Calcium waves serve as a pathway of intercellular signalling in such
diverse systems as the liver and the astrocyte networks of the nervous
system. Various schemes for intercellular waves have been proposed, in
which wave propagation relies on the diffusion of messengers through gap
junctions or across the extracellular space, or both. The schemes differ
with respect to the messenger species exchanged and the role of feedback
mechanisms that can regenerate the propagating signal. We have studied
intercellular wave propagation in a simple reaction-diffusion model
accounting for regenerative calcium release and gap-junctional diffusion of
calcium or IP3. The analysis shows that the types of signals that can be
obtained depend on the diffusivity of the messenger carrying intercellular
propagation. If propagation proceeds by calcium-induced calcium release and
calcium diffusion, one can find either travelling waves or localized
signals that fail to propagate beyond a stimulated cell or its immediate
neighbourhood. If propagation relies on the more readily diffusible
IP3, one additionally obtains signals with a long yet finite range of
propagation. Based on data recorded in rat striatal astrocytes, we
developed and analysed a more detailed model of intercellular calcium
signalling in astrocyte networks. The kinetic equations account for IP3
generation, including its activation by cytoplasmic calcium, IP3-induced
calcium liberation from intracellular stores and various other calcium
transports, and both cytoplasmic and gap-junctional diffusion of IP3 and
calcium ions. Rate constants for calcium release and sequestration were
estimated from experimental data; the kinetic parameters for
calcium-activated IP3 production and intercellular IP3 diffusion were taken
as control parameters in the analysis of the model. Depending on their
values, we find the three types of signals predicted by the simple
model: localised diffusive signals, limited regenerative signals, and fully
regenerative waves. The gap-junctional permeability for IP3 is the crucial
permissive factor for signal propagation, and heterogeneity of
gap-junctional coupling yields preferential pathways of
propagation. Processes involved in both signal initiation (IP3 production
activated by neurotransmitter) and regeneration (activation of IP3
production by calcium, loading of the calcium stores) exert the main
control on the signalling range. The refractory period of signalling
strongly depends on the refilling kinetics of the calcium stores. Thus the
model identifies multiple steps that may be involved in the regulation of
this intercellular signalling pathway.
Christian Giaume and Laurent Venance (Collège de France) are
gratefully acknowledged for stimulating collaboration.
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