PROPERTIES OF INTRACELLULAR CA2-BASED ON CA2+-INDUCED CA2+ RELEASE( WAVES GENERATED BY A MODEL)

Cytosolic Ca2+ waves occur in a number of cell types either spontaneou sly or after stimulation by hormones, neurotransmitters, or treatments promoting Ca2+ influx into the cells. These waves can be broadly clas sified into two types. Waves of type 1, observed in cardiac myocytes o r Xenopus oocytes, correspond to the propagation of sharp bands of Ca2 + throughout the cell at a rate that is high enough to permit the simu ltaneous propagation of several fronts in a given cell. Waves of type 2, observed in hepatocytes, endothelial cells, or Various kinds of egg s, correspond to the progressive elevation of cytosolic Ca2+ throughou t the cell, followed by its quasi-homogeneous return down to basal lev els. Here we analyze the propagation of these different types of intra cellular Ca2+ waves in a model based on Ca2+-induced Ca2+ release (CIC R). The model accounts for transient or sustained waves of type 1 or 2 , depending on the size of the cell and on the values of the kinetic p arameters that measure Ca2+ exchange between the cytosol, the extracel lular medium, and intracellular stores. Two versions of the model base d on CICR are considered. The first version involves two distinct Ca2 pools sensitive to inositol 1,4,5-trisphosphate (IP3) and Ca2+, respe ctively, whereas the second version involves a single pool sensitive b oth to Ca2+ and IP3 behaving as co-agonists for Ca2+ release. Intracel lular Ca2+ waves occur in the two versions of the model based on CICR, but fail to propagate in the one-pool model at subthreshold levels of IP3. For waves of type 1, we investigate the effect of the spatial di stribution of Ca2+-sensitive Ca2+ stores within the cytosol, and show that the wave fails to propagate when the distance between the stores exceeds a critical value on the order of a few mu m. We also determine how the period and velocity of the waves are affected by changes in p arameters measuring stimulation, Ca2+ influx into the cell, or Ca2+ pu mping into the stores. For waves of type 2, the numerical analysis ind icates that the best qualitative agreement with experimental observati ons is obtained for phase waves. Finally, conditions are obtained for the occurrence of ''echo'' waves that are sometimes observed in the ex periments.