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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.

Phase transitions are important to understand cell dynamics, and the maturation of liquid droplets is relevant to neurodegenerative disorders. We combined NMR and Raman spectroscopies with microscopy to follow, over a period of days to months, droplet maturation of the protein fused in sarcoma (FUS). Our study reveals that the surface of the droplets plays a critical role in this process, while RNA binding prevents it. The maturation kinetics are faster in an agarose-stabilized biphasic sample compared with a monophasic condensed sample, owing to the larger surface-to-volume ratio. In addition, Raman spectroscopy reports structural differences upon maturation between the inside and the surface of droplets, which is comprised of β-sheet content, as revealed by solid-state NMR. In agreement with these observations, a solid crust-like shell is observed at the surface using microaspiration. Ultimately, matured droplets were converted into fibrils involving the prion-like domain as well as the first RGG motif., (© 2024. The Author(s).)

We present a theoretical analysis of phase-separated compartments to facilitate enzymatic chemical reactions. While phase separation can facilitate reactions by increasing local concentration, it can also hinder the mobility of reactants. In particular, we find that the attractive interactions that concentrate reactants within the dense phase can inhibit reactions by lowering the mobility of the reactants. This mobility loss severely limits the potential to enhance reaction rates. Phase separation provides greater benefit in situations where multiple sequential reactions occur and/or high order reactions, provided the enzymes are unsaturated, transport to the condensate is not limiting, and the reactants are mobile. We show that mobility can be maintained if recruitment to the condensed phase is driven by multiple attractive moieties that can bind and release independently. However, the spacers necessary to ensure independence between stickers are prone to entangle with the dense phase scaffold. We find an optimal sticker affinity that balances the need for rapid binding/unbinding kinetics and minimal entanglement. Reaction rates can be accelerated by shrinking the size of the dense phase with a corresponding increase in the number of stickers. Our results showcase the potential capabilities of phase-separated compartments to act as biochemical reaction crucibles within living cells.

The central hallmark of Parkinson's disease pathology is the aggregation of the α-synuclein protein, which, in its healthy form, is associated with lipid membranes. Purified monomeric α-synuclein is relatively stable in vitro , but its aggregation can be triggered by the presence of lipid vesicles. Despite this central importance of lipids in the context of α-synuclein aggregation, their detailed mechanistic role in this process has not been established to date. Here, we use chemical kinetics to develop a mechanistic model that is able to globally describe the aggregation behaviour of α-synuclein in the presence of DMPS lipid vesicles, across a range of lipid and protein concentrations. Through the application of our kinetic model to experimental data, we find that the reaction is a co-aggregation process involving both protein and lipids and that lipids promote aggregation as much by enabling fibril elongation as by enabling their initial formation. Moreover, we find that the primary nucleation of lipid-protein co-aggregates takes place not on the surface of lipid vesicles in bulk solution but at the air-water and/or plate interfaces, where lipids and proteins are likely adsorbed. Our model forms the basis for mechanistic insights, also in other lipid-protein co-aggregation systems, which will be crucial in the rational design of drugs that inhibit aggregate formation and act at the key points in the α-synuclein aggregation cascade., Competing Interests: All authors except AS were, at the time of their contribution, employees, founders or consultants of WaveBreak Therapeutics., (This journal is © The Royal Society of Chemistry.)

Self-replication of amyloid fibrils via secondary nucleation is an intriguing physicochemical phenomenon in which existing fibrils catalyze the formation of their own copies. The molecular events behind this fibril surface-mediated process remain largely inaccessible to current structural and imaging techniques. Using statistical mechanics, computer modeling, and chemical kinetics, we show that the catalytic structure of the fibril surface can be inferred from the aggregation behavior in the presence and absence of a fibril-binding inhibitor. We apply our approach to the case of Alzheimer's A[Formula: see text] amyloid fibrils formed in the presence of proSP-C Brichos inhibitors. We find that self-replication of A[Formula: see text] fibrils occurs on small catalytic sites on the fibril surface, which are far apart from each other, and each of which can be covered by a single Brichos inhibitor., Competing Interests: Competing interests statement:The authors declare no competing interest.

In antibody development and manufacturing, protein aggregation is a common challenge that can lead to serious efficacy and safety issues. To mitigate this problem, it is important to investigate its molecular origins. This review discusses (1) our current molecular understanding and theoretical models of antibody aggregation, (2) how various stress conditions related to antibody upstream and downstream bioprocesses can trigger aggregation, and (3) current mitigation strategies employed towards inhibiting aggregation. We discuss the relevance of the aggregation phenomenon in the context of novel antibody modalities and highlight how in silico approaches can be exploited to mitigate it., Competing Interests: Declaration of Competing Interest The authors declare no conflict of interest., (Copyright © 2023 The Authors. Published by Elsevier Inc. All rights reserved.)

The aggregation of α-synuclein into amyloid fibrils has been under scrutiny in recent years because of its association with Parkinson's disease. This process can be triggered by a lipid-dependent nucleation process, and the resulting aggregates can proliferate through secondary nucleation under acidic pH conditions. It has also been recently reported that the aggregation of α-synuclein may follow an alternative pathway, which takes place within dense liquid condensates formed through phase separation. The microscopic mechanism of this process, however, remains to be clarified. Here, we used fluorescence-based assays to enable a kinetic analysis of the microscopic steps underlying the aggregation process of α-synuclein within liquid condensates. Our analysis shows that at pH 7.4, this process starts with spontaneous primary nucleation followed by rapid aggregate-dependent proliferation. Our results thus reveal the microscopic mechanism of α-synuclein aggregation within condensates through the accurate quantification of the kinetic rate constants for the appearance and proliferation of α-synuclein aggregates at physiological pH.

Biomolecular condensates in living cells can exhibit a complex rheology, including viscoelastic and glassy behavior. This rheological behavior of condensates was suggested to regulate polymerization of cytoskeletal filaments and aggregation of amyloid fibrils. Here, we theoretically investigate how the rheological properties of condensates can control the formation of linear aggregates. To this end, we propose a kinetic theory for linear aggregation in coexisting phases, which accounts for the aggregate size distribution and the exchange of aggregates between inside and outside of condensates. The rheology of condensates is accounted in our model via aggregate mobilities that depend on aggregate size. We show that condensate rheology determines whether aggregates of all sizes or dominantly small aggregates are exchanged between condensate inside and outside on the timescale of aggregation. As a result, the ratio of aggregate numbers inside to outside of condensates differs significantly. Strikingly, we also find that weak variations in the rheological properties of condensates can lead to a switch-like change of the number of aggregates. These results suggest a possible physical mechanism for how living cells could control linear aggregation in a switch-like fashion through variations in condensate rheology., Competing Interests: Declaration of interests The authors declare no competing interests., (Copyright © 2022 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

A self-consistent analytical solution for binodal concentrations of the two-component Flory-Huggins phase separation model is derived. We show that this form extends the validity of the Ginzburg-Landau expansion away from the critical point to cover the whole phase space. Furthermore, this analytical solution reveals an exponential scaling law of the dilute phase binodal concentration as a function of the interaction strength and chain length. We demonstrate explicitly the power of this approach by fitting experimental protein liquid-liquid phase separation boundaries to determine the effective chain length and solute-solvent interaction energies. Moreover, we demonstrate that this strategy allows us to resolve differences in interaction energy contributions of individual amino acids. This analytical framework can serve as a new way to decode the protein sequence grammar for liquid-liquid phase separation.

Fibrillar protein aggregates are a hallmark of a range of human disorders, from prion diseases to dementias, but are also encountered in several functional contexts. Yet, the fundamental links between protein assembly mechanisms and their functional or pathological roles have remained elusive. Here, we analyze the aggregation kinetics of a large set of proteins that self-assemble by a nucleated-growth mechanism, from those associated with disease, over those whose aggregates fulfill functional roles in biology, to those that aggregate only under artificial conditions. We find that, essentially, all such systems, regardless of their biological role, are capable of self-replication. However, for aggregates that have evolved to fulfill a structural role, the rate of self-replication is too low to be significant on the biologically relevant time scale. By contrast, all disease-related proteins are able to self-replicate quickly compared to the time scale of the associated disease. Our findings establish the ubiquity of self-replication and point to its potential importance across aggregation-related disorders.

Primary nucleation is the fundamental event that initiates the conversion of proteins from their normal physiological forms into pathological amyloid aggregates associated with the onset and development of disorders including systemic amyloidosis, as well as the neurodegenerative conditions Alzheimer's and Parkinson's diseases. It has become apparent that the presence of surfaces can dramatically modulate nucleation. However, the underlying physicochemical parameters governing this process have been challenging to elucidate, with interfaces in some cases having been found to accelerate aggregation, while in others they can inhibit the kinetics of this process. Here we show through kinetic analysis that for three different fibril-forming proteins, interfaces affect the aggregation reaction mainly through modulating the primary nucleation step. Moreover, we show through direct measurements of the Gibbs free energy of adsorption, combined with theory and coarse-grained computer simulations, that overall nucleation rates are suppressed at high and at low surface interaction strengths but significantly enhanced at intermediate strengths, and we verify these regimes experimentally. Taken together, these results provide a quantitative description of the fundamental process which triggers amyloid formation and shed light on the key factors that control this process.

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 self-assembly of peptides and proteins into amyloid fibrils plays a causative role in a wide range of increasingly common and currently incurable diseases. The molecular mechanisms underlying this process have recently been discovered, prompting the development of drugs that inhibit specific reaction steps as possible treatments for some of these disorders. A crucial part of treatment design is to determine how much drug to give and when to give it, informed by its efficacy and intrinsic toxicity. Since amyloid formation does not proceed at the same pace in different individuals, it is also important that treatment design is informed by local measurements of the extent of protein aggregation. Here, we use stochastic optimal control theory to determine treatment regimens for inhibitory drugs targeting several key reaction steps in protein aggregation, explicitly taking into account variability in the reaction kinetics. We demonstrate how these regimens may be updated "on the fly" as new measurements of the protein aggregate concentration become available, in principle, enabling treatments to be tailored to the individual. We find that treatment timing, duration, and drug dosage all depend strongly on the particular reaction step being targeted. Moreover, for some kinds of inhibitory drugs, the optimal regimen exhibits high sensitivity to stochastic fluctuations. Feedback controls tailored to the individual may therefore substantially increase the effectiveness of future treatments.

Prions consist of pathological aggregates of cellular prion protein and have the ability to replicate, causing neurodegenerative diseases, a phenomenon mirrored in many other diseases connected to protein aggregation, including Alzheimer's and Parkinson's diseases. However, despite their key importance in disease, the individual processes governing this formation of pathogenic aggregates, as well as their rates, have remained challenging to elucidate in vivo. Here we bring together a mathematical framework with kinetics of the accumulation of prions in mice and microfluidic measurements of aggregate size to dissect the overall aggregation reaction into its constituent processes and quantify the reaction rates in mice. Taken together, the data show that multiplication of prions in vivo is slower than in in vitro experiments, but efficient when compared with other amyloid systems, and displays scaling behavior characteristic of aggregate fragmentation. These results provide a framework for the determination of the mechanisms of disease-associated aggregation processes within living organisms.

Protein aggregation is associated with a wide range of degenerative human diseases with devastating consequences, as exemplified by Alzheimer's, Parkinson's, and Huntington's diseases. In vitro kinetic studies have provided a mechanistic understanding of the aggregation process at the molecular level. However, it has so far remained largely unclear to what extent the biophysical principles of amyloid formation learned in vitro translate to the complex environment of living organisms. Here, we take advantage of the unique properties of a Caenorhabditis elegans model expressing a fluorescently tagged polyglutamine (polyQ) protein, which aggregates into discrete micrometer-sized inclusions that can be directly visualized in real time. We provide a quantitative analysis of protein aggregation in this system and show that the data are described by a molecular model where stochastic nucleation occurs independently in each cell, followed by rapid aggregate growth. Global fitting of the image-based aggregation kinetics reveals a nucleation rate corresponding to 0.01 h -1 per cell at 1 mM intracellular protein concentration, and shows that the intrinsic molecular stochasticity of nucleation accounts for a significant fraction of the observed animal-to-animal variation. Our results highlight how independent, stochastic nucleation events in individual cells control the overall progression of polyQ aggregation in a living animal. The key finding that the biophysical principles associated with protein aggregation in small volumes remain the governing factors, even in the complex environment of a living organism, will be critical for the interpretation of in vivo data from a wide range of protein aggregation diseases., Competing Interests: The authors declare no competing interest., (Copyright © 2021 the Author(s). Published by PNAS.)

The aggregation of α-synuclein is a central event in Parkinsons's disease and related synucleinopathies. Since pharmacologically targeting this process, however, has not yet resulted in approved disease-modifying treatments, there is an unmet need of developing novel methods of drug discovery. In this context, the use of chemical kinetics has recently enabled accurate quantifications of the microscopic steps leading to the proliferation of protein misfolded oligomers. As these species are highly neurotoxic, effective therapeutic strategies may be aimed at reducing their numbers. Here, we exploit this quantitative approach to develop a screening strategy that uses the reactive flux toward α-synuclein oligomers as a selection parameter. Using this approach, we evaluate the efficacy of a library of flavone derivatives, identifying apigenin as a compound that simultaneously delays and reduces the formation of α-synuclein oligomers. These results demonstrate a compound selection strategy based on the inhibition of the formation of α-synuclein oligomers, which may be key in identifying small molecules in drug discovery pipelines for diseases associated with α-synuclein aggregation., (© 2020. The Author(s).)

Disordered proteins are challenging therapeutic targets, and no drug is currently in clinical use that modifies the properties of their monomeric states. Here, we identify a small molecule (10074-G5) capable of binding and sequestering the intrinsically disordered amyloid-β (Aβ) peptide in its monomeric, soluble state. Our analysis reveals that this compound interacts with Aβ and inhibits both the primary and secondary nucleation pathways in its aggregation process. We characterize this interaction using biophysical experiments and integrative structural ensemble determination methods. We observe that this molecule increases the conformational entropy of monomeric Aβ while decreasing its hydrophobic surface area. We also show that it rescues a Caenorhabditis elegans model of Aβ-associated toxicity, consistent with the mechanism of action identified from the in silico and in vitro studies. These results illustrate the strategy of stabilizing the monomeric states of disordered proteins with small molecules to alter their behavior for therapeutic purposes., (Copyright © 2020 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. Distributed under a Creative Commons Attribution License 4.0 (CC BY).)

Understanding the morphology of self-assembled fibrillar bundles and aggregates is relevant to a range of problems in molecular biology, supramolecular chemistry and materials science. Here, we propose a coarse-grained approach that averages over specific molecular details and yields an effective mechanical theory for the spatial complexity of self-assembling fibrillar structures that arises due to the competing effects of (the bending and twisting) elasticity of individual filaments and the adhesive interactions between them. We show that our theoretical framework accounting for this allows us to capture a number of diverse fibril morphologies observed in natural and synthetic systems, ranging from Filopodia to multi-walled carbon nanotubes, and leads to a phase diagram of possible fibril shapes. We also show how the extreme sensitivity of these morphologies can lead to spatially chaotic structures. Together, these results suggest a common mechanical basis for mesoscale fibril morphology as a function of the nanoscale mechanical properties of its filamentous constituents.

The formation of amyloid deposits in human tissues is a defining feature of more than 50 medical disorders, including Alzheimer's disease. Strong genetic and histological evidence links these conditions to the process of protein aggregation, yet it has remained challenging to identify a definitive connection between aggregation and pathogenicity. Using time-resolved fluorescence microscopy of individual synthetic vesicles, we show for the Aβ42 peptide implicated in Alzheimer's disease that the disruption of lipid bilayers correlates linearly with the time course of the levels of transient oligomers generated through secondary nucleation. These findings indicate a specific role of oligomers generated through the catalytic action of fibrillar species during the protein aggregation process in driving deleterious biological function and establish a direct causative connection between amyloid formation and its pathological effects.

Understanding the mechanism of action of compounds capable of inhibiting amyloid-fibril formation is critical to the development of potential therapeutics against protein-misfolding diseases. A fundamental challenge for progress is the range of possible target species and the disparate timescales involved, since the aggregating proteins are simultaneously the reactants, products, intermediates, and catalysts of the reaction. It is a complex problem, therefore, to choose the states of the aggregating proteins that should be bound by the compounds to achieve the most potent inhibition. We present here a comprehensive kinetic theory of amyloid-aggregation inhibition that reveals the fundamental thermodynamic and kinetic signatures characterizing effective inhibitors by identifying quantitative relationships between the aggregation and binding rate constants. These results provide general physical laws to guide the design and optimization of inhibitors of amyloid-fibril formation, revealing in particular the important role of on-rates in the binding of the inhibitors., Competing Interests: The authors declare no competing interest.

Bicyclic peptides have great therapeutic potential since they can bridge the gap between small molecules and antibodies by combining a low molecular weight of about 2 kDa with an antibody-like binding specificity. Here we apply a recently developed in silico rational design strategy to produce a bicyclic peptide to target the C-terminal region (residues 31-42) of the 42-residue form of the amyloid β peptide (Aβ42), a protein fragment whose aggregation into amyloid plaques is linked with Alzheimer's disease. We show that this bicyclic peptide is able to remodel the aggregation process of Aβ42 in vitro and to reduce its associated toxicity in vivo in a C. elegans worm model expressing Aβ42. These results provide an initial example of a computational approach to design bicyclic peptides to target specific epitopes on disordered proteins.

Many complex systems experience damage accumulation, which leads to aging, manifest as an increasing probability of system collapse with time. This naturally raises the question of how to maximize health and longevity in an aging system at minimal cost of maintenance and intervention. Here, we pose this question in the context of a simple interdependent network model of aging in complex systems and show that it exhibits cascading failures. We then use both optimal control theory and reinforcement learning alongside a combination of analysis and simulation to determine optimal maintenance protocols. These protocols may motivate the rational design of strategies for promoting longevity in aging complex systems with potential applications in therapeutic schedules and engineered system maintenance., Competing Interests: The authors declare no competing interest.

The misfolding and aberrant aggregation of proteins into fibrillar structures is a key factor in some of the most prevalent human diseases, including diabetes and dementia. Low molecular weight oligomers are thought to be a central factor in the pathology of these diseases, as well as critical intermediates in the fibril formation process, and as such have received much recent attention. Moreover, on-pathway oligomeric intermediates are potential targets for therapeutic strategies aimed at interrupting the fibril formation process. However, a consistent framework for distinguishing on-pathway from off-pathway oligomers has hitherto been lacking and, in particular, no consensus definition of on- and off-pathway oligomers is available. In this paper, we argue that a non-binary definition of oligomers' contribution to fibril-forming pathways may be more informative and we suggest a quantitative framework, in which each oligomeric species is assigned a value between 0 and 1 describing its relative contribution to the formation of fibrils. First, we clarify the distinction between oligomers and fibrils, and then we use the formalism of reaction networks to develop a general definition for on-pathway oligomers, that yields meaningful classifications in the context of amyloid formation. By applying these concepts to Monte Carlo simulations of a minimal aggregating system, and by revisiting several previous studies of amyloid oligomers in light of our new framework, we demonstrate how to perform these classifications in practice. For each oligomeric species we obtain the degree to which it is on-pathway, highlighting the most effective pharmaceutical targets for the inhibition of amyloid fibril formation., (This journal is © The Royal Society of Chemistry 2020.)

The spontaneous assembly of proteins into amyloid fibrils is a phenomenon central to many increasingly common and currently incurable human disorders, including Alzheimer's and Parkinson's diseases. Oligomeric species form transiently during this process and not only act as essential intermediates in the assembly of new filaments but also represent major pathogenic agents in these diseases. While amyloid fibrils possess a common, defining set of physicochemical features, oligomers, by contrast, appear much more diverse, and their commonalities and differences have hitherto remained largely unexplored. Here, we use the framework of chemical kinetics to investigate their dynamical properties. By fitting experimental data for several unrelated amyloidogenic systems to newly derived mechanistic models, we find that oligomers present with a remarkably wide range of kinetic and thermodynamic stabilities but that they possess two properties that are generic: they are overwhelmingly nonfibrillar, and they predominantly dissociate back to monomers rather than maturing into fibrillar species. These discoveries change our understanding of the relationship between amyloid oligomers and amyloid fibrils and have important implications for the nature of their cellular toxicity., Competing Interests: The authors declare no competing interest.

Oligomeric species populated during the aggregation of the Aβ42 peptide have been identified as potent cytotoxins linked to Alzheimer's disease, but the fundamental molecular pathways that control their dynamics have yet to be elucidated. By developing a general approach that combines theory, experiment and simulation, we reveal, in molecular detail, the mechanisms of Aβ42 oligomer dynamics during amyloid fibril formation. Even though all mature amyloid fibrils must originate as oligomers, we found that most Aβ42 oligomers dissociate into their monomeric precursors without forming new fibrils. Only a minority of oligomers converts into fibrillar structures. Moreover, the heterogeneous ensemble of oligomeric species interconverts on timescales comparable to those of aggregation. Our results identify fundamentally new steps that could be targeted by therapeutic interventions designed to combat protein misfolding diseases.

The formation of amyloid fibrils from soluble peptide is a hallmark of many neurodegenerative diseases such as Alzheimer's and Parkinson's diseases. Characterization of the microscopic reaction processes that underlie these phenomena have yielded insights into the progression of such diseases and may inform rational approaches for the design of drugs to halt them. Experimental evidence suggests that most of these reaction processes are intrinsically catalytic in nature and may display enzymelike saturation effects under conditions typical of biological systems, yet a unified modeling framework accounting for these saturation effects is still lacking. In this paper, we therefore present a universal kinetic model for biofilament formation in which every fundamental process in the reaction network can be catalytic. The single closed-form expression derived is capable of describing with high accuracy a wide range of mechanisms of biofilament formation and providing the first integrated rate law of a system in which multiple reaction processes are saturated. Moreover, its unprecedented mathematical simplicity permits us to very clearly interpret the effects of increasing saturation on the overall kinetics. The effectiveness of the model is illustrated by fitting it to the data of in vitro Aβ40 aggregation. Remarkably, we find that primary nucleation becomes saturated, demonstrating that it must be heterogeneous, occurring at interfaces and not in solution.

Localized deformation patterns are a common motif in morphogenesis and are increasingly finding applications in materials science and engineering, in such instances as mechanical memories. Here, we describe the emergence of spatially localized deformations in a minimal mechanical system by exploring the impact of growth and shear on the conformation of a semi-flexible filament connected to a pliable shearable substrate. We combine numerical simulations of a discrete rod model with theoretical analysis of the differential equations recovered in the continuum limit to quantify (in the form of scaling laws) how geometry, mechanics and growth act together to give rise to such localized structures in this system. We find that spatially localized deformations along the filament emerge for intermediate shear modulus and increasing growth. Finally, we use experiments on a 3D-printed multi-material model system to demonstrate that external control of the amount of shear and growth may be used to regulate the spatial extent of the localized strain texture., Competing Interests: We declare we have no competing interests., (© 2019 The Author(s).)

Protein aggregation has been implicated in many medical disorders, including Alzheimer's and Parkinson's diseases. Potential therapeutic strategies for these diseases propose the use of drugs to inhibit specific molecular events during the aggregation process. However, viable treatment protocols require balancing the efficacy of the drug with its toxicity, while accounting for the underlying events of aggregation and inhibition at the molecular level. To address this key problem, we combine here protein aggregation kinetics and control theory to determine optimal protocols that prevent protein aggregation via specific reaction pathways. We find that the optimal inhibition of primary and fibril-dependent secondary nucleation require fundamentally different drug administration protocols. We test the efficacy of our approach on experimental data for the aggregation of the amyloid-β(1-42) peptide of Alzheimer's disease in the model organism Caenorhabditis elegans Our results pose and answer the question of the link between the molecular basis of protein aggregation and optimal strategies for inhibiting it, opening up avenues for the design of rational therapies to control pathological protein aggregation.

We use perturbative renormalization group theory to study the kinetics of protein aggregation phenomena in a unified manner across multiple timescales. Using this approach, we find that, irrespective of the specific molecular details or experimental conditions, filamentous assembly systems display universal behavior in time. Moreover, we show that the universality classes for protein aggregation correspond to simple autocatalytic processes and that the diversity of behavior in these systems is determined solely by the reaction order for secondary nucleation with respect to the protein concentration, which labels all possible universality classes. We validate these predictions on experimental data for the aggregation of several different proteins at several different initial concentrations, which by appropriate coordinate transformations we are able to collapse onto universal kinetic growth curves. These results establish the power of the perturbative renormalization group in distilling the ultimately simple temporal behavior of complex protein aggregation systems, creating the possibility to study the kinetics of general self-assembly phenomena in a unified fashion.

Transient oligomeric species formed during the aggregation process of the 42-residue form of the amyloid-β peptide (Aβ 42 ) are key pathogenic agents in Alzheimer's disease (AD). To investigate the relationship between Aβ 42 aggregation and its cytotoxicity and the influence of a potential drug on both phenomena, we have studied the effects of trodusquemine. This aminosterol enhances the rate of aggregation by promoting monomer-dependent secondary nucleation, but significantly reduces the toxicity of the resulting oligomers to neuroblastoma cells by inhibiting their binding to the cellular membranes. When administered to a C. elegans model of AD, we again observe an increase in aggregate formation alongside the suppression of Aβ 42 -induced toxicity. In addition to oligomer displacement, the reduced toxicity could also point towards an increased rate of conversion of oligomers to less toxic fibrils. The ability of a small molecule to reduce the toxicity of oligomeric species represents a potential therapeutic strategy against AD.

A wide range of bacterial pathogens have been shown to form biofilms, which significantly increase their resistance to environmental stresses, such as antibiotics, and are thus of central importance in the context of bacterial diseases. One of the major structural components of these bacterial biofilms are amyloid fibrils, yet the mechanism of fibril assembly and its importance for biofilm formation are currently not fully understood. By studying fibril formation in vitro , in a model system of two common but unrelated biofilm-forming proteins, FapC from Pseudomonas fluorescens and CsgA from Escherichia coli , we found that the two proteins have a common aggregation mechanism. In both systems, fibril formation proceeds via nucleated growth of linear fibrils exhibiting similar measured rates of elongation, with negligible fibril self-replication. These similarities between two unrelated systems suggest that convergent evolution plays a key role in tuning the assembly kinetics of functional amyloid fibrils and indicates that only a narrow window of mechanisms and assembly rates allows for successful biofilm formation. Thus, the amyloid assembly reaction is likely to represent a means for controlling biofilm formation, both by the organism and by possible inhibitory drugs. IMPORTANCE Biofilms are generated by bacteria, embedded in the formed extracellular matrix. The biofilm's function is to improve the survival of a bacterial colony through, for example, increased resistance to antibiotics or other environmental stresses. Proteins secreted by the bacteria act as a major structural component of this extracellular matrix, as they self-assemble into highly stable amyloid fibrils, making the biofilm very difficult to degrade by physical and chemical means once formed. By studying the self-assembly mechanism of the fibrils from their monomeric precursors in two unrelated bacteria, our experimental and theoretical approaches shed light on the mechanism of functional amyloid assembly in the context of biofilm formation. Our results suggest that fibril formation may be a rate-limiting step in biofilm formation, which in turn has implications on the protein self-assembly reaction as a target for potential antibiotic drugs., (Copyright © 2019 Andreasen et al.)

The aggregation of proteins into fibrillar structures is a central process implicated in the onset and development of several devastating neuro-degenerative diseases, but can, in contrast to these pathological roles, also fulfil important biological functions. In both scenarios, an understanding of the mechanisms by which soluble proteins convert to their fibrillar forms represents a fundamental objective for molecular sciences. This chapter details the different classes of microscopic processes responsible for this conversion and discusses how they can be described by a mathematical formulation of the aggregation kinetics. We present easily accessible experimental quantities that allow the determination of the dominant pathways of aggregation, as well as a general strategy to obtain detailed solutions to the kinetic rate laws that yield the microscopic rate constants of the individual processes of nucleation and growth. This chapter discusses a framework for a structured approach to address key questions regarding the dynamics of protein aggregation and shows how the use of chemical kinetics to tackle complex biophysical systems can lead to a deeper understanding of the underlying physical and chemical principles.

The misfolding and aggregation of proteins into linear fibrils is widespread in human biology, for example, in connection with amyloid formation and the pathology of neurodegenerative disorders such as Alzheimer's and Parkinson's diseases. The oligomeric species that are formed in the early stages of protein aggregation are of great interest, having been linked with the cellular toxicity associated with these conditions. However, these species are not characterized in any detail experimentally, and their properties are not well understood. Many of these species have been found to have approximately spherical morphology and to be held together by hydrophobic interactions. We present here an analytical statistical mechanical model of globular oligomer formation from simple idealized amphiphilic protein monomers and show that this correlates well with Monte Carlo simulations of oligomer formation. We identify the controlling parameters of the model, which are closely related to simple quantities that may be fitted directly from experiment. We predict that globular oligomers are unlikely to form at equilibrium in many polypeptide systems but instead form transiently in the early stages of amyloid formation. We contrast the globular model of oligomer formation to a well-established model of linear oligomer formation, highlighting how the differing ensemble properties of linear and globular oligomers offer a potential strategy for characterizing oligomers from experimental measurements.

Small oligomers of the protein α-synuclein (αS) are highly cytotoxic species associated with Parkinson's disease (PD). In addition, αS can form co-aggregates with its mutational variants and with other proteins such as amyloid-β (Aβ) and tau, which are implicated in Alzheimer's disease. The processes of self-oligomerization and co-oligomerization of αS are, however, challenging to study quantitatively. Here, we have utilized single-molecule techniques to measure the equilibrium populations of oligomers formed in vitro by mixtures of wild-type αS with its mutational variants and with Aβ40, Aβ42, and a fragment of tau. Using a statistical mechanical model, we find that co-oligomer formation is generally more favorable than self-oligomer formation at equilibrium. Furthermore, self-oligomers more potently disrupt lipid membranes than do co-oligomers. However, this difference is sometimes outweighed by the greater formation propensity of co-oligomers when multiple proteins coexist. Our results suggest that co-oligomer formation may be important in PD and related neurodegenerative diseases.

To develop effective therapeutic strategies for protein misfolding diseases, a promising route is to identify compounds that inhibit the formation of protein oligomers. To achieve this goal, we report a structure-activity relationship (SAR) approach based on chemical kinetics to estimate quantitatively how small molecules modify the reactive flux toward oligomers. We use this estimate to derive chemical rules in the case of the amyloid beta peptide (Aβ), which we then exploit to optimize starting compounds to curtail Aβ oligomer formation. We demonstrate this approach by converting an inactive rhodanine compound into an effective inhibitor of Aβ oligomer formation by generating chemical derivatives in a systematic manner. These results provide an initial demonstration of the potential of drug discovery strategies based on targeting directly the production of protein oligomers., Competing Interests: The authors declare no conflict of interest., (Copyright © 2018 the Author(s). Published by PNAS.)

The release of nanoscale structures from microcapsules, triggered by changes in the capsule in response to external stimuli, has significant potential for active component delivery. Here, we describe an orthogonal strategy for controlling molecular species' release across oil/water interfaces by modulating their intrinsic self-assembly state. We show that although the soluble peptide Boc-FF can be stably encapsulated for days, its self-assembly into nanostructures triggers jet-like release within seconds. Moreover, we exploit this self-assembly-mediated release to deliver other molecular species that are transported as cargo. These results demonstrate the role of self-assembly in modulating the transport of peptides across interfaces.

Nucleation of new peptide and protein aggregates on the surfaces of amyloid fibrils of the same peptide or protein has emerged in the past two decades as a major pathway for both the generation of molecular species responsible for cellular toxicity and for the autocatalytic proliferation of peptide and protein aggregates. A key question in current research is the molecular mechanism and driving forces governing such processes, known as secondary nucleation. In this context, the analogies with other self-assembling systems for which monomer-dependent secondary nucleation has been studied for more than a century provide a valuable source of inspiration. Here, we present a short overview of this background and then review recent results regarding secondary nucleation of amyloid-forming peptides and proteins, focusing in particular on the amyloid β peptide (Aβ) from Alzheimer's disease, with some examples regarding α-synuclein from Parkinson's disease. Monomer-dependent secondary nucleation of Aβ was discovered using a combination of kinetic experiments, global analysis, seeding experiments and selective isotope-enrichment, which pinpoint the monomer as the origin of new aggregates in a fibril-catalyzed reaction. Insights into driving forces are gained from variations of solution conditions, temperature and peptide sequence. Selective inhibition of secondary nucleation is explored as an effective means to limit oligomer production and toxicity. We also review experiments aimed at finding interaction partners of oligomers generated by secondary nucleation in an ongoing aggregation process. At the end of this feature article we bring forward outstanding questions and testable mechanistic hypotheses regarding monomer-dependent secondary nucleation in amyloid formation.

Many molecular chaperones exist as oligomeric complexes in their functional states, yet the physical determinants underlying such self-assembly behavior, as well as the role of oligomerization in the activity of molecular chaperones in inhibiting protein aggregation, have proven to be difficult to define. Here, we demonstrate direct measurements under native conditions of the changes in the average oligomer populations of a chaperone system as a function of concentration and time and thus determine the thermodynamic and kinetic parameters governing the self-assembly process. We access this self-assembly behavior in real time under native-like conditions by monitoring the changes in the micrometer-scale diffusion of the different complexes in time and space using a microfluidic platform. Using this approach, we find that the oligomerization mechanism of the Hsp70 subdomain occurs in a cooperative manner and involves structural constraints that limit the size of the species formed beyond the limits imposed by mass balance. These results illustrate the ability of microfluidic methods to probe polydisperse protein self-assembly in real time in solution and to shed light on the nature and dynamics of oligomerization processes.

The ordered assembly of amyloidogenic proteins causes a wide spectrum of common neurodegenerative diseases, including Alzheimer's and Parkinson's diseases. These diseases share common features with prion diseases, in which misfolded proteins can self-replicate and transmit disease across different hosts. Deciphering the molecular mechanisms that underlie the amplification of aggregates is fundamental for understanding how pathological deposits can spread through the brain and drive disease. Here, we used single-molecule microscopy to study the assembly and replication of tau at the single aggregate level. We found that tau aggregates have an intrinsic ability to amplify by filament fragmentation, and determined the doubling times for this replication process by kinetic modeling. We then simulated the spreading time for aggregates through the brain and found this to be in good agreement with both the observed time frame for spreading of pathological tau deposits in Alzheimer's disease and in experimental models of tauopathies. With this work we begin to understand the physical parameters that govern the spreading rates of tau and other amyloids through the human brain.

Alzheimer's disease is a neurodegenerative disorder associated with the aberrant aggregation of the amyloid-β peptide. Although increasing evidence implicates cholesterol in the pathogenesis of Alzheimer's disease, the detailed mechanistic link between this lipid molecule and the disease process remains to be fully established. To address this problem, we adopt a kinetics-based strategy that reveals a specific catalytic role of cholesterol in the aggregation of Aβ42 (the 42-residue form of the amyloid-β peptide). More specifically, we demonstrate that lipid membranes containing cholesterol promote Aβ42 aggregation by enhancing its primary nucleation rate by up to 20-fold through a heterogeneous nucleation pathway. We further show that this process occurs as a result of cooperativity in the interaction of multiple cholesterol molecules with Aβ42. These results identify a specific microscopic pathway by which cholesterol dramatically enhances the onset of Aβ42 aggregation, thereby helping rationalize the link between Alzheimer's disease and the impairment of cholesterol homeostasis.

Networks of natural protein nanofibrils, such as cytoskeletal filaments, control the shape and the division of cells, yet mimicking this functionality in a synthetic setting has proved challenging. Here, we demonstrate that artificial networks of protein nanofibrils can induce controlled deformation and division of all-aqueous emulsion droplets with budding-like morphologies. We show that this process is driven by the difference in the immersional wetting energy of the nanofibril network, and that both the size and the number of the daughter droplets formed during division can be controlled by modulating the fibril concentration and the chemical properties of the fibril network. Our results demonstrate a route for achieving biomimetic division with synthetic self-assembling fibrils and offer an engineered approach to regulate the morphology of protein gels.

Mapping free-energy landscapes has proved to be a powerful tool for studying reaction mechanisms. Many complex biomolecular assembly processes, however, have remained challenging to access using this approach, including the aggregation of peptides and proteins into amyloid fibrils implicated in a range of disorders. Here, we generalize the strategy used to probe free-energy landscapes in protein folding to determine the activation energies and entropies that characterize each of the molecular steps in the aggregation of the amyloid-β peptide (Aβ42), which is associated with Alzheimer's disease. Our results reveal that interactions between monomeric Aβ42 and amyloid fibrils during fibril-dependent secondary nucleation fundamentally reverse the thermodynamic signature of this process relative to primary nucleation, even though both processes generate aggregates from soluble peptides. By mapping the energetic and entropic contributions along the reaction trajectories, we show that the catalytic efficiency of Aβ42 fibril surfaces results from the enthalpic stabilization of adsorbing peptides in conformations amenable to nucleation, resulting in a dramatic lowering of the activation energy for nucleation.

Understanding how normally soluble peptides and proteins aggregate to form amyloid fibrils is central to many areas of modern biomolecular science, ranging from the development of functional biomaterials to the design of rational therapeutic strategies against increasingly prevalent medical conditions such as Alzheimer's and Parkinson's diseases. As such, there is a great need to develop models to mechanistically describe how amyloid fibrils are formed from precursor peptides and proteins. Here we review and discuss how ideas and concepts from chemical reaction kinetics can help to achieve this objective. In particular, we show how a combination of theory, experiments, and computer simulations, based on chemical kinetics, provides a general formalism for uncovering, at the molecular level, the mechanistic steps that underlie the phenomenon of amyloid fibril formation.

The self-assembly of polypeptides into amyloid structures is associated with a range of increasingly prevalent neurodegenerative diseases as well as with a select set of functional processes in biology. The phenomenon of self-assembly results in species with dramatically different sizes, from small oligomers to large fibrils; however, the kinetic relationship between these species is challenging to characterize. In the case of prion aggregates, these structures can self-replicate and act as infectious agents. Here we use single molecule spectroscopy to obtain quantitative information on the oligomer populations formed during aggregation of the yeast prion protein Ure2. Global analysis of the aggregation kinetics reveals the molecular mechanism underlying oligomer formation and depletion. Quantitative characterization indicates that the majority of Ure2 oligomers are relatively short-lived, and their rate of dissociation is much higher than their rate of conversion into growing fibrils. We identify an initial metastable oligomer, which can subsequently convert into a structurally distinct oligomer, which in turn converts into growing fibrils. We also show that fragmentation is responsible for the autocatalytic self-replication of Ure2 fibrils, but that preformed fibrils do not promote oligomer formation, indicating that secondary nucleation of the type observed for peptides and proteins associated with neurodegenerative disease does not occur at a significant rate for Ure2. These results establish a framework for elucidating the temporal and causal relationship between oligomers and larger fibrillar species in amyloid forming systems, and provide insights into why functional amyloid systems are not toxic to their host organisms.

The formation of amyloid fibrils is a central phenomenon in the progressive pathology of many neurodegenerative diseases, as well as in the fabrication of functional materials. Several different molecular processes acting in concert are responsible for the formation of amyloid fibrils from monomeric protein in solution. Here, we describe a method to determine which microscopic processes drive the overall formation of fibrils by using chemical kinetics in combination with systematic experimental datasets analysed in a global manner. We outline general concepts for obtaining suitable kinetic data and detail the key stages of data analysis, from quality control to the verification of a specific mechanism of aggregation.

The self-assembly of peptides into ordered supramolecular structures, such as fibrils and crystals, is of relevance in such diverse areas as molecular medicine and materials science. However, little information is available about the fundamental thermodynamic driving forces of these types of self-assembly processes. Here, we investigate in detail the thermodynamics of assembly of diphenylalanine (FF). This dipeptide forms the central motif of the Aβ peptides, which are associated with Alzheimer's disease through their presence in amyloid plaques in the nervous systems of affected individuals. We identify the molecular origins of the self-assembly of FF in aqueous solution, and we evaluate these findings in the context of the aggregation free energies of longer peptides that are able to form amyloid fibrils. We find that the thermodynamics of FF assembly displays the typical characteristics of hydrophobic desolvation processes, and detailed analysis of the temperature dependence of the kinetics of assembly within the framework of crystallization theories reveals that the transition state from solution to crystalline aggregates is enthalpically unfavorable and entropically favorable, qualitatively similar to what has been found for longer sequences. This quantitative comparison of aggregating peptides of very different lengths is the basis of an in-depth understanding of the relationship between sequence and assembly behavior.

In nature, a wide range of functional materials is based on proteins. Increasing attention is also turning to the use of proteins as artificial biomaterials in the form of films, gels, particles, and fibrils that offer great potential for applications in areas ranging from molecular medicine to materials science. To date, however, most such applications have been limited to single component materials despite the fact that their natural analogues are composed of multiple types of proteins with a variety of functionalities that are coassembled in a highly organized manner on the micrometer scale, a process that is currently challenging to achieve in the laboratory. Here, we demonstrate the fabrication of multicomponent protein microcapsules where the different components are positioned in a controlled manner. We use molecular self-assembly to generate multicomponent structures on the nanometer scale and droplet microfluidics to bring together the different components on the micrometer scale. Using this approach, we synthesize a wide range of multiprotein microcapsules containing three well-characterized proteins: glucagon, insulin, and lysozyme. The localization of each protein component in multishell microcapsules has been detected by labeling protein molecules with different fluorophores, and the final three-dimensional microcapsule structure has been resolved by using confocal microscopy together with image analysis techniques. In addition, we show that these structures can be used to tailor the release of such functional proteins in a sequential manner. Moreover, our observations demonstrate that the protein release mechanism from multishell capsules is driven by the kinetic control of mass transport of the cargo and by the dissolution of the shells. The ability to generate artificial materials that incorporate a variety of different proteins with distinct functionalities increases the breadth of the potential applications of artificial protein-based materials and provides opportunities to design more refined functional protein delivery systems.

Many biological and synthetic systems exploit self-assembly to generate highly intricate closed supramolecular architectures, ranging from self-assembling cages to viral capsids. The fundamental design principles that control the structural determinants of the resulting assemblies are increasingly well-understood, but much less is known about the kinetics of such assembly phenomena and it remains a key challenge to elucidate how these systems can be engineered to assemble in an efficient manner and avoid kinetic trapping. We show here that simple scaling laws emerge from a set of kinetic equations describing the self-assembly of identical building blocks into closed supramolecular structures and that this scaling behavior provides general rules that determine efficient assembly in these systems. Using this framework, we uncover the existence of a narrow range of parameter space that supports efficient self-assembly and reveal that nature capitalizes on this behavior to direct the reliable assembly of viral capsids on biologically relevant timescales.