Influence of various factors on the liquid/liquid diffusion crystallization of proteins

From a numerical simulation of pre-nucleation solute transport in the liquid/liquid diffusion crystallization of proteins, it is derived that there are various factors influencing the spatial and temporal distributions of supersaturation. They include the ratio of the length of the protein solution to that of the salt solution in a tube crystallizer, the initial concentrations of protein and salt, and the initial salt concentration in the protein solution. Their influences on the protein crystallization have been demonstrated by the corresponding experiments of gel crystal growth. It may be deduced that the experimental conditions for the liquid/liquid diffusion growth of protein crystals could be optimized under given conditions in order to develop the advantages of this method.     

Modeling of the Biocrystal Growth Using Temperature Field

Crystallography Reports - A mathematical model has been developed and numerical calculations of lysozyme protein crystallization from a homogeneous aqueous solution under temperature field control...     

Supersaturation patterns in counter-diffusion crystallisation methods followed by Mach–Zehnder interferometry

We present experimental observation of the spatio-temporal pattern of supersaturation in counter-diffusion methods. These complex patterns were recorded by dynamical interferometric analysis using a Mach–Zehnder configuration. Tetragonal hen egg white lysozyme crystals were grown inside APCF (advanced protein crystallisation facility) reactors. Salt and protein diffusion profiles were obtained independently by performing duplicated experiments with and without protein in the protein chamber; salt gradients were observed directly while protein concentration profiles are computed from the differences in refractive index between the two experiments. As expected from computer simulations, the time evolution of supersaturation shows a maximum about 45 h after activation (although this value can change as a function of the starting conditions and the geometry of the reactor). Nucleation takes place before this maximum supersaturation is reached. This explains the trend of the growth rate versus time curves for experiments performed within APCF reactors (both on ground and in space) and in capillaries by the gel acupuncture technique. By using very low concentration agarose gel in the protein chamber, sedimentation and buoyancy effects are eliminated so that the effects of gravity on fluid dynamics and hence on the spatio-temporal evolution of supersaturation can be assessed. These results confirm experimentally the predicted behaviour of counter-diffusion systems and support their use in growing large high-quality protein single crystals.     

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.     

Optimization of the cascade crystallizers

For the cascade crystallization process a set of technological optimization conditions was established. The possibility of succesful application of proposed optimization conditions was pointed out by comparison with a mathematical model of Na₂SO₄ · 10 H₂O crystallization in multichamber crystallizer presented in the literature. The method has a general applicability and can be used for the optimization of any cascade-linked system, provided that the mathematical model was detailed enough to permit the operation of numerical derivation.     

Computer modelling of the non-isothermal crystallization kinetics of electroless nickel-phosphorus deposits

Non-isothermal differential scanning calorimetry (DSC) data of electroless nickel-phosphorus (EN) samples with three different phosphorus contents (9, 12 and 16 wt%) has been used in the computer modelling of crystallization kinetics based upon the Johnson-Mehl-Avrami (JMA) theory. The major crystallization processes of the EN samples are complex and could involve multiple reactions, as indicated by the corresponding DSC curves obtained at the heating rates of 5-50 °C/min. The degrees of transformation for major crystallization process of the samples were calculated from those DSC experimental data. Computer simulations of the degree of transformation as well as the corresponding DSC curves were performed using the JMA models, and the results were compared to those from the experiments. It was found that the JMA models could perform within the experimental accuracy of the samples with high (12 and 16 wt%) phosphorus contents. However, satisfactory application of the model to a sample with medium (9 wt%) phosphorus content was not achieved, probably due to the presence of crystalline phase in the deposit prior to crystallization process. The derived JMA kinetic exponents (n) are compared and discussed upon their kinetic interpretation to the non-isothermal crystallization processes of the samples.     

Practical experimental design techniques for automatic and manual protein crystallization

When crystallizers are searching for the optimum crystallization conditions, they often carry out experiments that are confusing and difficult to interpret. This confusion arises because there are several important variables in any protein crystallization experiment (including protein concentration, precipitant concentration, pH and temperature) and these variables often interact–that is to say, changes in the level of one variable often change the optimum settings of the others. Confusion can be avoided by using appropriate experimental designs where all of the important variables are varied in each experimental run. Some well known and practical designs for automatic and manual crystallization are presented, and a simple practical example is given.     

Improving the batch crystallizers operation

Using a mathematical model, from the literature, for the potassium sulphate crystallization, a computer programme was elaborated, aiming to optimize the operation of batch crystallizers through the minimization of the formed crystals number. Owing to the simplifications imposed by the numerical calculation a semnificative reduction of the crystals number was not obtained, comparatively with the constant supersaturation crystallization process, considered as a standard mode of operation. However, the model pointed out the direction for further process improving. Through systematical search, by generating different continuously diminishing functions for the supersaturation value, operating policies were founded, conducting to the reduction of the number of crystals formed in the process.     

The crystallization of lysozyme and thaumatin with ionic liquid

Three different ionic liquids (ILs) were used for the crystallization of lysozyme and thaumatin. It would be a promising solvent for applications in protein chemistry, due to its unusual features such as excellent solubility of inorganic and organic materials, enhancement of protein activity and stability, etc. Here, [BMIm][BF₄] was used as precipitants or union-precipitants in the experiments of thaumatin and lysozyme, respectively. And the experimental results indicated that the probability of single crystals appearance was significantly increased with the addition of [BMIm][BF₄].     

Investigation of the possibility of obtaining homogeneous Ga<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>In<Subscript>x</Subscript>Sb crystals under weak flow conditions

The possibility of growing macrohomogeneous Ga_{1 ? x}In_xSb crystals with x = 0.2 was studied using the axial heating process close to the melt/crystal interface. The grown ingots were analyzed by a JSM-5300 scanning electron microscope and the experimental results were compared with the results of numerical simulation. It was shown that, as a whole, the mathematical model adequately describes the processes of the steady-state heat and mass transfer. It was found that, at the crystallization of Ga_{1 ? x}In_xSb by the axial heating process under conditions of weak laminar flows, longitudinal homogeneity is observed when a dead zone is formed in the melt and that the crystallization regime is similar to diffusion. It was shown that the composition of the grown crystals strongly depends on the structure of a melt flow and its dynamics.     

A short overview on practical techniques for protein crystallization and a new approach using low intensity electromagnetic fields

This contribution deals with a practical overview of some popular and sophisticated crystallization methods that help increase the success rate of a crystallization project and introduces a newly developed method involving low intensity electromagnetic fields. Aiming to suggest a methodology to follow, the present contribution is divided into two main parts in a logical order to get the best crystals for high resolution X-ray crystallographic analysis. The first part starts with a short review of the chemical and physical fundamentals of each crystallization method through different strategies based on physicochemical approaches. Then, practical non-conventional techniques for protein crystallization are presented, not only for growing protein crystals, but also for controlling the size and number of crystals. These include crystal growth in gels, counter-diffusion, seeding, and macromolecular imprinted polymers (MIPs). The second part shows the effects of coupling low intensity electric fields (in the scale of units of  μAmperes) with weak magnetic fields (in the scale of milli Tesla) applied to protein crystallization. This approach consists of a novel experimental set up, which was used to study the influence of the coupled fields on the crystallization of lysozyme in solution and in gel media. This new approach is based on the classical theories of transport phenomena and offers a more accessible strategy to obtain suitable crystals for X-ray characterization or Neutron diffraction investigations.     

Crystal Growth in Gel: Nuclei and Precipitation Distribution in Gel

The investigation of the gel structure and properties influence upon the crystallization processes have been carried out and are reported in this paper. The gel acidity and nucleation centers distribution are chosen as the parameters describing this process. The analytical approximations for the nucleation and precipitation density along the gel column are proposed. It has been shown that in the view of the parameters chosen it is impossible separately to determine the gel structure and proton concentration effects on crystallization processes.     

In situ monitoring and control of lysozyme concentration during crystallization in a hanging drop

Fiber optic Raman spectroscopy combined with a partial least-squares regression model was demonstrated as a monitor of lysozyme concentration during crystallization in a hanging drop experiment in real time. Raman spectral features of the buffer and protein were employed to build the regression model. The use of fiber optic technology coupled with Raman spectroscopy, which is ideal for use with aqueous solutions, results in a powerful noninvasive probe of the changing environment within the solution. Lysozyme concentrations were monitored in experiments at a constant reservoir ionic strength. Data from these uncontrolled experiments were used to determine rates of supersaturation, induction times, and the number and size of the resultant lysozyme crystals. Control experiments were performed by introducing step changes in the reservoir ionic strength. The step changes were initiated by comparing in situ rates of supersaturation with the rates of supersaturation calculated from the uncontrolled data. Monitoring the concentration changes of the lysozyme within the hanging drop permits a measurement of the level of supersaturation of the system and enhances the possibility of dynamic control of the crystallization process.     

Kinetical study of the nonstoichiometric vapour growth process in the system ZnSe:I2

We have studied the growth of ZnSe crystals by chemical transport in a closed system in nonstoichiometric conditions, and we have deduced that the interface kinetics is the phenomenon limiting the growth process. The effect on the growth process of the deviation from stoichiometry of the II‐VI compound was investigated using a mathematical model that involves indirect data computed from directly obtained experimental values. The experimental crystallization rate was compared with the maximum value of the transport flux calculated using the Arizumi‐Nishinaga model. The influence of the stoichiometry of the source material and of the variations in the growth parameters (supercooling, geometrical dimension, specific loading of the ampoule and iodine concentration) on the ZnSe crystal growth process has also been studied. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Influence of impurity on rhythmic crystallization of calcium carbonate in agar gel

During the gel growth of calcite crystals in test tubes, for a narrow concentration of inner and outer electrolytes we observed rhythmic crystallization of calcium carbonate. In this paper the effect of adding impurities on the pattern of periodic crystallization of calcium carbonate has been presented. The addition of impurities either increases or decreases the solubility of reaction product and hence may affect the rate of nucleation of calcium carbonate crystals. The variation of spacing coefficient and velocity constant due to the addition of impurities has also been studied.     

Uncertainties in crystallization of hen‐egg white lysozyme: reproducibility issue

The reproducibility of biomacromolecular crystallization (tetragonal and orthorhombic lysozyme crystals) was studied by monitoring the evolution of protein concentration during the crystallization process using Mach‐Zehnder interferometer. It was found that formation of both tetragonal and orthorhombic crystals exhibited poor reproducibility. When the crystallization occurred under isothermal conditions, the protein concentration in the solution varied differently in different experiments under identical conditions (for both types of crystals). Moreover, in the case of orthorhombic lysozyme crystallization (under either isothermal or thermal gradient conditions), it is clear that the crystals could not be always readily formed. When formation of tetragonal lysozyme crystals was conducted at a temperature gradient condition, however, the evolution of concentration was reproducible. The phenomena found in this study revealed that biomacromolecular crystallization can be uncertain, which is probably caused by the process of nucleation. Such uncertainties will be harmful for the efforts of screening crystallization conditions for biomacromolecules. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Thermal and chemical methods for producing zinc silicate (willemite): A review

Thermal and chemical methods for producing zinc silicate, Zn₂SiO₄ phosphor on industrial and laboratory scales are reviewed. Zinc silicate has a promising future in advanced materials as a highly versatile luminescent material due to the wide range of multi-colors that can be obtained from various guest ions. Candidates for future industrial methods of producing zinc silicate are critically reviewed from the point of view of phase formation and compared with the conventional solid-state reaction. Conventional methods require calcination at temperatures higher than 1000 °C and long reaction times to form Zn₂SiO₄ phase and these processes limit particle shape and size. Sol–gel methods are performed in a solvent at ambient pressure, while hydrothermal and solvothermal methods tend use high temperatures and high pressures, and especially supercritical water methods tend use conditions higher than 400 °C and 25 MPa. Hydrothermal and sol–gel literature shows that crystallization of Zn₂SiO₄ requires at least temperatures of around 100 °C. Of all the growth methods, supercritical water is able to bring about phase formation in the shortest reaction time. Vapor methods are performed with a gas phase as the reaction medium. Vapor and sol–gel methods require post-calcination for crystallization and have the advantage of providing characteristic particles such as uniform shapes, spherical particles, or nano-sized particles by varying the experimental conditions; they may be combined with the other crystallization routes in the future.     

Evaluation of experimental parameters influencing the growth of large crystals of NaX zeolite

Following the Charnell's procedure, the influence of materials, methods of preparation and changes in composition of the gel on the process of NaX zeolite crystallization have been investigated in order to find conditions providing both the growth of crystals as large as possible and also good reproducibility of the result. The experimental conditions used are detailed described.