Modeling the crystallization of proteins and small organic molecules in nanoliter drops

Drop-based crystallization techniques are used to achieve a high degree of control over crystallization conditions in order to grow high-quality protein crystals for X-ray diffraction or to produce organic crystals with well-controlled size distributions. Simultaneous crystal growth and stochastic nucleation makes it difficult to predict the number and size of crystals that will be produced in a drop-based crystallization process. A mathematical model of crystallization in drops is developed using a Monte Carlo method. The model incorporates key phenomena in drop-based crystallization, including stochastic primary nucleation and growth rate dispersion (GRD) and can predict distributions of the number of crystals per drop and full crystal size distributions (CSD). Key dimensionless parameters are identified to quickly screen for crystallization conditions that are expected to yield a high fraction of drops containing one crystal and a narrow CSD. Using literature correlations for the solubilities, growth, and nucleation rates of lactose and lysozyme, the model is able to predict the experimentally observed crystallization behavior over a wide range of conditions. Model-based strategies for use in the design and optimization of a drop-based crystallization process for producing crystals of well-controlled CSD are identified.