Modeling oscillating polymerization/depolymerization processes
The process of protein aggregation and fragmentation is intimately linked to the development of a broad class of neurodegenerative diseases or amyloid disease. More particularly, oscillatory kinetic phenomena are identified in experiments on Prion diseases. As a first step, the analysis of experimental data leads us to build a parametric characterization oscillations in the frequency domain. We propose a numerical procedure to obtain these parameters. Then we build a statistical testing of hypotheses to quantitatively assert the presence of the or the absence of significant oscillations in the experimental signals. In a second step, we introduce and analyse mathematically a model kinetics of proteins capable of generating oscillations. The model is a variant of the polymerization/depolymerization system and considers two monomer species: a pathological monomer that polymerizes and a healthy monomer that depolymerizes. Unlike traditional models, the depolymerization is catalytic and nonlinear and an exchange phenomenon operates between the two species of monomers and polymers. The model couples a Lotka-Volterra system for monomers to a growth/fragmentation: Becker-Döring in the discrete size case, Lifshitz-Slyozov in the continuous case.
