BackgroundAutophagy and apoptosis are two important physiological processes that determine cell survival or death in response to different stress signals. The regulatory mechanisms of these two processes share B-cell lymphoma-2 family proteins and AMBRA1, which are present in both the endoplasmic reticulum and mitochondria. B-cell lymphoma-2 family proteins sense different stresses and interact with AMBRA1 to regulate autophagy and apoptosis, which are respectively mediated by Beclin1 and Caspases. Therefore, we investigated how different levels of stress on B-cell lymphoma-2 family proteins that bind to AMBRA1 in the endoplasmic reticulum and mitochondria regulate the switch from autophagy to apoptosis.MethodsIn this paper, we considered the responses of B-cell lymphoma-2 family proteins, which bind to AMBRA1 in both the endoplasmic reticulum and mitochondria, to two different levels of stress in a model originally proposed by Kapuy et al. We investigated how these two stress levels affect the transition from autophagy to apoptosis and their effects on apoptosis activation over time. Additionally, we analyzed how the feedback regulation in this model affects the bifurcation diagrams of two levels of stress and cell fate decisions between autophagy and apoptosis.ResultsAutophagy is activated for minor stress in mitochondria regardless of endoplasmic reticulum stress, while apoptosis is activated for only significant stress in mitochondria. Apoptosis is only sensitive to mitochondria stress. The time duration before apoptosis activation is longer in the presence of high AMBRA1 levels with high endoplasmic reticulum and mitochondria stress. AMBRA1 can compete with B-cell lymphoma-2 family proteins to bind and activate Beclin1 and thus promote the autophagy process for a long time before apoptosis. Furthermore, apoptosis is prone to occur with increasing activation of Caspases, inactivation of Beclin1-A and the Michaelis constant of Caspases.ConclusionA novel mathematical model has been developed to understand the complex regulatory mechanisms of autophagy and apoptosis. Our model may be applied to further autophagy-apoptosis dynamic modeling experiments and simulations.

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The widely-accepted hallmark pathology of Parkinson's disease (PD) is the presence of Lewy bodies (LB) with characteristic abnormal aggregated α-synuclein (αSyn). Growing physiological evidences suggest that there is a pivotal role for the autophagy-lysosome pathway in the clearance of misfolded αSyn (αSyn*) for maintaining homeostasis and neural cell function. In this work, we establish a new mathematical model for αSyn* degradation through the autophagy pathway. The qualitative simulations discover the tri-stability phenomena and dynamical behaviors of αSyn*, 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 αSyn*. It is also found that the double negative crosstalk feedback between autophagy and apoptosis is important to the robustness of tri-stability of αSyn* for this biodynamic system. Our novel results may be valuable for making further therapeutic strategies in prevention and treatment for PD.

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 (S1), 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 S1 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.