A theoretical model of intracellular devitrification

Devitrification of the intracellular solution can cause significant damage during warming of cells cryopreserved by freezing or vitrification. Whereas previous theoretical investigations of devitrification have not considered the effect of cell dehydration on intracellular ice formation, a new model which couples membrane-limited water transport equations, classical nucleation theory, and diffusion-limited crystal growth theory is presented. The model was used to explore the role of cell dehydration in devitrification of human keratinocytes frozen in the presence of glycerol. Numerical simulations demonstrated that water transport during cooling affects subsequent intracellular ice formation during warming, correctly predicting observations that critical warming rate increases with increasing cooling rate. However, for cells with a membrane transport activation energy less than approximately 50 kJ/mol, devitrification was also affected by cell dehydration during warming, leading to a reversal of the relationship between cooling rate and critical warming rate. Thus, for low warming rates (less than 10 degrees C/min for keratinocytes), the size and total volume fraction of intracellular ice crystals forming during warming decreased with decreasing warming rate, and the critical warming rate decreased with increasing cooling rate. The effects of water transport on the kinetics of intracellular nucleation and crystal growth were elucidated by comparison of simulations of cell warming with simulations of devitrification in H(2)O-NaCl-glycerol droplets of constant size and composition. These studies showed that the rate of intracellular nucleation was less sensitive to cell dehydration than was the crystal growth rate. The theoretical methods presented may be of use for the design and optimization of freeze-thaw protocols.     

A Method to Evaluate the Effect of Contact with Excipients on the Surface Crystallization of Amorphous Drugs

Amorphous drugs are used to improve the solubility, dissolution, and bioavailability of drugs. However, these metastable forms of drugs can transform into more stable, less soluble, crystalline counterparts. This study reports a method for evaluating the effect of commonly used excipients on the surface crystallization of amorphous drugs and its application to two model amorphous compounds, nifedipine and indomethacin. In this method, amorphous samples of the drugs were covered by excipients and stored in controlled environments. An inverted light microscope was used to measure in real time the rates of surface crystal nucleation and growth. For nifedipine, vacuum-dried microcrystalline cellulose and lactose monohydrate increased the nucleation rate of the β polymorph from two to five times when samples were stored in a desiccator, while d-mannitol and magnesium stearate increased the nucleation rate 50 times. At 50% relative humidity, the nucleation rates were further increased, suggesting that moisture played an important role in the crystallization caused by the excipients. The effect of excipients on the crystal growth rate was not significant, suggesting that contact with excipients influences the physical stability of amorphous nifedipine mainly through the effect on crystal nucleation. This effect seems to be drug specific because for two polymorphs of indomethacin, no significant change in the nucleation rate was observed under the excipients.KEY WORDS: amorphous, drugs, growth rate, nucleation rate, tablet excipients     

Pre-assembled clusters distort crystal nucleation kinetics in supersaturated lysozyme solutions

Efficient determination of three-dimensional protein structures is critical for unraveling structure-function relationships and for supporting targeted drug design. A major impediment to these efforts is our lack of control over the nucleation and growth of high-quality protein crystals for X-ray structure determinations. While basic research on protein crystal growth mechanisms has provided valuable new insights, studies of crystal nucleation have been plagued by inconsistent and outright contradictory results. Using dynamic light scattering and SDS gel electrophoresis, we have investigated possible causes of these inconsistencies. We find that commercial sources of lyophilized hen-egg white lysozyme (HEWL) used in nucleation studies contain significant populations of large (approximately 100 nm), pre-assembled lysozyme clusters that can readily evade standard assays of sample purity. In supersaturated solutions, these clusters act as heterogeneous nucleation centers that enhance the rate of crystal nucleation and significantly deteriorate the quality of macroscopic crystals.     

Probabilistic approach to lysozyme crystal nucleation kinetics

Nucleation of lysozyme crystals in quiescent solutions at a regime of progressive nucleation is investigated under an optical microscope at conditions of constant supersaturation. A method based on the stochastic nature of crystal nucleation and using discrete time sampling of small solution volumes for the presence or absence of detectable crystals is developed. It allows probabilities for crystal detection to be experimentally estimated. One hundred single samplings were used for each probability determination for 18 time intervals and six lysozyme concentrations. Fitting of a particular probability function to experimentally obtained data made possible the direct evaluation of stationary rates for lysozyme crystal nucleation, the time for growth of supernuclei to a detectable size and probability distribution of nucleation times. Obtained stationary nucleation rates were then used for the calculation of other nucleation parameters, such as the kinetic nucleation factor, nucleus size, work for nucleus formation and effective specific surface energy of the nucleus. The experimental method itself is simple and adaptable and can be used for crystal nucleation studies of arbitrary soluble substances with known solubility at particular solution conditions.     

Effect of polyethylene glycol-400 at low concentrations on long-term growth of muscle phosphoglucomutase crystals from concentrated salt solutions.

Although rabbit muscle phosphoglucomutase occasionally deposits tetragonal crystals from solutions of ammonium sulfate at about 47% of saturation, low concentrations of polyethylene glycol-400 (PEG), 1 to 4.5% w/v, must be included to sustain crystal growth. A comparison of long-term growth rates for macroscopic crystals in the presence and absence of added PEG suggests that at high salt concentration this cosolute exerts its primary effect on disordered protein aggregates, either in the external medium or at the surface of the crystal, and thereby allows the growth of much larger crystals. Since the observed effects may arise from a PEG-induced increase in the "solubility" of the aggregate that exceeds the induced increase in solubility of the crystalline phase under these conditions, the physical basis for a cosolute-induced increase in solubility in the presence of a precipitant is considered. The applicability of such a rationale to the present system is supported by an assessment of the relative effects of polyethylene glycol and beta-octylglucoside on amorphous, salt-induced precipitates of phosphoglucomutase. PEG also produces what appears to be a differential effect on nucleation efficiency and crystal growth rate. Thus, seed crystals cannot be enlarged at a significant rate at high salt concentration without producing showers of extraneous nucleation centers when the concentration of added PEG is 3% or less. But PEG concentrations of 4.5% essentially eliminate the showering problem, ostensibly by increasing the supersaturation required for nucleation to a greater extent than that required for crystal growth. The same type of effect is observed during de novo growth. Again a solubility-based mechanism is posed. Hysteretic effects related to properties of amorphous aggregates of the protein also are described.     

In Situ μGISAXS: I. Experimental Setup for Submicron Study of Protein Nucleation and Growth

In this study, we used microbeam grazing-incidence small-angle x-ray scattering (μGISAXS) to investigate in situ protein nucleation and crystal growth assisted by a protein nanotemplate, and introduced certain innovations to improve the method. Our aim was to understand the protein nanotemplate method in detail, as this method has been shown to be capable of accelerating and increasing crystal size and quality, as well as inducing crystallization of proteins that are not crystallizable by classical methods. The nanotemplate experimental setup was used for drops containing growing protein crystals at different stages of nucleation and growth. Two model proteins, lysozyme and thaumatin, were used under unique flow conditions to differentially probe protein crystal nucleation and growth.     

A novel dialysis procedure for the crystallization of proteins

Various dialysis methods are commonly employed for the crystallization of proteins. Typical procedures include the use of dialysis bags, dialysis buttons or Zeppezauer microdiffusion cells. The general principle involved is that the protein solution is gradually brought to a point of supersaturation by imposing a gradient of ionic strength or organic solvent concentration across the wall of the dialysis membrane. However, in some cases, the imposition of this gradient across the dialysis membrane can result in the formation of a large number of crystal nucleation sites, thereby giving rise to a reduction in the maximum size of the crystals which can be obtained. A novel 'double-dialysis' procedure which incorporates a second dialysis membrane, thus reducing the rate of equilibration in the crystallization experiment, has been developed in our laboratory. The system has been employed successfully on the delta toxin of Staphylococcus aureus resulting in a useful increase in crystal size. A more quantitative analysis of the technique has been carried out on rat liver malic enzyme. The results of a limited series of crystallization trials with this protein have shown that employment of the 'double-dialysis' technique allows a fine control of the rate of crystal nucleation and therefore provides a mechanism for the controlled growth of large crystals.     

Microscopic model of protein crystal growth

A microscopic, reversible model to study protein crystal nucleation and growth is presented. The probability of monomer attachment to the growing crystal was assumed to be proportional to the protein volume fraction and the orientational factor representing the anisotropy of protein molecules. The rate of detachment depended on the free energy of association of the given monomer in the lattice, as calculated from the buried surface area. The proposed algorithm allowed the simulation of the process of crystal growth from free monomers to complexes having 10(5) molecules, i.e. microcrystals with already formed faces. These simulations correctly reproduced the crystal morphology of the chosen model system--the tetragonal lysozyme crystal. We predicted the critical size, after which the growth rate rapidly increased to approximately 50 protein monomers. The major factors determining the protein crystallisation kinetics were the geometry of the protein molecules and the resulting number of kinetics traps on the growth pathway.     

Nucleation and Crystal Growth in a Vitrification Solution Tested for Organ Cryopreservation by Vitrification

Nucleation and crystal growth are investigated for vitrification solution VS41A (dimethyl sulfoxide, formamide, and 1,2-propanediol) in an aqueous carrier solution giving, when added to these three cryoprotectants, a concentration of other solutes in the whole solution the same as that in Euro-Collins, with a 55% (w/v) cryoprotectant concentration. This concentration is assumed to achieve physical properties under 1 atmosphere similar to those of solution VS4 used under 1000 atmospheres. The thermal range and the kinetics of nucleation and crystal growth are investigated by DSC through different thermal treatments. It is found that the nucleation thermal range is below -90 degrees C and that of crystal growth is above -85 degrees C for a relatively long experimental time. The nucleation density is also studied through direct observations by cryomicroscopy and is related to the amount of crystallization calorimetrically recorded. The effect of storage below the glass transition shows the possibility of a slow increase in nucleation below the glass transition, as already observed by other authors for different aqueous solutions. Isothermal crystallization is analyzed within the Johnson-Mehl-Avrami model for temperatures above -75 degrees C. The corresponding samples have been cooled and warmed at the same rate of 40 degrees C/min and calculations give, at constant nuclei numbers, an activation energy of 9.3 +/- 0.3 kcal/mol and the Avrami exponent n = 2.2 +/- 0.05. This shows a two-dimensional crystal growth as observed by cryomicroscopy. The estimated critical warming rate relevant to the preservation of rabbit kidneys by vitrification is 270 degrees C/min with or without an increase in the nucleus density during storage. The present results support the possibility of using VS4 solution for vitrification of rabbit kidneys if pressure is not a limiting factor. Copyright 1993, 1999 Academic Press.     

Protein purification by bulk crystallization: the recovery of ovalbumin

Crystallization is used industrially for the recovery and purification of many inorganic and organic materials. However, very little is reported on the application of bulk crystallization for proteins. In this work, ovalbumin was selected as a model protein to investigate the feasibility of using bulk crystallization for the recovery and purification of proteins. A stirred 1-L seeded batch crystallizer was used to obtain the crystal growth kinetics of ovalbumin in ammonium sulfate solutions at 30 degrees C. The width of the metastable region, in which crystal growth can occur without any nucleation, is equivalent to a relative supersaturation of about 20. The bulk crystallizations were undertaken within this range (using initial relative supersaturations less than 10) and nucleation was not observed. The ovalbumin concentration in solution was measured by UV absorbance and checked by crystal content measurement. Crystal size distributions were measured both by using a Malvern Mastersizer and by counting crystals through a microscope. The crystal growth rate was found to have a second-order dependence upon the ovalbumin supersaturation. While there is no discernible effect of ammonium sulfate concentration at pH 4.90, there is a slight effect at higher pH values. Overall the effect of ammonium sulfate concentration is small compared to the effect of pH, for which there is a 10-fold increase in the growth rate constant, k(Gsigma) over the range pH 4.6-5.4. To demonstrate the degree of purification which can be achieved by bulk crystallization, ovalbumin was crystallized from a solution containing conalbumin (80,000 Da) and lysozyme (14, 600 Da). After one crystallization and a crystal wash, ovalbumin crystals were produced with a protein purity greater than 99%. No contamination by the other proteins was observed when using overloaded sodium dodecyl sulfate-polyacrylamide gel electrophoresis (SDS-PAGE) stained with Coomassie blue stain and only trace amounts of lysozyme were observed using a silver stain. The presence of these other proteins in solution did not effect the crystal growth rate constant, k(Gsigma). The study demonstrates the feasibility of using bulk crystallization for the recovery and purification of ovalbumin. It should be readily applicable to other protein systems. (c) 1995 John Wiley & Sons, Inc.     

Physical problems with the vitrification of large biological systems

Vitrification is an attractive potential pathway to the successful cryopreservation of mature mammalian organs, but modern cryobiological research on vitrification to date has been devoted mostly to experiments with solutions and with biological systems ranging in diameter from about 6 through about 100 microns. The present paper focuses on concerns which are particularly relevant to large biological systems, i.e., those systems ranging in size from approximately 10 ml to approximately 1.5 liters. New qualitative data are provided on the effect of sample size on the probability of nucleation and the ultimate size of the resulting ice crystals as well as on the probability of fracture at or below Tg. Nucleation, crystal growth, and fracture depend on cooling velocity and the magnitude of thermal gradients in the sample, which in turn depend on sample size, geometry, and cooling technique (environmental thermal history and thermal uniformity). Quantitative data on thermal gradients, cooling rates, and fracture temperatures are provided as a function of sample size. The main conclusions are as follows. First, cooling rate (from about 0.2 to about 2.5 degrees C/min) has a profound influence on the temperature-dependent processes of nucleation and crystal growth in 47-50% (w/w) solutions of propylene glycol. Second, fracturing depends strongly on cooling rate and thermal uniformity and can be postponed to about 25 degrees C below Tg for a 482-ml sample if cooling is slow and uniform. Third, the presence of a carrier solution reduces the concentration of cryoprotectant needed for vitrification (CV). However, the CV of samples larger than about 10 ml is significantly higher than the CV of smaller samples whether a carrier solution is present or not.     

The effect of temperature and solution pH on the nucleation of tetragonal lysozyme crystals.

Part of the challenge of macromolecular crystal growth for structure determination is obtaining crystals with a volume suitable for x-ray analysis. In this respect an understanding of the effect of solution conditions on macromolecule nucleation rates is advantageous. This study investigated the effects of supersaturation, temperature, and pH on the nucleation rate of tetragonal lysozyme crystals. Batch crystallization plates were prepared at given solution concentrations and incubated at set temperatures over 1 week. The number of crystals per well with their size and axial ratios were recorded and correlated with solution conditions. Crystal numbers were found to increase with increasing supersaturation and temperature. The most significant variable, however, was pH; crystal numbers changed by two orders of magnitude over the pH range 4.0-5.2. Crystal size also varied with solution conditions, with the largest crystals obtained at pH 5.2. Having optimized the crystallization conditions, we prepared a batch of crystals under the same initial conditions, and 50 of these crystals were analyzed by x-ray diffraction techniques. The results indicate that even under the same crystallization conditions, a marked variation in crystal properties exists.     

Molecular dynamics study of the isothermal crystallization mechanism of polyethylene chain: the combined effects of chain length and temperature

A molecular level understanding of the polyethylene (PE) crystallization process was elucidated by molecular dynamics simulation of three states, with varying chain length and temperature. The process can be classified into the following three states: (1) nucleation controlled state, (2) competitive state of crystal growth process and new nuclei formation, and (3) crystal growth controlled state, which could be quantified by the evolution of nuclei number. With increasing chain length, two phenomena occur: the single crystallization mechanism changes from state (1) to (3), and the crystal size increases while the b/a axial ratio in the lateral surface decreases. These changes can be explained from a thermodynamic point of view, in that the van der Waals (vdW) interaction per CH₂ unit is strengthened and more nucleation sites are generated for longer chain. Size effect (meaning different surface fractions when the chain collapses into a globule) was an important factor determining vdW energy per unit and the crystallization states of a single PE chain. On the other hand, the crystallization states were independent of chain length for short chains systems with the same size effect. In both conditions, a long chain generates multi-crystal domains, and a short chain prefers a single crystal domain. Our results not only provide molecular level evidence for crystallization states but also clarify the influence of chain length on the crystallization process.     

Measurement of the nucleation of atmospheric aerosol particles

The formation of new atmospheric aerosol particles and their subsequent growth have been observed frequently at various locations all over the world. The atmospheric nucleation rate (or formation rate) and growth rate (GR) are key parameters to characterize the phenomenon. Recent progress in measurement techniques enables us to measure atmospheric nucleation at the size (mobility diameter) of 1.5 (±0.4) nm. The detection limit has decreased from 3 to 1 nm within the past 10 years. In this protocol, we describe the procedures for identifying new-particle-formation (NPF) events, and for determining the nucleation, formation and growth rates during such events under atmospheric conditions. We describe the present instrumentation, best practices and other tools used to investigate atmospheric nucleation and NPF at a certain mobility diameter (1.5, 2.0 or 3.0 nm). The key instruments comprise devices capable of measuring the number concentration of the formed nanoparticles and their size, such as a suite of modern condensation particle counters (CPCs) and air ion spectrometers, and devices for characterizing the pre-existing particle number concentration distribution, such as a differential mobility particle sizer (DMPS). We also discuss the reliability of the methods used and requirements for proper measurements and data analysis. The time scale for realizing this procedure is 1 year.     

Organization of extracellularly mineralized tissues: a comparative study of biological crystal growth

Biological mineralization processes are extremely diverse and, to date, it is an act of faith rather than an established principle that organisms utilize common mechanisms for forming crystals. A systematic analysis of the structural organization, as far as possible at the molecular level, of five different extracellularly mineralized tissues is presented to demonstrate that at least these mineralization processes are all part of the same continuum. The degrees of control exercised over crystal nucleation and crystal growth modulation are the basic variables. The five tissues, extracellularly mineralizing algae, radial and granular foraminifera, mammalian bone, mammalian enamel, and mollusk shell nacre, probably span the entire spectrum. Their crystal shapes, sizes, and the relations between the mineral phase and the organic phase, are primarily used to assess probable degrees of control exercised over crystal nucleation and modulation. Three different types of nucleation processes can be recognized: nonspecific, stereochemical, and epitaxial. Modulation of crystal growth after nucleation is either absent, achieved by adsorption of macromolecules onto specific crystal faces, or occurs by the prepositioning of matrix surfaces which interrupt crystal growth. The tissues in which active control is exercised over crystal growth all contain similar types of acidic matrix macromolecules. Significantly, the framework matrix macromolecules are all quite different and hence probably perform some tissue-specific functions. The study shows that there is a common basis for understanding these mineralization processes which is reflected in the nature of the protein-crystal interactions which occur in each tissue.     

Birth and growth kinetics of brome mosaic virus microcrystals

The early steps of crystal nucleation and growth in Brome Mosa?c virus and polyethylene glycol mixtures were analyzed using time-resolved x-ray scattering (at the European Synchrotron Radiation Facility, Grenoble, France). The system was chosen as a crystallization model since the phase diagram of the macromolecule/polymer mixture was known to present, at high polymer concentration, a solid, precipitated phase made of the synchronized formation of a large number of microcrystals. The precipitation and crystallization of the samples was induced by the controlled mixing of virus and polymer using a stopped-flow device. Appearance and growth of Bragg diffraction peaks were used to follow the crystal nucleation and growth as a function of time, virus and polymer concentration, and polymer size. In all samples, the crystallization starts after a few seconds and proceeds for approximately 1-20 min until there is almost no virus left in the solution. The crystalline system was found to be face-centered cubic, with a unit cell size of 391 angstroms. The data analysis allowed us to show the presence of viruses in only two states, in solution or in crystals, revealing that the formation of periodic order proceeds without any detectable intermediate amorphous state.     

Nucleation and growth of microbial lipase crystals from clarified concentrated fermentation broths

Bulk crystallization is emerging as a new industrial operation for protein recovery. Characterization of bulk protein crystallization is more complex than protein crystallization for structural study where single crystals are grown in flow cells. This is because both nucleation and crystal growth processes are taking place while the supersaturation falls. An algorithm is presented to characterize crystallization using the rates of the two kinetic processes, nucleation and growth. The values of these rates allow ready comparison of the crystallization process under different operating conditions. The crystallization, via adjustment to the isoelectric pH of a fungal lipase from clarified fermentation broth, is described for a batch stirred reactor. A maximum nucleation rate of five to six crystals formed per microliter of suspension per second and a high power dependency ( approximately 11) on the degree of supersaturation were found. The suspended protein crystals were found to grow at a rate of up to 15-20 nm/s and also to exhibit a high power dependency ( approximately 6) of growth rate on the degree of supersaturation.     

Non-native aggregation of alpha-chymotrypsinogen occurs through nucleation and growth with competing nucleus sizes and negative activation energies

The kinetics and structural transitions of non-native aggregation of alpha-chymotrypsinogen (aCgn) were investigated over a wide range of temperature and initial protein concentration at pH 3.5, where high molecular weight aggregates remained soluble throughout the reaction. A comparison of thermodynamic, kinetic, and spectroscopic data shows that aggregation under non-native-favoring conditions proceeds through a molten globule unfolded monomer state, with a nucleation and growth mechanism. Formation of irreversible aggregates and conversion to beta-sheet secondary structures occur simultaneously without detectable intermediates, suggesting that beta-sheet formation may be a commitment step during the nucleation and growth stages. Analysis of the kinetics using a Lumry-Eyring with nucleated polymerization (LENP) model provides the predominant nucleus size and the product of the intrinsic nucleation and intrinsic growth time scales at each state point. We find that the nucleus size depends on both temperature and protein concentration, and in some cases there is competition between two distinct nucleus sizes. The observed rate coefficient (kobs) for aggregation displays a maximum as a function of temperature because of the competition between folding-unfolding thermodynamics and the intrinsic growth and nucleation rates; the latter contribution has a large, negative activation enthalpy that dominates kobs at elevated temperatures. Temperature-jump experiments reveal that aggregates depolymerize at high temperatures, indicating that they are lower in enthalpy than the free monomer. Overall, the results suggest more generally that non-native aggregation may proceed through more than one nucleus size and that intrinsic kinetics of nucleation and growth may have significant entropic barriers.     

Analysis of crystal growth of methane hydrate using molecular dynamics simulation

Methane hydrate is a crystalline compound with methane molecules enclosed in cages formed by hydrogen-bonded water molecules. Understanding the mechanism of nucleation and crystal growth from methane vapour and liquid water is important for all hydrate applications. However, processes near the water/methane interface are still unclear. In this work, we focused on the crystal growth of methane hydrate seeds located near the water/methane interface. We performed molecular dynamics (MD) simulation and analysed the crystal growth of the hydrate seed at the interface. New cages formed in the liquid water phase were stabilised when they shared faces with the hydrate seed. We also investigated the crystal growth rate as the time development of the number of methane molecules trapped in hydrate cages, based on the trajectory of the MD simulation. The calculated growth rate in the direction that covers the interface was 1.38 times that in the direction towards the inside of the water phase.     

水/乙醇混合溶剂中的阿奇霉素结晶动力学

利用粒数密度和粒度之间的关系判别晶体生长模型;采用间歇动态法,以粒数衡算方程、溶质质量守恒和McCabe定律为基础,利用Beer-Lambert定律,借助光学关联的方法,建立了包含透光率变量的伴有成核和晶体生长的动力学模型;通过在线测量溶液密度与透光率数据,采用非线性最小二乘法拟合得到了晶体成核和生长动力学经验方程,并以实时浓度为目标验证了动力学参数的准确性以及模型表达式的正确性。