Bimodality, prion aggregates infectivity and prediction of strain phenomenon

Calvez, Vincent
Lenuzza, Natacha
Oelz, Dietmar
Deslys, Jean-Philippe
Laurent, Pascal
Mouthon, Franck
Perthame, Benoît
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We consider a model for the polymerization (fragmentation) process involved in infectious prion self-replication and study both its dynamics and non-zero steady state. We address several issues. Firstly, we give conditions leading to size repartitions of PrPsc aggregates that exhibit bimodal distributions, as indicated by recent experimental studies of prion aggregates distribution. Secondly, we show stability results for this steady state for general coefficients where reduction to a system of differential equations is not possible. We use a duality method based on recent ideas developed for population models. These results underline the potential influence of the amyloid precursor production rate in promoting amyloidogenic diseases. Finally, we numerically investigate the influence of different parameters of the model on PrPsc accumulation kinetics, in the aim to study specific features of prion strains.
Comment: 21 pages
Mathematics - Analysis of PDEs