Description of the molecular mechanism of cooperativity in human hemoglobin cannot be limited to a first-order free energy coupling concept

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Abstract
Studies of the linkage between ligand binding and subunit assembly of oligomeric proteins have extensively used the concept of free energy coupling. The "order" of these free energy couplings was introduced [Weber, G. (1984) Proc. Natl. Acad. Sci. U.S.A. 81, 7098-7102] as the number of subunits that must be liganded to alter specific intersubunit interactions. This concept dictates that the ligation of fewer subunits has no effect, but once the order number of subunits bocomes ligated, the specific intersubunit interaction energy between those particular subunits is completely eliminated. Weber''s report claims that the free energy coupling between oxygen binding and the dimer-tetramer subunit assembly in stripped human hemoglobin A is "first order". This conclusion is baed on the analysis of a set of previously published equilibrium constants [Mills, F. C., Johnson, M. L., and Ackers, G. K. (1976) Biochemistry 15, 5350-5362]. I subsequently reported that the original experimental data, from which the equilibrium constants were derived, are consistent with both the first-order and "second-order" free energy coupling concepts [Johnson, M. L. (1986) Biochemistry 25, 791-797]. I also demonstrated that more precise recent experimental data [Chu, A. H., Turner, B., W., and Ackers, G. K. (1984) Biochemistry, 23, 604-617] are consistent with both the first-order and second-order free energy coupling concepts. A recent article [Weber, G. (1987) Biochemistry 26, 331-332] disagrees that the oxygen-binding data for human hemoglobin A are consistent with a second-order model. This paper explains the difference in an assumption that led to different conclusions. In my first paper (Johnson, 1986) I assumed that .delta.2.alpha. need not be equal to .delta.4.alpha. and that .delta.2.beta. need to be equal to .delta.4.beta.. With that assumption I demonstrated that both the first- and second-order free energy coupling concepts are consistent with the experimental data. This paper demonstrates, assuming .delta.2.alpha. need not be equal to .delta.4.beta., that both the first- and second-order free energy coupling concepts predict a tetrameric molecule in which oxygenation promotes dissociation. If the assumption is made that .delta.2.alpha. = .delta.2.beta. = .delta.4.alpha. = .delta.4.beta., than neither the first- nor the second-order free energy coupling concept is consistent with the most current and precise experimental data (Chu et al., 1984). Consequently, with either assumption the first-order free energy coupling concept is not a necessary and sufficient condition to describe the molecular mechanism of cooperativity in human hemoglobin A.