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The binding of oxygen and 1-oxyl-2,2,6,6-tetramethylpiperidine 4-triphosphate (spin-labeled triphosphate) to normal adult human hemoglobin (HbA) covalently labeled at the beta-93 sulfhydryl groups with N-(2,2,6,6-tetramethyl-4-piperidinyl)iodoacetamide (I) was studied. HbA-I was used as a model for HbA labeled at the beta-93 SH groups with N-(1-oxyl-2,2,6,6-tetramethyl-4-piperidinyl)iodoacetamide (II) since the binding of SLTP to HbA-II could not be measured conveniently, in the presence of the paramagnetic resonance signal of II. Both HbA-I and HbA-II can be treated as variant hemoglobins with abnormal beta chains. The oxygen and SLTP binding data from HbA-I and oxygen binding data from HbA-II are consistent with a concerted transition model for cooperativity which assumes nonequivalence between alpha and beta subunits (GCT model). The distribution of environments "seen" by conformation sensitive probes such as II and trifluoracetone (19F NMR probe) attached to the beta-93 sulfhydryl groups of HbA can also be accounted for by the GCT model. It is proposed that the beta-93 probes sense the dramatic change in beta subunit structure resulting from the quaternary structure change (T leads to R) upon heme saturation as well as tertiary structure changes at the alpha1-beta2 contact region resulting from ligand binding to the beta-heme group. Structural changes caused by ligation of the alpha-hemes are not discussed.