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.
Bibliographical noteFunding Information:
This work was supported by NIH Grant GM 29123 (Hans G. Othmer) and NIH RO1 GM073846 (Anne K. Kenworthy).