The length-tension curve in muscle depends on lattice spacing

Mechanisms of myosin II force generation: insights from novel experimental techniques and approaches

Myosin II is a molecular motor that converts chemical energy derived from ATP hydrolysis into mechanical work. Myosin II isoforms are responsible for muscle contraction and a range of cell functions relying on the development of force and motion. When the motor attaches to actin, ATP is hydrolyzed and inorganic phosphate (Pi) and ADP are released from its active site. These reactions are coordinated with changes in the structure of myosin, promoting the so-called "power stroke" that causes the sliding of actin filaments. The general features of the myosin-actin interactions are well accepted, but there are critical issues that remain poorly understood, mostly due to technological limitations. In recent years, there has been a significant advance in structural, biochemical, and mechanical methods that have advanced the field considerably. New modeling approaches have also allowed researchers to understand actomyosin interactions at different levels of analysis. This paper reviews recent studies looking into the interaction between myosin II and actin filaments, which leads to power stroke and force generation. It reviews studies conducted with single myosin molecules, myosins working in filaments, muscle sarcomeres, myofibrils, and fibers. It also reviews the mathematical models that have been used to understand the mechanics of myosin II in approaches focusing on single molecules to ensembles. Finally, it includes brief sections on translational aspects, how changes in the myosin motor by mutations and/or posttranslational modifications may cause detrimental effects in diseases and aging, among other conditions, and how myosin II has become an emerging drug target.

The Relationship Between Length and Active Force for Submaximal Skeletal Muscle Contractions: a Review

The force-length relationship is usually obtained for isometric contractions with maximal activation, but less is known about how sarcomere length affects force during submaximal activation. During submaximal activation, length-dependent alterations in calcium sensitivity, owing to changes in cross-bridge kinetics (rate of attachment and/or detachment), result in an activation-dependent shift in optimal length to longer sarcomere lengths. It is known that sarcomere length, as well as temperature and phosphorylation of the regulatory light chains of myosin, can modify Ca2⁺ sensitivity by altering the probability of cross-bridge interaction. This altered calcium sensitivity is particularly important for submaximal force levels, as it can change the shape of the length dependence of force, with peak force occurring at sarcomere lengths longer than those associated with maximal filament overlap. In athletic contexts, contractions typically do not reach maximal intensity. Therefore, understanding that the ability to produce force under both maximal and submaximal conditions can differ, and that peak force can be generated at different lengths, could influence the development of targeted training regimens optimal for each sport.

Bayesian Estimation of Muscle Mechanisms and Therapeutic Targets Using 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 introducing earlier treatment. 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 twitches from control mice with the cardiac Troponin C (cTnC) I61Q variant and control twitches treated with the myosin activator Danicamtiv, as well as model parameters that recover the abnormal I61Q cTnC twitches.

A novel kinetic model to demonstrate the independent effects of ATP and ADP/Pi concentrations on sarcomere function

Understanding muscle contraction mechanisms is a standing challenge, and one of the approaches has been to create models of the sarcomere-the basic contractile unit of striated muscle. While these models have been successful in elucidating many aspects of muscle contraction, they fall short in explaining the energetics of functional phenomena, such as rigor, and in particular, their dependence on the concentrations of the biomolecules involved in the cross-bridge cycle. Our hypothesis posits that the stochastic time delay between ATP adsorption and ADP/Pi release in the cross-bridge cycle necessitates a modeling approach where the rates of these two reaction steps are controlled by two independent parts of the total free energy change of the hydrolysis reaction. To test this hypothesis, we built a two-filament, stochastic-mechanical half-sarcomere model that separates the energetic roles of ATP and ADP/Pi in the cross-bridge cycle's free energy landscape. Our results clearly demonstrate that there is a nontrivial dependence of the cross-bridge cycle's kinetics on the independent concentrations of ATP, ADP, and Pi. The simplicity of the proposed model allows for analytical solutions of the more basic systems, which provide novel insight into the dominant mechanisms driving some of the experimentally observed contractile phenomena.

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).

The effect of muscle ultrastructure on the force, displacement and work capacity of skeletal muscle

Skeletal muscle powers animal movement through interactions between the contractile proteins, actin and myosin. Structural variation contributes greatly to the variation in mechanical performance observed across muscles. In vertebrates, gross structural variation occurs in the form of changes in the muscle cross-sectional area : fibre length ratio. This results in a trade-off between force and displacement capacity, leaving work capacity unaltered. Consequently, the maximum work per unit volume-the work density-is considered constant. Invertebrate muscle also varies in muscle ultrastructure, i.e. actin and myosin filament lengths. Increasing actin and myosin filament lengths increases force capacity, but the effect on muscle fibre displacement, and thus work, capacity is unclear. We use a sliding-filament muscle model to predict the effect of actin and myosin filament lengths on these mechanical parameters for both idealized sarcomeres with fixed actin : myosin length ratios, and for real sarcomeres with known filament lengths. Increasing actin and myosin filament lengths increases stress without reducing strain capacity. A muscle with longer actin and myosin filaments can generate larger force over the same displacement and has a higher work density, so seemingly bypassing an established trade-off. However, real sarcomeres deviate from the idealized length ratio suggesting unidentified constraints or selective pressures.

The effects of muscle starting length on work loop power output of isolated mouse soleus and extensor digitorum longus muscle

Force-length relationships derived from isometric activations may not directly apply to muscle force production during dynamic contractions. As such, different muscle starting lengths between isometric and dynamic conditions could be required to achieve maximal force and power. Therefore, this study examined the effects of starting length [±5-10% of length corresponding to maximal twitch force (L0)] on work loop (WL) power output (PO), across a range of cycle frequencies, of the soleus (SOL) and extensor digitorum longus muscle (EDL; N=8-10) isolated from ∼8 week old C57 mice. Furthermore, passive work was examined at a fixed cycle frequency to determine the association of passive work and active net work. Starting length affected maximal WL PO of the SOL and EDL across evaluated cycle frequencies (P<0.030, ηp2>0.494). For the SOL, PO produced at -5% L0 was greater than that at most starting lengths (P<0.015, Cohen's d>0.6), except -10% L0 (P=0.135, d<0.4). However, PO produced at -10% L0 versus L0 did not differ (P=0.138, d=0.35-0.49), indicating -5% L0 is optimal for maximal SOL WL PO. For the EDL, WL PO produced at -10% L0 was lower than that at most starting lengths (P<0.032, d>1.08), except versus -5% L0 (P=0.124, d<0.97). PO produced at other starting lengths did not differ (P>0.163, d<1.04). For the SOL, higher passive work was associated with reduced PO (Spearman's r=0.709, P<0.001), but no relationship was observed between passive work and PO of the EDL (Pearson's r=0.191, r2=0.04, P=0.184). This study suggests that starting length should be optimised for both static and dynamic contractions and confirms that the force-length curve during dynamic contractions is muscle specific.

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.

Myosin-binding protein C regulates the sarcomere lattice and stabilizes the OFF states of myosin heads

Muscle contraction is produced via the interaction of myofilaments and is regulated so that muscle performance matches demand. Myosin-binding protein C (MyBP-C) is a long and flexible protein that is tightly bound to the thick filament at its C-terminal end (MyBP-CC8C10), but may be loosely bound at its middle- and N-terminal end (MyBP-CC1C7) to myosin heads and/or the thin filament. MyBP-C is thought to control muscle contraction via the regulation of myosin motors, as mutations lead to debilitating disease. We use a combination of mechanics and small-angle X-ray diffraction to study the immediate and selective removal of the MyBP-CC1C7 domains of fast MyBP-C in permeabilized skeletal muscle. We show that cleavage leads to alterations in crossbridge kinetics and passive structural signatures of myofilaments that are indicative of a shift of myosin heads towards the ON state, highlighting the importance of MyBP-CC1C7 to myofilament force production and regulation.

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.

Unlocking the Role of sMyBP-C: A Key Player in Skeletal Muscle Development and Growth

Skeletal muscle is the largest organ in the body, responsible for gross movement and metabolic regulation. Recently, variants in the MYBPC1 gene have been implicated in a variety of developmental muscle diseases, such as distal arthrogryposis. How MYBPC1 variants cause disease is not well understood. Here, through a collection of novel gene-edited mouse models, we define a critical role for slow myosin binding protein-C (sMyBP-C), encoded by MYBPC1, across muscle development, growth, and maintenance during prenatal, perinatal, postnatal and adult stages. Specifically, Mybpc1 knockout mice exhibited early postnatal lethality and impaired skeletal muscle formation and structure, skeletal deformity, and respiratory failure. Moreover, a conditional knockout of Mybpc1 in perinatal, postnatal and adult stages demonstrates impaired postnatal muscle growth and function secondary to disrupted actomyosin interaction and sarcomere structural integrity. These findings confirm the essential role of sMyBP-C in skeletal muscle and reveal specific functions in both prenatal embryonic musculoskeletal development and postnatal muscle growth and function.

Disruption of Z-Disc Function Promotes Mechanical Dysfunction in Human Myocardium: Evidence for a Dual Myofilament Modulatory Role by Alpha-Actinin 2

The ACTN2 gene encodes α-actinin 2, located in the Z-disc of the sarcomeres in striated muscle. In this study, we sought to investigate the effects of an ACTN2 missense variant of unknown significance (p.A868T) on cardiac muscle structure and function. Left ventricular free wall samples were obtained at the time of cardiac transplantation from a heart failure patient with the ACTN2 A868T heterozygous variant. This variant is in the EF 3-4 domain known to interact with titin and α-actinin. At the ultrastructural level, ACTN2 A868T cardiac samples presented small structural changes in cardiomyocytes when compared to healthy donor samples. However, contractile mechanics of permeabilized ACTN2 A868T variant cardiac tissue displayed higher myofilament Ca2+ sensitivity of isometric force, reduced sinusoidal stiffness, and faster rates of tension redevelopment at all Ca2+ levels. Small-angle X-ray diffraction indicated increased separation between thick and thin filaments, possibly contributing to changes in muscle kinetics. Molecular dynamics simulations indicated that while the mutation does not significantly impact the structure of α-actinin on its own, it likely alters the conformation associated with titin binding. Our results can be explained by two Z-disc mediated communication pathways: one pathway that involves α-actinin's interaction with actin, affecting thin filament regulation, and the other pathway that involves α-actinin's interaction with titin, affecting thick filament activation. This work establishes the role of α-actinin 2 in modulating cross-bridge kinetics and force development in the human myocardium as well as how it can be involved in the development of cardiac disease.

Myosin-binding protein C forms C-links and stabilizes OFF states of myosin

Contraction force in muscle is produced by the interaction of myosin motors in the thick filaments and actin in the thin filaments and is fine-tuned by other proteins such as myosin-binding protein C (MyBP-C). One form of control is through the regulation of myosin heads between an ON and OFF state in passive sarcomeres, which leads to their ability or inability to interact with the thin filaments during contraction, respectively. MyBP-C is a flexible and long protein that is tightly bound to the thick filament at its C-terminal end but may be loosely bound at its middle- and N-terminal end (MyBP-CC1C7). Under considerable debate is whether the MyBP-CC1C7 domains directly regulate myosin head ON/OFF states, and/or link thin filaments ("C-links"). Here, we used a combination of mechanics and small-angle X-ray diffraction to study the immediate and selective removal of the MyBP-CC1C7 domains of fast MyBP-C in permeabilized skeletal muscle. After cleavage, the thin filaments were significantly shorter, a result consistent with direct interactions of MyBP-C with thin filaments thus confirming C-links. Ca2+ sensitivity was reduced at shorter sarcomere lengths, and crossbridge kinetics were increased across sarcomere lengths at submaximal activation levels, demonstrating a role in crossbridge kinetics. Structural signatures of the thick filaments suggest that cleavage also shifted myosin heads towards the ON state - a marker that typically indicates increased Ca2+ sensitivity but that may account for increased crossbridge kinetics at submaximal Ca2+ and/or a change in the force transmission pathway. Taken together, we conclude that MyBP-CC1C7 domains play an important role in contractile performance which helps explain why mutations in these domains often lead to debilitating diseases.

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.

One size does not fit all: diversity of length-force properties of obliquely striated muscles

Obliquely striated muscles occur in 17+ phyla, likely evolving repeatedly, yet the implications of oblique striation for muscle function are unknown. Contrary to the belief that oblique striation allows high force output over extraordinary length ranges (i.e. superelongation), recent work suggests diversity in operating length ranges and length-force relationships. We hypothesize oblique striation evolved to increase length-force relationship flexibility. We predict that superelongation is not a general characteristic of obliquely striated muscles and instead that length-force relationships vary with operating length range. To test these predictions, we measured length-force relationships of five obliquely striated muscles from inshore longfin squid, Doryteuthis pealeii: tentacle, funnel retractor and head retractor longitudinal fibers, and arm and fin transverse fibers. Consistent with superelongation, the tentacle length-force relationship had a long descending limb, whereas all others exhibited limited descending limbs. The ascending limb at 0.6P0 was significantly broader (P<0.001) for the tentacle length-force relationship (0.43±0.04L0; where L0 is the preparation length that produced peak isometric stress, P0) than for the arm (0.29±0.03L0), head retractor (0.24±0.06L0), fin (0.20±0.04L0) and funnel retractor (0.27±0.03L0). The fin's narrow ascending limb differed significantly from those of the arm (P=0.004) and funnel retractor (P=0.012). We further characterized the tentacle preparation's maximum isometric stress (315±78 kPa), maximum unloaded shortening velocity (2.97±0.55L0 s-1) and ultrastructural traits (compared with the arm), which may explain its broader length-force relationship. Comparison of obliquely striated muscles across taxa revealed length-force relationship diversity, with only two species exhibiting superelongation.

The distinctive mechanical and structural signatures of residual force enhancement in myofibers

In muscle, titin proteins connect myofilaments together and are thought to be critical for contraction, especially during residual force enhancement (RFE) when force is elevated after an active stretch. We investigated titin's function during contraction using small-angle X-ray diffraction to track structural changes before and after 50% titin cleavage and in the RFE-deficient, mdm titin mutant. We report that the RFE state is structurally distinct from pure isometric contractions, with increased thick filament strain and decreased lattice spacing, most likely caused by elevated titin-based forces. Furthermore, no RFE structural state was detected in mdm muscle. We posit that decreased lattice spacing, increased thick filament stiffness, and increased non-crossbridge forces are the major contributors to RFE. We conclude that titin directly contributes to RFE.

A biomechanical model for the relation between bite force and mandibular opening angle in arthropods

Bite forces play a key role in animal ecology: they affect mating behaviour, fighting success, and the ability to feed. Although feeding habits of arthropods have a significant ecological and economical impact, we lack fundamental knowledge on how the morphology and physiology of their bite apparatus controls bite performance, and its variation with mandible gape. To address this gap, we derived a biomechanical model that characterizes the relationship between bite force and mandibular opening angle from first principles. We validate this model by comparing its geometric predictions with morphological measurements on the muscoloskeletal bite apparatus of Atta cephalotes leaf-cutter ants, using computed tomography (CT) scans obtained at different mandible opening angles. We then demonstrate its deductive and inductive utility with three examplary use cases: Firstly, we extract the physiological properties of the leaf-cutter ant mandible closer muscle from in vivo bite force measurements. Secondly, we show that leaf-cutter ants are specialized to generate extraordinarily large bite forces, equivalent to about 2600 times their body weight. Thirdly, we discuss the relative importance of morphology and physiology in determining the magnitude and variation of bite force. We hope that a more detailed quantitative understanding of the link between morphology, physiology, and bite performance will facilitate future comparative studies on the insect bite apparatus, and help to advance our knowledge of the behaviour, ecology and evolution of arthropods.

Ultrastructural and kinetic evidence support that thick filaments slide through the Z-disc

How myofilaments operate at short mammalian skeletal muscle lengths is unknown. A common assumption is that thick (myosin-containing) filaments get compressed at the Z-disc. We provide ultrastructural evidence of sarcomeres contracting down to 0.44 µm-approximately a quarter of thick filament resting length-in long-lasting contractions while apparently keeping a regular, parallel thick filament arrangement. Sarcomeres produced force at such extremely short lengths. Furthermore, sarcomeres adopted a bimodal length distribution with both modes below lengths where sarcomeres are expected to generate force in classic force-length measurements. Mammalian fibres did not restore resting length but remained short after deactivation, as previously reported for amphibian fibres, and showed increased forces during passive re-elongation. These findings are incompatible with viscoelastic thick filament compression but agree with predictions of a model incorporating thick filament sliding through the Z-disc. This more coherent picture of mechanical mammalian skeletal fibre functioning opens new perspectives on muscle physiology.

MgADP Promotes Myosin Head Movement toward Actin at Low [Ca2+] to Increase Force Production and Ca2+-Sensitivity of Contraction in Permeabilized Porcine Myocardial Strips

Myosin cross-bridges dissociate from actin following Mg²⁺-adenosine triphosphate (MgATP) binding. Myosin hydrolyses MgATP into inorganic phosphate (P_i) and Mg²⁺-adenosine diphosphate (ADP), and release of these hydrolysis products drives chemo-mechanical energy transitions within the cross-bridge cycle to power muscle contraction. Some forms of heart disease are associated with metabolic or enzymatic dysregulation of the MgATP-MgADP nucleotide pool, resulting in elevated cytosolic [MgADP] and impaired muscle relaxation. We investigated the mechanical and structural effects of increasing [MgADP] in permeabilized myocardial strips from porcine left ventricle samples. Sarcomere length was set to 2.0 µm at 28 °C, and all solutions contained 3% dextran T-500 to compress myofilament lattice spacing to near-physiological values. Under relaxing low [Ca²⁺] conditions (pCa 8.0, where pCa = -log₁₀[Ca²⁺]), tension increased as [MgADP] increased from 0-5 mM. Complementary small-angle X-ray diffraction measurements show that the equatorial intensity ratio, I_1,1/I_1,0, also increased as [MgADP] increased from 0 to 5 mM, indicating myosin head movement away from the thick-filament backbone towards the thin-filament. Ca²⁺-activated force-pCa measurements show that Ca²⁺-sensitivity of contraction increased with 5 mM MgADP, compared to 0 mM MgADP. These data show that MgADP augments tension at low [Ca²⁺] and Ca²⁺-sensitivity of contraction, suggesting that MgADP destabilizes the quasi-helically ordered myosin OFF state, thereby shifting the cross-bridge population towards the disordered myosin ON state. Together, these results indicate that MgADP enhances the probability of cross-bridge binding to actin due to enhancement of both thick and thin filament-based activation mechanisms.

Titin force in muscle cells alters lattice order, thick and thin filament protein formation

Skeletal muscle force production is increased at longer compared to shorter muscle lengths because of length-dependent priming of thick filament proteins in the contractile unit before contraction. Using small-angle X-ray diffraction in combination with a mouse model that specifically cleaves the stretch-sensitive titin protein, we found that titin cleavage diminished the length-dependent priming of the thick filament. Strikingly, a titin-sensitive, length-dependent priming was also present in thin filaments, which seems only possible via bridge proteins between thick and thin filaments in resting muscle, potentially myosin-binding protein C. We further show that these bridges can be forcibly ruptured via high-speed stretches. Our results advance a paradigm shift to the fundamental regulation of length-dependent priming, with titin as the key driver.

Frequency-dependent signaling in cardiac myocytes

Background: Recent experimental data support the view that signaling activity at the membrane depends on its geometric parameters such as surface area and curvature. However, a mathematical, biophysical concept linking shape to receptor signaling is missing. The membranes of cardiomyocytes are constantly reshaped due to cycles of contraction and relaxation. According to constant-volume behavior of cardiomyocyte contraction, the length shortening is compensated by Z-disc myofilament lattice expansion and dynamic deformation of membrane between two adjacent Z-discs. Both morphological changes are strongly dependent on the frequency of contraction. Here, we developed the hypothesis that dynamic geometry of cardiomyocytes could be important for their plasticity and signaling. This effect may depend on the frequency of the beating heart and may represent a novel concept to explain how changes in frequency affect cardiac signaling.

Methods: This hypothesis is almost impossible to answer with experiments, as the in-vitro cardiomyocytes are almost two-dimensional and flattened rather than being in their real in-vivo shape. Therefore, we designed a COMSOL multiphysics program to mathematically model the dynamic geometry of a human cardiomyocyte and explore whether the beating frequency can modulate membrane signal transduction. Src kinase is an important component of cardiac mechanotransduction. We first presented that Src mainly localizes at costameres. Then, the frequency-dependent signaling effect was studied mathematically by numerical simulation of Src-mediated PDGFR signaling pathway. The reaction-convection-diffusion partial differential equation was formulated to simulate PDGFR pathway in a contracting sarcomeric disc for a range of frequencies from 1 to 4 Hz. Results: Simulations exhibits higher concentration of phospho-Src when a cardiomyocyte beats with higher rates. The calculated phospho-Src concentration at 4, 2, and 1 Hz beat rates, comparing to 0 Hz, was 21.5%, 9.4%, and 4.7% higher, respectively.

Conclusion: Here we provide mathematical evidence for a novel concept in biology. Cell shape directly translates into signaling, an effect of importance particularly for the myocardium, where cells continuously reshape their membranes. The concept of locality of surface-to-volume ratios is demonstrated to lead to changes in membrane-mediated signaling and may help to explain the remarkable plasticity of the myocardium in response to biomechanical stress.

Shorter muscle fascicle operating lengths increase the metabolic cost of cyclic force production

During locomotion, force-producing limb muscles are predominantly responsible for an animal's whole body metabolic energy expenditure. Animals can change the length of their force-producing muscle fascicles by altering body posture (e.g., joint angles), the structural properties of their biological tissues over time (e.g., tendon stiffness), or the body's kinetics (e.g., body weight). Currently, it is uncertain whether relative muscle fascicle operating lengths have a measurable effect on the metabolic energy expended during cyclic locomotion-like contractions. To address this uncertainty, we quantified the metabolic energy expenditure of human participants, as they cyclically produced two distinct ankle moments at three ankle angles (90°, 105°, and 120°) on a fixed-position dynamometer using their soleus. Overall, increasing participant ankle angle from 90° to 120° (more plantar flexion) reduced minimum soleus fascicle length by 17% (both moment levels, P < 0.001) and increased metabolic energy expenditure by an average of 208% across both moment levels (both P < 0.001). For both moment levels, the increased metabolic energy expenditure was not related to greater fascicle positive mechanical work (higher moment level, P = 0.591), fascicle force rate (both P ≥ 0.235), or model-estimated active muscle volume (both P ≥ 0.122). Alternatively, metabolic energy expenditure correlated with average relative soleus fascicle length (r = -0.72, P = 0.002) and activation (r = 0.51, P < 0.001). Therefore, increasing active muscle fascicle operating lengths may reduce metabolic energy expended during locomotion.NEW & NOTEWORTHY During locomotion, active muscles undergo cyclic length-changing contractions. In this study, we isolated confounding variables and revealed that cyclically producing force at relatively shorter fascicle lengths increases metabolic energy expenditure. Therefore, muscle fascicle operating lengths likely have a measurable effect on the metabolic energy expenditure during locomotion.

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.

Corticospinal and peripheral responses to heat-induced hypo-hydration: potential physiological mechanisms and implications for neuromuscular function

Heat-induced hypo-hydration (hyperosmotic hypovolemia) can reduce prolonged skeletal muscle performance; however, the mechanisms are less well understood and the reported effects on all aspects of neuromuscular function and brief maximal contractions are inconsistent. Historically, a 4–6% reduction of body mass has not been considered to impair muscle function in humans, as determined by muscle torque, membrane excitability and peak power production. With the development of magnetic resonance imaging and neurophysiological techniques, such as electromyography, peripheral nerve, and transcranial magnetic stimulation (TMS), the integrity of the brain-to-muscle pathway can be further investigated. The findings of this review demonstrate that heat-induced hypo-hydration impairs neuromuscular function, particularly during repeated and sustained contractions. Additionally, the mechanisms are separate to those of hyperthermia-induced fatigue and are likely a result of modulations to corticospinal inhibition, increased fibre conduction velocity, pain perception and impaired contractile function. This review also sheds light on the view that hypo-hydration has ‘no effect’ on neuromuscular function during brief maximal voluntary contractions. It is hypothesised that irrespective of unchanged force, compensatory reductions in cortical inhibition are likely to occur, in the attempt of achieving adequate force production. Studies using single-pulse TMS have shown that hypo-hydration can reduce maximal isometric and eccentric force, despite a reduction in cortical inhibition, but the cause of this is currently unclear. Future work should investigate the intracortical inhibitory and excitatory pathways within the brain, to elucidate the role of the central nervous system in force output, following heat-induced hypo-hydration.

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.

Effect of Myosin Isoforms on Cardiac Muscle Twitch of Mice, Rats and Humans

To understand how pathology-induced changes in contractile protein isoforms modulate cardiac muscle function, it is necessary to quantify the temporal-mechanical properties of contractions that occur under various conditions. Pathological responses are much easier to study in animal model systems than in humans, but extrapolation between species presents numerous challenges. Employing computational approaches can help elucidate relationships that are difficult to test experimentally by translating the observations from rats and mice, as model organisms, to the human heart. Here, we use the spatially explicit MUSICO platform to model twitch contractions from rodent and human trabeculae collected in a single laboratory. This approach allowed us to identify the variations in kinetic characteristics of α- and β-myosin isoforms across species and to quantify their effect on cardiac muscle contractile responses. The simulations showed how the twitch transient varied with the ratio of the two myosin isoforms. Particularly, the rate of tension rise was proportional to the fraction of α-myosin present, while the β-isoform dominated the rate of relaxation unless α-myosin was >50%. Moreover, both the myosin isoform and the Ca2+ transient contributed to the twitch tension transient, allowing two levels of regulation of twitch contraction.

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.

Effect of calcium ion on the morphology structure and compression elasticity of muscle fibers from honeybee abdomen

Muscle contraction activated by calcium ion is the key to reveal that honeybee abdomen can achieve various physiological activities through flexible exercises and contributes to a powerful mechanical function of muscle fibers. To investigate the stimulating effect of calcium ion on muscle fibers of honeybee abdomen, atomic force microscopy was used to measure the morphology structure and mechanical properties of muscle fibers from honeybee abdomen in different calcium ion solutions. The periodic morphology structure of muscle fibers stimulated by different calcium ion concentration changed greatly, and the sarcomere length contracted from 6.53 μm to 4.29 μm as the calcium ion concentration increased from 0.11 mM to 10 mM. The mechanical measurement showed that the elastic modulus of Z-line reached the maximum, followed by M-line, overlap zone and I-band in sequence at the same calcium ion concentration, and was approximately 3.636, 2.450, 2.284, 2.748 times that of I-band from 0.11 mM to 10 mM calcium ion concentration. Combining the experimental analysis, the calcium ion threshold range was obtained based on the response surface method. This work adequately elucidates biological structure and biomechanics of muscle fibers from honeybee abdomen and could provide reference for other similar muscle system.

Amino terminus of cardiac myosin binding protein-C regulates cardiac contractility

Phosphorylation of cardiac myosin binding protein-C (cMyBP-C) regulates cardiac contraction through modulation of actomyosin interactions mediated by the protein's amino terminal (N')-region (C0-C2 domains, 358 amino acids). On the other hand, dephosphorylation of cMyBP-C during myocardial injury results in cleavage of the 271 amino acid C0-C1f region and subsequent contractile dysfunction. Yet, our current understanding of amino terminus region of cMyBP-C in the context of regulating thin and thick filament interactions is limited. A novel cardiac-specific transgenic mouse model expressing cMyBP-C, but lacking its C0-C1f region (cMyBP-C∆C0-C1f), displayed dilated cardiomyopathy, underscoring the importance of the N'-region in cMyBP-C. Further exploring the molecular basis for this cardiomyopathy, in vitro studies revealed increased interfilament lattice spacing and rate of tension redevelopment, as well as faster actin-filament sliding velocity within the C-zone of the transgenic sarcomere. Moreover, phosphorylation of the unablated phosphoregulatory sites was increased, likely contributing to normal sarcomere morphology and myoarchitecture. These results led us to hypothesize that restoration of the N'-region of cMyBP-C would return actomyosin interaction to its steady state. Accordingly, we administered recombinant C0-C2 (rC0-C2) to permeabilized cardiomyocytes from transgenic, cMyBP-C null, and human heart failure biopsies, and we found that normal regulation of actomyosin interaction and contractility was restored. Overall, these data provide a unique picture of selective perturbations of the cardiac sarcomere that either lead to injury or adaptation to injury in the myocardium.

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.

Influence of Woody Breast Myopathy on Sarcomere Length and Tensile Strength in Commercial Broiler Pectoralis major Muscle

Woody breast syndrome is characterized by degenerative changes at the muscle fiber level and accumulation of connective tissue between the fibers. This study explored effects of the syndrome on muscle properties by focusing on a comparison of the sarcomere lengths between normal and woody breast muscles, including cranial and middle parts, surface and deeper layers, electrically stimulated and nonstimulated muscles, and their combinations. Tensile strengths longitudinally and transversally to the muscle fiber direction in the cranial and middle parts of the muscles were determined. The overall sarcomere lengths of woody breasts were longer than normal muscles (1.93 μ m vs. 1.88 μm; P &lt; 0.05). The surface layer had overall longer sarcomere lengths than the deeper layer (cranial surface vs. cranial deeper layer: 1.97 vs. 1.89 μ m; middle surface vs. middle deeper layer: 1.93 vs.1.84 μ m; P &lt; 0.05). Compared with normal breast muscles, woody breast muscles had longer sarcomeres in the surface layer; however, sarcomere length did not differ in the deeper layer. Electrically stimulated chicken breasts generally had longer sarcomere lengths (2.00 vs. 1.82 μm; P &lt; 0.001). There was no significant difference in tensile strength between normal and focal woody breast (mild local lesion, usually in the cranial end) samples when fiber direction or sample location was studied (P &gt; 0.05), but there was a clear difference between normal and focal versus diffuse (severe woody breast lesion throughout the muscle) samples (P &lt; 0.001). Tensile strength was much greater in diffuse woody breast muscles when extended longitudinally or transversely to the fiber direction. In conclusion, although this study did not show sarcomere lengths in living muscle, it suggests an imbalance in sarcomere lengths in different parts of the breast muscle, which may induce a reduction in the functionality and strength of the muscle.

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.

The effect of variable troponin C mutation thin filament incorporation on cardiac muscle twitch contractions

One of the complexities of understanding the pathology of familial forms of cardiac diseases is the level of mutation incorporation in sarcomeres. Computational models of the sarcomere that are spatially explicit offer an approach to study aspects of mutational incorporation into myofilaments that are more challenging to get at experimentally. We studied two well characterized mutations of cardiac TnC, L48Q and I61Q, that decrease or increase the release rate of Ca²⁺ from cTnC, k_-Ca, resulting in HCM and DCM respectively [1]. Expression of these mutations in transgenic mice was used to provide experimental data for incorporation of 30 and 50% (respectively) into sarcomeres. Here we demonstrate that fixed length twitch contractions of trabeculae from mice containing mutant differ from WT; L48Q trabeculae have slower relaxation while I61Q trabeculae have markedly reduced peak tension. Using our multiscale modelling approach [2] we were able to describe the tension transients of WT mouse myocardium. Tension transients for the mutant cTnCs were simulated with changes in k_-Ca, measured experimentally for each cTnC mutant in whole troponin complex, a change in the affinity of cTnC for cTnI, and a reduction in the number of detached crossbridges available for binding. A major advantage of the multiscale explicit 3-D model is that it predicts the effects of variable mutation incorporation, and the effects of variations in mutation distribution within thin filaments in sarcomeres. Such effects are currently impossible to explore experimentally. We explored random and clustered distributions of mutant cTnCs in thin filaments, as well as distributions of individual thin filaments with only WT or mutant cTnCs present. The effects of variable amounts of incorporation and non-random distribution of mutant cTnCs are more marked for I61Q than L48Q cTnC. We conclude that this approach can be effective for study on mutations in multiple proteins of the sarcomere. SUMMARY: A challenge in experimental studies of diseases is accounting for the effect of variable mutation incorporation into myofilaments. Here we use a spatially explicit computational approach, informed by experimental data from transgenic mice expressing one of two mutations in cardiac Troponin C that increase or decrease calcium sensitivity. We demonstrate that the model can accurately describe twitch contractions for the data and go on to explore the effect of variable mutant incorporation and localization on simulated cardiac muscle twitches.

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 Multi-Scale, Three-Dimensional Nature of Skeletal Muscle Contraction

Muscle contraction is a three-dimensional process, as anyone who has observed a bulging muscle knows. Recent studies suggest that the three-dimensional nature of muscle contraction influences its mechanical output. Shape changes and radial forces appear to be important across scales of organization. Muscle architectural gearing is an emerging example of this process.

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.

Altered Sarcomeric Structure and Function in Woody Breast Myopathy of Avian Pectoralis Major Muscle

The "Woody" or "Wooden" breast disease is a severe myopathy of pectoralis major muscle recently identified within rapidly growing broiler lines all around the world with a prevalence rate around 20%, or even higher. Although of significant ethical and economic impact, little is known regarding the structural and functional aspects of the contractile apparatus in the woody breast muscle. The aim of the present study was to determine physiological properties of the contractile system in the morphologically intact muscle fibers of focally damaged woody breast in comparison with normal muscle fibers to gain insight into the muscle function of the animal and possibly mechanisms involved in the disease development. Muscle samples were taken from woody breast (non-lesioned areas) and normal breast muscles from broilers. Length-tension curves, maximal active stress, maximal shortening velocity, calcium sensitivity, rate of tension development, lattice spacing and muscle biochemical composition were investigated on single skinned fibers. Sarcomeres of woody breast fibers were more compliant, which is very likely related to the wider spacing (18% wider compared to controls) between thick and thin filament. No differences were found in optimal sarcomere length (2.68 ± 0.04 vs. 2.65 ± 0.05 μm) nor in maximal active stress (116 ± 17 vs. 125 ± 19 mN mm-2). However, woody breast fibers had less steep descending arm as shown in length-tension curve. Woody breast muscle fibers had 40% bigger sarcomeric volume compared to controls. Content of contractile proteins (myosin and actin), and maximal shortening velocity were unchanged indicating that the growth in woody breast muscle fiber was associated with synthesis of new contractile units with unaltered kinetics. Calcium sensitivity was decreased in woody breast muscle fibers significantly. In conclusion, the results show that the rapid growth of muscle in woody breast disease is associated with significant structural and functional changes in the pectoralis major musculature, associated with alterations in the mechanical anchoring of contractile filaments.

Internal fluid pressure influences muscle contractile force

Fluid fills intracellular, extracellular, and capillary spaces within muscle. During normal physiological activity, intramuscular fluid pressures develop as muscle exerts a portion of its developed force internally. These pressures, typically ranging between 10 and 250 mmHg, are rarely considered in mechanical models of muscle but have the potential to affect performance by influencing force and work produced during contraction. Here, we test a model of muscle structure in which intramuscular pressure directly influences contractile force. Using a pneumatic cuff, we pressurize muscle midcontraction at 260 mmHg and report the effect on isometric force. Pressurization reduced isometric force at short muscle lengths (e.g., -11.87% of P₀ at 0.9 L₀), increased force at long lengths (e.g., +3.08% of P₀ at 1.25 L₀), but had no effect at intermediate muscle lengths ∼1.1-1.15 L₀ This variable response to pressurization was qualitatively mimicked by simple physical models of muscle morphology that displayed negative, positive, or neutral responses to pressurization depending on the orientation of reinforcing fibers representing extracellular matrix collagen. These findings show that pressurization can have immediate, significant effects on muscle contractile force and suggest that forces transmitted to the extracellular matrix via pressurized fluid may be important, but largely unacknowledged, determinants of muscle performance in vivo.

Nebulin and titin modulate cross-bridge cycling and length-dependent calcium sensitivity

Various mutations in the structural proteins nebulin and titin that are present in human disease are known to affect the contractility of striated muscle. Loss of nebulin is associated with reduced actin filament length and impairment of myosin binding to actin, whereas titin is thought to regulate muscle passive elasticity and is likely involved in length-dependent activation. Here, we sought to assess the modulation of muscle function by these sarcomeric proteins by using the computational platform muscle simulation code (MUSICO) to quantitatively separate the effects of structural changes, kinetics of cross-bridge cycling, and calcium sensitivity of the thin filaments. The simulations show that variation in thin filament length cannot by itself account for experimental observations of the contractility in nebulin-deficient muscle, but instead must be accompanied by a decreased myosin binding rate. Additionally, to match the observed calcium sensitivity, the rate of TnI detachment from actin needed to be increased. Simulations for cardiac muscle provided quantitative estimates of the effects of different titin-based passive elasticities on muscle force and activation in response to changes in sarcomere length and interfilament lattice spacing. Predicted force-pCa relations showed a decrease in both active tension and sensitivity to calcium with a decrease in passive tension and sarcomere length. We conclude that this behavior is caused by partial redistribution of the muscle load between active muscle force and titin-dependent passive force, and also by redistribution of stretch along the thin filament, which together modulate the release of TnI from actin. These data help advance understanding of how nebulin and titin mutations affect muscle function.

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.

Slow-twitch skeletal muscle defects accompany cardiac dysfunction in transgenic mice with a mutation in the myosin regulatory light chain

Myosin light chain 2 ( MYL2) gene encodes the myosin regulatory light chain (RLC) simultaneously in heart ventricles and in slow-twitch skeletal muscle. Using transgenic mice with cardiac-specific expression of the human R58Q-RLC mutant, we sought to determine whether the hypertrophic cardiomyopathy phenotype observed in papillary muscles (PMs) of R58Q mice is also manifested in slow-twitch soleus (SOL) muscles. Skinned SOL muscles and ventricular PMs of R58Q animals exhibited lower contractile force that was not observed in the fast-twitch extensor digitorum longus muscles of R58Q vs. wild-type-RLC mice, but mutant animals did not display gross muscle weakness in vivo. Consistent with SOL muscle abnormalities in R58Q vs. wild-type mice, myosin ATPase staining revealed a decreased proportion of fiber type I/type II only in SOL muscles but not in the extensor digitorum longus muscles. The similarities between SOL muscles and PMs of R58Q mice were further supported by quantitative proteomics. Differential regulation of proteins involved in energy metabolism, cell-cell interactions, and protein-protein signaling was concurrently observed in the hearts and SOL muscles of R58Q mice. In summary, even though R58Q expression was restricted to the heart of mice, functional similarities were clearly observed between the hearts and slow-twitch skeletal muscle, suggesting that MYL2 mutated models of hypertrophic cardiomyopathy may be useful research tools to study the molecular, structural, and energetic mechanisms of cardioskeletal myopathy associated with myosin RLC.-Kazmierczak, K., Liang, J., Yuan, C.-C., Yadav, S., Sitbon, Y. H., Walz, K., Ma, W., Irving, T. C., Cheah, J. X., Gomes, A. V., Szczesna-Cordary, D. Slow-twitch skeletal muscle defects accompany cardiac dysfunction in transgenic mice with a mutation in the myosin regulatory light chain.

A stochastic simulation of skeletal muscle calcium transients in a structurally realistic sarcomere model using MCell

Skeletal muscle contraction is initiated when an action potential triggers the release of Ca2+ into the sarcomere in a process referred to as excitation-contraction coupling. The speed and scale of this process makes direct observation very challenging and invasive. To determine how the concentration of Ca2+ changes within the myofibril during a single activation, several simulation models have been developed. These models follow a common pattern; divide the half sarcomere into a series of compartments, then use ordinary differential equations to solve reactions occurring within and between the compartments. To further develop this type of simulation, we have created a realistic structural model of a skeletal muscle myofibrillar half-sarcomere using MCell software that incorporates the myofilament lattice structure. Using this simulation model, we were successful in reproducing the averaged calcium transient during a single activation consistent with both the experimental and previous simulation results. In addition, our simulation demonstrated that the inclusion of the myofilament lattice within our model produced an asymmetric distribution of Ca2+, with more Ca2+ accumulating near the Z-disk and less Ca2+ reaching the m-line. This asymmetric distribution of Ca2+ is also apparent when we examine how the Ca2+ are bound to the troponin-C proteins along the actin filaments. Our simulation model also allowed us to produce advanced visualizations of this process, including two simulation animations, allowing us to view Ca2+ release, diffusion, binding and uptake within the myofibrillar half-sarcomere.

Structural Determinants of Muscle Gearing During Dynamic Contractions

In skeletal muscle, interactions between contractile and connective tissue elements at multiple scales result in emergent properties that determine mechanical performance. One of these phenomena is architectural gearing, which is quantified as the ratio of muscle velocity to muscle fiber velocity. Many pennate muscles operate with a gear ratio greater than one because muscles shorten through a combination of muscle fiber shortening and fiber rotation. Within a muscle, gearing is variable across contractions. During low force contractions, muscles operate at high gear while muscles operate at low gear during high force contractions. This variable gearing has a significant impact on muscle performance as muscle architectural changes favor muscle speed during fast contractions and muscle force during slow, high force contractions. We hypothesize that gearing in any given contraction is determined by the dynamic interaction of fiber-generated forces, fluid force transmission, and the elastic behavior of intramuscular connective tissues. Because muscle is isovolumetric, muscle fibers must bulge radially when they shorten. Radial bulging and fiber-generated forces off-axis from the muscle line of action exert forces that load connective tissues that ensheath fibers, fascicles, and the whole muscle. The way in which fluid pressures and fiber forces interact to load connective tissues in three-dimensions remains poorly understood because of the complex and multiscale nature of these interactions. Here we review evidence for variable gearing in pennate muscles, present a conceptual model that describes the fundamental interactions that determine gearing, and discuss where gaps remain in our understanding of the determinants and consequences of muscle shape change and variable gearing.

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.

High tension in sarcomeres hinders myocardial relaxation: A computational study

Experiments have shown that the relaxation phase of cardiac sarcomeres during an isometric twitch is prolonged in muscles that reached a higher peak tension. However, the mechanism is not completely understood. We hypothesize that the binding of calcium to troponin is enhanced by the tension in the thin filament, thus contributing to the prolongation of contraction upon higher peak tension generation. To test this hypothesis, we developed a computational model of sarcomere mechanics that incorporates tension-dependence of calcium binding. The model was used to simulate isometric twitch experiments with time dependency in the form of a two-state cross-bridge cycle model and a transient intracellular calcium concentration. In the simulations, peak isometric twitch tension appeared to increase linearly by 51.1 KPa with sarcomere length from 1.9 μm to 2.2 μm. Experiments showed an increase of 47.3 KPa over the same range of sarcomere lengths. The duration of the twitch also increased with both sarcomere length and peak intracellular calcium concentration, likely to be induced by the inherently coupled increase of the peak tension in the thin filament. In the model simulations, the time to 50% relaxation (tR50) increased over the range of sarcomere lengths from 1.9 μm to 2.2 μm by 0.11s, comparable to the increased duration of 0.12s shown in experiments. Model simulated tR50 increased by 0.12s over the range of peak intracellular calcium concentrations from 0.87 μM to 1.45 μM. Our simulation results suggest that the prolongation of contraction at higher tension is a result of the tighter binding of Ca2+ to troponin in areas under higher tension, thus delaying the deactivation of the troponin.