Sarcomere lattice geometry influences cooperative myosin binding in muscle

Excess Intramyocellular Lipid Does Not Affect Muscle Fiber Biophysical Properties in Mice or People With Metabolically Abnormal Obesity

Observational studies have shown correlations between intramyocellular lipid (IMCL) content and muscle strength and contractile function in people with metabolically abnormal obesity. However, a clear physiologic mechanism for this association is lacking, and causation is debated. We combined immunofluorescent confocal imaging with force measurements on permeabilized muscle fibers from metabolically normal and metabolically abnormal mice and people with metabolically normal (defined as normal fasting plasma glucose and glucose tolerance) and metabolically abnormal (defined as prediabetes and type 2 diabetes) overweight/obesity to evaluate relationships among myocellular lipid droplet characteristics (droplet size and density) and biophysical (active contractile and passive viscoelastic) properties. The fiber type specificity of lipid droplet parameters varied by metabolic status and by species. It was different between mice and people across the board and different between people of different metabolic status. However, despite considerable quantities of IMCL in the metabolically abnormal groups, there were no significant differences in peak active tension or passive viscoelasticity between the metabolically abnormal and control groups in mice or people. Additionally, there were no significant relationships among IMCL parameters and biophysical variables. Thus, we conclude that IMCL accumulation per se does not impact muscle fiber biophysical properties or physically impede contraction.

ARTICLE HIGHLIGHTS

Identifying Mechanisms and Therapeutic Targets in Muscle using Bayesian Parameter Estimation with Conditional Variational Autoencoders

Cardiomyopathies, often caused by mutations in genes encoding muscle proteins, are traditionally treated by phenotyping hearts and addressing symptoms post irreversible damage. With advancements in genotyping, early diagnosis is now possible, potentially preventing such damage. However, the intricate structure of muscle and its myriad proteins make treatment predictions challenging. Here we approach the problem of estimating therapeutic targets for a mutation in mouse muscle using a spatially explicit half sarcomere muscle model. We selected 9 rate parameters in our model linked to both small molecules and cardiomyopathy-causing mutations. We then randomly varied these rate parameters and simulated an isometric twitch for each combination to generate a large training dataset. We used this dataset to train a Conditional Variational Autoencoder (CVAE), a technique used in Bayesian parameter estimation. Given simulated or experimental isometric twitches, this machine learning model is able to then predict the set of rate parameters which are most likely to yield that result. We then predict the set of rate parameters associated with both control and the cardiac Troponin C (cTnC) I61Q variant in mouse trabeculae and model parameters that recover the abnormal I61Q cTnC twitches.

SIGNIFICANCE

Machine learning techniques have potential to accelerate discoveries in biologically complex systems. However, they require large data sets and can be challenging in high dimensional systems such as cardiac muscle. In this study, we combined experimental measures of cardiac muscle twitch forces with mechanistic simulations and a newly developed mixture of Bayesian inference with neural networks (in autoencoders) to solve the inverse problem of determining the underlying kinetics for observed force generation by cardiac muscle. The autoencoders are trained on millions of simulations spanning parameter spaces that correspond to the mechanochemistry of cardiac sarcomeres. We apply the trained model to experimental data in order to infer parameters that can explain a diseased twitch and ways to recover it.

Cooperativity of weak actomyosin interaction

We report the discovery of a new regulatory mechanism of the actomyosin system in muscle. We show that the weak binding of the myosin-nucleotide complex with unregulated F-actin is a cooperative process. Hundreds of myosin heads must work together for efficient force production in muscle, but the precise mechanism by which they coordinate remains elusive. It is known that myosin initially binds actin weakly, then transitions into a strongly bound state to produce force. Using the contiguous cooperative binding model, we interpreted our experimental results in terms of a cooperativity parameter defined as an increased probability for a myosin head to bind to the actin filament next to the already bound head. Considering the geometric organization of a sarcomere, we propose the formation of cross-bridge clusters composed of up to six myosin heads bound consecutively to actin. The cooperativity of weak actomyosin interaction may explain several challenging questions in muscle physiology, such as the role of myosin isoforms in mixed-isoform hybrid muscles, or the yield of supramaximal rate of force production in decorated skinned muscle fibers.

Significance Statement

Force in striated muscle results from myosin interacting with actin. Initially, myosin attaches weakly to the thin filament, transitioning to a strongly bound state, generating force. Our experiments show high cooperativity in myosin's weak interaction with unregulated actin filament. This cooperative behavior may facilitate the formation of cross-bridge clusters and the cooperative steps of myosin heads between clusters. Consequently, the thin- and thick-filament regulation could govern the spacing between cross-bridge clusters and influence the probability of a myosin head stepping along the thin filament during force development in muscle.

Nanometer scale difference in myofilament lattice structure of muscle alter muscle function in a spatially explicit model

Crossbridge binding, state transitions, and force in active muscle is dependent on the radial spacing between the myosin-containing thick filament and the actin-containing thin filament in the filament lattice. This radial lattice spacing has been previously shown through spatially explicit modeling and experimental efforts to greatly affect quasi-static, isometric, force production in muscle. It has recently been suggested that this radial spacing might also be able to drive differences in mechanical function, or net work, under dynamic oscillations like those which occur in muscles in vivo. However, previous spatially explicit models either had no radial spacing dependence, meaning the lattice spacing could not be investigated, or did include radial spacing dependence but could not reproduce in vivo net work during dynamic oscillations and only investigated isometric contractions. Here we show the first spatially explicit model to include radial crossbridge dependence which can produce mechanical function similar to real muscle. Using this spatially explicit model of a half sarcomere, we show that when oscillated at strain amplitudes and frequencies like those in the hawk moth Manduca sexta, mechanical function (net work) does depend on the lattice spacing. In addition, since the trajectory of lattice spacing changes during dynamic oscillation can vary from organism to organism, we can prescribe a trajectory of lattice spacing changes in the spatially explicit half sarcomere model and investigate the extent to which the time course of lattice spacing changes can affect mechanical function. We simulated a half sarcomere undergoing dynamic oscillations and prescribed the Poisson's ratio of the lattice to be either 0 (constant lattice spacing) or 0.5 (isovolumetric lattice spacing changes). We also simulated net work using lattice spacing data taken from Manduca sexta which has a variable Poisson's ratio. Our simulation results indicate that the lattice spacing can change the mechanical function of muscle, and that in some cases a 1 nm difference can switch the net work of the half sarcomere model from positive (motor-like) to negative (brake-like).

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.

Design Principles and Benefits of Spatially Explicit Models of Myofilament Function

Spatially explicit models of muscle contraction include fine-scale details about the spatial, kinetic, and/or mechanical properties of the biological processes being represented within the model network. Over the past 25 years, this has primarily consisted of a set of mathematical and computational algorithms representing myosin cross-bridge activity, Ca2+-activation of contraction, and ensemble force production within a half-sarcomere representation of the myofilament network. Herein we discuss basic design principles associated with creating spatially explicit models of myofilament function, as well as model assumptions underlying model development. A brief overview of computational approaches is introduced. Opportunities for new model directions that could investigate coupled regulatory pathways between the thick-filament and thin-filaments are also presented. Given the modular design and flexibility associated with spatially explicit models, we highlight some advantages of this approach compared to other model formulations.

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.

Nucleus Mechanosensing in Cardiomyocytes

Cardiac muscle contraction is distinct from the contraction of other muscle types. The heart continuously undergoes contraction-relaxation cycles throughout an animal's lifespan. It must respond to constantly varying physical and energetic burdens over the short term on a beat-to-beat basis and relies on different mechanisms over the long term. Muscle contractility is based on actin and myosin interactions that are regulated by cytoplasmic calcium ions. Genetic variants of sarcomeric proteins can lead to the pathophysiological development of cardiac dysfunction. The sarcomere is physically connected to other cytoskeletal components. Actin filaments, microtubules and desmin proteins are responsible for these interactions. Therefore, mechanical as well as biochemical signals from sarcomeric contractions are transmitted to and sensed by other parts of the cardiomyocyte, particularly the nucleus which can respond to these stimuli. Proteins anchored to the nuclear envelope display a broad response which remodels the structure of the nucleus. In this review, we examine the central aspects of mechanotransduction in the cardiomyocyte where the transmission of mechanical signals to the nucleus can result in changes in gene expression and nucleus morphology. The correlation of nucleus sensing and dysfunction of sarcomeric proteins may assist the understanding of a wide range of functional responses in the progress of cardiomyopathic diseases.

Basic science methods for the characterization of variants of uncertain significance in hypertrophic cardiomyopathy

With the advent of next-generation whole genome sequencing, many variants of uncertain significance (VUS) have been identified in individuals suffering from inheritable hypertrophic cardiomyopathy (HCM). Unfortunately, this classification of a genetic variant results in ambiguity in interpretation, risk stratification, and clinical practice. Here, we aim to review some basic science methods to gain a more accurate characterization of VUS in HCM. Currently, many genomic data-based computational methods have been developed and validated against each other to provide a robust set of resources for researchers. With the continual improvement in computing speed and accuracy, in silico molecular dynamic simulations can also be applied in mutational studies and provide valuable mechanistic insights. In addition, high throughput in vitro screening can provide more biologically meaningful insights into the structural and functional effects of VUS. Lastly, multi-level mathematical modeling can predict how the mutations could cause clinically significant organ-level dysfunction. We discuss emerging technologies that will aid in better VUS characterization and offer a possible basic science workflow for exploring the pathogenicity of VUS in HCM. Although the focus of this mini review was on HCM, these basic science methods can be applied to research in dilated cardiomyopathy (DCM), restrictive cardiomyopathy (RCM), arrhythmogenic cardiomyopathy (ACM), or other genetic cardiomyopathies.

Biomechanical properties of honeybee abdominal muscles during stretch activation

The mechanical properties of the honeybee's abdominal muscles endow its abdomen with movement flexibility to perform various activities. However, the biomechanical properties of abdominal muscles during stretch activation remain unclear. To clarify this issue, we observed the microstructures of the abdominal muscles to obtain structural information. The similarity and symmetry of abdominal muscle distribution contribute to the ability to drive abdominal movement. Combined with the segmented structure characteristics, an experimental device to measure muscle stretch measurement of honeybees was developed to investigate the mechanical properties of the abdominal muscles. During measurement, the muscles were kept in a solution to maintain a physiological environment. The mechanical properties of abdominal muscles included phases: the ascending phase with proportional increase, stable phase with slight fluctuation, and decay phase with parabolic decline. These findings indicate that the nonlinear and rate-sensitive mechanical properties of the abdominal muscles enable them to rapidly adapt to environmental changes. The stretch force and stiffness coefficient reached 0.660 ± 0.139 mN and 14.364 ± 2.961 N/m, respectively. A simplified biomechanical model of the muscle fiber considering the hierarchical microstructure was introduced, in which the mechanical properties were consistent with the experimental data. Further analysis of the effects of the activation probability and the effective range of binding sites on the mechanical properties demonstrated the critical role in force generation, revealing the mechanism of underlying muscle stretch activation in the honeybee abdomen. The findings can provide a new reference for studying the biomechanical properties of the muscles of other arthropod insects.

Mitochondrial network configuration influences sarcomere and myosin filament structure in striated muscles

Sustained muscle contraction occurs through interactions between actin and myosin filaments within sarcomeres and requires a constant supply of adenosine triphosphate (ATP) from nearby mitochondria. However, it remains unclear how different physical configurations between sarcomeres and mitochondria alter the energetic support for contractile function. Here, we show that sarcomere cross-sectional area (CSA) varies along its length in a cell type-dependent manner where the reduction in Z-disk CSA relative to the sarcomere center is closely coordinated with mitochondrial network configuration in flies, mice, and humans. Further, we find myosin filaments near the sarcomere periphery are curved relative to interior filaments with greater curvature for filaments near mitochondria compared to sarcoplasmic reticulum. Finally, we demonstrate variable myosin filament lattice spacing between filament ends and filament centers in a cell type-dependent manner. These data suggest both sarcomere structure and myofilament interactions are influenced by the location and orientation of mitochondria within muscle cells.

FiberSim: A flexible open-source model of myofilament-level contraction

FiberSim is a flexible open-source model of myofilament-level contraction. The code uses a spatially explicit technique, meaning that it tracks the position and status of each contractile molecule within the lattice framework. This allows the model to simulate some of the mechanical effects modulated by myosin-binding protein C, as well as the dose dependence of myotropes and the effects of varying isoform expression levels. This paper provides a short introduction to FiberSim and presents simulations of tension-pCa curves with and without regulation of thick and thin filament activation by myosin-binding protein C. A myotrope dose-dependent response as well as slack/re-stretch maneuvers to assess rates of tension recovery are also presented. The software was designed to be flexible (the user can define their own model and/or protocol) and computationally efficient (simulations can be performed on a regular laptop). We hope that other investigators will use FiberSim to explore myofilament level mechanisms and to accelerate research focusing on the contractile properties of sarcomeres.

Hypertrophic cardiomyopathy β-cardiac myosin mutation (P710R) leads to hypercontractility by disrupting super relaxed state

Hypertrophic cardiomyopathy (HCM) is the most common inherited form of heart disease, associated with over 1,000 mutations, many in β-cardiac myosin (MYH7). Molecular studies of myosin with different HCM mutations have revealed a diversity of effects on ATPase and load-sensitive rate of detachment from actin. It has been difficult to predict how such diverse molecular effects combine to influence forces at the cellular level and further influence cellular phenotypes. This study focused on the P710R mutation that dramatically decreased in vitro motility velocity and actin-activated ATPase, in contrast to other MYH7 mutations. Optical trap measurements of single myosin molecules revealed that this mutation reduced the step size of the myosin motor and the load sensitivity of the actin detachment rate. Conversely, this mutation destabilized the super relaxed state in longer, two-headed myosin constructs, freeing more heads to generate force. Micropatterned human induced pluripotent derived stem cell (hiPSC)-cardiomyocytes CRISPR-edited with the P710R mutation produced significantly increased force (measured by traction force microscopy) compared with isogenic control cells. The P710R mutation also caused cardiomyocyte hypertrophy and cytoskeletal remodeling as measured by immunostaining and electron microscopy. Cellular hypertrophy was prevented in the P710R cells by inhibition of ERK or Akt. Finally, we used a computational model that integrated the measured molecular changes to predict the measured traction forces. These results confirm a key role for regulation of the super relaxed state in driving hypercontractility in HCM with the P710R mutation and demonstrate the value of a multiscale approach in revealing key mechanisms of disease.

Hypertrophic cardiomyopathy β-cardiac myosin mutation (P710R) leads to hypercontractility by disrupting super relaxed state

Hypertrophic cardiomyopathy (HCM) is the most common inherited form of heart disease, associated with over 1,000 mutations, many in β-cardiac myosin (MYH7). Molecular studies of myosin with different HCM mutations have revealed a diversity of effects on ATPase and load-sensitive rate of detachment from actin. It has been difficult to predict how such diverse molecular effects combine to influence forces at the cellular level and further influence cellular phenotypes. This study focused on the P710R mutation that dramatically decreased in vitro motility velocity and actin-activated ATPase, in contrast to other MYH7 mutations. Optical trap measurements of single myosin molecules revealed that this mutation reduced the step size of the myosin motor and the load sensitivity of the actin detachment rate. Conversely, this mutation destabilized the super relaxed state in longer, two-headed myosin constructs, freeing more heads to generate force. Micropatterned human induced pluripotent derived stem cell (hiPSC)-cardiomyocytes CRISPR-edited with the P710R mutation produced significantly increased force (measured by traction force microscopy) compared with isogenic control cells. The P710R mutation also caused cardiomyocyte hypertrophy and cytoskeletal remodeling as measured by immunostaining and electron microscopy. Cellular hypertrophy was prevented in the P710R cells by inhibition of ERK or Akt. Finally, we used a computational model that integrated the measured molecular changes to predict the measured traction forces. These results confirm a key role for regulation of the super relaxed state in driving hypercontractility in HCM with the P710R mutation and demonstrate the value of a multiscale approach in revealing key mechanisms of disease.

The Sliding Filament Theory Since Andrew Huxley: Multiscale and Multidisciplinary Muscle Research

Two groundbreaking papers published in 1954 laid out the theory of the mechanism of muscle contraction based on force-generating interactions between myofilaments in the sarcomere that cause filaments to slide past one another during muscle contraction. The succeeding decades of research in muscle physiology have revealed a unifying interest: to understand the multiscale processes-from atom to organ-that govern muscle function. Such an understanding would have profound consequences for a vast array of applications, from developing new biomimetic technologies to treating heart disease. However, connecting structural and functional properties that are relevant at one spatiotemporal scale to those that are relevant at other scales remains a great challenge. Through a lens of multiscale dynamics, we review in this article current and historical research in muscle physiology sparked by the sliding filament theory.

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.

The spatial distribution of thin filament activation influences force development and myosin activity in computational models of muscle contraction

Striated muscle contraction is initiated by Ca²⁺ binding to, and activating, thin filament regulatory units (RU) within the sarcomere, which then allows myosin cross-bridges from the opposing thick filament to bind actin and generate force. The amount of overlap between the filaments dictates how many potential cross-bridges are capable of binding, and thus how force is generated by the sarcomere. Myopathies and atrophy can impair muscle function by limiting cross-bridge interactions between the filaments, which can occur when the length of the thin filament is reduced or when RU function is disrupted. To investigate how variations in thin filament length and RU density affect ensemble cross-bridge behavior and force production, we simulated muscle contraction using a spatially explicit computational model of the half-sarcomere. Thin filament RUs were disabled either uniformly from the pointed end of the filament (to model shorter thin filament length) or randomly throughout the length of the half-sarcomere. Both uniform and random RU 'knockout' schemes decreased overall force generation during maximal and submaximal activation. The random knockout scheme also led to decreased calcium sensitivity and cooperativity of the force-pCa relationship. We also found that the rate of force development slowed with the random RU knockout, compared to the uniform RU knockout or conditions of normal RU activation. These findings imply that the relationship between RU density and force production within the sarcomere involves more complex coordination than simply the raw number of RUs available for myosin cross-bridge binding, and that the spatial pattern in which activatable RU are distributed throughout the sarcomere influences the dynamics of force production.

Multiscale modeling of twitch contractions in cardiac trabeculae

Understanding the dynamics of a cardiac muscle twitch contraction is complex because it requires a detailed understanding of the kinetic processes of the Ca2+ transient, thin-filament activation, and the myosin-actin cross-bridge chemomechanical cycle. Each of these steps has been well defined individually, but understanding how all three of the processes operate in combination is a far more complex problem. Computational modeling has the potential to provide detailed insight into each of these processes, how the dynamics of each process affect the complexity of contractile behavior, and how perturbations such as mutations in sarcomere proteins affect the complex interactions of all of these processes. The mechanisms involved in relaxation of tension during a cardiac twitch have been particularly difficult to discern due to nonhomogeneous sarcomere lengthening during relaxation. Here we use the multiscale MUSICO platform to model rat trabecular twitches. Validation of computational models is dependent on being able to simulate different experimental datasets, but there has been a paucity of data that can provide all of the required parameters in a single experiment, such as simultaneous measurements of force, intracellular Ca2+ transients, and sarcomere length dynamics. In this study, we used data from different studies collected under similar experimental conditions to provide information for all the required parameters. Our simulations established that twitches either in an isometric sarcomere or in fixed-length, multiple-sarcomere trabeculae replicate the experimental observations if models incorporate a length-tension relationship for the nonlinear series elasticity of muscle preparations and a scheme for thick-filament regulation. The thick-filament regulation assumes an off state in which myosin heads are parked onto the thick-filament backbone and are unable to interact with actin, a state analogous to the super-relaxed state. Including these two mechanisms provided simulations that accurately predict twitch contractions over a range of different conditions.

Hypothesis: Single Actomyosin Properties Account for Ensemble Behavior in Active Muscle Shortening and Isometric Contraction

Muscle contraction results from cyclic interactions between myosin II motors and actin with two sets of proteins organized in overlapping thick and thin filaments, respectively, in a nearly crystalline lattice in a muscle sarcomere. However, a sarcomere contains a huge number of other proteins, some with important roles in muscle contraction. In particular, these include thin filament proteins, troponin and tropomyosin; thick filament proteins, myosin binding protein C; and the elastic protein, titin, that connects the thin and thick filaments. Furthermore, the order and 3D organization of the myofilament lattice may be important per se for contractile function. It is possible to model muscle contraction based on actin and myosin alone with properties derived in studies using single molecules and biochemical solution kinetics. It is also possible to reproduce several features of muscle contraction in experiments using only isolated actin and myosin, arguing against the importance of order and accessory proteins. Therefore, in this paper, it is hypothesized that “single molecule actomyosin properties account for the contractile properties of a half sarcomere during shortening and isometric contraction at almost saturating Ca concentrations”. In this paper, existing evidence for and against this hypothesis is reviewed and new modeling results to support the arguments are presented. Finally, further experimental tests are proposed, which if they corroborate, at least approximately, the hypothesis, should significantly benefit future effective analysis of a range of experimental studies, as well as drug discovery efforts.

Predicting the effects of dATP on cardiac contraction using multiscale modeling of the sarcomere

2'-deoxy-ATP (dATP) is a naturally occurring small molecule that has shown promise as a therapeutic because it significantly increases cardiac myocyte force development even at low dATP/ATP ratios. To investigate mechanisms by which dATP alters myosin crossbridge dynamics, we used Brownian dynamics simulations to calculate association rates between actin and ADP- or dADP-bound myosin. These rates were then directly incorporated in a mechanistic Monte Carlo Markov Chain model of cooperative sarcomere contraction. A unique combination of increased powerstroke and detachment rates was required to match experimental steady-state and kinetic data for dATP force production in rat cardiac myocytes when the myosin attachment rate in the model was constrained by the results of a Brownian dynamics simulation. Nearest-neighbor cooperativity was seen to contribute to, but not fully explain, the steep relationship between dATP/ATP ratio and steady-state force-development observed at lower dATP concentrations. Dynamic twitch simulations performed using measured calcium transients as inputs showed that the effects of dATP on the crossbridge alone were not sufficient to explain experimentally observed enhancement of relaxation kinetics by dATP treatment. Hence, dATP may also affect calcium handling even at low concentrations. By enabling the effects of dATP on sarcomere mechanics to be predicted, this multi-scale modeling framework may elucidate the molecular mechanisms by which dATP can have therapeutic effects on cardiac contractile dysfunction.

Quadriceps Lipid Content Has Sex-Specific Associations With Whole-Muscle, Cellular, and Molecular Contractile Function in Older Adults

Increased adiposity is associated with reduced skeletal muscle function in older adults, but the mechanisms underlying this relationship remain unclear. To explore whether skeletal muscle properties track with adiposity, whole-muscle, cellular, and molecular function were examined in relation to adiposity measured at various anatomical levels in healthy older (60-80 years) men and women. Although women had greater absolute and relative body and thigh fat than men, quadriceps muscle attenuation, an index of intramuscular lipid content, was similar between sexes. At the whole-muscle level, greater quadriceps attenuation was associated with reduced knee extensor function in women, but not men. In women, decreased myosin heavy chain I and IIA fiber-specific force was associated with higher intramuscular lipid content, which may be explained, in part, by the reduced myofilament lattice stiffness found in myosin heavy chain IIA fibers. Longer myosin attachment times in myosin heavy chain I fibers from men and women were associated with greater amounts of adipose tissue, suggesting that fat deposits lead to slower myosin-actin cross-bridge kinetics. Our results indicate greater quantities of adipose tissue alter myofilament properties and cross-bridge kinetics, which may partially explain the adiposity-induced decrements in single-fiber and whole-muscle function of older adults, especially women.

Nanometer-scale structure differences in the myofilament lattice spacing of two cockroach leg muscles correspond to their different functions

Muscle is highly organized across multiple length scales. Consequently, small changes in the arrangement of myofilaments can influence macroscopic mechanical function. Two leg muscles of a cockroach have identical innervation, mass, twitch responses, length-tension curves and force-velocity relationships. However, during running, one muscle is dissipative (a 'brake'), while the other dissipates and produces significant positive mechanical work (bifunctional). Using time-resolved X-ray diffraction in intact, contracting muscle, we simultaneously measured the myofilament lattice spacing, packing structure and macroscopic force production of these muscles to test whether structural differences in the myofilament lattice might correspond to the muscles' different mechanical functions. While the packing patterns are the same, one muscle has 1 nm smaller lattice spacing at rest. Under isometric stimulation, the difference in lattice spacing disappeared, consistent with the two muscles' identical steady-state behavior. During periodic contractions, one muscle undergoes a 1 nm greater change in lattice spacing, which correlates with force. This is the first identified structural feature in the myofilament lattice of these two muscles that shares their whole-muscle dynamic differences and quasi-static similarities.

Cardiac muscle regulatory units are predicted to interact stronger than neighboring cross-bridges

Strong interactions between cross-bridges (XB) and regulatory units (RU) lead to a steep response of cardiac muscle to an increase in intracellular calcium. We developed a model to quantitatively assess the influence of different types of interactions within the sarcomere on the properties of cardiac muscle. In the model, the ensembles consisting of cross-bridge groups connected by elastic tropomyosin are introduced, and their dynamics is described by a set of partial differential equations. Through large scans in the free energy landscape, we demonstrate the different influence of RU-RU, XB-XB, and XB-RU interactions on the cooperativity coefficient of calcium binding, developed maximal force, and calcium sensitivity. The model solution was fitted to reproduce experimental data on force development during isometric contraction, shortening in physiological contraction, and ATP consumption by acto-myosin. On the basis of the fits, we quantified the free energy change introduced through RU-RU and XB-XB interactions and showed that RU-RU interaction leads to ~ 5 times larger change in the free energy profile of the reaction than XB-XB interaction. Due to the deterministic description of muscle contraction and its thermodynamic consistency, we envision that the developed model can be used to study heart muscle biophysics on tissue and organ levels.

The effects of inorganic phosphate on muscle force development and energetics: challenges in modelling related to experimental uncertainties

Muscle force and power are developed by myosin cross-bridges, which cyclically attach to actin, undergo a force-generating transition and detach under turnover of ATP. The force-generating transition is intimately associated with release of inorganic phosphate (Pi) but the exact sequence of events in relation to the actual Pi release step is controversial. Details of this process are reflected in the relationships between [Pi] and the developed force and shortening velocity. In order to account for these relationships, models have proposed branched kinetic pathways or loose coupling between biochemical and force-generating transitions. A key hypothesis underlying the present study is that such complexities are not required to explain changes in the force–velocity relationship and ATP turnover rate with altered [Pi]. We therefore set out to test if models without branched kinetic paths and Pi-release occurring before the main force-generating transition can account for effects of varied [Pi] (0.1–25 mM). The models tested, one assuming either linear or non-linear cross-bridge elasticity, account well for critical aspects of muscle contraction at 0.5 mM Pi but their capacity to account for the maximum power output vary. We find that the models, within experimental uncertainties, account for the relationship between [Pi] and isometric force as well as between [Pi] and the velocity of shortening at low loads. However, in apparent contradiction with available experimental findings, the tested models produce an anomalous force–velocity relationship at elevated [Pi] and high loads with more than one possible velocity for a given load. Nevertheless, considering experimental uncertainties and effects of sarcomere non-uniformities, these discrepancies are insufficient to refute the tested models in favour of more complex alternatives.

Sex- and fiber-type-related contractile properties in human single muscle fiber

This study aimed to examine the distribution and contractile properties of single muscle fiber sex/myosin heavy chain (MHC) type-related differences and to evaluate the correlation of cross-sectional area (CSA) and specific force (SF) in a single muscle fiber. Six young men and six young women were participated in this study. Muscle sample was obtained from vastus lateralis muscle. To examine potential gender differences within each fiber contractile properties (CSA, maximal isometric force, SF, maximal shortening velocity) and relationship between CSA and SF of single fiber using Pearson correlation. After mechanical measurements, single muscle fiber determined MHC isoforms using silver stain. MHC isoform composition did not differ by sex (chi-square=6.978, P=0.073). There were sex-related differences in CSA and maximal isometric force (P<0.05), but no fiber type-related differences (P>0.05). Related to SF and maximal shortening velocity, there were no sex-related differences only fiber type-related differences (P<0.05). However, there were differences in SF between single fiber types in men but not in women. A negative correlation was found between CSA and SF in both men and women (P<0.05). It is suggested that there might be different mechanical properties of cross-bridges according to sex.

Comparing models with one versus multiple myosin-binding sites per actin target zone: The power of simplicity

Mechanokinetic statistical models describe the mechanisms of muscle contraction on the basis of the average behavior of a large ensemble of actin-myosin motors. Such models often assume that myosin II motor domains bind to regularly spaced, discrete target zones along the actin-based thin filaments and develop force in a series of strain-dependent transitions under the turnover of ATP. The simplest models assume that there is just one myosin-binding site per target zone and a uniform spatial distribution of the myosin motor domains in relation to each site. However, most of the recently developed models assume three myosin-binding sites per target zone, and some models include a spatially explicit 3-D treatment of the myofilament lattice and thereby of the geometry of the actin-myosin contact points. Here, I show that the predictions for steady-state contractile behavior of muscle are very similar whether one or three myosin-binding sites per target zone is assumed, provided that the model responses are appropriately scaled to the number of sites. Comparison of the model predictions for isometrically contracting mammalian muscle cells suggests that each target zone contains three or more myosin-binding sites. Finally, I discuss the strengths and weaknesses of one-site spatially inexplicit models in relation to three-site models, including those that take into account the detailed 3-D geometry of the myofilament lattice. The results of this study suggest that single-site models, with reduced computational cost compared with multisite models, are useful for several purposes, e.g., facilitated molecular mechanistic insights.

A Spatially Explicit Model Shows How Titin Stiffness Modulates Muscle Mechanics and Energetics

In striated muscle, the giant protein titin spans the entire length of a half-sarcomere and extends from the backbone of the thick filament, reversibly attaches to the thin filaments, and anchors to the dense protein network of the z-disk capping the end of the half-sarcomere. However, little is known about the relationship between the basic mechanical properties of titin and muscle contractility. Here, we build upon our previous multi-filament, spatially explicit computational model of the half-sarcomere by incorporating the nonlinear mechanics of titin filaments in the I-band. We vary parameters of the nonlinearity to understand the effects of titin stiffness on contraction dynamics and efficiency. We do so by simulating isometric contraction for a range of sarcomere lengths (SLs; 1.6-3.25 µm). Intermediate values of titin stiffness accurately reproduce the passive force-SL relation for skeletal muscle. The maximum force-SL relation is not affected by titin for SL≤2.5 µm. However, as titin stiffness increases, maximum force for the four thick filament system at SL = 3.0 µm significantly decreases from 103.2 ± 2 to 58.8 ± 1 pN. Additionally, by monitoring ATP consumption, we measure contraction efficiency as a function of titin stiffness. We find that at SL = 3.0 µm, efficiency significantly decreases from 13.9 ± 0.4 to 7.0 ± 0.3 pN/ATP when increasing titin stiffness, with little or no effect below 2.5 µm. Taken together, our results suggest that, despite an increase in the fraction of motors bound to actin along the descending limb when titin is stiffer, the force-generating capacity of the motors is reduced. These results suggest that titin stiffness has the potential to affect contractile efficiency.

Acidosis affects muscle contraction by slowing the rates myosin attaches to and detaches from actin

The loss of muscle force and power during fatigue from intense contractile activity is associated with, and likely caused by, elevated levels of phosphate ([Formula: see text]) and hydrogen ions (decreased pH). To understand how these deficits in muscle performance occur at the molecular level, we used direct measurements of mini-ensembles of myosin generating force in the laser trap assay at pH 7.4 and 6.5. The data are consistent with a mechanochemical model in which a decrease in pH reduces myosin's detachment from actin (by slowing ADP release), increases non-productive myosin binding (by detached myosin rebinding without a powerstroke), and reduces myosin's attachment to actin (by slowing the weak-to-strong binding transition). Additional support of this mechanism is found by incorporating it into a branched pathway model for the effects of [Formula: see text] on myosin's interaction with actin. Including pH-dependence in one additional parameter (acceleration of [Formula: see text]-induced detachment), the model reproduces experimental measurements at high and low pH, and variable [Formula: see text], from the single molecule to large ensemble levels. Furthermore, when scaled up, the model predicts force-velocity relationships that are consistent with muscle fiber measurements. The model suggests that reducing pH has two opposing effects, a decrease in attachment favoring a decrease in muscle force and a decrease in detachment favoring an increase in muscle force. Depending on experimental details, the addition of [Formula: see text] can strengthen one or the other effect, resulting in either synergistic or antagonistic effects. This detailed molecular description suggests a molecular basis for contractile failure during muscle fatigue.

Flightin maintains myofilament lattice organization required for optimal flight power and courtship song quality in Drosophila

The indirect flight muscles (IFMs) of Drosophila and other insects with asynchronous flight muscles are characterized by a crystalline myofilament lattice structure. The high-order lattice regularity is considered an adaptation for enhanced power output, but supporting evidence for this claim is lacking. We show that IFMs from transgenic flies expressing flightin with a deletion of its poorly conserved N-terminal domain (fln^ΔN62 ) have reduced inter-thick filament spacing and a less regular lattice. This resulted in a decrease in flight ability by 33% and in skinned fibre oscillatory power output by 57%, but had no effect on wingbeat frequency or frequency of maximum power output, suggesting that the underlying actomyosin kinetics is not affected and that the flight impairment arises from deficits in force transmission. Moreover, we show that fln^ΔN62 males produced an abnormal courtship song characterized by a higher sine song frequency and a pulse song with longer pulses and longer inter-pulse intervals (IPIs), the latter implicated in male reproductive success. When presented with a choice, wild-type females chose control males over mutant males in 92% of the competition events. These results demonstrate that flightin N-terminal domain is required for optimal myofilament lattice regularity and IFM activity, enabling powered flight and courtship song production. As the courtship song is subject to female choice, we propose that the low amino acid sequence conservation of the N-terminal domain reflects its role in fine-tuning species-specific courtship songs.

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.

Multiscale and Multiaxial Mechanics of Vascular Smooth Muscle

Mathematical models can facilitate an integrative understanding of the complexity underlying biological structure and function, but they must be informed and validated by empirical data. Uniaxial contraction of an arterial ring is a well-used in vitro approach for studying characteristics of smooth muscle contractility even though this experimental arrangement does not mimic the in vivo vascular geometry or loading. In contrast, biaxial contraction of an inflated and axially extended excised vessel provides broader information, both passive and active, under more realistic conditions. Few investigations have compared these two in vitro approaches directly, namely how their results overlap, how they differ, or if each provides unique complementary information. Toward this end, we present, to our knowledge, a new multiscale mathematical model of arterial contractility accounting for structural and functional constituents at molecular, cellular, and tissue levels. The artery is assumed to be a thick-walled incompressible cylinder described by an anisotropic model of the extracellular matrix and, to our knowledge, novel model of smooth muscle contractility. The latter includes a 3D structural sensitivity to deformation, including microscale muscle filament overlap and filament lattice spacing. The overall model captures uniaxial and biaxial experimental contraction data, which was not possible when accounting for filament overlap alone. The model also enables parameter sensitivity studies, which confirmed that uniaxial contraction tests are not as efficient as biaxial tests for identifying changes in vascular smooth muscle function.

Three-dimensional stochastic model of actin-myosin binding in the sarcomere lattice

The effect of molecule tethering in three-dimensional (3-D) space on bimolecular binding kinetics is rarely addressed and only occasionally incorporated into models of cell motility. The simplest system that can quantitatively determine this effect is the 3-D sarcomere lattice of the striated muscle, where tethered myosin in thick filaments can only bind to a relatively small number of available sites on the actin filament, positioned within a limited range of thermal movement of the myosin head. Here we implement spatially explicit actomyosin interactions into the multiscale Monte Carlo platform MUSICO, specifically defining how geometrical constraints on tethered myosins can modulate state transition rates in the actomyosin cycle. The simulations provide the distribution of myosin bound to sites on actin, ensure conservation of the number of interacting myosins and actin monomers, and most importantly, the departure in behavior of tethered myosin molecules from unconstrained myosin interactions with actin. In addition, MUSICO determines the number of cross-bridges in each actomyosin cycle state, the force and number of attached cross-bridges per myosin filament, the range of cross-bridge forces and accounts for energy consumption. At the macroscopic scale, MUSICO simulations show large differences in predicted force-velocity curves and in the response during early force recovery phase after a step change in length comparing to the two simplest mass action kinetic models. The origin of these differences is rooted in the different fluxes of myosin binding and corresponding instantaneous cross-bridge distributions and quantitatively reflects a major flaw of the mathematical description in all mass action kinetic models. Consequently, this new approach shows that accurate recapitulation of experimental data requires significantly different binding rates, number of actomyosin states, and cross-bridge elasticity than typically used in mass action kinetic models to correctly describe the biochemical reactions of tethered molecules and their interaction energetics.

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.

Contributions of Ca2+-Independent Thin Filament Activation to Cardiac Muscle Function

Although Ca2+ is the principal regulator of contraction in striated muscle, in vitro evidence suggests that some actin-myosin interaction is still possible even in its absence. Whether this Ca2+-independent activation (CIA) occurs under physiological conditions remains unclear, as does its potential impact on the function of intact cardiac muscle. The purpose of this study was to investigate CIA using computational analysis. We added a structurally motivated representation of this phenomenon to an existing myofilament model, which allowed predictions of CIA-dependent muscle behavior. We found that a certain amount of CIA was essential for the model to reproduce reported effects of nonfunctional troponin C on myofilament force generation. Consequently, those data enabled estimation of ΔGCIA, the energy barrier for activating a thin filament regulatory unit in the absence of Ca2+. Using this estimate of ΔGCIA as a point of reference (∼7 kJ mol(-1)), we examined its impact on various aspects of muscle function through additional simulations. CIA decreased the Hill coefficient of steady-state force while increasing myofilament Ca2+ sensitivity. At the same time, CIA had minimal effect on the rate of force redevelopment after slack/restretch. Simulations of twitch tension show that the presence of CIA increases peak tension while profoundly delaying relaxation. We tested the model's ability to represent perturbations to the Ca2+ regulatory mechanism by analyzing twitch records measured in transgenic mice expressing a cardiac troponin I mutation (R145G). The effects of the mutation on twitch dynamics were fully reproduced by a single parameter change, namely lowering ΔGCIA by 2.3 kJ mol(-1) relative to its wild-type value. Our analyses suggest that CIA is present in cardiac muscle under normal conditions and that its modulation by gene mutations or other factors can alter both systolic and diastolic function.

Temperature effect on the chemomechanical regulation of substeps within the power stroke of a single Myosin II

Myosin IIs in the skeletal muscle are highly efficient nanoscale machines evolved in nature. Understanding how they function can not only bring insights into various biological processes but also provide guidelines to engineer synthetic nanoscale motors working in the vicinity of thermal noise. Though it was clearly demonstrated that the behavior of a skeletal muscle fiber, or that of a single myosin was strongly affected by the temperature, how exactly the temperature affects the kinetics of a single myosin is not fully understood. By adapting the newly developed transitional state model, which successfully explained the intriguing motor force regulation during skeletal muscle contraction, here we systematically explain how exactly the power stroke of a single myosin proceeds, with the consideration of the chemomechanical regulation of sub-steps within the stroke. The adapted theory is then utilized to investigate the temperature effect on various aspects of the power stroke. Our analysis suggests that, though swing rates, the isometric force, and the maximal stroke size all strongly vary with the temperature, the temperature can have a very small effect on the releasable elastic energy within the power stroke.

Direct Measurements of Local Coupling between Myosin Molecules Are Consistent with a Model of Muscle Activation

Muscle contracts due to ATP-dependent interactions of myosin motors with thin filaments composed of the proteins actin, troponin, and tropomyosin. Contraction is initiated when calcium binds to troponin, which changes conformation and displaces tropomyosin, a filamentous protein that wraps around the actin filament, thereby exposing myosin binding sites on actin. Myosin motors interact with each other indirectly via tropomyosin, since myosin binding to actin locally displaces tropomyosin and thereby facilitates binding of nearby myosin. Defining and modeling this local coupling between myosin motors is an open problem in muscle modeling and, more broadly, a requirement to understanding the connection between muscle contraction at the molecular and macro scale. It is challenging to directly observe this coupling, and such measurements have only recently been made. Analysis of these data suggests that two myosin heads are required to activate the thin filament. This result contrasts with a theoretical model, which reproduces several indirect measurements of coupling between myosin, that assumes a single myosin head can activate the thin filament. To understand this apparent discrepancy, we incorporated the model into stochastic simulations of the experiments, which generated simulated data that were then analyzed identically to the experimental measurements. By varying a single parameter, good agreement between simulation and experiment was established. The conclusion that two myosin molecules are required to activate the thin filament arises from an assumption, made during data analysis, that the intensity of the fluorescent tags attached to myosin varies depending on experimental condition. We provide an alternative explanation that reconciles theory and experiment without assuming that the intensity of the fluorescent tags varies.

Despite decades of study, there is no clear connection between muscle contraction at the molecular and the macroscopic scale. For example, we cannot yet predict how a genetic defect in a muscle protein will result in a physiological change in the heart. This multi-scale understanding is difficult, in part, because molecules cooperate during muscle contraction; that is, one molecule’s behavior is influenced by the behavior of its neighbors. It is difficult to make direct measurements from such coupled molecular systems and also difficult to describe them quantitatively. Despite these obstacles, we recently published experimental measurements and theoretical models of this coupling, but there were apparent discrepancies between the two. Here, we use detailed computer simulations of these experiments to show that, in fact, the measurements agree with the model to a remarkable extent. This agreement suggests that the model captures the essential molecular events that underlie the coupling between muscle molecules. This removes a major obstacle to a multi-scale understanding of muscle contraction and, while more work is necessary, suggests that a connection between the molecular and macroscopic scale is within reach.

Myosin MgADP release rate decreases at longer sarcomere length to prolong myosin attachment time in skinned rat myocardium

Cardiac contractility increases as sarcomere length increases, suggesting that intrinsic molecular mechanisms underlie the Frank-Starling relationship to confer increased cardiac output with greater ventricular filling. The capacity of myosin to bind with actin and generate force in a muscle cell is Ca(2+) regulated by thin-filament proteins and spatially regulated by sarcomere length as thick-to-thin filament overlap varies. One mechanism underlying greater cardiac contractility as sarcomere length increases could involve longer myosin attachment time (ton) due to slowed myosin kinetics at longer sarcomere length. To test this idea, we used stochastic length-perturbation analysis in skinned rat papillary muscle strips to measure ton as [MgATP] varied (0.05-5 mM) at 1.9 and 2.2 μm sarcomere lengths. From this ton-MgATP relationship, we calculated cross-bridge MgADP release rate and MgATP binding rates. As MgATP increased, ton decreased for both sarcomere lengths, but ton was roughly 70% longer for 2.2 vs. 1.9 μm sarcomere length at maximally activated conditions. These ton differences were driven by a slower MgADP release rate at 2.2 μm sarcomere length (41 ± 3 vs. 74 ± 7 s(-1)), since MgATP binding rate was not different between the two sarcomere lengths. At submaximal activation levels near the pCa50 value of the tension-pCa relationship for each sarcomere length, length-dependent increases in ton were roughly 15% longer for 2.2 vs. 1.9 μm sarcomere length. These changes in cross-bridge kinetics could amplify cooperative cross-bridge contributions to force production and thin-filament activation at longer sarcomere length and suggest that length-dependent changes in myosin MgADP release rate may contribute to the Frank-Starling relationship in the heart.

Magnetic susceptibility anisotropy of myocardium imaged by cardiovascular magnetic resonance reflects the anisotropy of myocardial filament α-helix polypeptide bonds

BACKGROUND

A key component of evaluating myocardial tissue function is the assessment of myofiber organization and structure. Studies suggest that striated muscle fibers are magnetically anisotropic, which, if measurable in the heart, may provide a tool to assess myocardial microstructure and function.

METHODS

To determine whether this weak anisotropy is observable and spatially quantifiable with cardiovascular magnetic resonance (CMR), both gradient-echo and diffusion-weighted data were collected from intact mouse heart specimens at 9.4 Tesla. Susceptibility anisotropy was experimentally calculated using a voxelwise analysis of myocardial tissue susceptibility as a function of myofiber angle. A myocardial tissue simulation was developed to evaluate the role of the known diamagnetic anisotropy of the peptide bond in the observed susceptibility contrast.

RESULTS

The CMR data revealed that myocardial tissue fibers that were parallel and perpendicular to the magnetic field direction appeared relatively paramagnetic and diamagnetic, respectively. A linear relationship was found between the magnetic susceptibility of the myocardial tissue and the squared sine of the myofiber angle with respect to the field direction. The multi-filament model simulation yielded susceptibility anisotropy values that reflected those found in the experimental data, and were consistent that this anisotropy decreased as the echo time increased.

CONCLUSIONS

Though other sources of susceptibility anisotropy in myocardium may exist, the arrangement of peptide bonds in the myofilaments is a significant, and likely the most dominant source of susceptibility anisotropy. This anisotropy can be further exploited to probe the integrity and organization of myofibers in both healthy and diseased heart tissue.

Constriction model of actomyosin ring for cytokinesis by fission yeast using a two-state sliding filament mechanism

We developed a model describing the structure and contractile mechanism of the actomyosin ring in fission yeast, Schizosaccharomyces pombe. The proposed ring includes actin, myosin, and α-actinin, and is organized into a structure similar to that of muscle sarcomeres. This structure justifies the use of the sliding-filament mechanism developed by Huxley and Hill, but it is probably less organized relative to that of muscle sarcomeres. Ring contraction tension was generated via the same fundamental mechanism used to generate muscle tension, but some physicochemical parameters were adjusted to be consistent with the proposed ring structure. Simulations allowed an estimate of ring constriction tension that reproduced the observed ring constriction velocity using a physiologically possible, self-consistent set of parameters. Proposed molecular-level properties responsible for the thousand-fold slower constriction velocity of the ring relative to that of muscle sarcomeres include fewer myosin molecules involved, a less organized contractile configuration, a low α-actinin concentration, and a high resistance membrane tension. Ring constriction velocity is demonstrated as an exponential function of time despite a near linear appearance. We proposed a hypothesis to explain why excess myosin heads inhibit constriction velocity rather than enhance it. The model revealed how myosin concentration and elastic resistance tension are balanced during cytokinesis in S. pombe.

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.

Molecular determinants of force production in human skeletal muscle fibers: effects of myosin isoform expression and cross-sectional area

Skeletal muscle contractile performance is governed by the properties of its constituent fibers, which are, in turn, determined by the molecular interactions of the myofilament proteins. To define the molecular determinants of contractile function in humans, we measured myofilament mechanics during maximal Ca(2+)-activated and passive isometric conditions in single muscle fibers with homogenous (I and IIA) and mixed (I/IIA and IIA/X) myosin heavy chain (MHC) isoforms from healthy, young adult male (n = 5) and female (n = 7) volunteers. Fibers containing only MHC II isoforms (IIA and IIA/X) produced higher maximal Ca(2+)-activated forces over the range of cross-sectional areas (CSAs) examined than MHC I fibers, resulting in higher (24-42%) specific forces. The number and/or stiffness of the strongly bound myosin-actin cross bridges increased in the higher force-producing MHC II isoforms and, in all isoforms, better predicted force than CSA. In men and women, cross-bridge kinetics, in terms of myosin attachment time and rate of myosin force production, were independent of CSA, although women had faster (7-15%) kinetics. The relative proportion of cross bridges and/or their stiffness was reduced as fiber size increased, causing a decline in specific force. Results from our examination of molecular mechanisms across the range of physiological CSAs explain the variation in specific force among the different fiber types in human skeletal muscle, which may have relevance to understanding how various physiological and pathophysiological conditions modulate single-fiber and whole muscle contractility.

Kinetics of cardiac myosin isoforms in mouse myocardium are affected differently by presence of myosin binding protein-C

We tested whether cardiac myosin binding protein-C (cMyBP-C) affects myosin cross-bridge kinetics in the two cardiac myosin heavy chain (MyHC) isoforms. Mice lacking cMyBP-C (t/t) and transgenic controls (WT(t/t)) were fed L-thyroxine (T4) to induce 90/10% expression of α/β-MyHC. Non-transgenic (NTG) and t/t mice were fed 6-n-propyl-2-thiouracil (PTU) to induce 100% expression of β-MyHC. Ca(2+)-activated, chemically-skinned myocardium underwent length perturbation analysis with varying [MgATP] to estimate the MgADP release rate (k(-ADP)) and MgATP binding rate (k(+ATP)). Values for (k(-ADP)) were not significantly different between t/t(T4) (102.2 ± 7.0 s(-1)) and WT(t/t)(T4) (91.3 ± 8.9 s(-1)), but k(+ATP)) was lower in t/t(T4) (165.9 ± 12.5 mM(-1) s(-1)) compared to WT(t/t)(T4) (298.6 ± 15.7 mM(-1) s(-1), P < 0.01). In myocardium expressing β-MyHC, values for k(-ADP) were higher in t/t(PTU) (24.8 ± 1.0 s(-1)) compared to NTG(PTU) (15.6 ± 1.3 s(-1), P < 0.01), and k(+ATP) was not different. At saturating [MgATP], myosin detachment rate approximates k(-ADP), and detachment rate decreased as sarcomere length (SL) was increased in both t/t(T4) and WT(t/t)(T4) with similar sensitivities to SL. In myocardium expressing β-MyHC, detachment rate decreased more as SL increased in t/t(PTU) (21.5 ± 1.3 s(-1) at 2.2 μm and 13.3 ± 0.9 s(-1) at 3.3 μm) compared to NTGPTU (15.8 ± 0.3 s(-1) at 2.2 μm and 10.9 ± 0.3 s(-1) at 3.3 μm) as detected by repeated-measures ANOVA (P < 0.01). These findings suggest that cMyBP-C reduces MgADP release rate for β-MyHC, but not for α-MyHC, even as the number of cMyBP-C that overlap with the thin filament is reduced to zero. Therefore, cMyBP-C appears to affect β-MyHC kinetics independent of its interaction with the thin filament.

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.

Is sarcomere lattice geometry optimal? Analysis of several potential virtual polygon cross-sectional patterns for actin and myosin myofilaments in muscle

The hexagonal arrangement of actin filaments in skeletal muscle is not the fundamental geometrical or functioning myofilament unit. This analysis of several possible sarcomere lattice geometries for the arrangement of the actin and myosin filaments identifies several geometrical constraints that can be compared for their effect on muscle sarcomere functioning and efficiency. Three distinct virtual polygons, with myosins at their vertices and that tessellate the plane, are compared for both centered actin and perimeter actin arrangements. The analysis evaluates the optimal ratio of myosin to actin filaments, the packing density, and the effect on new myofilament formation in muscle hypertrophy for the various lattice geometries. The results support the view that no single measure of geometrical effectiveness can evaluate definitively the efficiency of any particular arrangement of the myofilaments. The analysis provides quantitative measures of several parameters that, taken overall, support the effectiveness of the myofilament arrangement in Nature. It provides a new definition of the fundamental myofilament unit (FMU). It is possible to calculate the number of actin and myosin myofilaments that need to be added to each polygon arrangement of the myofilaments to create a new FMU for that specific geometry. This leads to useful conclusions about the biochemical efficiency involved in where such units arise in the course of muscle hypertrophy. It supports the idea that the evolutionary endpoint for optimizing muscle's force-generating function can be better understood via the concepts of a FMU and the polygon arrangement of the sarcomere lattice geometry.

Molecular and subcellular-scale modeling of nucleotide diffusion in the cardiac myofilament lattice

Contractile function of cardiac cells is driven by the sliding displacement of myofilaments powered by the cycling myosin crossbridges. Critical to this process is the availability of ATP, which myosin hydrolyzes during the cross-bridge cycle. The diffusion of adenine nucleotides through the myofilament lattice has been shown to be anisotropic, with slower radial diffusion perpendicular to the filament axis relative to parallel, and is attributed to the periodic hexagonal arrangement of the thin (actin) and thick (myosin) filaments. We investigated whether atomistic-resolution details of myofilament proteins can refine coarse-grain estimates of diffusional anisotropy for adenine nucleotides in the cardiac myofibril, using homogenization theory and atomistic thin filament models from the Protein Data Bank. Our results demonstrate considerable anisotropy in ATP and ADP diffusion constants that is consistent with experimental measurements and dependent on lattice spacing and myofilament overlap. A reaction-diffusion model of the half-sarcomere further suggests that diffusional anisotropy may lead to modest adenine nucleotide gradients in the myoplasm under physiological conditions.