Mathematical model for IP$_{3}$ dependent calcium oscillations and mitochondrial associate membranes in non-excitable cells

Theoretical studies on calcium oscillations within the cytosolic [Ca$^{2+}$], and mitochondria [Ca$^{2+}$]$_{mit}$ have been conducted using a mathematical model-based approach. The model incorporates the mechanism of calcium-induced calcium release (CICR) through the activation of inositol-trisphosphate receptors (IPR), with a focus on the endoplasmic reticulum (ER) as an internal calcium store. The production of 1,4,5 inositol-trisphosphate (IP$_{3}$) through the phospholipase \(C\) isoforms and its degradation via Ca$^{2+}$ are considered, with IP$_{3}$ playing a crucial role in modulating calcium release from the ER. The model includes a simple kinetic mechanism for mitochondrial calcium uptake, release and physical connections between the ER and mitochondria, known as mitochondrial associate membrane complexes (MAMs), which influence cellular calcium homeostasis. Bifurcation analysis is used to explore the different dynamic properties of the model, identifying various regimes of oscillatory behavior and how these regimes change in response to different levels of stimulation, highlighting the complex regulatory mechanisms governing intracellular calcium signaling.