Glutamate regulation of calcium and IP3 oscillating and pulsating dynamics in astrocytes

Recent years have witnessed an increasing interest in neuron-glia communication. This interest stems from the realization that glia participate in cognitive functions and information processing and are 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 (Ca2 + ) 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-variable (intracellular Ca2 + and inactive IP3 receptors) Li-Rinzel model for calcium-induced calcium release, we incorporate the regulation of IP3 production and phosphorylation. Doing so, we extend it to a three-variable model (which we refer to as the ChI model) that could account for Ca2 + oscillations with endogenous IP3 metabolism. This ChI model is then further extended into the G-ChI model to include regulation of IP3 production by external glutamate signals. Compared with previous similar models, our three-variable models include a more realistic description of 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 endow the system with self-consistent oscillatory 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 for the role of astrocytes in the synaptic transfer of information.