(747a) Modeling of Protein Crystal Aggregation in Batch Crystallization | AIChE

(747a) Modeling of Protein Crystal Aggregation in Batch Crystallization


Kwon, S., UCLA
Christofides, P., University of California, Los Angeles
Orkoulas, G., University of California, Los Angeles

Protein crystallization plays a crucial role in the $1 trillion pharmaceutical industry and has significantly contributed to both the scientific advancement and the economic development. For example more than 100 therapeutic proteins have been licensed and a number of additional therapeutic proteins are currently under investigation. In the last few years, researchers have attempted to model protein nucleation (e.g., [1]-[2]) and crystals growth (e.g., [3]-[4]) and their efforts make it possible to quantitatively describe and even control the shape and size distributions of the protein crystals. Although there has been a number of computational and theoretical studies of understanding the aggregation of fine particles, no significant work has been done in the modeling of protein crystal aggregation due to stirring in batch crystallization. Besides, no systematic approach has been established that visualizes the dependence of the aggregation mechanism of protein crystals on the temperature in the crystallizer and the solute concentration in the continuous phase where such information can be utilized to model and operate industrial-scale batch protein crystallization processes. In our previous works [5]-[6] batch crystallization of lysozyme accounting for crystal nucleation and growth was studied and a model predictive control strategy was proposed to regulate crystal shape and size distributions.

The present work focuses on the modeling of aggregation of protein crystals in addition to accounting for crystal nucleation and growth. First, we assume that the continuous phase is dilute enough to make only binary aggregation possible. In general crystallization experiments at higher stirrer speeds exhibit a reduced formation of crystal aggregates, which is favorable in the subsequent separation process by filtration where there is a physical limitation on the stirrer speeds that is achievable by a motor. Therefore an optimal hydromechanical stress is chosen, which enables the crystals to be maintained in suspension in industrial particulate processes [7]. Furthermore, the corresponding turbulent shear rate within the crystallizer can be characterized by the average velocity gradient of the flow field. An appropriate aggregation kernel is chosen which represents the rate at which a binary collision occurs and this rate strongly depends on the size of crystals as well as the crystallizer operating parameters [8]-[9]. Additionally, we assume that the aggregates of crystals are compact because they are subject to strong shear flow, and the corresponding collision efficiency to the impermeable aggregates is modeled [10]. Among the several physical behaviors that can induce particle aggregation, the aggregation for lysozyme crystals with a diameter approximately in the range 1-100 micrometer is mainly induced by shear forces according to its Kolmogorov microscale [9]. Lastly, an aggregate will be formed as two crystals completely merge along with their internal coordinates resulting in a decrease in the total number of crystals and an increase in the average crystal size. The subsequent shape changes in those crystals are accommodated by a set of internal coordinates into (110) and (101) directions. Extensive simulation studies are carried out to evaluate the influence of crystal aggregation on the shape and size distributions of the produced crystals at the end of a batch.


  1. Galkin O, Vekilov PG. Direct determination of the nucleation rates of protein crystals. J. Phys. Chem. B. 1999;103:10965-10971.
  2. Pusey ML, Nadarajah A. A model for tetragonal lysozyme crystal nucleation and growth. Crystal Growth & Design. 2002;2:475-483.
  3. Durbin SD, Feher G. Crystal growth studies of lysozyme as a model for  protein crystallization. J. Cryst. Growth. 1986;76:583-592.
  4. Forsythe EL, Nadarajah A, Pusey ML. Growth of (101) faces of tetragonal lysozyme crystals: measured growth-rate trends. Acta Cryst.D. 1999;55:1005-1011.
  5. Nayhouse M, Kwon S, Christofides PD, Orkoulas G. Crystal shape modeling and control in protein crystal growth. Chem. Eng. Sci. 2013;87:216-223.
  6. Kwon S, Nayhouse M, Christofides PD, Orkoulas G. Modeling and control of protein crystal shape and size in batch crystallization. AIChE J. in press.
  7. Henzler HJ. Particle stress in bioreactors. Biochem Eng Biotechnol. 2000;67:35-82.
  8. Saffman PG, Turner JS. On the collision of drops in turbulent clouds. J. Fluid Mechanics. 1954;1:448-462.
  9. Kusters KA, Wijers JD, Thoenes D. Aggregation kinetics of small particles in agitated vessels. Chem. Eng. Sci. 1997;52:107-121.
  10. Vanni M, Baldi G. Coagulation efficiency of colloidal particles in shear flow. Adv. Colloid Interface Sci. 2002;97:151-177.