Mesoscopic theories for protein crystal growth

A computer-simulation method is proposed for studying the hydrodynamic interactions of rigid protein molecules. It is a combination of Stokes dynamics and continuum hydrodynamics. The Stokes equations of motion for the protein molecules, the creeping-flow equation for the solvent together with the no-slip boundary conditions give a complete representation of the system. The resulting three-dimensional boundary-value problem can be rewritten in a two-dimensional form (without any loss of information) considering the surfaces of the particles only. Then, by solving the equations on discrete surface elements, the so-called mobility matrix is determined in which all hydrodynamic interactions are included. Finally, after calculation of the conservative forces and the stochastic force, the new velocities of the protein molecules can be determined. The simulation method can be applied to arbitrary particle shapes. It can also handle arbitrary flow fields, and the effects of applying a flow field to the system can be studied. From analysis of the trajectories, information can be gained on the kinetics and thermodynamics in the early stages of the crystallization process.