(393b) Modeling and Simulation of Globular Protein Crystal Growth

The production of highly-ordered, high quality protein crystals through batch crystallization processes is vital in devising proteins for therapeutic purposes.  Despite extensive experimental and theoretical work on understanding protein structure and function, there is lack of a systematic framework that relies on fundamental understanding of the nucleation and growth mechanisms of protein crystals at the microscopic level and utilizes such information to model and operate protein batch crystallization processes at the macroscopic level.  The present work focuses on investigating the growth of protein crystals via molecular dynamics and kinetic Monte Carlo simulations and using such knowledge to model and control batch protein crystallizers through population, mass and energy balances.  The modeling and simulation work is tested against available experimental data.

The crystal growth of globular proteins is a non-equilibrium process and it is thus simulated using kinetic Monte Carlo methods.  As is common practice in simulations of crystal growth, the solid-on-solid model, in which molecules are deposited on the growing crystal without voids or overhangs, is adopted.  In the simulations, only molecular attachment and detachment events are considered and surface diffusion effects are ignored.  The implementation of the kinetic Monte Carlo methodology requires knowledge of the binding energies, the impingement rate, and the crystallization driving force.  Previous work assigned a range of values to these parameters until satisfactory agreement between the calculated and the experimental growth rates was achieved.  In the present work, the parameters required for the growth of protein crystals are calculated from molecular dynamics simulations of coarse-grained models for protein solutions.

The calculated growth rates are used in macroscopic models describing the evolution of entire crystal size distributions to achieve optimal crystallizer design and operation for large scale production.  The population balance modeling framework is adopted to describe globular protein crystallization in batch systems from supersaturated solutions.  The mathematical description of batch crystallization also requires conservation equations for the solute (protein) and the energy.  The previous mathematical model is used in conjunction with stochastic model predictive control methodologies that account for model uncertainty to achieve a desired crystal size distribution at the end of the batch protein crystallization process.  In the model predictive control formalism, the cost function typically maximizes the expected value of the volume-averaged crystal size subject to input and state constraints.  Extensive simulation results covering the various aspects discussed above will be presented.