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• W2012591531 abstract "Associated with neurodegenerative disorders such as Alzheimer, Parkinson, or prion diseases, the conversion of soluble proteins into amyloid fibrils remains poorly understood. Extensive “in vitro” measurements of protein aggregation kinetics have been reported, but no consensus mechanism has emerged until now. This contribution aims at overcoming this gap by proposing a theoretically consistent crystallization-like model (CLM) that is able to describe the classic types of amyloid fibrillization kinetics identified in our literature survey. Amyloid conversion represented as a function of time is shown to follow different curve shapes, ranging from sigmoidal to hyperbolic, according to the relative importance of the nucleation and growth steps. Using the CLM, apparently unrelated data are deconvoluted into generic mechanistic information integrating the combined influence of seeding, nucleation, growth, and fibril breakage events. It is notable that this complex assembly of interdependent events is ultimately reduced to a mathematically simple model, whose two parameters can be determined by little more than visual inspection. The good fitting results obtained for all cases confirm the CLM as a good approximation to the generalized underlying principle governing amyloid fibrillization. A perspective is presented on possible applications of the CLM during the development of new targets for amyloid disease therapeutics. Associated with neurodegenerative disorders such as Alzheimer, Parkinson, or prion diseases, the conversion of soluble proteins into amyloid fibrils remains poorly understood. Extensive “in vitro” measurements of protein aggregation kinetics have been reported, but no consensus mechanism has emerged until now. This contribution aims at overcoming this gap by proposing a theoretically consistent crystallization-like model (CLM) that is able to describe the classic types of amyloid fibrillization kinetics identified in our literature survey. Amyloid conversion represented as a function of time is shown to follow different curve shapes, ranging from sigmoidal to hyperbolic, according to the relative importance of the nucleation and growth steps. Using the CLM, apparently unrelated data are deconvoluted into generic mechanistic information integrating the combined influence of seeding, nucleation, growth, and fibril breakage events. It is notable that this complex assembly of interdependent events is ultimately reduced to a mathematically simple model, whose two parameters can be determined by little more than visual inspection. The good fitting results obtained for all cases confirm the CLM as a good approximation to the generalized underlying principle governing amyloid fibrillization. A perspective is presented on possible applications of the CLM during the development of new targets for amyloid disease therapeutics. Amyloid fibrils are insoluble ordered structures sharing a common cross β-sheet conformation and formed by misassembly of soluble proteins and peptides (1Sunde M. Serpell L.C. Bartlam M. Fraser P.E. Pepys M.B. Blake C.C. Common core structure of amyloid fibrils by synchrotron x-ray diffraction.J. Mol. Biol. 1997; 273: 729-739Crossref PubMed Scopus (1424) Google Scholar, 2Kelly J.W. Amyloid fibril formation and protein misassembly: a structural quest for insights into amyloid and prion diseases.Structure. 1997; 5: 595-600Abstract Full Text Full Text PDF PubMed Scopus (204) Google Scholar, 3Greenwald J. Riek R. Biology of amyloid: structure, function, and regulation.Structure. 2010; 18: 1244-1260Abstract Full Text Full Text PDF PubMed Scopus (420) Google Scholar). Because these protein aggregates are associated with numerous neurodegenerative diseases, a great deal of effort has been put into understanding the mechanisms of amyloid fibril formation (4Morris A.M. Watzky M.A. Finke R.G. Protein aggregation kinetics, mechanism, and curve-fitting: a review of the literature.Biochim. Biophys. Acta. 2009; 1794: 375-397Crossref PubMed Scopus (529) Google Scholar, 5Roychaudhuri R. Yang M. Hoshi M.M. Teplow D.B. Amyloid β-protein assembly and Alzheimer disease.J. Biol. Chem. 2009; 284: 4749-4753Abstract Full Text Full Text PDF PubMed Scopus (533) Google Scholar, 6Bhak G. Choe Y.J. Paik S.R. Mechanism of amyloidogenesis: nucleation-dependent fibrillation versus double-concerted fibrillation.BMB Rep. 2009; 42: 541-551Crossref PubMed Scopus (68) Google Scholar). Several biophysical methods have been developed to measure the kinetics of protein aggregation “in vitro” (7Knowles T.P. Waudby C.A. Devlin G.L. Cohen S.I. Aguzzi A. Vendruscolo M. Terentjev E.M. Welland M.E. Dobson C.M. An analytical solution to the kinetics of breakable filament assembly.Science. 2009; 326: 1533-1537Crossref PubMed Scopus (818) Google Scholar, 8Nilsson M.R. Techniques to study amyloid fibril formation in vitro.Methods. 2004; 34: 151-160Crossref PubMed Scopus (759) Google Scholar, 9Bondos S.E. Methods for measuring protein aggregation.Curr. Anal. Chem. 2006; 2: 157-170Crossref Scopus (27) Google Scholar, 10Harper J.D. Lansbury P.T. Models of amyloid seeding in Alzheimer disease and scrapie: mechanistic truths and physiological consequences of the time-dependent solubility of amyloid proteins.Annu. Rev. Biochem. 1997; 66: 385-407Crossref PubMed Scopus (1412) Google Scholar, 11Frieden C. Protein aggregation processes: in search of the mechanism.Protein Sci. 2007; 16: 2334-2344Crossref PubMed Scopus (148) Google Scholar). Thioflavin-T binding fluorescence (12Naiki H. Higuchi K. Hosokawa M. Takeda T. Fluorometric determination of amyloid fibrils in vitro using the fluorescent dye, thioflavin T1.Anal. Biochem. 1989; 177: 244-249Crossref PubMed Scopus (988) Google Scholar) and turbidity measurements (13Jarrett J.T. Lansbury Jr., P.T. Amyloid fibril formation requires a chemically discriminating nucleation event: studies of an amyloidogenic sequence from the bacterial protein OsmB.Biochemistry. 1992; 31: 12345-12352Crossref PubMed Scopus (279) Google Scholar) are among the most widely adopted techniques. Despite the limitations of the classical methods (14Knowles T.P. Shu W. Devlin G.L. Meehan S. Auer S. Dobson C.M. Welland M.E. Kinetics and thermodynamics of amyloid formation from direct measurements of fluctuations in fibril mass.Proc. Natl. Acad. Sci. U.S.A. 2007; 104: 10016-10021Crossref PubMed Scopus (167) Google Scholar), they provide quantitative information about the mass increase of amyloid fibrils with time. Typically, the progress of fibrillization is expressed as the normalized fraction of amyloid protein converted into fibrils (α); on a mass basis, α corresponds to the quotient of the fibril mass increase Δm at a given instant divided by the total mass of fibrils formed at the end of the assay ΔmT. α=ΔmΔmT(Eq. 1) The time-course results represented in Fig. 1 exemplify well two types of kinetics usually observed during amyloid fibril formation. The sigmoidal α(t) trend obtained for β2-microglobulin (β2m) 2The abbreviations used are: β2mβ2-microglobulinCLMcrystallization-like modelM-TTRmonomeric transthyretin. (15Xue W.F. Homans S.W. Radford S.E. Systematic analysis of nucleation-dependent polymerization reveals new insights into the mechanism of amyloid self-assembly.Proc. Natl. Acad. Sci. U.S.A. 2008; 105: 8926-8931Crossref PubMed Scopus (367) Google Scholar) (open symbols) is characteristic of nucleation-dependent polymerization; an initial lag phase is followed by a phase of rapid growth and then by a stationary phase (16Naiki H. Hasegawa K. Yamaguchi I. Nakamura H. Gejyo F. Nakakuki K. Apolipoprotein E and antioxidants have different mechanisms of inhibiting Alzheimer β-amyloid fibril formation in vitro.Biochemistry. 1998; 37: 17882-17889Crossref PubMed Scopus (118) Google Scholar, 17Jarrett J.T. Lansbury Jr., P.T. Seeding “one-dimensional crystallization” of amyloid: a pathogenic mechanism in Alzheimer disease and scrapie?.Cell. 1993; 73: 1055-1058Abstract Full Text PDF PubMed Scopus (1918) Google Scholar). The hyperbolic shape obtained for transthyretin (closed symbols) is more frequently found during seeded aggregation, i.e. when an aliquot of solution containing preformed fibrils is added to the amyloidogenic solution to bypass the thermodynamically unfavorable nucleation step (8Nilsson M.R. Techniques to study amyloid fibril formation in vitro.Methods. 2004; 34: 151-160Crossref PubMed Scopus (759) Google Scholar, 17Jarrett J.T. Lansbury Jr., P.T. Seeding “one-dimensional crystallization” of amyloid: a pathogenic mechanism in Alzheimer disease and scrapie?.Cell. 1993; 73: 1055-1058Abstract Full Text PDF PubMed Scopus (1918) Google Scholar, 18Hurshman A.R. White J.T. Powers E.T. Kelly J.W. Transthyretin aggregation under partially denaturing conditions is a downhill polymerization.Biochemistry. 2004; 43: 7365-7381Crossref PubMed Scopus (287) Google Scholar). Nevertheless, as shown by this example, the absence of a lag phase is also reported for unseeded reactions (18Hurshman A.R. White J.T. Powers E.T. Kelly J.W. Transthyretin aggregation under partially denaturing conditions is a downhill polymerization.Biochemistry. 2004; 43: 7365-7381Crossref PubMed Scopus (287) Google Scholar, 19Naiki H. Gejyo F. Nakakuki K. Concentration-dependent inhibitory effects of apolipoprotein E on Alzheimer β-amyloid fibril formation in vitro.Biochemistry. 1997; 36: 6243-6250Crossref PubMed Scopus (98) Google Scholar). Between the classical sigmoidal kinetics, showing an inflection point at αi = 0.5, and the hyperbolic/seeded polymerization kinetics, showing no evident inflection point, there are a number of intermediate possibilities that have been comprehensively reviewed by Finke and co-workers (4Morris A.M. Watzky M.A. Finke R.G. Protein aggregation kinetics, mechanism, and curve-fitting: a review of the literature.Biochim. Biophys. Acta. 2009; 1794: 375-397Crossref PubMed Scopus (529) Google Scholar, 20Morris A.M. Watzky M.A. Agar J.N. Finke R.G. Fitting neurological protein aggregation kinetic data via a two-step, minimal/“Ockham's razor” model: the Finke-Watzky mechanism of nucleation followed by autocatalytic surface growth.Biochemistry. 2008; 47: 2413-2427Crossref PubMed Scopus (239) Google Scholar). As discussed in those reviews, the meaning of the different shapes has been interpreted over the last 50 years according to several thermodynamic and kinetic mechanisms. Given the complexity and variability of the protein aggregation models, a modular approach was recently proposed to systematically identify the mechanism that best describes nucleation (or prepolymerization), growth (or polymerization), and fragmentation steps (15Xue W.F. Homans S.W. Radford S.E. Systematic analysis of nucleation-dependent polymerization reveals new insights into the mechanism of amyloid self-assembly.Proc. Natl. Acad. Sci. U.S.A. 2008; 105: 8926-8931Crossref PubMed Scopus (367) Google Scholar). The available fundamental models are in general highly specific for the amyloid polypeptide under study. Models containing a high number of parameters cannot fit to experimental data in a unique way, whereas some of the theoretical elementary steps refer to time frames that are experimentally inaccessible. Overparameterization makes it hard to validate different parts of mechanistically elaborated models (21Schmidt H. Madsen M.F. Danø S. Cedersund G. Complexity reduction of biochemical rate expressions.Bioinformatics. 2008; 24: 848-854Crossref PubMed Scopus (32) Google Scholar), which is recognized as a problem in protein aggregation modeling (22Bernacki J.P. Murphy R.M. Model discrimination and mechanistic interpretation of kinetic data in protein aggregation studies.Biophys. J. 2009; 96: 2871-2887Abstract Full Text Full Text PDF PubMed Scopus (59) Google Scholar). In the pursuit of a consensual, two-parameter model for describing protein aggregation kinetics, the 1997 Finke-Watzky mechanism for transition-metal nanocluster formation (23Watzky M.A. Finke R.G. Transition metal nanocluster formation kinetic and mechanistic studies: a new mechanism when hydrogen is the reductant: slow, continuous nucleation and fast autocatalytic surface growth.J. Am. Chem. Soc. 1997; 119: 10382-10400Crossref Scopus (752) Google Scholar) was successfully applied to a wide range of kinetic data (4Morris A.M. Watzky M.A. Finke R.G. Protein aggregation kinetics, mechanism, and curve-fitting: a review of the literature.Biochim. Biophys. Acta. 2009; 1794: 375-397Crossref PubMed Scopus (529) Google Scholar, 20Morris A.M. Watzky M.A. Agar J.N. Finke R.G. Fitting neurological protein aggregation kinetic data via a two-step, minimal/“Ockham's razor” model: the Finke-Watzky mechanism of nucleation followed by autocatalytic surface growth.Biochemistry. 2008; 47: 2413-2427Crossref PubMed Scopus (239) Google Scholar). In the formulation of the Finke-Watzky model, slow continuous nucleation is followed by autocatalytic surface growth so that the overall rate of protein concentration decrease is given by -dCdt=k1C+k2C(C0-C)(Eq. 2) with k1 and k2 being, respectively, the nucleation and growth average rate constants. For an initial protein concentration C0, the solution of the ordinary differential equation can be expressed as C0-CC0=1-1+k1k2C1+k1k2C0exp{(1+k1k2C0)k2C0t}(Eq. 3) Note that the difference (C0 − C) corresponds, by mass balance, to the instantaneous concentration of protein aggregates (20Morris A.M. Watzky M.A. Agar J.N. Finke R.G. Fitting neurological protein aggregation kinetic data via a two-step, minimal/“Ockham's razor” model: the Finke-Watzky mechanism of nucleation followed by autocatalytic surface growth.Biochemistry. 2008; 47: 2413-2427Crossref PubMed Scopus (239) Google Scholar). The Finke-Watzky equation is interconvertible by algebraic manipulation into the Saitô and co-workers equation (24Kamihira M. Naito A. Tuzi S. Nosaka A.Y. Saitô H. Conformational transitions and fibrillation mechanism of human calcitonin as studied by high-resolution solid-state 13C NMR.Protein Sci. 2000; 9: 867-877Crossref PubMed Scopus (99) Google Scholar) and into the equation of Fernández et al. (25Fernández C.O. Hoyer W. Zweckstetter M. Jares-Erijman E.A. Subramaniam V. Griesinger C. Jovin T.M. NMR of α-synuclein-polyamine complexes elucidates the mechanism and kinetics of induced aggregation.EMBO J. 2004; 23: 2039-2046Crossref PubMed Scopus (209) Google Scholar), which, however, depart from different mechanistic assumptions (see supplemental Table S1). When the nucleation rates are very low (k1 → 0), Equation 2 reduces to the differential form of the logistic function, which is commonly used to fit sigmoidal aggregation data (4Morris A.M. Watzky M.A. Finke R.G. Protein aggregation kinetics, mechanism, and curve-fitting: a review of the literature.Biochim. Biophys. Acta. 2009; 1794: 375-397Crossref PubMed Scopus (529) Google Scholar, 16Naiki H. Hasegawa K. Yamaguchi I. Nakamura H. Gejyo F. Nakakuki K. Apolipoprotein E and antioxidants have different mechanisms of inhibiting Alzheimer β-amyloid fibril formation in vitro.Biochemistry. 1998; 37: 17882-17889Crossref PubMed Scopus (118) Google Scholar). Ferrone's equation (26Ferrone F. Analysis of protein aggregation kinetics.Methods Enzymol. 1999; 309: 256-274Crossref PubMed Scopus (470) Google Scholar) is another example of a two-parameter protein aggregation model available in literature that predicts the monomer concentration to decrease with the square of time. Although avoiding overparameterization, these models are very useful from a practical point of view, although some simplifying hypothesis adopted during their derivation may lack solid biophysical basis. For example, Saitô and co-workers (24Kamihira M. Naito A. Tuzi S. Nosaka A.Y. Saitô H. Conformational transitions and fibrillation mechanism of human calcitonin as studied by high-resolution solid-state 13C NMR.Protein Sci. 2000; 9: 867-877Crossref PubMed Scopus (99) Google Scholar) and Fernández et al. (25Fernández C.O. Hoyer W. Zweckstetter M. Jares-Erijman E.A. Subramaniam V. Griesinger C. Jovin T.M. NMR of α-synuclein-polyamine complexes elucidates the mechanism and kinetics of induced aggregation.EMBO J. 2004; 23: 2039-2046Crossref PubMed Scopus (209) Google Scholar) describe elementary kinetic steps by reaction-like rate equations that are first-order in relation to the fractional conversion of monomers into fibrils expressed as α and/or (1 − α). In an alternative formalism, Finke and co-workers consider (4Morris A.M. Watzky M.A. Finke R.G. Protein aggregation kinetics, mechanism, and curve-fitting: a review of the literature.Biochim. Biophys. Acta. 2009; 1794: 375-397Crossref PubMed Scopus (529) Google Scholar, 27Watzky M.A. Morris A.M. Ross E.D. Finke R.G. Fitting yeast and mammalian prion aggregation kinetic data with the Finke-Watzky two-step model of nucleation and autocatalytic growth.Biochemistry. 2008; 47: 10790-10800Crossref PubMed Scopus (71) Google Scholar) the fibrillar state as the autocatalytic, polymeric form of the protein and express the elementary rate laws as a function of the protein concentrations in the solubilized and aggregated forms. Although theoretically more appropriate, the Finke-Watzky formalism results in the paradox that according to Equation 2, all the dissolved protein is expected to convert into fibrils, i.e. the expected steady-state concentration is C∞ = 0. This is not possible in the light of the general phase equilibrium condition and is not supported by measurements of dissolved protein concentration after long incubation times (18Hurshman A.R. White J.T. Powers E.T. Kelly J.W. Transthyretin aggregation under partially denaturing conditions is a downhill polymerization.Biochemistry. 2004; 43: 7365-7381Crossref PubMed Scopus (287) Google Scholar, 28Sluzky V. Tamada J.A. Klibanov A.M. Langer R. Kinetics of insulin aggregation in aqueous solutions upon agitation in the presence of hydrophobic surfaces.Proc. Natl. Acad. Sci. U.S.A. 1991; 88: 9377-9381Crossref PubMed Scopus (454) Google Scholar, 29O'Nuallain B. Shivaprasad S. Kheterpal I. Wetzel R. Thermodynamics of Aβ(1–40) amyloid fibril elongation.Biochemistry. 2005; 44: 12709-12718Crossref PubMed Scopus (191) Google Scholar). Finally, the applicability of Ferrone's quadratic equation is inherently limited to the early data points corresponding to ∼10–20% of total monomer loss (22Bernacki J.P. Murphy R.M. Model discrimination and mechanistic interpretation of kinetic data in protein aggregation studies.Biophys. J. 2009; 96: 2871-2887Abstract Full Text Full Text PDF PubMed Scopus (59) Google Scholar). β2-microglobulin crystallization-like model monomeric transthyretin. Kinetic modeling of amyloid fibrillization reactions has also been performed using empirical equations such as linear and exponential decay functions (30Hasegawa K. Ono K. Yamada M. Naiki H. Kinetic modeling and determination of reaction constants of Alzheimer β-amyloid fibril extension and dissociation using surface plasmon resonance.Biochemistry. 2002; 41: 13489-13498Crossref PubMed Scopus (110) Google Scholar). As recently pointed out by Auer and Kashchiev (31Auer S. Kashchiev D. Insight into the correlation between lag time and aggregation rate in the kinetics of protein aggregation.Proteins. 2010; 78: 2412-2416Crossref PubMed Scopus (26) Google Scholar) while discussing the applicability of the Avrami equation, it does not seem coincidental that such mathematically simple models are able to describe the α(t) dependence for a wide range of polypeptides and amyloidogenic conditions. With the present contribution, we seek the general principle that seems to govern the kinetics of protein aggregation. We intend to do it in a theoretically consistent way that does not compromise the final simplicity of the model nor its quantitative usefulness. An infinite number of parameter combinations producing equally good agreement with the data should be avoided; that is to say, all the dynamic state variables shall be condensed in a two-parameter model that can be uniquely fit to protein aggregation kinetics. Then, the deepest meaning of each constant should be possible to be determined by using different types of experimental data. For this mechanistic refinement to be possible, oversimplified hypothesis such as those identified in our literature survey should also be avoided during the derivation of the model. Resemblances between amyloid fibril formation and protein crystallization have long been recognized (17Jarrett J.T. Lansbury Jr., P.T. Seeding “one-dimensional crystallization” of amyloid: a pathogenic mechanism in Alzheimer disease and scrapie?.Cell. 1993; 73: 1055-1058Abstract Full Text PDF PubMed Scopus (1918) Google Scholar). Both processes involve the thermodynamic equilibrium between phases, an initial assembly of macromolecules into stable nuclei (nucleation step), and the subsequent formation of supramolecular structures by the successive addition of growth units (growth or elongation step). We propose now to quantitatively describe the aggregation kinetics of amyloid proteins using fundamental principles that are familiar to crystal growth scientists. We will start by defining the thermodynamic driving force for amyloid fibril formation as the variation in chemical potential Δμ occurring when protein molecules in a supersaturated amyloid solution at temperature T are transferred to a fibrillar state Δμ=kTlnaa*(Eq. 4) where k is the Boltzmann constant and a and a* are the activities of supersaturated and saturated amyloid solutions. This is analogous to the definition of supersaturation adopted in crystallization from solution (32Markov I.V. Crystal Growth for Begginers. 2nd Ed. World Scientific Publishing, Singapore2003Crossref Google Scholar). Accurate activity coefficients are difficult to obtain for highly nonideal concentrated solutions. For this reason, and for mathematical simplicity, we will define an approximate amyloid supersaturation σ as a function of protein concentration C and protein solubility C* σ=C-C*C*(Eq. 5) The protein solubility corresponds to the concentration of dissolved protein that equilibrates the chemical potential of the insoluble fibrillar phase. In principle, C* is independent of the initial protein concentration and can be obtained from the remaining concentration of the polypeptide in solution after long reaction times (18Hurshman A.R. White J.T. Powers E.T. Kelly J.W. Transthyretin aggregation under partially denaturing conditions is a downhill polymerization.Biochemistry. 2004; 43: 7365-7381Crossref PubMed Scopus (287) Google Scholar). Nevertheless, when measuring protein aggregation in the presence of high macromolecular content (“macromolecular crowding”), volume-excluding effects may lead to different protein concentrations in equilibrium (33Minton A.P. Implications of macromolecular crowding for protein assembly.Curr. Opin. Struct. Biol. 2000; 10: 34-39Crossref PubMed Scopus (552) Google Scholar). We will return to this issue while discussing possible deviations from the CLM. The total amount of aggregates produced per unit of volume of solution ΔmT/V is given by the difference between the mass concentrations C0 and C*. Equation 5 can thus be rewritten to express amyloid supersaturation as a function of the fraction of protein converted into amyloid aggregates (α) and of the initial supersaturation (σ0). σ=(C0-C*)-(C0-C)C*=ΔmTVC*(1-α)=σ0(1-α)(Eq. 6) The mechanism leading to the formation of amyloid nuclei generally includes conformational changes of the native state (34Chiti F. Dobson C.M. Amyloid formation by globular proteins under native conditions.Nat. Chem. Biol. 2009; 5: 15-22Crossref PubMed Scopus (680) Google Scholar) and different intermediate structures such as polymorphous and oligomeric aggregates (35Stöhr J. Weinmann N. Wille H. Kaimann T. Nagel-Steger L. Birkmann E. Panza G. Prusiner S.B. Eigen M. Riesner D. Mechanisms of prion protein assembly into amyloid.Proc. Natl. Acad. Sci. U.S.A. 2008; 105: 2409-2414Crossref PubMed Scopus (114) Google Scholar, 36Bhak G. Lee J.H. Hahn J.S. Paik S.R. Granular assembly of α-synuclein leading to the accelerated amyloid fibril formation with shear stress.PLoS ONE. 2009; 4: e4177Crossref PubMed Scopus (50) Google Scholar), whose nature and importance vary from protein to protein (4Morris A.M. Watzky M.A. Finke R.G. Protein aggregation kinetics, mechanism, and curve-fitting: a review of the literature.Biochim. Biophys. Acta. 2009; 1794: 375-397Crossref PubMed Scopus (529) Google Scholar, 15Xue W.F. Homans S.W. Radford S.E. Systematic analysis of nucleation-dependent polymerization reveals new insights into the mechanism of amyloid self-assembly.Proc. Natl. Acad. Sci. U.S.A. 2008; 105: 8926-8931Crossref PubMed Scopus (367) Google Scholar). Although all of the transitions involve energy barriers of different magnitudes, we will consider that the rate-limiting step is the formation of a critical-sized amyloid nucleus. This postulation finds support in the well known fact that the addition of preformed fibrils to amyloidogenic solutions (seeding) completely eliminates the lag phase and induces immediate fibril formation. Classical nucleation theory (37Kashchiev D. Nucleation: Basic Theory with Applications. Butterworth-Heinemann, Oxford2000Google Scholar, 38Kashchiev D. Auer S. Nucleation of amyloid fibrils.J. Chem. Phys. 2010; 132: 215101Crossref PubMed Scopus (71) Google Scholar), based on which numerous phase transition phenomena occurring in nature and technology have been explained (39Zhang T.H. Liu X.Y. Nucleation: what happens at the initial stage?.Angew. Chem. Int. Ed. Engl. 2009; 48: 1308-1312Crossref PubMed Scopus (104) Google Scholar), will be used to estimate the frequency at which new fibrils are created. It is admitted that fluctuations in phase density give rise to the appearance of embryonic formations or nuclei that reduce the bulk free energy (due to the variation in chemical potential Δμ) and increase the surface free energy (due to the creation of a fibril/solution interface). Above a critical nucleus size, the process spontaneously evolves in the direction of amyloid fibril formation. Recently (38Kashchiev D. Auer S. Nucleation of amyloid fibrils.J. Chem. Phys. 2010; 132: 215101Crossref PubMed Scopus (71) Google Scholar), the following expression was proposed for the critical number of monomeric peptides constituting the amyloid nucleus n*=vΔμ2+1(Eq. 7) where ν is a constant accounting for the dimensions and interfacial energies of the nanosized fibril. In the same work, the nucleation rate J was expressed as a complex function of the thermodynamic driving force for amyloid fibril formation (38Kashchiev D. Auer S. Nucleation of amyloid fibrils.J. Chem. Phys. 2010; 132: 215101Crossref PubMed Scopus (71) Google Scholar). We will adopt a simplified version of this relationship that takes into account the very high supersaturation levels associated with amyloidogenic conditions (18Hurshman A.R. White J.T. Powers E.T. Kelly J.W. Transthyretin aggregation under partially denaturing conditions is a downhill polymerization.Biochemistry. 2004; 43: 7365-7381Crossref PubMed Scopus (287) Google Scholar, 28Sluzky V. Tamada J.A. Klibanov A.M. Langer R. Kinetics of insulin aggregation in aqueous solutions upon agitation in the presence of hydrophobic surfaces.Proc. Natl. Acad. Sci. U.S.A. 1991; 88: 9377-9381Crossref PubMed Scopus (454) Google Scholar, 29O'Nuallain B. Shivaprasad S. Kheterpal I. Wetzel R. Thermodynamics of Aβ(1–40) amyloid fibril elongation.Biochemistry. 2005; 44: 12709-12718Crossref PubMed Scopus (191) Google Scholar). For C/C* ratios much higher than 10, the equilibrium concentration of fibril nuclei is expected to increase linearly with C, greatly simplifying the expression of J to a second-order rate equation J≅Aσ2(Eq. 8) with A being a σ-independent kinetic factor expressed in units of frequency per solution volume. During this step, preformed fibrils grow by the successive addition of new structural units. Due to the existence of a preliminary fibril template, the growth (or elongation) step is thermodynamically favored over nucleation; although both processes co-exist during the early phases of incubation (16Naiki H. Hasegawa K. Yamaguchi I. Nakamura H. Gejyo F. Nakakuki K. Apolipoprotein E and antioxidants have different mechanisms of inhibiting Alzheimer β-amyloid fibril formation in vitro.Biochemistry. 1998; 37: 17882-17889Crossref PubMed Scopus (118) Google Scholar), fibril elongation is expected to become increasingly predominant (40Padrick S.B. Miranker A.D. Islet amyloid: phase partitioning and secondary nucleation are central to the mechanism of fibrillogenesis.Biochemistry. 2002; 41: 4694-4703Crossref PubMed Scopus (285) Google Scholar). Advanced microscopy techniques show indefinite evidences of unidirectional (41Heldt C.L. Zhang S. Belfort G. Asymmetric amyloid fibril elongation: a new perspective on a symmetric world.Proteins. 2011; 79: 92-98Crossref PubMed Scopus (21) Google Scholar, 42Ban T. Goto Y. Direct observation of amyloid growth monitored by total internal reflection fluorescence microscopy.Methods Enzymol. 2006; 413: 91-102Crossref PubMed Scopus (42) Google Scholar, 43Collins S.R. Douglass A. Vale R.D. Weissman J.S. Mechanism of prion propagation: amyloid growth occurs by monomer addition.PLoS Biol. 2004; 2: e321Crossref PubMed Scopus (420) Google Scholar, 44Patil S.M. Mehta A. Jha S. Alexandrescu A.T. 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• W2012591531 created "2016-06-24" @default.
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• W2012591531 date "2012-08-01" @default.
• W2012591531 modified "2023-10-01" @default.
• W2012591531 title "A Generic Crystallization-like Model That Describes the Kinetics of Amyloid Fibril Formation" @default.
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