Bimodality, prion aggregates infectivity and prediction of strain phenomenon

Details Bimodality, prion aggregates infectivity and prediction of strain phenomenon Bimodality, prion aggregates infectivity and prediction of strain phenomenon

2008-02-14

arxiv.org/abs/0802.2024v1

Mathematics

Analysis of PDEs

21 pages

Scientific paper

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.

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