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

A controversial issue: Can mitochondria modulate cytosolic calcium and contraction of skeletal muscle fibers?

Mitochondria are characterized by a high capacity to accumulate calcium thanks to the electrochemical gradient created by the extrusion of protons in the respiratory chain. Thereby calcium can enter crossing the inner mitochondrial membrane via MCU complex, a high-capacity, low-affinity transport mechanism. Calcium uptake serves numerous purposes, among them the regulation of three dehydrogenases of the citric cycle, apoptosis via permeability transition, and, in some cell types, modulation of cytosolic calcium transients. This Review is focused on mitochondrial calcium uptake in skeletal muscle fibers and aims to reanalyze its functional impact. In particular, we ask whether mitochondrial calcium uptake is relevant for the control of cytosolic calcium transients and therefore of contractile performance. Recent data suggest that this may be the case, at least in particular conditions, as modified expression of MCU complex subunits or of proteins involved in mitochondrial dynamics and ablation of the main cytosolic calcium buffer, parvalbumin.

Excitation-contraction coupling in mammalian skeletal muscle: Blending old and last-decade research

The excitation–contraction coupling (ECC) in skeletal muscle refers to the Ca²⁺-mediated link between the membrane excitation and the mechanical contraction. The initiation and propagation of an action potential through the membranous system of the sarcolemma and the tubular network lead to the activation of the Ca²⁺-release units (CRU): tightly coupled dihydropyridine and ryanodine (RyR) receptors. The RyR gating allows a rapid, massive, and highly regulated release of Ca²⁺ from the sarcoplasmic reticulum (SR). The release from triadic places generates a sarcomeric gradient of Ca²⁺ concentrations ([Ca²⁺]) depending on the distance of a subcellular region from the CRU. Upon release, the diffusing Ca²⁺ has multiple fates: binds to troponin C thus activating the contractile machinery, binds to classical sarcoplasmic Ca²⁺ buffers such as parvalbumin, adenosine triphosphate and, experimentally, fluorescent dyes, enters the mitochondria and the SR, or is recycled through the Na⁺/Ca²⁺ exchanger and store-operated Ca²⁺ entry (SOCE) mechanisms. To commemorate the 7^th decade after being coined, we comprehensively and critically reviewed “old”, historical landmarks and well-established concepts, and blended them with recent advances to have a complete, quantitative-focused landscape of the ECC. We discuss the: 1) elucidation of the CRU structures at near-atomic resolution and its implications for functional coupling; 2) reliable quantification of peak sarcoplasmic [Ca²⁺] using fast, low affinity Ca²⁺ dyes and the relative contributions of the Ca²⁺-binding mechanisms to the whole concert of Ca²⁺ fluxes inside the fibre; 3) articulation of this novel quantitative information with the unveiled structural details of the molecular machinery involved in mitochondrial Ca²⁺ handing to understand how and how much Ca²⁺ enters the mitochondria; 4) presence of the SOCE machinery and its different modes of activation, which awaits understanding of its magnitude and relevance in situ; 5) pharmacology of the ECC, and 6) emerging topics such as the use and potential applications of super-resolution and induced pluripotent stem cells (iPSC) in ECC. Blending the old with the new works better!

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.

Multi-Scale Computational Modeling of Spatial Calcium Handling From Nanodomain to Whole-Heart: Overview and Perspectives

Regulation of intracellular calcium is a critical component of cardiac electrophysiology and excitation-contraction coupling. The calcium spark, the fundamental element of the intracellular calcium transient, is initiated in specialized nanodomains which co-locate the ryanodine receptors and L-type calcium channels. However, calcium homeostasis is ultimately regulated at the cellular scale, by the interaction of spatially separated but diffusively coupled nanodomains with other sub-cellular and surface-membrane calcium transport channels with strong non-linear interactions; and cardiac electrophysiology and arrhythmia mechanisms are ultimately tissue-scale phenomena, regulated by the interaction of a heterogeneous population of coupled myocytes. Recent advances in imaging modalities and image-analysis are enabling the super-resolution reconstruction of the structures responsible for regulating calcium homeostasis, including the internal structure of nanodomains themselves. Extrapolating functional and imaging data from the nanodomain to the whole-heart is non-trivial, yet essential for translational insight into disease mechanisms. Computational modeling has important roles to play in relating structural and functional data at the sub-cellular scale and translating data across the scales. This review covers recent methodological advances that enable image-based modeling of the single nanodomain and whole cardiomyocyte, as well as the development of multi-scale simulation approaches to integrate data from nanometer to whole-heart. Firstly, methods to overcome the computational challenges of simulating spatial calcium dynamics in the nanodomain are discussed, including image-based modeling at this scale. Then, recent whole-cell models, capable of capturing a range of different structures (such as the T-system and mitochondria) and cellular heterogeneity/variability are discussed at two different levels of discretization. Novel methods to integrate the models and data across the scales and simulate stochastic dynamics in tissue-scale models are then discussed, enabling elucidation of the mechanisms by which nanodomain remodeling underlies arrhythmia and contractile dysfunction. Perspectives on model differences and future directions are provided throughout.

Comprehensive Simulation of Ca2+ Transients in the Continuum of Mouse Skeletal Muscle Fiber Types

Mag-Fluo-4 has revealed differences in the kinetics of the Ca2+ transients of mammalian fiber types (I, IIA, IIX, and IIB). We simulated the changes in [Ca2+] through the sarcomere of these four fiber types, considering classical (troponin -Tn-, parvalbumin -Pv-, adenosine triphosphate -ATP-, sarcoplasmic reticulum Ca2+ pump -SERCA-, and dye) and new (mitochondria -MITO-, Na+/Ca2+ exchanger -NCX-, and store-operated calcium entry -SOCE-) Ca2+ binding sites, during single and tetanic stimulation. We found that during a single twitch, the sarcoplasmic peak [Ca2+] for fibers type IIB and IIX was around 16 µM, and for fibers type I and IIA reached 10-13 µM. The release rate in fibers type I, IIA, IIX, and IIB was 64.8, 153.6, 238.8, and 244.5 µM ms-1, respectively. Both the pattern of change and the peak concentrations of the Ca2+-bound species in the sarcoplasm (Tn, PV, ATP, and dye), the sarcolemma (NCX, SOCE), and the SR (SERCA) showed the order IIB ≥ IIX > IIA > I. The capacity of the NCX was 2.5, 1.3, 0.9, and 0.8% of the capacity of SERCA, for fibers type I, IIA, IIX, and IIB, respectively. MITO peak [Ca2+] ranged from 0.93 to 0.23 µM, in fibers type I and IIB, respectively, while intermediate values were obtained in fibers IIA and IIX. The latter numbers doubled during tetanic stimulation. In conclusion, we presented a comprehensive mathematical model of the excitation-contraction coupling that integrated most classical and novel Ca2+ handling mechanisms, overcoming the limitations of the fast- vs. slow-fibers dichotomy and the use of slow dyes.

The Ryanodine Receptor as a Sensor for Intracellular Environments in Muscles

The ryanodine receptor (RyR) is a Ca²⁺ release channel in the sarcoplasmic reticulum of skeletal and cardiac muscles and plays a key role in excitation-contraction coupling. The activity of the RyR is regulated by the changes in the level of many intracellular factors, such as divalent cations (Ca²⁺ and Mg²⁺), nucleotides, associated proteins, and reactive oxygen species. Since these intracellular factors change depending on the condition of the muscle, e.g., exercise, fatigue, or disease states, the RyR channel activity will be altered accordingly. In this review, we describe how the RyR channel is regulated under various conditions and discuss the possibility that the RyR acts as a sensor for changes in the intracellular environments in muscles.

A brief contraction has complex effects on summation of twitch pairs in human adductor pollicis

NEW FINDINGS

What is the central question of this study? How do contraction-induced reductions in twitch duration, without changes in twitch force, affect summation of twitch pairs into higher force contractions in skeletal muscle? What is the main finding and its importance? Abbreviating twitch duration with a brief contraction resulted in enhanced summation of fully fused twitch pairs, but impaired summation in partially fused twitch pairs even after accounting for the differences in relaxation of the first twitch. An inherent mechanism which enhances relaxation without sacrificing force generation in forceful contractions would benefit cyclic muscle activities, such as locomotion.

ABSTRACT

During electrically evoked contractions of skeletal muscle, the interplay between twitch duration and the time between electrical stimuli (inter-pulse interval, IPI) determines how effectively twitch forces summate into high force contractions. A brief muscle contraction can impair summation by abbreviating twitch duration, though it is not clear if these impairments occur at all physiologically relevant IPI. This study was designed to test how a brief contraction affects summation of nominally isometric twitch pairs with IPIs lasting 10-5000 ms. Left adductor pollicis muscles of human participants (n = 9) were electrically activated using stimulus pairs applied both before (Pre) and after (Post) a 10 Hz, 1.0 s contraction. Force-time records were mathematically separated into Pulse 1 (single twitch) and Pulse 2 (summated twitch) components. The ratio of Pulse 2 peak force to Pulse 1 peak force was used as our measure of summation effectiveness. Consistent with the observed decline of Pulse 1 duration at Post relative to Pre (4.7 ± 0.6%; P < 0.001; duration was defined as the time from stimulation to the time required for active force to decline by 50%), summation effectiveness was higher at Pre than at Post at IPIs of 100-333 ms. Summation effectiveness was not different between Pre and Post at IPIs of 50-83 ms or 500-5000 ms. Intriguingly, summation effectiveness was higher at Post than at Pre at IPIs of 10-25 ms. In summary, a brief contraction has complex effects on the relationship between inter-pulse interval and summation effectiveness. Future experiments are needed to reveal the mechanisms behind this novel observation.