Oscillations and waves of increased intracellular free calcium concent
ration ([Ca2+]i) are observed in a wide range of cell types, Because o
f their inherent nonlinear nature and the consequent unreliability of
intuitive approaches, mathematical modeling has an important role to p
lay in the study of these phenomena, One important class of oscillatio
ns and waves is dependent on the presence of inositol (1,4,5)-trisphos
phate (IP3), which releases Ca2+ from internal stores via the IP3 rece
ptor/Ca2+ channel, With the minimum possible mathematical formalism, w
e review mechanistic models for IP3-dependent Ca2+ oscillations and wa
ves, These models are based on the regulation of the IP3 receptor by b
oth IP3 and Ca2+, and incorporate experimental data on the steady-stat
e and kinetic properties of the receptor, The extension of the models
to describe intracellular and intercellular Ca2+ waves is considered.