Steady State Relation between Cytoplasmic Free Ca(2+) Concentration and Force in Intact Frog Skeletal Muscle Fibers

The steady state relation between cytoplasmic Ca(2+) concentration ([Ca(2+)](i)) and force was studied in intact skeletal muscle fibers of frogs. Intact twitch fibers were injected with the dextran-conjugated Ca(2+) indicator, fura dextran, and the fluorescence signals of fura dextran were converted to [Ca(2+)](i) using calibration parameters previously estimated in permeabilized muscle fibers (Konishi and Watanabe. 1995. J. Gen. Physiol. 106:1123–1150). In the first series of experiments, [Ca(2+)](i) and isometric force were simultaneously measured during high K(+) depolarization. Slow changes in [Ca(2+)](i) and force induced by 15–30 mM K(+) appeared to be in equilibrium, as instantaneous [Ca(2+)](i) versus force plot tracked the common path in the rising and relaxation phases of K(+) contractures. In the second series of experiments, 2,5-di-tert-butylhydroquinone (TBQ), an inhibitor of the sarcoplasmic reticulum Ca(2+) pump, was used to decrease the rate of decline of [Ca(2+)](i) after tetanic stimulation. The decay time courses of both [Ca(2+)](i) and force were dose-dependently slowed by TBQ up to 5 μM; the instantaneous [Ca(2+)](i)– force relations were nearly identical at ≥1 μM TBQ, suggesting that the change in [Ca(2+)](i) was slow enough to reach equilibrium with force. The [Ca(2+)](i)–force data obtained from the two types of experiments were consistent with the Hill curve using a Hill coefficient of 3.2–3.9 and [Ca(2+)](i) for half activation (Ca(50)) of 1.5–1.7 μM. However, if fura dextran reacts with Ca(2+) with a 2.5-fold greater K (d) as previously estimated from the kinetic fitting (Konishi and Watanabe. 1995. J. Gen. Physiol. 106:1123–1150), Ca(50) would be 3.7–4.2 μM. We also studied the [Ca(2+)]–force relation in skinned fibers under similar experimental conditions. The average Hill coefficient and Ca(50) were estimated to be 3.3 and 1.8 μM, respectively. Although uncertainties remain about the precise levels of [Ca(2+)](i), we conclude that the steady state force is a 3rd to 4th power function of [Ca(2+)](i), and Ca(50) is in the low micromolar range in intact frog muscle fibers, which is in reasonable agreement with results obtained from skinned fibers.