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.     

Injection of highly supersaturated oxygen solutions without nucleation

It is possible to inject highly supersaturated aqueous solutions of gas through a small capillary into an aqueous environment without the formation of significant gas bubbles. Such a technique has considerable potential therapeutic value in the treatment, for example, of heart attacks and strokes. The present paper is the second in a series (see Brereton et al. [1]) investigating the basic phenomenon behind this surprising effect. Recent experiments clearly demonstrate that the nucleation, when it does occur, results from heterogeneous nucleation on the interior surface of the distal end of the capillary. This paper describes the effects of the treatment of this interior surface on the nucleation processes and the results of high speed video observations of the phenomena. A heterogeneous nucleation model is presented which is in accord with the experimental observations.     

Small angle neutron scattering from lysozyme solutions in unsaturated and supersaturated states (SANS from lysozyme solutions)

Small angle neutron scattering (SANS) method was used to study lysozyme solutions, with particular interest in an understanding of the crystallization process at the initial stage. It is found that (1) in the unsaturated solution, the protein molecules aggregate with a continuous increase in size when NaCl concentration is increased, and (2) in the supersaturated solution, an irreversible change, superimposed on the former process, occurs when the supersaturation is realized. These facts indicate the usefulness of SANS in detecting changes of protein molecules in solution on the nanometer scale. The reliability of the SANS results are indicated by (1) comparing them with those of small angle X-ray scattering (SAXS), and (2) comparing the effect of D(2)O and H(2)O as solvent. Since the interparticle interaction is essential in the crystallization process and a simple Guinier plot analysis is not allowed, a more rigorous framework of analyzing data with interference function is developed, through which both average interparticle distance and particle size are estimated.     

Analysis of the nucleation and crystal growth kinetics of lysozyme by a theory of self-assembly.

Concentration changes in supersaturated solutions during the nucleation and growth of the orthorhombic form of hen egg-white lysozyme crystals have been observed for 121 d at 35 degrees C and pH 4.6, and with 3% NaCl. The effect of a variation in the initial protein concentration on the rate of approach to solubility in equilibrium is analyzed, by applying a model, originally developed for the understanding of protein self-assembly. It is shown that the observed kinetics can be explained fairly well by this model, whose basic assumptions are that (a) the nucleation is induced by aggregation of i0 molecules into particular geometry, and (b) the growth proceeds via attachment of a monomer. The i0 value for this process is four, which agrees with the number of molecules in a unit cell. Similarity and dissimilarity of the observed crystal growth to that of low molecular weight substances are discussed.     

Factors affecting cholesterol monohydrate crystal nucleation time in model systems of supersaturated bile

We explored the influence of several compositional factors considered capable of influencing the nucleation time of model biles supersaturated in cholesterol. In addition to the classical techniques, e.g., electron microscopy and quasielastic light scattering, employed for size measurement and structural assessment, we employed a novel technique, i.e., video-enhanced microscopy, for particle evaluation in these polydisperse systems which often may simultaneously contain isolated small vesicles, their complex aggregates, and small cholesterol monohydrate crystals. The factors we studied included dilution, degree of cholesterol supersaturation, bile salt/lecithin molar ratio, and Ca2+ concentration. Dilution markedly raised the degree of cholesterol saturation, prolonged nucleation time for cholesterol monohydrate crystals, and favored formation of metastable small unilamellar vesicles. Increasing the degree of cholesterol supersaturation as an independent variable in more concentrated systems both shortened the nucleation time and favored spontaneous formation of a relatively small number of isolated vesicles. A decrease in bile salt/lecithin molar ratio within the physiologically relevant range was accompanied by a prolonged nucleation time and favored spontaneous vesicle formation. Large numbers of small unilamellar vesicles were observed even in concentrated model bile solutions (total lipids: 20 g/dl) when the bile salt/lecithin molar ratio was 1.9 or less. At physiological concentrations, Ca2+ promoted nucleation of cholesterol monohydrate crystals only in vesicle-containing solutions. Taken together, the following conclusions can be drawn. First, spontaneous vesicle formation in dilute systems prolongs solid cholesterol crystal nucleation. It can thus provide a supplementary non-micellar mode of cholesterol transport in micellar systems of supersaturated human bile. Second, dilution, degree of cholesterol supersaturation, and a decrease in bile salt/lecithin ratio prolong cholesterol crystal nucleation time and favor spontaneous vesicle formation. With increasing calcium concentrations, opposite effects are observed. Third, the presence of vesicles may help to account for the frequently observed and otherwise unexplained remarkable degree of metastable supersaturation and prolonged metastability (delayed nucleation time) for cholesterol in human bile.     

Bovine gallbladder mucin promotes cholesterol crystal nucleation from cholesterol-transporting vesicles in supersaturated model bile

This study examined the ability of purified gallbladder mucin to accelerate the nucleation of cholesterol monohydrate crystals from the cholesterol-transporting particles in supersaturated model bile. Mixed lipid micelles and cholesterol-phosphatidylcholine vesicles in supersaturated model bile were separated by Sephadex G-200 column chromatography. Mixed lipid micelles prepared by column chromatography had a low cholesterol-phosphatidylcholine ratio (0.30) and did not spontaneously nucleate cholesterol monohydrate crystals. In contrast, vesicles prepared by column chromatography had a cholesterol-phosphatidylcholine ratio of 1.00 and nucleated cholesterol crystals rapidly (P less than 0.001). Nucleation of cholesterol crystals was significantly accelerated in a concentration- and time-dependent manner by purified bovine gallbladder mucin in cholesterol containing vesicles, but not in mixed lipid micelles (P less than 0.001). A rapid filtration binding assay demonstrated significant binding of cholesterol and phosphatidylcholine in vesicles to gallbladder mucin but only minimal binding of cholesterol and phosphatidylcholine in mixed micelles. These data indicate that gallbladder mucin binds cholesterol and phosphatidylcholine in vesicles and accelerates the nucleation of cholesterol monohydrate crystals from these cholesterol-transporting particles in supersaturated model bile.     

Protein crystal growth. Growth kinetics for tetragonal lysozyme crystals

A method for immobilizing protein crystals has been devised for determining face growth rates, and used to investigate the growth kinetics of hen egg white lysozyme crystals. Growth rates were determined at 22 degrees C in 0.1 M sodium acetate, 5% NaCl, pH 4.0, on the visually identified (110) face of tetragonal lysozyme crystals. Protein concentrations ranged from 13 to 57 mg/ml (saturation concentration = 1.7 mg/ml). Growth rate data were fit to the equation R = kappa sigma ri, where R = rate in cm/s; kappa = constant; sigma i = solute growth interface supersaturation; and r = rate dependence upon super-saturation, with the result that kappa = 0.146 X 10(-8) cm/s and r = 2.0. A model of the growth process was developed and the experimental data were used to determine the relative roles of transport and interfacial kinetics in the growth of this crystal. Values for the width of the boundary layer delta, the interfacial concentration Ci, and growth rate R were determined. The model may be used to extrapolate to other growth conditions. The relative role of transport and interfacial kinetics can be expressed by the coefficient gamma = (CB - Ci)/(CB - Cs), when CB is the bulk concentration and Cs the saturation. Values for gamma were found to range from much less than 0.1 for submicron-size crystals to approximately 0.15 for cm sizes. The results indicate that attachment or surface effects are rate-limiting in lysozyme crystal growth in Earth's gravity because solutal convection always provides more transport of solute than can be accommodated by the interface. In order to grow such crystals under transport limiting conditions, it would be necessary to suppress this solutal convection.     

Monomer concentrations and dimerization constants in crystallizing lysozyme solutions by dialysis kinetics.

Dialysis kinetics measurements have been made to study the effect of ionic strength on the dimerization of lysozyme in acidic solutions that lead to the growth of tetragonal lysozyme crystals. Using glutaraldehyde cross-linked dimers of lysozyme, we have determined that both monomers and dimers can escape from 25,000 molecular weight cutoff dialysis membranes with velocity constants of 5.1 x 10(-7) and 1.0 x 10(-7) s(-1) for the monomer and dimer species, respectively. The flux from 25K MWCO membranes has been measured for lysozyme in pH 4.0 buffered solutions of 1, 3, 4, 5, and 7% NaCl over a wide range of protein concentrations. Assuming that dimerization is the first step in crystallization, a simple monomer to dimer equilibrium was used to model the flux rates. Dimerization constants calculated at low protein concentrations were 265, 750, 1212, and 7879 M(-1) for 3, 4, 5, and 7% NaCl, respectively. These values indicate that dimerization increases with the ionic strength of the solution suggesting that aggregation is moderated by electrostatic interactions. At high protein concentrations and high supersaturation, the dimerization model does not describe the data well. However, the Li model that uses a pathway of monomer <-> dimer <-> tetramer <-> octamer <-> 16-mer fits the measured flux data remarkably well suggesting the presence of higher order aggregates in crystallizing solutions.     

Vesicle aggregation in model systems of supersaturated bile: relation to crystal nucleation and lipid composition of the vesicular phase

The presence of small vesicles composed of phospholipid and cholesterol has recently been demonstrated in super-saturated model and in dilute native human biles by several groups using differing methods. Among compositional factors shown to favor spontaneous vesicle formation and prolong the cholesterol monohydrate nucleation time in model bile systems are dilution, a raised cholesterol saturation index (CSI), and a low bile salt/phospholipid ratio. Time-lapse video-enhanced microscopy of a series of model bile systems representing systematically designed variations in the above factors revealed strong evidence for an essential linkage between antecedent vesicle aggregation and subsequent crystal nucleation. Stability of vesicles was inversely related to their degree of cholesterol saturation, i.e., the greater the degree of vesicular cholesterol saturation, the less their stability (metastability). Instability of vesicles was reflected by their early aggregation followed by rapid cholesterol crystal nucleation. The lowest degree of vesicular cholesterol saturation was found in dilute systems which also exhibited the greatest metastability despite a high degree of cholesterol solubility (raised CSI). Conversely, the more concentrated and least metastable systems exhibited both rapid vesicle aggregation and rapid onset of crystal nucleation. These systems, while influenced by the other compositional factors, were found to have a high degree of vesicular cholesterol saturation, i.e., cholesterol/phospholipid molar ratio = 2.0. An additional finding was the extreme variability in the proportionate distribution of total solution cholesterol distributed to the vesicular phase, i.e., from zero to as high as 37%. Higher solute concentration, raised bile salt/lecithin ratio, and raised CSI were interactive and almost equally capable of increasing the proportionate amount of cholesterol in the vesicular phase. In conclusion, lipid compositional differences in model bile systems drastically affect the cholesterol saturation of spontaneously formed phospholipid-cholesterol vesicles. This effect, in turn, exerts a potent influence upon the metastability of vesicles, subsequently affecting the cholesterol crystal nucleation time.     

Liquid crystals and cholesterol nucleation during equilibration in supersaturated bile analogs

In recent work, apparent liquid crystal agglomeration to form typical solid cholesterol microcrystals was frequently observed photomicrographically in bile samples from prairie dogs fed a cholesterol-enriched diet, prior to solid crystal formation. We therefore have conducted a systematic study of time-course lipid compositional changes in the mesophase and micellar phase constituents of bile analog solutions while undergoing cholesterol nucleation during equilibration. On the basis of these studies, we conclude that the nucleation process for microcrystal formation most likely occurs within the mesophase component which is only the first of a two-step transition in a sequential series of physical ordering processes. We deduce that mesophase formation must have a lower kinetic energy requirement and that the second step (microcrystal formation) must be rate limiting. In keeping with theoretical considerations, structural evidence for increased hydration is demonstrable near the point of complete equilibration when the mesophase is dissolving.     

Cholesterol crystallite nucleation in supersaturated model biles from a thermodynamic standpoint

A rapid, silicone polymer film uptake method was used to determine the cholesterol (Ch) thermodynamic activity (A(T)) in taurocholate (TC)-lecithin (L) and taurochenodeoxycholate (TCDC)-L model biles supersaturated with Ch. Also, time-dependent quasielastic light scattering (QLS) measurements and microscopic observations were made to determine the nature of particle species and the Ch nucleation times. In all cases in which Ch-L vesicles were present, a linear relationship between the logarithm of Ch nucleation times and Ch A(T) was found. These findings support that Ch A(T) is the appropriate parameter that represents the Ch nucleation tendency and that vesicles are catalytic sites in the Ch nucleation process. When Ca2+, a nucleation promoter ion, was present in the supersaturated model biles, the increased values of Ch A(T) quantitatively correlated with shorter Ch nucleation times. These latter findings further demonstrate that Ch A(T) is the dominant factor in explaining the Ch nucleation tendencies in supersaturated model biles.     

Quantitative analysis of cholesterol nucleation with time in supersaturated model bile

The amount of cholesterol (Ch) crystals formed in supersaturated taurochenodeoxycholate (TCDC) - lecithin (L) solutions of the same Ch saturation index (CSI) but at different Ch thermodynamic activities (Ch A_T) was quantified at different time intervals. The initial Ch nucleation rate (i.e., amount of Ch crystals formed with respect to time) in a Ch A_T = 1.73 and TCDC to L molar ratio (TCDC:L) = 5.1 system was faster than that in a Ch A_T = 1.42 and TCDC:L = 3.4 system. Shaking could enhance the early appearance of Ch crystals and cause the fast initial Ch nucleation rates for the TCDC:L = 5.1 and the TCDC:L = 3.4 systems. The final Ch nucleation rates were faster than the initial Ch nucleation rates for the TCDC:L = 5.1 and the TCDC:L = 3.4 systems. According to a light scattering analysis of vesicle concentration in supersaturated TCDC–L solutions, vesicles provide nucleation sites only in the Ch nucleation process and the vesicle concentration may not be an important factor for the Ch nucleation rate. A model of a mixed TCDC–L micelle releasing Ch molecules together with the surface area of Ch crystals formed was used in the interpretation of the Ch nucleation.     

Control of nucleation in the crystallization of lysozyme.

This work investigates the influence of storage of lysozyme in solution on its crystallization. The crystallization of hen egg-white lysozyme exhibits a storage effect (aging) that depends on the length of time the lysozyme solution is stored, after dissolving from freeze-dried powder, before being brought to crystallization conditions. The number of crystals obtained increases, while their size decreases, as the solution ages. Observations suggest that this effect is due to the presence of fungi that multiply in the stored protein solution. This aging effect was used to control nucleation and determine the number and size of lysozyme crystals to be formed in a given sample.     

Evidence for nucleation in the folding of reduced hen egg lysozyme

We have examined the early intermediate products of the regeneration of lysozyme by acidifying the regeneration solution containing the partially folded products, alkylating the free sulfhydryls and digesting the proteins sequentially with pepsin and chymotrypsin. Peptide maps were produced. Results indicate that a limited number of different disulfide bonds is formed early in the regeneration. From this we conclude that a limited number of 3-dimensional structures is formed in the early stages of the refolding process, and the process is not a random search.     

Electroviscous effect of lysozyme in aqueous solutions

Reduced viscosity of a dilute aqueous solution of hen egg white lysozyme is measured in the pH range from 1.4 to 12.7 for various NaCI concentrations. The viscosity decreases with increasing pH below the isoelectric point (pH 11) on account of diminution in the electroviscous effect, reaches a minimum at pH 11, and then increases at high pH's because of coagulation. The electroviscous effect is depressed by the increase in the small ion concentration. The dependence of reduced viscosity on small ion concentration and pH is discussed on the basis of Booth's theory and a partial agreement between theory and experiment is obtained. The discrepancy between theory and experiment is attributed to non-spherical distribution of charges in the protein. The volume of lysozyme obtained through Einstein's equation by extrapolating the reduced viscosity to a sufficiently high ion concentration compares well with the molecular volume in the crystal.     

Regioselectivity of enzymatic glycosylation of 6-O-acyl glycosides in supersaturated solutions

The regioselectivity of enzymatic transglycosylation of 6-O-acetyl glycosides in supersaturated solutions was investigated using a range of commercially available enzymes, Escherichia coli, barley, and Kluyveromyces spp. beta-galactosidase, green coffee bean alpha-galactosidase, jack bean alpha-mannosidase, rice alpha-glucosidase, and almond beta-glucosidase. It has been shown that 6-O-acetyl glycosides serve as good substrates for these enzymes, which, under the reaction conditions, are "forced" to transfer monosaccharide units to the secondary hydroxyl groups of the acceptors. In a variety of transglycosylations studied the (1-3)-linked disaccharide products were the predominant regioisomers isolated. The selectivity of the reaction varied significantly depending on the acceptor glycosides and the enzyme used. Exquisite specificity was observed in some cases, but in others approximately equal quantities of two disaccharides products were isolated. In the best transfers the yield approached 30%. The methodology described offers a quick and facile route to disaccharides that may be difficult and/or time consuming to make by conventional chemical synthesis.     

Helix nucleation kinetics from molecular simulations in explicit solvent

We study the reversible folding/unfolding of short Ala and Gly-based peptides by molecular dynamics simulations of all-atom models in explicit water solvent. A kinetic analysis shows that the formation of a first alpha-helical turn occurs within 0.1-1 ns, in agreement with the analyses of laser temperature jump experiments. The unfolding times exhibit Arrhenius temperature dependence. For a rapidly nucleating all-Ala peptide, the helix nucleation time depends only weakly on temperature. For a peptide with enthalpically competing turn-like structures, helix nucleation exhibits an Arrhenius temperature dependence, corresponding to the unfolding of enthalpic traps in the coil ensemble. An analysis of structures in a "transition-state ensemble" shows that helix-to-coil transitions occur predominantly through breaking of hydrogen bonds at the helix ends, particularly at the C-terminus. The temperature dependence of the transition-state ensemble and the corresponding folding/unfolding pathways illustrate that folding mechanisms can change with temperature, possibly complicating the interpretation of high-temperature unfolding simulations. The timescale of helix formation is an essential factor in molecular models of protein folding. The rapid helix nucleation observed here suggests that transient helices form early in the folding event.     

Kinetic analysis of protein crystal nucleation in gel matrix

The effect of agarose on nucleation of hen egg white lysozyme crystal was examined quantitatively using a temperature-jumping technique. For the first time, to our knowledge, the inhibition of agarose during the nucleation of lysozyme was quantified in two respects: a), the effect of increasing interfacial nucleation barrier, described by the so-called interfacial correlation parameter f(m); and b), the ratio of diffusion to interfacial kinetics obtained from dynamic surface tension measurements. It follows from a dynamic surface tension analysis that the agarose network inhibits the nucleation of lysozyme by means of an enhancement of the repulsion and interfacial structure mismatch between foreign bodies and lysozyme crystals, slowing down the diffusion process of the protein molecules and clusters toward the crystal-fluid interface and inhibiting the rearrangement of protein molecules at the interface. Our results, based on ultraviolet-visible spectroscopy, also show no evidence of the supersaturation enhancement effect in protein agarose gels. The effects of nucleation suppression and transport limitation in gels result in bigger, fewer, and perhaps better quality protein crystals. The understandings obtained in this study will improve our knowledge in controlling the crystallization of proteins and other biomolecules.     

Mechanical denaturation of lysozyme in a crystal and film

A method for taking stress-strain diagrams in microsamples prepared from glutaraldehyde-treated monocrystals and amorphous films of hen egg-white lysozyme has been developed. Analysis of the diagrams has shown that the deformation obeys Hooke's law within 0-2%. Upon further deformation of a crystalline sample (up to 6-10%) when a critical tension, sigma cr, is reached, the protein molecules in the sample denature and become greatly extended. Depending on crystal type and crystallographic direction the sample length increases 2 to 4 times. The sample deformation accompanying denaturation is reversible: when the sample is kept at high temperature it restores completely its initial length. The critical stress is essentially dependent on temperature, hydration level, urea concentration, the factors affecting intra- and intermolecular interactions.