A model with excitability and relay properties for the generation and the propagation of a Ca2+morphogenetic wave in paramecium

Parameciumdisplays an elaborate surface pattern formed by the arrangement 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 cortex like a wave, originating from a single epicentre. Convergent experimental data suggest that the primary signal for cortical morphogenesis might be a calcium wave. The generation and the propagation of such a morphogenetic wave all over the cortex have been modeled by a system of transport and diffusion equations. This model takes into account specific ciliate characteristics such as the existence, under the cell membrane, of a layer of membrane vesicles, namely the cortical alveoli, which are known to be calcium reservoirs. Assuming solely an allosterically controlled calcium release from the cortical alveoli, the model exhibits excitability properties which allow the local amplification of a faint signal as an intracellular calcium relay response mechanism. 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 excitability conditions. When all the cortical units 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 simulate the occurrence of a calcium morphogenetic wave inParamecium.Results are discussed both from a morphogenetic and mechanistic points of view.