Crystal shape modeling and control in protein crystal growth

Abstract

Proteins play a key role as therapeutics in a number of diseases and protein crystallization is a central activity in the pharmaceutical industry. Protein crystals, usually produced through a batch crystallization process, are desired to be of high quality, of desired shape, and within a narrow size and shape distribution range. Motivated by the above considerations, the present work focuses on the modeling and control of protein crystal shape. The model protein used for this work is the tetragonal hen egg white lysozyme. The growth of an individual lysozyme crystal is modeled via kinetic Monte Carlo (kMC) simulations comprising adsorption, desorption, and migration events on the (110) and (101) faces, which are assumed to be independent. The expressions for the rate equations for each event type are similar to those of Durbin and Feher (1991). Extensive testing of the system parameters indicates crossover behavior between the growth rates of the two faces [i.e., (110) and (101)], a fact that has also been observed experimentally. A nonlinear algebraic equation that relates the steady-state growth rate ratios between the (110) and (101) faces, the temperature and concentration, is derived from the kMC simulation data. This nonlinear equation is then utilized by a model predictive controller which regulates the protein crystal to desired shapes subject to manipulated input constraints. The proposed method is shown to successfully regulate protein crystal shape, ranging from equidimensional to more elongated type of structures, in the presence of arbitrary variations of the protein concentration.