Although Ca i2+ 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 ͑IP 3 ͒ and adenosine-5Ј-triphosphate ͑ATP͔͒ 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 IP 3 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 Ca 2+ response patterns.
Calcium "Ca
2+… is one of the most versatile and widely used second-messenger molecules and plays a pivotal role in neurotransmission, muscle contraction, gene expression, and a variety of other intracellular processes.
13,37Because high levels of intracellular calcium are toxic, and because it cannot be degraded as many other signaling molecules are, cells control the intracellular calcium level at around 100 nM (compared to millimolar extracellular levels) by buffering, sequestration in specialized compartments, and by expulsion to the extracellular space.