Dynamic modelling and analysis of autophagy in the clearance of aggregated α-synuclein in Parkinson's disease

The widely-accepted hallmark pathology of Parkinsons disease (PD) is the presence of Lewy bodies (LB) with characteristic abnormal aggregated -synuclein (Syn). Growing physiological evidences suggest that there is a pivotal role for the autophagy-lysosome pathway in the clearance of misfolded Syn (Syn*) for maintaining homeostasis and neural cell function. In this work, we establish a new mathematical model for Syn* degradation through the autophagy pathway. The qualitative simulations discover the tri-stability phenomena and dynamical behaviors of Syn*, i.e., the coexistence of three stable steady states, in which the lower, medium and upper steady states correspond to the healthy, critical and diseased stages of pathological mechanism of PD, respectively. Diverse analyses on codimension-1 and -2 bifurcations suggest that autophagy can control the switches among the stable steady states for the aggregation of Syn*. It is also found that the double negative crosstalk feedback between autophagy and apoptosis is important to the robustness of tri-stability of Syn* for this biodynamic system. Our novel results may be valuable for making further therapeutic strategies in prevention and treatment for PD. Author summarySyn* is one of the most and primary remarkable targets for the universal neurodegenerative disease of PD. Efficient clearance mechanism of autophagy, contains a lot of molecular components to maintain the cellular homeostasis and cell renewal, could be the possible therapy for PD. Understand the complexity of autophagy in degrading Syn* requires the integration of both theoretical and experimental points of view. Here, we have proposed a novel mathematical model that analyses the temporal and dynamic behaviors of the biosystem for autophagy degrades Syn* to access PD states. The model explains that the tri-stability is of particularly relevance to this biosystem that switch among the healthy, critical and disease states, and captures that the critical intermedium state exits for preventing the system transform healthy to disease state directly, and further illustrates that the molecular signaling feedback loops of autophagy may be important for the robustness of tri-stability. Our work deepens the researches of PD by uncovering the important buffering medium state and providing promising potential therapeutic insights.