The stiffness of rabbit skeletal actomyosin cross-bridges determined with an optical tweezers transducer

Modeling thick filament activation suggests a molecular basis for force depression

Multiscale models aiming to connect muscle's molecular and cellular function have been difficult to develop, in part due to a lack of self-consistent multiscale data. To address this gap, we measured the force response from single, skinned rabbit psoas muscle fibers to ramp shortenings and step stretches performed on the plateau region of the force-length relationship. We isolated myosin from the same muscles and, under similar conditions, performed single-molecule and ensemble measurements of myosin's ATP-dependent interaction with actin using laser trapping and in vitro motility assays. We fit the fiber data by developing a partial differential equation model that includes thick filament activation, whereby an increase in force on the thick filament pulls myosin out of an inhibited state. The model also includes a series elastic element and a parallel elastic element. This parallel elastic element models a titin-actin interaction proposed to account for the increase in isometric force after stretch (residual force enhancement). By optimizing the model fit to a subset of our fiber measurements, we specified seven unknown parameters. The model then successfully predicted the remainder of our fiber measurements and also our molecular measurements from the laser trap and in vitro motility. The success of the model suggests that our multiscale data are self-consistent and can serve as a testbed for other multiscale models. Moreover, the model captures the decrease in isometric force observed in our muscle fibers after active shortening (force depression), suggesting a molecular mechanism for force depression, whereby a parallel elastic element combines with thick filament activation to decrease the number of cycling cross-bridges.

Modeling Thick Filament Activation Suggests a Molecular Basis for Force Depression

Multiscale models aiming to connect muscle's molecular and cellular function have been difficult to develop, in part, due to a lack of self-consistent multiscale data. To address this gap, we measured the force response from single skinned rabbit psoas muscle fibers to ramp shortenings and step stretches performed on the plateau region of the force-length relationship. We isolated myosin from the same muscles and, under similar conditions, performed single molecule and ensemble measurements of myosin's ATP-dependent interaction with actin using laser trapping and in vitro motility assays. We fit the fiber data by developing a partial differential equation model that includes thick filament activation, whereby an increase in force on the thick filament pulls myosin out of an inhibited state. The model also includes a series elastic element and a parallel elastic element. This parallel elastic element models a titin-actin interaction proposed to account for the increase in isometric force following stretch (residual force enhancement). By optimizing the model fit to a subset of our fiber measurements, we specified seven unknown parameters. The model then successfully predicted the remainder of our fiber measurements and also our molecular measurements from the laser trap and in vitro motility. The success of the model suggests that our multiscale data are self-consistent and can serve as a testbed for other multiscale models. Moreover, the model captures the decrease in isometric force observed in our muscle fibers after active shortening (force depression), suggesting a molecular mechanism for force depression, whereby a parallel elastic element combines with thick filament activation to decrease the number of cycling cross-bridges.

A mutation in switch I alters the load-dependent kinetics of myosin Va

Myosin Va is the molecular motor that drives intracellular vesicular transport, powered by the transduction of chemical energy from ATP into mechanical work. The coupling of the powerstroke and phosphate (P_i) release is key to understanding the transduction process, and crucial details of this process remain unclear. Therefore, we determined the effect of elevated P_i on the force-generating capacity of a mini-ensemble of myosin Va S1 (WT) in a laser trap assay. By increasing the stiffness of the laser trap we determined the effect of increasing resistive loads on the rate of P_i-induced detachment from actin, and quantified this effect using the Bell approximation. We observed that WT myosin generated higher forces and larger displacements at the higher laser trap stiffnesses in the presence of 30 mM P_i, but binding event lifetimes decreased dramatically, which is most consistent with the powerstroke preceding the release of P_i from the active site. Repeating these experiments using a construct with a mutation in switch I of the active site (S217A) caused a seven-fold increase in the load-dependence of the P_i-induced detachment rate, suggesting that the S217A region of switch I may help mediate the load-dependence of P_i-rebinding.

Particle-Based Microrheology As a Tool for Characterizing Protein-Based Materials

Microrheology based on video microscopy of embedded tracer particles has the potential to be used for high-throughput protein-based materials characterization. This potential is due to a number of characteristics of the techniques, including the suitability for measurement of low sample volumes, noninvasive and noncontact measurements, and the ability to set up a large number of samples for facile, sequential measurement. In addition to characterization of the bulk rheological properties of proteins in solution, for example, viscosity, microrheology can provide insight into the dynamics and self-assembly of protein-based materials as well as heterogeneities in the microenvironment being probed. Specifically, passive microrheology in the form of multiple particle tracking and differential dynamic microscopy holds promise for applications in high-throughput characterization because of the lack of user interaction required while making measurements. Herein, recent developments in the use of multiple particle tracking and differential dynamic microscopy are reviewed for protein characterization and their potential to be applied in a high-throughput, automatable setting.

Cardiac ventricular myosin and slow skeletal myosin exhibit dissimilar chemomechanical properties despite bearing the same myosin heavy chain isoform

The myosin II motors are ATP-powered force-generating machines driving cardiac and muscle contraction. Myosin II heavy chain isoform-beta (β-MyHC) is primarily expressed in the ventricular myocardium and in slow-twitch muscle fibers, such as M. soleus. M. soleus–derived myosin II (SolM-II) is often used as an alternative to the ventricular β-cardiac myosin (βM-II); however, the direct assessment of biochemical and mechanical features of the native myosins is limited. By employing optical trapping, we examined the mechanochemical properties of native myosins isolated from the rabbit heart ventricle and soleus muscles at the single-molecule level. We found purified motors from the two tissue sources, despite expressing the same MyHC isoform, displayed distinct motile and ATPase kinetic properties. We demonstrate βM-II was approximately threefold faster in the actin filament–gliding assay than SolM-II. The maximum actomyosin (AM) detachment rate derived in single-molecule assays was also approximately threefold higher in βM-II, while the power stroke size and stiffness of the “AM rigor” crossbridge for both myosins were comparable. Our analysis revealed a higher AM detachment rate for βM-II, corresponding to the enhanced ADP release rates from the crossbridge, likely responsible for the observed differences in the motility driven by these myosins. Finally, we observed a distinct myosin light chain 1 isoform (MLC1sa) that associates with SolM-II, which might contribute to the observed kinetics differences between βM-II and SolM-II. These results have important implications for the choice of tissue sources and justify prerequisites for the correct myosin heavy and light chains to study cardiomyopathies.

Force Measurements From Myofibril to Filament

Contractility, the generation of force and movement by molecular motors, is the hallmark of all muscles, including striated muscle. Contractility can be studied at every level of organization from a whole animal to single molecules. Measurements at sub-cellular level are particularly useful since, in the absence of the excitation-contraction coupling system, the properties of the contractile proteins can be directly investigated; revealing mechanistic details not accessible in intact muscle. Moreover, the conditions can be manipulated with ease, for instance changes in activator Ca²⁺, small molecule effector concentration or phosphorylation levels and introducing mutations. Subcellular methods can be successfully applied to frozen materials and generally require the smallest amount of tissue, thus greatly increasing the range of possible experiments compared with the study of intact muscle and cells. Whilst measurement of movement at the subcellular level is relatively simple, measurement of force is more challenging. This mini review will describe current methods for measuring force production at the subcellular level including single myofibril and single myofilament techniques.

FRET and optical trapping reveal mechanisms of actin activation of the power stroke and phosphate release in myosin V

Myosins generate force and motion by precisely coordinating their mechanical and chemical cycles, but the nature and timing of this coordination remains controversial. We utilized a FRET approach to examine the kinetics of structural changes in the force-generating lever arm in myosin V. We directly compared the FRET results with single-molecule mechanical events examined by optical trapping. We introduced a mutation (S217A) in the conserved switch I region of the active site to examine how myosin couples structural changes in the actin- and nucleotide-binding regions with force generation. Specifically, S217A enhanced the maximum rate of lever arm priming (recovery stroke) while slowing ATP hydrolysis, demonstrating that it uncouples these two steps. We determined that the mutation dramatically slows both actin-induced rotation of the lever arm (power stroke) and phosphate release (≥10-fold), whereas our simulations suggest that the maximum rate of both steps is unchanged by the mutation. Time-resolved FRET revealed that the structure of the pre- and post-power stroke conformations and mole fractions of these conformations were not altered by the mutation. Optical trapping results demonstrated that S217A does not dramatically alter unitary displacements or slow the working stroke rate constant, consistent with the mutation disrupting an actin-induced conformational change prior to the power stroke. We propose that communication between the actin- and nucleotide-binding regions of myosin assures a proper actin-binding interface and active site have formed before producing a power stroke. Variability in this coupling is likely crucial for mediating motor-based functions such as muscle contraction and intracellular transport.

Computational Tool for Ensemble Averaging of Single-Molecule Data

Molecular motors couple chemical transitions to conformational changes that perform mechanical work in a wide variety of biological processes. Disruption of this coupling can lead to diseases, and therefore there is a need to accurately measure mechanochemical coupling in motors in both health and disease. Optical tweezers with nanometer spatial and millisecond temporal resolution have provided valuable insights into these processes. However, fluctuations due to Brownian motion can make it difficult to precisely resolve these conformational changes. One powerful analysis technique that has improved our ability to accurately measure mechanochemical coupling in motor proteins is ensemble averaging of individual trajectories. Here, we present a user-friendly computational tool, Software for Precise Analysis of Single Molecules (SPASM), for generating ensemble averages of single-molecule data. This tool utilizes several conceptual advances, including optimized procedures for identifying single-molecule interactions and the implementation of a change-point algorithm, to more precisely resolve molecular transitions. Using both simulated and experimental data, we demonstrate that these advances allow for accurate determination of the mechanics and kinetics of the myosin working stroke with a smaller set of data. Importantly, we provide our open-source MATLAB-based program with a graphical user interface that enables others to readily apply these advances to the analysis of their own data.

Single-Molecule Biophysical Techniques to Study Actomyosin Force Transduction

Inside the cellular environment, molecular motors can work in concert to conduct a variety of important physiological functions and processes that are vital for the survival of a cell. However, in order to decipher the mechanism of how these molecular motors work, single-molecule microscopy techniques have been popular methods to understand the molecular basis of the emerging ensemble behavior of these motor proteins.In this chapter, we discuss various single-molecule biophysical imaging techniques that have been used to expose the mechanics and kinetics of myosins. The chapter should be taken as a general overview and introductory guide to the many existing techniques; however, since other chapters will discuss some of these techniques more thoroughly, the readership should refer to those chapters for further details and discussions. In particular, we will focus on scattering-based single-molecule microscopy methods, some of which have become more popular in the recent years and around which the work in our laboratories has been centered.

An ensemble of flexible conformations underlies mechanotransduction by the cadherin-catenin adhesion complex

Adherens junctions are specialized cell–cell adhesion complexes found in epithelial, endothelial, and neuronal tissues of multicellular organism. The cadherin–catenin complex is the core component of the adherens junction and transmits mechanical stress from cell to cell. This study reveals that the cadherin–catenin complex displays a wide spectrum of flexible structures, which suggests a dynamic mechanism for this complex in mechanotransduction for cell–cell adhesion.

The cadherin–catenin adhesion complex is the central component of the cell–cell adhesion adherens junctions that transmit mechanical stress from cell to cell. We have determined the nanoscale structure of the adherens junction complex formed by the α-catenin•β-catenin•epithelial cadherin cytoplasmic domain (ABE) using negative stain electron microscopy, small-angle X-ray scattering, and selective deuteration/small-angle neutron scattering. The ABE complex is highly pliable and displays a wide spectrum of flexible structures that are facilitated by protein-domain motions in α- and β-catenin. Moreover, the 107-residue intrinsically disordered N-terminal segment of β-catenin forms a flexible “tongue” that is inserted into α-catenin and participates in the assembly of the ABE complex. The unanticipated ensemble of flexible conformations of the ABE complex suggests a dynamic mechanism for sensitivity and reversibility when transducing mechanical signals, in addition to the catch/slip bond behavior displayed by the ABE complex under mechanical tension. Our results provide mechanistic insight into the structural dynamics for the cadherin–catenin adhesion complex in mechanotransduction.

Anisotropic mechanics and dynamics of a living mammalian cytoplasm

During physiological processes, cells can undergo morphological changes that can result in a significant redistribution of the cytoskeleton causing anisotropic behavior. Evidence of anisotropy in cells under mechanical stimuli exists; however, the role of cytoskeletal restructuring resulting from changes in cell shape in mechanical anisotropy and its effects remain unclear. In the present study, we examine the role of cell morphology in inducing anisotropy in both intracellular mechanics and dynamics. We change the aspect ratio of cells by confining the cell width and measuring the mechanical properties of the cytoplasm using optical tweezers in both the longitudinal and transverse directions to quantify the degree of mechanical anisotropy. These active microrheology measurements are then combined with intracellular movement to calculate the intracellular force spectrum using force spectrum microscopy (FSM), from which the degree of anisotropy in dynamics and force can be quantified. We find that unrestricted cells with aspect ratio (AR) ∼1 are isotropic; however, when cells break symmetry, they exhibit significant anisotropy in cytoplasmic mechanics and dynamics.

Nonlinear Actomyosin Elasticity in Muscle?

Cyclic interactions between myosin II motor domains and actin filaments that are powered by turnover of ATP underlie muscle contraction and have key roles in motility of nonmuscle cells. The elastic characteristics of actin-myosin cross-bridges are central in the force-generating process, and disturbances in these properties may lead to disease. Although the prevailing paradigm is that the cross-bridge elasticity is linear (Hookean), recent single-molecule studies suggest otherwise. Despite convincing evidence for substantial nonlinearity of the cross-bridge elasticity in the single-molecule work, this finding has had limited influence on muscle physiology and physiology of other ordered cellular actin-myosin ensembles. Here, we use a biophysical modeling approach to close the gap between single molecules and physiology. The model is used for analysis of available experimental results in the light of possible nonlinearity of the cross-bridge elasticity. We consider results obtained both under rigor conditions (in the absence of ATP) and during active muscle contraction. Our results suggest that a wide range of experimental findings from mechanical experiments on muscle cells are consistent with nonlinear actin-myosin elasticity similar to that previously found in single molecules. Indeed, the introduction of nonlinear cross-bridge elasticity into the model improves the reproduction of key experimental results and eliminates the need for force dependence of the ATP-induced detachment rate, consistent with observations in other single-molecule studies. The findings have significant implications for the understanding of key features of actin-myosin-based production of force and motion in living cells, particularly in muscle, and for the interpretation of experimental results that rely on stiffness measurements on cells or myofibrils.

Step Sizes and Rate Constants of Single-headed Cytoplasmic Dynein Measured with Optical Tweezers

A power stroke of dynein is thought to be responsible for the stepping of dimeric dynein. However, the actual size of the displacement driven by a power stroke has not been directly measured. Here, the displacements of single-headed cytoplasmic dynein were measured by optical tweezers. The mean displacement of dynein interacting with microtubule was ~8 nm at 100 µM ATP, and decreased sigmoidally with a decrease in the ATP concentration. The ATP dependence of the mean displacement was explained by a model that some dynein molecules bind to microtubule in pre-stroke conformation and generate 8-nm displacement, while others bind in the post-stroke one and detach without producing a power stroke. Biochemical assays showed that the binding affinity of the post-stroke dynein to a microtubule was ~5 times higher than that of pre-stroke dynein, and the dissociation rate was ~4 times lower. Taking account of these rates, we conclude that the displacement driven by a power stroke is 8.3 nm. A working model of dimeric dynein driven by the 8-nm power stroke was proposed.

Dissecting myosin-5B mechanosensitivity and calcium regulation at the single molecule level

Myosin-5B is one of three members of the myosin-5 family of actin-based molecular motors. Despite its fundamental role in recycling endosome trafficking and in collective actin network dynamics, the molecular mechanisms underlying its motility are inherently unknown. Here we combine single-molecule imaging and high-speed laser tweezers to dissect the mechanoenzymatic properties of myosin-5B. We show that a single myosin-5B moves processively in 36-nm steps, stalls at ~2 pN resistive forces, and reverses its directionality at forces >2 pN. Interestingly, myosin-5B mechanosensitivity differs from that of myosin-5A, while it is strikingly similar to kinesin-1. In particular, myosin-5B run length is markedly and asymmetrically sensitive to force, a property that might be central to motor ensemble coordination. Furthermore, we show that Ca2+ does not affect the enzymatic activity of the motor unit, but abolishes myosin-5B processivity through calmodulin dissociation, providing important insights into the regulation of postsynaptic cargoes trafficking in neuronal cells.

Effects of cross-bridge compliance on the force-velocity relationship and muscle power output

Muscles produce force and power by utilizing chemical energy through ATP hydrolysis. During concentric contractions (shortening), muscles generate less force compared to isometric contractions, but consume greater amounts of energy as shortening velocity increases. Conversely, more force is generated and less energy is consumed during eccentric muscle contractions (lengthening). This relationship between force, energy use, and the velocity of contraction has important implications for understanding muscle efficiency, but the molecular mechanisms underlying this behavior remain poorly understood. Here we used spatially-explicit, multi-filament models of Ca2+-regulated force production within a half-sarcomere to simulate how force production, energy utilization, and the number of bound cross-bridges are affected by dynamic changes in sarcomere length. These computational simulations show that cross-bridge binding increased during slow-velocity concentric and eccentric contractions, compared to isometric contractions. Over the full ranges of velocities that we simulated, cross-bridge cycling and energy utilization (i.e. ATPase rates) increased during shortening, and decreased during lengthening. These findings are consistent with the Fenn effect, but arise from a complicated relationship between velocity-dependent cross-bridge recruitment and cross-bridge cycling kinetics. We also investigated how force production, power output, and energy utilization varied with cross-bridge and myofilament compliance, which is impossible to address under typical experimental conditions. These important simulations show that increasing cross-bridge compliance resulted in greater cross-bridge binding and ATPase activity, but less force was generated per cross-bridge and throughout the sarcomere. These data indicate that the efficiency of force production decreases in a velocity-dependent manner, and that this behavior is sensitive to cross-bridge compliance. In contrast, significant effects of myofilament compliance on force production were only observed during isometric contractions, suggesting that changes in myofilament compliance may not influence power output during non-isometric contractions as greatly as changes in cross-bridge compliance. These findings advance our understanding of how cross-bridge and myofilament properties underlie velocity-dependent changes in contractile efficiency during muscle movement.

Cell volume change through water efflux impacts cell stiffness and stem cell fate

Cells alter their mechanical properties in response to their local microenvironment; this plays a role in determining cell function and can even influence stem cell fate. Here, we identify a robust and unified relationship between cell stiffness and cell volume. As a cell spreads on a substrate, its volume decreases, while its stiffness concomitantly increases. We find that both cortical and cytoplasmic cell stiffness scale with volume for numerous perturbations, including varying substrate stiffness, cell spread area, and external osmotic pressure. The reduction of cell volume is a result of water efflux, which leads to a corresponding increase in intracellular molecular crowding. Furthermore, we find that changes in cell volume, and hence stiffness, alter stem-cell differentiation, regardless of the method by which these are induced. These observations reveal a surprising, previously unidentified relationship between cell stiffness and cell volume that strongly influences cell biology.

Kinetic coupling of phosphate release, force generation and rate-limiting steps in the cross-bridge cycle

A basic goal in muscle research is to understand how the cyclic ATPase activity of cross-bridges is converted into mechanical force. A direct approach to study the chemo-mechanical coupling between P_i release and the force-generating step is provided by the kinetics of force response induced by a rapid change in [P_i]. Classical studies on fibres using caged-P_i discovered that rapid increases in [P_i] induce fast force decays dependent on final [P_i] whose kinetics were interpreted to probe a fast force-generating step prior to P_i release. However, this hypothesis was called into question by studies on skeletal and cardiac myofibrils subjected to P_i jumps in both directions (increases and decreases in [P_i]) which revealed that rapid decreases in [P_i] trigger force rises with slow kinetics, similar to those of calcium-induced force development and mechanically-induced force redevelopment at the same [P_i]. A possible explanation for this discrepancy came from imaging of individual sarcomeres in cardiac myofibrils, showing that the fast force decay upon increase in [P_i] results from so-called sarcomere 'give'. The slow force rise upon decrease in [P_i] was found to better reflect overall sarcomeres cross-bridge kinetics and its [P_i] dependence, suggesting that the force generation coupled to P_i release cannot be separated from the rate-limiting transition. The reasons for the different conclusions achieved in fibre and myofibril studies are re-examined as the recent findings on cardiac myofibrils have fundamental consequences for the coupling between P_i release, rate-limiting steps and force generation. The implications from P_i-induced force kinetics of myofibrils are discussed in combination with historical and recent models of the cross-bridge cycle.

Size- and speed-dependent mechanical behavior in living mammalian cytoplasm

Active transport in the cytoplasm plays critical roles in living cell physiology. However, the mechanical resistance that intracellular compartments experience, which is governed by the cytoplasmic material property, remains elusive, especially its dependence on size and speed. Here we use optical tweezers to drag a bead in the cytoplasm and directly probe the mechanical resistance with varying size a and speed V We introduce a method, combining the direct measurement and a simple scaling analysis, to reveal different origins of the size- and speed-dependent resistance in living mammalian cytoplasm. We show that the cytoplasm exhibits size-independent viscoelasticity as long as the effective strain rate V/a is maintained in a relatively low range (0.1 s^-1 < V/a < 2 s^-1) and exhibits size-dependent poroelasticity at a high effective strain rate regime (5 s^-1 < V/a < 80 s^-1). Moreover, the cytoplasmic modulus is found to be positively correlated with only V/a in the viscoelastic regime but also increases with the bead size at a constant V/a in the poroelastic regime. Based on our measurements, we obtain a full-scale state diagram of the living mammalian cytoplasm, which shows that the cytoplasm changes from a viscous fluid to an elastic solid, as well as from compressible material to incompressible material, with increases in the values of two dimensionless parameters, respectively. This state diagram is useful to understand the underlying mechanical nature of the cytoplasm in a variety of cellular processes over a broad range of speed and size scales.

Vinculin forms a directionally asymmetric catch bond with F-actin

Vinculin is an actin-binding protein thought to reinforce cell-cell and cell-matrix adhesions. However, how mechanical load affects the vinculin-F-actin bond is unclear. Using a single-molecule optical trap assay, we found that vinculin forms a force-dependent catch bond with F-actin through its tail domain, but with lifetimes that depend strongly on the direction of the applied force. Force toward the pointed (-) end of the actin filament resulted in a bond that was maximally stable at 8 piconewtons, with a mean lifetime (12 seconds) 10 times as long as the mean lifetime when force was applied toward the barbed (+) end. A computational model of lamellipodial actin dynamics suggests that the directionality of the vinculin-F-actin bond could establish long-range order in the actin cytoskeleton. The directional and force-stabilized binding of vinculin to F-actin may be a mechanism by which adhesion complexes maintain front-rear asymmetry in migrating cells.

Rolling Adhesion of Schizont Stage Malaria-Infected Red Blood Cells in Shear Flow

To avoid clearance by the spleen, red blood cells infected with the human malaria parasite Plasmodium falciparum (iRBCs) adhere to the vascular endothelium through adhesive protrusions called "knobs" that the parasite induces on the surface of the host cell. However, the detailed relation between the developing knob structure and the resulting movement in shear flow is not known. Using flow chamber experiments on endothelial monolayers and tracking of the parasite inside the infected host cell, we find that trophozoites (intermediate-stage iRBCs) tend to flip due to their biconcave shape, whereas schizonts (late-stage iRBCs) tend to roll due to their almost spherical shape. We then use adhesive dynamics simulations for spherical cells to predict the effects of knob density and receptor multiplicity per knob on rolling adhesion of schizonts. We find that rolling adhesion requires a homogeneous coverage of the cell surface by knobs and that rolling adhesion becomes more stable and slower for higher knob density. Our experimental data suggest that schizonts are at the border between transient and stable rolling adhesion. They also allow us to establish an estimate for the molecular parameters for schizont adhesion to the vascular endothelium and to predict bond dynamics in the contact region.

Cooperativity of myosin interaction with thin filaments is enhanced by stabilizing substitutions in tropomyosin

Muscle contraction is powered by myosin interaction with actin-based thin filaments containing Ca²⁺-regulatory proteins, tropomyosin and troponin. Coiled-coil tropomyosin molecules form a long helical strand that winds around actin filament and either shields actin from myosin binding or opens it. Non-canonical residues G126 and D137 in the central part of tropomyosin destabilize its coiled-coil structure. Their substitutions for canonical ones, G126R and D137L, increase structural stability and the velocity of sliding of reconstructed thin filaments along myosin coated surface. The effect of these stabilizing mutations on force of the actin-myosin interaction is unknown. It also remains unclear whether the stabilization affects single actin-myosin interactions or it modifies the cooperativity of the binding of myosin molecules to actin. We used an optical trap to measure the effects of the stabilization on step size, unitary force and duration of the interactions at low and high load and compared the results with those obtained in an in vitro motility assay. We found that significant prolongation of lifetime of the actin-myosin complex under high load observed at high extent of tropomyosin stabilization, i.e. with double mutant, G126R/D137L, correlates with higher force in the motility assay. Also, the higher the extent of stabilization of tropomyosin, the fewer myosin molecules are needed to propel the thin filaments. The data suggest that the effects of the stabilizing mutations in tropomyosin on the myosin interaction with regulated thin filaments are mainly realized via cooperative mechanisms by increasing the size of cooperative unit.

The molecular basis of thin filament activation: from single molecule to muscle

For muscles to effectively power locomotion, trillions of myosin molecules must rapidly attach and detach from the actin thin filament. This is accomplished by precise regulation of the availability of the myosin binding sites on actin (i.e. activation). Both calcium (Ca⁺⁺) and myosin binding contribute to activation, but both mechanisms are simultaneously active during contraction, making their relative contributions difficult to determine. Further complicating the process, myosin binding accelerates the attachment rate of neighboring myosin molecules, adding a cooperative element to the activation process. To de-convolve these two effects, we directly determined the effect of Ca⁺⁺ on the rate of attachment of a single myosin molecule to a single regulated actin thin filament, and separately determined the distance over which myosin binding increases the attachment rate of neighboring molecules. Ca⁺⁺ alone increases myosin’s attachment rate ~50-fold, while myosin binding accelerates attachment of neighboring molecules 400 nm along the actin thin filament.

Optical trapping for biosensing: materials and applications

Optical trapping has been evidence as a very powerful tool for the manipulation and study of biological entities. This review explains the main concepts regarding the use of optical trapping for biosensing, focusing its attention to those applications involving the manipulation of particles which are used as handles, force transducers and sensors.

Measuring the Kinetic and Mechanical Properties of Non-processive Myosins Using Optical Tweezers

The myosin superfamily of molecular motors utilizes energy from ATP hydrolysis to generate force and motility along actin filaments in a diverse array of cellular processes. These motors are structurally, kinetically, and mechanically tuned to their specific molecular roles in the cell. Optical trapping techniques have played a central role in elucidating the mechanisms by which myosins generate force and in exposing the remarkable diversity of myosin functions. Here, we present thorough methods for measuring and analyzing interactions between actin and non-processive myosins using optical trapping techniques.

Self-organization of actin networks by a monomeric myosin

The organization of actomyosin networks lies at the center of many types of cellular motility, including cell polarization and collective cell migration during development and morphogenesis. Myosin-IXa is critically involved in these processes. Using total internal reflection fluorescence microscopy, we resolved actin bundles assembled by myosin-IXa. Electron microscopic data revealed that the bundles consisted of highly ordered lattices with parallel actin polarity. The myosin-IXa motor domains aligned across the network, forming cross-links at a repeat distance of precisely 36 nm, matching the helical repeat of actin. Single-particle image processing resolved three distinct conformations of myosin-IXa in the absence of nucleotide. Using cross-correlation of a modeled actomyosin crystal structure, we identified sites of additional mass, which can only be accounted for by the large insert in loop 2 exclusively found in the motor domain of class IX myosins. We show that the large insert in loop 2 binds calmodulin and creates two coordinated actin-binding sites that constrain the actomyosin interactions generating the actin lattices. The actin lattices introduce orientated tracks at specific sites in the cell, which might install platforms allowing Rho-GTPase-activating protein (RhoGAP) activity to be focused at a definite locus. In addition, the lattices might introduce a myosin-related, force-sensing mechanism into the cytoskeleton in cell polarization and collective cell migration.

Statistical mechanics of the Huxley-Simmons model

The chemomechanical model of Huxley and Simmons (HS) [A. F. Huxley and R. M. Simmons, Nature 233, 533 (1971)NATUAS0028-083610.1038/233533a0] provides a paradigmatic description of mechanically induced collective conformational changes relevant in a variety of biological contexts, from muscles power stroke and hair cell gating to integrin binding and hairpin unzipping. We develop a statistical mechanical perspective on the HS model by exploiting a formal analogy with a paramagnetic Ising model. We first study the equilibrium HS model with a finite number of elements and compute explicitly its mechanical and thermal properties. To model kinetics, we derive a master equation and solve it for several loading protocols. The developed formalism is applicable to a broad range of allosteric systems with mean-field interactions.

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 ∼1/f^{3/2} to the well-known ∼1/sqrt[f]-dependence of the end-to-end extension.

Mechanics and Activation of Unconventional Myosins

Many types of cellular motility are based on the myosin family of motor proteins ranging from muscle contraction to exo- and endocytosis, cytokinesis, cell locomotion or signal transduction in hearing. At the center of this wide range of motile processes lies the adaptation of the myosins for each specific mechanical task and the ability to coordinate the timing of motor protein mobilization and targeting. In recent years, great progress has been made in developing single molecule technology to characterize the diverse mechanical properties of the unconventional myosins. Here, we discuss the basic mechanisms and mechanical adaptations of unconventional myosins, and emerging principles regulating motor mobilization and targeting.

Stabilizing the central part of tropomyosin increases the bending stiffness of the thin filament

A two-beam optical trap was used to measure the bending stiffness of F-actin and reconstructed thin filaments. A dumbbell was formed by a filament segment attached to two beads that were held in the two optical traps. One trap was static and held a bead used as a force transducer, whereas an acoustooptical deflector moved the beam holding the second bead, causing stretch of the dumbbell. The distance between the beads was measured using image analysis of micrographs. An exact solution to the problem of bending of an elastic filament attached to two beads and subjected to a stretch was used for data analysis. Substitution of noncanonical residues in the central part of tropomyosin with canonical ones, G126R and D137L, and especially their combination, caused an increase in the bending stiffness of the thin filaments. The data confirm that the effect of these mutations on the regulation of actin-myosin interactions may be caused by an increase in tropomyosin stiffness.

Beam finite-element model of a molecular motor for the simulation of active fibre networks

Molecular motors are proteins that excessively increase the efficiency of subcellular transport processes. They allow for cell division, nutrient transport and even macroscopic muscle movement. In order to understand the effect of motors in large biopolymer networks, e.g. the cytoskeleton, we require a suitable model of a molecular motor. In this contribution, we present such a model based on a geometrically exact beam finite-element formulation. We discuss the numerical model of a non-processive motor such as myosin II, which interacts with actin filaments. Based on experimental data and inspired by the theoretical understanding offered by the power-stroke model and the swinging-cross-bridge model, we parametrize our numerical model in order to achieve the effect that a physiological motor has on its cargo. To this end, we introduce the mechanical and mathematical foundations of the model, then discuss its calibration, prove its usefulness by conducting finite-element simulations of actin-myosin motility assays and assess the influence of motors on the rheology of semi-flexible biopolymer networks.

Methods for Determining the Cellular Functions of Vimentin Intermediate Filaments

The type III intermediate filament protein vimentin was once thought to function mainly as a static structural protein in the cytoskeleton of cells of mesenchymal origin. Now, however, vimentin is known to form a dynamic, flexible network that plays an important role in a number of signaling pathways. Here, we describe various methods that have been developed to investigate the cellular functions of the vimentin protein and intermediate filament network, including chemical disruption, photoactivation and photoconversion, biolayer interferometry, soluble bead binding assay, three-dimensional substrate experiments, collagen gel contraction, optical-tweezer active microrheology, and force spectrum microscopy. Using these techniques, the contributions of vimentin to essential cellular processes can be probed in ever further detail.

The lifetime of the actomyosin complex in vitro under load corresponding to stretch of contracting muscle

During eccentric contraction, muscle is lengthening so that the actin-myosin cross-bridges bear a load that exceeds the force they generate during isometric contraction. Using the optical trap technique, we simulated eccentric contraction at the single molecule level and investigated the effect of load on the skeletal actomyosin lifetime at different ATP concentrations. The range of the loads was up to 17 pN above the isometric level. We found that the frequency distribution of the lifetime of the actin-bound state of the myosin molecule was biphasic: it quickly rose and then decreased slowly. The rate of the slow phase of this distribution increased with both the load and the ATP concentration. The fast phase accelerated sharply with the load, but it was independent of ATP concentration. The presence of the fast phase demonstrates that some transition(s) in the actomyosin complex occur before the myosin head becomes able to bind ATP and detach from actin. Its high sensitivity to the load indicates that the transition is load-dependent.

Poorly understood aspects of striated muscle contraction

Muscle contraction results from cyclic interactions between the contractile proteins myosin and actin, driven by the turnover of adenosine triphosphate (ATP). Despite intense studies, several molecular events in the contraction process are poorly understood, including the relationship between force-generation and phosphate-release in the ATP-turnover. Different aspects of the force-generating transition are reflected in the changes in tension development by muscle cells, myofibrils and single molecules upon changes in temperature, altered phosphate concentration, or length perturbations. It has been notoriously difficult to explain all these events within a given theoretical framework and to unequivocally correlate observed events with the atomic structures of the myosin motor. Other incompletely understood issues include the role of the two heads of myosin II and structural changes in the actin filaments as well as the importance of the three-dimensional order. We here review these issues in relation to controversies regarding basic physiological properties of striated muscle. We also briefly consider actomyosin mutation effects in cardiac and skeletal muscle function and the possibility to treat these defects by drugs.

Ensemble velocity of non-processive molecular motors with multiple chemical states

We study the ensemble velocity of non-processive motor proteins, described with multiple chemical states. In particular, we discuss the velocity as a function of ATP concentration. Even a simple model which neglects the strain dependence of transition rates, reverse transition rates and nonlinearities in the elasticity can show interesting functional dependencies, which deviate significantly from the frequently assumed Michaelis-Menten form. We discuss how the order of events in the duty cycle can be inferred from the measured dependence. The model also predicts the possibility of velocity reversal at a certain ATP concentration if the duty cycle contains several conformational changes of opposite directionalities.

A new mechanokinetic model for muscle contraction, where force and movement are triggered by phosphate release

The atomic structure of myosin-S1 suggests that its working stroke, which generates tension and shortening in muscle, is triggered by the release of inorganic phosphate from the active site. This mechanism is the basis of a new mechanokinetic model for contractility, using the biochemical actomyosin ATPase cycle, strain-dependent kinetics and dimeric myosins on buckling rods. In this model, phosphate-dependent aspects of contractility arise from a rapid reversible release of phosphate from the initial bound state (A.M.ADP.Pi), which triggers the stroke. Added phosphate drives bound myosin towards this initial state, and the transient tension response to a phosphate jump reflects the rate at which it detaches from actin. Predictions for the tensile and energetic properties of striated muscle as a function of phosphate level, including the tension responses to length steps and Pi-jumps, are compared with experimental data from rabbit psoas fibres at 10 °C. The phosphate sensitivity of isometric tension is maximal when the actin affinity of M.ADP.Pi is near unity. Hence variations in actin affinity modulate the phosphate dependence of isometric tension, and may explain why phosphate sensitivity is temperature-dependent or absent in different muscles.

Altered cross-bridge properties in skeletal muscle dystrophies

Force and motion generated by skeletal muscle ultimately depends on the cyclical interaction of actin with myosin. This mechanical process is regulated by intracellular Ca²⁺ through the thin filament-associated regulatory proteins i.e.; troponins and tropomyosin. Muscular dystrophies are a group of heterogeneous genetic affections characterized by progressive degeneration and weakness of the skeletal muscle as a consequence of loss of muscle tissue which directly reduces the number of potential myosin cross-bridges involved in force production. Mutations in genes responsible for skeletal muscle dystrophies (MDs) have been shown to modify the function of contractile proteins and cross-bridge interactions. Altered gene expression or RNA splicing or post-translational modifications of contractile proteins such as those related to oxidative stress, may affect cross-bridge function by modifying key proteins of the excitation-contraction coupling. Micro-architectural change in myofilament is another mechanism of altered cross-bridge performance. In this review, we provide an overview about changes in cross-bridge performance in skeletal MDs and discuss their ultimate impacts on striated muscle function.

Probing the stochastic, motor-driven properties of the cytoplasm using force spectrum microscopy

Molecular motors in cells typically produce highly directed motion; however, the aggregate, incoherent effect of all active processes also creates randomly fluctuating forces, which drive diffusive-like, nonthermal motion. Here, we introduce force-spectrum-microscopy (FSM) to directly quantify random forces within the cytoplasm of cells and thereby probe stochastic motor activity. This technique combines measurements of the random motion of probe particles with independent micromechanical measurements of the cytoplasm to quantify the spectrum of force fluctuations. Using FSM, we show that force fluctuations substantially enhance intracellular movement of small and large components. The fluctuations are three times larger in malignant cells than in their benign counterparts. We further demonstrate that vimentin acts globally to anchor organelles against randomly fluctuating forces in the cytoplasm, with no effect on their magnitude. Thus, FSM has broad applications for understanding the cytoplasm and its intracellular processes in relation to cell physiology in healthy and diseased states.

Direct observation of phosphate inhibiting the force-generating capacity of a miniensemble of Myosin molecules

Elevated levels of phosphate (Pi) reduce isometric force, providing support for the notion that the release of Pi from myosin is closely associated with the generation of muscular force. Pi is thought to rebind to actomyosin in an ADP-bound state and reverse the force-generating steps, including the rotation of the lever arm (i.e., the powerstroke). Despite extensive study, this mechanism remains controversial, in part because it fails to explain the effects of Pi on isometric ATPase and unloaded shortening velocity. To gain new insight into this process, we determined the effect of Pi on the force-generating capacity of a small ensemble of myosin (∼12 myosin heads) using a three-bead laser trap assay. In the absence of Pi, myosin pulled the actin filament out of the laser trap an average distance of 54 ± 4 nm, translating into an average peak force of 1.2 pN. By contrast, in the presence of 30 mM Pi, myosin generated only enough force to displace the actin filament by 13 ± 1 nm, generating just 0.2 pN of force. The elevated Pi also caused a >65% reduction in binding-event lifetime, suggesting that Pi induces premature detachment from a strongly bound state. Definitive evidence of a Pi-induced powerstroke reversal was not observed, therefore we determined if a branched kinetic model in which Pi induces detachment from a strongly bound, postpowerstroke state could explain these observations. The model was able to accurately reproduce not only the data presented here, but also the effects of Pi on both isometric ATPase in muscle fibers and actin filament velocity in a motility assay. The ability of the model to capture the findings presented here as well as previous findings suggests that Pi-induced inhibition of force may proceed along a kinetic pathway different from that of force generation.

Molecular mechanism regulating myosin and cardiac functions by ELC

The essential myosin light chain (ELC) is involved in modulation of force generation of myosin motors and cardiac contraction, while its mechanism of action remains elusive. We hypothesized that ELC could modulate myosin stiffness which subsequently determines its force production and cardiac contraction. Therefore, we generated heterologous transgenic mouse (TgM) strains with cardiomyocyte-specific expression of ELC with human ventricular ELC (hVLC-1; TgM(hVLC-1)) or E56G-mutated hVLC-1 (hVLC-1(E56G); TgM(E56G)). hVLC-1 or hVLC-1(E56G) expression in TgM was around 39% and 41%, respectively of total VLC-1. Laser trap and in vitro motility assays showed that stiffness and actin sliding velocity of myosin with hVLC-1 prepared from TgM(hVLC-1) (1.67 pN/nm and 2.3 μm/s, respectively) were significantly higher than myosin with hVLC-1(E56G) prepared from TgM(E56G) (1.25 pN/nm and 1.7 μm/s, respectively) or myosin with mouse VLC-1 (mVLC-1) prepared from C57/BL6 (1.41 pN/nm and 1.5 μm/s, respectively). Maximal left ventricular pressure development of isolated perfused hearts in vitro prepared from TgM(hVLC-1) (80.0 mmHg) were significantly higher than hearts from TgM(E56G) (66.2 mmHg) or C57/BL6 (59.3±3.9 mmHg). These findings show that ELCs decreased myosin stiffness, in vitro motility, and thereby cardiac functions in the order hVLC-1>hVLC-1(E56G)≈mVLC-1. They also suggest a molecular pathomechanism of hypertrophic cardiomyopathy caused by hVLC-1 mutations.

The role of vimentin intermediate filaments in cortical and cytoplasmic mechanics

The mechanical properties of a cell determine many aspects of its behavior, and these mechanics are largely determined by the cytoskeleton. Although the contribution of actin filaments and microtubules to the mechanics of cells has been investigated in great detail, relatively little is known about the contribution of the third major cytoskeletal component, intermediate filaments (IFs). To determine the role of vimentin IF (VIF) in modulating intracellular and cortical mechanics, we carried out studies using mouse embryonic fibroblasts (mEFs) derived from wild-type or vimentin(-/-) mice. The VIFs contribute little to cortical stiffness but are critical for regulating intracellular mechanics. Active microrheology measurements using optical tweezers in living cells reveal that the presence of VIFs doubles the value of the cytoplasmic shear modulus to ∼10 Pa. The higher levels of cytoplasmic stiffness appear to stabilize organelles in the cell, as measured by tracking endogenous vesicle movement. These studies show that VIFs both increase the mechanical integrity of cells and localize intracellular components.

Myosin-10 produces its power-stroke in two phases and moves processively along a single actin filament under low load

Myosin-10 is an actin-based molecular motor that participates in essential intracellular processes such as filopodia formation/extension, phagocytosis, cell migration, and mitotic spindle maintenance. To study this motor protein's mechano-chemical properties, we used a recombinant, truncated form of myosin-10 consisting of the first 936 amino acids, followed by a GCN4 leucine zipper motif, to force dimerization. Negative-stain electron microscopy reveals that the majority of molecules are dimeric with a head-to-head contour distance of ∼50 nm. In vitro motility assays show that myosin-10 moves actin filaments smoothly with a velocity of ∼310 nm/s. Steady-state and transient kinetic analysis of the ATPase cycle shows that the ADP release rate (∼13 s(-1)) is similar to the maximum ATPase activity (∼12-14 s(-1)) and therefore contributes to rate limitation of the enzymatic cycle. Single molecule optical tweezers experiments show that under intermediate load (∼0.5 pN), myosin-10 interacts intermittently with actin and produces a power stroke of ∼17 nm, composed of an initial 15-nm and subsequent 2-nm movement. At low optical trap loads, we observed staircase-like processive movements of myosin-10 interacting with the actin filament, consisting of up to six ∼35-nm steps per binding interaction. We discuss the implications of this load-dependent processivity of myosin-10 as a filopodial transport motor.

To understand muscle you must take it apart

Striated muscle is an elegant system for study at many levels. Much has been learned about the mechanism of contraction from studying the mechanical properties of intact and permeabilized (or skinned) muscle fibers. Structural studies using electron microscopy, X-ray diffraction or spectroscopic probes attached to various contractile proteins were possible because of the highly ordered sarcomeric arrangement of actin and myosin. However, to understand the mechanism of force generation at a molecular level, it is necessary to take the system apart and study the interaction of myosin with actin using in vitro assays. This reductionist approach has lead to many fundamental insights into how myosin powers muscle contraction. In addition, nature has provided scientists with an array of muscles with different mechanical properties and with a superfamily of myosin molecules. Taking advantage of this diversity in myosin structure and function has lead to additional insights into common properties of force generation. This review will highlight the development of the major assays and methods that have allowed this combined reductionist and comparative approach to be so fruitful. This review highlights the history of biochemical and biophysical studies of myosin and demonstrates how a broad comparative approach combined with reductionist studies have led to a detailed understanding of how myosin interacts with actin and uses chemical energy to generate force and movement in muscle contraction and motility in general.

Stiffness, working stroke, and force of single-myosin molecules in skeletal muscle: elucidation of these mechanical properties via nonlinear elasticity evaluation

In muscles, the arrays of skeletal myosin molecules interact with actin filaments and continuously generate force at various contraction speeds. Therefore, it is crucial for myosin molecules to generate force collectively and minimize the interference between individual myosin molecules. Knowledge of the elasticity of myosin molecules is crucial for understanding the molecular mechanisms of muscle contractions because elasticity directly affects the working and drag (resistance) force generation when myosin molecules are positively or negatively strained. The working stroke distance is also an important mechanical property necessary for elucidation of the thermodynamic efficiency of muscle contractions at the molecular level. In this review, we focus on these mechanical properties obtained from single-fiber and single-molecule studies and discuss recent findings associated with these mechanical properties. We also discuss the potential molecular mechanisms associated with reduction of the drag effect caused by negatively strained myosin molecules.

R1 motif is the major actin-binding domain of TRIOBP-4

TRIOBP is an actin-bundling protein. Mutations of TRIOBP are associated with human deafness DFNB28. In vitro, TRIOBP isoform 4 (TRIOBP-4) forms dense F-actin bundles resembling the inner ear hair cell rootlet structure. Deletion of TRIOBP isoforms 4 and 5 leads to hearing loss in mice due to the absence of stereocilia rootlets. The mechanism of actin bundle formation by TRIOBP is not fully understood. The amino acid sequences of TRIOBP isoforms 4 and 5 contain two repeated motifs, referred to here as R1 and R2. To examine the potential role of R1 and R2 motifs in F-actin binding, we generated TRIOBP-4 mutant proteins deleted for R1 and/or R2, and then assessed their actin-binding activity and bundle formation in vitro using actin cosedimentation assays, and fluorescence and electron microscopy. Cellular distributions of the TRIOBP-4 mutants were examined by confocal microscopy. We showed that deletion of both R1 and R2 motifs completely disrupted the actin binding/bundling activities of TRIOBP-4 and impaired its localization to cellular actin cytoskeleton structures. By contrast, TRIOBP-4, lacking only R2 motif, retained its F-actin bundling ability and remained localized to actin filaments in cells, similar to full length TRIOBP-4. On the contrary, the R1 motif-deleted TRIOBP-4 mutant, which mainly consists of the R2 motif, formed thin F-actin bundles in vitro but failed to colocalize to actin filaments in cells. These results indicate that R1 motif is the major actin-binding domain of TRIOBP-4, and the binding of R2 motif with actin filaments is nonspecific.

Tilting and wobble of myosin V by high-speed single-molecule polarized fluorescence microscopy

Myosin V is biomolecular motor with two actin-binding domains (heads) that take multiple steps along actin by a hand-over-hand mechanism. We used high-speed polarized total internal reflection fluorescence (polTIRF) microscopy to study the structural dynamics of single myosin V molecules that had been labeled with bifunctional rhodamine linked to one of the calmodulins along the lever arm. With the use of time-correlated single-photon counting technology, the temporal resolution of the polTIRF microscope was improved ~50-fold relative to earlier studies, and a maximum-likelihood, multitrace change-point algorithm was used to objectively determine the times when structural changes occurred. Short-lived substeps that displayed an abrupt increase in rotational mobility were detected during stepping, likely corresponding to random thermal fluctuations of the stepping head while it searched for its next actin-binding site. Thus, myosin V harnesses its fluctuating environment to extend its reach. Additional, less frequent angle changes, probably not directly associated with steps, were detected in both leading and trailing heads. The high-speed polTIRF method and change-point analysis may be applicable to single-molecule studies of other biological systems.

Method for measuring single-molecule adhesion forces and attachment lifetimes of protein-membrane interactions

Many proteins that reside in the cytoplasm bind directly to cell membranes and play roles in signaling, adhesion, metabolism, cell structure, and cell motility. Several of these membrane-binding proteins, especially cytoskeletal proteins, have mechanical functions that result in the transmission of forces to the plasma membrane and organelle-membranes. Despite the importance of these interactions, remarkably little is known about the mechanical properties of the bonds between membranes and proteins. In this chapter, we describe a single-molecule, optical-trapping method for the measurement of protein-membrane adhesion forces and force-dependent attachment-lifetimes.

Kinetic characterization of nonmuscle myosin IIb at the single molecule level

Nonmuscle myosin IIB (NMIIB) is a cytoplasmic myosin, which plays an important role in cell motility by maintaining cortical tension. It forms bipolar thick filaments with ~14 myosin molecule dimers on each side of the bare zone. Our previous studies showed that the NMIIB is a moderately high duty ratio (~20-25%) motor. The ADP release step (~0.35 s(-1)) of NMIIB is only ~3 times faster than the rate-limiting phosphate release (0.13 ± 0.01 s(-1)). The aim of this study was to relate the known in vitro kinetic parameters to the results of single molecule experiments and to compare the kinetic and mechanical properties of single- and double-headed myosin fragments and nonmuscle IIB thick filaments. Examination of the kinetics of NMIIB interaction with actin at the single molecule level was accomplished using total internal reflection fluorescence (TIRF) with fluorescence imaging with 1-nm accuracy (FIONA) and dual-beam optical trapping. At a physiological ATP concentration (1 mm), the rate of detachment of the single-headed and double-headed molecules was similar (~0.4 s(-1)). Using optical tweezers we found that the power stroke sizes of single- and double-headed heavy meromyosin (HMM) were each ~6 nm. No signs of processive stepping at the single molecule level were observed in the case of NMIIB-HMM in optical tweezers or TIRF/in vitro motility experiments. In contrast, robust motility of individual fluorescently labeled thick filaments of full-length NMIIB was observed on actin filaments. Our results are in good agreement with the previous steady-state and transient kinetic studies and show that the individual nonprocessive nonmuscle myosin IIB molecules form a highly processive unit when polymerized into filaments.

Physically based principles of cell adhesion mechanosensitivity in tissues

The minimal structural unit that defines living organisms is a single cell. By proliferating and mechanically interacting with each other, cells can build complex organization such as tissues that ultimately organize into even more complex multicellular living organisms, such as mammals, composed of billions of single cells interacting with each other. As opposed to passive materials, living cells actively respond to the mechanical perturbations occurring in their environment. Tissue cell adhesion to its surrounding extracellular matrix or to neighbors is an example of a biological process that adapts to physical cues. The adhesion of tissue cells to their surrounding medium induces the generation of intracellular contraction forces whose amplitude adapts to the mechanical properties of the environment. In turn, solicitation of adhering cells with physical forces, such as blood flow shearing the layer of endothelial cells in the lumen of arteries, reinforces cell adhesion and impacts cell contractility. In biological terms, the sensing of physical signals is transduced into biochemical signaling events that guide cellular responses such as cell differentiation, cell growth and cell death. Regarding the biological and developmental consequences of cell adaptation to mechanical perturbations, understanding mechanotransduction in tissue cell adhesion appears as an important step in numerous fields of biology, such as cancer, regenerative medicine or tissue bioengineering for instance. Physicists were first tempted to view cell adhesion as the wetting transition of a soft bag having a complex, adhesive interaction with the surface. But surprising responses of tissue cell adhesion to mechanical cues challenged this view. This, however, did not exclude that cell adhesion could be understood in physical terms. It meant that new models and descriptions had to be created specifically for these biological issues, and could not straightforwardly be adapted from dead matter. In this review, we present physical concepts of tissue cell adhesion and the unexpected cellular responses to mechanical cues such as external forces and stiffness sensing. We show how biophysical approaches, both experimentally and theoretically, have contributed to our understanding of the regulation of cellular functions through physical force sensing mechanisms. Finally, we discuss the different physical models that could explain how tissue cell adhesion and force sensing can be coupled to internal mechanosensitive processes within the cell body.

Mechanical coupling between myosin molecules causes differences between ensemble and single-molecule measurements

In contracting muscle, individual myosin molecules function as part of a large ensemble, hydrolyzing ATP to power the relative sliding of actin filaments. The technological advances that have enabled direct observation and manipulation of single molecules, including recent experiments that have explored myosin's force-dependent properties, provide detailed insight into the kinetics of myosin's mechanochemical interaction with actin. However, it has been difficult to reconcile these single-molecule observations with the behavior of myosin in an ensemble. Here, using a combination of simulations and theory, we show that the kinetic mechanism derived from single-molecule experiments describes ensemble behavior; but the connection between single molecule and ensemble is complex. In particular, even in the absence of external force, internal forces generated between myosin molecules in a large ensemble accelerate ADP release and increase how far actin moves during a single myosin attachment. These myosin-induced changes in strong binding lifetime and attachment distance cause measurable properties, such as actin speed in the motility assay, to vary depending on the number of myosin molecules interacting with an actin filament. This ensemble-size effect challenges the simple detachment limited model of motility, because even when motility speed is limited by ADP release, increasing attachment rate can increase motility speed.