Prionics or the kinetic basis of prion diseases

Aβ-protein polymerization in Alzheimer disease: Optimal control for nucleation parameter estimation

In this paper, we are interested in the modeling of Alzheimer's disease from the angle of the amyloid cascade hypothesis, where the pathogenic agent is the Aβ protein in its oligomeric form. The formation dynamics of this pathogenic form is modeled by a Becker-Doring type model where APP (Amyloid Precursor Protein) protein, after cleavage by specific enzymes, forms monomeric Aβ proteins, which, by polymerization and/or nucleation, lead to the formation of oligomeric Aβ. We propose an optimal control problem to estimate the rate of nucleation which seems to be at the base of this amyloid cascade hypothesis and for which no (experimental) measurement exists for the moment.

MIL-CELL: a tool for multi-scale simulation of yeast replication and prion transmission

The single-celled baker's yeast, Saccharomyces cerevisiae, can sustain a number of amyloid-based prions, the three most prominent examples being [URE3], [PSI+], and [PIN+]. In the laboratory, haploid S. cerevisiae cells of a single mating type can acquire an amyloid prion in one of two ways (i) spontaneous nucleation of the prion within the yeast cell, and (ii) receipt via mother-to-daughter transmission during the cell division cycle. Similarly, prions can be lost due to (i) dissolution of the prion amyloid by its breakage into non-amyloid monomeric units, or (ii) preferential donation/retention of prions between the mother and daughter during cell division. Here we present a computational tool (Monitoring Induction and Loss of prions in Cells; MIL-CELL) for modelling these four general processes using a multiscale approach describing both spatial and kinetic aspects of the yeast life cycle and the amyloid-prion behavior. We describe the workings of the model, assumptions upon which it is based and some interesting simulation results pertaining to the wave-like spread of the epigenetic prion elements through the yeast population. MIL-CELL is provided as a stand-alone GUI executable program for free download with the paper. MIL-CELL is equipped with a relational database allowing all simulated properties to be searched, collated and graphed. Its ability to incorporate variation in heritable properties means MIL-CELL is also capable of simulating loss of the isogenic nature of a cell population over time. The capability to monitor both chronological and reproductive age also makes MIL-CELL potentially useful in studies of cell aging.

Mechanistic Models of Protein Aggregation Across Length-Scales and Time-Scales: From the Test Tube to Neurodegenerative Disease

Through advances in the past decades, the central role of aberrant protein aggregation has been established in many neurodegenerative diseases. Crucially, however, the molecular mechanisms that underlie aggregate proliferation in the brains of affected individuals are still only poorly understood. Under controlled in vitro conditions, significant progress has been made in elucidating the molecular mechanisms that take place during the assembly of purified protein molecules, through advances in both experimental methods and the theories used to analyse the resulting data. The determination of the aggregation mechanism for a variety of proteins revealed the importance of intermediate oligomeric species and of the interactions with promotors and inhibitors. Such mechanistic insights, if they can be achieved in a disease-relevant system, provide invaluable information to guide the design of potential cures to these devastating disorders. However, as experimental systems approach the situation present in real disease, their complexity increases substantially. Timescales increase from hours an aggregation reaction takes in vitro, to decades over which the process takes place in disease, and length-scales increase to the dimension of a human brain. Thus, molecular level mechanistic studies, like those that successfully determined mechanisms in vitro, have only been applied in a handful of living systems to date. If their application can be extended to further systems, including patient data, they promise powerful new insights. Here we present a review of the existing strategies to gain mechanistic insights into the molecular steps driving protein aggregation and discuss the obstacles and potential paths to achieving their application in disease. First, we review the experimental approaches and analysis techniques that are used to establish the aggregation mechanisms in vitro and the insights that have been gained from them. We then discuss how these approaches must be modified and adapted to be applicable in vivo and review the existing works that have successfully applied mechanistic analysis of protein aggregation in living systems. Finally, we present a broad mechanistic classification of in vivo systems and discuss what will be required to further our understanding of aggregate formation in living systems.

Inflammasome regulation by adaptor isoforms, ASC and ASCb, via differential self-assembly

ASC is an essential adaptor of the inflammasome, a micrometer-size multiprotein complex that processes proinflammatory cytokines. Inflammasome formation depends on ASC self-association into large assemblies via homotypic interactions of its two death domains, PYD and CARD. ASCb, an alternative splicing isoform, activates the inflammasome to a lesser extent compared with ASC. Thus, it has been postulated that adaptor isoforms differentially regulate inflammasome function. At the amino acid level, ASC and ASCb differ only in the length of the linker connecting the two death domains. To understand inflammasome regulation at the molecular level, we investigated the self-association properties of ASC and ASCb using real-time NMR, dynamic light scattering (DLS), size-exclusion chromatography, and transmission electron microscopy (TEM). The NMR data indicate that ASC self-association is faster than that of ASCb; a kinetic model for this oligomerization results in differing values for both the reaction order and the rate constants. Furthermore, DLS analysis indicates that ASC self-associates into more compact macrostructures compared with ASCb. Finally, TEM data show that ASCb has a reduced tendency to form densely packed filaments relative to ASC. Overall, these differences can only be explained by an effect of the linker length, as the NMR results show structural equivalence of the PYD and CARD in both proteins. The effect of linker length was corroborated by molecular docking with the procaspase-1 CARD domain. Altogether, our results indicate that ASC’s faster and less polydisperse polymerization is more efficient, plausibly explaining inflammasome activation differences by ASC isoforms at the molecular level.

Scaling analysis reveals the mechanism and rates of prion replication in vivo

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.

A reaction-diffusion model of spatial propagation of A[Formula: see text] oligomers in early stage Alzheimer's disease

The misconformation and aggregation of the protein Amyloid-Beta (A[Formula: see text]) is a key event in the propagation of Alzheimer's Disease (AD). Different types of assemblies are identified, with long fibrils and plaques deposing during the late stages of AD. In the earlier stages, the disease spread is driven by the formation and the spatial propagation of small amorphous assemblies called oligomers. We propose a model dedicated to studying those early stages, in the vicinity of a few neurons and after a polymer seed has been formed. We build a reaction-diffusion model, with a Becker-Döring-like system that includes fragmentation and size-dependent diffusion. We hereby establish the theoretical framework necessary for the proper use of this model, by proving the existence of solutions using a fixed point method.

From Seeds to Fibrils and Back: Fragmentation as an Overlooked Step in the Propagation of Prions and Prion-Like Proteins

Many devastating neurodegenerative diseases are driven by the misfolding of normal proteins into a pathogenic abnormal conformation. Examples of such protein misfolding diseases include Alzheimer’s disease, Parkinson’s disease, Huntington’s disease, amyotrophic lateral sclerosis, and prion diseases. The misfolded proteins involved in these diseases form self-templating oligomeric assemblies that recruit further correctly folded protein and induce their conversion. Over time, this leads to the formation of high molecular and mostly fibrillar aggregates that are increasingly inefficient at converting normal protein. Evidence from a multitude of in vitro models suggests that fibrils are fragmented to form new seeds, which can convert further normal protein and also spread to neighboring cells as observed in vivo. While fragmentation and seed generation were suggested as crucial steps in aggregate formation decades ago, the biological pathways involved remain largely unknown. Here, we show that mechanisms of aggregate clearance—namely the mammalian Hsp70–Hsp40–Hsp110 tri-chaperone system, macro-autophagy, and the proteasome system—may not only be protective, but also play a role in fragmentation. We further review the challenges that exist in determining the precise contribution of these mechanisms to protein misfolding diseases and suggest future directions to resolve these issues.

The molecular processes underpinning prion-like spreading and seed amplification in protein aggregation

The formation of aggregates from a range of normally soluble peptides and proteins is the hallmark of several neurodegenerative disorders, including Parkinson's and Alzheimer's diseases. Certain such aggregates possess the ability to replicate and spread pathology, within tissues and in some case also between organisms. An understanding of which processes govern the overall rate of aggregate formation is thus of key interest. Here, we discuss the fundamental molecular processes of protein aggregation, review how their rates can be determined by kinetic measurements in the test-tube, and explore the mechanistic similarities and differences to animal models and human disease. We conclude that a quantitative mathematical model for aggregate replication and spreading in vivo requires additional information but would provide a theoretical framework to understand results from different experiments and how they connect to human disease.

Theoretical and computational advances in protein misfolding

Misfolded proteins escape the cellular quality control mechanism and fail to fold properly or remain correctly folded leading to a loss in their functional specificity. Thus misfolding of proteins cause a large number of very different diseases ranging from errors in metabolism to various types of complex neurodegenerative diseases. A theoretical and computational perspective of protein misfolding is presented with a special emphasis on its salient features, mechanism and consequences. These insights quantitatively analyze different determinants of misfolding, that may be applied to design disease specific molecular targets.

There and back again: from the origin of life to single molecules

What is life? There is hardly a more fundamental question raised by aspiring researchers, and one less prone to ever be answered in a scientifically satisfying way. In the long, productive and highly influential period of research following his Nobel-recognised work on relaxation kinetics, Manfred Eigen made seminal contributions towards a quantifiable definition of life, with a strong focus on its evolutionary character. In the last years of his time as an active researcher, however, he devoted himself to another, purely experimental topic: the detection and analysis of single biomolecules in aqueous solution. In this short review, I will give an overview of the groundbreaking contributions to the field of single molecule research made by Eigen and coworkers, and show that both, in its intrinsic motivation, and in its consequences, single molecule research strongly relates to the question of the physical-chemical essence of life. In fact, research on living systems with single molecule sensitivity will always refer the researcher to the question of the simplest possible representation, and thus the origin, of any biological phenomenon.

Boltzmann-distribution-equivalent for Lévy noise and how it leads to thermodynamically consistent epicatalysis

Nonequilibrium systems commonly exhibit Lévy noise. This means that the distribution for the size of the Brownian fluctuations has a "fat" power-law tail. Large Brownian kicks are then more common as compared to the ordinary Gaussian distribution. We consider a two-state system, i.e., two wells and a barrier in between. The barrier is sufficiently high for a barrier crossing to be a rare event. When the noise is Lévy, we do not get a Boltzmann distribution between the two wells. Instead we get a situation where the distribution between the two wells also depends on the height of the barrier that is in between. Ordinarily, a catalyst, by lowering the barrier between two states, speeds up the relaxation to an equilibrium, but does not change the equilibrium distribution. In an environment with Lévy noise, on the other hand, we have the possibility of epicatalysis, i.e., a catalyst effectively altering the distribution between two states through the changing of the barrier height. After deriving formulas to quantitatively describe this effect, we discuss how this idea may apply in nuclear reactors and in the biochemistry of a living cell.

Mathematical Modeling of Protein Misfolding Mechanisms in Neurological Diseases: A Historical Overview

Protein misfolding refers to a process where proteins become structurally abnormal and lose their specific 3-dimensional spatial configuration. The histopathological presence of misfolded protein (MP) aggregates has been associated as the primary evidence of multiple neurological diseases, including Prion diseases, Alzheimer's disease, Parkinson's disease, and Creutzfeldt-Jacob disease. However, the exact mechanisms of MP aggregation and propagation, as well as their impact in the long-term patient's clinical condition are still not well understood. With this aim, a variety of mathematical models has been proposed for a better insight into the kinetic rate laws that govern the microscopic processes of protein aggregation. Complementary, another class of large-scale models rely on modern molecular imaging techniques for describing the phenomenological effects of MP propagation over the whole brain. Unfortunately, those neuroimaging-based studies do not take full advantage of the tremendous capabilities offered by the chemical kinetics modeling approach. Actually, it has been barely acknowledged that the vast majority of large-scale models have foundations on previous mathematical approaches that describe the chemical kinetics of protein replication and propagation. The purpose of the current manuscript is to present a historical review about the development of mathematical models for describing both microscopic processes that occur during the MP aggregation and large-scale events that characterize the progression of neurodegenerative MP-mediated diseases.

Pre-aggregation kinetics and intermediates of α-synuclein monitored by the ESIPT probe 7MFE

The defining feature of the extensive family of amyloid diseases is the formation of networks of entangled elongated protein fibrils and amorphous aggregates exhibiting crossed β-sheet secondary structure. The time course of amyloid conversion has been studied extensively in vitro with the proteins involved in the neurodegenerative pathology of Parkinson's disease (α-synuclein), Alzheimer's disease (Tau) and Huntington's disease (Huntingtin). Although much is known about the thermodynamics and kinetics of the transition from a soluble, intrinsically disordered monomer to the fibrillar end state, the putative oligomeric intermediates, currently considered to be the major initiators of cellular toxicity, are as yet poorly defined. We have detected and characterized amyloid precursors by monitoring AS aggregation with ESIPT (excited state intramolecular protein transfer) probes, one of which, 7MFE [7-(3-maleimido-N-propanamide)-2-(4-diethyaminophenyl)-3-hydroxychromone], is introduced here and compared with a related compound, 6MFC, used previously. A series of 140 spectra for sparsely labeled AS was acquired during the course of aggregation, and resolved into the relative contributions (spectra, intensities) of discrete molecular species including the monomeric, fibrillar, and ensemble of intermediate forms. Based on these findings, a kinetic scheme was devised to simulate progress curves as a function of key parameters. An essential feature of the model, one not previously invoked in schemes of amyloid aggregation, is the catalysis of molecular fuzziness by discrete colloidal nanoparticles arising spontaneously via monomer condensation upon exposure of AS to ≥ 37 °C.

Biosafety of Prions

Prions are the infectious agents that cause devastating and untreatable disorders known as Transmissible Spongiform Encephalopathies (TSEs). The pathologic events and the infectious nature of these transmissible agents are not completely understood yet. Due to the difficulties in inactivating prions, working with them requires specific recommendations and precautions. Moreover, with the advent of innovative technologies, such as the Protein Misfolding Cyclic Amplification (PMCA) and the Real Time Quaking-Induced Conversion (RT-QuIC), prions could be amplified in vitro and the infectious features of the amplified products need to be carefully assessed.

A critical appraisal of the pathogenic protein spread hypothesis of neurodegeneration

There has been an explosion in the number of papers discussing the hypothesis of 'pathogenic spread' in neurodegenerative disease - the idea that abnormal forms of disease-associated proteins, such as tau or α-synuclein, physically move from neuron to neuron to induce disease progression. However, whether inter-neuronal spread of protein aggregates actually occurs in humans and, if so, whether it causes symptom onset remain uncertain. Even if pathogenic spread is proven in humans, it is unclear how much this would alter the specific therapeutic approaches that are in development. A critical appraisal of this increasingly popular hypothesis thus seems both important and timely.

Intermediates caught in the act: tracing insulin amyloid fibril formation in time by combined optical spectroscopy, light scattering, mass spectrometry and microscopy

Insulin under acidic conditions. PDB-Databank structure visualized with VMD.

Effects of environmental factors on MSP21-25 aggregation indicate the roles of hydrophobic and electrostatic interactions in the aggregation process

Merozoite surface protein 2 (MSP2), one of the most abundant proteins on the merozoite surface of Plasmodium falciparum, is recognized to be important for the parasite's invasion into the host cell and is thus a promising malaria vaccine candidate. However, mediated mainly by its conserved N-terminal 25 residues (MSP21-25), MSP2 readily forms amyloid fibril-like aggregates under physiological conditions in vitro, which impairs its potential as a vaccine component. In addition, there is evidence that MSP2 exists in aggregated forms on the merozoite surface in vivo. To elucidate the aggregation mechanism of MSP21-25 and thereby understand the behavior of MSP2 in vivo and find ways to avoid the aggregation of relevant vaccine in vitro, we investigated the effects of agitation, pH, salts, 1-anilinonaphthalene-8-sulfonic acid (ANS), trimethylamine N-oxide dihydrate (TMAO), urea, and sub-micellar sodium dodecyl sulfate (SDS) on the aggregation kinetics of MSP21-25 using thioflavin T (ThT) fluorescence. The results showed that MSP21-25 aggregation was accelerated by agitation, while repressed by acidic pHs. The salts promoted the aggregation in an anion nature-dependent pattern. Hydrophobic surface-binding agent ANS and detergent urea repressed MSP21-25 aggregation, in contrast to hydrophobic interaction strengthener TMAO, which enhanced the aggregation. Notably, sub-micellar SDS, contrary to its micellar form, promoted MSP21-25 aggregation significantly. Our data indicated that hydrophobic interactions are the predominant driving force of the nucleation of MSP21-25 aggregation, while the elongation is controlled mainly by electrostatic interactions. A kinetic model of MSP21-25 aggregation and its implication were also discussed.

Seeded fibrillation as molecular basis of the species barrier in human prion diseases

Prion diseases are transmissible spongiform encephalopathies in humans and animals, including scrapie in sheep, bovine spongiform encephalopathy (BSE) in cattle, chronic wasting disease (CWD) in deer, and Creutzfeldt-Jakob disease (CJD) in humans. The hallmark of prion diseases is the conversion of the host-encoded prion protein (PrP^C) to its pathological isoform PrP^Sc, which is accompanied by PrP fibrillation. Transmission is not restricted within one species, but can also occur between species. In some cases a species barrier can be observed that results in limited or unsuccessful transmission. The mechanism behind interspecies transmissibility or species barriers is not completely understood. To analyse this process at a molecular level, we previously established an in vitro fibrillation assay, in which recombinant PrP (recPrP) as substrate can be specifically seeded by PrP^Sc as seed. Seeding with purified components, with no additional cellular components, is a direct consequence of the “prion-protein-only” hypothesis. We therefore hypothesise, that the species barrier is based on the interaction of PrP^C and PrP^Sc. Whereas in our earlier studies, the interspecies transmission in animal systems was analysed, the focus of this study lies on the transmission from animals to humans. We therefore combined seeds from species cattle, sheep and deer (BSE, scrapie, CWD) with human recPrP. Homologous seeding served as a control. Our results are consistent with epidemiology, other in vitro aggregation studies, and bioassays investigating the transmission between humans, cattle, sheep, and deer. In contrast to CJD and BSE seeds, which show a seeding activity we can demonstrate a species barrier for seeds from scrapie and CWD in vitro. We could show that the seeding activity and therewith the molecular interaction of PrP as substrate and PrP^Sc as seed is sufficient to explain the phenomenon of species barriers. Therefore our data supports the hypothesis that CWD is not transmissible to humans.

The autocatalytic step is an integral part of the hydrogenase cycle

We earlier proved the involvement of an autocatalytic step in the oxidation of H(2) by HynSL hydrogenase from Thiocapsa roseopersicina, and demonstrated that two enzyme forms interact in this step. Using a modified thin-layer reaction chamber which permits quantitative analysis of the concentration of the reaction product (reduced benzyl viologen) in the reaction volume during the oxidation of H(2), we now show that the steady-state concentration of the product displays a strong enzyme concentration dependence. This experimental fact can be explained only if the previously detected autocatalytic step occurs inside the catalytic enzyme-cycle and not in the enzyme activation process. Consequently, both interacting enzyme forms should participate in the catalytic cycle of the enzyme. As far as we are aware, this is the first experimental observation of such a phenomenon resulting in an apparent inhibition of the enzyme. It is additionally concluded that the interaction of the two enzyme forms should result in a conformational change in the enzyme-substrate form. This scheme is very similar to that of prion reactions. Since merely a few molecules are involved at some point of the reaction, this process is entirely stochastic in nature. We have therefore developed a stochastic calculation method, calculations with which lent support to the conclusion drawn from the experiment.

Exploring the essential collective dynamics of interacting proteins: application to prion protein dimers

Essential collective dynamics is a promising and robust approach for analysing the slow motions of macromolecules from short molecular dynamics trajectories. In this study, an extension of the method to treat a collection of interacting protein molecules is presented. The extension is applied to investigate the effects of dimerization on the collective dynamics of ovine prion protein molecules in two different arrangements. Examination of the structural plasticity shows that aggregation has a restricting effect on the local mobility of the prion protein molecules in the interfacial regions. Domain motions of the two dimeric ovine prion protein conformations are distinctly different and can be related to interatomic correlations at the interface. Correlated motions are among the slow collective modes extensively analysed by considering both main-chain and side-chain atoms. Correlation maps reveal the existence of a vast network of dynamically correlated side groups, which extends beyond individual subunits via interfacial interconnections. The network is formed by a core of hydrophobic side chains surrounded by hydrophilic groups at the periphery. The relevance of these findings are discussed in the context of mutations associated with prion diseases. The binding free energy of the dimeric conformations is evaluated to probe their thermodynamic stability. The descriptions afforded by the analysis of the essential collective dynamics of the prion dimers are consistent with their binding free energies. The agreement validates the extension of the methodology and provides a means of interpreting the collective dynamics in terms of the thermodynamic stability of ovine prion proteins.

THE SPREAD OF PRION DISEASES IN THE BRAIN — MODELS OF REACTION AND TRANSPORT ON NETWORKS

In this paper we will present a modeling approach to describe the progression and the spread of prion diseases in the brain. Although there exist a number of mathematical models for the interaction of prions with their native counterpart, prion transport and spread is usually neglected. The concentration dynamics of prions, and thus the dynamics of the disease progression, however, are influenced by prion transport, especially in a medium as complex as the brain. Therefore, we focus here on the interaction between prion concentration dynamics and prion transport. The model is constructed by combining a model of prion-prion interaction with transport on networks. The approach leads to a system of reaction-diffusion equations, whereby the diffusion term is discrete. The equations are solved numerically on domains given as large networks. We show that the prion concentration grows faster on networks characterized by a higher degree heterogeneity. Furthermore, we introduce cell death as a consequence of increasing prion concentration, leading to network decomposition. We show that infectious diseases destroy networks similarly to targeted attacks, namely by affecting the nodes with the highest degree first. Relating the incubation period and disease progression to the process of network decomposition, we find that, interestingly, a long incubation time followed by sudden onset and fast progression of the disease does not need to be reflected in the overall concentration dynamics of the infective agent.

Modeling amyloid fibril formation

No detailed step-by-step model of protein rearrangements during amyloid structure formation has been presented in the literature. The aim of this work was to design a kinetic model for description of the amyloid formation process on the basis of the most recent experimental data. A general kinetic model is proposed for description of the amyloid formation process including the nucleation mechanism of polymerization with consecutive monomer attachment to oligomer and autocatalytic growth of amyloid aggregates implying all types of exponential growth such as branching, fragmentation, and growth from the surface. Computer simulations have shown that the model correctly describes experimentally observed growth stages of amyloid fibrils and that the presence of exponential growth stage in the model is critical for modeling amyloid fibril formation. The key feature of the proposed model is the stage of the exponential growth of the aggregate. Such stage can simultaneously describe several versions of aggregate enlargement by branching, fragmentation, or growth from the surface. Data obtained using this model suggest conclusions concerning the significance of each stage in amyloid fibril assembly.

There is no safe dose of prions

Understanding the circumstances under which exposure to transmissible spongiform encephalopathies (TSEs) leads to infection is important for managing risks to public health. Based upon ideas in toxicology and radiology, it is plausible that exposure to harmful agents, including TSEs, is completely safe if the dose is low enough. However, the existence of a threshold, below which infection probability is zero has never been demonstrated experimentally. Here we explore this question by combining data and mathematical models that describe scrapie infections in mice following experimental challenge over a broad range of doses. We analyse data from 4338 mice inoculated at doses ranging over ten orders of magnitude. These data are compared to results from a within-host model in which prions accumulate according to a stochastic birth-death process. Crucially, this model assumes no threshold on the dose required for infection. Our data reveal that infection is possible at the very low dose of a 1000 fold dilution of the dose that infects half the challenged animals (ID50). Furthermore, the dose response curve closely matches that predicted by the model. These findings imply that there is no safe dose of prions and that assessments of the risk from low dose exposure are right to assume a linear relationship between dose and probability of infection. We also refine two common perceptions about TSE incubation periods: that their mean values decrease linearly with logarithmic decreases in dose and that they are highly reproducible between hosts. The model and data both show that the linear decrease in incubation period holds only for doses above the ID50. Furthermore, variability in incubation periods is greater than predicted by the model, not smaller. This result poses new questions about the sources of variability in prion incubation periods. It also provides insight into the limitations of the incubation period assay.

Kinetic analysis of protein aggregation monitored by real-time 2D solid-state NMR spectroscopy

It is shown that real-time 2D solid-state NMR can be used to obtain kinetic and structural information about the process of protein aggregation. In addition to the incorporation of kinetic information involving intermediate states, this approach can offer atom-specific resolution for all detectable species. The analysis was carried out using experimental data obtained during aggregation of the 10.4 kDa Crh protein, which has been shown to involve a partially unfolded intermediate state prior to aggregation. Based on a single real-time 2D (13)C-(13)C transition spectrum, kinetic information about the refolding and aggregation step could be extracted. In addition, structural rearrangements associated with refolding are estimated and several different aggregation scenarios were compared to the experimental data.

Extinction times in autocatalytic systems

Systems evolving under the influence of autocatalytic processes have been the subject of much study due to their appearance in a wide variety of contexts. Well known examples range from the simplest autocatalytic chemical reactions, biochemical models of ribozyme or prion replication, right up to the duplication of entire organisms in models of population dynamics. While the deterministic approach frequently taken to model such systems is adequate in the limit of large reactant numbers, the intrinsic fluctuations exert an important influence on the dynamics when the supply of reactants is limited. In particular, when combined with spontaneous degradation of the autocatalytic reactant population, such fluctuations can lead to the extinction of that population. In this paper, we study reversible autocatalytic processes of the form X + Y ⇌ 2X in the limit that there exists a surplus of Y and in the presence of a spontaneous degradation process X → Z. Through the use of the Poisson representation, we identify an exact analytical expression for the mean extinction time of the X population. We show that the exact result can be neatly approximated by an Arrhenius-like expression involving an effective activation energy separating a quasi-stationary state from the extinct state.

Toward a molecular theory of early and late events in monomer to amyloid fibril formation

Quantitative understanding of the kinetics of fibril formation and the molecular mechanism of transition from monomers to fibrils is needed to obtain insights into the growth of amyloid fibrils and more generally self-assembly multisubunit protein complexes. Significant advances using computations of protein aggregation in a number of systems have established generic and sequence-specific aspects of the early steps in oligomer formation. Theoretical considerations, which view oligomer and fibril growth as diffusion in a complex energy landscape, and computational studies, involving minimal lattice and coarse-grained models, have revealed general principles governing the transition from monomeric protein to ordered fibrillar aggregates. Detailed atomistic calculations have explored the early stages of the protein aggregation pathway for a number of amyloidogenic proteins, most notably amyloid β- (Aβ-) protein and fragments from proteins linked to various diseases. These computational studies have provided insights into the role of sequence, role of water, and specific interatomic interactions underlying the thermodynamics and dynamics of elementary kinetic steps in the aggregation pathway. Novel methods are beginning to illustrate the structural basis for the production of Aβ-peptides through interactions with secretases in the presence of membranes. We show that a variety of theoretical approaches, ranging from scaling arguments to minimal models to atomistic simulations, are needed as a complement to experimental studies probing the principles governing protein aggregation.

Molecular interactions between prions as seeds and recombinant prion proteins as substrates resemble the biological interspecies barrier in vitro

Prion diseases like Creutzfeldt-Jakob disease in humans, Scrapie in sheep or bovine spongiform encephalopathy are fatal neurodegenerative diseases, which can be of sporadic, genetic, or infectious origin. Prion diseases are transmissible between different species, however, with a variable species barrier. The key event of prion amplification is the conversion of the cellular isoform of the prion protein (PrP^C) into the pathogenic isoform (PrP^Sc). We developed a sodiumdodecylsulfate-based PrP conversion system that induces amyloid fibril formation from soluble α-helical structured recombinant PrP (recPrP). This approach was extended applying pre-purified PrP^Sc as seeds which accelerate fibrillization of recPrP. In the present study we investigated the interspecies coherence of prion disease. Therefore we used PrP^Sc from different species like Syrian hamster, cattle, mouse and sheep and seeded fibrillization of recPrP from the same or other species to mimic in vitro the natural species barrier. We could show that the in vitro system of seeded fibrillization is in accordance with what is known from the naturally occurring species barriers.

Epigenetics in the extreme: prions and the inheritance of environmentally acquired traits

Prions are an unusual form of epigenetics: Their stable inheritance and complex phenotypes come about through protein folding rather than nucleic acid-associated changes. With intimate ties to protein homeostasis and a remarkable sensitivity to stress, prions are a robust mechanism that links environmental extremes with the acquisition and inheritance of new traits.

Spontaneous generation of mammalian prions

Prions are transmissible agents that cause lethal neurodegeneration in humans and other mammals. Prions bind avidly to metal surfaces such as steel wires and, when surface-bound, can initiate infection of brain or cultured cells with remarkable efficiency. While investigating the properties of metal-bound prions by using the scrapie cell assay to measure infectivity, we observed, at low frequency, positive assay results in control groups in which metal wires had been coated with uninfected mouse brain homogenate. This phenomenon proved to be reproducible in rigorous and exhaustive control experiments designed to exclude prion contamination. The infectivity generated in cell culture could be readily transferred to mice and had strain characteristics distinct from the mouse-adapted prion strains used in the laboratory. The apparent "spontaneous generation" of prions from normal brain tissue could result if the metal surface, possibly with bound cofactors, catalyzed de novo formation of prions from normal cellular prion protein. Alternatively, if prions were naturally present in the brain at levels not detectable by conventional methods, metal surfaces might concentrate them to the extent that they become quantifiable by the scrapie cell assay.

Highly polar environments catalyze the unfolding of PrP C helix 1

The first alpha-helix (H1) likely plays an important role in the conversion of the cellular prion protein (PrP(C)) into its pathogenic isoform (PrP(Sc)). In this conversion, H1 may either have to unfold or may represent a site of intermolecular contact. A recent molecular dynamics simulation suggested that H1 can unfold if it is detached from the protein core (Hirschberger et al. in Biophys J 90:3908, 2006). It has been hypothesized that the high dielectric constant epsilon (S) of the bulk water environment facilitates the unfolding of H1. To check this hypothesis, we performed a number of replica exchange molecular dynamics simulations of an H1 peptide in solvents of different epsilon (S). We found that the equilibrium helix fraction in water is less than 40%, in agreement with previous experimental findings, and that the helix unfolds much faster in water than in less polar solvents. The kinetically stabilizing effect of the organic solvents is largely unspecific and correlates well with their dielectric constant epsilon (S).

Applicability of an EM-CCD for spatially resolved TIR-ICS

In this work we systematically explored performance of an EM-CCD as a detector for spatially resolved total internal reflection image correlation spectroscopy (TIR-ICS) with respect to adjustable parameters. We show that variations in the observation volume (pixel binning) can be well described by a simple structural term omega. To test the sensitivity of camera-based TIR-ICS we measured diffusion coefficients and particle numbers (PN) of fluorescent probes of different sizes (Fluorospheres, GFP and labeled antibodies) at varying viscosities, concentrations, and sampling rates. TIR-ICS allowed distinguishing between different probe concentrations with differences in PN of 5% and differences of 6% in D by acquiring only 15 independent measurement runs.

Simulation-based model selection for dynamical systems in systems and population biology

MOTIVATION

Computer simulations have become an important tool across the biomedical sciences and beyond. For many important problems several different models or hypotheses exist and choosing which one best describes reality or observed data is not straightforward. We therefore require suitable statistical tools that allow us to choose rationally between different mechanistic models of, e.g. signal transduction or gene regulation networks. This is particularly challenging in systems biology where only a small number of molecular species can be assayed at any given time and all measurements are subject to measurement uncertainty.

RESULTS

Here, we develop such a model selection framework based on approximate Bayesian computation and employing sequential Monte Carlo sampling. We show that our approach can be applied across a wide range of biological scenarios, and we illustrate its use on real data describing influenza dynamics and the JAK-STAT signalling pathway. Bayesian model selection strikes a balance between the complexity of the simulation models and their ability to describe observed data. The present approach enables us to employ the whole formal apparatus to any system that can be (efficiently) simulated, even when exact likelihoods are computationally intractable.

Prion dynamics and the quest for the genetic determinant in protein-only inheritance

According to the prion hypothesis, proteins may act in atypical roles as genetic elements of infectivity and inheritance by undergoing self-replicating changes in physical state. While the preponderance of evidence strongly supports this concept particularly in fungi, the detailed mechanisms by which distinct protein forms specify unique phenotypes are emerging concepts. A particularly active area of investigation is the molecular nature of the heritable species, which has been probed through genetic, biochemical, and cell biological experimentation as well as by mathematical modeling. Here, we suggest that these studies are converging to implicate small aggregates composed of prion-state conformers as the transmissible genetic determinants of protein-based phenotypes.

Investigating the conformational stability of prion strains through a kinetic replication model

Prion proteins are known to misfold into a range of different aggregated forms, showing different phenotypic and pathological states. Understanding strain specificities is an important problem in the field of prion disease. Little is known about which PrP^Sc structural properties and molecular mechanisms determine prion replication, disease progression and strain phenotype. The aim of this work is to investigate, through a mathematical model, how the structural stability of different aggregated forms can influence the kinetics of prion replication. The model-based results suggest that prion strains with different conformational stability undergoing in vivo replication are characterizable in primis by means of different rates of breakage. A further role seems to be played by the aggregation rate (i.e. the rate at which a prion fibril grows). The kinetic variability introduced in the model by these two parameters allows us to reproduce the different characteristic features of the various strains (e.g., fibrils' mean length) and is coherent with all experimental observations concerning strain-specific behavior.

Prion diseases are caused by the accumulation of a cellular prion protein with an altered conformation, which acts as a catalyst for the further recruitment and the modification of the normal form of the protein. Protein polymerization appears to have a central role in the progression of the disease, an aspect shared with several other neurodegenerative diseases. The aim of this work is to investigate at the kinetic level the “prion strain phenomenon”, i.e., the ability of prion proteins to misfold into a range of different aggregated forms exhibiting different replication and propagation properties. The dynamics of prion replication is investigated with the help of a mathematical model. We relate a measurement accessible in vitro (prion structural stability) to a mathematical description of the fibrils' kinetics in vivo. The analysis of the model suggests that the replication kinetics of the different prion strains is characterizable by means of two parameters, representing the rates of breakage and aggregation. This result is coherent with various experimental findings concerning strain-specific behavior, such as, for example, the observation of the fibril mean length of the various strains.

Concentration-dependent front velocity of the autocatalytic hydrogenase reaction

HynSL hydrogenase from Thiocapsa roseopersicina was applied to catalyze the oxidation of molecular hydrogen in a new, improved, thin-layer reaction chamber. Investigation of the nature of this catalysis via the development of reduced benzyl viologen showed clearly the typical characteristics of an autocatalytic reaction: propagation of a reaction front originating from a single point, with a constant velocity of front propagation. The dependence of the reaction velocity on enzyme concentration was a power function with a positive enzyme concentration threshold, with an exponent of 0.4 +/- 0.05. This indicates that the autocatalyst is an enzyme form. The front velocity decreased on increase of the electron acceptor concentration, as a sign that the autocatalyst interacts directly with the final electron acceptor. Overall, it may be concluded that the autocatalyst is an enzyme form in which [FeS]distal is reduced. Model calculations corroborate this. Because the reduction of all [FeS] clusters would be possible in a nonautocatalytic reaction, we hypothesize a small conformational change in the enzyme, catalyzed by the autocatalyst, which removes a block in the electron flow in either [NiFe] --> [FeS]proximal or the [FeS]proximal --> [FeS]distal reaction step, or removes a block of the penetration of gaseous hydrogen from the surface to the [NiFe] cluster.

Bovine spongiform encephalopathy

Bovine spongiform encephalopathy is an infectious disease of cattle that is transmitted through the consumption of meat-and-bone meal from infected cattle. The etiologic agent is an aberrant isoform of the native cellular prion protein that is a normal component of neurologic tissue. There currently are no approved tests that can detect BSE in live cattle.

Spontaneous and BSE-prion-seeded amyloid formation of full length recombinant bovine prion protein

The conversion of the cellular isoform of the prion protein into the pathogenic isoform PrP(Sc) is the key event in prion diseases. The disease can occur spontaneously genetically or by infection. In earlier studies we presented an in vitro conversion system which simulates the structural transition in recPrP by varying low concentrations of SDS at constant NaCl. In the present study we adopted the conversion system from experimental Scrapie in hamster to bovine recPrP and generated amyloid fibrils. The intermediate state which is optimal for fibril formation is a soluble, beta-rich state. The system was extended using BSE-prions as seeds and led to an acceleration of fibril formation by orders of magnitude. This seeded amyloid formation assay avoids any PK-treatment, is therefore able to detect even PK-sensitive PrP(Sc) and does not require cellular components.

Differential effects of prion particle size on infectivity in vivo and in vitro

The conversion of cellular prion protein to the disease-associated isoform (PrP(Sc)) has been suggested to follow a mechanism of seeded aggregation. Here, we show that fragmentation of PrP(Sc) aggregates by sonication increases converting activity in cell culture in a way similar to in vitro conversion assays. In contrast, under the same conditions the infectious titer of sonicated samples in vivo was reduced. We modified the size distribution of PrP(Sc) by adsorption to nitrocellulose, which resulted in a reduction of the infectious titer in non-sonicated samples and an increase in sonicated samples. Our results indicate that NC-adsorption can (i) block some active sites of PrP(Sc) aggregates and (ii) reduce the rate of clearance from the brain. For large particles with low clearance the effect of NC-particles on the number of available active sites may dominate, whereas for smaller particles (i.e. sonicated samples) the effect of NC-adsorption on clearance dominates resulting in increased infectivity.

Mechanisms of prion protein assembly into amyloid

The conversion of the alpha-helical, cellular isoform of the prion protein (PrP(C)) to the insoluble, beta-sheet-rich, infectious, disease-causing isoform (PrP(Sc)) is the key event in prion diseases. In an earlier study, several forms of PrP were converted into a fibrillar state by using an in vitro conversion system consisting of low concentrations of SDS and 250 mM NaCl. Here, we characterize the structure of the fibril precursor state, that is, the soluble state under fibrillization conditions. CD spectroscopy, analytical ultracentrifugation, and chemical cross-linking indicate that the precursor state exists in a monomer-dimer equilibrium of partially denatured, alpha-helical PrP, with a well defined contact site of the subunits in the dimer. Using fluorescence with thioflavin T, we monitored and quantitatively described the kinetics of seeded fibril formation, including dependence of the reaction on substrate and seed concentrations. Exponential, seed-enhanced growth can be achieved in homogeneous solution, which can be enhanced by sonication. From these data, we propose a mechanistic model of fibrillization, including the presence of several intermediate structures. These studies also provide a simplified amplification system for prions.

Fitting neurological protein aggregation kinetic data via a 2-step, minimal/"Ockham's razor" model: the Finke-Watzky mechanism of nucleation followed by autocatalytic surface growth

The aggregation of proteins has been hypothesized to be an underlying cause of many neurological disorders including Alzheimer's, Parkinson's, and Huntington's diseases; protein aggregation is also important to normal life function in cases such as G to F-actin, glutamate dehydrogenase, and tubulin and flagella formation. For this reason, the underlying mechanism of protein aggregation, and accompanying kinetic models for protein nucleation and growth (growth also being called elongation, polymerization, or fibrillation in the literature), have been investigated for more than 50 years. As a way to concisely present the key prior literature in the protein aggregation area, Table 1 in the main text summarizes 23 papers by 10 groups of authors that provide 5 basic classes of mechanisms for protein aggregation over the period from 1959 to 2007. However, and despite this major prior effort, still lacking are both (i) anything approaching a consensus mechanism (or mechanisms), and (ii) a generally useful, and thus widely used, simplest/"Ockham's razor" kinetic model and associated equations that can be routinely employed to analyze a broader range of protein aggregation kinetic data. Herein we demonstrate that the 1997 Finke-Watzky (F-W) 2-step mechanism of slow continuous nucleation, A --> B (rate constant k1), followed by typically fast, autocatalytic surface growth, A + B --> 2B (rate constant k2), is able to quantitatively account for the kinetic curves from all 14 representative data sets of neurological protein aggregation found by a literature search (the prion literature was largely excluded for the purposes of this study in order provide some limit to the resultant literature that was covered). The F-W model is able to deconvolute the desired nucleation, k1, and growth, k2, rate constants from those 14 data sets obtained by four different physical methods, for three different proteins, and in nine different labs. The fits are generally good, and in many cases excellent, with R2 values >or=0.98 in all cases. As such, this contribution is the current record of the widest set of protein aggregation data best fit by what is also the simplest model offered to date. Also provided is the mathematical connection between the 1997 F-W 2-step mechanism and the 2000 3-step mechanism proposed by Saitô and co-workers. In particular, the kinetic equation for Saitô's 3-step mechanism is shown to be mathematically identical to the earlier, 1997 2-step F-W mechanism under the 3 simplifying assumptions Saitô and co-workers used to derive their kinetic equation. A list of the 3 main caveats/limitations of the F-W kinetic model is provided, followed by the main conclusions from this study as well as some needed future experiments.

Bistability and the species barrier in prion diseases: stepping across the threshold or not

The infectious agent of transmissible spongiform encephalopathies is thought to be a cellular protein, the prion protein, which undergoes, under some circumstances, a dramatic conformational change leading to pathogenesis. The conversion between the normal and pathogenic isoforms corresponds to a autocatalytic mechanism and the metabolism of the prion protein exhibits switches between a normal, stable steady state and a pathogenic one. When the disease can be transmitted between two species, a primary infection from a heterologous donor has to be followed by two passages in the same host species so that the incubation period is stabilized. Sometimes, no pathogenic isoform of the prion protein is detected after the first passage, although corresponding brain extracts remain infectious. The observation that three and only three passages are needed in order to stabilize the strain strongly suggests that, during the course of the primary infection by the heterologous donor, an intermediary conformational species is formed. Within this assumption, a common mechanism involving only conformational changes of the prion protein can give a unifying interpretation of the problem of species barrier, lag characteristics and apparent lack of detection of the pathogenic isoform after the first passage in experiments dealing with interspecies transmission of prion diseases.