(413a) Advancing Protein Crystallization: A Groundbreaking Kinetic Monte Carlo Model for Accurate Prediction of Morphology and Growth across Diverse Operating Conditions

Proteins, as vital biochemicals, play a diverse range of roles in living organisms, which are essential to regulating numerous aspects of human health. Consequently, understanding proteins is crucial for developing effective treatments for diseases and other conditions [1]. The use of protein pharmaceuticals has experienced rapid growth in recent years, boasting successful applications such as insulin, interferons, human growth hormone, and tissue plasminogen activator [2]. To aid in the pursuit of high-impact drug discovery, the pharmaceutical industry requires high-quality protein crystals to determine the structure of target proteins. Even though the theoretical framework for crystal nucleation and evolution is well-established, current theories frequently prove to be oversimplified and limited to specific cases, resulting in discrepancies between experimental and theoretical investigations [3, 4]. Specifically, microscopic models that predict crystal morphology and growth rate tend to be tailored to particular crystal systems and operating conditions. This necessitates resource-intensive investigation of accurate theoretical models and subsequently delays crucial testing and production of vital drugs. As such, the crystallization community greatly values advancements in developing a generalizable microscopic crystal model that can be easily fine-tuned for different systems.

Motivated by this need, we propose a novel unifying model that accurately predicts the crystal growth and surface morphology of protein crystals across various operating conditions by connecting different crystal growth regimes (i.e., spiral, step, rough growth, etc.). Specifically, we developed a kinetic Monte Carlo (kMC) model that employs several microkinetic steps, such as (a) adsorption, (b) dissolution, and (c) diffusion of individual crystal unit cells on the lattice surface [6]. To enable switching among numerous crystal growth regimes, we incorporated transitional state kinetics (controlled by the inherent properties of the protein molecule) along with computing the thermodynamically driven stable state during each kMC step. As a result, out kMC simulations demonstrate a smooth transition between spiral, step, and rough crystal growth regimes with varying supersaturation, which was not attainable with previous models [4,5]. We validated the kMC model’s morphology and growth predictions using TEM observations of protein crystals.

Recognizing the importance of crystallizer design and optimization in achieving crystallization with effective control of the crystal size distribution (CSD) [7], we extended our model to encompass both single crystal growth, and a population balance model (PBM) that considers the influence of environmental factors, thus developing a high-fidelity multiscale model. We utilized a coarse time-stepper using a Gap-Tooth approach to rapidly couple the surface-level kMC and continuum-level PBM, resulting in a 100 times computational boost. In conclusion, our model provides a broad-scale prediction of crystallization and, due to its bottom-up approach, can be employed to analyze various spatiotemporal aspects of crystal morphology and growth in key pharmaceutical applications.

Literature Cited:

1. Blundell, T. L. Protein crystallography and drug discovery: recollections of knowledge exchange between academia and industry. IUCrJ, 4, 308-321 (2017).
2. Zang, Y., Kammerer, B., Eisenkolb, M., Lohr, K., & Kiefer, H. Towards Protein Crystallization as a Process Step in Downstream Processing of Therapeutic Antibodies: Screening and Optimization at Microbatch Scale. PLOS ONE, 6(9), e25282 (2011).
3. Zhou, J., Yang, Y., Yang, Y. et al. Observing crystal nucleation in four dimensions using atomic electron tomography. Nature 570, 500–503 (2019).
4. Ou, Z., Wang, Z., Luo, B., Luijten, E., & Chen, Q. Kinetic pathways of crystallization at the nanoscale. Nature Materials, 19(4), 450-455 (2020).
5. James F. Lutsko, D. Maes, Simulation studies of the combined effect of mass transport and impurities on step growth, Journal of Crystal Growth, Volume 602 (2023).
6. Nayhouse, J. S. Kwon, P. D. Christofides and G. Orkoulas, Crystal shape modeling, and control in protein crystal growth, Chem. Eng. Sci., 87, 216-223 (2013).
7. S. Kwon, M. Nayhouse, P. D. Christofides and G. Orkoulas, Modeling, and control of protein crystal shape and size in batch crystallization, AIChE J., 59(7), 2317-2327 (2013).