Modeling and control of protein crystal shape and size in batch crystallization

In this work, the modeling and control of a batch crystallization process used to produce tetragonal hen egg white lysozyme crystals are studied. Two processes are considered, crystal nucleation and growth. Crystal nucleation rates are obtained from previous experiments. The growth of each crystal progresses via kinetic Monte Carlo simulations comprising of adsorption, desorption, and migration on the (110) and (101) faces. The expressions of the rate equations are similar to Durbin and Feher. To control the nucleation and growth of the protein crystals and produce a crystal population with desired shape and size, a model predictive control (MPC) strategy is implemented. Specifically, the steady‐state growth rates for the (110) and (101) faces are computed and their ratio is expressed in terms of the temperature and protein concentration via a nonlinear algebraic equation. The MPC method is shown to successfully regulate both the crystal size and shape distributions to different set‐point values.