A mathematical model of agonist-induced propagation of calcium waves in astrocytes

In astrocytes, calcium signals evoked by neurotransmitters appear as waves within single cells, which spread to other cells in the network. Recent analysis has shown that waves are initiated at a single invariant site in the cell and propagated within the cell in a nonlinear and saltatory manner by regenerative amplification at specific predestined cellular sites. In order to gain insight into local cellular waves and wave collisions we have developed a mathematical model of cellular wave amplification loci. This model is in good agreement with experimental data which includes: ambient calcium gradients in resting cells, wave origination and local amplification and generation of local waves. As observed in experiments, the model also predicts that different locations in the cell can have different frequencies of oscillation. The amplification loci are thought to be specialized areas of the endoplasmic reticulum membrane containing a higher density or higher sensitivity of IP3 receptors. Our analysis suggests that the cellular loci act as weakly coupled oscillators each with its intrinsic latency and frequency of oscillation. Thus the appearance of the propagated calcium wave may be a reflection of these differences rather than an actual diffusional wave propagation.