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

Microscale velocity-dependent unbinding generates a macroscale performance-efficiency tradeoff in actomyosin systems

Myosin motors are fundamental biological actuators that power diverse mechanical tasks in eukaryotic cells via ATP hydrolysis. Previous work has linked myosin's velocity-dependent detachment rate to macroscopic scale muscle dynamics described by Hill's model, yet its impact on energetic flows - power consumption, output, and efficiency - remains unclear. We develop an analytical model relating myosin unbinding, quantified by a dimensionless parameter α, to energetics. Our model agrees with published in-vivo muscle data and reveals a performance-efficiency tradeoff governed by α. To experimentally validate this tradeoff, we build HillBot, a robophysical Hill muscle model that mimics nonlinearity and decouples α's concurrent effects on performance and efficiency, demonstrating that nonlinearity sensitively drives efficiency. We analyze 136 published α measurements from in-vivo muscle samples and find a distribution centered at α* = 3.85 ± 2.32. Importantly, both our analytical model and HillBot - despite operating under entirely different mechanisms - converge on the finding that this value α* of nonlinearity observed in muscle corresponds to generalist actuators that balance power and efficiency. These insights inform a nonlinear variable-impedance protocol that directly shifts along a performance-efficiency axis, which could be implemented in robotics applications.

Fluid mechanics of sarcomeres as porous media

Muscle contraction, both in skeletal and cardiac tissue, is driven by sarcomeres, the microscopic units inside muscle cells where thick myosin and thin actin filaments slide past each other. During contraction and relaxation, the sarcomere's volume changes, causing sarcoplasm (intra-sarcomeric fluid) to flow out during contraction and back in as the sarcomere relaxes. We present a quantitative model of this sarcoplasmic flow, treating the sarcomere as an anisotropic porous medium with regions defined by the presence and absence of thick and thin filaments. Using semi-analytic methods, we solve for axial and lateral fluid flow within the filament lattice, calculating the permeabilities of this porous structure. We then apply these permeabilities within a Darcy model to determine the flow field generated during contraction. The predictions of our continuum model show excellent agreement with finite element simulations, reducing computational time by several orders of magnitude while maintaining accuracy in modelling the biophysical flow dynamics.

Post-natal muscle growth and protein turnover: a narrative review of current understanding

A model explaining the dietary-protein-driven post-natal skeletal muscle growth and protein turnover in the rat is updated, and the mechanisms involved are described, in this narrative review. Dietary protein controls both bone length and muscle growth, which are interrelated through mechanotransduction mechanisms with muscle growth induced both from stretching subsequent to bone length growth and from internal work against gravity. This induces satellite cell activation, myogenesis and remodelling of the extracellular matrix, establishing a growth capacity for myofibre length and cross-sectional area. Protein deposition within this capacity is enabled by adequate dietary protein and other key nutrients. After briefly reviewing the experimental animal origins of the growth model, key concepts and processes important for growth are reviewed. These include the growth in number and size of the myonuclear domain, satellite cell activity during post-natal development and the autocrine/paracrine action of IGF-1. Regulatory and signalling pathways reviewed include developmental mechanotransduction, signalling through the insulin/IGF-1-PI3K-Akt and the Ras-MAPK pathways in the myofibre and during mechanotransduction of satellite cells. Likely pathways activated by maximal-intensity muscle contractions are highlighted and the regulation of the capacity for protein synthesis in terms of ribosome assembly and the translational regulation of 5-TOPmRNA classes by mTORC1 and LARP1 are discussed. Evidence for and potential mechanisms by which volume limitation of muscle growth can occur which would limit protein deposition within the myofibre are reviewed. An understanding of how muscle growth is achieved allows better nutritional management of its growth in health and disease.

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 optimized approach to study nanoscale sarcomere structure utilizing super-resolution microscopy with nanobodies

The sarcomere is the fundamental contractile unit in skeletal muscle, and the regularity of its structure is critical for function. Emerging data demonstrates that nanoscale changes to the regularity of sarcomere structure can affect the overall function of the protein dense ~2μm sarcomere. Further, sarcomere structure is implicated in many clinical conditions of muscle weakness. However, our understanding of how sarcomere structure changes in disease, especially at the nanoscale, has been limited in part due to the inability to robustly detect and measure at sub-sarcomere resolution. We optimized several methodological steps and developed a robust pipeline to analyze sarcomere structure using structured illumination super-resolution microscopy in conjunction with commercially-available and fluorescently-conjugated Variable Heavy-Chain only fragment secondary antibodies (nanobodies), and achieved a significant increase in resolution of z-disc width (353nm vs. 62nm) compared to confocal microscopy. The combination of these methods provides a unique approach to probe sarcomere protein localization at the nanoscale and may prove advantageous for analysis of other cellular structures.

Mouse Models of Cardiomyopathies Caused by Mutations in Troponin C

Cardiac muscle contraction is regulated via Ca2+ exchange with the hetero-trimeric troponin complex located on the thin filament. Binding of Ca2+ to cardiac troponin C, a Ca2+ sensing subunit within the troponin complex, results in a series of conformational re-arrangements among the thin filament components, leading to an increase in the formation of actomyosin cross-bridges and muscle contraction. Ultimately, a decline in intracellular Ca2+ leads to the dissociation of Ca2+ from troponin C, inhibiting cross-bridge cycling and initiating muscle relaxation. Therefore, troponin C plays a crucial role in the regulation of cardiac muscle contraction and relaxation. Naturally occurring and engineered mutations in troponin C can lead to altered interactions among components of the thin filament and to aberrant Ca2+ binding and exchange with the thin filament. Mutations in troponin C have been associated with various forms of cardiac disease, including hypertrophic, restrictive, dilated, and left ventricular noncompaction cardiomyopathies. Despite progress made to date, more information from human studies, biophysical characterizations, and animal models is required for a clearer understanding of disease drivers that lead to cardiomyopathies. The unique use of engineered cardiac troponin C with the L48Q mutation that had been thoroughly characterized and genetically introduced into mouse myocardium clearly demonstrates that Ca2+ sensitization in and of itself should not necessarily be considered a disease driver. This opens the door for small molecule and protein engineering strategies to help boost impaired systolic function. On the other hand, the engineered troponin C mutants (I61Q and D73N), genetically introduced into mouse myocardium, demonstrate that Ca2+ desensitization under basal conditions may be a driving factor for dilated cardiomyopathy. In addition to enhancing our knowledge of molecular mechanisms that trigger hypertrophy, dilation, morbidity, and mortality, these cardiomyopathy mouse models could be used to test novel treatment strategies for cardiovascular diseases. In this review, we will discuss (1) the various ways mutations in cardiac troponin C might lead to disease; (2) relevant data on mutations in cardiac troponin C linked to human disease, and (3) all currently existing mouse models containing cardiac troponin C mutations (disease-associated and engineered).

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.

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.