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.     

Initial stages of SiC crystal growth by PVT method

Initial stages of SiC crystal growth by Physical Vapor Transport method were investigated. The following features were observed: (a) many nucleation crystallization centres appeared on the seed surface during the initial stage of the growth, (b) at the same places many separate flat faces generated on the crystallization front, (c) the number of facets was dependent on the shape of the crystallization front and decreased during growth, (d) appearance of many facets lead to decrease of structural quality of crystals due to degradation of regions where crystallization steps from independent centres met. The results revealed that the optimal crystallization front should be slightly convex, which permits the growth of crystals with single nucleation centre and evolution of single facet on the crystallization front. The subjects of study were the shape and the morphology of growth interface. Defects in the crystallization fronts and wafers cut from the crystals were studied by optical microscopy, atomic force microscopy (AFM) combined with KOH etching and X‐ray diffraction. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

Batch crystallization of soluble proteins: effect of precipitant, temperature and additive

Although techniques used for protein crystallization have been progressing greatly, successful crystallization is still largely empirical and operatordependent. The crystallization of biological macromolecules is a pretty complicated process involving numerous parameters, thus the detailed understanding of the effect of crystallization conditions on macromolecule crystallization is advantageous. In this study, we have investigated the effect of precipitant, temperature, and additive on the crystallization of lysozyme and chymotrypsinogen A. As the precipitant, sodium chloride is more effective to the crystallization of lysozyme, and ammonium sulfate is more suitable to the crystallization of chymotrypsinogen A. Temperature is found to have no effect on the crystal habit of chymotrypsinogen A, while lysozyme crystallization displays highly sensitive temperature dependence, gradually varied temperature can result in better crystal habit and quality of lysozyme crystals. Furthermore, non-electrolytic additives dimethyl sulfoxide (DMSO) and glycerol are found to not only to increase the protein's solubility, but also decrease the critical supersaturation S_c for explosive nucleation of highly supersaturated protein solution. It is suggested that these additives can affect the interactions between protein molecules, thermodynamic equilibrium, surface energy of the crystal, and nucleation process of protein crystallization.     

A Stochastic Model for Nucleation Kinetics Determination in Droplet-Based Microfluidic Systems

The measured induction times in droplet-based microfluidic systems are stochastic and are not described by the deterministic population balances or moment equations commonly used to model the crystallization of amino acids, proteins, and active pharmaceutical ingredients. A stochastic model in the form of a Master equation is formulated for crystal nucleation in droplet-based microfluidic systems for any form of nucleation rate expression under conditions of time-varying supersaturation. An analytical solution is provided to describe the (1) time evolution of the probability of crystal nucleation, (2) the average number of crystals that will form at time t for a large number of droplets, (3) the induction time distribution, and (4) the mean, most likely, and median induction times. These expressions are used to develop methods for determining the nucleation kinetics. Nucleation kinetics are determined from induction times measured for paracetamol and lysozyme at high supersaturation in an evaporation-based high-throughput crystallization platform, which give low prediction errors when the nucleation kinetics were used to predict induction times for other experimental conditions. The proposed stochastic model is relevant to homogeneous and heterogeneous crystal nucleation in a wide range of droplet-based and microfluidic crystallization platforms.     

In situ study of the growth and degradation processes in tetragonal lysozyme crystals on a silicon substrate by high-resolution X-ray diffractometry

The results of an in situ study of the growth of tetragonal lysozyme crystals by high-resolution X-ray diffractometry are considered. The crystals are grown by the sitting-drop method on crystalline silicon substrates of different types: both on smooth substrates and substrates with artificial surface-relief structures using graphoepitaxy. The crystals are grown in a special hermetically closed crystallization cell, which enables one to obtain images with an optical microscope and perform in situ X-ray diffraction studies in the course of crystal growth. Measurements for lysozyme crystals were carried out in different stages of the crystallization process, including crystal nucleation and growth, developed crystals, the degradation of the crystal structure, and complete destruction.     

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)     

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.     

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.     

Crystallization behavior and microstructure of (CaO·ZrO2·SiO2)–Cr2O3 based glasses

The effects of chromium oxide on the crystallization behavior of glass compositions in the calcium, zirconium and silicon oxides system were investigated by differential thermal analysis, X-ray diffraction and scanning electron microscopic. Results indicate that crystallization is predominantly controlled by a surface nucleation mechanism, even though a partial bulk nucleation has been encountered in compositions containing more than 1.0 mol% of doping oxide. The effect of heating rate on differential thermal analysis curves was studied in order to investigate nucleation mechanisms and to extract the corresponding crystal growth activation energies E_c for the different crystalline phases. Activation energy (E_c) was found to be 490 ± 5 kJ/mol for 5.0 mol% chromium oxide in glasses. The most suitable nucleation temperature was determined as 810 °C for the above mentioned glass. The results of this study have highlighted that a small percentage of chromium oxide strongly affects the crystal formation thereby reducing the time and temperature of the thermal treatment and enhancing the degree of crystallization of calcium, zirconium and silicon oxides glasses.     

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.     

药物结晶中的经典与非经典结晶路径

晶体的结晶路径分为经典结晶路径和非经典结晶路径。经典结晶路径往往涉及一些简单的化学结构,晶体的成核、生长是通过单体的依次添加实现的,经过长期研究,目前研究人员已对其有了较为深刻的理解并形成了一套相对完善的理论体系;但对于非经典的结晶路径,由于涉及复杂中间态粒子的形成和多步结晶过程,尚未获得全面、统一的理论支持。在药物结晶领域,有机分子构象自由度的引入增加了体系的复杂性,分子间弱的相互作用使得固态药物分子存在多晶型现象。由于药物的理化性质及生物利用度与其晶型息息相关,同时,药物结晶过程中出现的一些复杂中间态粒子往往会改变最终得到的药物晶型,因此迫切需要加强对药物晶体成核和生长路径的研究,以期发展能实现对药物晶体成核和生长过程主动控制的方法。本文简要综述了目前药物在溶液或熔体中结晶的经典与非经典结晶路径,包括奥斯特瓦尔德阶段定律、独立成核、交叉成核。从溶液化学的角度看,分子在浓溶液中会通过自组装形成结构合成子,成核与溶液中的生长单元、结构合成子密切相关。从分子水平上探索溶液中有关分子运动的信息、分析各体系下晶核与结构合成子之间的关系是区分两种结晶路径的关键所在,非经典结晶在药物结晶领域是机遇也是挑战。     

以晶体生长原理重塑蚕丝柔性材料世界的未来

本文通过先进的结构表征手段,证实了包括丝蛋白材料在内的多种柔性材料内存在典型的介观多级结构和晶体网络结构。由于柔性材料中介观结构特别是晶体网络结构对于其宏观性能的有决定性影响,全面深入了解内部晶体的生长动力学和晶体网络结构的介观重构尤为重要。根据丝蛋白分子折叠成丝蛋白材料的最新研究成果,将晶体研究的方法,包括结晶动力学,应用到柔性材料的研究之中后,确定丝蛋白材料的形成过程遵循典型的“成核-结晶”机理。不仅如此,通过定向设计和控制晶体网络的形成及关键结构参数,如晶体密度、取向度、掺杂分子成核引发剂等,还可以实现柔性材料的介观重构与介观功能化,为发展全新的柔性介观光、电子学提供了可能。     

Crystallization of n-doped amorphous silicon PECVD films: comparison between SPC and RTA methods

Amorphous silicon films are deposited by radio-frequency plasma-enhanced chemical-vapor deposition (RF-PECVD) with different n-doping rates. The amorphous films are subsequently crystallized using either solid phase crystallization (SPC) or rapid thermal annealing (RTA). We compare the effect of the n-doping rate on some properties of the microcrystalline silicon films obtained with both techniques. In the SPC process, the time required for the beginning of the crystallization decreases with increasing phosphorus doping. Moreover, doped films present slightly higher crystal size than intrinsic films but the doping rate does not significantly influence the grain size. For RTA, the doping rate decreases the crystallization temperature and increases significantly the crystal size. Whatever the doping rate, the average grain sizes obtained by RTA are larger than those obtained by SPC. The electrical resistance of the crystallized films also depends on the crystallization process: RTA films present a lower dark conductivity than SPC films. These results are discussed taking into account the different kinetics of both crystallization techniques and the role played by the silicon dangling bonds and their charge states on the crystal growth.     

The induction time,interfacial energy and growth mechanism of maltitol in batch cooling crystallization

Maltitol is crystallized with seeds by cooling mode in industry, often with large amount of fine crystals and wide crystal size distribution. To eliminate the fine nucleation, it's necessary to understand the nucleation kinetics. In this work, the solubility of maltitol in water was measured by the gravimetric method, the nucleation kinetics of maltitol in batch cooling crystallization was investigated using focus beam reflectance measurement (FBRM), and a novel method was proposed to determine the induction time from the trend of the crystal median chord given by FBRM. Based on the relationship between the induction time and the supersaturation, the nucleation mechanism was obtained, including homogenous nucleation at high supersaturation and heterogenous nucleation at low supersaturation. Additionally, combining the classical nucleation theory (CNT) and Arrhenius’ principle, the crystal‐solution interfacial energy and the energy barrier of homogenous nucleation were calculated. From the scanning electron microscope (SEM) images, the growth mechanism of maltitol was identified as surface nucleation growth and the surface entropy factor calculated from the kinetic analyses of t_ind data corroborated this growth mechanism.     

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.

     

Main regularities of crystallization of calcium oxalate in the presence of amino acids

Processes of crystallization of calcium oxalate from aqueous solutions are investigated. Main regularities of the nucleation and crystal growth of calcium oxalate during mass crystallization without admixtures and in the presence of amino acids are established. The inhibiting action of the aspartic and glutamic amino acids on the growth of calcium oxalate crystals is demonstrated. Addition of amino acids does not affect the nucleation kinetics.     

Crystallization mechanisms of acicular crystals

In this contribution, we present an experimental investigation of the growth of four different organic molecules produced at industrial scale with a view to understand the crystallization mechanism of acicular or needle-like crystals. For all organic crystals studied in this article, layer-by-layer growth of the lateral faces is very slow and clear, as soon as the supersaturation is high enough, there is competition between growth and surface-activated secondary nucleation. This gives rise to pseudo-twinned crystals composed of several needle individuals aligned along a crystallographic axis; this is explained by regular over- and inter-growths as in the case of twinning. And when supersaturation is even higher, nucleation is fast and random.In an industrial continuous crystallization, the rapid growth of needle-like crystals is to be avoided as it leads to fragile crystals or needles, which can be partly broken or totally detached from the parent crystals especially along structural anisotropic axis corresponding to weaker chemical bonds, thus leading to slower growing faces. When an activated mechanism is involved such as a secondary surface nucleation, it is no longer possible to obtain a steady state. Therefore, the crystal number, size and habit vary significantly with time, leading to troubles in the downstream processing operations and to modifications of the final solid-specific properties.These results provide valuable information on the unique crystallization mechanisms of acicular crystals, and show that it is important to know these threshold and critical values when running a crystallizer in order to obtain easy-to-handle crystals.     

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.     

Crystal growth and solubility studies of Aspergillus niger acid proteinase A in the presence of both a salt and an organic solvent

The quality of proteinase A crystals improves considerably, as judged from the X-ray diffraction limit, in the presence of an organic solvent, dimethylsulfoxide (DMSO). The effects of DMSO have therefore been studied through the observation of crystallization and protein concentration versus time. It was found that DMSO increases the nucleation rate, and decreases the crystal solubility as does ammonium sulfate. It is suggested that organic solvents may be used to alter the protein crystal growth usually obtained by salting-out.