A discrete probability model of information support during early embryonic development

Abstract

A percolation model of the diffuse redistribution of morphogenetic information in early regulative development is analyzed. It is demonstrated that the statistical average values of cell connectedness remaining below the percolation threshold of the spatial redistribution of developmental determinants do not provide for the formation of cell structures of the necessary size. The average number of cell interactions should exceed the percolation threshold, and, therefore, the carriers of morphogenetic information in early development can move over distances comparable with the size of the entire embryo. The assumption concerning the percolation mechanism of cell death is used as a basis for estimating the statistical average value of cell connectedness at which the predicted number of cells theoretically isolated from the flow of signal molecules corresponds to the observed frequencies of dying embryonic cells. The estimated average number of cell interactions significantly exceeds the threshold of information resource percolation in the embryonic space and agrees with estimations of other authors, based on direct observations. The probable role of the diffusion front, or percolation cluster shell, in the regionalization of embryonic structures differing in their prospective values is discussed. It is shown that the duration of the communicative period, along with the statistical average number of channels providing for the intercellular transfer of signal molecules by diffusion, is a parameter controlling the processes of determination of embryonic structures.