Neuron Scale Modeling of Prion Production with the Unfolded Protein Response
Résumé
We develop a mathematical model that describes the concentration dynamics of PrPC (Prion Protein Cellular) and PrPSc (Prion Protein Scrapie) prion proteins at the neuron scale and includes the effect of the unfolded protein response (UPR). We first introduce a single neuron model taking the UPR mechanism into account. We investigate it and propose a stability study among which a bifurcation analysis with respect to three of its parameters. Then, we generalize it to two neurons showing PrPSc proteins interaction. Stability results are given when neurons exhibit identical parameters but interact differently (strong, weak, or no interaction).
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