Interactions between Connected Half-Sarcomeres Produce Emergent Mechanical Behavior in a Mathematical Model of Muscle

Most reductionist theories of muscle attribute a fiber's mechanical properties to the scaled behavior of a single half-sarcomere. Mathematical models of this type can explain many of the known mechanical properties of muscle but have to incorporate a passive mechanical component that becomes ∼300% stiffer in activating conditions to reproduce the force response elicited by stretching a fast mammalian muscle fiber. The available experimental data suggests that titin filaments, which are the mostly likely source of the passive component, become at most ∼30% stiffer in saturating Ca2+ solutions. The work described in this manuscript used computer modeling to test an alternative systems theory that attributes the stretch response of a mammalian fiber to the composite behavior of a collection of half-sarcomeres. The principal finding was that the stretch response of a chemically permeabilized rabbit psoas fiber could be reproduced with a framework consisting of 300 half-sarcomeres arranged in 6 parallel myofibrils without requiring titin filaments to stiffen in activating solutions. Ablation of inter-myofibrillar links in the computer simulations lowered isometric force values and lowered energy absorption during a stretch. This computed behavior mimics effects previously observed in experiments using muscles from desmin-deficient mice in which the connections between Z-disks in adjacent myofibrils are presumably compromised. The current simulations suggest that muscle fibers exhibit emergent properties that reflect interactions between half-sarcomeres and are not properties of a single half-sarcomere in isolation. It is therefore likely that full quantitative understanding of a fiber's mechanical properties requires detailed analysis of a complete fiber system and cannot be achieved by focusing solely on the properties of a single half-sarcomere

A Mathematical Model of Muscle Containing Heterogeneous Half-Sarcomeres Exhibits Residual Force Enhancement

A skeletal muscle fiber that is stimulated to contract and then stretched from L1 to L2 produces more force after the initial transient decays than if it is stimulated at L2. This behavior has been well studied experimentally, and is known as residual force enhancement. The underlying mechanism remains controversial. We hypothesized that residual force enhancement could reflect mechanical interactions between heterogeneous half-sarcomeres. To test this hypothesis, we subjected a computational model of interacting heterogeneous half-sarcomeres to the same activation and stretch protocols that produce residual force enhancement in real preparations. Following a transient period of elevated force associated with active stretching, the model predicted a slowly decaying force enhancement lasting >30 seconds after stretch. Enhancement was on the order of 13% above isometric tension at the post-stretch muscle length, which agrees well with experimental measurements. Force enhancement in the model was proportional to stretch magnitude but did not depend strongly on the velocity of stretch, also in agreement with experiments. Even small variability in the strength of half-sarcomeres (2.1% standard deviation, normally distributed) was sufficient to produce a 5% force enhancement over isometric tension. Analysis of the model suggests that heterogeneity in half-sarcomeres leads to residual force enhancement by storing strain energy introduced during active stretch in distributions of bound cross-bridges. Complex interactions between the heterogeneous half-sarcomeres then dissipate this stored energy at a rate much slower than isolated cross-bridges would cycle. Given the variations in half-sarcomere length that have been observed in real muscle preparations and the stochastic variability inherent in all biological systems, half-sarcomere heterogeneity cannot be excluded as a contributing source of residual force enhancement

Approximation for Cooperative Interactions of a Spatially-Detailed Cardiac Sarcomere Model

We developed a novel ordinary differential equation (ODE) model, which produced results that correlated well with the Monte Carlo (MC) simulation when applied to a spatially-detailed model of the cardiac sarcomere. Configuration of the novel ODE model was based on the Ising model of myofilaments, with the “co-operative activation” effect introduced to incorporate nearest-neighbor interactions. First, a set of parameters was estimated using arbitrary Ca transient data to reproduce the combinational probability for the states of three consecutive regulatory units, using single unit probabilities for central and neighboring units in the MC simulation. The parameter set thus obtained enabled the calculation of the state transition of each unit using the ODE model with reference to the neighboring states. The present ODE model not only provided good agreement with the MC simulation results but was also capable of reproducing a wide range of experimental results under both steady-state and dynamic conditions including shortening twitch. The simulation results suggested that the nearest-neighbor interaction is a reasonable approximation of the cooperativity based on end-to-end interactions. Utilizing the modified ODE model resulted in a reduction in computational costs but maintained spatial integrity and co-operative effects, making it a powerful tool in cardiac modeling

Axial and Radial Forces of Cross-Bridges Depend on Lattice Spacing

Nearly all mechanochemical models of the cross-bridge treat myosin as a simple linear spring arranged parallel to the contractile filaments. These single-spring models cannot account for the radial force that muscle generates (orthogonal to the long axis of the myofilaments) or the effects of changes in filament lattice spacing. We describe a more complex myosin cross-bridge model that uses multiple springs to replicate myosin's force-generating power stroke and account for the effects of lattice spacing and radial force. The four springs which comprise this model (the 4sXB) correspond to the mechanically relevant portions of myosin's structure. As occurs in vivo, the 4sXB's state-transition kinetics and force-production dynamics vary with lattice spacing. Additionally, we describe a simpler two-spring cross-bridge (2sXB) model which produces results similar to those of the 4sXB model. Unlike the 4sXB model, the 2sXB model requires no iterative techniques, making it more computationally efficient. The rate at which both multi-spring cross-bridges bind and generate force decreases as lattice spacing grows. The axial force generated by each cross-bridge as it undergoes a power stroke increases as lattice spacing grows. The radial force that a cross-bridge produces as it undergoes a power stroke varies from expansive to compressive as lattice spacing increases. Importantly, these results mirror those for intact, contracting muscle force production

Factors Underlying the Early Limb Muscle Weakness in Acute Quadriplegic Myopathy Using an Experimental ICU Porcine Model

The basic mechanisms underlying acquired generalized muscle weakness and paralysis in critically ill patients remain poorly understood and may be related to prolonged mechanical ventilation/immobilization (MV) or to other triggering factors such as sepsis, systemic corticosteroid (CS) treatment and administration of neuromuscular blocking agents (NMBA). The present study aims at exploring the relative importance of these factors by using a unique porcine model. Piglets were all exposed to MV together with different combinations of endotoxin-induced sepsis, CS and NMBA for five days. Peroneal motor nerve conduction velocity and amplitude of the compound muscle action potential (CMAP) as well as biceps femoris muscle biopsy specimens were obtained immediately after anesthesia on the first day and at the end of the 5-day experimental period. Results showed that peroneal nerve motor conduction velocity is unaffected whereas the size of the CMAP decreases independently of the type of intervention, in all groups after 5 days. Otherwise, despite a preserved size, muscle fibre specific force (maximum force normalized to cross-sectional area) decreased dramatically for animals exposed to MV in combination with CS or/and sepsis. These results suggest that the rapid declines in CMAP amplitude and in force generation capacity are triggered by independent mechanisms with significant clinical and therapeutic implications

β-alanine supplementation improves in-vivo fresh and fatigued skeletal muscle relaxation speed

Purpose: In fresh muscle, supplementation with the rate-limiting precursor of carnosine, β-alanine (BA), results in a decline in muscle half-relaxation time (HRT) potentially via alterations to calcium (Ca2+) handling. Accumulation of hydrogen cation (H+) has been shown to impact Ca2+ signalling during muscular contraction, carnosine has the potential to serve as a cytoplasmic regulator of Ca2+ and H+ coupling, since it binds to both ions. The present study examined the effect of BA supplementation on intrinsic in-vivo isometric knee extensor force production and muscle contractility in both fresh and fatigued human skeletal muscle assessed during voluntary and electrically evoked (nerve and superficial muscle stimulation) contractions. Methods: Twenty-three males completed two experimental sessions, pre- and post- 28 day supplementation with 6.4 g.day−1 of BA (n=12) or placebo (PLA; n=11). Isometric force was recorded during a series of voluntary and electrically evoked knee extensor contractions. Results: BA supplementation had no effect on voluntary or electrically  evoked isometric force production, or twitch electromechanical delay and time-to-peak tension. There was a significant decline in muscle HRT in fresh and fatigued muscle conditions  during both resting (3±13%; 19±26%) and potentiated (1±15%; 2±20%) twitch contractions. Conclusions: The mechanism for reduced HRT in fresh and fatigued skeletal muscle following BA supplementation is unclear. Due to the importance of muscle relaxation on total energy consumption, especially during short, repeated contractions, BA supplementation may prove to be beneficial in minimising contractile slowing induced by fatigue. Trial registration The trial is registered with Clinicaltrials.gov, ID number NCT02819505

The cardiac troponin C mutation Leu29Gln found in a patient with hypertrophic cardiomyopathy does not alter contractile parameters in skinned murine myocardium

The present study investigates the effects of the first mutation of troponin C (hcTnCL29Q) found in a patient with hypertrophic cardiomyopathy (HCM) on force–pCa relations and the interplay with phosphorylation of sarcomeric PKA substrates. In triton-skinned murine cardiac fibers, the endogenous mcTnC was extracted and the fibers were subsequently reconstituted with recombinant wild-type and mutant hcTnC. Force–pCa relations of preparations containing hcTnCL29Q or hcTnCWT were similar. Incubation of fibers reconstituted with the recombinant proteins with phosphatase to dephosphorylate sarcomeric PKA substrates induced an increase in Ca2+ sensitivity, slightly more pronounced (0.04 pCa units) in hcTnCL29Q-containing fibers. Incubation of the dephosphorylated fibers with PKA induced significant rightward shifts of force–pCa relations of similar magnitude with both, hcTnCL29Q and hcTnCWT. No significant effects of hcTnCL29Q on the velocity of unloaded shortening were observed. In conclusion, no major differences in contractile parameters of preparations containing hcTnCL29Q compared to hcTnCWT were observed. Therefore, it appears unlikely that hcTnCL29Q induces the development of HCM by affecting the regulation of Ca2+-activated force and interference with PKA-mediated modulation of the Ca2+ sensitivity of contraction

Open Data for Global Science

The global science system stands at a critical juncture. On the one hand, it is overwhelmed by a hidden avalanche of ephemeral bits that are central components of modern research and of the emerging ‘cyberinfrastructure’4 for e-Science.5 The rational management and exploitation of this cascade of digital assets offers boundless opportunities for research and applications. On the other hand, the ability to access and use this rising flood of data seems to lag behind, despite the rapidly growing capabilities of information and communication technologies (ICTs) to make much more effective use of those data. As long as the attention for data policies and data management by researchers, their organisations and their funders does not catch up with the rapidly changing research environment, the research policy and funding entities in many cases will perpetuate the systemic inefficiencies, and the resulting loss or underutilisation of valuable data resources derived from public investments. There is thus an urgent need for rationalised national strategies and more coherent international arrangements for sustainable access to public research data, both to data produced directly by government entities and to data generated in academic and not-for-profit institutions with public funding. In this chapter, we examine some of the implications of the ‘data driven’ research and possible ways to overcome existing barriers to accessibility of public research data. Our perspective is framed in the context of the predominantly publicly funded global science system. We begin by reviewing the growing role of digital data in research and outlining the roles of stakeholders in the research community in developing data access regimes. We then discuss the hidden costs of closed data systems, the benefits and limitations of openness as the default principle for data access, and the emerging open access models that are beginning to form digitally networked commons. We conclude by examining the rationale and requirements for developing overarching international principles from the top down, as well as flexible, common-use contractual templates from the bottom up, to establish data access regimes founded on a presumption of openness, with the goal of better capturing the benefits from the existing and future scientific data assets. The ‘Principles and Guidelines for Access to Research Data from Public Funding’ from the Organisation for Economic Cooperation and Development (OECD), reported on in another article by Pilat and Fukasaku,6 are the most important recent example of the high-level (inter)governmental approach. The common-use licenses promoted by the Science Commons are a leading example of flexible arrangements originating within the community. Finally, we should emphasise that we focus almost exclusively on the policy—the institutional, socioeconomic, and legal aspects of data access—rather than on the technical and management practicalities that are also important, but beyond the scope of this article