Modeling of the Biocrystal Growth Using Temperature Field
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Modeling of the Biocrystal Growth Using Temperature Field V. I. Strelova,*, V. P. Ginkinb, and I. Zh. Bezbakha a Shubnikov
Institute of Crystallography, Federal Scientific Research Centre “Crystallography and Photonics,” Russian Academy of Sciences, Moscow, 119333 Russia b Leipunsky Institute of Physics and Power Engineering, Obninsk, Kaluga oblast, 249033 Russia *e-mail: [email protected] Received March 6, 2018; revised March 27, 2018; accepted April 3, 2018
Abstract—A mathematical model has been developed and numerical calculations of lysozyme protein crystallization from a homogeneous aqueous solution under temperature field control have been performed in order to develop a controlled method for growing high-quality protein crystals from solutions using a point temperature field effect. This mathematical model describes the formation of crystal nuclei and their growth in dependence of local values of supersaturation and temperature, as well as the heat and mass transfer in the entire volume of solution, including protein crystals. DOI: 10.1134/S1063774519020305
INTRODUCTION Protein crystals are applied to determine the spatial structure of vitally important biomacromolecules using X-ray analysis (XRD) diffraction. Data on spatial structure are necessary for developing efficient new-generation medicinal tools and studying the mechanisms of disease development. Despite the significant recent success in the methods for growing protein crystals applicable for XRD analysis, specifically the crystallization stage remains least predictable and often determines the time spent on studying the spatial protein structure. The number of studies devoted to biocrystal growth is very large. The influence of convection on biocrystal growth was investigated in [1–5]. The growth kinetics was described by a linear dependence of protein mass flux on supersaturation. Generally, the crystal growth rate in most of inorganic systems increases in the presence of convection, because convection enhances mass transfer. This is not always true for protein crystals, whose growth rate is often limited by the kinetics on the surface of growing crystals. An experiment [6] on growth of tetragonal lysozyme crystals with a forced convective flow revealed a significant decrease in the growth rate with time. Tetragonal lysozyme crystals, suspended in ascending solution flow in a thermosyphon loop, were grown in [7]. At high supersaturations, crystals ceased to grow when their size reached ~0.1 mm. However, seed crystals continued to grow to large sizes in solutions without forced flows. These effects indicate that the mechanism of influence of convection on crystal growth has not been studied sufficiently well.
The mechanism of step growth from a face edge was investigated in [3]; the face nucleation time was presented probabilistically. Stepwise face growth was observed in the photographs made in the experiment; it could be compared with the calculated process. Monte Carlo simulation was applied in [8] to the nucleation and stepwis
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