Theoretical and Practical Studies on Effects of External Electrostatic Electric Field on Nucleation and Growth Kinetics of Protein Crystals

The crystallization technique where an electric field is applied is an extremely powerful tool to control the crystallization processes of various materials. In particular, the method with application of an external electrostatic electric field can have a significant effect on the phase equilibrium of the liquid and solid phases. This review demonstrates that the crystallization processes of proteins are significantly impacted by the application of an external electrostatic electric field: (1) Control of both the increase and decrease in the nucleation rate can be achieved by changing the applied frequency of the external electrostatic electric field. (2) The effect of the external electrostatic electric field on the nucleation rate can be controlled by regulating the thickness of the electric double layer (EDL) formed at the interface. (3) The quality of the grown crystals can be improved by an increase in the step free energy under application of an external electrostatic electric field at 1 MHz. The effect of the external electrostatic electric field on nucleation and growth kinetics during crystal growth of proteins is also discussed based on a thermodynamic perspective.     

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.     

Nucleation rate enhancement of porcine insulin by application of an external AC electric field

The nucleation rate of porcine insulin increased under application of an external AC electric field at 3 MHz. This is attributed to the electrostatic energy added to the chemical potentials of both the liquid and solid phases; the chemical potential of the solid was significantly changed compared with that of the liquid, which lead to an increase in the driving force for nucleation. Therefore, application of an external AC electric field can be a useful technique for protein crystallization.     

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.     

Effect of an External Electric Field on Polytypic Growth of CdI2 Crystals from Solutions

The effect of an external steady electric field on polytypic growth of CdI₂ crystals was investigated. Crystals were grown at four temperatures: 5, 25, 35, and 50°C with the use of four solvents: H₂O, C₂H₅OH, 3 H₂O + 1 C₂H₅OH and 1 H₂O + 1 C₂H₅OH. The electric field of the intensity 500 to 2500 V/cm was oriented in two directions: perpendicular or parallel to the c-axis of hexagonal plates of CdI₂ crystals. The analysis of the effect of the field on polytypism of CdI₂ was based on the analysis of the structure of about 800 crystals grown in the presence of electric field and of about 1000 crystals grown in neutral conditions. It was established that the weak electric field used for crystallization of CdI₂ does not influence noticeably the relative stability of basic polytypes (2H, 4H) and of complex polytypic structures (ordered and disordered). The electric field may influence the structure of CdI₂ crystals in two ways: (i) the polytypes formed in the presence of the field have on average two times larger cells than the polytypes formed in neutral conditions, (ii) the polytypes formed in neutral conditions have usually hexagonal cells; only 6 to 30% of polytypes are of rhombohedral type. When the electric field was used the percentage of rhombohedral polytypes increased to about 65%.     

Advancements (and challenges) in the study of protein crystal nucleation and growth; thermodynamic and kinetic explanations and comparison with small-molecule crystallization

This paper reviews advancements and some novel ideas (not yet covered by reviews and monographs) concerning thermodynamics and kinetics of protein crystal nucleation and growth, as well as some outcomes resulting therefrom. By accounting the role of physical and biochemical factors, the paper aims to present a comprehensive (rather than complete) review of recent studies and efforts to elucidate the protein crystallization process. Thermodynamic rules that govern both protein and small-molecule crystallization are considered firstly. The thermodynamically substantiated EBDE method (meaning equilibration between the cohesive energy which maintains the integrity of a crystalline cluster and the destructive energies tending to tear-up it) determines the supersaturation dependent size of stable nuclei (i.e., nuclei that are doomed to grow). The size of the stable nucleus is worth-considering because it is exactly related to the size of the critical crystal nucleus, and permits calculation of the latter. Besides, merely stable nuclei grow to visible crystals, and are detected experimentally. EBDE is applied for considering protein crystal nucleation in pores and hydrophobicity assisted protein crystallization. The logistic functional kinetics of nucleation (expressed as nuclei number density vs. nucleation time) explains quantitatively important aspects of the crystallization process, such as supersaturation dependence of crystal nuclei number density at fixed nucleation time and crystal size distribution (CSD) resulting from batch crystallization. It is shown that the CSD is instigated by the crystal nucleation stage, which produces an ogee-curve shaped CSD vs. crystal birth moments. Experimental results confirm both the logistic functional nucleation kinetics and the calculated CSD. And even though Ostwald ripening modifies the latter (because the smallest crystals dissolve rendering material for the growth of larger crystals), CSD during this terminal crystallization stage retains some traces of the CSD shape inherited from the nucleation stage. Another objective of this paper is to point-out some biochemical aspects of the protein crystallization, such as bond selection mechanism (BSM) of protein crystal nucleation and growth and the effect of electric fields exerted on the process. Finally, an in-silico study on crystal polymorph selection is reviewed.     

Effect of various precipitants on the nucleation rate of tetragonal hen egg-white lysozyme crystals in an AC external electric field

It was observed that the effect of an external electric field on the nucleation rate of tetragonal hen egg-white lysozyme crystals varied depending on the precipitant used (NaCl, NiCl₂ or YbCl₃) and that the electric double layer (EDL) played an important role in generating an external electric field of the necessary strength to control the nucleation rate. This phenomenon depended on the ionic strength of the precipitant used; that is, a precipitant of greater ionic strength resulted in a thinner EDL and increased the effect of the external electric field as the driving force for nucleation. The dependence of the nucleation rate on the precipitant was attributed to the magnitudes of the external electric fields generated in EDLs of varying thickness which were formed in the presence of different precipitants.     

Formation of unusual nonferroic domains in TeO2 single crystals under external electric field

The formation of unusual slowly relaxing domains under an external dc electric field has been revealed in paratellurite (TeO₂) crystals. These domains differ from those arising in ferroics (ferromagnets, ferroelectrics, ferroelastics, etc.). The effect is characterized by the existence of a threshold field strength (at which domains begin to be formed) and long equilibrium settling times (up to a few hours, depending on the electric field strength). A crystal returns to the initial single-domain state also after a few hours after the field is switched off. High-resolution triple-crystal X-ray diffractometry has revealed that domains retaining the paraelastic tetragonal phase rotate with respect to each other in space without changing their lattice parameter. The domain sizes are 2–4 mm, depending on the field strength. Currently, the exact mechanisms of domain formation are unclear. Possible reasons for the formation of these defects and an analogy of the observed effects with the behavior of liquid crystals under electric field are discussed.     

Growth aspects of barium oxalate monohydrate single crystals in gel medium

Single crystals of barium oxalate monohydrate (BaC₂O₄.H₂O, BOM) were grown in pure form by controlled diffusion of Ba²⁺ using the gel technique at different temperatures. Starting from aqueous Ba²⁺ chloride (BaCl₂) and acetic acid (C₂H₂O₄) in gel, this method offers a low‐cost and an easiest alternative to other preparation methods for the production of barium oxalate bulky single crystals. The optimal conditions for the growth of BOM crystals in silica gel were found by investigating different growth parameters such as gel pH, gel aging and crystallization temperature. Irrespective of all such crystallization environments, growth rate of the crystals were initially less and then exhibited supersaturation effect leading to non‐linearity. Gel aging and temperature has profound effect on nucleation density that resulted less number of crystals of maximum size in the gel matrix. Perfect single crystals were grown on gels of higher pH. The macropore morphology and porosity was controlled by changing age of the gel. It has been found that temperature has a fabulous effect in controlling the nucleation density by altering the supersaturation conditions for the formation of critical nuclei. The entire growth kinetics informed that the grown crystals were derived by the one dimensional diffusion controlled process. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Measurement of piezoelectric constants of lanthanum-gallium tantalate crystal by X-ray diffraction methods

A method for measuring piezoelectric constants of crystals of intermediate systems by X-ray quasi-multiple-wave diffraction is proposed and implemented. This technique makes it possible to determine the piezoelectric coefficient by measuring variations in the lattice parameter under an external electric field. This method has been approved, its potential is evaluated, and a comparison with high-resolution X-ray diffraction data is performed.     

Implementation of Temperature-Controlled Method of Protein Crystallization in Microgravity

An experimental scientific equipment for implementing temperature-controlled protein crystallization in capillaries under microgravity has been developed, fabricated, and tested. This crystallization method, providing on-line separate control of crystal growth both in the stage of nucleation of crystals and during their further growth, requires small amounts of protein solution. The equipment has been tested on board of Foton-M4 spacecraft (growth of lysozyme protein crystals of high structural quality in microgravity) using a cyclogram developed in ground-based experiments. The results obtained have demonstrated efficiency and importance of the developed equipment and method for growing biomacromolecular crystals of high-structural quality.

     

Growth, dielectric, ferroelectric and optical properties of Ca0.28Ba0.72Nb2O6 single crystals

Calcium barium niobate Ca_0.28Ba_0.72Nb₂O₆ (CBN-28) crystals were grown by the Czochralski method. The effective segregation coefficients of Ca, Ba, Na elements in CBN-28 crystal growth were measured, and the rocking curve from 0 0 2 reflection of CBN-28 wafer was also measured by the high-resolution X-ray diffractometer D5005, and the full-width at half-maximum value was measured to be 70.6″. The measured dependence of dielectric constants on temperature showed the Curie temperature of the CBN-28 crystals is between 246.8 and 260 °C. Typical polarization–electric field (P–E) hysteresis loops were measured at room temperature. Ferroelectric 180° domains were observed by scanning electron microscopy (SEM) on the etched (0 0 1) surface of the CBN-28 crystals. The transmittance of [0 0 1]-oriented CBN-28 crystals was measured and the result shows that optical properties of CBN-28 crystal are almost the same as those of SBN for wavelengths between 2500 and 7500 nm.     

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)     

Crystallization of a germanium melt in an external electric field

Data are presented on experimental studies of the influence of an external electric field on crystallization of a germanium melt under the layer of a B₂O₃ flux. It has been found out that with the field supercoolings of the melt sharply change. This effect is due to the change of the number of active nucleation centres at the germanium – B₂O₃ flux interface. The maximum supercoolings of the germanium melt ΔT⁻ = 190 K were obtained when a negative potential was connected to germanium. The dependences of supercooling on preliminary melt overheating were measured.     

Study of the crystal shape and its influence on the anti‐tumor activity of tumor necrosis factor‐related apoptosis‐inducing ligand (Apo2L/TRAIL)

This paper describes a method about the crystal shape control improving the anti‐tumor activity of tumor necrosis factor‐related apoptosis‐inducing ligand (Apo2L/TRAIL) in a batch cooling suspension crystallization by selecting pH values as a controllable variable. Three shaped TRAIL crystals could be obtained under different pH conditions, among which the hexagonal plate crystals had the highest specific activities against tumor cell line. The relationship among pH values, trimer contents and the specific activities of crystals and the purified TRAIL solutions were investigated. The results showed that different trimer contents resulted from pH altering in crystals and protein solutions is a main reason for their different specific activities. The studies may supply a new method to improve the bioactivity of TRAIL agent during its production and storage. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effects of purification on the crystallization of lysozyme

We have additionally purified a commercial lysozyme preparation by cation exchange chromatography, followed by recrystallization. This material is 99.96% pure with respect to macromolecular impurities. At basic pH, the purified lysozyme gave only tetragonal crystals at 20°C. Protein used directly from the bottle, prepared by dialysis against distilled water, or which did not bind to the cation exchange column had considerably altered crystallization behavior. Lysozyme which did not bind to the cation exchange column was subsequently purified by size exclusion chromatography. This material gave predominately bundles of rod-shaped crystals with some small tetragonal crystals at lower pHs. The origin of the bundled rod habit was postulated to be a thermally dependent tetragonal ↔ orthorhombic change in the protein structure. This was subsequently ruled out on the basis of crystallization behavior and growth rate experiments. This suggests that heterogeneous forms of lysozyme may be responsible. These results demonstrate three classes of impurities: (1) small molecules, which may be removed by dialysis; (2) macromolecules, which are removable by chromatographic techniques; and (3) heterogeneous forms of the protein, which can be removed in this case by cation exchange chromatography. Of these, heterogeneous forms of the lysozyme apparently have the greatest affect on its crystallization behavior.     

Inhibitory effect of polyelectrolytes on crystallization kinetics of hydroxyapatite

Modelling of the biologic materials, well-organized multifunctional structures and systems found in nature has attracted the interest of scientists working in many scientific disciplines. A new and rapidly growing field of biomimetics has stimulated an increased focus on biological materials as the researchers attempt to mimic the features, characteristics and growth of these naturally-occurring materials. This review discusses the principal features of biomineralization in relation to the controlled crystallization of inorganic materials and biomimetic routes to the formation of nanometer hydroxyapatite particles. This approach can be compared with biologic mineralization and has the potential for providing much greater control of particle size and distribution than would conventional methods. The constant-composition method has been used to study the influence of polyelectrolytes on the kinetics of crystal growth of hydroxyapatite (HAP), the thermodynamically most stable calcium phosphate phase, on HAP seed crystals at pH 7.4 and 37 °C. The results indicate that polyelectrolyte concentration and the larger number of negatively charged functional groups markedly affect the growth rate. The fit of the Langmuir adsorption model to the experimental data supports a mechanism of inhibition through molecular adsorption of polymers on the surface of growing crystals. This system may allow insights into biomineralization processes.     

Propagation of elastic waves near acoustic axes in crystals under the action of extreme external forces: I. Piezoelectric crystal in an electric field

The directions of an external electric field at which extreme changes occur in the difference in the velocities of elastic waves propagating along the initial acoustic axis in a piezoelectric medium of arbitrary symmetry are theoretically determined. The problem of degeneracy in an external electric field is considered for elastic waves propagating in a given direction from the vicinity of an initial acoustic axis. The extreme electric fields and corresponding changes in the characteristics of transverse waves are calculated by the example of the behavior of acoustic axes in Bi₁₂GeO₂₀, Bi₁₂SiO₂₀, La₃Ga₅SiO₁₄, and LiNbO₃ crystals.     

Simulation of electrooptical effects and dynamics of ferroelectric liquid crystals

The behavior of ferroelectric liquid crystals in an external electric field is simulated numerically. The equations that describe the dynamics of the director of a liquid crystal are derived within the continuum theory of elasticity with due regard for compressibility of smectic layers, finite anchoring energy, and dielectric properties of orienting coatings and external elements of a real electric circuit. These equations make the basis for simulation of the electrooptics of ferroelectric liquid crystals. The specific features and mechanisms of the surface-stabilized bistability and hysteresis-free electrooptical switching (the V-shape effect) are discussed.     

Ageing of spherulites of an industrial relevant aromatic amine derivative

Polycrystalline spherulites of an aromatic amine derivative have been precipitated in a batch process by pH‐shift with hydrochloric acid from stirred aqueous solutions. The time dependent behaviour of the spherulites has been studied during crystallization in the temperature range from 5 °C to 60 °C. Cake resistance values have been obtained from batch filtration tests performed at 2 bar pressure difference at different stages of the crystallization process. The FBRM mean chord length of the crystals decreases with time as a result of crystal ageing into plate‐like crystals. The rate of the ageing process increases with temperature. XRD‐studies show no significant differences in the crystal structure during the ageing process, and the mechanism of the transformation was not established. The filterability of aromatic amine crystals deteriorates as the crystallization progresses. The decrease in the filterability is attributed to the appearance of small plate‐like crystals and a change in the interaction between the crystal surface and the solution, during the ageing of the particles. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)