Statistical analysis of data pertaining to complex state systems by stepwise regression with reformulated parameters;...

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.