| Ca2+ 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. Many cells have developed sophisticated intracellular signal transduction pathways that involve different proteins modulated by Ca2+ for communication between intracellular compartments or neighboring cells. The astrocytes, which are the dominant glial cell type, had been regarded as maintenance and support cells for neurons until recent years. But, with a series of discoveries of propagating calcium waves in networks of astrocytes, people began to believe that astrocytes modulate neural network activities. One example of the cross-talk is reflected in the observed ATP-mediated calcium waves, which demonstrate the coupling between intracellular calcium dynamics and cell-cell communication via the extracellular space.; In this thesis, a model of glutamate-induced Ca2+ oscillations in astrocytes will be studied. To study temporal aspect, a system of ODE will be derived and the derived full ODE model will be reduced to a lower dimensional system of ODE by nondimensional analysis. Using the temporal model, we will attempt to understand recent observations on the different types of intracellular Ca2+ response patterns in terms of PKC and PLC that determine the intracellular level of IP3.; Following this, we will develop a PDE model for wave propagation between astrocytes from the reduced ODE system. To study how the different configuartions of geometry influence the [Ca2+]i wave propagation, the PDE model was solved on two different geometries: a retangular array of cells for astrocytes in vitro and a complex geometry mimicking astrocyte network in vivo. The PDE model demonstrates that temporal [Ca2+] i response patterns in cells are different from one cell to another, and even more [Ca2+]i response patterns evolve from one type to another as [Ca2+]i wave propagates. Also, the spatial patterns of [Ca2+]i wave propagations are different when IP3 and/or ATP are/is mediating messenger(s). Finally, the effects of extracellular space volume on ATP and [Ca2+ ]i waves propagation and regenertivity of ATP release will be studied. |
