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

Excitation–contraction coupling involves sarcoplasmic reticular (SR) ryanodine receptor (RyR)-mediated Ca2+ release. The latter is driven by cisternal SR (CSR) [Ca2+], which, in turn, is determined by SR intraluminal Ca2+ diffusion patterns over timescales and spatial features precluding direct experimental study. We modeled 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 modeled 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. SR anatomy was quantifiable as a CSR giving rise to multiple longitudinal SR (LSR), with a radius of 15 nm and length of 1,800 nm, extensions. The CSR Ca2+ release produced time-dependent spatial SR Ca2+ color 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 timescales longer than <2 s. However, both longitudinal and radial [Ca2+] gradients were now undetectable, suggesting that diffusional equilibrium had now been reached along the SR axis. Available electron microscopic evidence permitted a quantitative description of SR geometry. This underpinned the 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 milliseconds, approximating equilibration over second timescales. These and the consequent SR Ca2+ effluxes were significantly sustained by calsequestrin buffering, but not background SERCA activity.