The effect of diluting crystallization droplets on protein crystallization in vapor diffusion method

In this study, effects of diluting either protein or crystallization agents in the droplets on the success rate of protein crystallization was investigated. Diluting the crystallization agent was found to increase the success rate of protein crystallization. Theoretical analysis showed that, concentration ranges of both protein and crystallization agent that can be scanned during the vapor diffusion process are wider with diluting the crystallization agent than that without dilution, resulting in more opportunities for the crystallization solution to be in the nucleation zone. On the other hand, diluting protein could lead to controversial results depending on the location of the initial concentration relative to that of the nucleation zone in the phase diagram. The method of diluting the crystallization agent is therefore proposed as an alternative modification to the conventional vapor diffusion method for obtaining more crystallization conditions in protein crystallization screening. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A more clear insight of the lysozyme crystal composition

Crystallization can be used as a purification method for proteins. Lysozyme was chosen as a model substance. Changing crystallization conditions will lead as shown to different lysozyme crystal morphologies with different properties. Beside others, lysozyme crystals can show a Tetragonal, High Temperature and Low Temperature Orthorhombic crystal morphology. Experiments such as conductivity measurements, pH tests, chloride detection tests, experiments using methylene blue as a dye and dissolution experiments were carried out to investigate the composition of the lysozyme crystals. It is proven that lysozyme crystals are made up of the initial buffer solution components: lysozyme (the protein), water which is part of the crystal lattice, salt ions which are attached to the protein molecule and voids filled with the buffer solution containing the crystallization agent (e.g. salt). Interesting dissolution behaviours of the lysozyme crystals were observed which are not described so far elsewhere (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical and experimental analysis of periodic patterns and sedimentation of lysozyme

This paper deals with experimental investigation, mathematical modelling and numerical simulation of the crystallization processes induced by counter diffusion method of a precipitant agent in a lysozyme protein solution. Novel mathematical strategies are introduced to simulate the experiments and in particular to take into account the kinetics of the growth process and the motion of the crystals due to the combined effect of gravitational force and viscous drag if the sedimenting process is allowed (protein chamber free of gel). Comparison between experimental observations and numerical simulations in the presence of convection and sedimentation and without them provides a validation of the model. The crystal formation in gel results modulated in space. If the gel matrix is not present, convective cells arise in the protein chamber due to local inversions in the density distribution associated to nucleation phenomena. As time passes, these vortex cells migrate towards the top of the protein chamber exhibiting a different wave number according to the distance from the gel interface. The sedimentating particles produce a wake due to depletion of protein from the surrounding liquid. The models and the experiments may represent a useful methodology for the determination of the parameters and conditions that may lead to protein crystallization.     

Protein crystallization in low gravity by step gradient diffusion method.

Two-step crystallization experiments were conducted in low gravity employing a liquid-liquid diffusion method in an effort to eliminate problems associated with protein crystal growth under the supersaturating conditions required for nucleation. Experiments were performed in diffusion cells formed by the sliding of blocks on orbit. Step gradient diffusion experiments consisted of first exposing protein solutions in diffusion half-wells for brief periods to initiating buffer solutions of high precipitant concentrations to induce nucleation followed by expoure of the same protein solutions to solutions of lower precepitant concentration to promote growth of induced nuclei into crystals. To avoid convective disturbances that occur when solutions of discrepant densities are interfaced at normal gravity, crystallization of hen egg-white lysozyme and rabbit skeletal muscle aldolase by step gradient diffusion was investigated in low gravity on four NASA space shuttle flights. In general, the largest ctystals of both proteins formed at the highest initiating precipitant concentration used, which is consistent with nuclei formation upon brief exposure to high precipitant concentration, and that these nuclei are competent for sustained growth at lower precipitant concentration. The two-step approach dissociates nucleation events from crystal growth allowing parameters affecting nucleation kinetics such as time, precipitant concentration and temperature of nucleation to be varied separately from conditions used for post-nucleation growth.     

Estimation of the effect of relative humidity on protein crystallization

The effect of relative humidity in a crystallization box on the rate of establishment of supersaturation conditions during protein crystallization by diffusion of solvent vapors is estimated. A modified crystallization box is designed, which provides the formation of a stable air flow with a specified relative humidity and its measurement directly in the closed space between a drop and a reservoir. The range of relative humidities necessary to obtain the supersaturation conditions in a drop with a protein crystallization solution is determined.     

Development of an Automated High Throughput LCP-FRAP Assay to Guide Membrane Protein Crystallization in Lipid Mesophases

Crystallization in lipidic mesophases (in meso) has been successfully used to obtain a number of high-resolution membrane protein structures including challenging members of the human G protein-coupled receptor (GPCR) family. Crystallogenesis in arguably the most successful mesophase, lipidic cubic phase (LCP), critically depends on the ability of protein to diffuse in the LCP matrix and to form specific protein-protein contacts to support crystal nucleation and growth. The ability of an integral membrane protein to diffuse in LCP is strongly affected by the protein aggregation state, the structural parameters of LCP, and the chemical environment. In order to satisfy both requirements of diffusion and specific interactions, one must balance multiple parameters, such as identity of LCP host lipid, composition of precipitant solution, identity of ligand, and protein modifications. Screening within such multi-dimensional crystallization space presents a significant bottleneck in obtaining initial crystal leads. To reduce this combinatorial challenge, we developed a pre-crystallization screening assay to measure the diffusion characteristics of a protein target in LCP. Utilizing the Fluorescence Recovery After Photobleaching (FRAP) technique in an automated and high throughput manner, we were able to map conditions that support adequate diffusion in LCP using a minimal amount of protein. Data collection and processing protocols were validated using two model GPCR targets: the β(2)-adrenergic receptor and the A(2A) adenosine receptor.     

Simplex optimization of protein crystallization conditions

Simplex algorithms have been used to optimize for size, number and morphology of lysozyme and apoferritin crystals. This approach requires fewer experiments than the single-factor-at-a-time method or factorial designs and will be useful in conserving materials on the International Space Station. The simplex method has the possible advantage that it conserves on materials by reducing the number of experiments required to optimize a crystallization system. The process is iterative and exploratory and should allow optimum microgravity conditions to be determined which might very well be different from the optimum conditions on Earth. Because the simplex method uses simple mathematical operations to calculate the next set of crystallization conditions it will be easier for crystal growers to implement than factorial designs. Factorial experiments are based on varying all factors simultaneously at a limited number of factor levels. This results in a model that is used to determine the influence of each factor and their interactions. Factorial design experiments are especially useful at the beginning of an experimental study and as a screening tool to investigate a large number of factors. The simplex method is an optimization method which is model-independent and requires no fitting of models to data. Also, when applied to protein crystal growth the simplex method does not rely on an absolute quality score. Instead, with each iteration a comparison is made to the last experiment and the results are assigned as being “better or worse”. In this study, commercially obtained apoferritin was purified from 65% monomeric apoferritin to 92% monomeric apoferritin by size exclusion chromatography. Simplex optimization found the best apoferritin crystals were obtained at 15 mg/ml apoferritin, 2.0% CdSO₄, 25°C using the hanging drop vapor diffusion method of crystallization and at 24 mg/ml apoferritin, 1.5% CdSO₄, 25°C using the containerless crystallization method. For lysozyme, the simplex method found the best crystals at 19 mg/ml lysozyme, 7.0% (w/v) NaCl, pH 4.0, 25°C using the hanging drop vapor diffusion method of crystallization. For both proteins, the optimum conditions were found with less than ten experiments using very little protein. Finally, we report that the factors to be considered in the successful application of this method to crystallization are the number of variables to be studied, the initial conditions, step size and analysis of crystal quality.     

On the dependence of the critical crystallization rate on the initial impurity concentration in melt

The dependence of the critical crystallization rate on the initial impurity concentration in melt is derived by determining the condition at which a nonplanar solution to the stationary diffusion problem arises. It is suggested that the conditions at which defects arise at the interface differ from those obtained when crystallization becomes stationary. The initial transient process of binary melt solidification under crystal pulling at a constant rate has been studied numerically within a 1D model. It is shown that the character of the time dependence of the crystallization rate is determined by the ratio of the crystal pulling rate to solidification rate V _c, when a constitutional supercooling zone is formed in the melt.     

Coarse crystal layer growth and liquid entrapment study with gradient freeze technology

The coarse crystal layer growth and liquid entrapment processes were investigated with gradient freeze technology in this paper. The research system was hemihydrate phosphoric acid (H₃PO₄·0.5H₂O) crystal‐phosphoric acid aqueous solution. The distribution coefficients of ions (Ca²⁺, Fe³⁺ and Na⁺) in this system were measured. The effect of supercooling degree gradient on layer growth and the effect layer growth rate on ions redistribution were studied. The result indicated that the layer growth rate increased with supercooling degree gradient as an exponential curve. The distribution coefficient tended to increase as an approximate ‘S’ curve when coarse crystal layer growth rate increased. The ‘three region’ theory was applied to explain this phenomenon. Each ion's diffusion parameter was obtained, which contributed to explain the separation differences between different ions. The work in this paper also indicated that layer crystallization was an effective separation technology for electronic grade phosphoric acid preparation.     

Protein interactions in concentrated ribonuclease solutions

To investigate the protein interactions involved in the crystallization process of ribonuclease A, dynamic light scattering (DLS) and small angle X-ray scattering experiments (SAXS) were performed on concentrated solutions. Whereas the translational diffusion coefficient obtained from DLS is sensitive to thermodynamic and hydrodynamic interactions and permits to calculate an interaction parameter, the shape of the SAXS curves is related to the type of interaction (attractive or repulsive). We compared the effect of pH on protein interactions in the case of two types of crystallizing agents: a mixture of salts (3 M sodium chloride plus 0.2 M ammonium sulfate) and an organic solvent (ethanol). The results show that in the presence of ethanol, as in low salt, protein interactions become more attractive as the pH increases from 4 to 8 and approaches the isoelectric point. In contrast, a reverse effect is observed in high salt conditions: the strength of attractive interactions decreases as the pH increases. The range of the pH effect can be related to ionization of histidine residues, particularly those located in the active site of the protein. The present observations point out the important role played by localized charges in crystallization conditions, whatever the precipitating agent.     

Crystallization of proteins under an external electric field

An external electric field affects the crystallization of proteins when applied under some conditions of temperature, pH, and precipitating agent composition. As suggested in the theoretical part of this paper, it produces large protein concentration gradients inside the mother liquor leading to a local supersaturation area in the crystallization solution. Such an experiment has been used for the first time on the crystallization of a protein. The effects of an external electric field on the crystallization of hen egg-white lysozyme at 293 K, pH 4.5, and two NaCl concentrations (0.6–0.7 M) have been investigated using the vapor diffusion method. The application of electric field results in a smaller number of crystals with larger size. The crystals grew at the droplet surface, near the cathode. The nucleation rate is drastically reduced and this experimental method could be used to control the number of crystals in the droplet.     

The crystallization of lysozyme in the system of ionic liquid [BMIm][BF4]‐water

Lysozyme crystallization was conducted in the ionic liquid (IL) 1‐butyl‐3‐methylimidizolium tetrafluoroborate ([BMIm][BF₄]) with different buffer/IL proportions. It was found that the addition of [BMIm][BF₄] could promote the crystallization process, during which more lager single crystals with controllable morphologies could be obtained due to the manageable crystal growth velocity. A probable explanation was proposed based on the influence of the ionic polarization and kinetics in the lysozyme crystallization. Moreover, the transform in coordination number and the relative growth rate of different crystal faces were discussed. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling analysis of liquid encapsulated Czochralski growth of GaAs and InP crystals

The results of three‐dimensional unsteady modeling of melt turbulent convection with prediction of the crystallization front geometry in liquid encapsulated Czochralski growth of InP bulk crystals and vapor pressure controlled Czochralski growth of GaAs bulk crystals are presented. The three‐dimensional model is combined with axisymmetric calculations of heat and mass transfer in the entire furnace. A comprehensive numerical analysis using various two‐dimensional steady and three‐dimensional unsteady models is also performed to explore their possibilities in predicting the melt/crystal interface geometry. The results obtained with different numerical approaches are analyzed and compared with available experimental data. It has been found that three‐dimensional unsteady consideration of heat and mass transfer in the crystallization zone provides a good reproduction of the solidification front geometry for both GaAs and InP crystal growth.     

Self-assembly of apoferritin molecules into crystals: thermodynamics and kinetics of molecular level processes

Aside from the biological, biomedical and materials importance of ferritin and apoferritin, the self-assembly of these molecules into crystals is of interest because it is a suitable model for protein crystallization and aggregation that impact many fundamental and applied fields. We use the atomic force microscope in-situ, during the crystallization of apoferritin to visualize and quantify at the molecular level the processes responsible for crystal growth. We image the configuration of the incorporation sites, “kinks”, on the surface of a growing crystal. We show that the kinks are due to thermal fluctuations of the molecules at the crystal-solution interface. This allows evaluation of the free energy of the intermolecular bond φ = 3.0 k_BT = 7.3 kJ/mol. The crystallization free energy, extracted from the protein solubility, is − 42 kJ/mol. Thermodynamics analyses based on these two values suggest that the main component in the crystallization driving force is the entropy gain of the waters bound to the protein molecules in solution and released upon crystallization. Furthermore, we determine the characteristic frequency of attachment of individual molecules into the kinks at one set of conditions. We show that the macroscopic step growth velocity, scaled by the molecular size, equals the product of independently determined kink density and attachment frequency, i.e., these are the molecular-level parameters for crystallization. Finally, we show that although new crystal layers are generated by intrinsically stochastic surface nucleation, for crystals > 200 μm layer generation predominantly occurs at the crystal edges. Numerical simulations of the concentration fields in the solution allow us to assign this localization to higher interfacial concentration at the edges. As the steps propagate to cover the crystal face, step density waves, or bunches, develop and may lead to non-uniformity and lower quality and utility of the growing crystal.     

Spherulitic branching in the crystallization of liquid selenium

Liquid selenium is a spherulite-forming liquid. In a previous study [G. Ryschenkow and G. Faivre, J. Crystal Growth 87 (1988) 221], several spherulitic modes of crystallization have been observed to coexist, at a given undercooling of the liquid, with the growth of single crystals. The spherulitic modes were thought to be basically due to a mechanism inducing a regular polygonization of crystal during growth (small-angle branching). We present a morphological investigation of the spherulites of selenium, by optical and electron microscopy, which substantiate this conjecture. At medium undercooling of the liquid, the small-angle branching periodically triggers a homoepitaxial large-angle branching. This gives rise to nonringed spherulites. At higher undercooling the spherulites are ringed, which we attribute to the ineffectiveness of the large-angle branching. The existence of several spherulitic modes signifies that several stable regimes of the small-angle branching exist.     

Incidence of crystal growth conditions on the formation of macroscopic liquid inclusions in ciclopirox crystals

Using an accurate and rigorous protocol, the crystal growth behavior in solution of the antifungal drug ciclopirox was investigated with the aim to identify the experimental factors responsible for the appearance of macroscopic inclusions of saturated solution. Counterintuitively, these inclusions are produced only when the relative supersaturation is below a critical threshold; simultaneously the crystals exhibit a hexagonal morphology. An increase in the driving force leads to a rod-shaped morphology without inclusion and without any change of the crystal phase, as confirmed by X-ray diffraction. The correlation between this morphological transition and the occurrence of liquid inclusions could be rationalized by considering the associated change of growth rates of {(1 1 1)} and {(1 1 -1)} faces. However, the nature of the solvent, the presence of impurities and diffusion in solution appeared to have no detectable incidence on the formation of liquid inclusions, inducing that the presumed contribution of a chemical adsorption phenomenon—side products or solvents—could not be established.     

Second virial coefficient: variations with lysozyme crystallization conditions

Interparticle lysozyme interactions in solution have been studied by small angle X-ray scattering (SAXS) as a function of salt type (NaCl, NaNO₃, NaSCN and NaOAc), salt concentration, and as a function of temperature between 30°C and 10°C. The choice of conditions was made to cover variations from (undersaturated) solutions to (supersaturated) crystallization conditions. The second virial coefficients (A₂) were determined from the X-ray structure factors extrapolated to the origin, as a function of protein concentration. The A₂ values which correspond to lysozyme crystallization conditions were found to be in a range from about zero to −8.0×10⁻⁴ mol ml g⁻², in agreement with previous determinations by other groups. The variations of the second virial coefficient from positive (repulsive interactions) to negative (attractive interactions) were found to follow the efficiency of salts to induce crystallization. The choice of the second virial coefficient as a tool to predict crystallization conditions is discussed.     

In-situ liquid phase TEM observations of nucleation and growth processes

Nucleation and growth of crystals is a pervasive phenomenon in the synthesis of man-made materials, as well as mineral formation within geochemical and biological environments. Over the past two decades, numerous ex situ studies of crystallization have concluded that nucleation and growth pathways are more complex than envisioned within classical models. The recent development of in situ liquid phase TEM (LP-TEM) has led to new insights into such pathways by enabling direct, real-time observations of nucleation and growth events. Here we report results from LP-TEM studies of Au nanoparticle, CaCO₃ and iron oxide formation. We show how these in situ data can be used to obtain direct evidence for the mechanisms underlying crystallization, as well as dynamic information that provides constraints on important kinetic and thermodynamic parameters not available through ex situ methods.     

Static and dynamic crystallization in Mg–Cu–Y bulk metallic glass

The static and dynamic crystallization behavior of Mg₆₅Cu₂₅Y₁₀ bulk metallic glass was investigated by X-ray diffraction, differential scanning calorimetry and transmission electron microscopy. It was found that the kinetics of both anisothermal and isothermal crystallization were adequately represented by the Kissinger and KJMA relations, respectively. The apparent activation energy for crystallization was calculated to be 139 kJ/mol; this value is close to the self diffusion of Mg in both a crystalline and non-crystalline matrix. The Avrami exponent was found to vary from 2.2 to 2.5 with increasing annealing temperature which implies that, at high annealing temperatures, nucleation occurs at a constant rate accompanied by diffusion-controlled growth of spherical grains. Tensile straining in the supercooled liquid region indicated that crystallization is slightly accelerated compared with static crystallization; this phenomenon was found to adversely affect the ductility of the alloy.     

Understanding protein crystallization on the basis of the phase diagram

The phase diagram of a protein–water system is described with a simple model with parameters for the interaction between the protein molecules in the crystal and in the solution. For a certain range of these parameters the phase diagram shows a metastable liquid–liquid immiscibility region. It is shown that this region corresponds to the “crystallization slot” for growing crystals, as proposed by George and Wilson [Acta Crystallogr. D 50 (1994) 361]. Nucleation in this region proceeds in two steps. First small liquid droplets with a high protein concentration are formed; then small crystalline nuclei grow inside these droplets. In the crystallization slot crystals are covered by a thin liquid film with a high protein concentration. We discuss NMR experiments on lysozyme, which show that nucleation is a transient process with an induction time.