This page implements a compact Li-Rinzel-style IP3 receptor oscillator. Cytosolic calcium c rises when IP3-bound receptor channels release Ca²⁺ from the endoplasmic reticulum, while SERCA pumps calcium back into the ER. The ER store is tracked through total calcium conservation, c_ER = (c0−c)/c1. A slow inactivation/recovery gate h closes the release channel after cytosolic Ca becomes high and reopens as Ca falls. This delayed negative feedback creates calcium oscillations in a middle IP3 window: low IP3 rests, intermediate IP3 produces repeated release pulses, and high IP3 can settle at elevated calcium. The simulator plots cytosolic Ca and scaled ER store, release/leak flux versus SERCA pump flux, and the (c,h) phase portrait after the transient.
Who it's for: Students in cell physiology, systems biology, biophysics, or nonlinear dynamics learning intracellular calcium signaling and excitable biochemical oscillators.
Key terms
Calcium oscillation
IP3 receptor
Endoplasmic reticulum
SERCA pump
Li-Rinzel model
CICR
Phase portrait
Slow inactivation
This single-cell model shows temporal calcium oscillations. Spatial calcium waves need diffusion/coupled cells; here the ER store trace is scaled to fit on the cytosolic Ca graph.
Live graphs
How it works
IP3-driven calcium oscillator: cytosolic Ca, ER store, release/pump fluxes, and a phase portrait reveal calcium-induced calcium release with slow channel inactivation.
Key equations
dc/dt = c₁(J_IP3R + J_leak) − J_SERCA, dh/dt = (h∞(c,p) − h)/τ_h, with c_ER = (c₀ − c)/c₁. IP₃ and Ca activate release; high Ca lowers h.
Frequently asked questions
Why does calcium oscillate instead of just reaching a steady level?
Calcium both promotes its own release from the ER and, with a delay, inactivates that release through the h gate. The pump then lowers cytosolic calcium and refills the store, letting the gate recover and another pulse begin.
Does this simulate spatial calcium waves?
Not directly. It is a single well-mixed cell or compartment. Spatial waves require diffusion and coupling between compartments, but the local release-and-recovery oscillator here is the building block for those waves.
What should I look for in the phase portrait?
A closed loop in the (c,h) plane indicates a limit cycle: fast Ca release pushes c upward, h slowly falls, release shuts off, then c drops while h recovers.