Rotating spiral waves in fertilized ascidian eggs

Excitable systems modelled by reaction-diffusion equation may be expected to produce quite complex spatial patterns. Winfree [1974] demonstrated experimentally, in the Belousov-Zhabotinskii reaction, the existence of particular waves called rotating spiral waves. Later Keener and Tyson [1986] presented a thorough analysis of these waves in excitable systems. Spiral waves can also be observed in brain tissue (Shibata and Bures [1974]), while it seems that the precursor to cardiac fibrillation is the appearance of rotating waves of electrical impulses (Winfree [1983]). In this work we suppose the appearance of Ca++ spiral waves in the vegetal pole of ascidian egg cells after the first ooplasmic segregation. Previously we observed that (Ballarò and Reas [2000a]), when the myoplasm is completely localized in the vegetal region (excitable stage) and the ascidian egg cell is perturbed by an increase of Ca++ concentration in the culture medium, the cell reacts by showing persistent mechanical waves of contraction which exist as long as the cell is perturbed. Experimentally we observed the production of a polar lobe located in the vegetal region and the change of the inclination of mitotic furrow, after the appearance of a myoplasmic spiral wave in the vegetal pole. So we suppose that the myoplasmic spiral wave is due to a Ca++ spiral wave, and the myoplasmic spiral wave then causes the changes in the shape of the cell (polar lobe, inclination of mitotic furrow, etc.). Moreover we give a simple geometrical description of a spiral wave.