Abstract
This study investigated the stability and bifurcation of a nonlinear system model developed by Marhl et al. based on the total Ca2+ concentration among three different Ca2+ stores. In this study, qualitative theories of center manifold and bifurcation were used to analyze the stability of equilibria. The bifurcation parameter drove the system to undergo two supercritical bifurcations. It was hypothesized that the appearance and disappearance of Ca2+ oscillations are driven by them. At the same time, saddle-node bifurcation and torus bifurcation were also found in the process of exploring bifurcation. Finally, numerical simulation was carried out to determine the validity of the proposed approach by drawing bifurcation diagrams, time series, phase portraits, etc.
Highlights
Ca2+ is one of the vital ions for information processing in humans
Catot corresponds to the total intracellular Ca2+ concentration including free Ca2+ in the cytosol, endoplasmic reticulum, and mitochondria
Oscillations of Ca2+ in the cytosol, endoplasmic reticulum, and mitochondria were studied using the total concentration of Ca2+ in the cytosol, mitochondria, and endoplasmic reticulum as the bifurcation parameter
Summary
Ca2+ is one of the vital ions for information processing in humans. It generally acts as a biological messenger in different cell types and is an indispensable ion for various physiological activities in the human body [1,2,3,4]. Chay proposed a model for Ca2+ oscillations in excitable cells [21], and Shen and Larter (1995) studied complex Ca2+ oscillations and chaotic phenomena in non-excitable cells [22,23] In these models, it is almost certain that the burst results from changes in IP3 yields because IP3 can stimulate Ca2+ channels and release a large number of Ca2+ into the cytosol or take up Ca2+ from the cytosol, thereby participating in Ca2+ regulation. One mechanism proposed by Borghans et al to explain complex Ca2+ oscillations is that bursting oscillations are associated with Ca2+-releasing channel activities in the endoplasmic reticulum. The advantage is that it confirms our conclusions [31,32]
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