Spark-to-wave transition: saltatory transmission of calcium waves in cardiac myocytes

Using a modular approach, in which kinetic models of various mechanisms of calcium handling in cells are fine-tuned to in vivo and in vitro measurements before combining them into whole-cell models, three distinct modes of transmission of calcium waves in mature and immature frog eggs have been defined. Two modes of transmission are found in immature eggs, where the inositol 1,4,5-trisphosphate receptor (IP3R) controls release of calcium from the endoplasmic reticulum (ER). The first mode corresponds to an excitable physiological state of the cytoplasm and results in solitary waves that can appear as circular or spiral waves in two dimensions with the wave speed proportional to the square root of the diffusion constant of calcium. A second mode occurs when the state of the cytoplasm is oscillatory and because of the small size of the buffered diffusion constant for calcium, the wave speed can appear to be weakly dependent on diffusion. In the mature frog egg, where the sperm-induced Ca2+ fertilization wave is a propagating front, the cytoplasm appears to be bistable and in this mode the wave speed is also proportional to the square root of the diffusion constant. Here we investigate a fourth mode of propagation for cardiac myocytes, in which calcium release from the sarcoplasmic reticulum (SR) is dominated by clusters of ryanodine receptors spaced at regular intervals. In myocytes a stochastically excitable myoplasm leads to the spontaneous production of calcium 'sparks' that under certain conditions can merge into saltatory waves with a speed proportional to the diffusion constant.