One area of my research involves understanding the nucleation and growth of crystals of globular proteins from an initially homogeneous protein solution. Globular proteins are crucial to the function of living cells and biological processes. Thus biologists are trying to determine the structure of these proteins. The function of proteins depends in large part on their structure. As a consequence, scientists are currently trying to determine their molecular structure using X-ray crystallography. This in turn requires growing high quality crystals from aqueous solutions of proteins, which is very difficult to do. Crystal nucleation is the crucial bottleneck in this process and is known to depend sensitively on the initial conditions of the solution. My current research involves using theory and simulation to understand the optimal conditions for crystal nucleation. This requires determining the phase diagrams and nucleation rates for various models of globular proteins in solution, including both continuum phase field models and microscopic models of systems with short range attractive forces. The subject is quite rich, as several types of phases can occur, in addition to crystallization. For example, a liquid-liquid phase transition can take place, in which protein-rich and protein-poor liquid solutions coexist. The coexistence curve that describes this coexistence of liquid phases is metastable and terminates in a metastable critical point. The phase separation is initiated by the formation of protein-rich liquid droplets in a background of protein-poor liquid. It has been shown that the existence of this liquid-liquid phase separation can enhance crystal nucleation, although the precise mechanism by which this occurs has not yet been determined. In addition, a gel state can form, in which clusters of proteins are linked together to form a space-filling structure. Such a state is non-ergodic, as the system becomes "stuck". The gel phase is undesirable as it takes a long time for such a state to subsequently crystallize. Another state that often occurs is aggregation, in which disordered clusters of protein form in solution. Although aggregates sometimes reorder to form crystals, experimentalists try to prevent their formation.

I am also quite interested in understanding the condensation mechanisms involved in certain human diseases. Certain types of human cataracts, sickle cell anemia and Alzheimer's disease are thought to involve the (undesired) condensation of globular proteins from solution. Our group is currently studying models of these diseases, with the long range goal of understanding the microscopic basis for nucleation/condensation. This will ultimately permit scientists to avoid or slow down the undesired nucleation and hence prevent the onset of the disease. My current research in this area involves developing and solving a model for the liquid-liiquid and crystallization phase transitions associated with certain antibodies, such as the immunoglobulin IgG, which has been the subject of recent experimental studies. This work, as well as studies of other antibodies, suggest that liquid-liquid phase separation may be ubiquitous in antibody solutions. This has important biotechnological and pharmaceutical applications; in addition, such phase transitions should be important in our understanding of the cause of cryoglobulinemia, which is a condition found in several human diseases.  I am also interested in studying possible phase transitions within cells that are thought to be associated with cell compartmentalization.

Our group has also been studying the aggregation of ellipsoidal Janus particles, to see the effect of geometry on the aggregation process. We have shown that the type of aggregation depends in particular on the aspect ratio of these ellipsoids.  We have also developed a model for drug encapsulation, using the fact that ellipsoidal micelles have a relatively large empty space inside the micelles which can serve as encapsulation vehicles.  This yields a very efficient method of encapsulation.