Model of Sarcomeric Ca(2+) Movements, Including ATP Ca(2+) 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 (Ca(2+)) 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) Ca(2+) release are located radially around each myofibril at the Z line, their model calculated the spread of released Ca(2+) both along and into the half sarcomere. During diffusion, Ca(2+) was assumed to react with metal-binding sites on parvalbumin (a diffusible Ca(2+)- and Mg(2+)-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 Ca(2+) release. We use a myoplasmic diffusion constant for free Ca(2+) that is twofold smaller and an SR Ca(2+) release function in response to an action potential that is threefold briefer than used previously. Additionally, our model includes the effects of Ca(2+) and Mg(2+) binding by adenosine 5′-triphosphate (ATP) and the diffusion of Ca(2+)-bound ATP (CaATP). Under the assumption that the total myoplasmic concentration of ATP is 8 mM and that the amplitude of SR Ca(2+) release is sufficient to drive the peak change in free [Ca(2+)] (Δ[Ca(2+)]) 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 Ca(2+) is high along the entire thin filament; and (c) the half-width of Δ[Ca(2+)] is consistent with that observed experimentally. Without ATP, the calculated half-width of spatially averaged Δ[Ca(2+)] is abnormally brief, and troponin saturation away from the release sites is markedly reduced. We conclude that Ca(2+) binding by ATP and diffusion of CaATP make important contributions to the determination of the amplitude and the time course of Δ[Ca(2+)].