(747b) Shape Control of Protein Crystals

Proteins play a key role as therapeutics in a number of diseases and protein crystallization is a central activity in the pharmaceutical industry. Specifically, the production of highly-ordered, high-quality protein crystals through batch crystallization processes is vital in devising proteins for therapeutic purposes. However, despite extensive experimental and computational work on understanding protein structure and function, there remains a lack of knowledge to model and control batch protein crystallizers.

Motivated by the above considerations the present work focuses on the simulation and control of globular proteins. Since the crystal growth of globular proteins is a non-equilibrium process, it will be simulated using kinetic Monte Carlo (kMC) methods. As is common practice in simulations of crystal growth, the solid-on-solid model will be adopted. In the solid-on-solid approximation, particles are deposited on the growing crystal without voids or overhangs and the resulting crystal is highly compacted. The implementation of the kinetic Monte Carlo methodology requires knowledge of the binding energies, the impingement rate, and the crystallization driving force. In previous simulations, a range of values was assigned to the previous parameters until satisfactory agreement with experiments was obtained for the protein under consideration. In the kMC simulations, molecular attachment, detachment, and migration events are considered and growth rates on the (101) and (110) faces can be obtained.Depending on the relative attachment energy of the crystal faces and assuming that the independentcrystal faces that are likely to appear during the growth are (101) and (110) faces, kMC simulations reproduce the experimentally observed cross-over behavior in the crystal growth rates between the two faces of the protein crystal.

This work focuses on control of the growth rate ratio between the two independent faces in single protein crystallization process using the temperature as the manipulated control input. A 3-D plot of steady-state relative growth rates versus solute concentration and temperature is derived to describe the evolution of the crystal growth accounting for the effect of solute concentration variations and temperature changes in batch systems from supersaturated solutions. The developed 3-D plot is then used as the basis for the design of a model predictive control algorithm that includes penalty on the deviation of crystals from its desired crystal shapes, specifically, subject to limit on the rate of change of the temperature of the batch crystallization.The calculated temperatures are used in the kMC models to achieve optimal crystal shape and to operate until the next sampling time.

The shape of the crystal is determined by the two faces and their relative face growth rates. Therefore it is possible to control the evolution of crystal shapes by controlling the ratio between the two face growth rates. Based on needs, more elongated to the direction of either horizon or vertical crystal can be obtained. Extensive simulation results covering the various aspects discussed above will be presented.