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Trapping quaternary structures of hemoglobin in single crystals or by encapsulation in silica gels has provided a demanding set of data to test statistical mechanical models of allostery. In this work, we compare the results of those experiments with predictions of the four major allosteric models for hemoglobin: the quaternary two-state model of Monod, Wyman, and Changeux; the tertiary two-state model of Henry et al., which is the simplest extension of the Monod-Wyman-Changeux model to include pre-equilibria of tertiary as well as quaternary conformations; the structure-based model of Szabo and Karplus; and the modification of the latter model by Lee and Karplus. We show that only the tertiary two-state model can provide a near quantitative explanation of the single-crystal and gel experimental results.

Monod, Wyman, and Changeux (MWC) explained allostery in multisubunit proteins with a widely applied theoretical model in which binding of small molecules, so-called allosteric effectors, affects reactivity by altering the equilibrium between more reactive (R) and less reactive (T) quaternary structures. In their model, each quaternary structure has a single reactivity. Here, we use silica gels to trap protein conformations and a new kind of laser photolysis experiment to show that hemoglobin, the paradigm of allostery, exhibits two ligand binding phases with the same fast and slow rates in both R and T quaternary structures. Allosteric effectors change the fraction of each phase but not the rates. These surprising results are readily explained by the simplest possible extension of the MWC model to include a preequilibrium between two tertiary conformations that have the same functional properties within each quaternary structure. They also have important implications for the long-standing question of a structural explanation for the difference in hemoglobin oxygen affinity of the two quaternary structures.

A quadruple mutant of sperm whale myoglobin was constructed to mimic the structure found in Ascaris suum hemoglobin. The replacements include His(E7)--Gln, Leu(B10)--Tyr, Thr(E10)--Arg, and Ile(G8)--Phe. Single, double, and triple mutants were characterized to dissect out the effects of the individual substitutions. The crystal structures of the deoxy and oxy forms of the quadruple mutant were determined and compared with that of native Ascaris hemoglobin. Tyr(B10) myoglobin displays low O(2) affinity, high dissociation rate constants, and heterogeneous kinetic behavior, suggesting unfavorable steric interactions between the B10 phenol side chain and His(E7). In contrast, all mutants containing the Tyr(B10)/Gln(E7) pair show high O(2) affinity, low dissociation rate constants, and simple, monophasic kinetic behavior. Replacement of Ile(107) with Phe enhances nanosecond geminate recombination singly and in combination with the Tyr(B10)/Gln(E7)/Arg(E10) mutation by limiting access to the Xe4 site. These kinetic results and comparisons with native Ascaris hemoglobin demonstrate the importance of distal pocket cavities in governing the kinetics of ligand binding. The approximately 150-fold higher O(2) affinity of Ascaris hemoglobin compared with that for Tyr(B10)/Gln(E7)-containing myoglobin mutants appears to be the result of favorable proximal effects in the Ascaris protein, due to a staggered orientation of His(F8), the lack of a hydrogen bonding lattice between the F4, F7, and F8 residues, and the presence of a large polar Trp(G5) residue in the interior portion of the proximal heme pocket.