness. The low value is close to our previous optical trapping with β-MyHC (0.38 ± 0.06 pN/nm; Brenner et al., JMRCM 2012), the about 3-fold increase in head stiffness agrees well with our previous estimate from rigor stiffness in fibers with the same mutation (Seebohm et al., BJ 2009) while the absolute value of head stiffness from fibers was about 25% lower than determined here.

The Elasticity of the Myosin Motor and Myofilaments in the Muscle Sarcomere

During muscle contraction, the myosin motors emerging from the myosin filament in each half-sarcomere form cross-bridges with the opposing actin filament, pulling it towards the center of the sarcomere through a structural working stroke. Motors are mechanically coupled via their filament attachments, and the co-operative action of this coupled system is the basic functional unit of muscle, so determining the elastic properties of the half-sarcomere components is crucial for understanding the mechanism of this collective motor. To that end we used mechanical and X-ray diffraction measurements on single fibers and whole muscles of the frog. 4kHz length oscillations were imposed on single fibers (4°C, 2.15µm sarcomere length) to determine how the half-sarcomere compliance (Chs) is modulated by force. The results indicate the presence of an elastic element in parallel with the array of cross-bridges with a compliance of 200 nm/MPa, ca20 times larger than that attributed to the cross-bridges. X-ray diffraction from whole frog muscles allows precise measurements of the spacing of the high-order myosin- and actin-based reflections, which report changes in the strain of the two filaments. We found that, at forces >0.4 the isometric tetanic force, the filament compliance is constant and contributes 13.1±1.1 nm/MPa to Chs, from which a cross-bridge compliance of 0.35±0.13 nm/pN is calculated. This value is not significantly different from that of the myosin head alone, 0.38±0.06 nm/pN, estimated from changes in the intensity of the 14.5-nm X-ray reflection from the axial repeat of myosin heads during rapid length oscillations in rigor fibers. We conclude that cross-bridge compliance is low and fully accounted for by the compliance of the myosin head, without a significant contribution from the rod connecting the head to the filament backbone. Supported by MIUR-PRIN and FIRB (ITALY).

The sedimentation of flexible filaments

AbstractThe dynamics of a flexible filament sedimenting in a viscous fluid are explored analytically and numerically. Compared with the well-studied case of sedimenting rigid rods, the introduction of filament compliance is shown to cause a significant alteration in the long-time sedimentation orientation and filament geometry. A model is developed by balancing viscous, elastic and gravitational forces in a slender-body theory for zero-Reynolds-number flows, and the filament dynamics are characterized by a dimensionless elasto-gravitation number. Filaments of both non-uniform and uniform cross-sectional thickness are considered. In the weakly flexible regime, a multiple-scale asymptotic expansion is used to obtain expressions for filament translations, rotations and shapes. These are shown to match excellently with full numerical simulations. Furthermore, we show that trajectories of sedimenting flexible filaments, unlike their rigid counterparts, are restricted to a cloud whose envelope is determined by the elasto-gravitation number. In the highly flexible regime we show that a filament sedimenting along its long axis is susceptible to a buckling instability. A linear stability analysis provides a dispersion relation, illustrating clearly the competing effects of the compressive stress and the restoring elastic force in the buckling process. The instability travels as a wave along the filament opposite the direction of gravity as it grows and the predicted growth rates are shown to compare favourably with numerical simulations. The linear eigenmodes of the governing equation are also studied, which agree well with the finite-amplitude buckled shapes arising in simulations.

Molecular Origins of Cofilin-Linked Changes in Actin Filament Mechanics

The actin regulatory protein cofilin plays a central role in actin assembly dynamics by severing filaments and increasing the concentration of ends from which subunits add and dissociate. Cofilin binding modifies the average structure and mechanical properties of actin filaments, thereby promoting fragmentation of partially decorated filaments at boundaries of bare and cofilin-decorated segments. Despite extensive evidence for cofilin-dependent changes in filament structure and mechanics, it is unclear how the two processes are linked at the molecular level. Here, we use molecular dynamics simulations and coarse-grained analyses to evaluate the molecular origins of the changes in filament compliance due to cofilin binding. Filament subunits with bound cofilin are less flat and maintain a significantly more open nucleotide cleft than bare filament subunits. Decorated filament segments are less twisted, thinner (considering only actin), and less connected than their bare counterparts, which lowers the filament bending persistence length and torsional stiffness. Using coarse-graining as an analysis method reveals that cofilin binding increases the average distance between the adjacent long-axis filament subunit, thereby weakening their interaction. In contrast, a fraction of lateral filament subunit contacts are closer and presumably stronger with cofilin binding. A cofilactin interface contact identified by cryo-electron microscopy is unstable during simulations carried out at 310K, suggesting that this particular interaction may be short lived at ambient temperatures. These results reveal the molecular origins of cofilin-dependent changes in actin filament mechanics that may promote filament severing.

Mechanics of intermediate filament networks assembled from keratins K8 and K18

We have investigated intermediate filament networks assembled from the recombinant keratins K8 and K18 in vitro at various protein and MgCl2 concentrations using mechanical rheometry. Experimental parameters were chosen such that artifacts from sample surface elasticity or wall slip were avoided, and the gap width did not affect network formation. The modulus G0 depends weakly on the protein concentration (G0 ∼ c0.5) and the critical deformation γcrit at which non-linear response sets in is concentration independent. These findings can be rationalized assuming that the cross-link density decreases with decreasing protein concentration, while the filament contour length between cross-links remains unchanged. Thus, filaments are more stretched at lower protein concentrations and this increase in conformational energy partly compensates the free energy decrease related to the change in cross-link density. G0 is independent of the MgCl2 concentration indicating that the contribution of stretched filaments decreases when the cross-link density increases. Networks rupture when a critical strain is exceeded, but fully recover within 30 minutes. The non-linear network response is characterized by pronounced strain stiffening with increasing shear stress σ. Reduced differential modulus K′ data obtained at different protein or MgCl2 concentrations collapse onto a master curve. Two scaling regimes K′ ∼ σα are observed with α = 1 at intermediate and α = 0.6 at high stresses. These exponents may be rationalized in terms of the glassy wormlike chain model assuming sticky contacts with finite, constant bond strength. Two distinct scaling regimes could also result from the existence of two types of filament contacts with different bond energies or by the compliance of individual filaments.

Molecular Origins of Cofilin-Linked Changes in Actin Filament Mechanics

The actin regulatory protein, cofilin, plays a central role in actin assembly dynamics by severing filaments and increasing the concentration of ends from which subunits add and dissociate. Cofilin binding modifies the average structure and mechanical properties of actin filaments, thereby promoting fragmentation of partially decorated filaments at boundaries of bare and cofilin-decorated segments. Despite extensive evidence for cofilin-dependent changes in filament structure and mechanics, it is unclear how the two processes are linked at the molecular level. Here, we use molecular dynamics (MD) simulations and coarse-grained (CG) analyses to evaluate the molecular origins of the changes in filament compliance due to cofilin binding. Filament subunits with bound cofilin are less “flat” and maintain a significantly more open nucleotide cleft than bare filament subunits. Decorated filament segments are less twisted, thinner (considering only actin), and less connected than their bare counterparts, which lowers the filament bending persistence length and torsional stiffness. using coarse-graining as an analytical method reveals that cofilin binding increases the average distance between the adjacent long-axis filament subunit, thereby weakening their interaction. In contrast, a fraction of lateral filament subunit contacts are closer and presumably stronger with cofilin binding. These results reveal the molecular origins of cofilin-dependent changes in actin filament mechanics that promote filament severing.

Filament Compliance Influences Cooperative Activation of Thin Filaments and the Dynamics of Force Production in Skeletal Muscle

Striated muscle contraction is a highly cooperative process initiated by Ca2+ binding to the troponin complex, which leads to tropomyosin movement and myosin cross-bridge (XB) formation along thin filaments. Experimental and computational studies suggest skeletal muscle fiber activation is greatly augmented by cooperative interactions between neighboring thin filament regulatory units (RU-RU cooperativity; 1 RU = 7 actin monomers+1 troponin complex+1 tropomyosin molecule). XB binding can also amplify thin filament activation through interactions with RUs (XB-RU cooperativity). Because these interactions occur with a temporal order, they can be considered kinetic forms of cooperativity. Our previous spatially-explicit models illustrated that mechanical forms of cooperativity also exist, arising from XB-induced XB binding (XB-XB cooperativity). These mechanical and kinetic forms of cooperativity are likely coordinated during muscle contraction, but the relative contribution from each of these mechanisms is difficult to separate experimentally. To investigate these contributions we built a multi-filament model of the half sarcomere, allowing RU activation kinetics to vary with the state of neighboring RUs or XBs. Simulations suggest Ca2+ binding to troponin activates a thin filament distance spanning 9 to 11 actins and coupled RU-RU interactions dominate the cooperative force response in skeletal muscle, consistent with measurements from rabbit psoas fibers. XB binding was critical for stabilizing thin filament activation, particularly at submaximal Ca2+ levels, even though XB-RU cooperativity amplified force less than RU-RU cooperativity. Similar to previous studies, XB-XB cooperativity scaled inversely with lattice stiffness, leading to slower rates of force development as stiffness decreased. Including RU-RU and XB-RU cooperativity in this model resulted in the novel prediction that the force-[Ca2+] relationship can vary due to filament and XB compliance. Simulations also suggest kinetic forms of cooperativity occur rapidly and dominate early to get activation, while mechanical forms of cooperativity act more slowly, augmenting XB binding as force continues to develop.

Mechanics of myosin function in white muscle fibres of the dogfish, Scyliorhinus canicula

The contractile properties of muscle fibres have been extensively investigated by fast perturbation in sarcomere length to define the mechanical characteristics of myofilaments and myosin heads that underpin refined models of the acto-myosin cycle. Comparison of published data from intact fast-twitch fibres of frog muscle and demembranated fibres from fast muscle of rabbit shows that stiffness of the rabbit myosin head is only ∼62% of that in frog. To clarify if and how much the mechanical characteristics of the filaments and myosin heads vary in muscles of different animals we apply the same high resolution mechanical methods, in combination with X-ray diffraction, to fast-twitch fibres from the dogfish (Scyliorhinus canicula). The values of equivalent filament compliance (Cf) measured by X-ray diffraction and in mechanical experiments are not significantly different; the best estimate from combining these values is 17.1 ± 1.0 nm MPa−1. This value is larger than Cf in frog, 13.0 ± 0.4 nm MPa−1. The longer thin filaments in dogfish account for only part of this difference. The average isometric force exerted by each attached myosin head at 5°C, 4.5 pN, and the maximum sliding distance accounted for by the myosin working stroke, 11 nm, are similar to those in frog, while the average myosin head stiffness of dogfish (1.98 ± 0.31 pN nm−1) is smaller than that of frog (2.78 ± 0.30 pN nm−1). Taken together these results indicate that the working stroke responsible for the generation of isometric force is a larger fraction of the total myosin head working stroke in the dogfish than in the frog.

Cofilin-Linked Changes in Actin Filament Flexibility Promote Severing

The actin regulatory protein, cofilin, increases the bending and twisting elasticity of actin filaments and severs them. It has been proposed that filaments partially decorated with cofilin accumulate stress from thermally driven shape fluctuations at bare (stiff) and decorated (compliant) boundaries, thereby promoting severing. This mechanics-based severing model predicts that changes in actin filament compliance due to cofilin binding affect severing activity. Here, we test this prediction by evaluating how the severing activities of vertebrate and yeast cofilactin scale with the flexural rigidities determined from analysis of shape fluctuations. Yeast actin filaments are more compliant in bending than vertebrate actin filaments. Severing activities of cofilactin isoforms correlate with changes in filament flexibility. Vertebrate cofilin binds but does not increase the yeast actin filament flexibility, and does not sever them. Imaging of filament thermal fluctuations reveals that severing events are associated with local bending and fragmentation when deformations attain a critical angle. The critical severing angle at boundaries between bare and cofilin-decorated segments is smaller than in bare or fully decorated filaments. These measurements support a cofilin-severing mechanism in which mechanical asymmetry promotes local stress accumulation and fragmentation at boundaries of bare and cofilin-decorated segments, analogous to failure of some nonprotein materials.

Cytoskeleton fluidization versus resolidification: Prestress effect

The differential elastic modulus of an active actomyosin network is computed as a function of applied stress, taking into account both thermal and motor contributions to filament compliance in the low-frequency domain. It is shown that, due to a dual nature of motor activity, increasing motor concentration may either stiffen the network due to stronger prestress or soften it due to motor agitation, in accordance with experimental data. Prestress anisotropy, which may be induced by redistribution of motors triggered by external force, causes anisotropy of the elastic moduli. This helps to explain the contradictory phenomena of cell fluidization and resolidification in response to transient stretch observed in recent experiments.