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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.

Exploring the behaviors of beta oscillations in the basal ganglia is helpful to understand the mechanism of Parkinson’s disease. Studies have shown that the external and internal segments (GPe, GPi) of the globus pallidus receive different intensities of signals from the striatum in Parkinson’s disease and play different roles in the production of beta oscillations, but the relevant mechanism still remains unclear. Based on a model of the subthalamic nucleus (STN) and globus pallidus (GP), we propose an extended STN-GPe-GPi model and analyze the dynamical behaviors of beta oscillations in this model. The stability condition is obtained through theoretical analyses, and the generation of beta oscillations by the inputs from the cortex and striatum is further considered. The influence of some parameters related to GPi on its firing rate oscillations is discussed. The results obtained in this paper are expected to play a guiding role in the medical treatment of Parkinson’s disease.

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