Spatiotemporal characteristics of calcium dynamics in astrocytes

Although Ca _i ²⁺ waves in networks of astrocytes in vivo are well documented, propagation in vivo is much more complex than in culture, and there is no consensus concerning the dominant roles of intercellular and extracellular messengers [inositol 1,4,5-trisphosphate (IP₃) and adenosine-5^′-triphosphate (ATP)] that mediate Ca _i ²⁺ waves. Moreover, to date only simplified models that take very little account of the geometrical struture of the networks have been studied. Our aim in this paper is to develop a mathematical model based on realistic cellular morphology and network connectivity, and a computational framework for simulating the model, in order to address these issues. In the model, Ca _i ²⁺ wave propagation through a network of astrocytes is driven by IP₃ diffusion between cells and ATP transport in the extracellular space. Numerical simulations of the model show that different kinetic and geometric assumptions give rise to differences in Ca _i ²⁺ wave propagation patterns, as characterized by the velocity, propagation distance, time delay in propagation from one cell to another, and the evolution of Ca²⁺ response patterns. The temporal Ca _i ²⁺ response patterns in cells are different from one cell to another, and the Ca _i ²⁺ response patterns evolve from one type to another as a Ca _i ²⁺ wave propagates. In addition, the spatial patterns of Ca _i ²⁺ wave propagation depend on whether IP₃, ATP, or both are mediating messengers. Finally, two different geometries that reflect the in vivo and in vitro configuration of astrocytic networks also yield distinct intracellular and extracellular kinetic patterns. The simulation results as well as the linear stability analysis of the model lead to the conclusion that Ca _i ²⁺ waves in astrocyte networks are probably mediated by both intercellular IP₃ transport and nonregenerative (only the glutamate-stimulated cell releases ATP) or partially regenerative extracellular ATP signaling.