A theoretical analysis of binding to the Ca2+-specific sites on troponin incorporated into thin filaments

Recent data on the binding of Ca2+ to the specific sites on troponin, alone, in regulated actin, and in regulated actomyosin, as well as data on the Ca2+ activation of the actomyosin ATPase (Grabarek, Z., J. Grabarek, P.C. Leavis, and J. Gergely, 1983, J. Biol. Chem., 258:14098–14102.), are analyzed on the basis of a model used previously for qualitative theoretical studies of the Ca2+ activation of muscle contraction (Shiner and Solaro, 1982). The data allow and require an extension of the model to consider the effects of tropomyosin explicitly. Three major results of the analysis are at variance with previous investigations. A repulsive interaction between tropomyosins; and an attractive interaction between actins (or myosin heads attached to actin) are found, whereas others have found or assumed an attractive tropomyosin-tropomyosin interaction and no actin-actin interaction. The parameter values found here predict hysteresis under the conditions of the ATPase experiments; no other existing model for the interactions manifest in the Ca2+ activation of contraction can predict hysteresis. The prediction is of increased interest in light of experimental reports of hysteresis in the Ca2+ activation of isometric force (Ridgeway, E. B., A. M. Gordon, and D. A. Martyn, 1983, Science (Wash. DC), 219:1075–1077; Gordon, A. M., E. B. Ridgeway, and D. A. Martyn, 1984, Plenum Publishing Corp., New York, 553–563; Brandt, P. W., B. Gluck, M. Mini, and C. Cerri, 1985, J. Mus. Res. Cell Motil. 6:197–205.)