The inverse scattering problem is based on the scattering theory in physics, where measured data such as radiation from an object is used to determine the unique structure of the object in question. This approach has been widely successful in fields ranging from geophysics and medical imaging, to quantum field theory. In 1996 Henrik Flyvbjerg suggested that a similar approach could be used to study a reaction far from equilibrium of the self-assembly of a nucleation dependent biopolymer and, under certain conditions, uniquely determine the kinetics of the assembly. Here we use this approach to elucidate the unique structure of human islet amyloid polypeptide, also known as amylin, in-vitro. We use a systematic phenomenological analysis of the amount of monomer in fibril, of amylin, for various initial concentrations from an unstructured monomer pool. Using the assumption that nucleation is the rate-limiting step in fibril formation, we invoke mass action to develop our model. We find that the fibrillogenesis of amylin is well described by a nucleation dependent polymerization event that is characteristic of the sigmoidal shape of the reaction profile generated by our data. Furthermore, we find a second nucleation event is needed to accurately match model predictions to the observed data for the kinetic profiles of fibril formation, and the experimental length distributions of mature fibrils from in-vitro assays. This analysis allows for the theoretical determination of each step of assembly in the nucleation process. Specifically, we find the number of steps to nucleation, the size of each oligomer formed in the nucleation process, the nucleus size, and the elongation kinetics of fibrils. The secondary nucleation process is found to be a fibril dependent surface mediated nucleation event and is similar in reaction order to the primary nucleation step. Model predictions are found to be congruent with experimental assay results of oligomer populations and monomer concentration. We demonstrate that, a persistent oligomer formation is a natural and necessary consequence of nucleated fibril formation, given certain qualitative features of the kinetic profile of fibril formation. Furthermore, the modeling assumptions about monomer and fibril mass are in agreement with experiment.

The inverse scattering problem is based on the scattering theory in physics, where measured data such as radiation from an object is used to determine the unique structure of the object in question. This approach has been widely successful in fields ranging from geophysics and medical imaging, to quantum field theory. In 1996 Henrik Flyvbjerg suggested that a similar approach could be used to study a reaction far from equilibrium of the self-assembly of a nucleation dependent biopolymer and, under certain conditions, uniquely determine the kinetics of the assembly. Here we use this approach to elucidate the unique structure of human islet amyloid polypeptide, also known as amylin, in-vitro. We use a systematic phenomenological analysis of the amount of monomer in fibril, of amylin, for various initial concentrations from an unstructured monomer pool. Using the assumption that nucleation is the rate-limiting step in fibril formation, we invoke mass action to develop our model. We find that the fibrillogenesis of amylin is well described by a nucleation dependent polymerization event that is characteristic of the sigmoidal shape of the reaction profile generated by our data. Furthermore, we find a second nucleation event is needed to accurately match model predictions to the observed data for the kinetic profiles of fibril formation, and the experimental length distributions of mature fibrils from in-vitro assays. This analysis allows for the theoretical determination of each step of assembly in the nucleation process. Specifically, we find the number of steps to nucleation, the size of each oligomer formed in the nucleation process, the nucleus size, and the elongation kinetics of fibrils. The secondary nucleation process is found to be a fibril dependent surface mediated nucleation event and is similar in reaction order to the primary nucleation step. Model predictions are found to be congruent with experimental assay results of oligomer populations and monomer concentration. We demonstrate that, a persistent oligomer formation is a natural and necessary consequence of nucleated fibril formation, given certain qualitative features of the kinetic profile of fibril formation. Furthermore, the modeling assumptions about monomer and fibril mass are in agreement with experiment.

The inverse scattering problem is based on the scattering theory in physics, where measured data such as radiation from an object is used to determine the unique structure of the object in question. This approach has been widely successful in fields ranging from geophysics and medical imaging, to quantum field theory. In 1996 Henrik Flyvbjerg suggested that a similar approach could be used to study a reaction far from equilibrium of the self-assembly of a nucleation dependent biopolymer and, under certain conditions, uniquely determine the kinetics of the assembly. Here we use this approach to elucidate the unique structure of human islet amyloid polypeptide, also known as amylin, in-vitro. We use a systematic phenomenological analysis of the amount of monomer in fibril, of amylin, for various initial concentrations from an unstructured monomer pool. Using the assumption that nucleation is the rate-limiting step in fibril formation, we invoke mass action to develop our model. We find that the fibrillogenesis of amylin is well described by a nucleation dependent polymerization event that is characteristic of the sigmoidal shape of the reaction profile generated by our data. Furthermore, we find a second nucleation event is needed to accurately match model predictions to the observed data for the kinetic profiles of fibril formation, and the experimental length distributions of mature fibrils from in-vitro assays. This analysis allows for the theoretical determination of each step of assembly in the nucleation process. Specifically, we find the number of steps to nucleation, the size of each oligomer formed in the nucleation process, the nucleus size, and the elongation kinetics of fibrils. The secondary nucleation process is found to be a fibril dependent surface mediated nucleation event and is similar in reaction order to the primary nucleation step. Model predictions are found to be congruent with experimental assay results of oligomer populations and monomer concentration. We demonstrate that, a persistent oligomer formation is a natural and necessary consequence of nucleated fibril formation, given certain qualitative features of the kinetic profile of fibril formation. Furthermore, the modeling assumptions about monomer and fibril mass are in agreement with experiment. / Science, Faculty of / Mathematics, Department of / Graduate

Deposition of protein fibers with a characteristic cross-β sheet structure is the molecular marker associated with human disorders ranging from Alzheimer's disease to type II diabetes and spongiform encephalopathy. Given the large number of non-disease related proteins and peptides that have been shown to form amyloid fibrils in vitro, it has been suggested that amyloid fibril formation represents a generic protein phase transition. In the last two decades it has become clear that the same protein/peptide can assemble into distinct morphologically and structurally amyloid aggregates depending on the solution conditions. Moreover, recent studies have shown that the early stage, oligomeric amyloid assemblies are the main culprit in vivo. We have investigated the amyloid assemblies formed under denaturing conditions for Hen Egg White Lysozyme (HewL) whose human homologue is directly implicated in hereditary non-neuropathic systemic amyloidosis. Our early investigations showed that HewL can aggregate via at least two distinct assembly pathways depending on solution ionic strength at fixed pH, temperature, and protein concentration. By combining Dynamic Light Scattering (DLS), Static Light Scattering (SLS) and Atomic Force Microscopy (AFM) we showed that at low ionic strength, the pathway is characterized by the nucleation and growth of long (several micron), rigid fibrils (RF) via monomers assembly. A second, high ionic strength pathway is characterized by the rapid assembly of monomers into globular oligomers that further polymerize into curvilinear fibrils (aO/CF). At NaCl concentrations above 400 mM, aggregation resulted in precipitate formation. Next, we used Foureir Transform Infrared spectroscopy (FTIR) and an amyloid-specific dye, Thioflavin T (ThT), to show that both RF and (a)O/CF are amyloidogenic species, but they have detectable structural differences. Moreover, we have determined that each assembly pathway has unique SLS, DLS, FTIR and ThT response signatures that help determine the assembly type prior to AFM imaging of aggregates. Taking advantage of the morphological, structural and kinetic signatures for the two distinct HewL amyloid aggregates I mapped out their amyloid aggregates phase diagram spanning over two orders of magnitude in protein concentration and from 50 to 800 mM NaCl in ionic strength. This is the most complete phase diagram for amyloid aggregates of a given protein up to date. The phase diagram has three distinct regions delineated by sharp boundaries. The RF- aO/CF was called Critical Oligomer Concentration, and we commonly refer to “above the COC” as the region were aO/CF are kinetically favored.. In the region of low salt/high protein concentrations, RF were the only amyloid species to nucleate and grow. As both salt and protein concentrations increase, aO/CF become the kinetically favored species, and RF nucleate and grow after several days of incubation. At high protein and high salt concentrations, aO/CF form very fast and eventually lose solubility forming a precipitate (Ppt). Cross-seeding experiments showed that RF is the thermodynamically stable aggregate phase, while the O/CF are the metastable species. Finally, we used the phase diagram to design experiments that would allow us to reveal the RF nucleation mechanism in presence of aO/CF. RF nucleation above the COC can undergo either via internal restructuring of aO/CF (NCC) or through a random coalescence of monomers into a nucleus (NP). The experimental results obtained so far strongly indicate that RF nucleate via NP mechanism both below and above the COC.

Les maladies à Prions sont des maladies neurodégénératives fatales, touchant l'homme et l'animal. Même si le risque de transmission de la maladie de la vache folle à l'homme semble maîtrisé, il persiste actuellement un risque de santé publique lié à la transmission iatrogène de cette forme, notamment par transfusion sanguine. Pour contrôler cette transmission, il est donc essentiel de mieux comprendre les mécanismes moléculaires et cellulaires de réplication et de dissémination des Prions. Ces mécanismes de réplication se produisent à des échelles de temps et de taille difficilement accessibles expérimentalement, et ont ainsi fait l'objet de nombreuses modélisations théoriques utiles pour aider à la compréhension des mécanismes. L'objectif de cette thèse est de compléter ces modèles mathématiques, afin d'étudier plus spécifiquement les conséquences dynamiques sur la réplication des Prions, des propriétés de réplication taille-dépendante d'une part, et de l'hétérogénéité des cellules impliquées dans la réplication d'autre part. Dans un premier temps, nous avons généralisé un modèle de polymérisation nucléée pour prendre en compte un taux d'élongation des fibrilles dépendant de leur taille. Nous avons principalement déduit de cette étude que la distribution en taille des agrégats semble une donnée expérimentale très informative sur les mécanismes élémentaires de réplication, au contraire du profil cinétique d'accumulation de la PrPres peu sensibles aux propriétés de réplication taille-dépendantes. Dans un second temps, après une caractérisation expérimentale de l'hétérogénéité cellulaire de réplication, nous avons intégré le mécanisme de réplication intracellulaire à un modèle multicellulaire par automate cellulaire continu stochastique. De manière appliquée, cette étude nous a permis d'identifier des étapes du processus de culture cellulaire critiques pour l'établissement d'une infection chronique, et nous a permis de proposer plusieurs protocoles pour augmenter la sensibilité des cultures cellulaires aux infections à Prions. / Prion diseases are neurodegenerative, fatal and transmissible diseases, with no effective treatment. The risk of transmission of bovine spongiform encephalopathy to humans is now under control ; however the risk of human-to-human transmission of variant Creutzfeldt-Jakob disease via medical treatments (notably through blood transfusion) remains. Thus, understanding cellular and molecular mechanisms responsible for Prion replication and dissemination is critical to efficiently control Prion transmission. The mechanisms of Prion replication are poorly characterised and occur at time and size scale achieved experimentally with difficulty. Thus, mathematical models can help us understand prion multiplication by testing which mechanisms best fit to experimental data. Therefore the objectives of our study are to complete existing mathematical model in order to investigate the size-dependent replicative properties of prion aggregates and the cellular heterogeneity. Firstly, we have extended a previous study of the nucleated polymerization model to take into account size dependent replicative properties of prion aggregates. This is achieved by a choice of coefficients in the model that are not constant. Our results suggest that the size distribution of prion aggregates could be one of the most informative experimental data to study elementary replication mechanisms and to investigate strain phenomenon. Secondly, we have modelled the multicellular dynamics of prion replication by integrating intracellular replication (by nucleated polymerization) into a continuous and stochastic cellular automaton. The model formulation is based on an experimental characterisation of cellular heterogeneity. From an applicative point of view, this theoretical study has allowed us to propose several protocols to increase cell culture sensitivity to prion infection.

The effect of environmental condition on the mechanism and kinetics of fibril formation for bovine insulin were investigated. Results showed environmental conditions played a significant role in determining the mechanism and kinetics of fibril formation. Increased protein concentration, elevated temperature, and higher ionic strengths induced insulin to form fibrils through oligomeric intermediates that were consistent with the nucleated conformational conversion (NCC) mechanism. Bovine insulin was also shown to generate fibrils without formation of oligomeric intermediates at study conditions of lower protein concentration, lower temperature, and lower ionic strength. Fibril formation without oligomeric intermediate can be described by the nucleated polymerization (NP) mechanism. Different relative amounts of oligomeric intermediate were generated at the various combinations of protein concentration, temperature, and ionic strength. The kinetic parameters, lag time, and rate of fibril formation, correlated with the relative amount of oligomeric intermediates detected. Longer lag times and slower rates of fibril formation were observed with greater amounts of oligomeric intermediate present. The effects of excipients, trifluoroethanol, ethanol, glycerol, and urea on the apparent rate constants of oligomeric intermediate and fibril formation were also investigated. At the concentrations studied, all the excipients tested were observed to decrease the rate and relative amount of oligomeric intermediate formation in an excipient concentration-dependent manner. The excipients were less effective at preventing fibril formation. In conclusion, bovine insulin can form fibrils with and without oligomeric intermediates. Protein concentration and environmental conditions, such as temperature, ionic strength, and excipients played a significant role in determining the relative amount of oligomeric intermediates, which in turn, determined the mechanism and kinetics of bovine insulin fibril formation under the conditions studied.