Modeling and control of protein crystal shape distribution

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The production of highly ordered, high quality protein crystals through batch crystallization processes is vital in devising proteins for therapeutic purposes in a number of diseases. Additionally, protein crystallization is a central activity in the pharmaceutical industry. The present work focuses on the modeling and control for a population of tetragonal hen egg-white (HEW) lysozyme protein crystals. First, a model is presented which will consider nucleation of lysozyme crystals followed by kinetic Monte Carlo (kMC) simulations to model the crystal growth on the (110) and (101) faces, respectively. These kMC simulations comprise of adsorption, desorption, and migration events where the rate equations for each type of event are similar to those of Durbin and Feher [10]. The computation of the growth rate for each face requires the use of kMC simulations due to the dependence of the desorption and migration rates on the surface micro-configuration, and thus it cannot be computed simply by subtracting the adsorption and desorption rates. Next, the data obtained from the kMC simulations will be used to generate a nonlinear algebraic equation which relates the solute concentration and temperature to the growth rate ratio between the two independent crystal faces. A model predictive controller will use this nonlinear equation to regulate the protein crystals to desired shapes in the presence of disturbance in the operating conditions. The proposed method demonstrates that it can successfully achieve the desired crystal shapes which range from equidimensional to more elongated type of structures for the entire crystal population while in the presence of arbitrary variations in the solute concentration.