Dynamic modelling and tristability analysis of misfolded α-synuclein degraded via autophagy in Parkinson's disease

Abstract

The widely-accepted hallmark pathology of Parkinson's disease (PD) is the presence of Lewy bodies with characteristic abnormal aggregated α-synuclein (αSyn). Growing physiological evidence suggests that there is a pivotal role for the autophagy-lysosome pathway (ALP) in the clearance of misfolded αSyn (αSyn∗). This work establishes a mathematical model for αSyn∗ degradation through the ALP. Qualitative simulations are used to uncover the tristable behavior of αSyn∗, i.e., the lower, medium, and upper steady states, which correspond to the healthy, critical, and disease stages of PD, respectively. Time series and codimension-1 bifurcation analysis suggest that the system shows tristability dynamics. Furthermore, variations in the key parameters influence the tristable dynamic behavior, and the distribution of tristable regions is exhibited more comprehensively in codimension-2 bifurcation diagrams. In addition, robustness analysis demonstrates that tristability is a robust property of the system. These results may be valuable in therapeutic strategies for the prevention and treatment of PD.