Abortive and Propagating Intracellular Calcium Waves: Analysis from a Hybrid Model

The functional properties of inositol(1,4,5)-triphosphate (IP3) receptors allow a variety of intracellular Ca(2+) phenomena. In this way, global phenomena, such as propagating and abortive Ca(2+) waves, as well as local events such as puffs, have been observed. Several experimental studies suggest that many features of global phenomena (e.g., frequency, amplitude, speed wave) depend on the interplay of biophysical processes such as diffusion, buffering, efflux and influx rates, which in turn depend on parameters such as buffer concentration, Ca(2+) pump density, cytosolic IP3 level, and intercluster distance. Besides, it is known that cells are able to modify some of these parameters in order to regulate the Ca(2+) signaling. By using a hybrid model, we analyzed different features of the hierarchy of calcium events as a function of two relevant parameters for the calcium signaling, the intercluster distance and the pump strength or intensity. In the space spanned by these two parameters, we found two modes of calcium dynamics, one dominated by abortive calcium waves and the other by propagating waves. Smaller distances between the release sites promote propagating calcium waves, while the increase of the efflux rate makes the transition from propagating to abortive waves occur at lower values of intercluster distance. We determined the frontier between these two modes, in the parameter space defined by the intercluster distance and the pump strength. Furthermore, we found that the velocity of simulated calcium waves accomplishes Luther's law, and that an effective rate constant for autocatalytic calcium production decays linearly with both the intercluster distance and the pump strength.