A Novel Nonlinear IP$_3$R State Transition Model and Calcium Oscillation

We present a novel nonlinear state transition model for inositol 1,4,5-trisphosphate receptors (IP$_3$Rs) that incorporates a pre-activated state, as suggested by electron microscopy observations. Our model provides a theoretical framework for the biphasic Ca$^{2+}$ dependence of IP$_3$Rs and accurately reproduces their experimentally observed state distribution under saturating IP$_3$ conditions. By integrating receptor dynamics with cytoplasmic and endoplasmic reticulum (ER) calcium exchange, we simulate IP$_3$R-mediated Ca$^{2+}$ oscillations governed by six key conformational states. A pivotal finding is that IP$_3$ regulates these oscillations in a switch-like manner: once a critical IP$_3$ concentration is reached, the system abruptly transitions to sustained, constant-amplitude oscillations that quickly terminate when the concentration exceeds a secondary threshold. These results underscore the crucial role of the pre-activated state in modulating calcium signaling.