The kinetics of mechanically coupled myosins exhibit group size-dependent regimes

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.

Deciphering Mechanochemical Influences of Emergent Actomyosin Crosstalk using QCM-D

Cytoskeletal protein ensembles exhibit emergent mechanics where behavior exhibited in teams is not necessarily the sum of the components' single molecule properties. In addition, filaments may act as force sensors that distribute feedback and influence motor protein behavior. To understand the design principles of such emergent mechanics, we developed an approach utilizing QCM-D to measure how actomyosin bundles respond mechanically to environmental variables that alter constituent myosin II motor behavior. We demonstrate that QCM-D can detect changes in actomyosin viscoelasticity due to molecular-level alterations, such as motor concentration and nucleotide state, thus providing evidence for actin's role as a mechanical force-feedback sensor and a new approach for deciphering the fundamental mechanisms of emergent cytoskeletal ensemble crosstalk.

Justification

Cytoskeletal ensembles exhibit mechanics that are not necessarily the sum of the components' single molecule properties, and this emergent behavior is not well understood. Cytoskeletal filaments may also act as force sensors that influence constituent motor protein behavior. To understand the elusive design principles of such emergent mechanics, we innovated an approach using QCM-D to measure how actomyosin bundles sense and respond mechanically to environmental variables. We demonstrate for the first time that QCM-D can detect changes in actomyosin viscoelasticity due to molecular-level alterations, thus providing evidence for actin's role as a mechanical force-feedback sensor and a new approach for deciphering the fundamentals of emergent cytoskeletal ensemble crosstalk.

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.

Cooperativity of myosin II motors in the non-regulated and regulated thin filaments investigated with high-speed AFM

Skeletal myosins II are non-processive molecular motors that work in ensembles to produce muscle contraction while binding to the actin filament. Although the molecular properties of myosin II are well known, there is still debate about the collective work of the motors: is there cooperativity between myosin motors while binding to the actin filaments? In this study, we use high-speed AFM to evaluate this issue. We observed that the initial binding of small arrays of myosin heads to the non-regulated actin filaments did not affect the cooperative probability of subsequent bindings and did not lead to an increase in the fractional occupancy of the actin binding sites. These results suggest that myosin motors are independent force generators when connected in small arrays, and that the binding of one myosin does not alter the kinetics of other myosins. In contrast, the probability of binding of myosin heads to regulated thin filaments under activating conditions (at high Ca2+ concentration in the presence of 2 μM ATP) was increased with the initial binding of one myosin, leading to a larger occupancy of available binding sites at the next half-helical pitch of the filament. The result suggests that myosin cooperativity is observed over five pseudo-repeats and defined by the activation status of the thin filaments.

Myosin II Adjusts Motility Properties and Regulates Force Production Based on Motor Environment

Introduction

Myosin II has been investigated with optical trapping, but single motor-filament assay arrangements are not reflective of the complex cellular environment. To understand how myosin interactions propagate up in scale to accomplish system force generation, we devised a novel actomyosin ensemble optical trapping assay that reflects the hierarchy and compliancy of a physiological environment and is modular for interrogating force effectors.

Methods

Hierarchical actomyosin bundles were formed in vitro. Fluorescent template and cargo actin filaments (AF) were assembled in a flow cell and bundled by myosin. Beads were added in the presence of ATP to bind the cargo AF and activate myosin force generation to be measured by optical tweezers.

Results

Three force profiles resulted across a range of myosin concentrations: high force with a ramp-plateau, moderate force with sawtooth movement, and baseline. The three force profiles, as well as high force output, were recovered even at low solution concentration, suggesting that myosins self-optimize within AFs. Individual myosin steps were detected in the ensemble traces, indicating motors are taking one step at a time while others remain engaged in order to sustain productive force generation.

Conclusions

Motor communication and system compliancy are significant contributors to force output. Environmental conditions, motors taking individual steps to sustain force, the ability to backslip, and non-linear concentration dependence of force indicate that the actomyosin system contains a force-feedback mechanism that senses the local cytoskeletal environment and communicates to the individual motors whether to be in a high or low duty ratio mode.

Supplementary Information

The online version contains supplementary material available at 10.1007/s12195-022-00731-1.

Force-velocity and tension transient measurements from Drosophila jump muscle reveal the necessity of both weakly-bound cross-bridges and series elasticity in models of muscle contraction

Muscle contraction is a fundamental biological process where molecular interactions between the myosin molecular motor and actin filaments result in contraction of a whole muscle, a process spanning size scales differing in eight orders of magnitude. Since unique behavior is observed at every scale in between these two extremes, to fully understand muscle function it is vital to develop multi-scale models. Based on simulations of classic measurements of muscle heat generation as a function of work, and shortening rate as a function of applied force, we hypothesize that a model based on molecular measurements must be modified to include a weakly-bound interaction between myosin and actin in order to fit measurements at the muscle fiber or whole muscle scales. This hypothesis is further supported by the model's need for a weakly-bound state in order to qualitatively reproduce the force response that occurs when a muscle fiber is rapidly stretched a small distance. We tested this hypothesis by measuring steady-state force as a function of shortening velocity, and the force transient caused by a rapid length step in Drosophila jump muscle fibers. Then, by performing global parameter optimization, we quantitatively compared the predictions of two mathematical models, one lacking a weakly-bound state and one with a weakly-bound state, to these measurements. Both models could reproduce our force-velocity measurements, but only the model with a weakly-bound state could reproduce our force transient measurements. However, neither model could concurrently fit both measurements. We find that only a model that includes weakly-bound cross-bridges with force-dependent detachment and an elastic element in series with the cross-bridges is able to fit both of our measurements. This result suggests that the force response after stretch is not a reflection of distinct steps in the cross-bridge cycle, but rather arises from the interaction of cross-bridges with a series elastic element. Additionally, the model suggests that the curvature of the force-velocity relationship arises from a combination of the force-dependence of weakly- and strongly-bound cross-bridges. Overall, this work presents a minimal cross-bridge model that has predictive power at the fiber level.

Mechanosensitive self-assembly of myosin II minifilaments

Self-assembly and force generation are two central processes in biological systems that usually are considered in separation. However, the signals that activate nonmuscle myosin II molecular motors simultaneously lead to self-assembly into myosin II minifilaments as well as progression of the motor heads through the cross-bridge cycle. Here we investigate theoretically the possible effects of coupling these two processes. Our assembly model, which builds on a consensus architecture of the minifilament, predicts a critical aggregation concentration at which the assembly kinetics slows down dramatically. The combined model predicts that increasing actin filament concentration and force both lead to a decrease in the critical aggregation concentration. We suggest that due to these effects, myosin II minifilaments in a filamentous context might be in a critical state that reacts faster to varying conditions than in solution. We finally compare our model to experiments by simulating fluorescence recovery after photobleaching.

Spreading of perturbations in myosin group kinetics along actin filaments

Global changes in the state of spatially distributed systems can often be traced back to perturbations that arise locally. Whether such local perturbations grow into global changes depends on the system geometry and the spatial spreading of these perturbations. Here, we investigate how different spreading behaviors of local perturbations determine their global impact in 1-dimensional systems of different size. Specifically, we assessed sliding arrest events in in vitro motility assays where myosins propel actin, and simulated the underlying mechanochemistry of myosins that bind along the actin filament. We observed spontaneous sliding arrest events that occurred more frequently for shorter actin filaments. This observation could be explained by spontaneous local arrest of myosin kinetics that stabilizes once it spreads throughout an entire actin filament. When we introduced intermediate concentrations of the actin cross-linker filamin, longer actin was arrested more frequently. This observation was reproduced by simulations where filamin binding induces persistent local arrest of myosin kinetics, which subsequently spreads throughout the actin filament. A spin chain model with nearest-neighbor coupling reproduced key features of our experiments and simulations, thus extending to other linear systems with nearest-neighbor coupling the following conclusions: 1) perturbations that are persistent only once they spread throughout the system are more effective in smaller systems, and 2) perturbations that are persistent upon their establishment are more effective in larger systems. Beyond these general conclusions, our work also provides a theoretical model of collective myosin kinetics with a finite range of mechanical coupling along the actin filament.

Rapid time-stamped analysis of filament motility

The in vitro motility assay is a valuable tool to understand motor protein mechanics, but existing algorithms are not optimized for accurate time resolution. We propose an algorithm that combines trace detection with a time-stamped analysis. By tracking filament ends, we minimize data loss from overlapping and crossing filaments. A movement trace formed by each filament end is created by time-stamping when the filament either first (filament tip) or last (filament tail) occupies a pixel. A frame number vs. distance curve is generated from this trace, which is segmented into regions by slope to detect stop-and-go movement. We show, using generated mock motility videos, accurate detection of velocity and motile fraction changes for velocities < 0.05 pixels per frame, without manual trace dropping and regardless of filament crossings. Compared with established algorithms we show greatly improved accuracy in velocity and motile fraction estimation, with greatly reduced user effort. We tested two actual motility experiments: (1) adenosine triphosphate (ATP) added to skeletal myosin in rigor; (2) myosin light chain phosphatase (MLCP) added to phasic smooth muscle myosin. Our algorithm revealed previously undetectable features: (1) rapid increase in motile fraction paralleled by a slow increase in velocity as ATP concentration increases; (2) simultaneous reductions in velocity and motile fraction as MLCP diffuses into the motility chamber at very low velocities. Our algorithm surpasses existing algorithms in the resolution of time dependent changes in motile fraction and velocity at a wide range of filament lengths and velocities, with minimal user input and CPU time.

Chemomechanical regulation of myosin Ic cross-bridges: Deducing the elastic properties of an ensemble from single-molecule mechanisms

Myosin Ic is thought to be the principal constituent of the motor that adjusts mechanical responsiveness during adaptation to prolonged stimuli by hair cells, the sensory receptors of the inner ear. In this context myosin molecules operate neither as filaments, as occurs in muscles, nor as single or few molecules, as characterizes intracellular transport. Instead, myosin Ic molecules occur in a complex cluster in which they may exhibit cooperative properties. To better understand the motor’s remarkable function, we introduce a theoretical description of myosin Ic’s chemomechanical cycle based on experimental data from recent single-molecule studies. The cycle consists of distinct chemical states that the myosin molecule stochastically occupies. We explicitly calculate the probabilities of the occupancy of these states and show their dependence on the external force, the availability of actin, and the nucleotide concentrations as required by thermodynamic constraints. This analysis highlights that the strong binding of myosin Ic to actin is dominated by the ADP state for small external forces and by the ATP state for large forces. Our approach shows how specific parameter values of the chemomechanical cycle for myosin Ic result in behaviors distinct from those of other members of the myosin family. Integrating this single-molecule cycle into a simplified ensemble description, we predict that the average number of bound myosin heads is regulated by the external force and nucleotide concentrations. The elastic properties of such an ensemble are determined by the average number of myosin cross-bridges. Changing the binding probabilities and myosin’s stiffness under a constant force results in a mechanical relaxation which is large enough to account for fast adaptation in hair cells.

Myosin molecules are biological nanomachines that transduce chemical energy into mechanical work and thus produce directed motion in living cells. These molecules proceed through cyclic reactions in which they change their conformational states upon the binding and release of nucleotides while attaching to and detaching from filaments. The myosin family consists of many distinct members with diverse functions such as muscle contraction, cargo transport, cell migration, and sensory adaptation. How these functions emerge from the biophysical properties of the individual molecules is an open question. We present an approach that integrates recent findings from single-molecule experiments into a thermodynamically consistent description of myosin Ic and demonstrate how the specific parameter values of the cycle result in a distinct function. The free variables of our description are the chemical input and external force, both of which are experimentally accessible and define the cellular environment in which these proteins function. We use this description to predict the elastic properties of an ensemble of molecules and discuss the implications for myosin Ic’s function in the inner ear as a tension regulator mediating adaptation, a hallmark of biological sensory systems. In this situation myosin molecules cooperate in an intermediate regime, neither as a large ensemble as in muscle nor as a single or a few molecules as in intracellular transport.

Actomyosin based contraction: one mechanokinetic model from single molecules to muscle?

Bridging the gaps between experimental systems on different hierarchical scales is needed to overcome remaining challenges in the understanding of muscle contraction. Here, a mathematical model with well-characterized structural and biochemical actomyosin states is developed to that end. We hypothesize that this model accounts for generation of force and motion from single motor molecules to the large ensembles of muscle. In partial support of this idea, a wide range of contractile phenomena are reproduced without the need to invoke cooperative interactions or ad hoc states/transitions. However, remaining limitations exist, associated with ambiguities in available data for model definition e.g.: (1) the affinity of weakly bound cross-bridges, (2) the characteristics of the cross-bridge elasticity and (3) the exact mechanistic relationship between the force-generating transition and phosphate release in the actomyosin ATPase. Further, the simulated number of attached myosin heads in the in vitro motility assay differs several-fold from duty ratios, (fraction of strongly attached ATPase cycle times) derived in standard analysis. After addressing the mentioned issues the model should be useful in fundamental studies, for engineering of myosin motors as well as for studies of muscle disease and drug development.

Sensitivity of small myosin II ensembles from different isoforms to mechanical load and ATP concentration

Based on a detailed crossbridge model for individual myosin II motors, we systematically study the influence of mechanical load and adenosine triphosphate (ATP) concentration on small myosin II ensembles made from different isoforms. For skeletal and smooth muscle myosin II, which are often used in actomyosin gels that reconstitute cell contractility, fast forward movement is restricted to a small region of phase space with low mechanical load and high ATP concentration, which is also characterized by frequent ensemble detachment. At high load, these ensembles are stalled or move backwards, but forward motion can be restored by decreasing ATP concentration. In contrast, small ensembles of nonmuscle myosin II isoforms, which are found in the cytoskeleton of nonmuscle cells, are hardly affected by ATP concentration due to the slow kinetics of the bound states. For all isoforms, the thermodynamic efficiency of ensemble movement increases with decreasing ATP concentration, but this effect is weaker for the nonmuscle myosin II isoforms.

Engineering Circular Gliding of Actin Filaments Along Myosin-Patterned DNA Nanotube Rings To Study Long-Term Actin-Myosin Behaviors

Nature has evolved molecular motors that are critical in cellular processes occurring over broad time scales, ranging from seconds to years. Despite the importance of the long-term behavior of molecular machines, topics such as enzymatic lifetime are underexplored due to the lack of a suitable approach for monitoring motor activity over long time periods. Here, we developed an "O"-shaped Myosin Empowered Gliding Assay (OMEGA) that utilizes engineered micron-scale DNA nanotube rings with precise arrangements of myosin VI to trap gliding actin filaments. This circular gliding assay platform allows the same individual actin filament to glide over the same myosin ensemble (50-1000 motors per ring) multiple times. First, we systematically characterized the formation of DNA nanotubes rings with 4, 6, 8, and 10 helix circumferences. Individual actin filaments glide along the nanotube rings with high processivity for up to 12.8 revolutions or 11 min in run time. We then show actin gliding speed is robust to variation in motor number and independent of ring curvature within our sample space (ring diameter of 0.5-4 μm). As a model application of OMEGA, we then analyze motor-based mechanical influence on "stop-and-go" gliding behavior of actin filaments, revealing that the stop-to-go transition probability is dependent on motor flexibility. Our circular gliding assay may provide a closed-loop platform for monitoring long-term behavior of broad classes of molecular motors and enable characterization of motor robustness and long time scale nanomechanical processes.

Velocity Fluctuations in Kinesin-1 Gliding Motility Assays Originate in Motor Attachment Geometry Variations

Motor proteins such as myosin and kinesin play a major role in cellular cargo transport, muscle contraction, cell division, and engineered nanodevices. Quantifying the collective behavior of coupled motors is critical to our understanding of these systems. An excellent model system is the gliding motility assay, where hundreds of surface-adhered motors propel one cytoskeletal filament such as an actin filament or a microtubule. The filament motion can be observed using fluorescence microscopy, revealing fluctuations in gliding velocity. These velocity fluctuations have been previously quantified by a motional diffusion coefficient, which Sekimoto and Tawada explained as arising from the addition and removal of motors from the linear array of motors propelling the filament as it advances, assuming that different motors are not equally efficient in their force generation. A computational model of kinesin head diffusion and binding to the microtubule allowed us to quantify the heterogeneity of motor efficiency arising from the combination of anharmonic tail stiffness and varying attachment geometries assuming random motor locations on the surface and an absence of coordination between motors. Knowledge of the heterogeneity allows the calculation of the proportionality constant between the motional diffusion coefficient and the motor density. The calculated value (0.3) is within a standard error of our measurements of the motional diffusion coefficient on surfaces with varying motor densities calibrated by landing rate experiments. This allowed us to quantify the loss in efficiency of coupled molecular motors arising from heterogeneity in the attachment geometry.

Simultaneous nano-tracking of multiple motor proteins via spectral discrimination of quantum dots

Simultaneous nanometric tracking of multiple motor proteins was achieved by combining multicolor fluorescent labeling of target proteins and imaging spectroscopy, revealing dynamic behaviors of multiple motor proteins at the sub-diffraction-limit scale. Using quantum dot probes of distinct colors, we experimentally verified the localization precision to be a few nanometers at temporal resolution of 30 ms or faster. One-dimensional processive movement of two heads of a single myosin molecule and multiple myosin molecules was successfully traced. Furthermore, the system was modified for two-dimensional measurement and applied to tracking of multiple myosin molecules. Our approach is useful for investigating cooperative movement of proteins in supramolecular nanomachinery.

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.

Phosphate and ADP differently inhibit coordinated smooth muscle myosin groups

Actin filaments propelled in vitro by groups of skeletal muscle myosin motors exhibit distinct phases of active sliding or arrest, whose occurrence depends on actin length (L) within a range of up to 1.0 μm. Smooth muscle myosin filaments are exponentially distributed with ≈150 nm average length in vivo--suggesting relevance of the L-dependence of myosin group kinetics. Here, we found L-dependent actin arrest and sliding in in vitro motility assays of smooth muscle myosin. We perturbed individual myosin kinetics with varying, physiological concentrations of phosphate (Pi, release associated with main power stroke) and adenosine diphosphate (ADP, release associated with minor mechanical step). Adenosine triphosphate was kept constant at physiological concentration. Increasing [Pi] lowered the fraction of time for which actin was actively sliding, reflected in reduced average sliding velocity (ν) and motile fraction (fmot, fraction of time that filaments are moving); increasing [ADP] increased the fraction of time actively sliding and reduced the velocity while sliding, reflected in reduced ν and increased fmot. We introduced specific Pi and ADP effects on individual myosin kinetics into our recently developed mathematical model of actin propulsion by myosin groups. Simulations matched our experimental observations and described the inhibition of myosin group kinetics. At low [Pi] and [ADP], actin arrest and sliding were reflected by two distinct chemical states of the myosin group. Upon [Pi] increase, the probability of the active state decreased; upon [ADP] increase, the probability of the active state increased, but the active state became increasingly similar to the arrested state.

Mechanical coordination in motor ensembles revealed using engineered artificial myosin filaments

The sarcomere of muscle is composed of tens of thousands of myosin motors that self-assemble into thick filaments and interact with surrounding actin-based thin filaments in a dense, near-crystalline hexagonal lattice. Together, these actin-myosin interactions enable large-scale movement and force generation, two primary attributes of muscle. Research on isolated fibres has provided considerable insight into the collective properties of muscle, but how actin-myosin interactions are coordinated in an ensemble remains poorly understood. Here, we show that artificial myosin filaments, engineered using a DNA nanotube scaffold, provide precise control over motor number, type and spacing. Using both dimeric myosin V- and myosin VI-labelled nanotubes, we find that neither myosin density nor spacing has a significant effect on the gliding speed of actin filaments. This observation supports a simple model of myosin ensembles as energy reservoirs that buffer individual stochastic events to bring about smooth, continuous motion. Furthermore, gliding speed increases with cross-bridge compliance, but is limited by Brownian effects. As a first step to reconstituting muscle motility, we demonstrate human β-cardiac myosin-driven gliding of actin filaments on DNA nanotubes.

Isoforms Confer Characteristic Force Generation and Mechanosensation by Myosin II Filaments

Myosin II isoforms with varying mechanochemistry and filament size interact with filamentous actin (F-actin) arrays to generate contractile forces in muscle and nonmuscle cells. How myosin II force production is shaped by isoform-specific motor properties and environmental stiffness remains poorly understood. Here, we used computer simulations to analyze force production by an ensemble of myosin motors against an elastically tethered actin filament. We found that force output depends on two timescales: the duration of F-actin attachment, which varies sharply with the ensemble size, motor duty ratio, and external load; and the time to build force, which scales with the ensemble stall force, gliding speed, and environmental stiffness. Although force-dependent kinetics were not required to sense changes in stiffness, the myosin catch bond produced positive feedback between the attachment time and force to trigger switch-like transitions from transient attachments, generating small forces, to high-force-generating runs. Using parameters representative of skeletal muscle myosin, nonmuscle myosin IIB, and nonmuscle myosin IIA revealed three distinct regimes of behavior, respectively: 1) large assemblies of fast, low-duty ratio motors rapidly build stable forces over a large range of environmental stiffness; 2) ensembles of slow, high-duty ratio motors serve as high-affinity cross-links with force buildup times that exceed physiological timescales; and 3) small assemblies of low-duty ratio motors operating at intermediate speeds are poised to respond sharply to changes in mechanical context-at low force or stiffness, they serve as low-affinity cross-links, but they can transition to force production via the positive-feedback mechanism described above. Together, these results reveal how myosin isoform properties may be tuned to produce force and respond to mechanical cues in their environment.

A microfluidic chamber to study the dynamics of muscle-contraction-specific molecular interactions

In vitro motility and laser trap assays are commonly used for molecular mechanics measurements. However, chemicals cannot be added during these measurements, because they create flows that alter the molecular mechanics. Thus, we designed a microfluidic device that allows the addition of chemicals without creating bulk flows. Biocompatibility of the components of this device was tested. A microchannel chamber was created by photolithography with the patterns transferred to polydimethylsiloxane (PDMS). The PDMS chamber was bound to a polycarbonate membrane, which itself was bound to a molecular mechanics chamber. The microchannels ensured rapid distribution of the chemicals over the membrane, whereas the membrane ensured efficient delivery to the mechanics chamber while preventing bulk flow. The biocompatibility of the materials was tested by comparing the velocity (ν(max)) of propulsion by myosin of fluorescently labeled actin filaments to that of the conventional assay; no difference in ν(max) was observed. To estimate total chemical delivery time, labeled bovine serum albumin was injected in the channel chamber and TIRF was used to determine the time to reach the assay surface (2.7 ± 0.1 s). Furthermore, the standard distance of a trapped microsphere calculated during buffer diffusion using the microfluidic device (14.9 ± 3.2 nm) was not different from that calculated using the conventional assay (15.6 ± 5.3 nm, p = 0.922). Finally, ν(max) obtained by injecting adenosine triphosphate (ATP) in the microchannel chamber (2.37 ± 0.48 μm/s) was not different from that obtained when ATP was delivered directly to the mechanics chamber (2.52 ± 0.42 μm/s, p = 0.822). This microfluidic prototype validates the design for molecular mechanics measurements.

Muscle activation described with a differential equation model for large ensembles of locally coupled molecular motors

Molecular motors, by turning chemical energy into mechanical work, are responsible for active cellular processes. Often groups of these motors work together to perform their biological role. Motors in an ensemble are coupled and exhibit complex emergent behavior. Although large motor ensembles can be modeled with partial differential equations (PDEs) by assuming that molecules function independently of their neighbors, this assumption is violated when motors are coupled locally. It is therefore unclear how to describe the ensemble behavior of the locally coupled motors responsible for biological processes such as calcium-dependent skeletal muscle activation. Here we develop a theory to describe locally coupled motor ensembles and apply the theory to skeletal muscle activation. The central idea is that a muscle filament can be divided into two phases: an active and an inactive phase. Dynamic changes in the relative size of these phases are described by a set of linear ordinary differential equations (ODEs). As the dynamics of the active phase are described by PDEs, muscle activation is governed by a set of coupled ODEs and PDEs, building on previous PDE models. With comparison to Monte Carlo simulations, we demonstrate that the theory captures the behavior of locally coupled ensembles. The theory also plausibly describes and predicts muscle experiments from molecular to whole muscle scales, suggesting that a micro- to macroscale muscle model is within reach.

The role of caldesmon and its phosphorylation by ERK on the binding force of unphosphorylated myosin to actin

BACKGROUND

Studies conducted at the whole muscle level have shown that smooth muscle can maintain tension with low Adenosine triphosphate (ATP) consumption. Whereas it is generally accepted that this property (latch-state) is a consequence of the dephosphorylation of myosin during its attachment to actin, free dephosphorylated myosin can also bind to actin and contribute to force maintenance. We investigated the role of caldesmon (CaD) in regulating the binding force of unphosphorylated tonic smooth muscle myosin to actin.

METHODS

To measure the effect of CaD on the binding of unphosphorylated myosin to actin (in the presence of ATP), we used a single beam laser trap assay to quantify the average unbinding force (Funb) in the absence or presence of caldesmon, extracellular signal-regulated kinase (ERK)-phosphorylated CaD, or CaD plus tropomyosin.

RESULTS

Funb from unregulated actin (0.10±0.01pN) was significantly increased in the presence of CaD (0.17±0.02pN), tropomyosin (0.17±0.02pN) or both regulatory proteins (0.18±0.02pN). ERK phosphorylation of CaD significantly reduced the Funb (0.06±0.01pN). Inspection of the traces of the Funb as a function of time suggests that ERK phosphorylation of CaD decreases the binding force of myosin to actin or accelerates its detachment.

CONCLUSIONS

CaD enhances the binding force of unphosphorylated myosin to actin potentially contributing to the latch-state. ERK phosphorylation of CaD decreases this binding force to very low levels.

GENERAL SIGNIFICANCE

This study suggests a mechanism that likely contributes to the latch-state and that explains the muscle relaxation from the latch-state.

Molecular mechanical differences between isoforms of contractile actin in the presence of isoforms of smooth muscle tropomyosin

The proteins involved in smooth muscle's molecular contractile mechanism - the anti-parallel motion of actin and myosin filaments driven by myosin heads interacting with actin - are found as different isoforms. While their expression levels are altered in disease states, their relevance to the mechanical interaction of myosin with actin is not sufficiently understood. Here, we analyzed in vitro actin filament propulsion by smooth muscle myosin for [Formula: see text]-actin ([Formula: see text]A), [Formula: see text]-actin-tropomyosin-[Formula: see text] ([Formula: see text]A-Tm[Formula: see text]), [Formula: see text]-actin-tropomyosin-[Formula: see text] ([Formula: see text]A-Tm[Formula: see text]), [Formula: see text]-actin ([Formula: see text]A), [Formula: see text]-actin-tropomyosin-[Formula: see text] ([Formula: see text]A-Tm[Formula: see text]), and [Formula: see text]-actin-tropomoysin-[Formula: see text] ([Formula: see text]A-Tm[Formula: see text]). Actin sliding analysis with our specifically developed video analysis software followed by statistical assessment (Bootstrapped Principal Component Analysis) indicated that the in vitro motility of [Formula: see text]A, [Formula: see text]A, and [Formula: see text]A-Tm[Formula: see text] is not distinguishable. Compared to these three 'baseline conditions', statistically significant differences ([Formula: see text]) were: [Formula: see text]A-Tm[Formula: see text] - actin sliding velocity increased 1.12-fold, [Formula: see text]A-Tm[Formula: see text] - motile fraction decreased to 0.96-fold, stop time elevated 1.6-fold, [Formula: see text]A-Tm[Formula: see text] - run time elevated 1.7-fold. We constructed a mathematical model, simulated actin sliding data, and adjusted the kinetic parameters so as to mimic the experimentally observed differences: [Formula: see text]A-Tm[Formula: see text] - myosin binding to actin, the main, and the secondary myosin power stroke are accelerated, [Formula: see text]A-Tm[Formula: see text] - mechanical coupling between myosins is stronger, [Formula: see text]A-Tm[Formula: see text] - the secondary power stroke is decelerated and mechanical coupling between myosins is weaker. In summary, our results explain the different regulatory effects that specific combinations of actin and smooth muscle tropomyosin have on smooth muscle actin-myosin interaction kinetics.