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⁺].