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.     

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.     

Factorially designed crystallization trials of the full-length P0 myelin membrane glycoprotein. I. Precipitation diagram

P0 glycoprotein is the abundant membrane protein of myelin of the peripheral nervous system. We report now the statistical design of the crystallization experiments; based on our belief that important information regarding supersaturation of protein or its solubility nature, as well as metastable state, nucleation or precipitation, are hidden in the trials in which no crystals grow. It is possible to work out this information when the whole set of experiments is designed in such a way as to allow statistical analyses. We selected seven factors, which we believe to be important for crystallization: protein concentration, pH of buffer, nature of precipitant, concentration of precipitant, nature of detergent, additives and temperature. The experimental matrix and detailed work sheet to make 148 solutions having random but balanced combination of these levels were calculated using the program DESIGN. A visual evaluation of crystallization drops was performed using light microscopy. We were able to plot the precipitation boundary diagram. Based on this diagram we have eliminated factors (and levels) that were driving the protein into precipitation. It is known that the precipitation boundary is related to the solubility curves for protein crystals, in the neighborhood of which nucleation and further crystallization is most likely to occur. These conditions are currently being refined to identify important factors (or its levels) that can be crucial in obtaining large and well diffracting crystals. Full-length P0 protein has never been crystallized for structural determination.     

Numerical and experimental analysis of periodic patterns and sedimentation of lysozyme

This paper deals with experimental investigation, mathematical modelling and numerical simulation of the crystallization processes induced by counter diffusion method of a precipitant agent in a lysozyme protein solution. Novel mathematical strategies are introduced to simulate the experiments and in particular to take into account the kinetics of the growth process and the motion of the crystals due to the combined effect of gravitational force and viscous drag if the sedimenting process is allowed (protein chamber free of gel). Comparison between experimental observations and numerical simulations in the presence of convection and sedimentation and without them provides a validation of the model. The crystal formation in gel results modulated in space. If the gel matrix is not present, convective cells arise in the protein chamber due to local inversions in the density distribution associated to nucleation phenomena. As time passes, these vortex cells migrate towards the top of the protein chamber exhibiting a different wave number according to the distance from the gel interface. The sedimentating particles produce a wake due to depletion of protein from the surrounding liquid. The models and the experiments may represent a useful methodology for the determination of the parameters and conditions that may lead to protein crystallization.     

Understanding protein crystallization on the basis of the phase diagram

The phase diagram of a protein–water system is described with a simple model with parameters for the interaction between the protein molecules in the crystal and in the solution. For a certain range of these parameters the phase diagram shows a metastable liquid–liquid immiscibility region. It is shown that this region corresponds to the “crystallization slot” for growing crystals, as proposed by George and Wilson [Acta Crystallogr. D 50 (1994) 361]. Nucleation in this region proceeds in two steps. First small liquid droplets with a high protein concentration are formed; then small crystalline nuclei grow inside these droplets. In the crystallization slot crystals are covered by a thin liquid film with a high protein concentration. We discuss NMR experiments on lysozyme, which show that nucleation is a transient process with an induction time.     

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.     

Nucleation time-lag from nucleation and growth experiments in deeply undercooled glass-forming liquids

A new approach is proposed to explain the strong difference between the induction periods (nucleation time-lags) obtained from nucleation rate measurements and from crystal growth experiments for lithium silicate glasses; and their similar magnitude for a Na₂O · 2CaO · 3SiO₂ glass. For these two glass families, the time-lags for nucleation estimated from crystal growth kinetics were compared with those directly obtained from nucleation experiments. A theoretical analysis was performed employing analytical solutions of the Frenkel-Zeldovich equation. In such analysis, the frequently assumed condition of size-independence of the thermodynamic properties of the crystallites was used. Provided this assumption is correct, time-lag data obtained in the two above mentioned ways should coincide. Consequently the significant difference between the values of nucleation time-lag for lithium silicate glasses from nucleation and growth data gives a strong indirect evidence for the deviation of the properties of critical nuclei from the respective parameters characterizing the state of the newly evolving macrophase. For Na₂O · 2CaO · 3SiO₂ glass at intermediate stages of crystallization we show that the average composition of the growing crystals is close to that of the near-critical nuclei. The fact that the nucleation and growth rates of this soda-lime-silica glass refer to the same phase provides an explanation for the similarity of the induction periods estimated from nucleation and growth experiments.     

Effect of additives in supersaturated binary and ternary solutions on cluster growth by gravity driven concentration gradient studies

The concentration gradients formed in long column supersaturated solutions of the binary systems Potassium dihydrogen phosphate ‐ Water, Benzophenone ‐ Ethanol, Ammonium dihydrogen phosphate – Water, Potassium hydrogen phthalate – Water and ternary systems Potassium dihydrogen phosphate – Potassium chloride ‐ Water, Benzophenone – Urea ‐ Ethanol, Ammonium dihydrogen phosphate – Urea ‐ Water, Potassium hydrogen phthalate – Ethylenediaminetetraacetic acid – Water under stirred and non‐stirred conditions have been studied. The solution concentration was measured at different heights, at different degrees of supersaturation and at different times. Weight average molecular weight, Degree of Association, Number average molecular weight, Average number of molecules per cluster and weight average cluster diameter were calculated for binary and ternary supersaturated solutions under stirred and non‐stirred conditions. Under stirred conditions concentration gradient of all the above mentioned systems decrease compared to non‐stirred conditions. The cluster sizes are estimated from concentration gradient data in the presence and absence of additives and also corresponding changes in metastable zonewidths are studied. The changes in concentration gradients of supersaturated solutions appear to be a reliable indicator of the effect of additives on cluster growth and nucleation. As long column of solution is used in growing crystal by Sankaranarayanan‐Ramasamy method the effect of gravity driven concentration gradient on critical column length is investigated. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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

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

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)     

DTA peak shift studies of primary crystallization in glasses

Following the recognition during the last decade that knowledge of the shift in the exothermic crystallization DTA peak as a function of pre-DTA isothermal heat-treatment times and temperatures, can provide quantitative information about the crystallization kinetics, there has been renewed interest in DTA investigations of crystallization of glasses. Most studies to date, however, have focussed on the kinetics of polymorphic crystallization (where the compositions of the crystal and the parent glass are the same). These studies have established that the DTA peak shifts to lower temperatures with increased pre-DTA heat-treatment times and JMAK-based formalisms have been developed to extract the steady state nucleation rate from the DTA peak shift data. In this paper, we report new results on the DTA peak shift in systems undergoing primary crystallization (where the compositions of the crystal and glass are different). The DTA results show that the exothermic peak temperature decreases initially but increases later on, becoming significantly larger than the initial value, with increase in the pre-DTA heat-treatment time at a fixed temperature. This increase at long times has not been reported previously and is qualitatively different than the monotonic decrease reported for polymorphic crystallization. To rationalize these new results, a model of primary crystallization has been developed which includes homogeneous nucleation, diffusion-controlled growth, Gibbs-Thomson effect, and a mean field soft-impingement correction during growth. Based on this model and experimental results, it is concluded that the initial shift to lower temperatures is due to an increase in the number of nuclei (as concluded previously by others for the case of polymorphic crystallization) and the later shift towards high temperatures in our experiments is due to diffusion-controlled growth during the pre-DTA heat treatment.     

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.     

Rapid sonocrystallization in the salting-out process

Power ultrasound is applied as a mechanical aid to blend and cavitate the medium during the process of salting-out crystallization. Immediately following the addition of the total precipitant needed to the solution, the ultrasound is turned on. The sonoprocess including nucleation and crystal growth is completed in seconds. The experimental results indicate that the variation of ultrasonic energy, duration or mixture volume can be used to yield advantageous control of the mean size and size distribution of resulting crystals. The crystals insonated have perfect shape and show little agglomeration. Since crystallization in such highly supersaturated solutions is uncontrollable by conventional methods, the insonation plays an irreplaceable role in the process. Based on our experiment, it should be feasible and valuable to scale up this sonoprocess for industrial application.     

Development of an Automated High Throughput LCP-FRAP Assay to Guide Membrane Protein Crystallization in Lipid Mesophases

Crystallization in lipidic mesophases (in meso) has been successfully used to obtain a number of high-resolution membrane protein structures including challenging members of the human G protein-coupled receptor (GPCR) family. Crystallogenesis in arguably the most successful mesophase, lipidic cubic phase (LCP), critically depends on the ability of protein to diffuse in the LCP matrix and to form specific protein-protein contacts to support crystal nucleation and growth. The ability of an integral membrane protein to diffuse in LCP is strongly affected by the protein aggregation state, the structural parameters of LCP, and the chemical environment. In order to satisfy both requirements of diffusion and specific interactions, one must balance multiple parameters, such as identity of LCP host lipid, composition of precipitant solution, identity of ligand, and protein modifications. Screening within such multi-dimensional crystallization space presents a significant bottleneck in obtaining initial crystal leads. To reduce this combinatorial challenge, we developed a pre-crystallization screening assay to measure the diffusion characteristics of a protein target in LCP. Utilizing the Fluorescence Recovery After Photobleaching (FRAP) technique in an automated and high throughput manner, we were able to map conditions that support adequate diffusion in LCP using a minimal amount of protein. Data collection and processing protocols were validated using two model GPCR targets: the β(2)-adrenergic receptor and the A(2A) adenosine receptor.     

Anti‐solvent effect of crystallization by feeding ethanol under microwave radiation

The nucleation and crystal growth of sodium chloride in aqueous solution during crystallization by ethanol droplet feeding were investigated by determining the suspension density and crystal size distribution. Crystallization was conducted in a microwave reactor, and the effect of the power, stirring speed, and ethanol concentration were investigated to clarify the anti‐solvent effect under microwave radiation. Molecular diffusion was accelerated by fine particle production due to microwave radiation when the stirring speed was low and ethanol concentration was high. However, moderate microwave power and stirring speed were required for efficient molecular diffusion.     

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

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

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。     

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。     

Nucleation kinetics in deionized charged colloidal suspension

A systematic experimental study on the nucleation, crystallization and crystal-growth of one-component charged colloidal particles (122 nm diluted in pure water with densities between 0.5 μm⁻³ < n_p < 5 μm⁻³) is present by means of time resolved static light scattering spectroscopy revealing the heterogeneous and homogenous nature of the crystallization. The interactions between the charged colloidal particles are sufficiently strong to cause crystallization which described in terms of Debye-Hückel approximation. Crystallization starts always with the formation of compressed structurally heterogeneous precursor domains. The results show that the heterogeneous nucleation at the cell walls starts simultaneously with the homogeneous bulk nucleation and the rate density of the heterogeneous nucleation appears slightly higher. It has been also found that the overall crystallization consists of at least a two-step nucleation process involving formation of early stage nuclei or crystal precursor then followed by the main crystallization. The induction time, the number density of nuclei and the growth rate of crystals, is strongly dependent on particle concentration and on whether the nucleation are homogeneous in cell center or heterogeneous on cell walls.     

Spatiotemporal protein crystal growth studies using microfluidic silicon devices

Fundamental investigations of protein crystallization using miniaturized microfluidic silicon devices were presented towards achieving spatiotemporal nucleation and subsequent post-nucleation growth. The developed microfluidic silicon device was typically composed of crystal growth cell, reservoir cell, and optionally of heater elements for supersaturation control. A specific fine pattern area in the growth cell which was fabricated on the silicon substrate with doped p- and n-type silicon layers, served as spatially selective nucleation site of dissolved protein molecules through electrostatic attractive force. In a model material, hen egg white lysozyme, a large number of crystals were grown on the defined nucleation site evenly spaced from each other, whereas parasitic crystal growth positioned around the selective nucleation site, was suppressed by the effects of electrostatic repulsive force between the doped silicon surface and charged protein molecules. A possible crystallization mechanism of describing the heterogeneous nucleation during the initial stage and during the growth of the crystal at the electrolyte–semiconductor silicon surface is proposed and discussed.