A Kinetic Model To Simulate Protein Crystal Growth in an Evaporation-Based Crystallization Platform

The quality, size, and number of protein crystals grown under conditions of continuous solvent extraction are dependent on the rate of solvent extraction and the initial protein and salt concentration. An increase in the rate of solvent extraction leads to a larger number of crystals. The number of crystals decreases, however, when the experiment is started with an initial protein concentration that is closer to the solubility boundary. Here we develop a kinetic model capable of predicting changes in the number and size of protein crystals as a function of time under continuous evaporation. Moreover, this model successfully predicts the initial condition of drops that will result in gel formation. We test this model with experimental crystal growth data of hen egg white lysozyme for which crystal nucleation and growth rate parameters are known from other studies. The predicted and observed rates of crystal growth are in excellent agreement, which suggests that kinetic constants for nucleation and crystal growth for different proteins can be extracted by applying a kinetic model in combination with observations from a few evaporation-based crystallization experiments.