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

Abstract

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. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2317–2327, 2013

Crystal shape and size control using a plug flow crystallization configuration

“…Initially, we model a continuous plug flow crystallizer with 5 segments for the production of lysozyme crystals through kinetic Monte Carlo (kMC) simulation methods in the way described in Kwon et al (2013) using the rate equations originally developed by Durbin and Feher (1991). A seeding strategy is used to decouple the nucleation from the crystal growth processes (Liu et al, 2010;Eder et al, 2011;Besenhard et al, 2014;Ferguson et al, in press).…”

“…Therefore, the necessity of incorporating the constraints to account for the physical limitations on the manipulated inputs and operating conditions makes the model-based control strategy (Miller and Rawlings, 1994;Worlitschek and Mazzotti, 2004;Shi et al, 2005;Mesbah et al, 2010) the method of choice for crystal size distribution control. Specifically, the model predictive control (MPC) scheme was employed by Kalbasenka et al (2007) and Kwon et al (2013Kwon et al ( , 2014 in order to control the crystal size and shape distributions along with the consideration of the crystal growth and nucleation processes in both batch and MSMPR processes based on a reduced-order model. Furthermore, in addition to model-based optimization to compute optimal jacket temperature values, a feed-forward control (FFC) is proposed in the present work for the production of crystals with desired size and shape distributions owing to its unique ability to deal with feed flow disturbances that occur during the operation of the PFC though the use of the online measurements of the inflow solute concentration, PFC temperature, and crystal seed size.…”

Measurement, modelling, and closed-loop control of crystal shape distribution: Literature review and future perspectives

“…Therefore, the effective dimensionality of the problem became very small, allowing simulation of a population of asymmetric crystals with minimal computational effort. Other research in multi-dimensional and morphological PB modelling of crystallisation processes include the work of Majumder and Nagy [102] who studied the influence of crystal growth modifiers, Kwon et al [40,103] and Liu et al [104][105][106] who studied the simulation, optimisation and control of protein crystals.…”

“…Patience and Rawlings [18] investigated the use of impurities to manipulate the shape of crystals for sodium chlorate, which also represents an important direction since the use of impurity is considered in industry as a very effective handle for shape control. A model predictive controller with PB modelling of protein crystallisation was used to produce crystals with a desired shape distribution [40]. Ma [190] developed a methodology to generate an optimum operation profile of a crystallisation process based on the optimization of firstprinciple model with the objective function being the length and width ratio for validation simplicity and the optimisation being subject to upper and lower bounds of cooling rate, operating temperature and time.…”

Multi-Impurity Adsorption Model for Modeling Crystal Purity and Shape Evolution during Crystallization Processes in Impure Media

“…Population balance modeling is widely used in order to describe the evolution of crystal properties such as size and shape distribution 43,44 . Multidimensional population balance models are suitable for investigation and simulation of crystal morphology when the shape of the particles is described by the sizes of the characteristic crystal faces 9,[45][46][47][48][49][50][51][52][53]78 .…”