Numerical model of protein crystal growth in a diffusive field such as the microgravity environment

Abstract

It is said that the microgravity environment positively affects the quality of protein crystal growth. The formation of a protein depletion zone and an impurity depletion zone due to the suppression of convection flow were thought to be the major reasons. In microgravity, the incorporation of molecules into a crystal largely depends on diffusive transport, so the incorporated molecules will be allocated in an orderly manner and the impurity uptake will be suppressed, resulting in highly ordered crystals. Previously, these effects were numerically studied in a steady state using a simplified model and it was determined that the combination of the diffusion coefficient of the protein molecule (D) and the kinetic constant for the protein molecule () could be used as an index of the extent of these depletion zones. In this report, numerical analysis of these depletion zones around a growing crystal in a non-steady (i.e. transient) state is introduced, suggesting that this model may be used for the quantitative analysis of these depletion zones in the microgravity environment.

Methods for Obtaining Better Diffractive Protein Crystals: From Sample Evaluation to Space Crystallization

“…The authors devised a numerical calculation model to determine the crystal growth process closer to actual crystallization [60]. For the sake of simplicity, partial differential equations describing both the diffusion process in the virtual sphere and the crystal growth process in the center of the sphere are described.…”

Methods to Grow better Diffractive Protein Crystals Acquired through Space Experiments

“…The authors devised a numerical calculation model to understand the crystal growth process closer to actual crystallization [56]. For the sake of simplicity, partial differential equations describing both the diffusion process in the virtual sphere and the crystal growth process in the center of the sphere are described.…”

“…By applying various constants of the crystallization process of lysozyme to this model, the impurity concentration is low in the portion close to the center in the crystals grown in microgravity, and on the contrary, in the peripheral portion, the impurity concentration is higher than the crystals grown on the ground [56,57]. In this simulation, β is set to a constant value, but, in reality, β increases as the impurity concentration decreases as described above.…”

Methods to Grow Better Diffractive Protein Crystals Acquired through Space Experiments

“…The authors devised a numerical calculation model to determine the crystal growth process closer to actual crystallization [58]. For the sake of simplicity, partial differential equations describing both the diffusion process in the virtual sphere and the crystal growth process in the center of the sphere are described.…”

“…By applying various constants of the crystallization process of the lysozyme to this model, the impurity concentration is low in the portion close to the center in the crystals grown in microgravity, while in the peripheral portion, the impurity concentration is higher than that of the crystals grown on the ground [58,59]. In this simulation, β is set to a constant value, but, in reality, β increases as the impurity concentration decreases, as described above.…”