The cooperative equilibrium binding of Ca2+ by sarcoplasmic reticulum ATPase, as modulated by pH, is analyzed by statistical mechanical treatment of a theoretical model. The model consists offour equivalent subunits, in the form ofa square, with nearest-neighbor interactions. Each subunit has one site for binding of one Ca2+ or one proton, but not both. Binding ofeither ligand on a subunit induces a conformational change in the subunit that alters its interaction with its two neighbors. The model gives good agreement with experimental binding data. It should prove useful as a starting point in the analysis of steady-state ATPase activity as a function of Ca2+ and H+ concentrations.Calcium binding is an absolute requirement for activation of sarcoplasmic reticulum (SR) ATPase. Of various classes of binding sites found in SR vesicles (1-4), only a class of high affinity sites is specifically involved in enzyme activation and calcium transport (5-7). Occupation of these sites is accompanied by protein (ATPase) conformational changes, as shown with various spectroscopic methods (8-11).Under equilibrium conditions, the Ca2+ concentration dependence of binding and of Ca2+-induced conformational changes are identical, and the shape ofthe Ca2O titration curves suggests a cooperative binding mechanism (12). In fact, the experimental points obtained at neutral pH were satisfactorily fitted by the use of empirical equations assuming two interacting binding-site domains and were consistent with the notion that two calcium ions are transported per enzyme cycle (13,14). With the more elaborate analysis of the present paper, using a different pCa scale, we find that two interacting domains are not sufficient.Subsequent studies (15) A family of curves displaying calcium binding to SR vesicles as a function of molar Ca2+(c1) and H+(c2) concentrations is shown in Fig. 1. Most of these data were presented previously (12,15). The two different values for maximal binding mentioned in the figure legend reflect the different specific activity of SR preparations over a 3-yr period. The fractional saturation 6 is used as ordinate in the figure.THE MODEL AND ITS PROPERTIES The Ca2+ binding curves in Fig. 1 The publication costs ofthis article were defrayed in part by page charge payment. This article must therefore be hereby marked "advertisement" in accordance with 18 U. S. C. §1734 solely to indicate this fact.