Equations for InsP3 Receptor-mediated [Ca2+]i Oscillations Derived from a Detailed Kinetic Model: A Hodgkin-Huxley Like Formalism

Exploring Oscillations in a Point Model of the Intracellular Ca2+ Concentration

“…• The original De Young Keizer model (De Young and Keizer 1992) • The Li-Rinzel approximation of the De Young Keizer model (Li and Rinzel 1994) • XPPAUT (http://www.math.pitt.edu/~bard/xpp/xpp.html)…”

“…Locate the two ODEs -one for the Ca 2+ concentration and one for the fraction of non-inhibited IP3Rs ℎ − in (Li and Rinzel 1994): …”

Dynamics of a minimal neural model consisting of an astrocyte, a neuron, and an interneuron

“…It is worth mentioning that in the calcium model adopted by Nadkarni and Jung [51,52,61] the Ca +2 fluxes through the cellular membrane are absent. How do these results change when, while keeping the r PY value fixed, the stimulation current is increased?…”

Dynamics of excitable elements with time-delayed coupling

“…However, for our current purpose it suffices to assume an individual cluster to be one dynamical element. It has been shown by several authors that the collective dynamics of channels in a cluster can be described by FitzHugh-Nagumo-type equations (Meinhold & Schimansky-Geier, 2002;Li & Rinzel, 1994), where an activator variable represents, for instance, the calcium concentration and an inhibitor variable stands for the number of inhibited channels. Thul & Falcke (2004), particularly, showed that deterministic oscillatory local dynamics may be difficult to achieve in realistic models of clusters, given the large local concentrations of calcium in the surrounding of the channels.…”

“…However, for sake of comparison with experiments on the IP 3 receptor, we are now expanding this work by analysis of models that are biologically more realistic. One important example for such is model are the Li-Rinzel equations (Li & Rinzel, 1994). We are presently analyzing both the case of delay-coupled discrete Li-Rinzel elements as well as the case of localized Li-Rinzel elements in a spatially continuous calcium bath (to be published).…”