(231a) Shape Control of Protein Crystal Aggregates

Protein crystal shape is a key variable that strongly influences the bioavailability of pharmaceutical drugs. Over the last few years, significant efforts have been made in shape control of crystals in a variety of crystallization systems (e.g., [1]-[3]). An important unresolved problem that arises in an industrial setting is the one of controlling the shape of protein crystal aggregates. Crystal aggregation is important in the crystal shape modification mechanism that takes place in batch crystallization systems owing to crystal solution stirring. The crystal aggregation rate is a function of the stirrer speed (influencing the shear force exerted on the crystals and the crystal collision probability) as well as the crystal diameter and crystallizer operating parameters.

Motivated by the above considerations the present work focuses on the simulation and control of protein crystallization and its crystal aggregates. We initially present a population balance model for the process which accounts for simultaneous nucleation, shear induced aggregation, and crystal growth. High-dimensionality of the system leads to complicated controller design and high-order controllers, which cannot be implemented in practice [4]. To circumvent these problems, the method of moments is employed to compute approximate models that describe the dynamic evolution of the three leading moments of crystal volume distribution in the turbulent shear regime [5]. The moment description of the system is closed according to the assumption that crystal volume can be properly approximated by a lognormal volume distribution where the assumption is verified later with the results from kMC simulations. The energy and mass balance models that describe the changes of the temperature in the crystallizer and the solute concentration in the continuous phase are developed. The method of moments, along with a nonlinear algebraic equation that describes the dependence of crystal growth on temperature and protein solute concentration (visualized by a 3-D plot), is used to design a model predictive controller (MPC) [6]-[7]. The proposed model predictive control scheme is used to drive the crystal shapes of crystal aggregates to a desired set-point value with a low polydispersity. One main contribution of this work is a comparative study of the performance of the proposed MPC scheme to those of two other conventional operating policies, constant temperature control (CTC) and constant supersaturation control (CSC) [8], by effectively regulating the crystal growth conditions in the crystallizer through the manipulation of the jacket temperature to produce crystals with a desired morphology.

References:

1. Liu JJ, Ma CY, Hu YD, Wang XZ. Effect of seed loading and cooling rate on crystal size and shape distributions in protein crystallization-A study using morphological population balance simulation. Comp. & Chem. Eng. 2010;34:1945-1952.
2. Liang M, Jin F, Liu R, Yu Y, Su R, Wang L, Qi W, He Z. Shape evolution and thermal stability of lysozyme crystals: effect of pH and temperature. Bioprocess & Biosystems Eng. 2013;36:91-99.
3. Wang L, Lee MH, Barton J, Hughes L, Odom TW. Shape-control of protein crystals in patterned microwells. J. Am. Chem. Soc. 2008;130:2142-2143.
4. Chiu T, Christofides PD. Nonlinear control of particulate processes. AIChE J. 1999;45:1279-1297.
5. Kalani A, Christofides PD. Simulation, estimation and control of size distribution in aerosol processes with simultaneous reaction, nucleation, condensation and coagulation. Comp. & Chem. Eng. 2002;26:1153-1169.
6. Nayhouse M, Kwon JS, Christofides PD, Orkoulas G. Crystal shape modeling and control in protein crystal growth. Chem. Eng. Sci. 2013;87:216-223.
7. Kwon JS, Nayhouse M, Christofides PD, Orkoulas G. Modeling and control of protein crystal shape and size in batch crystallization. AIChE J. in press.
8. Shi D, Mhaskar P, El-Farra NH, Christofides PD. Predictive control of crystal size distribution in protein crystallization. Nanotechnology. 2005;16:S562-S574.