Simplification of a Realistic Model of IP3-induced Ca2+ Oscillations

We explore a recent mechanism for IP3-induced Ca2+ oscillations based on the properties of the IP3 receptor/Ca2+ channel in the endoplasmic reticulum. Analysis of the differential equations reveals three essential characteristics of the mechanism: Ca2+-activation of Ca2+ release, Ca2+-inhibition of Ca2+ release, and activation by IP3. Using these features we reduce the system of differential equations from nine dynamical variables down to five, three, and ultimately two variables, the simplest of which has a structure similar to the FitzHugh-Nagumo model. The two-variable model is valid in the limit that Ca2+ dynamics are fast. In this limit it is the receptor dynamics that are primarily responsible for setting the time scale for the oscillations, in contrast to models based exclusively on Ca2+-induced Ca2+ release. The reduced equations exhibit IP3-induced Ca2+ oscillations, Ca2+-induced Ca2+ release, and other features similar to those seen in the full nine-variable model.