Deterministic and stochastic approaches to a minimal model for the transition from autophagy to apoptosis

Bojie Yang; Zhuoqin Yang; Bojie Yang; Zhuoqin Yang

doi:10.3934/mbe.2024142

Mathematical Biosciences and Engineering

2024, Volume 21, Issue 2: 3207-3228. doi: 10.3934/mbe.2024142

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Research article Special Issues

Deterministic and stochastic approaches to a minimal model for the transition from autophagy to apoptosis

Bojie Yang ,
Zhuoqin Yang ^,

School of Mathematical Sciences, Beihang University, Beijing 100191, China

Academic Editor: Congping Lin

Received: 18 December 2023 Revised: 09 January 2024 Accepted: 21 January 2024 Published: 01 February 2024

Autophagy and apoptosis are crucial cellular mechanisms. The cytoprotective function of autophagy is mediated by the negative regulation of apoptosis, which in turn inhibits autophagy. Although research into the molecular connection between autophagy and apoptosis is booming, the intricate regulatory mechanisms of this process are still not completely understood. Therefore, the objective of this study was to develop a minimal model to explore the transition from autophagy to apoptosis. This biological system was analyzed by comprehensively integrating both the deterministic and the stochastic dynamics of the cells. The system exhibited bistability, and the statistical properties of cells undergoing autophagy and apoptosis were analyzed at two different stress levels with varying noise strengths. Moreover, we investigated how noise affected the double negative feedback loops between autophagy and apoptosis and further triggered transitions at two different stress levels and initial conditions. Finally, the effect of noise on transition was comprehensively studied under continuous stress variations and the two different initial conditions, showing that stronger noise results in more randomness during the switching process. Our work may provide novel insights for further experiments and modeling.
- autophagy,
- apoptosis,
- bifurcation,
- stochastic,
- noise
Citation: Bojie Yang, Zhuoqin Yang. Deterministic and stochastic approaches to a minimal model for the transition from autophagy to apoptosis[J]. Mathematical Biosciences and Engineering, 2024, 21(2): 3207-3228. doi: 10.3934/mbe.2024142

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Abstract

Autophagy and apoptosis are crucial cellular mechanisms. The cytoprotective function of autophagy is mediated by the negative regulation of apoptosis, which in turn inhibits autophagy. Although research into the molecular connection between autophagy and apoptosis is booming, the intricate regulatory mechanisms of this process are still not completely understood. Therefore, the objective of this study was to develop a minimal model to explore the transition from autophagy to apoptosis. This biological system was analyzed by comprehensively integrating both the deterministic and the stochastic dynamics of the cells. The system exhibited bistability, and the statistical properties of cells undergoing autophagy and apoptosis were analyzed at two different stress levels with varying noise strengths. Moreover, we investigated how noise affected the double negative feedback loops between autophagy and apoptosis and further triggered transitions at two different stress levels and initial conditions. Finally, the effect of noise on transition was comprehensively studied under continuous stress variations and the two different initial conditions, showing that stronger noise results in more randomness during the switching process. Our work may provide novel insights for further experiments and modeling.

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