Mechanism of accelerated assembly of beta-amyloid filaments into fibrils by KLVFFK(6)

Extracellular senile plaques are a central pathological feature of Alzheimer's disease. At the core of these plaques are fibrillar deposits of beta-amyloid peptide (Abeta). In vitro, Abeta spontaneously assembles into amyloid fibrils of cross-beta sheet structure. Although it was once believed that the fibrils themselves were toxic, more recent data supports the hypothesis that aggregation intermediates, rather than fully formed fibrils, are the most damaging to neuronal tissue. In previously published work, we identified several small peptides that interact with Abeta and increase its aggregation rate while decreasing its toxicity. In this work, we examined in detail the interaction between Abeta and one of these peptides. Using a mathematical model of Abeta aggregation kinetics, we show that the dominant effect of the peptide is to accelerate lateral association of Abeta filaments into fibrils.     

Temperature dependence of the nucleation constant rate in beta amyloid fibrillogenesis

Beta-amyloid peptide (A beta), in fibrillar form, is the primary constituent of senile plaques, a defining feature of Alzheimer's disease (AD). In solution assays, fibrils form with a lag time, interpreted as a nucleation/condensation-dependent process. The kinetics of fibrillogenesis is controlled by two key parameters: nucleation and elongation rate constants. We report here the study of the temperature dependence of the nucleation rate constant on an A beta monomer concentration of 18.4 microM at pH 7.4 and at temperatures ranging from 302 to 318 K. We found that the nucleation constant varied as in the Arrhenius law, giving an activation energy of 311.2 kJ mol(-1). The corresponding values of enthalpy of activation (deltaH*), entropy of activation (deltaS*) and Gibbs energy of activation (deltaG*) were evaluated by Eyring's equation of absolute reaction rate. A Gibbs energy of activation of approximately 110 kJ mol(-1) was obtained.     

Targeted control of kinetics of beta-amyloid self-association by surface tension-modifying peptides

Brain tissue from Alzheimer's patients contains extracellular senile plaques composed primarily of deposits of fibrillar aggregates of beta-amyloid peptide. beta-Amyloid aggregation is postulated to be a major factor in the onset of this neurodegenerative disease. Recently proposed is the hypothesis that oligomeric intermediates, rather than fully formed insoluble fibrils, are cytotoxic. Previously, we reported the discovery of peptides that accelerate beta-amyloid aggregation yet inhibit toxicity in vitro, in support of this hypothesis. These peptides contain two domains: a recognition element designed to bind to beta-amyloid and a disrupting element that alters beta-amyloid aggregation kinetics. Here we show that the aggregation rate-enhancing activity of the disrupting element correlates strongly with its ability to increase surface tension of aqueous solutions. Using the Hofmeister series as a guide, we designed a novel peptide with terminal side-chain trimethylammonium groups in the disrupting domain. The derivatized peptide greatly increased solvent surface tension and accelerated beta-amyloid aggregation kinetics by severalfold. Equivalent increases in surface tension in the absence of a recognition domain had no effect on beta-amyloid aggregation. These results suggest a novel strategy for targeting localized changes in interfacial energy to specific proteins, as a way to selectively alter protein folding, stability, and aggregation.     

Energy landscape theory for Alzheimer's amyloid beta-peptide fibril elongation

Recent experiments on the kinetics of deposition and fibril elongation of the Alzheimer's beta-amyloid peptide on preexisting fibrils are analyzed. A mechanism is developed based on the dock-and-lock scheme recently proposed by Maggio and coworkers to organize their experimental observations of the kinetics of deposition of beta-peptide on preexisting amyloid fibrils and deposits. Our mechanism includes channels for (1) a one-step prion-like direct deposition on fibrils of activated monomeric peptide in solution, and (2) a two-step deposition of unactivated peptide on fibrils and subsequent reorganization of the peptide-fibril complex. In this way, the mechanism and implied "energy landscape" unify a number of schemes proposed to describe the process of fibril elongation. This beta-amyloid landscape mechanism (beta ALM) is found to be in good agreement with existing experimental data. A number of experimental tests of the mechanism are proposed. The mechanism leads to a clear definition of overall equilibrium or rate constants in terms of the energetics of the elementary underlying processes. Analysis of existing experimental data suggests that fibril elongation occurs through a two-step mechanism of nonspecific peptide absorption and reorganization. The mechanism predicts a turnover in the rate of fibril elongation as a function of temperature and denaturant concentration. Proteins 2001;42:217-229.     

Effect of environmental factors on the kinetics of insulin fibril formation: elucidation of the molecular mechanism

In the search for the molecular mechanism of insulin fibrillation, the kinetics of insulin fibril formation were studied under different conditions using the fluorescent dye thioflavin T (ThT). The effect of insulin concentration, agitation, pH, ionic strength, anions, seeding, and addition of 1-anilinonaphthalene-8-sulfonic acid (ANS), urea, TMAO, sucrose, and ThT on the kinetics of fibrillation was investigated. The kinetics of the fibrillation process could be described by the lag time for formation of stable nuclei (nucleation) and the apparent rate constant for the growth of fibrils (elongation). The addition of seeds eliminated the lag phase. An increase in insulin concentration resulted in shorter lag times and faster growth of fibrils. Shorter lag times and faster growth of fibrils were seen at acidic pH versus neutral pH, whereas an increase in ionic strength resulted in shorter lag times and slower growth of fibrils. There was no clear correlation between the rate of fibril elongation and ionic strength. Agitation during fibril formation attenuated the effects of insulin concentration and ionic strength on both lag times and fibril growth. The addition of ANS increased the lag time and decreased the apparent growth rate for insulin fibril formation. The ANS-induced inhibition appears to reflect the formation of amorphous aggregates. The denaturant, urea, decreased the lag time, whereas the stabilizers, trimethylamine N-oxide dihydrate (TMAO) and sucrose, increased the lag times. The results indicated that both nucleation and fibril growth were controlled by hydrophobic and electrostatic interactions. A kinetic model, involving the association of monomeric partially folded intermediates, whose concentration is stimulated by the air-water interface, leading to formation of the critical nucleus and thence fibrils, is proposed.     

Kinetics of inhibition of beta-amyloid aggregation by transthyretin

Deposition of beta-amyloid (Abeta) fibrils is an early event in the neurodegenerative processes associated with Alzheimer's disease. According to the "amyloid cascade" hypothesis, Abeta aggregation, and its subsequent deposition as fibrils, is the underlying cause of disease. Abeta is a proteolytic product of amyloid precursor protein (APP); several mutations in APP have been identified that are associated with early onset of disease. Transgenic mice overexpressing APP with the Swedish mutation develop numerous plaques but, surprisingly, lack the neurofibrillary tangles and neuronal loss characteristic of Alzheimer's disease, in apparent contradiction of the amyloid cascade hypothesis. However, recent studies suggest that coproduction of sAPPalpha, an alternative proteolytic product of APP, increases synthesis of transthyretin that, in turn, interacts directly with Abeta to inhibit its toxicity. Here we report results from biophysical analysis of Abeta aggregation kinetics in the presence of transthryetin. At substoichiometric ratios, transthyretin drastically decreased the rate of aggregation without affecting the fraction of Abeta in the aggregate pool. Detailed analysis of the data using a mathematical model demonstrated that the decrease in aggregation rate was due to both a decrease in the rate of elongation relative to the rate of initiation of filaments and a decrease in lateral association of filaments to fibrils. Tryptophan quenching data indicated that transthyretin binds weakly to Abeta, with an estimated apparent KS of 2300 M-1. Taken together, the data support a hypothesis wherein transthyretin preferentially binds to aggregated rather than monomeric Abeta and arrests further growth of the aggregates.     

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.     

Kinetic analysis of beta-amyloid fibril elongation

We used surface plasmon resonance biosensors to evaluate the kinetics associated with the initial events of beta-amyloid (Abeta) fibril elongation. Fibrils were immobilized on the sensor chip surface and extended by exposure to soluble Abeta(1-40) peptide. The fibril surfaces bound Congo red, a marker for beta sheet structures, and exhibited a slow linear background decay that is consistent with fibril depolymerization. Sonicated fibrils supported elongation better than unsonicated fibrils, which is consistent with fibril extension reactions. The kinetic data revealed that peptide association and dissociation occurred in multiple steps. Kinetic rate constants for fibril extension were determined by globally fitting the response data with a three-step polymerization model. In the first step, the soluble peptide binds to the growing fibril tip in a readily reversible reaction. The subsequent steps likely allow bound peptide to be stabilized into the growing fiber through postbinding transitional events. Using a mutant peptide, F19P Abeta(1-40), we illustrate how the biosensor assay can be used to probe structure/function relationships of fibril elongation.     

Kinetics of aggregation of synthetic beta-amyloid peptide.

beta-Amyloid peptide is the major protein component of senile plaques and cerebrovascular amyloid deposits in patients with Alzheimer's disease. The peptide deposits extracellularly in the form of amyloid fibrils, in a cross-beta conformation. beta-amyloid peptide is a 39- to 43-residue segment of a normal membrane precursor protein. In this work, a peptide homologous to the first 40 amino acids of beta-amyloid peptide, beta(1-40), was synthesized and characterized. beta(1-40) exhibited a sharp change in solubility near physiological pH and gel formation at concentrations of 3 mg/ml or greater. Circular dichroism indicated that beta(1-40) contained approximately two-thirds beta-structure, but no alpha-helical character. Quasi-elastic and classical light scattering measurements showed that beta(1-40) aggregated end-to-end in solution, reaching average molecular weights greater than 4 x 10(6) after 13 days. The aggregates were best modeled as rigid rods of 5 nm diameter, similar to the diameter of amyloid fibrils purified from plaques. A mathematical model based on diffusion-limited aggregation was developed to describe the kinetics of aggregation.     

Light scattering analysis of fibril growth from the amino-terminal fragment beta(1-28) of beta-amyloid peptide.

beta-Amyloid protein (beta-A/4) is the major protein component of Alzheimer disease-related senile plaques and has been postulated to be a significant contributing factor in the onset and/or progression of the disease. In the senile plaque, beta-A/4 appears as bundles of amyloid fibrils. The biological activity of beta-A/4 may be related to its state of aggregation. In this work, self-assembly, fibril formation, and interfibrillary aggregation of beta(1-28), a synthetic peptide homologous with the amino-terminal fragment of beta-A/4, were investigated. The predominant form of beta(1-28) detected by size-exclusion chromatography and polyacrylamide gel electrophoresis was apparently a tetramer which does not bind Congo red. Aggregates containing cross-beta sheet structures which bind Congo red and thioflavin T were observed at concentrations of approximately 0.3 mg/ml or greater. Concentrations of 0.5-1 mg/ml were necessary for aggregation into fibrils to be detectable by classical or quasielastic light scattering. Both fibril elongation and fibril-fibril aggregation occur over the time scale investigated. The kinetics of aggregation were much faster at physiological salt concentrations than at lower ionic strength. Ionic strength also appeared to influence the morphology of the fibril aggregates. The data indicate that sample preparation method and sample history influence fibril size and number density.     

Influence of heparin and dendrimers on the aggregation of two amyloid peptides related to Alzheimer's and prion diseases

Amyloid plaques composed of proteinaceous aggregates are commonly found in brains affected by Alzheimer's disease and spongiform encephalopaties. A structural homology has been recently described for the Alzheimer's peptide Abeta1-28 and the segment of the prion protein Prp185-208. In the present paper, further elements in common are reported: the aggregation processes are in both cases enhanced by the model glucosaminoglycan heparin and dendrimers can modulate the aggregation process by affecting the nucleation rate at low concentrations and the elongation rate at high concentrations. Nucleation and elongation rate constants are derived from fittings to a nucleation dependent polymerization model.     

Fibril growth kinetics reveal a region of beta2-microglobulin important for nucleation and elongation of aggregation

Amyloid is a highly ordered form of aggregate comprising long, straight and unbranched proteinaceous fibrils that are formed with characteristic nucleation-dependent kinetics in vitro. Currently, the structural molecular mechanism of fibril nucleation and elongation is poorly understood. Here, we investigate the role of the sequence and structure of the initial monomeric precursor in determining the rates of nucleation and elongation of human β₂-microglobulin (β₂m). We describe the kinetics of seeded and spontaneous (unseeded) fibril growth of wild-type β₂m and 12 variants at pH 2.5, targeting specifically an aromatic-rich region of the polypeptide chain (residues 62-70) that has been predicted to be highly amyloidogenic. The results reveal the importance of aromatic residues in this part of the β₂m sequence in fibril formation under the conditions explored and show that this region of the polypeptide chain is involved in both the nucleation and the elongation phases of fibril formation. Structural analysis of the conformational properties of the unfolded monomer for each variant using NMR relaxation methods revealed that all variants contain significant non-random structure involving two hydrophobic clusters comprising regions 29-51 and 58-79, the extent of which is critically dependent on the sequence. No direct correlation was observed, however, between the extent of non-random structure in the unfolded state and the rates of fibril nucleation and elongation, suggesting that the early stages of aggregation involve significant conformational changes from the initial unfolded state. Together, the data suggest a model for β₂m amyloid formation in which structurally specific interactions involving the highly hydrophobic and aromatic-rich region comprising residues 62-70 provide a complementary interface that is key to the generation of amyloid fibrils for this protein at acidic pH.     

Solvent effects on self-assembly of beta-amyloid peptide.

beta-amyloid peptide (A beta) is the primary protein component of senile plaques in Alzheimer's disease patients. Synthetic A beta spontaneously assembles into amyloid fibrils and is neurotoxic to cortical cultures. Neurotoxicity has been associated with the degree of peptide aggregation, yet the mechanism of assembly of A beta into amyloid fibrils is poorly understood. In this work, A beta was dissolved in several different solvents commonly used in neurotoxicity assays. In pure dimethylsulfoxide (DMSO), A beta had no detectable beta-sheet content; in 0.1% trifluoroacetate, the peptide contained one-third beta-sheet; and in 35% acetonitrile/0.1% trifluoroacetate, A beta was two-thirds beta-sheet, equivalent to the fibrillar peptide in physiological buffer. Stock solutions of peptide were diluted into phosphate-buffered saline, and fibril growth was followed by static and dynamic light scattering. The growth rate was substantially faster when the peptide was predissolved in 35% acetonitrile/0.1% trifluoroacetate than in 0.1% trifluoroacetate, 10% DMSO, or 100% DMSO. Differences in growth rate were attributed to changes in the secondary structure of the peptide in the stock solvent. These results suggest that formation of an intermediate with a high beta-sheet content is a controlling step in A beta self-assembly.     

Role of aggregation conditions in structure, stability, and toxicity of intermediates in the Abeta fibril formation pathway

beta-amyloid peptide (Abeta) is one of the main protein components of senile plaques associated with Alzheimer's disease (AD). Abeta readily aggregates to forms fibrils and other aggregated species that have been shown to be toxic in a number of studies. In particular, soluble oligomeric forms are closely related to neurotoxicity. However, the relationship between neurotoxicity and the size of Abeta aggregates or oligomers is still under investigation. In this article, we show that different Abeta incubation conditions in vitro can affect the rate of Abeta fibril formation, the conformation and stability of intermediates in the aggregation pathway, and toxicity of aggregated species formed. When gently agitated, Abeta aggregates faster than Abeta prepared under quiescent conditions, forming fibrils. The morphology of fibrils formed at the end of aggregation with or without agitation, as observed in electron micrographs, is somewhat different. Interestingly, intermediates or oligomers formed during Abeta aggregation differ greatly under agitated and quiescent conditions. Unfolding studies in guanidine hydrochloride indicate that fibrils formed under quiescent conditions are more stable to unfolding in detergent than aggregation associated oligomers or Abeta fibrils formed with agitation. In addition, Abeta fibrils formed under quiescent conditions were less toxic to differentiated SH-SY5Y cells than the Abeta aggregation associated oligomers or fibrils formed with agitation. These results highlight differences between Abeta aggregation intermediates formed under different conditions and provide insight into the structure and stability of toxic Abeta oligomers.     

Quantitative connection between polyglutamine aggregation kinetics and neurodegenerative process in patients with Huntington's disease

ABSTRACT: BACKGROUND: Despite enormous progress in elucidating the biophysics of aggregation, no cause-and-effect relationship between protein aggregation and neurodegenerative disease has been unequivocally established. Here, we derived several risk-based stochastic kinetic models that assess genotype/phenotype correlations in patients with Huntington's disease (HD) caused by the expansion of a CAG repeat. Fascinating disease-specific aspects of HD include the polyglutamine (polyQ)-length dependence of both age at symptoms onset and the propensity of the expanded polyQ protein to aggregate. In vitro, aggregation of polyQ peptides follows a simple nucleated growth polymerization pathway. Our models that reflect polyQ aggregation kinetics in a nucleated growth polymerization divided aggregate process into the lengthdependent nucleation and the nucleation-dependent elongation. In contrast to the repeatlength dependent variability of age at onset, recent studies have shown that the extent of expansion has only a subtle effect on the rate of disease progression, suggesting possible differences in the mechanisms underlying the neurodegenerative process. RESULTS: Using polyQ-length as an index, these procedures enabled us for the first time to establish a quantitative connection between aggregation kinetics and disease process, including onset and the rate of progression. Although the complexity of disease process in HD, the time course of striatal neurodegeneration can be precisely predicted by the mathematical model in which neurodegeneration occurs by different mechanisms for the initiation and progression of disease processes. Nucleation is sufficient to initiate neuronal loss as a series of random events in time. The stochastic appearance of nucleation in a cell population acts as the constant risk of neuronal cell damage over time, while elongation reduces the risk by nucleation in proportion to the increased extent of the aggregates during disease progression. CONCLUSIONS: Our findings suggest that nucleation is a critical step in gaining toxic effects to the cell, and provide a new insight into the relationship between polyQ aggregation and neurodegenerative process in HD.     

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     

Heterogeneous amylin fibril growth mechanisms imaged by total internal reflection fluorescence microscopy

Total internal reflection fluorescence microscopy has been used to visualize the fibrillization of amylin, a hormone which in aggregated forms plays a role in type 2 diabetes pathology. Data were obtained at acidic pH where fibrillization is hindered by the charging of histidine 18 and at slightly basic pH where the loss of charge on the histidine promotes aggregation. The experiments show three types of aggregate growth processes. In the earliest steps globular seeds are formed with some expanding radially during the course of the reaction. The dimensions of the globular seeds as well as their staining with the amyloid-specific dye thioflavin T indicate that they are plaques of short fibrils. The next species observed are fibrils that invariably grow from large globular seeds or smaller punctate granules. Fibril elongation appears to be unidirectional, although in some cases multiple fibrils radiate from a single seed or granule. After fibrils are formed, some show an increase in fluorescence intensity that we attribute to the growth of new fibrils alongside those previously formed. All three aggregation processes are suggestive of secondary (heterogeneous) nucleation mechanisms in which nucleation occurs on preformed fibrils. Consistently, electron micrographs show changes in fibril morphology well after fibrils are first formed, and the growth processes observed by fluorescence microscopy occur after the corresponding solution reactions have reached an initial apparent plateau. Taken together, the results highlight the importance of secondary nucleation in the fibrillization of amylin, as this could provide a pathway to continue fibril growth once an initial population of fibrils is established.     

Amyloid fibril formation requires a chemically discriminating nucleation event: studies of an amyloidogenic sequence from the bacterial protein OsmB.

The sequence of the Escherichia coli OsmB protein was found to resemble that of the C-terminal region of the beta amyloid protein of Alzheimer's disease, which seems to be the major determinant of its unusual structural and solubility properties. A peptide corresponding to residues 28-44 of the OsmB protein was synthesized, and its conformational properties and aggregation behavior were analyzed. The peptide OsmB(28-44) was shown to form amyloid fibrils, as did two sequence analogs designed to test the sequence specificity of fibril formation. These fibrils bound Congo red, and two of the peptides showed birefringence. The peptide fibrils were analyzed by electron microscopy and Fourier transform infrared spectroscopy. Subtle differences were observed which were not interpretable at the molecular level. The rate of fibril formation by each peptide was followed by monitoring the turbidity of supersaturated aqueous solutions. The kinetics of aggregation were characterized by a delay period during which the solution remained clear, followed by a nucleation event which led to a growth phase, during which the solution became viscous and turbid due to the presence of insoluble fibrils. The observation of a kinetic barrier to aggregation is typical of a crystallization event. The delay period could be eliminated by seeding the supersaturated solution with previously formed fibrils. Each peptide could be nucleated by fibrils formed from that same peptide, but not by fibrils from closely related sequences, suggesting that fibril growth requires specific hydrophobic interactions. It appears likely that this repeated sequence motif, which comprises most of the OsmB protein sequence, dictates the structure and possibly the function of that protein.(ABSTRACT TRUNCATED AT 250 WORDS)     

Mutagenic analysis of the nucleation propensity of oxidized Alzheimer's beta-amyloid peptide

The formation of polypeptide aggregates represents a nucleated polymerization reaction in which an initial nucleation event (lag phase) is followed by the extension of newly formed nuclei into larger aggregates, including fibrils (growth phase). The efficiencies of these reactions relate to the lag time (lag phase) and to the rate of aggregation (growth phase), which can be determined from experimental aggregation curves. Here we present a mutagenic analysis in which we replace valine 18 of the Alzheimer's Abeta (1-40) peptide with 17 different amino acids and determine its effect on the lag time, and therefore, on the propensity of nucleation. Comparison with various physico-chemical properties shows that nucleation is affected in a predictable manner depending on the beta-sheet propensity and hydrophobicity of residue 18. In addition, we observe a direct proportionality between the lag time and the rate of aggregation. These data imply that the two reactions, nucleation and polymerization, are governed by very similar physicochemical principles and that they involve the formation of the same types of noncovalent interactions.