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)     

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.     

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)     

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.     

Nucleation of protein crystals

Protein crystal nucleation is a central problem in biological crystallography and other areas of science, technology, and medicine. Recent studies have demonstrated that protein crystal nuclei form within crucial precursors. Data for several proteins provided by these methods have demonstrated that the nucleation precursors are clusters consisting of protein dense liquid, which are metastable with respect to the host protein solution. The clusters are several hundred nanometers in size, they occupy from 10⁻⁷ to 10⁻³ of the solution volume, and their properties in solutions supersaturated with respect to crystals are similar to those in homogeneous, i.e., undersaturated, solutions. The clusters exist due to the conformation flexibility of the protein molecules, leading to the exposure of hydrophobic surfaces and enhanced intermolecular binding. These results indicate that protein conformational flexibility might be the mechanism behind the metastable mesoscopic clusters and crystal nucleation. The investigations of the cluster properties are still in their infancy. Results on direct imaging of cluster behaviors and characterization of cluster mechanisms with a variety of proteins will soon lead to major breakthroughs in protein biophysics.     

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.     

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)     

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)     

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.     

Brittleness of protein crystals

A simple technique for studying the brittleness of small crystals is reported. The limits of fracture toughness of tetragonal hen‐egg white lysozyme crystals, oriented with their c‐axis normally to the substrate, were measured. The strong mechanics anisotropy of those crystals was confirmed. The role of the water present in the protein crystal lattice was re‐considered in seek for a more holistic understanding of the process, the idea being that the intra‐crystalline solution sustains the globular protein molecules in their native configuration. Also it is argued that this water may contribute for holding together the huge bio‐molecules in the crystal lattice (that is to act as additional “glue” in the crystal). The hypothesis is that dynamic chains of H‐bonds in the intra‐crystalline water are likely to be prolonged to connect protein‐to‐water‐to‐protein.     

On the Vitality of the Classical Theory of Crystal Nucleation; Crystal Nucleation in Pure Own Melt; Atmospheric Ice and Snow; Ice in Frozen Foods

The main reason for the longevity of the Classical Nucleation Theory (CNT) is its firm thermodynamic basis; reviewing the discussion about the molecular-scale mechanism of crystal nucleation from solutions, and especially the mechanism of protein crystal nucleation, we note that the diverse nucleation pathways across the metastable phase cannot contradict the thermodynamic conclusions of the CNT. In this review paper, revisiting the basic postulates of CNT, we argue that not only the energy barrier for crystal nucleation but the entire dependence of Gibbs’ thermodynamic potential on the crystal size is worth interpreting. In doing so, two supplementations to CNT have been elaborated. The first one concerns the theoretical method employing Equilibration between the Bond energy (i.e., the intra-crystalline cohesive energy which maintains the integrity of a crystalline cluster), and the surface Destructive Energy (tending to tear-up the crystal) - abbreviated EBDE. Second, we show that the dependence of the Gibbs’ thermodynamic potential on the crystal size determines not only the birth, but also the initial growth (or dissolution during Ostwald ripening) of the just born nuclei of the new phase; this is predicted in the negative branch of the said dependence. Initially, EBDE was used for explaining crystal nucleation from solutions, but most recently, this method was redefined for considering crystal nucleation in melts. The purposively redefined EBDE was applied for considering ice nucleation, which is an important case of spontaneous melt crystallization in nature - the quantitative consideration of the ice crystal nucleation is needed for better understanding of atmospheric processes, such as snowfall, white frost, sleet, hail, and ice fog. By focusing on the action of ice nucleating particles (INPs), which engender heterogeneous nucleation of ice, the snowfall is elucidated in a new way - ice nucleation in the atmosphere is considered as a two-step process, the first one being vapor condensation in liquid droplets, and the second one - water freezing. Also, ice nucleation in frozen foods is re-considered applying EBDE. (It is known that freezing ensures a high-quality product and long shelf life of a wide range of food products, such as fish, meat, vegetables, tropical fruits, coffee, flavor essence, etc.) And because numbers and sizes of ice crystals are decisive for the degree of deterioration of food quality due to freezing, the mean sizes of the ice crystals (which depend on their number) are considered in a quantitative manner. Also, another consideration concerns ice crystal nucleation and growth occurring by freeze concentration of liquid foods. Although aimed at reviewing fundamental aspects of crystal nucleation, it is to be hoped that some results of the considerations in this paper may also be beneficial for practical applications; suggestions in this respect are mentioned throughout the paper. For instance, the direct comparison between ice crystal nucleation in pure water and in frozen foods suggests how the dynamic food freezing step may be optimized, etc. The review ends with a short paragraph presenting the advantages and disadvantages of CNT.     

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)     

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.     

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)     

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.     

‘Intra-cluster rearrangement' model for the α-process in supercooled liquids, as opposed to ‘cooperative rearrangement of whole molecules within a cluster'

A new model for the α-relaxation process in supercooled liquids and glasses is proposed which distinguishes between a structurally correlated region (cluster) of molecules and a unit of molecules for rather independent, correlated rearrangement motion. The essential aspects of the model are that the α-process is due to rearrangement of one or a few molecules within the cluster, while essentially the same motion in the space between the clusters is responsible for the β-process. The model leads to the following expectations: (i) absence of divergent behavior of α-relaxation times at non-zero temperature (e.g., Kauzmann temperature), (ii) close agreement between the glass transition temperatures, T_g, for the α-relaxation in liquid and crystalline phases of the same composition and (iii) possibility of crystal nucleation proceeding much below the T_g, and evidence for the latter two is presented.     

Study on crystallization kinetics and the crystal internal defects of HMX

In this paper, the solubility data of HMX (1,3,5,7‐tetranitro‐1,3,5,7‐tetrazocane) in acetone from 323.15 K to 293.15 K were accurately measured by use of the laser‐monitoring observation technique. Intermittent dynamic method was utilized to study crystallization kinetics of HMX in acetone. The data of crystallization kinetics were obtained by moment analysis, and the parameters of the growth rate and nucleation rate equations were derived by using multiple linear least squares method. Subsequently, growth rate and nucleation rate at different conditions were calculated according to these equations. In addition, Optical Microscopy Images (qualitative) and Particle Apparent Density (quantitative) experiments were applied to study the crystal internal defects of HMX under different crystallization conditions. It can be found that the crystal apparent density of HMX is in the range of 1.8993 g·cm⁻³ to 1.9017 g·cm⁻³, very close to the theory density of HMX; the internal defects and the crystal size do not increase after 25 °C, from which we predict that the HMX crystal growth reaches the steady growth segment. These results suggest that the nucleation rate is a significant factor influencing the crystal internal defects, and larger nucleation kinetics can reduce crystal internal defects.     

In situ AFM investigation of 2D nucleation on the (100) face of KDP

Surface morphology of the (100) face of potassium dihydrogen phosphate (KDP) crystals which were grown at different supersaturations at 25 °C was investigated by in situ atomic force microscopy (AFM). Various AFM images of 2D nucleation under different growth conditions were presented. It is found that the growth of KDP is controlled by polynuclear nucleation mechanism at the high supersaturation. With reduction of the supersaturation, the growth velocity of 2D nuclei becomes very slow and shows typical anisotropy. It is found that the process of coalescence of 2D nuclei does not lead to defect. The experiments show that the growth mechanism for KDP at 25 °C changes between step flow and 2D nucleation in the supersaturation range of 4.5‐5%. The triangular nuclei which are close to equilateral triangle are observed in the experiment at the supersaturation σ = 6% for the first time, showing typical anisotropic growth. Through observing the dissolution of 2D nuclei, the dissolving process can be regarded as the reverse process of growth. We also find that the microcrystals landing on the surface at σ = 9% would grow and coalesce with each other and there is no observable defect in the coalescence. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.