Model of Sarcomeric Ca 2 1 Movements , Including ATP Ca 2 1 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 1 ) 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 1 release are located radially around each myofibril at the Z line, their model calculated the spread of released Ca 2 1 both along and into the half sarcomere. During diffusion, Ca 2 1 was assumed to react with metal-binding sites on parvalbumin (a diffusible Ca 2 1 and Mg 2 1 -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 1 release. We use a myoplasmic diffusion constant for free Ca 2 1 that is twofold smaller and an SR Ca 2 1 release function in response to an action potential that is threefold briefer than used previously. Additionally, our model includes the effects of Ca 2 1 and Mg 2 1 binding by adenosine 5 9 -triphosphate (ATP) and the diffusion of Ca 2 1 -bound ATP (CaATP). Under the assumption that the total myoplasmic concentration of ATP is 8 mM and that the amplitude of SR Ca 2 1 release is sufficient to drive the peak change in free [Ca 2 1 ] ( D [Ca 2 1 ]) to 18 m M (the approximate spatially averaged value that is observed experimentally), our model calculates that ( a ) the spatially averaged peak increase in [CaATP] is 64 m M; ( b ) the peak saturation of troponin with Ca 2 1 is high along the entire thin filament; and ( c ) the half-width of D [Ca 2 1 ] is consistent with that observed experimentally. Without ATP, the calculated half-width of spatially averaged D [Ca 2 1 ] is abnormally brief, and troponin saturation away from the release sites is markedly reduced. We conclude that Ca 2 1 binding by ATP and diffusion of CaATP make important contributions to the determination of the amplitude and the time course of D [Ca 2 1 ]. key words: calcium transients • calcium diffusion • CaATP • ATP diffusion • muscle activation i n t r o d u c t i o n During normal activation of a skeletal muscle fiber, an action potential in the transverse tubular membranes triggers the opening of Ca 2 1 release channels in the sarcoplasmic reticulum (SR). 1 The released Ca 2 1 produces an increase in the myoplasmic free [Ca] ( D [Ca 2 1 ]), which activates the fiber’s contractile response. The SR calcium release channels (“ryanodine receptors”) are found primarily at triadic junctions, where the transverse tubules and the terminal cisternae membranes of the SR are closely apposed. In frog fibers, the triadic junctions are located primarily at the Z lines of the sarcomeres and surround each myofibril with a geometry that approximates an annulus (Peachey, 1965). With this anatomical arrangement, intra-sarcomeric gradients in myoplasmic free [Ca 2 1 ] are expected when Ca 2 1 release is active. An understanding of these gradients and the associated movements of Ca 2 1 is important in the interpretation of spatially averaged Ca 2 1 measurements of the type that have been made with a variety of Ca 2 1 indicators. They are also important in the interpretation of local Ca 2 1 measurements of the type that have been made recently with high-affinity indicators and confocal microscopy (Escobar et al., 1994; Tsugorka et al., 1995; Klein et al., 1996). Cannell and Allen (1984) were the first to use a computer model of a half-sarcomere to estimate the binding and diffusion of Ca 2 1 after its release at the Z line in response to an action potential. A principal motivation was to compare the model predictions about the amplitude and time course of D [Ca 2 1 ] with measurements of D [Ca 2 1 ] that had been obtained from frog single fibers injected with the indicator aequorin. In this article, we describe a similar computer model developed from a similar motivation. In comparison with Cannell and Allen (1984), our model incorporates three significant differences about the myoplasmic environment and the SR Ca 2 1 release process. First, we assume a twofold smaller diffusion constant for myoplasmic free Ca 2 1 (3 3 10 2 6 cm 2 s 2 1 at 16 8 C vs. 7 3 10 2 6 cm 2 s 2 1 at 20 8 C). This difference is based on the A preliminary account of some of these results was previously published in abstract form (Baylor, S.M. , and S. Hollingworth. 1998. Bio-