Model of Sarcomeric Ca2+ Movements, Including ATP Ca2+ Binding and Diffusion, during Activation of Frog Skeletal Muscle

Cannell and Allen (1984. Biophys. J. 45:913–925) introduced the use of a multi-compartment model to estimate the time course of spread of calcium ions (Ca2+) within a half sarcomere of a frog skeletal muscle fiber activated by an action potential. Under the assumption that the sites of sarcoplasmic reticulum (SR) Ca2+ release are located radially around each myofibril at the Z line, their model calculated the spread of released Ca2+ both along and into the half sarcomere. During diffusion, Ca2+ was assumed to react with metal-binding sites on parvalbumin (a diffusible Ca2+- and Mg2+-binding protein) as well as with fixed sites on troponin. We have developed a similar model, but with several modifications that reflect current knowledge of the myoplasmic environment and SR Ca2+ release. We use a myoplasmic diffusion constant for free Ca2+ that is twofold smaller and an SR Ca2+ release function in response to an action potential that is threefold briefer than used previously. Additionally, our model includes the effects of Ca2+ and Mg2+ binding by adenosine 5′-triphosphate (ATP) and the diffusion of Ca2+-bound ATP (CaATP). Under the assumption that the total myoplasmic concentration of ATP is 8 mM and that the amplitude of SR Ca2+ release is sufficient to drive the peak change in free [Ca2+] (Δ[Ca2+]) to 18 μM (the approximate spatially averaged value that is observed experimentally), our model calculates that (a) the spatially averaged peak increase in [CaATP] is 64 μM; (b) the peak saturation of troponin with Ca2+ is high along the entire thin filament; and (c) the half-width of Δ[Ca2+] is consistent with that observed experimentally. Without ATP, the calculated half-width of spatially averaged Δ[Ca2+] is abnormally brief, and troponin saturation away from the release sites is markedly reduced. We conclude that Ca2+ binding by ATP and diffusion of CaATP make important contributions to the determination of the amplitude and the time course of Δ[Ca2+].