The reaction of 5,5'-dithiobis(2-nitrobenzoate), DTNB, with hemoglobin sulfhydryl groups is linked to three negatively contributing Bohr effect groups: His2β is present in all avian hemoglobins but absent in some mammalian hemoglobins; His77β and His143β are absent in avian but present in nearly all mammalian hemoglobins. To probe the consequences of these differences, we determined the influence of inositol hexakisphosphate (inositol-P6) on the DTNB affinities of avian and mammalian carbonmonoxyhemoglobins. Inositol-P6decreases by two orders of magnitude the DTNB affinity of guinea pig hemoglobin, which has His2β and the R2 quaternary structure. It decreases, or has no effect on, the DTNB affinities of hemoglobins that have His2β and whose structures lie along the R2 ⇌ R quaternary equilibrium. Finally, inositol-P6increases by one to two orders of magnitude the DTNB affinities of hemoglobins that lack His2β. Thus His2β, DTNB and inositol-P6, in combination, distinguish the R2 from the R quaternary structure.