The relationship between tension and Ca2+ concentration in single skinned muscle fibers has been determined with a high density of experimental points and the data have been fitted by a least squares method to the Hill equation. We find that the mean Hill coefficient for the slope of the tension/Ca2+ relationship is between 5 and 6, and the pKd is about 5.9. Because there are four Ca2+ binding sites on troponin C, and only two of these regulate hydrolysis of MgATP, we conclude that the regulation of tension by Ca2+ binding is greatly modified by other factors. One important factor is the time required for a cross-bridge to complete a cycle once initiated, relative to the time Ca2+ remains bound to troponin C. The pCa/tension relationship will shift to higher pCa values as the ratio of cross-bridge cycle time to the Ca2+ bound time increases. For example, the pCa/tension curve may progressively shift to the left with increase in tension because strain in the myofilament lattice progressively increases the cycle time. This left shift will produce a pCa/tension relationship that is steeper than the actual Ca2+ binding curve. The anticipated shift of the pCa/tension curve with cycle time also bears on interpretations of earlier experiments on the "active state" and on the effects of Ca2+ on the maximal velocity of shortening.

Brandt, P. W., Cox, R. N., & Kawai, M. (1980). Can the binding of Ca2+ to two regulatory sites on troponin C determine the steep pCa/tension relationship of skeletal muscle? Proceedings of the National Academy of Sciences, 77(8), 4717–4720.