Statistical Mechanics Applied to Cooperative Ligand Binding to Proteins

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By using the lattice statistical argument, we have shown that for a protein whose subunits have the same number of neighbors, the three parameters (KAB, KBB, and KSKt) 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 (ΔF°I) by Z = exp (-ΔF°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.

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