Hemoglobin S polymerization and gelation under shear II. The joint concentration and shear dependence of kinetics

The kinetics of hemoglobin S gelation are critical in sickle disease because microvascular obstruction can be avoided if red blood cells pass these vessels during the delay time, before polymerization and gelation occur in sufficient degree to rigidify the cells. Kinetics, including the delay time and the closely related exponential progress rate, are highly sensitive to hemoglobin concentration and degree of deoxygenation. Kinetics are also greatly accelerated by shear, an effect that may contribute to pathogenesis, since red blood cells deform and can undergo shear in vivo. Here we examine the joint dependence of kinetics on shear and hemoglobin concentration. As shear rate increases, the concentration dependence of the exponential progress rate decreases. The large decrease in concentration dependence supports the conclusion that acceleration of gelation by shear is due to breakage and not to enhancement of heterogeneous nucleation. Under shear, new fibers are created by breakage of existing ones, as well as by heterogeneous nucleation. At high shear, the rate of new fiber creation by breakage is very great and dominates that by heterogeneous nucleation. Therefore, if breakage depended only on shear rate and were independent of the concentration of hemoglobin in solution, the concentration dependence of kinetics should vanish. Although it decreases, it does not disappear. The concentration dependence that remains at high shear arises from (1) the direct contribution of fiber growth rate to the exponential progress rate, (2) the dependence of breakage rate on fiber growth rate, and (3) the dependence of solution viscosity on hemoglobin concentration.