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.Author summary: In this study we develop a structural stochastic diffusion model, to study how calcium ions diffuse and interact within a skeletal muscle sarcomere following a simulated muscle activation. This type of model allows us to explore how structural elements, namely the actin and myosin filaments, within the sarcomere affect calcium diffusion, and the model provides a level of resolution for ligand-protein reactions that is currently unattainable with other types of diffusion models. This type of model is novel in that we topologically represent common protein structures within the sarcomere model. This topological representation of the myofibril includes the actin and myosin proteins which compose the filament lattice, the shape of the sarcoplasmic reticulum (SR), the placement of the SR bound calcium pumps (SERCA), as well as the position of the calcium release sites (RYR receptors) within the triad (SR and T-tubule connection), which together describe the micro-architecture of the sarcomere. This type of modelling is also unique as it allows the results to emerge from the interaction of the defined parameters powered by the random nature of diffusion. Using this new model we are able to show that calcium ions do not diffuse in a uniform fashion from the calcium release site, instead the diffusion is biased towards z-disks where there are fewer myosin filaments. We also see evidence that previous modelling techniques may be underestimating both the release rate from troponin-c, and the transfer rate of SERCA.