Protein Crystal Shape and Size Control in Batch Crystallization: Comparing Model Predictive Control with Conventional Operating Policies

Abstract

In this paper, we focus on a batch protein crystallization process used to produce tetragonal hen egg white lysozyme crystals and present a comparative study of the performance of a model predictive control (MPC) strategy formulated to account for crystal shape and size distribution with conventional operating strategies used in industry, namely, constant temperature control (CTC) and constant supersaturation control (CSC). Initially, a comprehensive, batch crystallizer model is presented involving a kinetic Monte Carlo (kMC) simulation model which describes the nucleation and crystal growth via adsorption, desorption, and migration mechanisms on the (110) and (101) faces and mass and energy balances for the continuous phase, which are developed to estimate the depletion in the protein solute concentration and the variation in the crystallizer temperature. Existing experimental data are used to calibrate the crystal growth rate and to develop an empirical expression for the nucleation rate. Simulation results demonstrate that the proposed MPC, adjusting the crystallizer jacket temperature, is able to drive the crystal shape to a desired set-point value with a low polydispersity for crystal size compared to CTC and CSC operating policies, respectively. The proposed MPC determines the optimal operating conditions needed to obtain protein crystals of a desired shape and size distribution as it helps avoid the small crystal fines at the end of the batch run.