Dynamics of a model for the degradation mechanism of aggregated α-synuclein in Parkinson's disease

Accumulation of the misfolded synaptic protein α-synuclein (αSyn(*)) is a hallmark of neurodegenerative disease in Parkinson's disease (PD). Recent studies suggest that the autophagy lysosome pathway (ALP) including both the Beclin1-associated and mTOR-signaling pathways is involved in the αSyn(*) clearance mechanism. In this study, a mathematical model is proposed for the degradation of αSyn(*) by ALP with the crosstalk element of mTOR. Using codimension-1 bifurcation analysis, the tri-stability of αSyn(*) is surveyed under three different stress signals and, in addition, consideration is given to the regulatory mechanisms for the Beclin1- and mTOR-dependent rates on αSyn(*) degradation using the codimension-1 and−2 bifurcation diagrams. It was found that, especially under internal and external oxidative stresses (S(1)), the bistable switch of the aggregation of αSyn(*) can be transformed from an irreversible to a reversible condition through the ALP degradation pathways. Furthermore, the robustness of the tri-stable state for the stress S(1) to the parameters related to mTOR-mediated ALP was probed. It was confirmed that mTOR-mediated ALP is important for maintaining the essential dynamic features of the tri-stable state. This study may provide a promising avenue for conducting further experiments and simulations of the degradation mechanism of dynamic modeling in PD.