Chemical potential measurements of deoxyhemoglobin S polymerization. Determination of the phase diagram of an assembling protein

We have used the "osmotic stress" method to determine the phase diagram of deoxyhemoglobin S polymerization. This method involves equilibration, through a semipermeable membrane, of the protein with solutions of inert polymers of known osmotic pressure. With deoxyhemoglobin A and S solutions, in which we have demonstrated achievement of equilibrium, plots of osmotic pressure versus concentration initially agree closely with the results of other methods of measurement of colligative properties. However, once the known solubility value is exceeded for the deoxyhemoglobin S solutions at various temperatures, there is a rapid rise in hemoglobin concentration over a narrow osmotic pressure range and then a more gradual increase in concentration. We believe that these two regions correspond, respectively, to the onset of the polymerization process, and of subsequent continuing growth and compression or alignment of polymer. We derive the thermodynamic values for these processes and show that the behavior of the deoxyhemoglobin S system is analogous to the phase transition for a simple chemical system. These results are relevant to understanding the intracellular polymerization of deoxyhemoglobin S in sickle cell disease, and these concepts are applicable to other protein assembly systems.