Bimodality, prion aggregates infectivity and prediction of strain phenomenon

Vincent Calvez (1) , Natacha Lenuzza (2) , Dietmar Oelz (3) , Jean-Philippe Deslys (2) , Pascal Laurent (4) , Franck Mouthon (2) , Benoît Perthame (5)

1 DMA - Département de Mathématiques et Applications - ENS Paris
2 Groupe d'Innovation Diagnostique et Thérapeutique sur les Infections à Prions
3 Institute for Analysis and Scientific Computing [Wien]
4 MAS - Mathématiques Appliquées aux Systèmes - EA 4037
5 LJLL - Laboratoire Jacques-Louis Lions

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.

Mots clés: Fragmentation; Bimodal distribution; eigenvalue problem; dual method; Prion strain; species barrier

Domaines: Equations aux dérivées partielles [math.AP]

Vincent Calvez, Natacha Lenuzza, Dietmar Oelz, Jean-Philippe Deslys, Pascal Laurent, et al.. Bimodality, prion aggregates infectivity and prediction of strain phenomenon. 2008. ⟨hal-00255790⟩