Mitochondrial permeability transition pore (PTP), a key regulator of cell life and death processes, is triggered by calcium ions (Ca2+) and potentiated by reactive oxygen species (ROS). Although the two modes of PTP opening, i.e., transient and persistent, have been identified for a long time, its dynamical mechanism is still not fully understood. To test a proposed hypothesis that PTP opening acts as a tristable switch, which is characterized by low, medium, and high open probability, we develop a three-variable model that focused on PTP opening caused by Ca2+ and ROS. For the system reduced to two differential equations for Ca2+ and ROS, both the stability analysis and the potential landscape feature that it exhibits tristability under standard parameters. For the full system, the bifurcation analysis suggests that it can achieve tristability over a wide range of input parameters. Furthermore, parameter sensitivity analysis demonstrates that the existence of tristability is a robust property. In addition, we show how the deterministic tristable property can be understood within a stochastic framework, which also explains the PTP dynamics at the level of a single channel. Overall, this study may yield valuable insights into the intricate regulatory mechanism of PTP opening.

Inositol 1,4,5-trisphosphate receptors (IP 3 R)-mediated calcium ion (Ca 2+ ) release plays a central role in the regulation of cell survival and death. Bcl-2 limits the Ca 2+ release function of the IP 3 R through a direct or indirect mechanism. However, the two mechanisms are overwhelmingly complex and not completely understood. Here, we convert the mechanisms into a set of ordinary differential equations. We firstly simulate the time evolution of Ca 2+ concentration under two different levels of Bcl-2 for the direct and indirect mechanism models and compare them with experimental results available in the literature. Secondly, we employ one-and two-parameter bifurcation analysis to demonstrate that Bcl-2 can suppress Ca 2+ signal from a global point of view both in the direct and indirect mechanism models. We then use mathematical analysis to clarify that the indirect mechanism is more efficient than the direct mechanism in repressing Ca 2+ signal. Lastly, we predict that the two mechanisms restrict Ca 2+ signal synergistically. Together, our study provides theoretical insights into Bcl-2 regulation in IP 3 R-mediated Ca 2+ release, which may be instrumental for the successful development of therapies to target Bcl-2 for cancer treatment.