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.     

Mechanisms of homogeneous nucleation of polymers of sickle cell anemia hemoglobin in deoxy state

The primary pathogenic event of sickle cell anemia is the polymerization of the mutant hemoglobin (Hb) S within the red blood cells, occurring when HbS is in deoxy state in the venous circulation. Polymerization is known to start with nucleation of individual polymer fibers, followed by growth and branching via secondary nucleation, yet the mechanisms of nucleation of the primary fibers have never been subjected to dedicated tests. We implement a technique for direct determination of rates and induction times of primary nucleation of HbS fibers, based on detection of emerging HbS polymers using optical differential interference contrast microscopy after laser photolysis of CO-HbS. We show that: (i). nucleation throughout these determinations occurs homogeneously and not on foreign substrates; (ii). individual nucleation events are independent of each other; (iii). the nucleation rates are of the order of 10(6)-10(8)cm(-3)s(-1); (iv). nucleation induction times agree with an a priori prediction based on Zeldovich's theory; (v). in the probed parameter space, the nucleus contains 11 or 12 molecules. The nucleation rate values are comparable to those leading to erythrocyte sickling in vivo and suggest that the mechanisms deduced from in vitro experiments might provide physiologically relevant insights. While the statistics and dynamics of nucleation suggest mechanisms akin to those for small-molecule and protein crystals, the nucleation rate values are nine to ten orders of magnitude higher than those known for protein crystals. These high values cannot be rationalized within the current understanding of the nucleation processes.     

Cunning simplicity of protein folding landscapes

Funnel-like landscapes are widely used to visualize protein folding. It might seem that any funnel-like energy landscape helps to avoid the 'Levinthal paradox', i.e. to avoid sampling the impossibly large number of conformations for a folding protein. This cunning suggestion, reinforced by beautiful drawings of the energy funnels, stimulated some simple models of protein folding; one of them [D.J. Bicout and A. Szabo (2000) Protein Sci., 9, 452-465] is especially straightforward and instructive. A thorough analysis of this strict funnel model (which does not consider a nucleation of phase separation in the course of folding) shows that it cannot provide a simultaneous explanation for both major features observed for protein folding: (i) folding within non-astronomical time, and (ii) co-existence of the native and the unfolded states during the folding process. On the contrary, the nucleation mechanism of protein folding can account for both these major features simultaneously.     

Nucleation and growth of insulin fibrils in bulk solution and at hydrophobic polystyrene surfaces

A technique was developed for studying the nucleation and growth of fibrillar protein aggregates. Fourier transform infrared and attenuated total reflection spectroscopy were used to measure changes in the intermolecular beta-sheet content of bovine pancreatic insulin in bulk solution and on model polystyrene (PS) surfaces at pH 1. The kinetics of beta-sheet formation were shown to evolve in two stages. Combined Fourier transform infrared, dynamic light scattering, atomic force microscopy, and thioflavin-T fluorescence measurements confirmed that the first stage in the kinetics was related to the formation of nonfibrillar aggregates that have a radius of 13 +/- 1 nm. The second stage was found to be associated with the growth of insulin fibrils. The beta-sheet kinetics in this second stage were used to determine the nucleation and growth rates of fibrils over a range of temperatures between 60 degrees C and 80 degrees C. The nucleation and growth rates were shown to display Arrhenius kinetics, and the associated energy barriers were extracted for fibrils formed in bulk solution and at PS surfaces. These experiments showed that fibrils are nucleated more quickly in the presence of hydrophobic PS surfaces but that the corresponding fibril growth rates decrease. These observations are interpreted in terms of the differences in the attempt frequencies and energy barriers associated with the nucleation and growth of fibrils. They are also discussed in the context of differences in protein concentration, mobility, and conformational and colloidal stability that exist between insulin molecules in bulk solution and those that are localized at hydrophobic PS interfaces.     

Growth of Collagen Fibril Seeds from Embryonic Tendon: Fractured Fibril Ends Nucleate New Tip Growth

Collagen fibrils are the principal tensile element of vertebrate tissues where they occur in the extracellular matrix as spatially organised arrays. A major challenge is to understand how the mechanisms of nucleation, growth and remodelling yield fibrils of tissue-specific diameter and length. Here we have developed a seeding system whereby collagen fibrils were isolated from avian embryonic tendon and added to purified collagen solution, in order to characterise fibril surface nucleation and growth mechanisms. Fragmentation of tendon in liquid nitrogen followed by Dounce homogenisation generated fibril length fragments. Most (> 94%) of the fractured ends of fibrils, which show an abrupt square profile, were found to act as nucleation sites for further growth by molecular accretion. The mechanism of this nucleation and growth process was investigated by transmission electron microscopy, atomic force microscopy and scanning transmission electron microscopy mass mapping. Typically, a single growth spur occurred on the N-terminal end of seed fibrils whilst twin spurs frequently formed on the C-terminal end before merging into a single tip projection. The surface nucleation and growth process generated a smoothly tapered tip that achieved maximum diameter when the axial extension reached ∼ 13 μm. Lateral growth also occurred along the entire length of all seed fibrils that contained tip projections. The data support a model of collagen fibril growth in which the broken ends of fibrils are nucleation sites for propagation in opposite axial directions. The observed fibril growth behaviour has direct relevance to tendon matrix remodelling and repair processes that might involve rupture of collagen fibrils.     

Noninvasive in situ observation of the crystallization kinetics of biological macromolecules by confocal laser scanning microscopy

High-resolution confocal laser scanning microscopy (CLSM) is a powerful tool for in situ observation and analysis of protein crystal growth kinetics. Because the resolution of CLSM is not diffraction-limited by the object, it is possible to visualize, under certain conditions, objects in molecular dimensions. A modified batch technique is applied which allows the growth kinetics of sufficiently small crystallites fixed at the lower side of a cover glass, within a hanging drop, to be studied in reflected light near the total reflection angle. A gap, or cavity, filled with solution is formed between the cover glass and the upper crystal face, which acts to fix small crystallites by hydrodynamic friction forces. The cavity height enables the propagation of molecular steps across the upper crystal face without constraint, so that the propagation velocity and geometrical parameters can be measured by CLSM. The layer growth kinetics of monoclinic crystallites of a long-acting insulin derivative (Insulin Glargine) is investigated. For a twofold supersaturation of the solution, the growth is governed by 2D nucleation at the edges of the crystallites followed by a spreading of molecular steps. The layer growth kinetics are well fitted by the simple cubic kinetic lattice model. We find that only about one of a thousand solute (protein) molecules which push a kink place due to their Brownian motion becomes really incorporated into the growing crystal.     

Beta poly(L-lysine): a model system for biological self-assembly

The beta structure of poly(l-lysine) is formed in solutions of pH above 9.5 and temperatures above 45 °C. We have followed the extent of the transition by measuring the light scattering, the fluorescence of a beta-specific dye (2-toluidino-6-naphthalene sulfonate) or the optical rotation. During the time course of the transition, the fractional changes of all three quantities are, within experimental error, the same. The progress of the reaction is sigmoid; therefore, we consider two reaction steps: nucleation and growth on a folded template. Since the rate does not depend on the concentration, the intramolecular folding of single molecules is the nucleation step. Since the end product does not accelerate the folding of unfolded molecules, the growth of each beta particle ends when the particle reaches a certain (equilibrium) size. This size is approx. 100 molecules per particle. Studies of single and double reversal show hysteresis: there is a range where the unfolded material will not fold and the folded material will not unfold. Unfolding is easier, the smaller the degree of folding at the time of the reversal. Seeding, i.e. rate enhancement by the artificial introduction of nuclei, is observed (1) when folding is caused with a small amount of 1 n-base, rather than with buffer and (2) when solutions in which the reaction has been reversed by cooling are again heated. These observations are typical of the behavior of polymers crystallizing in dilute solution. However, the finite size of the particles is unusual, and makes this system, in which assembly and conformation change are nearly inextricably linked, a possible model of self-assembling biological structures.     

Protein crystals and their growth

Recent results on the associations between protein molecules in crystal lattices, crystal-solution surface energy, elastic properties, strength, and spontaneous crystal cracking are reviewed and discussed. In addition, some basic approaches to understanding the solubility of proteins are followed by an overview of crystal nucleation and growth. It is argued that variability of mixing in batch crystallization may be a source of the variation in the number of crystals ultimately appearing in the sample. The frequency at which new molecules join a crystal lattice is measured by the kinetic coefficient and is related to the observed crystal growth rate. Numerical criteria used to discriminate diffusion- and kinetic-limited growth are discussed on this basis. Finally, the creation of defects is discussed with an emphasis on the role of impurities and convection on macromolecular crystal perfection.     

Osmolyte controlled fibrillation kinetics of insulin: New insight into fibrillation using the preferential exclusion principle

Amyloid proteins are converted from their native‐fold to long β‐sheet‐rich fibrils in a typical sigmoidal time‐dependent protein aggregation curve. This reaction process from monomer or dimer to oligomer to nuclei and then to fibrils is the subject of intense study. The main results of this work are based on the use of a well‐studied model amyloid protein, insulin, which has been used in vitro by others. Nine osmolyte molecules, added during the protein aggregation process for the production of amyloid fibrils, slow‐down or speed up the process depending on the molecular structure of each osmolyte. Of these, all stabilizing osmolytes (sugars) slow down the aggregation process in the following order: tri > di > monosaccharides, whereas destabilizing osmolytes (urea, guanidium hydrochloride) speed up the aggregation process in a predictable way that fits the trend of all osmolytes. With respect to kinetics, we illustrate, by adapting our earlier reaction model to the insulin system, that the intermediates (trimers, tetramers, pentamers, etc.) are at very low concentrations and that nucleation is orders of magnitude slower than fibril growth. The results are then collated into a cogent explanation using the preferential exclusion and accumulation of osmolytes away from and at the protein surface during nucleation, respectively. Both the heat of solution and the neutral molecular surface area of the osmolytes correlate linearly with two fitting parameters of the kinetic rate model, that is, the lag time and the nucleation rate prior to fibril formation. These kinetic and thermodynamic results support the preferential exclusion model and the existence of oligomers including nuclei and larger structures that could induce toxicity. © 2009 American Institute of Chemical Engineers Biotechnol. Prog., 2009     

Porous silicon: an effective nucleation-inducing material for protein crystallization

Protein crystals play a pivotal part in structural genomics, hence there is an urgent requirement for new and improved methodology to aid crystal growth. Considerable effort has been invested in the search of substances (nucleants) that will induce efficient nucleation of protein crystals in a controlled manner. To date, nucleation has been facilitated mainly by seeding, epitaxy, charged surfaces or mechanical means. A different approach is introduced here, involving the use of a mesoporous material that is likely to constrain protein molecules and thereby encourage them to aggregate in crystalline order. Large single crystals were obtained using porous silicon at conditions that are not sufficient for spontaneous nucleation, for five out of six proteins that were investigated. We propose that this success is due to the size distribution of pores in the specially designed porous silicon.     

Nucleation, growth, and activation energies for seeded and unseeded aggregation of alpha-chymotrypsinogen A

The intrinsic time scales for nonnative aggregate nucleation (tau0(n)) and chain growth (tau0(g)) were determined for alpha-chymotrypsinogen A as a function of temperature under acidic conditions where the resulting aggregates do not appreciably condense. Previous results (Andrews and Roberts (2007) Biochemistry 46, 7558) indicated that the product tau0(n)tau0(g) increases with increasing temperature but could not distinguish tau0(n) and tau0(g). Separate experimental values of tau0(n) and tau0(g) are reported here from two approaches based on either (i) combining unseeded monomer loss kinetics with static light scattering of the resulting aggregates or (ii) seeded monomer loss kinetics as a function of number concentration of seed. Values of tau0(n) and tau0(g) from (i) and (ii) agree quantitatively, and indicate that nucleation has a large, negative effective activation energy (ca. -76 kcal/mol) while growth has at most a weak dependence on temperature. The results are consistent with a model in which nucleation requires significant conformational changes within a nonnative oligomer, beyond those for monomer unfolding. The results more generally illustrate the potential utility of approaches (i) and (ii) for quantitatively determining in vitro tau0(n) and tau0(g) values, as well as how the effects of seeding can be predicted purely from unseeded kinetics and static light scattering measurements prior to significant aggregate condensation.     

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.     

Simulations of nucleation and early growth stages of protein crystals.

Analysis of known protein crystal structures reveals that interaction energies between monomer pairs alone are not sufficient to overcome entropy loss related to fixing monomers in the crystal lattice. Interactions with several neighbors in the crystal are required for stabilization of monomers in the lattice. A microscopic model of nucleation and early growth stages of protein crystals, based on the above observations, is presented. Anisotropy of protein molecules is taken into account by assigning free energies of association (proportional to the buried surface area) to individual monomer-monomer contacts in the lattice. Lattice simulations of the tetragonal lysozyme crystal based on the model correctly reproduce structural features of the movement of dislocation on the (110) crystal face. The dislocation shifts with the speed equal to the one determined experimentally if the geometric probability of correct orientation is set to 10(-5), in agreement with previously published estimates. At this value of orientational probability, the first nuclei, the critical size of which for lysozyme is four monomers, appear in 1 ml of supersaturated solution on a time scale of microseconds. Formation of the ordered phase proceeds through the growth of nuclei (rather then their association) and requires nucleations on the surface at certain stages.     

Protein nucleation and crystallization by homologous protein thin film template

A new method of protein nucleation and crystallization based on Langmuir-Blodgett technology is here utilized for the template stimulation of crystal growth of so far non-crystallized proteins. Microcrystals (60-120 microm) of bovine cytochrome P450scc and human protein kinase CKII alpha subunit were obtained with use of the homologous protein thin film template by vapor diffusion modified hanging drop method. The induction of microcrystals nucleation by the thin template confirms in the two different important classes of proteins, until now never crystallized, the positive stimulatory influence for crystal formation of protein thin film template, which was observed in an earlier study with a model system (chicken egg white lysozyme) as an unexpected acceleration and enhancement in the crystal growth.     

Fitting neurological protein aggregation kinetic data via a 2-step, minimal/"Ockham's razor" model: the Finke-Watzky mechanism of nucleation followed by autocatalytic surface growth

The aggregation of proteins has been hypothesized to be an underlying cause of many neurological disorders including Alzheimer's, Parkinson's, and Huntington's diseases; protein aggregation is also important to normal life function in cases such as G to F-actin, glutamate dehydrogenase, and tubulin and flagella formation. For this reason, the underlying mechanism of protein aggregation, and accompanying kinetic models for protein nucleation and growth (growth also being called elongation, polymerization, or fibrillation in the literature), have been investigated for more than 50 years. As a way to concisely present the key prior literature in the protein aggregation area, Table 1 in the main text summarizes 23 papers by 10 groups of authors that provide 5 basic classes of mechanisms for protein aggregation over the period from 1959 to 2007. However, and despite this major prior effort, still lacking are both (i) anything approaching a consensus mechanism (or mechanisms), and (ii) a generally useful, and thus widely used, simplest/"Ockham's razor" kinetic model and associated equations that can be routinely employed to analyze a broader range of protein aggregation kinetic data. Herein we demonstrate that the 1997 Finke-Watzky (F-W) 2-step mechanism of slow continuous nucleation, A --> B (rate constant k1), followed by typically fast, autocatalytic surface growth, A + B --> 2B (rate constant k2), is able to quantitatively account for the kinetic curves from all 14 representative data sets of neurological protein aggregation found by a literature search (the prion literature was largely excluded for the purposes of this study in order provide some limit to the resultant literature that was covered). The F-W model is able to deconvolute the desired nucleation, k1, and growth, k2, rate constants from those 14 data sets obtained by four different physical methods, for three different proteins, and in nine different labs. The fits are generally good, and in many cases excellent, with R2 values >or=0.98 in all cases. As such, this contribution is the current record of the widest set of protein aggregation data best fit by what is also the simplest model offered to date. Also provided is the mathematical connection between the 1997 F-W 2-step mechanism and the 2000 3-step mechanism proposed by Sait? and co-workers. In particular, the kinetic equation for Sait?'s 3-step mechanism is shown to be mathematically identical to the earlier, 1997 2-step F-W mechanism under the 3 simplifying assumptions Sait? and co-workers used to derive their kinetic equation. A list of the 3 main caveats/limitations of the F-W kinetic model is provided, followed by the main conclusions from this study as well as some needed future experiments.     

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.     

Fitting yeast and mammalian prion aggregation kinetic data with the Finke-Watzky two-step model of nucleation and autocatalytic growth

Recently, we reported 14 amyloid protein aggregation kinetic data sets that were fit using the "Ockham's razor"/minimalistic Finke-Watzky (F-W) two-step model of slow nucleation (A --> B, rate constant k 1) and fast autocatalytic growth (A + B --> 2B, rate constant k 2), yielding quantitative (average) rate constants for nucleation ( k 1) and growth ( k 2), where A is the monomeric protein and B is the polymeric protein [Morris, A. M., et al. (2008) Biochemistry 47, 2413-2427]. Herein, we apply the F-W model to 27 representative prion aggregation kinetic data sets obtained from the literature. Each prion data set was successfully fit with the F-W model, including three different yeast prion proteins (Sup35p, Ure2p, and Rnq1p) as well as mouse and human prions. These fits yield the first quantitative rate constants for the steps of nucleation and growth in prion aggregation. Examination of a Sup35p system shows that the same rate constants are obtained for nucleation and for growth within experimental error, regardless of which of six physical methods was used, a unique set of important control experiments in the protein aggregation literature. Also provided herein are analyses of several factors influencing the aggregation of prions such as glutamine/asparagine rich regions and the number of oligopeptide repeats in the prion domain. Where possible, verification or refutation of previous correlations to glutamine/asparagine regions, or the number of repeat sequences, in literature aggregation kinetics is given in light of the quantitative rate constants obtained herein for nucleation and growth during prion aggregation. The F-W model is then contrasted to four literature mechanisms that address the molecular picture of prion transmission and propagation. Key limitations of the F-W model are listed to prevent overinterpretation of the data being analyzed, limitations that derive ultimately from the model's simplicity. Finally, possible avenues of future research are suggested.     

Determination of the transition-state entropy for aggregation suggests how the growth of sickle cell hemoglobin polymers can be slowed

Sickle cell anemia is associated with the mutant hemoglobin HbS, which forms polymers in red blood cells of patients. The growth rate of the polymers is several micrometers per second, ensuring that a polymer fiber reaches the walls of an erythrocyte (which has a 7-μm diameter) within a few seconds after its nucleation. To understand the factors that determine this unusually fast rate, we analyze data on the growth rate of the polymer fibers. We show that the fiber growth follows a first-order Kramers-type kinetics model. The entropy of the transition state for incorporation into a fiber is 95 J mol^− 1 K^− 1, very close to the known entropy of polymerization. This agrees with a recent theoretical estimate for the hydrophobic interaction and suggests that the gain of entropy in the transition state is due to the release of the last layer of water molecules structured around contact sites on the surface of the HbS molecules. As a result of this entropy gain, the free-energy barrier for incorporation of HbS molecules into a fiber is negligible and fiber growth is unprecedentedly fast. This finding suggests that fiber growth can be slowed by components of the red cell cytosol, native or intentionally introduced, which restructure the hydration layer around the HbS molecules and thus lower the transition state entropy for incorporation of an incoming molecule into the growing fiber.     

Effects of high pressure on the solubility and growth kinetics of monoclinic lysozyme crystals.

Average growth rates of the (0 1 0) and (0 1 0) faces (R<0 1 0>) of monoclinic lysozyme crystals were measured in situ under 0.1 and 100 MPa. From the dependence of the growth rates on the lysozyme concentration, we determined the solubility of the crystal as a function of temperature at 0.1 and 100 MPa. The solubility increased with an increase in pressure. From the comparison between the growth rates under 0.1 and 100 MPa at the same supersaturation level, we found that the growth rates of the monoclinic lysozyme crystals kinetically increase with an increase in pressure. Supersaturation dependencies of the growth rates under 0.1 and 100 MPa were well fitted with a two-dimensional (2D) nucleation growth model of a birth-and-spread type. The fitting results suggest that the increase in the growth rates with pressure can be explained by the decrease in the average ledge surface energy of 2D island, the average distance between the kinks on a step and the activation energies in the incorporation processes of solute molecules.     

Effect of dietary garlic and onion on biliary proteins and lipid peroxidation which influence cholesterol nucleation in bile

Formation of cholesterol gallstones in gallbladder is controlled by procrystallizing and anticrystallizing factors present in bile. Dietary garlic and onion have been recently observed to possess anti-lithogenic potential in experimental mice. In this investigation, the role of biliary proteins from rats fed lithogenic diet or garlic/onion-containing diet in the formation of cholesterol gallstones in model bile was studied. Cholesterol nucleation time of the bile from lithogenic diet group was prolonged when mixed with bile from garlic or onion groups. High molecular weight proteins of bile from garlic and onion groups delayed cholesterol crystal growth in model bile. Low molecular weight (LMW) proteins from the bile of lithogenic diet group promoted cholesterol crystal growth in model bile, while LMW protein fraction isolated from the bile of garlic and onion groups delayed the same. Biliary LMW protein fraction was subjected to affinity chromatography using Con-A and the lectin-bound and unbound fractions were studied for their influence on cholesterol nucleation time in model bile. Major portion of biliary LMW proteins in lithogenic diet group was bound to Con-A, and this protein fraction promoted cholesterol nucleation time and increased cholesterol crystal growth rate, whereas Con-A unbound fraction delayed the onset of cholesterol crystallization. Biliary protein from garlic/onion group delayed the crystallization and interfered with pronucleating activity of Con-A bound protein fraction. These data suggest that apart from the beneficial modulation of biliary cholesterol saturation index, these Allium spices also influence cholesterol nucleating and antinucleating protein factors that contribute to their anti-lithogenic potential.