Insight into the correlation between lag time and aggregation rate in the kinetics of protein aggregation

Self-Assembly of Metallo-Supramolecular Amphiphiles based on Azadipyrromethenes: Consecutive Pathways to Nanodiscs and Nanosheets

A new class of metallo-supramolecular amphiphilic dyes 1 a, b was constructed by using two azadipyrromethene units which were respectively modified with two hydrophobic alkyl and two hydrophilic oligo(ethylene glycol) chains. The spectroscopic and morphological studies revealed the consecutive self-assembly pathways of 1 a in EtOH/H2O mixed solvent. The monomers of 1 a firstly aggregated into the kinetic-controlled, nanodisc-shaped Agg. I upon cooling and the latter spontaneously transformed into the thermodynamically more stable Agg. II with a nanosheet morphology. While the non-fluorescent Agg. I displayed a broad absorption band (λmax=615 nm), the Agg. II displayed a more intensive and narrowed J-band (λmax=693 nm) and a fluorescence band with a maximum at 760 nm (Φfl=0.1), which could be ascribed to the J-aggregation induced emission enhancement. The kinetics of Agg. I to Agg. II transformation was further modulated by seed-initiated supramolecular polymerization with various ratios of Seedagg.II, in which the transformation rate was significantly increased by ca. 2 orders of magnitude compared to the spontaneous process. The supramolecular amphiphile 1 b bearing longer hydrophilic chains formed only one type aggregate, which exhibited spectroscopic and morphological properties that were highly comparable with that of Agg. I.

Curating models from BioModels: Developing a workflow for creating OMEX files

The reproducibility of computational biology models can be greatly facilitated by widely adopted standards and public repositories. We examined 50 models from the BioModels Database and attempted to validate the original curation and correct some of them if necessary. For each model, we reproduced these published results using Tellurium. Once reproduced we manually created a new set of files, with the model information stored by the Systems Biology Markup Language (SBML), and simulation instructions stored by the Simulation Experiment Description Markup Language (SED-ML), and everything included in an Open Modeling EXchange (OMEX) file, which could be used with a variety of simulators to reproduce the same results. On the one hand, the reproducibility procedure of 50 models developed a manual workflow that we would use to build an automatic platform to help users more easily curate and verify models in the future. On the other hand, these exercises allowed us to find the limitations and possible enhancement of the current curation and tooling to verify and curate models.

Curating models from BioModels: Developing a workflow for creating OMEX files

The reproducibility of computational biology models can be greatly facilitated by widely adopted standards and public repositories. We examined 50 models from the BioModels Database and attempted to validate the original curation and correct some of them if necessary. For each model, we reproduced these published results using Tellurium. Once reproduced we manually created a new set of files, with the model information stored by the Systems Biology Markup Language (SBML), and simulation instructions stored by the Simulation Experiment Description Markup Language (SED-ML), and everything included in an Open Modeling EXchange (OMEX) file, which could be used with a variety of simulators to reproduce the same results. On the one hand, the reproducibility procedure of 50 models developed a manual workflow that we would use to build an automatic platform to help users more easily curate and verify models in the future. On the other hand, these exercises allowed us to find the limitations and possible enhancement of the current curation and tooling to verify and curate models.

Thermal Input/Concentration Output Systems Processed by Chemical Reactions of Helicene Oligomers

This article describes thermal input/concentration output systems processed by chemical reactions. Various sophisticated thermal inputs can be converted into concentration outputs through the double-helix formation of helicene oligomers exhibiting thermal hysteresis. The inputs include high or low temperature, cooling or heating state, slow or fast cooling state, heating state, and cooling history. The chemical basis for the properties of the chemical reactions includes the reversibility out of chemical equilibrium, sigmoidal relationship and kinetics, bistability involving metastable states, positive feedback by self-catalytic chemical reactions, competitive chemical reactions, and fine tunability for parallel processing. The interfacing of concentration outputs in other systems is considered, and biological cells are considered to have been utilizing such input/output systems processed by chemical reactions.

Reaction Rate Governs the Viscoelasticity and Nanostructure of Folded Protein Hydrogels

Hydrogels constructed from folded protein domains are of increasing interest as resilient and responsive biomaterials, but their optimization for applications requires time-consuming and costly molecular design. Here, we explore a complementary approach to control their properties by examining the influence of crosslinking rate on the structure and viscoelastic response of a model hydrogel constructed from photochemically crosslinked bovine serum albumin (BSA). Gelation is observed to follow a heterogeneous nucleation pathway in which BSA monomers crosslink into compact nuclei that grow into fractal percolated networks. Both the viscoelastic response probed by shear rheology and the nanostructure probed by small-angle X-ray scattering (SAXS) are shown to depend on the photochemical crosslinking reaction rate, with increased reaction rates corresponding to higher viscoelastic moduli, lower fractal dimension, and higher fractal cluster size. Reaction rate-dependent changes are shown to be consistent with a transition between diffusion- and rate-limited assembly, and the corresponding changes to viscoelastic response are proposed to arise from the presence of nonfractal depletion regions, as confirmed by SAXS. This controllable nanostructure and viscoelasticity constitute a potential route for the precise control of hydrogel properties, without the need for molecular modification.

Modulation of the competition between renaturation and aggregation of lysozyme by additive mixtures

The effects of 17 kinds of additive mixtures have been studied on refolding and aggregation of a model protein, lysozyme. Most of the prepared mixtures were efficient in inhibiting aggregation of the protein, and, surprisingly, four novel additive mixtures, i.e., lactic acid: l-arginine, lactic acid: l-glutamine, choline chloride: lactic acid, and imidazolium salt: β-cyclodextrin as well as choline chloride: urea exhibited a more remarkable efficacy in suppressing aggregation. Among these, lactic acid: l-arginine was identified as the most efficient additive, and lactic acid: l-glutamine and choline chloride: lactic acid were inefficient to recover the enzyme activity. In contrast, choline chloride: ethylene glycol: imidazole, choline chloride: glycerol: imidazole, imidazole: betaine: ethylene glycol were found to be less effective mixtures in preventing enzyme aggregation. Totally, it was demonstrated that the protective effects of the mixtures were improved as their concentrations increased. The improvement was more remarkable for imidazolium salt: β-cyclodextrin and choline chloride: urea, where the denatured lysozyme was reactivated and recovered up to 85% of its initial activity by enhancing their concentrations from 1 to 5% (V/V). It is suggested that such solution additives may be further employed as artificial chaperones to assist protein folding and stability.

Obstacles to translating the promise of nanoparticles into viable amyloid disease therapeutics

Nanoparticles (NPs) constitute a powerful therapeutic platform with exciting prospects as potential inhibitors of amyloid-[Formula: see text] (Aβ) aggregation, a process associated with Alzheimer's disease (AD). Researchers have synthesized and tested a large collection of NPs with disparate sizes, shapes, electrostatic properties and surface ligands that evoke a variety of responses on Aβ aggregation. In spite of a decade of research on the NP-Aβ system and many promising experimental results, NPs have failed to progress to any level of clinical trials for AD. A theoretical framework with which to approach this physical system is presented featuring two simple metrics, (1) the extent to which NPs adsorb Aβ, and (2) the degree to which interaction with a NP alters Aβ conformation relative to aggregation propensity. Most of our current understanding of these two interactions has been gained through experimentation, and many of these studies are reviewed herein. We also provide a potential roadmap for studies that we believe could produce viable NPs as an effective AD therapeutic platform.

The Impact of Mathematical Modeling in Understanding the Mechanisms Underlying Neurodegeneration: Evolving Dimensions and Future Directions

Neurodegenerative diseases are a heterogeneous group of disorders that are characterized by the progressive dysfunction and loss of neurons. Here, we distil and discuss the current state of modeling in the area of neurodegeneration, and objectively compare the gaps between existing clinical knowledge and the mechanistic understanding of the major pathological processes implicated in neurodegenerative disorders. We also discuss new directions in the field of neurodegeneration that hold potential for furthering therapeutic interventions and strategies.

Modeling the Effect of Monomer Conformational Change on the Early Stage of Protein Self-Assembly into Fibrils

Filamentous self-assembly of proteins is an important process implicated in a plethora of human diseases and of interest for nanotechnology. Using rate equations, we analyze the early stage of the process in solutions that initially contain fibrillation-passive protein monomers and in which the nascent fibrils are practically insoluble. The analysis is based on a model accounting for the conformational and/or other changes the passive monomers experience to transform themselves into fibrillation-active monomers and thus become fibril nuclei. The model allows exact, comprehensive, and simple mathematical description of the early stage of fibrillation, which reveals the usually neglected role of the nucleation nonstationarity in this stage of fibrillation. We obtain exact and user-friendly expressions for experimentally accessible quantities such as the size distribution of fibrils, their number and mass concentrations, the rate and nonstationary period of fibril nucleation, and the delay time of fibril formation. Analyzing available experimental data, we find that the theory successfully describes the fibrillation time course of pathological and nonpathological ataxin-3, a protein involved in the neurodegenerative disorder spinocerebellar ataxia type-3. The analysis provides mechanistic insight into the reason for the higher fibril nucleation and elongation rates of the pathological ataxin-3.

Insulin Formulation Characterization-the Thioflavin T Assays

The insulin molecule was discovered in 1921. Shortly thereafter, its propensity towards amyloid fibril formation, fibrillation, was observed and described in the literature as a "precipitate." In the past decades, the increased incidence of type 2 diabetes has reached global epidemic proportions. This has emphasized the demands for both insulin production and the development of modern insulin products for unmet medical needs. Bringing such new insulin drug products to the market for the benefit of patients requires that many CMC-related processes are understood, described, and controlled. One potential undesired process is insulin fibril formation. The compound thioflavin T (ThT) is known as a fluorescent probe for amyloid fibrils. As such, ThT is utilized in a versatile research assay in microtiter plate format, the ThT assay. This review will describe an experimental set-up using not only a ThT microtiter plate assay but also two orthogonal methods. The use of the ThT assay in research and characterization of insulin analogues, as well as formulations of insulin, is described by cases drawn from the scientific literature and patents. The ThT assay is compared to other physical stability tests and in conclusion the advantages and limitations of the assay are compared.

Probing the Impact of Acidification on Spider Silk Assembly Kinetics

Spiders utilize fine adjustment of the physicochemical conditions within its silk spinning system to regulate spidroin assembly into solid silk fibers with outstanding mechanical properties. However, the exact mechanism about which this occurs remains elusive and is still hotly debated. In this study, the effect of acidification on spider silk assembly was investigated on native spidroins from the major ampullate (MA) gland fluid excised from Latrodectus hesperus (Black Widow) spiders. Incubating the protein-rich MA silk gland fluid at acidic pH conditions results in the formation of silk fibers that are 10-100 μm in length and ∼2 μm in diameter as judged by optical and electron microscope methods. The in vitro spider silk assembly kinetics were monitored as a function of pH with a (13)C solid-state MAS NMR approach. The results confirm the importance of acidic pH in the spider silk self-assembly process with observation of a sigmoidal nucleation-elongation kinetic profile. The rates of nucleation and elongation as well as the percentage of β-sheet structure in the grown fibers depend on the pH. These results confirm the importance of an acidic pH gradient along the spinning duct for spider silk formation and provide a powerful spectroscopic approach to probe the kinetics of spider silk formation under various biochemical conditions.

Kinetics of protein fibrillation controlled by fibril elongation

Numerous proteins have the ability to assemble into fibrillar aggregates which are of great interest, because they feature in scores of human diseases and many technological products. In the present work, we analyze the kinetics of protein fibrillation when the process is governed solely by elongation of initially appeared fibrils in the protein solution. We derive exact expressions for the time dependences of the fibrillation degree, the concentration of monomeric protein in the solution, and the average fibril size. Furthermore, we present formulas for the initial fibrillation rate and the half-fibrillation time in terms of experimentally controllable quantities. The results obtained provide a mechanistic insight into the kinetics of protein fibrillation mediated by fibril elongation. We confront theory with experiment and find that it allows a good description of available experimental data for fibrillation of the Alzheimer's disease-associated protein Aβ(1-40) and the yeast prion protein Sup35.

Relationship between the initial rate of protein aggregation and the lag period for amorphous aggregation

Lag period is an inherent characteristic of the kinetic curves registered for protein aggregation. The appearance of a lag period is connected with the nucleation stage and the stages of the formation of folding or unfolding intermediates prone to aggregation (for example, the stage of protein unfolding under stress conditions). Discovering the kinetic regularities essential for elucidation of the protein aggregation mechanism comprises deducing the relationship between the lag period and aggregation rate. Fändrich proposed the following equation connecting the duration of the lag phase (tlag) and the aggregate growth rate (kg) in the amyloid fibrillation: kg=const/tlag. To establish the relationship between the initial rate of protein aggregation (v) and the lag period (t0) in the case of amorphous aggregation, the kinetics of dithithreitol-induced aggregation of holo-α-lactalbumin from bovine milk was studied (0.1M Na-phosphate buffer, pH 6.8; 37°C). The order of aggregation with respect to protein (n) was calculated from the dependence of the initial rate of protein aggregation on the α-lactalbumin concentration (n=5.3). The following equation connecting v and t0 has been proposed: v(1/n)=const/(t0-t0,lim), where t0,lim is the limiting value of t0 at high concentrations of the protein.

Protein fibrillation due to elongation and fragmentation of initially appeared fibrils: a simple kinetic model

The assembly of various proteins into fibrillar aggregates is an important phenomenon with wide implications ranging from human disease to nanoscience. Employing a new model, we analyze the kinetics of protein fibrillation in the case when the process occurs by elongation of initially appeared fibrils which multiply solely by fragmentation, because fibril nucleation is negligible. Owing to its simplicity, our model leads to mathematically friendly and physically clear formulas for the time dependence of the fibrillation degree and for a number of experimental observables such as the maximum fibrillation rate, the fibrillation lag time, and the half-fibrillation time. These formulas provide a mechanistic insight into the kinetics of fragmentation-affected fibrillation of proteins. We confront theory with experiment and find that our model allows a good global description of a large dataset [W.-F. Xue, S. W. Homans, and S. E. Radford, Proc. Natl. Acad. Sci. U.S.A. 105, 8926 (2008)] for the fibrillation kinetics of beta-2 microglobulin. Our analysis leads to new methods for experimental determination of the fibril solubility, elongation rate constant, and nucleation rate from data for the time course of protein fibrillation.

Solubility and supersaturation-dependent protein misfolding revealed by ultrasonication

Although alcohols are useful cosolvents for producing amyloid fibrils, the underlying mechanism of alcohol-dependent fibrillation is unclear. We studied the alcohol-induced fibrillation of hen egg-white lysozyme at various concentrations of ethanol, 2,2,2-trifluoroethanol (TFE), and 1,1,1,3,3,3-hexafluoro-2-propanol (HFIP). Under the conditions where the alcohol-denatured lysozyme retained metastability, ultrasonication effectively triggered fibrillation. The optimal alcohol concentration depended on the alcohol species. HFIP showed a sharp maximum at 12-16%. For TFE, a broad maximum at 40-80% was observed. Ethanol exhibited only an increase in fibrillation above 60%. These profiles were opposite to the equilibrium solubility of lysozyme in water/alcohol mixtures. The results indicate that although fibrillation is determined by solubility, supersaturation prevents conformational transitions and ultrasonication is highly effective in minimizing an effect of supersaturation. We propose an alcohol-dependent protein misfolding funnel useful for examining amyloidogenicity. This misfolding funnel will apply to fibrillation under physiological conditions where biological environments play important roles in decreasing the solubility.

Modelling amyloid fibril formation kinetics: mechanisms of nucleation and growth

Amyloid and amyloid-like fibrils are self-assembling protein nanostructures, of interest for their robust material properties and inherent biological compatibility as well as their putative role in a number of debilitating mammalian disorders. Understanding fibril formation is essential to the development of strategies to control, manipulate or prevent fibril growth. As such, this area of research has attracted significant attention over the last half century. This review describes a number of different models that have been formulated to describe the kinetics of fibril assembly. We describe the macroscopic implications of mechanisms in which secondary processes such as secondary nucleation, fragmentation or branching dominate the assembly pathway, compared to mechanisms dominated by the influence of primary nucleation. We further describe how experimental data can be analysed with respect to the predictions of kinetic models.

Kinetic profile of amyloid formation in the presence of an aromatic inhibitor by nuclear magnetic resonance

The self-assembly of amyloid proteins into β-sheet rich assemblies is associated with human amyloidoses including Alzheimer's disease, Parkinson's disease, and type 2 diabetes. An attractive therapeutic strategy therefore is to develop small molecules that would inhibit protein self-assembly. Natural polyphenols are potential inhibitors of β-sheet formation. How these compounds affect the kinetics of self-assembly studied by thioflavin T (ThT) fluorescence is not understood primarily because their presence interferes with ThT fluorescence. Here, we show that by plotting peak intensities from nuclear magnetic resonance (NMR) against incubation time, kinetic profiles in the presence of the polyphenol can be obtained from which kinetic parameters of self-assembly can be easily determined. In applying this technique to the self-assembly of the islet amyloid polypeptide in the presence of curcumin, a biphenolic compound found in turmeric, we show that the kinetic profile is atypical in that it shows a prenucleation period during which there is no observable decrease in NMR peak intensities.

A generic crystallization-like model that describes the kinetics of amyloid fibril formation

Associated with neurodegenerative disorders such as Alzheimer, Parkinson, or prion diseases, the conversion of soluble proteins into amyloid fibrils remains poorly understood. Extensive "in vitro" measurements of protein aggregation kinetics have been reported, but no consensus mechanism has emerged until now. This contribution aims at overcoming this gap by proposing a theoretically consistent crystallization-like model (CLM) that is able to describe the classic types of amyloid fibrillization kinetics identified in our literature survey. Amyloid conversion represented as a function of time is shown to follow different curve shapes, ranging from sigmoidal to hyperbolic, according to the relative importance of the nucleation and growth steps. Using the CLM, apparently unrelated data are deconvoluted into generic mechanistic information integrating the combined influence of seeding, nucleation, growth, and fibril breakage events. It is notable that this complex assembly of interdependent events is ultimately reduced to a mathematically simple model, whose two parameters can be determined by little more than visual inspection. The good fitting results obtained for all cases confirm the CLM as a good approximation to the generalized underlying principle governing amyloid fibrillization. A perspective is presented on possible applications of the CLM during the development of new targets for amyloid disease therapeutics.

Two-step nucleation of amyloid fibrils: omnipresent or not?

Amyloid protein fibrils feature in various diseases and nanotechnological products. Currently, it is debated whether they nucleate in one step (i.e., directly from the protein solution) or in two steps (step one being the appearance of nonfibrillar oligomers in the solution and step two being the oligomer conversion into fibrils). We employ nucleation theory to gain insight into the idiosyncrasy of two-step fibril nucleation and to determine the conditions under which this process can take place. Presenting an expression for the rate of two-step fibril nucleation, we use it to qualitatively describe experimental data for two-step nucleated amyloid-β fibrils. Our analysis helps in understanding why, in some experiments, oligomers rather than fibrils form and remain structurally unchanged and why, in others, the oligomers convert into fibrils.

Stoichiometry for binding and transport by the twin arginine translocation system

Twin arginine translocation (Tat) systems transport large folded proteins across sealed membranes. Tat systems accomplish this feat with three membrane components organized in two complexes. In thylakoid membranes, cpTatC and Hcf106 comprise a large receptor complex containing an estimated eight cpTatC-Hcf106 pairs. Protein transport occurs when Tha4 joins the receptor complex as an oligomer of uncertain size that is thought to form the protein-conducting structure. Here, binding analyses with intact membranes or purified complexes indicate that each receptor complex could bind eight precursor proteins. Kinetic analysis of translocation showed that each precursor-bound site was independently functional for transport, and, with sufficient Tha4, all sites were concurrently active for transport. Tha4 titration determined that ∼26 Tha4 protomers were required for transport of each OE17 (oxygen-evolving complex subunit of 17 kD) precursor protein. Our results suggest that, when fully saturated with precursor proteins and Tha4, the Tat translocase is an ∼2.2-megadalton complex that can individually transport eight precursor proteins or cooperatively transport multimeric precursors.

Size distribution of amyloid nanofibrils

We consider the size distribution of amyloid nanofibrils (protofilaments) in nucleating protein solutions when the nucleation process occurs by the mechanism of direct polymerization of β-strands (extended peptides or protein segments) into β-sheets. Employing the atomistic nucleation theory, we derive a general expression for the stationary size distribution of amyloid nanofibrils constituted of successively layered β-sheets. The application of this expression to amyloid β(1-40) (Aβ(40)) fibrils allows us to determine the nanofibril size distribution as a function of the protein concentration and temperature. The distribution is most remarkable with its exhibiting a series of peaks positioned at "magic" nanofibril sizes (or lengths), which are due to deep local minima in the work for fibril formation. This finding of magic sizes or lengths is consistent with experimental results for the size distribution of aggregates in solutions of Aβ(40) proteins. Also, our approach makes it possible to gain insight into the effect of point mutations on the nanofibril size distribution, an effect that may play a role in experimentally observed substantial differences in the fibrillation lag-time of wild-type and point-mutated amyloid-β proteins.

Nucleated polymerisation in the presence of pre-formed seed filaments

We revisit the classical problem of nucleated polymerisation and derive a range of exact results describing polymerisation in systems intermediate between the well-known limiting cases of a reaction starting from purely soluble material and for a reaction where no new growth nuclei are formed.

Atomistic theory of amyloid fibril nucleation

We consider the nucleation of amyloid fibrils at the molecular level when the process takes place by a direct polymerization of peptides or protein segments into β-sheets. Employing the atomistic nucleation theory (ANT), we derive a general expression for the work to form a nanosized amyloid fibril (protofilament) composed of successively layered β-sheets. The application of this expression to a recently studied peptide system allows us to determine the size of the fibril nucleus, the fibril nucleation work, and the fibril nucleation rate as functions of the supersaturation of the protein solution. Our analysis illustrates the unique feature of ANT that the size of the fibril nucleus is a constant integer in a given supersaturation range. We obtain the ANT nucleation rate and compare it with the rates determined previously in the scope of the classical nucleation theory (CNT) and the corrected classical nucleation theory (CCNT). We find that while the CNT nucleation rate is orders of magnitude greater than the ANT one, the CCNT and ANT nucleation rates are in very good quantitative agreement. The results obtained are applicable to homogeneous nucleation, which occurs when the protein solution is sufficiently pure and/or strongly supersaturated.

DHPC strongly affects the structure and oligomerization propensity of Alzheimer's Aβ(1-40) peptide

Alzheimer's disease (AD) is thought to depend on the deleterious action of amyloid fibrils or oligomers derived from β-amyloid (Aβ) peptide. Out of various known Aβ alloforms, the 40-residue peptide Aβ(1-40) occurs at highest concentrations inside the brains of AD patients. Its aggregation properties critically depend on lipids, and it was thus proposed that lipids could play a major role in AD. To better understand their possible effects on the structure of Aβ and on the ability of this peptide to form potentially detrimental amyloid structures, we here analyze the interactions between Aβ(1-40) and 1,2-dihexanoyl-sn-glycero-3-phosphocholine (DHPC). DHPC has served, due to its controlled properties, as a major model system for studying general lipid properties. Here, we show that DHPC concentrations of 8 mM or higher exert dramatic effects on the conformation of soluble Aβ(1-40) peptide and induce the formation of β-sheet structure at high levels. By contrast, we find that DHPC concentrations well below the critical micelle concentration present no discernible effect on the conformation of soluble Aβ, although they substantially affect the peptide's oligomerization and fibrillation kinetics. These data imply that subtle lipid-peptide interactions suffice in controlling the overall aggregation properties and drastically accelerate, or delay, the fibrillation kinetics of Aβ peptide in near-physiological buffer solutions.