A MODEL WITH EXCITABILITY AND RELAY PROPERTIES FOR THE GENERATION ANDTHE PROPAGATION OF A CA2+ MORPHOGENETIC WAVE IN PARAMECIUM

Paramecium displays an elaborate surface pattern formed by the arrange ment of several thousand juxtaposed cortical units that are duplicated during mitosis. The morphogenesis of the cortex at cell division has been shown to involved transcellular signals which spread across the c ortex like a wave, originating from a single epicentre. Convergent exp erimental data suggest that the primary signal for cortical morphogene sis might be a calcium wave. The generation and the propagation of suc h a morphogenetic wave all over the cortex have been modeled by a syst em of transport and diffusion equations. This model takes into account specific ciliate characteristics such as the existence, under the cel l membrane, of a layer of membrane vesicles, namely the cortical alveo li, which are known to be calcium reservoirs. Assuming solely an allos terically controlled calcium release from the cortical alveoli,the mod el. exhibits excitability properties which-allow the local amplificati on of a faint signal as an intracellular calcium relay response mechan ism. In this simple calcium-induced calcium-release type process, the propagation over the whole cortex of a single calcium wave is ensured by the two-dimensional diffusion of the amplified initial signal from one alveolus to the next and the subsequent spatial transmission of ex citability conditions. When all the cortical unit have been reached by the propagating wave, the two wavefronts collide and annihilate as a result of the refractory properties of excitable systems. This minimal model is compared with previous attempts that have been made to simul ate the occurrence of a calcium morphogenetic wave in Paramecium. Resu lts are discussed both from a morphogenetic and mechanistic points of view.