  Recent years have witnessed an increasing interest in neuron-glia
communication. This interest stems from the realization that glia participates
in cognitive functions and information processing and is involved in many brain
disorders and neurodegenerative diseases. An important process in neuron-glia
communications is astrocyte encoding of synaptic information transfer: the
modulation of intracellular calcium dynamics in astrocytes in response to
synaptic activity. Here, we derive and investigate a concise mathematical model
for glutamate-induced astrocytic intracellular Ca2+ dynamics that captures the
essential biochemical features of the regulatory pathway of inositol
1,4,5-trisphosphate (IP3). Starting from the well-known two-state Li-Rinzel
model for calcium-induced-calcium release, we incorporate the regulation of the
IP3 production and phosphorylation. Doing so we extended it to a three-state
model (referred as the G-ChI model), that could account for Ca2+ oscillations
triggered by endogenous IP3 metabolism as well as by IP3 production by external
glutamate signals. Compared to previous similar models, our three-state models
include a more realistic description of the IP3 production and degradation
pathways, lumping together their essential nonlinearities within a concise
formulation. Using bifurcation analysis and time simulations, we demonstrate
the existence of new putative dynamical features. The cross-couplings between
IP3 and Ca2+ pathways endows the system with self-consistent oscillator
properties and favor mixed frequency-amplitude encoding modes over pure
amplitude modulation ones. These and additional results of our model are in
general agreement with available experimental data and may have important
implications on the role of astrocytes in the synaptic transfer of information.
