Statistical mechanics applied to cooperative ligand binding to proteins

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.

Direct measurement of the pK values of an alkaline Bohr group in human hemoglobin

Proton nuclear magnetic resonance spectra of normal and des-(his 146beta) human hemoglobin in the aromatic resonance region have been compared at different pH values. From these measurements, a pK value for histidine 146beta of 7.1 in carbonmonoxyhemoglobin and 8.0 in deoxyhemoglobin has been found. These pK values confirm the proposed role of histidine 146beta in the alkaline Bohr effect.

Functional nonequivalence of and hemes in human adult hemoglobin

Nuclear magnetic resonance studies of the contact-shifted spectra of heme protons in deoxyhemoglobin A from human adults show conclusively that oxygen binds to the alpha hemes in preference to the beta hemes. The preferential binding is produced in 10% hemoglobin solution at neutral pH by either a 15-fold molar excess of 2,3-diphosphoglycerate or a 5-fold molar excess of inositol hexaphosphate. Preferential binding is not observable in the absence of the organic phosphates. The results indicate that the oxygenation of hemoglobin may be described by a sequential model, or by a concerted model that allows the alpha hemes to bind ligand first.

Electron paramagnetic resonance studies of spin-labeled hemoglobins and their implications to the nature of cooperative oxygen binding to hemoglobin

The spin label technique has been used to study human hemoglobins A, F, Zürich, and Chesapeake as a function of carbon monoxide saturation. The experimental results suggest that the changes in the electron paramagnetic resonance spectra of hemoglobin labeled with N-(1-oxyl-2,2,6,6-tetramethyl-4-piperidinyl)iodoacetamide depend on the state of ligation of more than one heme group. For those hemoglobins with full or large cooperative ligand binding (such as A, F, and Zürich), there is a lack of isosbestic points in the spectra as a function of CO saturation. However, for those hemoglobins with little or no cooperative ligand binding (such as Chesapeake and methemoglobins), there is a sharp set of isosbestic points. These findings confirm and extend the early work of McConnell and co-workers. The absence of a set of isosbestic points in those hemoglobins with full cooperative ligand binding is consistent with the sequential model of Koshland, Némethy, and Filmer for cooperative oxygen binding to hemoglobin. The present results, with hemoglobin variants having known amino acid substitutions, also focus on the importance of the interactions among the amino acid residues located at alpha(1)-beta(2) or alpha(2)-beta(1) subunit contacts for the functioning of hemoglobin as an oxygen carrier. In addition, the resonance spectra of the spin label are very sensitive to small structural variations around the heme groups in the beta- or gamma-chains where the labels are attached. The results of the spin label experiment are discussed in relation to recent findings on the mechanism of oxygenation of hemoglobin from the nuclear magnetic resonance studies of this laboratory and the x-ray crystallographic analysis of Perutz and co-workers.