Modeling and control of shape distribution of protein crystal aggregates

We focus on the modeling and control of protein crystal aggregates in a large-scale batch crystallizer used to produce tetragonal hen-egg-white (HEW) lysozyme crystals. We initially present a kinetic Monte Carlo (kMC) simulation for the modeling of the crystal nucleation, growth, and shear-induced aggregation in an effort to control the evolution of the crystal shape distribution. Through experimental data, the crystal growth rate is calibrated and an empirical expression for the nucleation rate is also developed. Then, the method of moments is applied to a comprehensive population balance model to derive a reduced-order moment model that describes the dynamic evolution of the three leading moments of the crystal volume distribution. Along with mass and energy balances for the continuous phase, the moment model is used to design a model predictive control (MPC) strategy which drives the crystal shape distribution to a desired set-point value through the manipulation of the crystallizer jacket temperature. Compared to conventional operating strategies used in industry, it is demonstrated that the proposed MPC strategy is able to produce crystal aggregates with a desired shape distribution and a low polydispersity effectively dealing with the undesired effects of biased nucleation, depletion in the solute concentration, and changes in the average crystal shape due to the aggregation process. (C) 2013 Elsevier Ltd. All rights reserved.