Mathematical models for intra- and inter-cellular Ca2+ wave propagations

Intra- and inter-cellular Ca 2+ waves play key roles in cellular functions. Focal stimulation triggers Ca 2+ wave propagation from the stimulation point to neighboring cells through the cytoplasm, which involves localized metabolism reactions and specific diffusion processes. Briefly, inositol 1,4,5-trisphosphate (IP 3 ) is produced at membranes and diffuses into the cytoplasm, resulting in Ca 2+ release from the endoplasmic reticulum (ER). Particu-larly, Ca 2+ released from the ER is mediated by two princi-ples, the IP 3 -induced Ca 2+ and Ca 2+ -induced Ca 2+ releases. Ca 2+ is diffused through the cytoplasm and, furthermore, transported into neighboring cells through gap junctions. These intra- and inter-cellular Ca 2+ waves have been widely investigated using theoretical and experimental methods in various cell types. In this review we summarize the mathematical models used for the numerical simulation of intra-and inter-cellular Ca 2+ wave propagations.