Ostwald-like ripening of the anomalous mesoscopic clusters in protein solutions.

Metastable clusters of mesoscopic dimensions composed of protein-rich liquid exist in protein solutions, both in the homogeneous region of the solution phase diagram and in the region supersaturated with respect to an ordered solid phase, such as crystals; in the latter region they are crucial nucleation sites for ordered solids. We monitor, using three optical techniques, the long-term evolution of the clusters in lysozyme solutions at conditions where no condensed phases, liquid or solid, are stable or present as long-lived metastable domains. We show that cluster formation is a reversible process and that the clusters are in near equilibrium with the solution, up to a capillary correction. In contrast to classical phase transformations, the solution concentration at cluster-solution equilibrium is close to its initial value; this is akin to chemical reaction equilibria and demonstrates the complex chemical composition of the clusters. However, similar to classical phase transformations, en route to full equilibration, the average cluster size grows with time following a universal law t(0.26±0.03), independent of the cluster volume fraction; the cluster size distribution is scale-invariant at all stages of cluster evolution. Despite the correspondence of these behaviors to the Lifshitz-Slyozov-Wagner (LSW) theory predictions, the cluster sizes are about 10× smaller than the LSW prediction, likely due to the complex cluster composition. The observed cluster evolution helps us to understand nucleation mysteries, such as nucleation rates lower by orders of magnitude than classical theory predictions, nucleation rate variable under steady conditions, and others.

Viscoelasticity in homogeneous protein solutions.

We probe the transport properties in protein solutions stable with respect to any, solid or liquid, phase separation as a step in the understanding of transport in the cytosol of live cells. We determine the mean-squared displacement of probe particles in the time range 10;{-3}-10 s in solutions of a model protein. The tested solutions exhibit significant elasticity at high frequencies, while at low frequencies, they are purely viscous. We attribute this viscoelasticity to a dense network of weakly-bound chains of protein molecules with characteristic lifetime of 10-100 ms. The found intrinsic viscoelasticity of protein solutions should be considered in biochemical kinetics models.

Two-step mechanism of homogeneous nucleation of sickle cell hemoglobin polymers.

Sickle cell anemia is a debilitating genetic disease that affects hundreds of thousands of babies born each year worldwide. Its primary pathogenic event is the polymerization of a mutant, sickle cell, hemoglobin (HbS); and this is one of a line of diseases (Alzheimer's, Huntington's, prion, etc.) in which nucleation initiates pathophysiology. We show that the homogeneous nucleation of HbS polymers follows a two-step mechanism with metastable dense liquid clusters serving as precursor to the ordered nuclei of the HbS polymer. The evidence comes from data on the rates of fiber nucleation and growth and nucleation delay times, the interaction of fibers with polarized light, and mesoscopic metastable HbS clusters in solution. The presence of a precursor in the HbS nucleation mechanism potentially allows low-concentration solution components to strongly affect the nucleation kinetics. The variations of these concentrations in patients might account for the high variability of the disease in genetically identical patients. In addition, these components can potentially be utilized for control of HbS polymerization and treatment of the disease.

Metastable mesoscopic clusters in solutions of sickle-cell hemoglobin.

Sickle cell hemoglobin (HbS) is a mutant, whose polymerization while in deoxy state in the venous circulation underlies the debilitating sickle cell anemia. It has been suggested that the nucleation of the HbS polymers occurs within clusters of dense liquid, existing in HbS solutions. We use dynamic light scattering with solutions of deoxy-HbS, and, for comparison, of oxy-HbS and oxy-normal adult hemoglobin, HbA. We show that solutions of all three Hb variants contain clusters of dense liquid, several hundred nanometers in size, which are metastable with respect to the Hb solutions. The clusters form within a few seconds after solution preparation and their sizes and numbers remain relatively steady for up to 3 h. The lower bound of the cluster lifetime is 15 ms. The clusters exist in broad temperature and Hb concentration ranges, and occupy 10(-5)-10(-2) of the solution volume. The results on the cluster properties can serve as test data for a potential future microscopic theory of cluster stability and kinetics. More importantly, if the clusters are a part of the nucleation mechanism of HbS polymers, the rate of HbS polymerization can be controlled by varying the cluster properties.

Spinodal for the solution-to-crystal phase transformation.

The formation of crystalline nuclei from solution has been shown for many systems to occur in two steps: the formation of quasidroplets of a disordered intermediate, followed by the nucleation of ordered crystalline embryos within these droplets. The rate of each step depends on a respective free-energy barrier and on the growth rate of its near-critical clusters. We address experimentally the relative significance of the free-energy barriers and the kinetic factors for the nucleation of crystals from solution using a model protein system. We show that crystal nucleation is 8-10 orders of magnitude slower than the nucleation of dense liquid droplets, i.e., the second step is rate determining. We show that at supersaturations of three or four k(B)T units, crystal nuclei of five, four, or three molecules transform into single-molecule nuclei, i.e., the significant nucleation barrier vanishes below the thermal energy of the molecules. We show that the main factor, which determines the rate of crystal nucleation, is the slow growth of the near-critical ordered clusters within the quasidroplets of the disordered intermediate. Analogous to the spinodal in supersaturated fluids, we define a solution-to-crystal spinodal from the transition to single-molecule crystalline nuclei. We show that heterogeneous nucleation centers accelerate nucleation not only because of the wettinglike effects that lower the nucleation barrier, as envisioned by classical theory, but by helping the kinetics of growth of the ordered crystalline embryos.

Thermodynamics of the hydrophobicity in crystallization of insulin.

For insight into the solvent structure around protein molecules and its role in phase transformations, we investigate the thermodynamics of crystallization of the rhombohedral form of porcine insulin crystals. We determine the temperature dependence of the solubility at varying concentration of the co-solvent acetone, Cac=0%, 5%, 10%, 15%, and 20%, and find that, as a rule, the solubility of insulin increases as temperature increases. The enthalpy of crystallization, undergoes a stepwise shift from approximately -20 kJ mol(-1) at Cac=0%, 5%, and 10% to approximately -55 kJ mol(-1) at Cac=15% and 20%. The entropy change upon crystallization is approximately 35 J mol(-1) K(-1) for the first three acetone concentrations, and drops to approximately -110 J mol(-1) K(-1) at Cac=15% and 20%. DeltaS degrees cryst>0 indicates release of solvent, mostly water, molecules structured around the hydrophobic patches on the insulin molecules' surface in the solution. As Cac increases to 15% and above, unstructured acetone molecules apparently displace the waters and their contribution to DeltaS degrees cryst is minimal. This shifts DeltaS degrees cryst to a negative value close to the value expected for tying up of one insulin molecule from the solution. The accompanying increase in DeltaH degrees cryst suggests that the water structured around the hydrophobic surface moieties has a minimal enthalpy effect, likely due to the small size of these moieties. These findings provide values of the parameters needed to better control insulin crystallization, elucidate the role of organic additives in the crystallization of proteins, and help us to understand the thermodynamics of the hydrophobicity of protein molecules and other large molecules.