Sickle hemoglobin gelation. Reaction order and critical nucleus size

Sickle hemoglobin (Hb S) gelation displays kinetics consistent with a rate-limiting nucleation step. The approximate size of the critical nucleus can be inferred from the order of the reaction with respect to Hb S activity, but determination of the reaction order is complicated by the fact that Hb S activity is substantially different from Hb S concentration at the high protein concentrations required for gelation. Equilibrium and kinetic experiments on Hb S gelation were designed to evaluate the relative activity coefficient of Hb S as a function of concentration. These experiments used non-Hb S proteins to mimic, and thus evaluate, the effect on activity coefficients of increasing Hb S concentration. At Hb S concentrations near 20% the change in Hb S activity coefficient generates two-thirds of the apparent dependence of nucleation rate on Hb S concentration. When this effect is explicitly accounted for, the nucleation reaction is seen to be approximately 10th-order with respect to effective number concentration of Hb S. The closeness of the reaction order to the number of strands in models of Hb S fibers suggests a nucleus close to the size of one turn of the Hb S fiber. These experiments introduce a new approach to the study of Hb S gelation, the equal activity isotherm, used here also to show that Hb S.Hb A (normal adult hemoglobin) hybrids do incorporate into growing nuclei and stable microtubules but that A.S hybridization is neutral with respect to promotion of Hb S nucleation and the sol-gel equilibrium.