Self-replication of Aß42 aggregates occurs on small and isolated fibril sites.

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.

A solid beta-sheet structure is formed at the surface of FUS droplets during aging.

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 ß-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.

Spontaneous nucleation and fast aggregate-dependent proliferation of α-synuclein aggregates within liquid condensates at neutral pH.

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.

Adsorption free energy predicts amyloid protein nucleation rates.

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.

Kinetic analysis reveals that independent nucleation events determine the progression of polyglutamine aggregation in C. elegans.

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.

Aggregation controlled by condensate rheology.

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.

Optimal control of aging in complex networks.

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.

Kinetic diversity of amyloid oligomers.

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.

Thermodynamic and kinetic design principles for amyloid-aggregation inhibitors.

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.

Kinetic profiling of therapeutic strategies for inhibiting the formation of amyloid oligomers.

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.

Optimal control strategies for inhibition of protein aggregation.

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-ß(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.

Feedback control of protein aggregation.

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.

SAR by kinetics for drug discovery in protein misfolding 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 (Aß), which we then exploit to optimize starting compounds to curtail Aß oligomer formation. We demonstrate this approach by converting an inactive rhodanine compound into an effective inhibitor of Aß 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.

Mechanical basis for fibrillar bundle morphology.

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 catalytic nature of protein aggregation.

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 Aß40 aggregation. Remarkably, we find that primary nucleation becomes saturated, demonstrating that it must be heterogeneous, occurring at interfaces and not in solution.

Chemical Kinetics for Bridging Molecular Mechanisms and Macroscopic Measurements of Amyloid Fibril Formation.

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.

Dynamics and Control of Peptide Self-Assembly and Aggregation.

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.

Cooperative Assembly of Hsp70 Subdomain Clusters.

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.

Direct Observation of Oligomerization by Single Molecule Fluorescence Reveals a Multistep Aggregation Mechanism for the Yeast Prion Protein Ure2.

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.

Force generation by the growth of amyloid aggregates.

The generation of mechanical forces are central to a wide range of vital biological processes, including the function of the cytoskeleton. Although the forces emerging from the polymerization of native proteins have been studied in detail, the potential for force generation by aberrant protein polymerization has not yet been explored. Here, we show that the growth of amyloid fibrils, archetypical aberrant protein polymers, is capable of unleashing mechanical forces on the piconewton scale for individual filaments. We apply microfluidic techniques to measure the forces released by amyloid growth for two systems: insulin and lysozyme. The level of force measured for amyloid growth in both systems is comparable to that observed for actin and tubulin, systems that have evolved to generate force during their native functions and, unlike amyloid growth, rely on the input of external energy in the form of nucleotide hydrolysis for maximum force generation. Furthermore, we find that the power density released from growing amyloid fibrils is comparable to that of high-performance synthetic polymer actuators. These findings highlight the potential of amyloid structures as active materials and shed light on the criteria for regulation and reversibility that guide molecular evolution of functional polymers.