Microcalorimetry, pH potentiometry, and direct binding studies by equilibrium dialysis or gel filtration were performed to determine the thermodynamic functions delta Ho, delta Go, and delta So guiding the interactions of Ca2+, Mg2+, and H+ with bovine brain calmodulin. At pH 7.5, Ca2+ and Mg2+ binding are both endothermic with enthalpy changes of 19.5 and 72.8 kJ X (mol of calmodulin)-1, respectively. These enthalpy changes are identical for each of the four ion-binding domains. The affinity constants also are identical with intrinsic values of 10(5) M-1 for Ca2+ and 140 M-1 for Mg2+. Ca2+ and Mg2+ do not compete for the same binding sites: at high concentrations of both ions, a calmodulin-Ca4-Mg4 species is formed with an enthalpy value of 24.4 kJ X mol-1 with respect to calmodulin-Ca4 and -28.8 kJ X mol-1 with respect to calmodulin-Mg4. Moreover, in the presence of high concentrations of Ca2+, the affinity of each of the four ion-binding domains in calmodulin for Mg2+ is decreased by a factor of 4 and vice versa, indicative of negative free-energy coupling between Ca2+ and Mg2+ binding. Protons antagonize Ca2+ and Mg2+ binding in a different manner. Ca2+-H+ antagonism is identical in each of the four Ca2+-binding domains in the pH range 7.5-5.2. Our analyses suggest that three chemical geometries, probably carboxyl-carboxylate interactions, are responsible for this antagonism with ionization constants of 10(6.2) M-1 in the metal-free protein. Mg2+-H+ antagonism also is identical for each of the Mg2+-binding sites but is qualitatively different from Ca2+-H+ antagonism.(ABSTRACT TRUNCATED AT 250 WORDS)