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)     

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)     

Investigation of nucleation kinetics and crystal defects of HMX

The nucleation kinetics of HMX (cyclotetramethylene tetranitramine, C₄H₈N₈O₈) in γ‐butyrolactone was studied in cooling process by induction time method. The laser scattering method was used to measure the solubility data and metastable region of HMX in γ‐butyrolactone. The induction time was measured over a range of supersaturation at different temperatures. Then, the nucleation mechanism of HMX in γ‐butyrolactone was investigated by analysis the relationships between induction time and supersaturation. The results indicated homogeneous nucleation dominated at high supersaturation of S >1.35, while the heterogeneous nucleation dominated at low supersaturation of S < 1.35. The values of interfacial tension at different final temperatures were calculated to indicate the ability of HMX to be crystallized. The growth mechanism of HMX was investigated by the data fitting applying different growth mechanism models and identified as two‐dimensional nucleation‐mediated (2D) growth. Finally, the effects of supersaturation and temperature on the crystal defects were analyzed based on the nucleation kinetics. When the temperature is below 303.15K, homogeneous nucleation dominated the nucleation process at higher supersaturation. Fine HMX crystals with more defects were produced. On the contrary, heterogeneous nucleation mechanism dominated at lower supersaturation. large regular HMX crystals with fewer defects were formed when the temperature is above 318.15K.     

Kinetics and intimate mechanism of protein crystal nucleation

Experimental and theoretical investigations on protein crystal nucleation are reviewed. Various experimental applications of the classical principle, which requires separation of the nucleation and growth stages of the crystallization process, are described. Temperature control is used most frequently, hypergravity and concentration changes being auxiliary techniques. Nucleation time-lags are measured by imposing temperature evoked supersaturation gradients. Application perspectives are revealed. Nucleation rates are measured according to the classical principle mentioned above, and energy barriers for crystal nucleation and numbers of molecules constituting the critical nuclei are calculated. Surprisingly, although requiring unusually high supersaturation, protein crystal nucleation occurs much more slowly than that with small molecule substances. On this basis novel notions are suggested for the elementary mechanism of protein crystal bond formation. Due to the selection of the crystalline bonding patches a successful collision between protein molecules, resulting in the formation of a crystalline connection, requires not only sufficiently close approach of the species, but also their proper spatial orientation. Imposing a rigid steric constraint, the latter requirement postpones the crystal nucleus formation. Besides, it was shown that cluster coalescence is not a factor, hampering the protein crystal nucleation. The comparison of the model predictions with experimental results proved that nucleation kinetics is governed by kinetic (not by energetic) factors.     

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)     

Determination of nucleation kinetics of lovastatin in acetone solution

The metastable zone widths of lovastatin in acetone solution were determined at different temperatures, cooling rates and initial concentrations by polythermal method. It decreases with the increase of temperature and initial concentration, increases with the increase of cooling rate. The induction periods of lovastatin in acetone solution were also investigated as a function of supersaturation ratios. The crystal‐liquid interfacial tension, thus the fundermental nucleation parameters including Gibbs free energy change for the formation of critical nucleus, radius of critical nucleus and number of molecules in the critical nucleus have been gotten based on the classical homogeneous nucleation theory. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Metastable zone width and nucleation threshold of aluminium hydroxyfluoride hydrate

This paper considers the metastable zone width (MSZW) of aluminium hydroxyfluoride hydrate (AHF, AlF₂OH.H₂O) crystallizing solution, with a view to identifying suitable conditions for crystal growth. Speciation calculations combined with experimental validations have been used to estimate the degree of saturation at varying pHs leading to the identification of the metastable zone width (MSZW). From the results obtained, the solutions are saturated at pH 3.0 ± 0.3 and remain metastable until the nucleation threshold is reached at pH 5.0 ± 0.3. A narrowing of the MSZW at elevated temperatures has been observed and is attributed to the decrease in AHF solubility with increasing temperatures. This phenomenon was applied to obtain a tripling of the crystal particles in 30 minutes. The pH profile of the crystallizing solution is similar to that of acid/base titration curves and is found to be a quick and accurate method of estimating the MSZW. Using similar terminologies, the equivalent point corresponds to solution saturation while the mid‐point corresponds to the nucleation threshold. These results are applicable in the recovery of fluoride values of spent pot lining.     

Heterogeneous versus bulk nucleation of lysozyme crystals

Heterogeneous (on‐glass) protein crystal nucleation was separated from the bulk one in systems of thin protein solution layers, confined between two glass plates of custom made quasi two‐dimensional all‐glass cells, as well as by applying forced protein solution flow. Two commercial samples of hen‐egg‐white lysozyme, Seikagaku and Sigma were used as model proteins. Applying the classical technique of separation in time of nucleation and growth stages with protein solution layers of thickness 0.05 cm we found that the on‐glass crystal nucleation prevailed highly with Seikagaku HEWL, while on the opposite, bulk nucleated crystals represented the main crystal fraction in Sigma solution. Also using 0.05 cm solution layers nucleation rates were measured separately for the on‐glass and bulk protein crystals. The process was investigated by varying solution layer thicknesses as well, from 0.05 down to 0.01, 0.0065 and 0.002 cm. Studying the influence of the forced protein solution flow on HEWL crystal nucleation the classical double‐pulse technique was modified by separating the nucleation and growth stages not only in time, but simultaneously also in place. In this case we found that the ratio of on‐glass formed crystal nuclei to bulk nuclei depended on the flow velocity, but in different manner with Seikagaku HEWL and Sigma HEWL. A plausible explanation of our experimental results is that the bulk crystal nucleation occurs on foreign surfaces as well, e.g. on rests of source biomaterial, which are always present in the protein solutions. Moreover, biomaterial seems to be more active nucleant than glass. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Evaluation of nucleation rate by in‐situ focused beam reflectance measurement in an unseeded batch cooling crystallization

Nucleation kinetics in the cooling crystallization of hexahydro‐1,3,5‐trinitro‐1,3,5‐triazine (RDX) from γ‐butyrolactone was studied by converting total counts/s measured by in situ focused beam reflectance measurement (FBRM) into number of crystals. The classical nucleation rate model, which is derived exclusively from the thermodynamic state for the nucleation and molecular collision frequency, was found to be inadequate to describe the experimentally measured nucleation rates. However, the nucleation rates predicted by the modified classical nucleation rate model, inclusive of an additional temperature term, were found to be in good agreement with those measured in the present work. Furthermore, the metastable zone widths are also found to be more accurately predicted by the modified classical nucleation rate model than the classical approach, which assumes that the mass‐based nucleation rate is an exponential function of supersaturation and is equal to the supersaturation rate.     

L-精氨酸掺杂下ZTS溶液的稳定性研究

研究了L-精氨酸掺杂下硫脲硫酸锌(ZTS)溶液中的成核过程,测量了在不同掺杂浓度下ZTS溶液的亚稳区和诱导期.结果表明:随掺杂浓度的增加,溶液的亚稳区变宽,诱导期增大;根据经典成核理论计算了晶体的成核热、动力学参数,分析了溶液稳定性与掺杂浓度的关系,即随着L-精氨酸掺杂浓度的增加,溶液的稳定性得到明显提高.利用化学腐蚀法对ZTS晶体(100)面进行了腐蚀,并用光学显微镜对腐蚀面进行观察,得到了清晰的位错蚀坑.当L-精氨酸掺杂浓度为1.5mol;时,ZTS晶体(100)面位错蚀坑密度最小,适合高光学质量晶体的生长.     

超声波对甲硝唑溶液结晶热力学性质的影响

本文采用降温结晶的方法,在搅拌和超声波作用下,分别测量了甲硝唑溶液结晶成核的介稳区和诱导期.通过分析超声波对甲硝唑溶液结晶的介稳区、诱导期产生的影响,从扩散系数、温度及能量角度分析了超声波促进晶体成核作用的机理.通过比较搅拌和超声波下得到的产品,从理论上对影响晶体粒度及结晶产率的因素进行了分析.     

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.     

Effect of temperature programmes on protein crystallisation

Varying the temperature has been proven to be beneficial for improving the screening efficiency of protein crystallisation, and thus a crystallisation screening strategy based on this phenomenon can be developed. Such a temperature varying strategy can be applied in practical crystallisation screening, however, there are no guidelines for determining what temperature programme should be utilised. It is therefore necessary to investigate how the temperature programme affects the crystallisation process, so as to help people design a suitable temperature programme. For this purpose, we investigated the effect of temperature programmes on the protein crystallisation (lysozyme, proteinase K, and concanavalin A) that are characterised by different solubility behaviours with respect to temperature. Judging from the reproducibility studies of protein crystallisation with different temperature programmes, we recommend using linear temperature programmes for a moderate time period (24 to 48 h) and a large temperature range according to the properties of the proteins. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Vibrational control of crystal growth from liquid phase

Modeling and numerical simulations of the convective flows induced by the vibration of the monocrystal during crystal growth have been performed for two configurations simulating the Cz and FZ methods. This permitted to emphasize the role of different vibrational mechanisms in the formation of the average flows. It is shown that an appropriate combination of these mechanisms can be used to counteract the usual convective flows (buoyancy- and/or thermocapillary-driven) inherent to crystal growth processes from the liquid phase. While vibrational convection is rather complex due to these identified mechanisms, the new modeling used in the present paper opens up very promising perspectives to efficiently control heat and mass transfer during real industrial applications of crystal growth from the liquid phase.     

A novel method of temperature control for a crystal growth puller

A facile method to control the contracting rate of the thermal expansible bars for pulling crystal is first suggested. The thermal expansible bars, set in a modified Dewar flask whose vacuum degree is controlled, are heated to designed temperature and then switch off the power to let it cool down at a desired rate, which depends largely on the changeable vacuum degree. This new approach is expected to completely eliminate the effects, which possibly reduces the smooth extent of thermal expansion, caused by the minor temperature fluctuations during crystal growth process and to realize the utmost smooth and slow pulling rate. It is expected to install this apparatus in optical floating zone furnace, instead of traditional motor, to grow peritectic crystal, such as crystal Bi‐2223, since for the peritectic reaction, in principle, the extremely slow growing rate is considerably essential.     

Optimization of thermal environment during crystal growth of large‐sized Nd:YAG by Temperature Gradient Technique

A finite‐element model is employed to analysis the thermal environments in Temperature Gradient Technique (TGT) furnace during the growth of large‐sized Nd:YAG crystal. The obtained results show that when the crucible is located at the lower position inside of the heater, a flatter solid‐liquid interface is established, which makes it easier to obtain the core‐free Nd:YAG crystal. Meanwhile, the lower crucible position can induce higher axial temperature gradient, which is beneficial to the release of latent heat. (© 2007 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.     

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.     

Polyhedral stability ‐ on the growth of flat crystal faces on small molecule and protein crystals

The old standing problem of face morphology is discussed. A special emphasis is put on the macroscopically flat faces, appearing on small molecule crystals mostly during calm growth, under low supersaturations. As distinct, protein crystals are growing with macroscopically flat faces even under surprisingly high supersaturations. Explanations of these facts are suggested by considering the surface micro‐profile of crystal faces which growth is driven by screw dislocations. It is shown that, due to kinetic reasons, the tips of the growth hillocks and the valley between them have to be levelled to some extent (at least on a quasi‐atomic scale) under low enough supersaturations. The amplitude of the surface roughness has to be suppressed also due to the surface energy gain, especially under quasi‐equilibrium. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Low Temperature Crystal Structures of Two Rhodanine Derivatives, 3-Amino Rhodanine and 3-Methyl Rhodanine: Geometry of the Rhodanine Ring

Abstract  Rhodanines (2-thio-4-oxothiazolidines) are synthetic small molecular weight organic molecules with diverse applications in biochemistry, medicinal chemistry, photochemistry, coordination chemistry and industry. The X-ray crystal structure determination of two rhodanine derivatives, namely (I), 3-aminorhodanine [3-amino-2-thio-4-oxothiazolidine], C₃H₄N₂OS_2, and (II) 3-methylrhodanine [3-methyl-2-thio-4-oxothiazolidine], C₄H₅NOS₂, have been conducted at 100 K. I crystallizes in the monoclinic space group P2₁/n with unit cell parameters a = 9.662(2), b = 9.234(2), c = 13.384(2) ?, β = 105.425(3)°, V = 1151.1(3) ?³, Z = 8 (2 independent molecules per asymmetric unit), density (calculated) = 1.710 mg/m³, absorption coefficient = 0.815 mm⁻¹. II crystallizes in the orthorhombic space group Iba2 with unit cell a = 20.117(4), b = 23.449(5), c = 7.852(2) ?, V = 3703.9(12) ?³, Z = 24 (three independent molecules per asymmetric unit), density (calculated) = 1.584 mg/m³, absorption coefficient 0.755 mm⁻¹. For I in the final refinement cycle the data/restraints /parameter ratios were 2639/0/161, goodness-of-fit on F² = 0.934, final R indices [I > 2sigma(I)] were R1 = 0.0299, wR2 = 0.0545 and R indices (all data) R1 = 0.0399, wR2 = 0.0568. The largest difference peak and hole were 0.402 and −0.259 e ?⁻³. For II in the final refinement cycle the data/restraints/parameter ratios were 3372/1/221, goodness-of-fit on F² = 0.950, final R indices [I > 2sigma(I)] were R1 = 0.0407, wR2 = 0.1048 and R indices (all data) R1 = 0.0450, wR2 = 0.1088. The absolute structure parameter = 0.19(9) and largest difference peak and hole 0.934 and −0.301 e ?⁻³. Details of the geometry of the five molecules (two for I and three for II) and the crystal structures are fully discussed. Corresponding features of the molecular geometry are highly consistent and firmly establish the geometry of the rhodanine ring. Index Abstract  Low temperature X-ray structures of (I) 3-aminorhodanine [3-amino-2-thio-4-oxothiazolidine] and (II) 3-methylrhodanine3-methyl-2-thio-4-oxothiazolidine are presented. Crystals of I are monoclinic and occupy space group P2₁/n with eight molecules (2 per asymmetric unit cell) and (II) is orthorhombic in space group Iba2 with 24 molecules (3 per asymmetric unit). This study has provided five highly consistent copies of the rhodanine ring at high resolution thus enabling its geometry to be established with confidence. The two independent molecules in the asymmetric unit of 3-aminorhodanine (left) and the three independent molecules in the asymmetric unit of 3-methylrhodanine (right) showing space filling and van der Waals contacts (drawn with MERCURY [Bruno et al. Acta Cryst B58:389, 2002]).