Axial and radial forces of cross-bridges depend on lattice spacing

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.

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).

An In Silico Cardiomyocyte Reveals the Impact of Changes in CaMKII Signalling on Cardiomyocyte Contraction Kinetics in Hypertrophic Cardiomyopathy

Hypertrophic cardiomyopathy (HCM) is characterised by asymmetric left ventricular hypertrophy, ventricular arrhythmias, and cardiomyocyte dysfunction that may cause sudden death. HCM is associated with mutations in sarcomeric proteins and is usually transmitted as an autosomal-dominant trait. The aim of this in silico study was to assess the mechanisms that underlie the altered electrophysiological activity, contractility, regulation of energy metabolism, and crossbridge cycling in HCM at the single-cell level. To investigate this, we developed a human ventricular cardiomyocyte model that incorporates electrophysiology, metabolism, and force generation. The model was validated by its ability to reproduce the experimentally observed kinetic properties of human HCM induced by (a) remodelling of several ion channels and Ca2+-handling proteins arising from altered Ca2+/calmodulin kinase II signalling pathways and (b) increased Ca2+ sensitivity of the myofilament proteins. Our simulation showed a decreased phosphocreatine-to-ATP ratio (-9%) suggesting a negative mismatch between energy expenditure and supply. Using a spatial myofilament half-sarcomere model, we also compared the fraction of detached, weakly bound, and strongly bound crossbridges in the control and HCM conditions. Our simulations showed that HCM has more crossbridges in force-producing states than in the control condition. In conclusion, our model reveals that impaired crossbridge kinetics is accompanied by a negative mismatch between the ATP supply and demand ratio. This suggests that improving this ratio may reduce the incidence of sudden death in HCM.

Potentiation of force by extracellular potassium is not dependent on muscle length in mouse EDL muscle

Increases in myofiber extracellular potassium with prolonged contractile activity can potentiate twitch force. Activity-dependent potentiation, another mechanism of force increase in skeletal muscle, has a strong dependence on muscle or sarcomere length. Thus, potassium-mediated twitch potentiation could also be length-dependent. However, this has not been previously investigated. To this end, we used isolated C57BL/6 mouse extensor digitorum longus (EDL) muscles and elicited twitches at 0.9 Lo, Lo, and 1.1 Lo (Lo refers to optimal length) in normal (5 mM) and high (10 mM) potassium solutions. Potentiation magnitude was similar to previous observations and was not significantly different between lengths (0.9 Lo: 12.3 ± 4.4%, Lo: 12.2 ± 3.6%, 1.1 Lo: 11.8 ± 4.8%, values are means ± SD). Exposure to dantrolene sodium, a compound that attenuates calcium release, reduced twitch force across lengths by ∼70%. When dantrolene-affected muscles were subsequently exposed to high potassium, potentiation was similar to that observed in the absence of the former. In total, these findings provide novel information on potassium-mediated twitch potentiation.NEW & NOTEWORTHY Here, we investigated the length-dependence of twitch force potentiation by extracellular potassium in mouse extensor digitorum longus (EDL) in vitro, at 25°C. Potentiation magnitude did not display a statistically significant difference between the examined muscle lengths. These results describe, for the first time, the relationship of this form of potentiation with muscle length, thus furthering the understanding of how it is integrated in in vivo muscle function.

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.

Machine learning meets Monte Carlo methods for models of muscle's molecular machinery to classify mutations

The timing and magnitude of force generation by a muscle depend on complex interactions in a compliant, contractile filament lattice. Perturbations in these interactions can result in cardiac muscle diseases. In this study, we address the fundamental challenge of connecting the temporal features of cardiac twitches to underlying rate constants and their perturbations associated with genetic cardiomyopathies. Current state-of-the-art metrics for characterizing the mechanical consequence of cardiac muscle disease do not utilize information embedded in the complete time course of twitch force. We pair dimension reduction techniques and machine learning methods to classify underlying perturbations that shape the timing of twitch force. To do this, we created a large twitch dataset using a spatially explicit Monte Carlo model of muscle contraction. Uniquely, we modified the rate constants of this model in line with mouse models of cardiac muscle disease and varied mutation penetrance. Ultimately, the results of this study show that machine learning models combined with biologically informed dimension reduction techniques can yield excellent classification accuracy of underlying muscle perturbations.

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.

The effect of muscle length on post-tetanic potentiation of C57BL/6 and skMLCK-/- mouse EDL muscles

Post-tetanic potentiation of fast-twitch skeletal muscle is dependent on muscle length, with greater potentiation observed at shorter compared to longer lengths. The structural effects of the primary potentiation mechanism, phosphorylation of the regulatory light chain (RLC) of myosin, are thought to explain this relationship. The purpose of these experiments was to determine whether the length-dependence of potentiation would be attenuated in the absence of RLC phosphorylation. To this end, we compared isometric twitch potentiation of mouse extensor digitorum longus (EDL) muscles with (wildtype, WT) and without (skeletal myosin light chain kinase knockout, skMLCK^-/-) phosphorylation. Force was measured at five muscle lengths (0.90 L_o, 0.95 L_o, L_o, 1.05 L_o, 1.10 L_o, where L_o refers to optimal length) prior to and following a tetanic train. In accordance with prior findings, potentiation was dependent on muscle length, with greater values observed at short (e.g., 44.3 ± 4.6% for WT, 33.5 ± 6.2% for skMLCK^-/-, at 0.90 L_o) compared to long lengths (e.g., 16.9 ± 1.3% for WT, 9.1 ± 1.8% for skMLCK^-/-, at 1.10 L_o) in both genotypes. WT muscles displayed greater potentiation compared to their skMLCK^-/- counterparts across lengths (e.g., 16.9 ± 1.6% vs 7.3 ± 1.5% at L_o). However, the relationship between potentiation and muscle length was not different between genotypes. Thus, the alternative mechanisms of potentiation, present in the skMLCK^-/- EDL, display a length-dependence of post-tetanic potentiation similar to RLC phosphorylation-dominant potentiation. Additional mechanisms may be required to explain the length-dependence of potentiation.

Muscle active force-length curve explained by an electrophysical model of interfilament spacing

The active isometric force-length relation (FLR) of striated muscle sarcomeres is central to understanding and modeling muscle function. The mechanistic basis of the descending arm of the FLR is well explained by the decreasing thin:thick filament overlap that occurs at long sarcomere lengths. The mechanistic basis of the ascending arm of the FLR (the decrease in force that occurs at short sarcomere lengths), alternatively, has never been well explained. Because muscle is a constant-volume system, interfilament lattice distances must increase as sarcomere length shortens. This increase would decrease thin and thick-filament electrostatic interactions independently of thin:thick filament overlap. To examine this effect, we present here a fundamental, physics-based model of the sarcomere that includes filament molecular properties, calcium binding, sarcomere geometry including both thin:thick filament overlap and interfilament radial distance, and electrostatics. The model gives extremely good fits to existing FLR data from a large number of different muscles across their entire range of measured activity levels, with the optimized parameter values in all cases lying within anatomically and physically reasonable ranges. A local first-order sensitivity analysis (varying individual parameters while holding the values of all others constant) shows that model output is most sensitive to a subset of model parameters, most of which are related to sarcomere geometry, with model output being most sensitive to interfilament radial distance. This conclusion is supported by re-running the fits with only this parameter subset being allowed to vary, which increases fit errors only moderately. These results show that the model well reproduces existing experimental data, and indicate that changes in interfilament spacing play as central a role as changes in filament overlap in determining the FLR, particularly on its ascending arm.

Small Angle X-ray Diffraction as a Tool for Structural Characterization of Muscle Disease

Small angle X-ray fiber diffraction is the method of choice for obtaining molecular level structural information from striated muscle fibers under hydrated physiological conditions. For many decades this technique had been used primarily for investigating basic biophysical questions regarding muscle contraction and regulation and its use confined to a relatively small group of expert practitioners. Over the last 20 years, however, X-ray diffraction has emerged as an important tool for investigating the structural consequences of cardiac and skeletal myopathies. In this review we show how simple and straightforward measurements, accessible to non-experts, can be used to extract biophysical parameters that can help explain and characterize the physiology and pathology of a given experimental system. We provide a comprehensive guide to the range of the kinds of measurements that can be made and illustrate how they have been used to provide insights into the structural basis of pathology in a comprehensive review of the literature. We also show how these kinds of measurements can inform current controversies and indicate some future directions.

Subcellular Remodeling in Filamin C Deficient Mouse Hearts Impairs Myocyte Tension Development during Progression of Dilated Cardiomyopathy

Dilated cardiomyopathy (DCM) is a life-threatening form of heart disease that is typically characterized by progressive thinning of the ventricular walls, chamber dilation, and systolic dysfunction. Multiple mutations in the gene encoding filamin C (FLNC), an actin-binding cytoskeletal protein in cardiomyocytes, have been found in patients with DCM. However, the mechanisms that lead to contractile impairment and DCM in patients with FLNC variants are poorly understood. To determine how FLNC regulates systolic force transmission and DCM remodeling, we used an inducible, cardiac-specific FLNC-knockout (icKO) model to produce a rapid onset of DCM in adult mice. Loss of FLNC reduced systolic force development in single cardiomyocytes and isolated papillary muscles but did not affect twitch kinetics or calcium transients. Electron and immunofluorescence microscopy showed significant defects in Z-disk alignment in icKO mice and altered myofilament lattice geometry. Moreover, a loss of FLNC induces a softening myocyte cortex and structural adaptations at the subcellular level that contribute to disrupted longitudinal force production during contraction. Spatially explicit computational models showed that these structural defects could be explained by a loss of inter-myofibril elastic coupling at the Z-disk. Our work identifies FLNC as a key regulator of the multiscale ultrastructure of cardiomyocytes and therefore plays an important role in maintaining systolic mechanotransmission pathways, the dysfunction of which may be key in driving progressive DCM.

A mechanism for sarcomere breathing: volume change and advective flow within the myofilament lattice

During muscle contraction, myosin motors anchored to thick filaments bind to and slide actin thin filaments. These motors rely on energy derived from ATP, supplied, in part, by diffusion from the sarcoplasm to the interior of the lattice of actin and myosin filaments. The radial spacing of filaments in this lattice may change or remain constant during contraction. If the lattice is isovolumetric, it must expand when the muscle shortens. If, however, the spacing is constant or has a different pattern of axial and radial motion, then the lattice changes volume during contraction, driving fluid motion and assisting in the transport of molecules between the contractile lattice and the surrounding intracellular space. We first create an advective-diffusive-reaction flow model and show that the flow into and out of the sarcomere lattice would be significant in the absence of lattice expansion. Advective transport coupled to diffusion has the potential to substantially enhance metabolite exchange within the crowded sarcomere. Using time-resolved x-ray diffraction of contracting muscle, we next show that the contractile lattice is neither isovolumetric nor constant in spacing. Instead, lattice spacing is time varying, depends on activation, and can manifest as an effective time-varying Poisson ratio. The resulting fluid flow in the sarcomere lattice of synchronous insect flight muscles is even greater than expected for constant lattice spacing conditions. Lattice spacing depends on a variety of factors that produce radial force, including cross-bridges, titin-like molecules, and other structural proteins. Volume change and advective transport varies with the phase of muscle stimulation during periodic contraction but remains significant at all conditions. Although varying in magnitude, advective transport will occur in all cases in which the sarcomere is not isovolumetric. Akin to "breathing," advective-diffusive transport in sarcomeres is sufficient to promote metabolite exchange and may play a role in the regulation of contraction itself.

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.

The Energy of Muscle Contraction. II. Transverse Compression and Work

In this study we examined how the strain energies within a muscle are related to changes in longitudinal force when the muscle is exposed to an external transverse load. We implemented a three-dimensional (3D) finite element model of contracting muscle using the principle of minimum total energy and allowing the redistribution of energy through different strain energy-densities. This allowed us to determine the importance of the strain energy-densities to the transverse forces developed by the muscle. We ran a series of in silica experiments on muscle blocks varying in initial pennation angle, muscle length, and external transverse load. As muscle contracts it maintains a near constant volume. As such, any changes in muscle length are balanced by deformations in the transverse directions such as muscle thickness or muscle width. Muscle develops transverse forces as it expands. In many situations external forces act to counteract these transverse forces and the muscle responds to external transverse loads while both passive and active. The muscle blocks used in our simulations decreased in thickness and pennation angle when passively compressed and pushed back on the load when they were activated. Activation of the compressed muscle blocks led either to an increase or decrease in muscle thickness depending on whether the initial pennation angle was less than or greater than 15°, respectively. Furthermore, the strain energy increased and redistributed across the different strain-energy potentials during contraction. The volumetric strain energy-density varied with muscle length and pennation angle and was reduced with greater transverse load for most initial muscle lengths and pennation angles. External transverse load reduced the longitudinal muscle force for initial pennation angles of β₀ = 0°. Whereas for pennate muscle (β₀ > 0°) longitudinal force changed (increase or decrease) depending on the muscle length, pennation angle and the direction of the external load relative to the muscle fibres. For muscle blocks with initial pennation angles β₀ ≤ 20° the reduction in longitudinal muscle force coincided with a reduction in volumetric strain energy-density.

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.

In vivo X-ray diffraction and simultaneous EMG reveal the time course of myofilament lattice dilation and filament stretch

Muscle function within an organism depends on the feedback between molecular and meter-scale processes. Although the motions of muscle's contractile machinery are well described in isolated preparations, only a handful of experiments have documented the kinematics of the lattice occurring when multi-scale interactions are fully intact. We used time-resolved X-ray diffraction to record the kinematics of the myofilament lattice within a normal operating context: the tethered flight of Manduca sexta As the primary flight muscles of M.sexta are synchronous, we used these results to reveal the timing of in vivo cross-bridge recruitment, which occurred 24 ms (s.d. 26) following activation. In addition, the thick filaments stretched an average of 0.75% (s.d. 0.32) and thin filaments stretched 1.11% (s.d. 0.65). In contrast to other in vivo preparations, lattice spacing changed an average of 2.72% (s.d. 1.47). Lattice dilation of this magnitude significantly affects shortening velocity and force generation, and filament stretching tunes force generation. While the kinematics were consistent within individual trials, there was extensive variation between trials. Using a mechanism-free machine learning model we searched for patterns within and across trials. Although lattice kinematics were predictable within trials, the model could not create predictions across trials. This indicates that the variability we see across trials may be explained by latent variables occurring in this naturally functioning system. The diverse kinematic combinations we documented mirror muscle's adaptability and may facilitate its robust function in unpredictable conditions.

The Energy of Muscle Contraction. I. Tissue Force and Deformation During Fixed-End Contractions

During contraction the energy of muscle tissue increases due to energy from the hydrolysis of ATP. This energy is distributed across the tissue as strain-energy potentials in the contractile elements, strain-energy potential from the 3D deformation of the base-material tissue (containing cellular and extracellular matrix effects), energy related to changes in the muscle's nearly incompressible volume and external work done at the muscle surface. Thus, energy is redistributed through the muscle's tissue as it contracts, with only a component of this energy being used to do mechanical work and develop forces in the muscle's longitudinal direction. Understanding how the strain-energy potentials are redistributed through the muscle tissue will help enlighten why the mechanical performance of whole muscle in its longitudinal direction does not match the performance that would be expected from the contractile elements alone. Here we demonstrate these physical effects using a 3D muscle model based on the finite element method. The tissue deformations within contracting muscle are large, and so the mechanics of contraction were explained using the principles of continuum mechanics for large deformations. We present simulations of a contracting medial gastrocnemius muscle, showing tissue deformations that mirror observations from magnetic resonance imaging. This paper tracks the redistribution of strain-energy potentials through the muscle tissue during fixed-end contractions, and shows how fibre shortening, pennation angle, transverse bulging and anisotropy in the stress and strain of the muscle tissue are all related to the interaction between the material properties of the muscle and the action of the contractile elements.

Reduced Active Muscle Stiffness after Intermittent Submaximal Isometric Contractions

PURPOSE

Whether muscle stiffness is influenced by fatigue remains unclear. Classical methods used to assess muscle stiffness provide a global measure at the joint level. As fatigue may selectively affect specific muscles, a joint-level approach may not be sensitive enough to detect potential changes in muscle stiffness. Taking advantage of ultrasound shear wave elastography, this study aimed to determine the influence of a fatiguing protocol involving intermittent submaximal isometric contractions on muscle shear modulus (an index of stiffness).

METHODS

Shear modulus was measured on either the vastus lateralis (n = 9) or the abductor digiti minimi (n = 10) before and after 15 min of intermittent submaximal isometric contractions at 60% of maximal voluntary contraction (MVC) (4 s ON, 4 s OFF). An index of active muscle stiffness was estimated PRE- and POST-fatigue as the slope of the linear regression established between shear modulus and absolute joint force up to 60% MVC.

RESULTS

After the fatiguing exercise, MVC was significantly decreased by 22% ± 7% and 32% ± 15% for knee extension and little finger abduction, respectively (P < 0.001). When compared to PRE-fatigue, the index of active muscle stiffness was 12% ± 15% lower for the vastus lateralis (P < 0.031) and 44% ± 19% lower for the abductor digiti minimi (P < 0.001) POST-fatigue.

CONCLUSIONS

Although the present results cannot clearly determine the involved mechanisms, they demonstrate a decreased active muscle stiffness after a fatiguing task involving intermittent submaximal isometric contractions. Further studies should now determine whether this change in stiffness affects performance and risk of injury.

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.

A Dynamic Escape Problem of Molecular Motors

Animal skeletal muscle exhibits very interesting behavior at near-stall forces (when the muscle is loaded so strongly that it can barely contract). Near this physical limit, the myosin II proteins may be unable to reach advantageous actin binding sites through simple attractive forces. It has been shown that the advantageous utilization of thermal agitation is a likely source for an increased force-production capacity and reach in myosin-V (a processing motor protein), and here we explore the dynamics of a molecular motor without hand-over-hand motion including Brownian motion to show how local elastic energy well boundaries may be overcome. We revisit a spatially two-dimensional mechanical model to illustrate how thermal agitation can be harvested for useful mechanical work in molecular machinery inspired by this biomechanical phenomenon without rate functions or empirically inspired spatial potential functions. Additionally, the model accommodates variable lattice spacing, and it paves the way for a full three-dimensional model of cross-bridge interactions where myosin II may be azimuthally misaligned with actin binding sites. With potential energy sources based entirely on realizable components, this model lends itself to the design of artificial, molecular-scale motors.

Changes in the Viscoelastic Properties of the Vastus Lateralis Muscle With Fatigue

We investigated the in vivo effects of voluntary fatiguing isometric contractions of the knee extensor muscles on the viscoelastic properties of the vastus lateralis (VL). Twelve young males (29.0 ± 4.5 years) performed an intermittent voluntary fatigue protocol consisting of 6 sets × 10 repetitions of 5-s voluntary maximal isometric contractions with 5-s passive recovery periods between repetitions. Voluntary and evoked torque were assessed before, immediately after, and 20 min after exercise. The shear modulus (μ) of the VL muscle was estimated at rest and during a ramped isometric contraction using a conventional elastography technique. An index of active muscle stiffness was then calculated (slope from the relationship between shear modulus and absolute torque). Resting muscle viscosity (η) was quantified using a shear-wave spectroscopy sequence to measure the shear-wave dispersion. Voluntary and evoked torque decreased by ∼37% (P < 0.01) immediately after exercise. The resting VL μ was lower at the end of the fatigue protocol (-57.9 ± 5.4%, P < 0.001), whereas the resting VL η increased (179.0 ± 123%, P < 0.01). The active muscle stiffness index also decreased with fatigue (P < 0.05). By 20 min post-fatigue, there were no significant differences from the pre-exercise values for VL η and the active muscle stiffness index, contrary to the resting VL μ. We show that the VL μ is greatly reduced and η greatly enhanced by fatigue, reflecting a more compliant and viscous muscle. The quantification of both shear μ and η moduli in vivo may contribute to a better understanding of the mechanical behavior of muscles during fatigue in sports medicine, as well as in clinical situations.

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.

Low temperature traps myosin motors of mammalian muscle in a refractory state that prevents activation

The active force of mammalian skeletal muscle is reduced at low temperatures. Caremani et al. reveal that this is due to the rise of a population of myosin motors captured in a refractory state insensitive to muscle activation.

Myosin motors in the thick filament of resting striated (skeletal and cardiac) muscle are trapped in an OFF state, in which the motors are packed in helical tracks on the filament surface, inhibiting their interactions with actin and utilization of ATP. To investigate the structural changes induced in the thick filament of mammalian skeletal muscle by changes in temperature, we collected x-ray diffraction patterns from the fast skeletal muscle extensor digitorum longus of the mouse in the temperature range from near physiological (35°C) to 10°C, in which the maximal isometric force (T₀) shows a threefold decrease. In resting muscle, x-ray reflections signaling the OFF state of the thick filament indicate that cooling produces a progressive disruption of the OFF state with motors moving away from the ordered helical tracks on the surface of the thick filament. We find that the number of myosin motors in the OFF state at 10°C is half of that at 35°C. At T₀, changes in the x-ray signals that report the fraction and conformation of actin-attached motors can be explained if the threefold decrease in force associated with lowering temperature is due not only to a decrease in the force-generating transition in the actin-attached motors but also to a twofold decrease in the number of such motors. Thus, lowering the temperature reduces to the same extent the fraction of motors in the OFF state at rest and the fraction of motors attached to actin at T₀, suggesting that motors that leave the OFF state accumulate in a disordered refractory state that makes them unavailable for interaction with actin upon stimulation. This regulatory effect of temperature on the thick filament of mammalian skeletal muscle could represent an energetically convenient mechanism for hibernating animals.

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

Models of muscle contraction often assume that a myosin motor interacts with areas of one to three distinct binding sites along an actin filament. Månsson shows that computational models employing different numbers of sites return similar predictions, suggesting one-site models are often sufficient.

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.

Cardiac Disorders and Pathophysiology of Sarcomeric Proteins

The sarcomeric proteins represent the structural building blocks of heart muscle, which are essential for contraction and relaxation. During recent years, it has become evident that posttranslational modifications of sarcomeric proteins, in particular phosphorylation, tune cardiac pump function at rest and during exercise. This delicate, orchestrated interaction is also influenced by mutations, predominantly in sarcomeric proteins, which cause hypertrophic or dilated cardiomyopathy. In this review, we follow a bottom-up approach starting from a description of the basic components of cardiac muscle at the molecular level up to the various forms of cardiac disorders at the organ level. An overview is given of sarcomere changes in acquired and inherited forms of cardiac disease and the underlying disease mechanisms with particular reference to human tissue. A distinction will be made between the primary defect and maladaptive/adaptive secondary changes. Techniques used to unravel functional consequences of disease-induced protein changes are described, and an overview of current and future treatments targeted at sarcomeric proteins is given. The current evidence presented suggests that sarcomeres not only form the basis of cardiac muscle function but also represent a therapeutic target to combat cardiac disease.

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.

Structural and functional impact of troponin C-mediated Ca2+ sensitization on myofilament lattice spacing and cross-bridge mechanics in mouse cardiac muscle

Acto-myosin cross-bridge kinetics are important for beat-to-beat regulation of cardiac contractility; however, physiological and pathophysiological mechanisms for regulation of contractile kinetics are incompletely understood. Here we explored whether thin filament-mediated Ca²⁺ sensitization influences cross-bridge kinetics in permeabilized, osmotically compressed cardiac muscle preparations. We used a murine model of hypertrophic cardiomyopathy (HCM) harboring a cardiac troponin C (cTnC) Ca²⁺-sensitizing mutation, Ala8Val in the regulatory N-domain. We also treated wild-type murine muscle with bepridil, a cTnC-targeting Ca²⁺ sensitizer. Our findings suggest that both methods of increasing myofilament Ca²⁺ sensitivity increase cross-bridge cycling rate measured by the rate of tension redevelopment (k_TR); force per cross-bridge was also enhanced as measured by sinusoidal stiffness and I_1,1/I_1,0 ratio from X-ray diffraction. Computational modeling suggests that Ca²⁺ sensitization through this cTnC mutation or bepridil accelerates k_TR primarily by promoting faster cross-bridge detachment. To elucidate if myofilament structural rearrangements are associated with changes in k_TR, we used small angle X-ray diffraction to simultaneously measure myofilament lattice spacing and isometric force during steady-state Ca²⁺ activations. Within in vivo lattice dimensions, lattice spacing and steady-state isometric force increased significantly at submaximal activation. We conclude that the cTnC N-domain controls force by modulating both the number and rate of cycling cross-bridges, and that the both methods of Ca²⁺ sensitization may act through stabilization of cTnC's D-helix. Furthermore, we propose that the transient expansion of the myofilament lattice during Ca²⁺ activation may be an additional factor that could increase the rate of cross-bridge cycling in cardiac muscle. These findings may have implications for the pathophysiology of HCM.

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.

Myosin MgADP Release Rate Decreases as Sarcomere Length Increases in Skinned Rat Soleus Muscle Fibers

Actin-myosin cross-bridges use chemical energy from MgATP hydrolysis to generate force and shortening in striated muscle. Previous studies show that increases in sarcomere length can reduce thick-to-thin filament spacing in skinned muscle fibers, thereby increasing force production at longer sarcomere lengths. However, it is unclear how changes in sarcomere length and lattice spacing affect cross-bridge kinetics at fundamental steps of the cross-bridge cycle, such as the MgADP release rate. We hypothesize that decreased lattice spacing, achieved through increased sarcomere length or osmotic compression of the fiber via dextran T-500, could slow MgADP release rate and increase cross-bridge attachment duration. To test this, we measured cross-bridge cycling and MgADP release rates in skinned soleus fibers using stochastic length-perturbation analysis at 2.5 and 2.0 μm sarcomere lengths as pCa and [MgATP] varied. In the absence of dextran, the force-pCa relationship showed greater Ca²⁺ sensitivity for 2.5 vs. 2.0 μm sarcomere length fibers (pCa₅₀ = 5.68 ± 0.01 vs. 5.60 ± 0.01). When fibers were compressed with 4% dextran, the length-dependent increase in Ca²⁺ sensitivity of force was attenuated, though the Ca²⁺ sensitivity of the force-pCa relationship at both sarcomere lengths was greater with osmotic compression via 4% dextran compared to no osmotic compression. Without dextran, the cross-bridge detachment rate slowed by ∼15% as sarcomere length increased, due to a slower MgADP release rate (11.2 ± 0.5 vs. 13.5 ± 0.7 s^-1). In the presence of dextran, cross-bridge detachment was ∼20% slower at 2.5 vs. 2.0 μm sarcomere length due to a slower MgADP release rate (10.1 ± 0.6 vs. 12.9 ± 0.5 s^-1). However, osmotic compression of fibers at either 2.5 or 2.0 μm sarcomere length produced only slight (and statistically insignificant) slowing in the rate of MgADP release. These data suggest that skeletal muscle exhibits sarcomere-length-dependent changes in cross-bridge kinetics and MgADP release that are separate from, or complementary to, changes in lattice spacing.

Contractile properties of developing human fetal cardiac muscle

KEY POINTS

The contractile properties of human fetal cardiac muscle have not been previously studied. Small-scale approaches such as isolated myofibril and isolated contractile protein biomechanical assays allow study of activation and relaxation kinetics of human fetal cardiac muscle under well-controlled conditions. We have examined the contractile properties of human fetal cardiac myofibrils and myosin across gestational age 59-134 days. Human fetal cardiac myofibrils have low force and slow kinetics of activation and relaxation that increase during the time period studied, and kinetic changes may result from structural maturation and changes in protein isoform expression. Understanding the time course of human fetal cardiac muscle structure and contractile maturation can provide a framework to study development of contractile dysfunction with disease and evaluate the maturation state of cultured stem cell-derived cardiomyocytes.

ABSTRACT

Little is known about the contractile properties of human fetal cardiac muscle during development. Understanding these contractile properties, and how they change throughout development, can provide valuable insight into human heart development, and provide a framework to study the early stages of cardiac diseases that develop in utero. We characterized the contractile properties of isolated human fetal cardiac myofibrils across 8-19 weeks of gestation. Mechanical measurements revealed that in early stages of gestation there is low specific force and slow rates of force development and relaxation, with increases in force and the rates of activation and relaxation as gestation progresses. The duration and slope of the initial, slow phase of relaxation, related to myosin detachment and thin filament deactivation rates, decreased with gestation age. F-actin sliding on human fetal cardiac myosin-coated surfaces slowed significantly from 108 to 130 days of gestation. Electron micrographs showed human fetal muscle myofibrils elongate and widen with age, but features such as the M-line and Z-band are apparent even as early as day 52. Protein isoform analysis revealed that β-myosin is predominantly expressed even at the earliest time point studied, but there is a progressive increase in expression of cardiac troponin I (TnI), with a concurrent decrease in slow skeletal TnI. Together, our results suggest that cardiac myofibril force production and kinetics of activation and relaxation change significantly with gestation age and are influenced by the structural maturation of the sarcomere and changes in contractile filament protein isoforms.

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.

The embryonic myosin R672C mutation that underlies Freeman-Sheldon syndrome impairs cross-bridge detachment and cycling in adult skeletal muscle

Distal arthrogryposis is the most common known heritable cause of congenital contractures (e.g. clubfoot) and results from mutations in genes that encode proteins of the contractile complex of skeletal muscle cells. Mutations are most frequently found in MYH3 and are predicted to impair the function of embryonic myosin. We measured the contractile properties of individual skeletal muscle cells and the activation and relaxation kinetics of isolated myofibrils from two adult individuals with an R672C substitution in embryonic myosin and distal arthrogryposis syndrome 2A (DA2A) or Freeman-Sheldon syndrome. In R672C-containing muscle cells, we observed reduced specific force, a prolonged time to relaxation and incomplete relaxation (elevated residual force). In R672C-containing muscle myofibrils, the initial, slower phase of relaxation had a longer duration and slower rate, and time to complete relaxation was greatly prolonged. These observations can be collectively explained by a small subpopulation of myosin cross-bridges with greatly reduced detachment kinetics, resulting in a slower and less complete deactivation of thin filaments at the end of contractions. These findings have important implications for selecting and testing directed therapeutic options for persons with DA2A and perhaps congenital contractures in general.

Random myosin loss along thick-filaments increases myosin attachment time and the proportion of bound myosin heads to mitigate force decline in skeletal muscle

Diminished skeletal muscle performance with aging, disuse, and disease may be partially attributed to the loss of myofilament proteins. Several laboratories have found a disproportionate loss of myosin protein content relative to other myofilament proteins, but due to methodological limitations, the structural manifestation of this protein loss is unknown. To investigate how variations in myosin content affect ensemble cross-bridge behavior and force production we simulated muscle contraction in the half-sarcomere as myosin was removed either (i) uniformly, from the Z-line end of thick-filaments, or (ii) randomly, along the length of thick-filaments. Uniform myosin removal decreased force production, showing a slightly steeper force-to-myosin content relationship than the 1:1 relationship that would be expected from the loss of cross-bridges. Random myosin removal also decreased force production, but this decrease was less than observed with uniform myosin loss, largely due to increased myosin attachment time (ton) and fractional cross-bridge binding with random myosin loss. These findings support our prior observations that prolonged ton may augment force production in single fibers with randomly reduced myosin content from chronic heart failure patients. These simulations also illustrate that the pattern of myosin loss along thick-filaments influences ensemble cross-bridge behavior and maintenance of force throughout the sarcomere.

Enhanced contractility with 2-deoxy-ATP and EMD 57033 is correlated with reduced myofibril structure and twitch power in neonatal cardiomyocytes

As cardiomyocytes mature, their sarcomeres and Z-band widths increase in length in order for their myofibrils to produce stronger twitch forces during a contraction. In this study, we tested the hypothesis that tensional homeostasis is affected by altering myofibril forces. To assess this hypothesis, neonatal rat cardiomyocytes were cultured on arrays of microposts to measure cellular contractility. An optical line scanning technique was used to measure the deflections in the microposts with high temporal resolution, enabling the analysis of twitch force, twitch velocity, and twitch power. Myofibril force production was elevated by vector-mediated overexpression of ribonucleotide reductase (RR) to increase cellular dATP content or by adding the inotropic agent EMD 57033 (EMD). We found that RR and EMD treatment did not affect cardiomyocyte twitch force, but it did lead to reduced twitch velocity and twitch power. Immunofluorescent analysis of α-actinin revealed that RR-over-expressing cardiomyocytes and EMD-treated cardiomyocytes had lower spread area, sarcomere length, and Z-band width as compared to control cells. These results indicate a correlation between myofibril structure and cardiac power. This correlation was confirmed by exposing the cells to the myosin II inhibitor blebbistatin, and then subsequently washing it out. After wash-out, cardiomyocytes exhibited a reduction in twitch force, velocity, and power due to shorter sarcomere length and Z-band widths. Our results suggest that cardiac myofibril structure is regulated by tensional homeostasis. If myofibril-generated forces in cardiomyocytes are elevated, a state of tensional homeostasis is maintained by producing sufficient twitch forces with a lower degree myofibril structure.

The length-tension curve in muscle depends on lattice spacing

Classic interpretations of the striated muscle length-tension curve focus on how force varies with overlap of thin (actin) and thick (myosin) filaments. New models of sarcomere geometry and experiments with skinned synchronous insect flight muscle suggest that changes in the radial distance between the actin and myosin filaments, the filament lattice spacing, are responsible for between 20% and 50% of the change in force seen between sarcomere lengths of 1.4 and 3.4 µm. Thus, lattice spacing is a significant force regulator, increasing the slope of muscle's force-length dependence.

Novel role for vinculin in ventricular myocyte mechanics and dysfunction

Vinculin (Vcl) plays a key structural role in ventricular myocytes that, when disrupted, can lead to contractile dysfunction and dilated cardiomyopathy. To investigate the role of Vcl in myocyte and myocardial function, cardiomyocyte-specific Vcl knockout mice (cVclKO) and littermate control wild-type mice were studied with transmission electron microscopy (TEM) and in vivo magnetic resonance imaging (MRI) tagging before the onset of global ventricular dysfunction. MRI revealed significantly decreased systolic strains transverse to the myofiber axis in vivo, but no changes along the muscle fibers or in fiber tension in papillary muscles from heterozygous global Vcl null mice. Myofilament lattice spacing from TEM was significantly greater in cVclKO versus wild-type hearts fixed in the unloaded state. AFM in Vcl heterozygous null mouse myocytes showed a significant decrease in membrane cortical stiffness. A multiscale computational model of ventricular mechanics incorporating cross-bridge geometry and lattice mechanics showed that increased transverse systolic stiffness due to increased lattice spacing may explain the systolic wall strains associated with Vcl deficiency, before the onset of ventricular dysfunction. Loss of cardiac myocyte Vcl may decrease systolic transverse strains in vivo by decreasing membrane cortical tension, which decreases transverse compression of the lattice thereby increasing interfilament spacing and stress transverse to the myofibers.

Elastic energy storage and radial forces in the myofilament lattice depend on sarcomere length

We most often consider muscle as a motor generating force in the direction of shortening, but less often consider its roles as a spring or a brake. Here we develop a fully three-dimensional spatially explicit model of muscle to isolate the locations of forces and energies that are difficult to separate experimentally. We show the strain energy in the thick and thin filaments is less than one third the strain energy in attached cross-bridges. This result suggests the cross-bridges act as springs, storing energy within muscle in addition to generating the force which powers muscle. Comparing model estimates of energy consumed to elastic energy stored, we show that the ratio of these two properties changes with sarcomere length. The model predicts storage of a greater fraction of energy at short sarcomere lengths, suggesting a mechanism by which muscle function shifts as force production declines, from motor to spring. Additionally, we investigate the force that muscle produces in the radial or transverse direction, orthogonal to the direction of shortening. We confirm prior experimental estimates that place radial forces on the same order of magnitude as axial forces, although we find that radial forces and axial forces vary differently with changes in sarcomere length.

Locomotion requires energy. Very fast locomotion requires a larger amount of energy than muscle can produce in such a short time period, thus muscle must use energy that it previously produced and stored as elastic deformation. Cyclical or repeated movements can be directly powered by muscle, but energy may be conserved in such cases through elastic energy storage. Traditionally we've looked primarily at tendons, insect exoskeletons, and bones as locations where this energy is stored. However, a small but growing body of literature has recently suggested the backbone filament proteins in muscle act as elastic storage locations. We suggest that the myosin motors themselves are capable of storing more energy than the filaments, energy that may be released to power very fast movements or reduce the cost of cyclical movements. We further suggest that this energy is stored in the radial deformations of myosin motors, in a direction that is perpendicular to the axis of muscle shortening.

Impact of myocyte strain on cardiac myofilament activation

When cardiac myocytes are stretched by a longitudinal strain, they develop proportionally more active force at a given sub-maximal Ca(2+) concentration than they did at the shorter length. This is known as length-dependent activation. It is one of the most important contributors to the Frank-Starling relationship, a critical part of normal cardiovascular function. Despite intense research efforts, the mechanistic basis of the Frank-Starling relationship remains unclear. Potential mechanisms involving myofibrillar lattice spacing, titin-based effects, and cooperative activation have all been proposed. This review summarizes some of these mechanisms and discusses two additional potential theories that reflect the effects of localized strains that occur within and between half-sarcomeres. The main conclusion is that the Frank-Starling relationship is probably the integrated result of many interacting molecular mechanisms. Multiscale computational modeling may therefore provide the best way of determining the key processes that underlie length-dependent activation and their relative strengths.