Finite element modelling of sarcoplasmic reticular intraluminal Ca2+ diffusional fluxes during amphibian striated muscle excitation-contraction coupling

Introduction. Excitation-contraction coupling involves sarcoplasmic reticular (SR) ryanodine receptor (RyR)-mediated Ca2+ release. The latter is driven by cisternal SR (CSR) [Ca2+], in turn determined by SR intraluminal Ca2+ diffusion patterns over timescales and spatial features precluding direct experimental study. Materials and Methods. We modelled these diffusive fluxes and consequent total, [Ca2+]total, and free Ca2+ concentration, [Ca2+]free, patterns. This utilized established amphibian skeletal muscle SR anatomy, initial resting [Ca2+]total, [Ca2+]free, calsequestrin concentrations [Casq] and dissociation constants, and their related Ca2+ diffusion coefficients. Step increases in CSR membrane Ca2+ permeabilities were modelled to give initial CSR Ca2+ release rates compatible with previous reports. The latter were either held constant or permitted to decay with the consequent CSR [Ca2+]free depletion. Results. SR anatomy was quantifiable as a CSR giving rise to multiple longitudinal SR (LSR), radius 15 nm, length 1800 nm, extensions. The CSR Ca2+ release produced time-dependent spatial SR Ca2+ colour maps. These showed time-evolving, axial SR [Ca2+]free and [Ca2+]total gradients over 0-20 ms. Calsequestrin increased the absolute [Ca2+]free and [Ca2+]total values, slowed their temporal decays and reduced their axial gradients. There were no significant radial LSR [Ca2+] gradients. These findings implicated both calsequestrin and LSR geometry in determining the Ca2+ diffusion patterns. Calsequestrin also slowed the decays of the resulting T-SR membrane Ca2+ fluxes with time. Background SERCA activity levels contrastingly contributed negligibly to either [Ca2+] patterns or these diffusional fluxes. Patterns of declining [Ca2+]free and [Ca2+]total and SR Ca2+ effluxes and effects or otherwise of calsequestrin and/or SERCA activity also occurred over longer <2 s, timescales. However, both longitudinal and radial [Ca2+] gradients were now undetectable, suggesting diffusional equilibrium had now been reached along the SR axis. Conclusion. Available electronmicroscopic evidence permitted a quantitative description of SR geometry. This underpinned simplified modeling of SR intraluminal Ca2+ diffusion, Ca2+-calsequestrin buffering and background SERCA activity following the CSR Ca2+ release initiating excitation-contraction coupling. This predicted one-dimensional SR axial but not radial diffusional gradients over ms approximating equilibration over second timescales. These, and the consequent SR Ca2+ effluxes were significantly sustained by calsequestrin buffering but not background SERCA activity.