Samuel I. A. Cohen

An analytical solution to the kinetics of breakable filament assembly.

Dissecting Amyloid Formation Amyloid fibrils are associated with clinical disorders ranging from Alzheimers disease to type II diabetes. Their self-assembly can be described by a master equation that takes into account nucleation-dependent polymerization and fragmentation. Knowles et al. (p. 1533) now present an analytical solution to the master equation, which shows that amyloid growth kinetics is often limited by the fragmentation rate rather than by the rate of primary nucleation. In addition, the results reveal relationships between system properties (scaling laws) that provide mechanistic insight not only into amyloid growth, but also into related self-assembly processes. The growth kinetics of amyloid fibrils and related self-assembly phenomena are revealed by analytical theory. We present an analytical treatment of a set of coupled kinetic equations that governs the self-assembly of filamentous molecular structures. Application to the case of protein aggregation demonstrates that the kinetics of amyloid growth can often be dominated by secondary rather than by primary nucleation events. Our results further reveal a range of general features of the growth kinetics of fragmenting filamentous structures, including the existence of generic scaling laws that provide mechanistic information in contexts ranging from in vitro amyloid growth to the in vivo development of mammalian prion diseases.

Proliferation of amyloid-β42 aggregates occurs through a secondary nucleation mechanism

The generation of toxic oligomers during the aggregation of the amyloid-β (Aβ) peptide Aβ42 into amyloid fibrils and plaques has emerged as a central feature of the onset and progression of Alzheimer’s disease, but the molecular pathways that control pathological aggregation have proved challenging to identify. Here, we use a combination of kinetic studies, selective radiolabeling experiments, and cell viability assays to detect directly the rates of formation of both fibrils and oligomers and the resulting cytotoxic effects. Our results show that once a small but critical concentration of amyloid fibrils has accumulated, the toxic oligomeric species are predominantly formed from monomeric peptide molecules through a fibril-catalyzed secondary nucleation reaction, rather than through a classical mechanism of homogeneous primary nucleation. This catalytic mechanism couples together the growth of insoluble amyloid fibrils and the generation of diffusible oligomeric aggregates that are implicated as neurotoxic agents in Alzheimer’s disease. These results reveal that the aggregation of Aβ42 is promoted by a positive feedback loop that originates from the interactions between the monomeric and fibrillar forms of this peptide. Our findings bring together the main molecular species implicated in the Aβ aggregation cascade and suggest that perturbation of the secondary nucleation pathway identified in this study could be an effective strategy to control the proliferation of neurotoxic Aβ42 oligomers.

Direct Observation of the Interconversion of Normal and Toxic Forms of α-Synuclein

Summary Here, we use single-molecule techniques to study the aggregation of α-synuclein, the protein whose misfolding and deposition is associated with Parkinsons disease. We identify a conformational change from the initially formed oligomers to stable, more compact proteinase-K-resistant oligomers as the key step that leads ultimately to fibril formation. The oligomers formed as a result of the structural conversion generate much higher levels of oxidative stress in rat primary neurons than do the oligomers formed initially, showing that they are more damaging to cells. The structural conversion is remarkably slow, indicating a high kinetic barrier for the conversion and suggesting that there is a significant period of time for the cellular protective machinery to operate and potentially for therapeutic intervention, prior to the onset of cellular damage. In the absence of added soluble protein, the assembly process is reversed and fibrils disaggregate to form stable oligomers, hence acting as a source of cytotoxic species.

From Macroscopic Measurements to Microscopic Mechanisms of Protein Aggregation

The ability to relate bulk experimental measurements of amyloid formation to the microscopic assembly processes that underlie protein aggregation is critical in order to achieve a quantitative understanding of this complex phenomenon. In this review, we focus on the insights from classical and modern theories of linear growth phenomena and discuss how theory allows the roles of growth and nucleation processes to be defined through the analysis of experimental in vitro time courses of amyloid formation. Moreover, we discuss the specific signatures in the time course of the reactions that correspond to the actions of primary and secondary nucleation processes, and outline strategies for identifying and characterising the nature of the dominant process responsible in each case for the generation of new aggregates. We highlight the power of a global analysis of experimental time courses acquired under different conditions, and discuss how such an analysis allows a rigorous connection to be established between the macroscopic measurements and the rates of the individual microscopic processes that underlie the phenomenon of amyloid formation.

Nucleated polymerization with secondary pathways. I. Time evolution of the principal moments

Self-assembly processes resulting in linear structures are often observed in molecular biology, and include the formation of functional filaments such as actin and tubulin, as well as generally dysfunctional ones such as amyloid aggregates. Although the basic kinetic equations describing these phenomena are well-established, it has proved to be challenging, due to their non-linear nature, to derive solutions to these equations except for special cases. The availability of general analytical solutions provides a route for determining the rates of molecular level processes from the analysis of macroscopic experimental measurements of the growth kinetics, in addition to the phenomenological parameters, such as lag times and maximal growth rates that are already obtainable from standard fitting procedures. We describe here an analytical approach based on fixed-point analysis, which provides self-consistent solutions for the growth of filamentous structures that can, in addition to elongation, undergo internal fracturing and monomer-dependent nucleation as mechanisms for generating new free ends acting as growth sites. Our results generalise the analytical expression for sigmoidal growth kinetics from the Oosawa theory for nucleated polymerisation to the case of fragmenting filaments. We determine the corresponding growth laws in closed form and derive from first principles a number of relationships which have been empirically established for the kinetics of the self-assembly of amyloid fibrils.

Differences in nucleation behavior underlie the contrasting aggregation kinetics of the Aβ40 and Aβ42 peptides

Significance Alzheimers disease and several related disorders are associated with the assembly of specific proteins into ordered fibrillar aggregates. In Alzheimers disease, the key component of pathological aggregates, the Aβ peptide, is produced from a precursor protein in variable lengths: Aβ40 is more abundant and Aβ42 more aggregation-prone. To shed light on the molecular basis of disease progression, the aggregation process has been studied in vitro. New theoretical models allow us to relate kinetic measurements to the rates of the individual processes underlying the aggregation reaction. We find that the loss of two residues in Aβ40 relative to Aβ42 significantly slows nucleation of aggregates in solution, thereby shifting the mechanism yet more strongly towards nucleation on the surface of fibrils. The two major forms of the amyloid-beta (Aβ) peptide found in plaques in patients suffering from Alzheimer’s disease, Aβ40 and Aβ42, only differ by two amino acids in the C-terminal region, yet they display markedly different aggregation behavior. The origins of these differences have remained challenging to connect to specific molecular-level processes underlying the aggregation reaction. In this paper we use a general strategy to apply the conventional workflow of chemical kinetics to the aggregation of the Aβ40 peptide to identify the differences between Aβ40 and Aβ42 in terms of the microscopic determinants of the aggregation reaction. Our results reveal that the major source of aggregates in the case of Aβ40 is a fibril-catalyzed nucleation process, the multistep nature of which is evident through its saturation behavior. Moreover, our results show that the significant differences in the observed behavior of the two proteins originate not simply from a uniform increase in all microscopic rates for Aβ42 compared with Aβ40, but rather are due to a shift of more than one order of magnitude in the relative importance of primary nucleation versus fibril-catalyzed secondary nucleation processes. This analysis sheds light on the microscopic determinants of the aggregation behavior of the principal forms of Aβ and outlines a general approach toward achieving an understanding at the molecular level of the aberrant deposition of insoluble peptides in neurodegenerative disorders.

Nucleated polymerization with secondary pathways. II. Determination of self-consistent solutions to growth processes described by non-linear master equations

Nucleated polymerisation processes are involved in many growth phenomena in nature, including the formation of cytoskeletal filaments and the assembly of sickle hemoglobin and amyloid fibrils. Closed form rate equations have, however, been challenging to derive for these growth phenomena in cases where secondary nucleation processes are active, a difficulty exemplified by the highly non-linear nature of the equation systems that describe monomer dependent secondary nucleation pathways. We explore here the use of fixed point analysis to provide self-consistent solutions to such growth problems. We present iterative solutions and discuss their convergence behaviour. We establish a range of closed form results for linear growth processes, including the scaling behaviours of the maximum growth rate and of the reaction end-point. We further show that a self-consistent approach applied to the master equation of filamentous growth allows the determination of the evolution of the shape of the length distribution including the mean, the standard deviation, and the mode. Our results highlight the power of fixed-point approaches in finding closed form self-consistent solutions to growth problems characterised by the highly non-linear master equations.

Observation of spatial propagation of amyloid assembly from single nuclei

The crucial early stages of amyloid growth, in which normally soluble proteins are converted into fibrillar nanostructures, are challenging to study using conventional techniques yet are critical to the protein aggregation phenomena implicated in many common pathologies. As with all nucleation and growth phenomena, it is difficult to track individual nuclei in traditional macroscopic experiments, which probe the overall temporal evolution of the sample, but do not yield detailed information on the primary nucleation step as they mix independent stochastic events into an ensemble measurement. To overcome this limitation, we have developed microdroplet assays enabling us to detect single primary nucleation events and to monitor their subsequent spatial as well as temporal evolution, both of which we find to be determined by secondary nucleation phenomena. By deforming the droplets to high aspect ratio, we visualize in real-time propagating waves of protein assembly emanating from discrete primary nucleation sites. We show that, in contrast to classical gelation phenomena, the primary nucleation step is characterized by a striking dependence on system size, and the filamentous protein self-assembly process involves a highly nonuniform spatial distribution of aggregates. These findings deviate markedly from the current picture of amyloid growth and uncover a general driving force, originating from confinement, which, together with biological quality control mechanisms, helps proteins remain soluble and therefore functional in nature.

Nucleated polymerization with secondary pathways. III. Equilibrium behavior and oligomer populations

We explore the long-time behavior and equilibrium properties of a system of linear filaments growing through nucleated polymerisation. We show that the length distribution for breakable filaments evolves through two well defined limiting cases: first, a steady state distribution determined by the balance of breakage and elongation is reached; upon monomer depletion at the end of the growth phase, an equilibrium length distribution biased towards smaller filament fragments emerges. We furthermore compute the time evolution of the concentration of small oligomeric filament fragments. For frangible filaments, oligomers are present both at early times and at equilibrium, whereas in the absence of fragmentation, oligomers are only present in significant quantities at the beginning of the polymerisation reaction. Finally, we discuss the significance of these results for the biological consequences of filamentous protein aggregation.

An anticancer drug suppresses the primary nucleation reaction that initiates the production of the toxic Aβ42 aggregates linked with Alzheimer's disease.

An approved anticancer drug selectively targets the first step in the molecular cascade resulting in Alzheimer’s disease. The conversion of the β-amyloid (Aβ) peptide into pathogenic aggregates is linked to the onset and progression of Alzheimer’s disease. Although this observation has prompted an extensive search for therapeutic agents to modulate the concentration of Aβ or inhibit its aggregation, all clinical trials with these objectives have so far failed, at least in part because of a lack of understanding of the molecular mechanisms underlying the process of aggregation and its inhibition. To address this problem, we describe a chemical kinetics approach for rational drug discovery, in which the effects of small molecules on the rates of specific microscopic steps in the self-assembly of Aβ42, the most aggregation-prone variant of Aβ, are analyzed quantitatively. By applying this approach, we report that bexarotene, an anticancer drug approved by the U.S. Food and Drug Administration, selectively targets the primary nucleation step in Aβ42 aggregation, delays the formation of toxic species in neuroblastoma cells, and completely suppresses Aβ42 deposition and its consequences in a Caenorhabditis elegans model of Aβ42-mediated toxicity. These results suggest that the prevention of the primary nucleation of Aβ42 by compounds such as bexarotene could potentially reduce the risk of onset of Alzheimer’s disease and, more generally, that our strategy provides a general framework for the rational identification of a range of candidate drugs directed against neurodegenerative disorders.