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Oscillatory processes during the aggregation and the fragmentation of amyloid fibrils

Abstract : This thesis focuses on the study of the process of protein aggregation and fragmentation. In particular, oscillatory kinetic phenomena are identified in experiments on prion diseases, a subcategory of amyloid diseases. First, we notice that attenuated and localized oscillations at specific locations on the experimental signals are observable. These oscillations highlight the presence of complex, underlying kinetic phenomena during protein kinetic processes. We define a parametric characterization of oscillations in the frequency domain. Then, we construct a statistical hypothesis test to confirm the presence of oscillations in the experimental signals. In a second step, we introduce and mathematically analyze a kinetic model capable of generating oscillations. The model considers two species of monomers: a pathological monomer that polymerizes and a healthy monomer that depolymerizes. The model combines a Lotka-Volterra system for monomers with a growth/fragmentation system: Becker-Döring in the discrete case in size, Lifshitz-Slyozov in the continuous case. The mathematical study of these models leads to new and interesting problems and improves the understanding of the underlying physical phenomena.
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Submitted on : Friday, February 12, 2021 - 12:25:07 PM
Last modification on : Thursday, March 4, 2021 - 4:20:11 PM


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  • HAL Id : tel-02435325, version 2


Mathieu Mezache. Oscillatory processes during the aggregation and the fragmentation of amyloid fibrils. Analysis of PDEs [math.AP]. Sorbonne Université, 2019. English. ⟨NNT : 2019SORUS533⟩. ⟨tel-02435325v2⟩



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