Formation of new amyloid fibrils and oligomers from monomeric protein on the surfaces of existing fibrils is an important driver of many disorders such as Alzheimer's and Parkinson's diseases. The structural basis of this secondary nucleation process, however, is poorly understood. Here, we ask whether secondary nucleation sites are found predominantly at rare growth defects: irregularities in the fibril core structure incorporated during their original assembly. We first demonstrate using the specific inhibitor of secondary nucleation, Brichos, that secondary nucleation sites on Alzheimer's disease-associated fibrils composed of Aβ40 and Aβ42 peptides are rare compared to the number of protein molecules they contain. We then grow Aβ40 fibrils under conditions designed to eliminate most growth defects while leaving the regular fibril morphology unchanged, and confirm the latter using cryo-electron microscopy. We measure both the ability of these annealed fibrils to promote secondary nucleation and the stoichiometry of their secondary nucleation sites, finding that both are greatly reduced as predicted. Re-analysis of published data for other proteins suggests that fibril growth defects may also drive secondary nucleation generally across most amyloids. These findings could unlock structure-based drug design of therapeutics that aim to halt amyloid disorders by inhibiting secondary nucleation sites.

“Seeding” is the addition of preformed fibrils to a solution of monomeric protein to accelerate its aggregation into new fibrils. It is a versatile and widely-used tool for scientists studying protein aggregation kinetics, as it enables the isolation and separate study of discrete reaction steps contributing to protein aggregation, specifically elongation and secondary nucleation. However, the seeding levels required to achieve dominating effects on each of these steps separately have been established largely by trial-and-error, due in part to the lack of availability of integrated rate laws valid for moderate to high seeding levels and generally applicable to all common underlying reaction mechanisms. Here, we improve on a recently developed mathematical method based on Lie symmetries for solving differential equations, and with it derive such an integrated rate law. We subsequently develop simple expressions for the amounts of seed required to isolate each step. We rationalize the empirical observation that fibril seeds must often be broken up into small pieces to successfully isolate elongation. We also derive expressions for average fibril lengths at different times in the aggregation reaction, and explore different methods to break up fibrils. This paper will provide an invaluable reference for future experimental and theoretical studies in which seeding techniques are employed, and should enable more sophisticated analyses than have been performed to date.

Analyzing kinetic experiments on protein aggregation using integrated rate laws has led to numerous advances in our understanding of the fundamental chemical mechanisms behind amyloidogenic disorders such as Alzheimer's and Parkinson's diseases. However, the description of biologically relevant processes may require rate equations that are too complex to solve using existing methods, hindering mechanistic insights into these processes. An example of significance is coaggregation in environments containing multiple amyloid-beta (Aβ) peptide alloforms, which may play a crucial role in the biochemistry of Alzheimer's disease but whose mechanism is still poorly understood. Here, we use the mathematics of Lie symmetry to derive a general integrated rate law valid for most plausible linear self-assembly reactions. We use it in conjunction with experimental data to determine the mechanism of coaggregation of the most physiologically abundant Aβ alloforms: Aβ42, Aβ40, Aβ38 and Aβ37 peptides. We find that Aβ42 fibril surfaces catalyze the formation of co-oligomers, which accelerate new Aβ40, Aβ38 and Aβ37 fibril formation whilst inhibiting secondary nucleation of new Aβ42 fibrils. The simplicity, accuracy and broad applicability of our general integrated rate law will enable kinetic analysis of more complex filamentous self-assembly reactions, both with and without coaggregation.

Biomolecular condensates are central to cellular physiology, yet their pathological aging into fibrillar aggregates underlies neurodegenerative diseases such as ALS and other disorders of protein aggregation. Yet, this process remains poorly understood and is typically assumed to be a slow and passive process. Here, we show that one of the simplest building blocks of life, Adenosine 5'-triphosphate (ATP), can form condensates that undergo rapid aging in macromolecularly crowded environments, transforming from liquid droplets to urchin-like fibrillar aggregates. Using experiments and theory, we report a suite of previously unrecognized mechanisms of fibril aggregation from droplets, including wetting-induced engulfment, self-organized flows within condensates and directed droplet swimming (dialytaxis). These behaviors originate from Marangoni flows triggered by ATP fibrillization, which accelerate aging dynamics and demonstrate that condensate aging is an active process. These findings uncover fundamental physical principles underlying condensate aging and offer broadly relevant insights into neurodegenerative diseases, bio-inspired material engineering, and soft matter physics.

Hysteresis — the dependence of a system’s state on its history — is functionally exploited in biology to achieve robustness and memory, for example in cell cycle commitment, ion channel gating, and enzyme regulation. Here we show that hysteresis naturally emerges in reversible amyloid formation, establishing a physicochemical basis for information storage at the molecular level. Using pH-induced reversible amyloid formation by pyruvate kinase M2 (PKM2) as a model, we demonstrate that hysteresis arises from the distinct pathways of aggregation and disaggregation: as with most amyloids, metastable intermediates are required for nucleation but bypassed during disassembly. In the PKM2 system the solubilities of intermediates and fibrils are affected differently by the protonation-dependent charge of the amyloid core. Mutations that alter this charge profile shift the hysteresis window in predictable ways, illustrating how the phenomenon can be rationally tuned. Our results provide a mechanistic framework for hysteresis in protein self-assembly and identify reversible amyloids as a new class of memory-encoding molecular systems.

Aberrant aggregates of the 42-residue form of the amyloid-β peptide (Aβ 42 ) are cytotoxic in Alzheimer’s disease (AD). Cost-effective and chronically safe disease-modifying therapeutics are needed to address the AD medical emergency worldwide. To increase our understanding of the mechanisms of Aβ 42 -induced cytotoxicity and to investigate clinically relevant aminosterols, we study the impact of claramine on the aggregation kinetics and properties of Aβ 42 aggregates, as well as the ability of these proteotoxic species to bind and disrupt cell membranes. Whereas previously studied aminosterols accelerated Aβ 42 aggregation, we show that claramine potently inhibits Aβ 42 amyloid fibril formation. We find that claramine stabilizes soluble Aβ 42 , speeding up primary and secondary nucleation into species with antiparallel β-sheet structure that are elongation incompetent, thereby depleting Aβ 42 monomers from the aggregation reaction. This steroid–polyamine also dissociates Aβ 42 fibrillar aggregates, resulting in the abrogation of the autocatalytic capacity of Aβ 42 fibrils, and it also inhibits the aggregation of a tau fragment relevant to AD. Upon exposure of human neuroblastoma cells to stabilized Aβ 42 oligomers, claramine effectively neutralized Aβ 42 oligomer-induced cytotoxicity by preventing their binding to cell membranes. Owing to the unique mechanism of action of aminosterols to reduce the toxicity of soluble Aβ 42 aggregates by protecting cell membranes, and the newly characterized ability of claramine to inhibit Aβ 42 fibril formation and dissociate fibrillar Aβ 42 resulting in the interruption of the positive feedback loop in Aβ 42 aggregation, our findings further emphasize the relevance of this family of natural products as potential treatments for AD and other protein misfolding diseases.

Perturbation theory plays a central role in the approximate solution of nonlinear differential equations. The resultant series expansions are usually divergent and require treatment by singular perturbation methods to generate uniformly valid solutions. However, applying these methods is a subtle art owing to the lack of globally applicable algorithms. Inspired by the fact that all exact solutions of differential equations are consequences of (Lie) symmetries, we reformulate perturbation theory for differential equations in terms of approximate symmetries, via expansions of the Lie symmetries of the solutions. This is a change in perspective from the usual method for obtaining series expansions of the solutions themselves. We show that these approximate symmetries are straightforward to calculate and are never singular; their integration is therefore a powerful way of constructing uniformly convergent solutions. This geometric viewpoint naturally implies that several key singular perturbation methods such as the general perturbative RG-inspired approach of Chen, Goldenfeld and Oono (CGO RG), the method of multiple scales (MMS), and the Poincare-Lindstedt method (PLM), exploit a fundamental class of approximate symmetries that we term “hidden scale symmetries”. In turn, this clarifies when and why these methods succeed and just as importantly, when they fail. Our algorithmic method directly identifies and integrates these hidden scale symmetries, making it often simpler to implement, and permitting solution of problems where other methods are impractical. Finally, we show how other kinds of approximate symmetry can be exploited to solve systems that do not possess integrable hidden scale symmetries.

Low-molecular-weight oligomers formed from amyloidogenic peptides and proteins have been identified as key cytotoxins across a range of neurodegenerative disorders, including Alzheimer's disease and Parkinson's disease. Developing therapeutic strategies that target oligomers is therefore emerging as a promising approach for combating protein misfolding diseases. As such, there is a great need to understand the fundamental properties, dynamics, and mechanisms associated with oligomer formation. In this review, we discuss how chemical kinetics provides a powerful tool for studying these systems. We review the chemical kinetics approach to determining the underlying molecular pathways of protein aggregation and discuss its applications to oligomer formation and dynamics. We discuss how this approach can reveal detailed mechanisms of primary and secondary oligomer formation, including the role of interfaces in these processes. We further use this framework to describe the processes of oligomer conversion and dissociation, and highlight the distinction between on-pathway and off-pathway oligomers. Furthermore, we showcase on the basis of experimental data the diversity of pathways leading to oligomer formation in various in vitro and in silico systems. Finally, using the lens of the chemical kinetics framework, we look at the current oligomer inhibitor strategies both in vitro and in vivo.

The aggregation of α -synuclein into amyloid fibrils is a hallmark of Parkinson’s disease. This process has been shown to directly involve interactions between proteins and lipid surfaces when the latter are present. Despite this importance, the molecular mechanisms of lipid-induced amyloid aggregation have remained largely elusive. Here, we present a global kinetic model to describe lipid-induced amyloid aggregation of α -synuclein. Using this framework, we find that α -synuclein fibrils form via a two-step primary nucleation mechanism and that lipid molecules are directly involved in both the nucleation and fibril elongation steps, giving rise to lipid–protein coaggregates. To illustrate the applicability of this kinetic approach to drug discovery, we identify the mechanism of action of squalamine, a known inhibitor of lipid-induced α -synuclein aggregation, revealing that this small molecule reduces the rate of lipid-dependent primary nucleation. Our work will likely guide the rational design of α -synuclein aggregation inhibitors.

Oligomeric assemblies consisting of only a few protein subunits are key species in the cytotoxicity of neurodegenerative disorders, such as Alzheimer's and Parkinson's diseases. Their lifetime in solution and abundance, governed by the balance of their sources and sinks, are thus important determinants of disease. While significant advances have been made in elucidating the processes that govern oligomer production, the mechanisms behind their dissociation are still poorly understood. Here, we use chemical kinetic modeling to determine the fate of oligomers formed in vitro and discuss the implications for their abundance in vivo. We discover that oligomeric species formed predominantly on fibril surfaces, a broad class which includes the bulk of oligomers formed by the key Alzheimer's disease-associated Aβ peptides, also dissociate overwhelmingly on fibril surfaces, not in solution as had previously been assumed. We monitor this "secondary nucleation in reverse" by measuring the dissociation of Aβ42 oligomers in the presence and absence of fibrils via two distinct experimental methods. Our findings imply that drugs that bind fibril surfaces to inhibit oligomer formation may also inhibit their dissociation, with important implications for rational design of therapeutic strategies for Alzheimer's and other amyloid diseases.

Functional amyloids formed by the protein FapC in Pseudomonas bacteria are key structural components of Pseudomonas biofilms, which mediate chronic infections and also contribute to antimicrobial resistance. Here, we combine kinetic experiments with mechanistic modelling to probe the role of surfaces in FapC functional amyloid formation. We find that nucleation of new fibrils is predominantly heterogeneous in vitro, being catalysed by reaction vessel walls but not by the air/water interface. Removal of such interfaces by using microdroplets greatly slows heterogeneous nucleation and reveals a hitherto undetected fibril surface-catalysed "secondary nucleation" reaction step. We tune the degree of catalysis by varying the interface chemistry of the reaction vessel and by adding nanoparticles with tailored surface properties that catalyse fibril nucleation. In so doing, we discover that the rate of nucleation is controlled predominantly by the strength with which FapC binds to the catalytic sites on the interface, and by its surface area. Surprisingly, neither primary nucleation rate nor catalytic site binding strength appear closely correlated to the charge and hydrophilicity of the interface. This indicates the importance of considering experimental design in terms of surface chemistry of the reaction container while also highlighting the notion that fibril nucleation during protein aggregation is a heterogeneous process. Fibril nucleation during protein aggregation is a heterogeneous process highly dependent on the surfaces present during the process.

We develop a new mathematical model to describe the kinetics of protein aggregation under conditions when aggregation-prone protein is being produced during the aggregation.

Shear forces affect self-assembly processes ranging from crystallization to fiber formation. Here, the effect of mild agitation on amyloid fibril formation was explored for four peptides and investigated in detail for A β 42, which is associated with Alzheimer’s disease. To gain mechanistic insights into the effect of mild agitation, nonseeded and seeded aggregation reactions were set up at various peptide concentrations with and without an inhibitor. First, an effect on fibril fragmentation was excluded by comparing the monomer-concentration dependence of aggregation kinetics under idle and agitated conditions. Second, using a secondary nucleation inhibitor, Brichos, the agitation effect on primary nucleation was decoupled from secondary nucleation. Third, an effect on secondary nucleation was established in the absence of inhibitor. Fourth, an effect on elongation was excluded by comparing the seeding potency of fibrils formed under idle or agitated conditions. We find that both primary and secondary nucleation steps are accelerated by gentle agitation. The increased shear forces facilitate both the detachment of newly formed aggregates from catalytic surfaces and the rate at which molecules are transported in the bulk solution to encounter nucleation sites on the fibril and other surfaces. Ultrastructural evidence obtained with cryogenic transmission electron microscopy and free-flow electrophoresis in microfluidics devices imply that agitation speeds up the detachment of nucleated species from the fibril surface. Our findings shed light on the aggregation mechanism and the role of detachment for efficient secondary nucleation. The results inform on how to modulate the relative importance of different microscopic steps in drug discovery and investigations.

Oligomeric species arising during the aggregation of α-synuclein are implicated as a major source of toxicity in Parkinson's disease, and thus a major potential drug target. However, both their mechanism of formation and role in aggregation are largely unresolved. Here we show that, at physiological pH and in the absence of lipid membranes, α-synuclein aggregates form by secondary nucleation, rather than simple primary nucleation, and that this process is enhanced by agitation. Moreover, using a combination of single molecule and bulk level techniques, we identify secondary nucleation on the surfaces of existing fibrils, rather than formation directly from monomers, as the dominant source of oligomers. Our results highlight secondary nucleation as not only the key source of oligomers, but also the main mechanism of aggregate formation, and show that these processes take place under conditions which recapitulate the neutral pH and ionic strength of the cytosol.

Lipids are an important factor in the disease-associated aggregation of α-synuclein. Here we develop a kinetic model that allows the determination of mechanistic details and rate constants of this process.

Full understanding of proteostasis and energy utilization in cells will require knowledge of the fraction of cell proteins being degraded with different half-lives and their rates of synthesis. We therefore developed a method to determine such information that combines mathematical analysis of protein degradation kinetics obtained in pulse-chase experiments with Bayesian data fitting using the maximum entropy principle. This approach will enable rapid analyses of whole-cell protein dynamics in different cell types, physiological states, and neurodegenerative disease. Using it, we obtained surprising insights about protein stabilities in cultured cells normally and upon activation of proteolysis by mTOR inhibition and increasing cAMP or cGMP. It revealed that >90% of protein content in dividing mammalian cell lines is long-lived, with half-lives of 24 to 200 h, and therefore comprises much of the proteins in daughter cells. The well-studied short-lived proteins (half-lives < 10 h) together comprise <2% of cell protein mass, but surprisingly account for 10 to 20% of measurable newly synthesized protein mass. Evolution thus appears to have minimized intracellular proteolysis except to rapidly eliminate misfolded and regulatory proteins.

The self-assembly of the amyloid beta 42 (A beta 42) peptide is linked to Alzheimer's disease, and oligomeric intermediates are linked to neuronal cell death during the pathology of the disease. These oligomers are produced prolifically during secondary nucleation, by which the aggregation of monomers is catalyzed on fibril surfaces. Significant progress has been made in understanding the aggregation mechanism of A beta 42; still, a detailed molecular-level understanding of secondary nucleation is lacking. Here, we explore the role of four hydrophobic residues on the unstructured N-terminal region of A beta 42 in secondary nucleation. We create eight mutants with single Secondary nuclestion at flexible Nrernenal region Secondary nucleation at the WM core substitutions at one of the four positions-Ala2, Phe4, Tyr10, and Val12-to decrease the hydrophobicity at respective positions (A2T, A2S, F4A, F4S, Y10A, Y10S, V12A, and V12S) and one mutant (Y10F) to remove the polar nature of Tyr10. Kinetic analyses of aggregation data reveal that the hydrophobicity at the Nterminal region of A beta 42, especially at positions 10 and 12, affects the rate of fibril mass generated via secondary nucleation. Cryoelectron micrographs reveal that most of the mutants with lower hydrophobicity form fibrils that are markedly longer than WT A beta 42, in line with the reduced secondary nucleation rates for these peptides. The dominance of secondary nucleation, however, is still retained in the aggregation mechanism of these mutants because the rate of primary nucleation is even more reduced. This highlights that secondary nucleation is a general phenomenon that is not dependent on any one particular feature of the peptide and is rather robust to sequence perturbations.

Protein self-assembly into amyloid fibrils underlies several neurodegenerative conditions, including Alzheimer's and Parkinson's diseases. It has become apparent that the small oligomers formed during this process constitute neurotoxic molecular species associated with amyloid aggregation. Targeting the formation of oligomers represents, therefore, a possible therapeutic avenue to combat these diseases. However, it remains challenging to establish which microscopic steps should be targeted to suppress most effectively the generation of oligomeric aggregates. Recently, we have developed a kinetic model of oligomer dynamics during amyloid aggregation. Here, we use this approach to derive explicit scaling relationships that reveal how key features of the time evolution of oligomers, including oligomer peak concentration and lifetime, are controlled by the different rate parameters. We discuss the therapeutic implications of our framework by predicting changes in oligomer concentrations when the rates of the individual microscopic events are varied. Our results identify the kinetic parameters that control most effectively the generation of oligomers, thus opening a new path for the systematic rational design of therapeutic strategies against amyloid-related diseases.

The pathology of Alzheimer's disease is connected to the aggregation of β-amyloid (Aβ) peptide, which in vivo exists as a number of length-variants. Truncations and extensions are found at both the N- and C-termini, relative to the most commonly studied 40- and 42-residue alloforms. Here, we investigate the aggregation of two physiologically abundant alloforms, Aβ37 and Aβ38, as pure peptides and in mixtures with Aβ40 and Aβ42. A variety of molar ratios were applied in quaternary mixtures to investigate whether a certain ratio is maximally inhibiting of the more toxic alloform Aβ42. Through kinetic analysis, we show that both Aβ37 and Aβ38 self-assemble through an autocatalytic secondary nucleation reaction to form fibrillar β-sheet-rich aggregates, albeit on a longer timescale than Aβ40 or Aβ42. Additionally, we show that the shorter alloforms co-aggregate with Aβ40, affecting both the kinetics of aggregation and the resulting fibrillar ultrastructure. In contrast, neither Aβ37 nor Aβ38 forms co-aggregates with Aβ42; however, both short alloforms reduce the rate of Aβ42 aggregation in a concentration-dependent manner. Finally, we show that the aggregation of Aβ42 is more significantly impeded by a combination of Aβ37, Aβ38, and Aβ40 than by any of these alloforms independently. These results demonstrate that the aggregation of any given Aβ alloform is significantly perturbed by the presence of other alloforms, particularly in heterogeneous mixtures, such as is found in the extracellular fluid of the brain.

Knowledge of the mechanisms of assembly of amyloid proteins into aggregates is of central importance in building an understanding of neurodegenerative disease. Given that oligomeric intermediates formed during the aggregation reaction are believed to be the major toxic species, methods to track such intermediates are clearly needed. Here we present a method, electron paramagnetic resonance (EPR), by which the amount of intermediates can be measured over the course of the aggregation, directly in the reacting solution, without the need for separation. We use this approach to investigate the aggregation of α-synuclein (αS), a synaptic protein implicated in Parkinson’s disease and find a large population of oligomeric species. Our results show that these are primary oligomers, formed directly from monomeric species, rather than oligomers formed by secondary nucleation processes, and that they are short-lived, the majority of them dissociates rather than converts to fibrils. As demonstrated here, EPR offers the means to detect such short-lived intermediate species directly in situ. As it relies only on the change in size of the detected species, it will be applicable to a wide range of self-assembling systems, making accessible the kinetics of intermediates and thus allowing the determination of their rates of formation and conversion, key processes in the self-assembly reaction.