Protein crystal nucleation: Recent notions

The nucleation of protein crystals is reconsidered taking into account the specificity of the protein molecules. In contrast to the homogeneous surface properties of small molecules, the protein molecule surface is highly inhomogeneous. Over their surfaces proteins exhibit high anisotropic distribution of patches, which are able to form crystalline bonds, the crystallization patch representing only a small fraction of the total surface of the protein molecule. Therefore, an appropriate spatial orientation of the colliding protein molecules is required in order to create a crystalline cluster. This scenario decreases considerably the success ratio of the attempt frequency for crystal nucleation. On the other hand a heterogeneous nucleation of (protein) crystals may be accelerated due to the arrival on some support of under‐critical clusters that are formed in bulk solution; when arriving there they may acquire the property of critical nuclei. Thus, a plausible explanation of important peculiarities of protein crystal nucleation, as inferred from the experimental data, is suggested. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Heterogeneous Nucleation of Hen‐Egg‐White Lysozyme — Molecular Approach

The heterogeneous nucleation of hen‐egg‐white lysozyme (HEWL) crystals has been repeatedly investigated using a double‐(thermal)‐pulse technique, thus detaching nucleation from growth stage. n(t) dependencies of the nucleus number n, on templates of poly‐L‐lysine, vs time, t were plotted and the steady‐state nucleation rates I were determined. They were compared with the results obtained earlier for surfaces rendered hydrophobic (by means of hexamethyl‐disilazane) as well as for bare glass surfaces. In the present paper we determine the number of HEWL molecules in the (heterogeneously formed) critical nucleus. It turned out that it is build of 3 (to 4) HEWL molecules on glass substrate and 8 molecules for both hexamethyl‐disilazane and poly‐L‐lysine templates. The energy Ak required for heterogeneous formation of a critical nucleus on poly‐L‐lysine has been calculated, on the basis of the steady‐state nucleation rates I. Intermolecular binding energy in the HEWL crystal lattice has been estimated again (approximately 10‐9 erg/molecule). This time the basis was the adhesion of HEWL crystals to poly‐L‐lysine substrate.     

Temperature control of protein crystal nucleation

The thermal variant of the classical nucleation‐growth‐separation principle is shown, both theoretically and experimentally, to be a reliable tool for studying protein crystal nucleation. The classical nucleation theory is used to elucidate the temperature dependence of crystal nucleus size. A one‐to‐one ratio of the number density of nuclei formed to crystals grown to visible size is achieved using the nucleation‐growth‐separation method. The experiments conducted in such a way show that new nuclei are prevented from appearing while avoiding any crystal loss due to dissolution. The same method is used to study experimentally the interval of growth temperatures where the number density of (nucleated) crystals is relatively insensitive to the growth temperature. It is argued that this temperature interval corresponds to the width of the so‐called metastable zone.     

On slow protein crystal nucleation: cluster‐cluster aggregation on diffusional encounters

With a view to experimental results on protein crystal nucleation the effects of cluster coalescence are probed semi‐quantitatively. The steric association restriction, which stems from the patchy surface of the protein molecules, explains both experimentally measured low crystal nucleation rate and coalescence limitations for crystalline clusters of protein molecules. The conclusion is that due to its action, and the impact of rotational diffusion, the coalescence of critical (and/or supercritical) clusters should be rejected as a conceivable alternative for explaining the slow nucleation of protein crystals. Besides, the analysis of cluster‐cluster aggregation on diffusional encounters may be of more general interest; it may be helpful by considering the coalescence of structured bio‐nano‐particles. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Adhesion of protein crystals: Measurement of the detachment force

The degree of adhesion of protein crystals, heterogeneously nucleated and grown on different supports (e.g. glass plates and plates coated with poly‐L‐lysine, hexamethyl‐disilazane and silicon) is measured directly with a purposely‐developed technique. The sticking force crystal/support is determined by means of a flexible glass fibre, which bending is calibrated by means of series of weights. In this way an elastic constant, specific for each glass fiber is determined individually. Appropriate glass fibres with relative bending less than 10% (Hook's law) are used. The force which is necessary to be exerted, by means of a micro‐manipulator, in order to detach the crystal from the support is taken as a quantitative measure for the adhesion strength. Forces between 10 N cm^‐2 and 1 N cm^‐2 for differently oriented tetragonal hen‐egg‐white lysozyme and cubic ferritin crystals, and 0.1 N cm^‐2 for rhombohedral (porcine) insulin and orthorhombic trypsin crystals are measured. The tetragonal HEWL and rhombohedral insulin crystals show anisotropy of the adhesion strength. In contrast, the cubic ferritin crystals are isotropic also in this respect. For comparison purposes adhesion measurements are performed with NaCl and sugar crystals. An attempt is made to evaluate also the adhesion energy of the protein crystals. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Heterogeneous nucleation (and adhesion) of lysozyme crystals

The heterogeneous nucleation of hen-egg-white lysozyme (HEWL) crystals has been investigated using a double-(thermal)-pulse technique, thus detaching nucleation from the growth stage. n(t) dependencies of the nucleus number, n, vs. time, t, were plotted for surfaces rendered hydrophobic (by means of hexamethyl-disilazane) and for bare glass surfaces. Preferred crystallite orientation supplied additional information. The discussion is based on the classical Stranski–Kaischew theory of crystal nucleation. With a purposely developed new technique the adhesion energies have been measured for HEWL crystals, grown on different supports.     

Influence of emulsion types on nucleation kinetics and growth habit in the cooling crystallization

Experiments on unseeded batch cooling crystallization were made to investigate the influence of emulsion [solution in non‐solvent (S/NS) emulsion and non‐solvent in solution (NS/S) emulsion] on crystal size and growth habit of various materials such as hexahydro‐1,3,5‐trinitro‐1,3,5‐triazine, ammonium sulfate, potassium dihydrogen phosphate (KDP), and γ‐glycine. Size of crystals obtained from the S/NS emulsions was found to be significantly larger than that obtained from the NS/S emulsions. Those results were explained by broad induction time distribution of nucleation in the isolated solution droplets and subsequent seeding effect by free movement of early‐induced crystals by vigorous agitation. As a result, the population density of crystals was shown to be smaller in the S/NS emulsions than that in the NS/S emulsions. In the S/NS emulsions, desupersaturation rate should be slow and high supersaturation is subsequently generated during crystal growth stage. Therefore, it may be concluded that crystal morphology of the materials with supersaturation dependent growth habit, such as ammonium sulfate, KDP and γ‐glycine, can be controlled by selection of emulsion type.     

A study of primary nucleation of calcium oxalate monohydrate: II. Effect of urinary species

Kidney stones consist of various organic and inorganic compounds. Calcium oxalate monohydrate (COM) is the main inorganic constituent of kidney stones. However, the mechanisms for the formation of calcium oxalate kidney stones are not well understood. In this regard, there are several hypotheses including nucleation, crystal growth and/or aggregation of formed COM crystals. The effect of some urinary species such as oxalate, calcium, citrate, and protein on nucleation and crystallization characteristics of COM is determined by measuring the weight of formed crystals and their size distributions under different chemical conditions, which simulate the urinary environment. Statistical experimental designs are used to determine the interaction effects among various factors. The data clearly show that oxalate and calcium promote nucleation and crystallization of COM. This is attributed to formation of a thermodynamically stable calcium oxalate monohydrate resulting from supersaturation. Citrate, however, inhibits nucleation and further crystal growth. These results are explained on the basis of the high affinity of citrate to combine with calcium to form soluble calcium citrate complexes. Thus, citrate competes with oxalate ion for binding to calcium cations. These conditions decrease the amount of free calcium ions available to form calcium oxalate crystals. In case of protein (mucin), however, the results suggest that no significant effect could be measured of mucin on nucleation and crystal growth. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Probabilistic approach to protein crystal nucleation

Simple probabilistic model for step‐wise growth of polymers is used for making some parallels with the nucleation of protein crystals. Although the considerations are made within 1D case, this approximation still shows some important peculiarities of protein crystal nucleation and growth. Thus, the present approach turns out to be useful for interpretation of some important experimental results regarding these processes. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

F-及SiF2-6对α型半水硫酸钙结晶成核及形貌的影响

本文模拟了半水法湿法磷酸生产过程中α型半水硫酸钙(α-HH)的结晶过程。在30%P₂O₅,反应温度95 ℃,过饱和度S=1.64~2.10条件下,通过浊度仪监测溶液中浊度变化,测定了不同F^-及SiF^2-₆浓度下α-HH结晶诱导时间,采用经典成核理论公式计算了α-HH的临界晶核半径及成核速率,并通过扫描电子显微镜(SEM)、X射线衍射(XRD)、X射线光电子能谱(XPS)表征分析了F^-及SiF^2-₆对α-HH结晶过程的影响。结果表明:随着F^-、SiF^2-₆浓度的升高,α-HH晶体的结晶诱导时间延长,表面能和临界晶核半径都增大,然而成核速率减小。当过饱和度S=1.64时,加入0.06 mol·L^-1 F^-,α-HH结晶诱导时间延长了465 s,成核速率减小到0.403×10²⁹ 晶核数·cm^-3·s^-1,然而,加入0.06 mol·L^-1 SiF^2-₆,α-HH结晶诱导时间延长了710 s,成核速率减小到0.339×10²⁹晶核数·cm^-3·s^-1。SiF^2-₆对α-HH晶体抑制成核作用大于F^-。F^-、SiF^2-₆阻碍了α-HH晶体沿C轴方向生长,使得晶体长径比减小,晶体形貌向短柱状变化。F^-、SiF^2-₆影响了α-HH晶体(200)、(310)、(400)晶面衍射峰强度和结晶度。控制半水法湿法磷酸中F^-及SiF^2-₆浓度水平,可以得到短柱状的α-HH晶体,有利于过滤洗涤。     

Application of mean‐separation‐works method to protein crystal nucleation

Using mean‐separation‐works method of Stranski and Kaischew calculations of nucleus form and energy barrier for its formation are performed for globular protein crystals. This is done on the basis of a simple model suggested for crystal nucleation of such proteins. The prerequisite for the model is the fact that strict selection of definite sticky patches on protein molecule surface is obligatory for forming crystal lattices. The calculation results are in agreement with experimental data. (© 2008 WILEY ‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Understanding the effect of solvent polarity on the habit modification of monoclinic paracetamol in terms of molecular recognition at the solvent crystal/interface

The habit change of monoclinic paracetamol crystallized from solutions with different solvents such as water, ethanol, methanol, acetone, isopropyl alcohol, tetrahydrofuran, cyclohexanone, acetonitrile and 1, 4 ‐ dioxane was investigated. Change in solubility, pH and nucleation time of paracetamol in these solvents at ambient condition was studied. The polymorphic form of the nucleated paracetamol was observed under in‐situ optical microscopy. Solutions with different solvents having different chemical nature and polarity yielded paracetamol crystals with different habits: columnar morphology from polar protic water and prismatic morphology from other selected polar protic, aprotic and in non‐polar solvents. The significant differences on the growth rate of various crystal habit faces of the monoclinic paracetamol grown from different solvents are attributed in context with the solubility of the solute, solvent polarity, evaporation number of the solvent, rate of generation of supersaturation and the role of hydrogen bonding interaction between the solvent molecules and protruding solute molecules on the crystal surface. Among the solution with different solvents, bulk monoclinic paracetamol single crystal was grown from ethanolic solution using seed rotation technique by controlled cooling method.     

Nucleation kinetics of the formation of low dimensional calcium sulfate dihydrate crystals in isopropyl alcohol medium

Calcium sulfate dihydrate, constituted as uniform crystals of low dimensions, is a potential biomaterial for clinical applications like bone graft substitution and drug delivery. In this work, isopropyl alcohol has been used as a solvent to obtain low dimensional calcium sulfate dihydrate crystals from calcium nitrate ‐ sulfuric acid system. Reactants in 0.5 molar concentration at ambient conditions generated uniform rod‐shaped crystals of length 3–5 µm. Analysis using X‐ray Diffractometry and Fourier Transform Infrared Spectrometry showed the material to be well crystallized, phase‐pure calcium sulfate dihydrate. The nucleation kinetics has been studied by observing the induction time of phase formation in solutions of millimolar concentrations through turbidimetry at 300 K. The data have been analysed using classical nucleation theory to deduce parameters like interfacial tension (or surface free energy), nucleation rate and critical radius. The surface free energy obtained (5.6 mJ/m²) is comparatively lower than that reported for aqueous precipitation, which could be attributed to the presence of isopropyl alcohol. On escalating the supersaturation ratio, the nucleation rate drastically increased and the critical radius decreased exponentially. Particles formed at supersaturation 1.39 showed a monomodal distribution centered at 8.2 nm in Dynamic Light Scattering analysis. Comparable particle sizes were obtained in Transmission Electron Microscopy.     

Thermodynamics of Crystal Nucleation in an External Electric Field

The influence of electric field on crystal nucleation in a saturated solution has been studied both theoretically and experimentally. The classical equations for nucleation have been used to determine the free energy of formation, critical radius of the cluster and the concentration of the critical nuclei. The theory shows that an externally applied electric field can modify the free energy of formation of a crystalline cluster in its aqueous solution. The impact of the field will be stronger on large molecules. Two experimental set ups have been designed to study the nucleation of crystals in saturated aqueous solutions, in the presence of electric fields. Experiments conducted using a metal coordination compound bis‐ thiourea zinc chloride show that electric fields of strength around 10⁵ V/m would increase its nucleation.     

Investigation on the regeneration of Z‐cut KDP crystals

The regeneration of Z‐cut KDP crystals is explored by analyzing the growth of thin surface layers formed. The structural defects and crystalline perfection of the thin surface layers are evaluated by white‐beam synchrotron radiation topography and high‐resolution X‐Ray diffraction respectively. It shows that the thin surface layers have the same crystal structure as KDP crystal. There are large numbers of defects in thin surface layers and the crystalline quality is very poor. The growth velocity of thin surface layers is firstly accurately measured by a newly‐designed in‐situ crystal growth observation setup. It is found that the growth velocity of the thin surface layers strongly depends on the flow rate of the growth solution. The hindering effect of pyrophosphate (K₄P₂O₇) on the growth of the thin surface layers is discussed. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Bond selection during protein crystallization: Crystal shapes

The so‐called bond selection mechanism, BSM (C.N. Nanev, Progress in Crystal Growth and Characterization of Materials, 59 , 133–169, 2013) allows explaining a set of traits in both protein crystal nucleation and growth processes. BSM explanatory and predictive power are enhanced now, when intra‐crystalline repulsive interactions are assumed to act in parallel with the attractive forces, the former arising due to protein surface patch‐to‐patch incompatibility. Shapes of 1D and 2D protein crystals are considered from such a perspective. Using BSM the strong directional kinetic anisotropy in the edge growth rates of 2D protein crystals is tackled. The shapes of near‐critically sized apoferritin crystals and of experimentally grown 3D apoferritin crystals are considered.     

Metastable zone width for secondary nucleation and secondary nucleation inside the metastable zone

This study presents an evaluation of a new method, called zero growth activation free energy, used to determine the metastable zone width for the secondary nucleation case. It predicts the metastable zone width with a maximum error of 5‐10%. Estimation of the metastable zone width for different isothermal crystallization conditions can be modeled according to a chosen reference set of growth experiments carried out in the volume diffusion regime at different initial supersaturations, using seed crystals of a certain characteristic size. Moreover, the activation free energy of the secondary nucleation was estimated. The role of the enthalpy of immersion in the formation of secondary nucleation events inside the metastable zone was pointed out, as well as its effect in causing extra‐fast growth rate. Furthermore, sucrose crystal surface free energy was estimated. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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 zinc doping on pentaerythritol tetranitrate single crystals

In this study, the effect of zinc impurity on the organic high explosive pentaerythritol tetranitrate (PETN) single crystal has been investigated with optical microscopy and ex situ atomic force microscopy (AFM). The optical images show that the crystal shape has a transition with a predictable trend from long crystal to compact one as the zinc concentration is increased. Also, the 2‐dimentional (2‐D) growth hillocks are observed clearly on (110) face with contact AFM. The crystal growth occurs on monomolecular steps generated by 2‐D nucleation and followed by layer‐by‐layer expansion, and the macro‐steps formed onto the surface before spreading laterally as step bunches. The zinc ions are incorporated in growth steps as the zinc concentration is increased. The mechanism of inorganic impurity on molecular crystallization growth is still unclear. However, the incorporation of impurities may significantly affect growth kinetics of defect structure, and the bulk properties of molecular crystals. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A study of primary nucleation of calcium oxalate monohydrate: I‐Effect of supersaturation

There are various organic and inorganic constituents in kidney stones. Among them, calcium oxalate monohydrate (COM) is the primary inorganic constituent of kidney stones. However, the mechanisms of formation of kidney stones are not well understood. In this regard, a basic study is carried out for better understanding of nucleation, crystal growth and/or aggregation of formed COM crystals. The primary nucleation of calcium oxalate monohydrate is studied at the laboratory scale using turbidity measurements. Calcium chloride and potassium oxalate solutions are mixed and then added to a Turbidimeter tube for continuous recording of turbidity. Induction time (time to induce formation of detectable crystals) is estimated from time‐turbidity graphs. The effect of some urinary species, such as oxalate and calcium, on nucleation and crystallization characteristics of COM is determined by particle size distribution analysis, measuring weight of crystals and calculation of relative supersaturation. The classical nucleation theory is applied at high supersaturation ratios (SR) ranging from 1.6 to 2.2. The results indicate that nucleation rate increases with increasing supersaturation ratio from 0.81 × 10²⁸ nuclei/cm³.sec at 1.6 SR, to 18.02 × 10²⁸ nuclei/cm³.sec at 2.2 SR. On the other hand, free energy change and radius of critical nucleus are decreased as supersaturation ratio is increased. The nucleation rates are higher than those reported in literature. Such discrepancy is discussed on the bases of differences in experimental techniques. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)