A Single Model can Account for the Main Asymmetries of the Cortex of Paramecium: Application to Homopolar Doublets

In two previous papers (Le Guyader & Hyver, 1990, J. theor. Biol.143, 233-250; 1991, J. theor. Biol.150, 261-276) we proposed a one- and subsequently a two-dimensional model to account for the existence and shape of invariant zones in the cortex of Paramecium. The hypothesis was made that a Ca2+ wave stopped at the boundary of the invariant zones, thus determining their shapes. The distribution of Ca2+ conductances was assumed to be known and was approximately the same as that determined experimentally. In this paper we have attempted to model the distribution of these conductances so as to reduce the arbitrariness of the model. The proposed model therefore now has three main levels. The first level simulates the distribution of Ca2+ conductances; the second represents the Ca2+/calmodulin interaction; and the third level simulates the phosphorylated and dephosphorylated forms of a kinase. The only factor generating asymmetry is the difference in the values of some constants on opposite sides of the ventral suture. It has thus been demonstrated theoretically that the basic asymmetries of the Paramecium cell can be thought of as the consequences of a morphological asymmetry. The validity of the model was tested by simulation of the temporal development of homopolar doublets of Paramecium, which agreed well with experimental results.