Section: New Results

Contribution to the interaction between Alzheimer’s disease and prion with the analysis of a mathematical model arising from in vitro experiments

Alzheimer’s disease (AD) is a fatal incurable disease leading to progressive neuron destruction. AD is caused in part by the accumulation of $A\beta$ monomers inside the brain, which have the faculty to aggregate into oligomers and fibrils. Oligomers are the most toxic structures as they can interact with neurons via membrane receptors, including PrPc proteins. This interaction leads to the misconformation of $PrPc$ into pathogenic oligomeric prions, $PrPol$. The objective of our collaboration with the Inra team lead by Human Rezaei (Jouy en Josas), is to design and study a brand new model describing in vitro $A\beta$ polymerization process (see [25]). We include interactions between oligomers and $PrPc$ that induces the misconformation of PrPc into PrPol. The model consists of nine equations, including size structured transport equations, ordinary differential equations and delayed differential equations. Our collaboration is only at its beginning and we applied for an ANR grant highlighting this interdisciplinary work.