By using the lattice statistical argument, we have shown that for a protein whose subunits have the same number of neighbors, the three parameters (K(AB), K(BB), and K(S)K(t)) in the sequential theory formulated by Koshland, Nemethy, and Filmer [Biochemistry (1966) 5, 365] can be reduced to two parameters. One of the parameters, Z, measures the strength of the subunit interactions and is related to the apparent free energy of interaction (DeltaF degrees I) by Z = exp (-DeltaF degrees I/2mkT), where m is the number of neighbors in a subunit and kT has the usual meaning. In addition, we relate Wyman's allosteric binding potential [Advan. Protein Chem. (1964) 19, 223] to the canonical partition function of the McMillan-Mayer theory [J. Chem. Phys. (1945) 13, 276]. An explicit form relating the apparent free energy of interaction and the Hill coefficient is given for an allosteric protein that has nonequivalent and independent ligand-binding sites. The present formulation can be used to account for a number of recent experimental results on hemoglobins.