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

Intra-and inter-cellular Ca²⁺ waves play key roles in cellular functions. Focal stimulation triggers Ca²⁺ 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 (IP₃) is produced at membranes and diffuses into the cytoplasm, resulting in Ca²⁺ release from the endoplasmic reticulum (ER). Particu-larly, Ca²⁺ released from the ER is mediated by two princi-ples, the IP₃-induced Ca²⁺ and Ca²⁺-induced Ca²⁺ releases. Ca²⁺ is diffused through the cytoplasm and, furthermore, transported into neighboring cells through gap junctions. These intra-and inter-cellular Ca²⁺ 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 Ca²⁺ wave propagations.