Weighting functions and parameter resolvability for oxygenation data subject to error in the independent variable

Statistical analysis of data pertaining to complex state systems by stepwise regression with reformulated parameters; application to spectroscopically monitored hemoglobin oxygen binding data

A method is described for the statistical analysis of data pertaining to complex state systems, based on the concept of reformulating the parameters describing the system as a hierarchy of interactions, and this method demonstrated on the analysis of spectroscopically monitored hemoglobin oxygen binding data [K. Imai, Biophys. Chem. 37 (1990) 197-210]. The concept of reformulation was first extended to state parameters other than delta G degree s, such as the extinction coefficients (epsilon s) associated with different ligation states during hemoglobin oxygen binding. The reformulated parameters are incrementally allowed to vary in the data fitting procedure, and the statistical significance of the added parameters tested by F and Kolmogorov-Smirnov tests. The result of this method is the minimal set of statistically significant parameters required to describe the data. The hierarchical nature of reformulated parameters allows the physical significance of the subset of statistically significant parameters to be discussed even when all reformulated terms may not be statistically significant. Applying this method to hemoglobin oxygen binding data with the reformulated Adair model demonstrated that at least two, and at most three, of the four reformulated Adair constants are statistically significant. A reformulated square model was found to give a statistically indistinguishable fit from the Adair model, with the statistically significant thermodynamic terms essentially those proposed by Linus Pauling in 1935. A change in delta epsilon with subsequent oxygen binding events was found to be significant in both models. These results are consistent with a model for hemoglobin oxygen binding where a subunit changes its conformation upon oxygen binding, and affects the conformation of adjacent subunits.

Effects of NaCl on the linkages between O2 binding and subunit assembly in human hemoglobin: titration of the quaternary enhancement effect

Oxygen binding by human hemoglobin (Hb) and the coupled reactions of dimer-tetramer assembly were studied over a range of NaCl concentrations (from 0.08 M to 1.4 M) at pH 7.4 and 21.5 degrees C. A strategy of multi-dimensional analysis was employed [G.K. Ackers and H.R. Halvorson, Proc. Natl. Acad. Sci. U.S.A., 91, (1974) 4312] to optimize the resolution of the contributions to cooperativity and their heterotropic salt linkages at each stoichiometric degree of O2 binding. A wide range of Hb concentration was utilized at each [NaCl] in which O2-linked subunit assembly reactions contributed significantly to the positions and shapes of the binding isotherms. Kinetic determinations yielded forward and reverse rate constants for assembly of the unligated species. Amplitudes for the assembly rate data had concentration dependences in agreement with the independently determined dimer-tetramer assembly constants of oxyhemoglobin. Concentration-dependent binding isotherms were analyzed, in combination with the kinetically determined equilibrium constants, to yield salt-linked components of cooperativity at the four stages of oxygenation. The principal results of this study were as follows. (i) Assembly of fully oxygenated Hb tetramers is opposed by NaCl: the dimer-to-tetramer equilibrium constant becomes two orders of magnitude less favorable over the [NaCl] range 0.08 M to 1.4 M. By contrast, for deoxy-Hb the assembly equilibrium constant is reduced only two-fold. (ii) Oxygen binding to dimers is non-cooperative over the entire salt range, whereas dimer affinity is slightly favored by increasing the NaCl concentration. (iii) Overall affinity of tetramers for O2 is opposed by NaCl, becoming an order of magnitude less favorable over the range employed. Most of this decrease occurs at the fourth binding step, which shows a large, salt-mediated quaternary enhancement effect; i.e., the assembly of dimers into tetramers at 0.08 M NaCl is accompanied by an eight-fold increase in O2 affinity. (iv) The quaternary enhancement effect at the last O2-binding step is titrated progressively by salt until it reaches a negligible value near the highest [NaCl] of this study. The lowest [NaCl] condition (0.08 M) elicits the greatest tetramer cooperativity with the largest maximal Hill coefficient and the greatest suppression of intermediates. Possible origins and mechanistic implications of these phenomena are considered.

Regulation of oxygen affinity by quaternary enhancement: does hemoglobin Ypsilanti represent an allosteric intermediate?

Recent crystallographic studies on the mutant human hemoglobin Ypsilanti (beta 99 Asp-->Tyr) have revealed a previously unknown quaternary structure called "quaternary Y" and suggested that the new structure may represent an important intermediate in the cooperative oxygenation pathway of normal hemoglobin. Here we measure the oxygenation and subunit assembly properties of hemoglobin Ypsilanti and five additional beta 99 mutants (Asp beta 99-->Val, Gly, Asn, Ala, His) to test for consistency between their energetics and those of the intermediate species of normal hemoglobin. Overall regulation of oxygen affinity in hemoglobin Ypsilanti is found to originate entirely from 2.6 kcal of quaternary enhancement, such that the tetramer oxygenation affinity is 85-fold higher than for binding to the dissociated dimers. Equal partitioning of this regulatory energy among the four tetrameric binding steps (0.65 kcal per oxygen) leads to a noncooperative isotherm with extremely high affinity (pmedian = .14 torr). Temperature and pH studies of dimer-tetramer assembly and sulfhydryl reaction kinetics suggest that oxygenation-dependent structural changes in hemoglobin Ypsilanti are small. These properties are quite different from the recently characterized allosteric intermediate, which has two ligands bound on the same side of the alpha 1 beta 2 interface (see ref. 1 for review). The combined results do, however, support the view that quaternary Y may represent the intermediate cooperativity state of normal hemoglobin that binds the last oxygen.