Cell proliferation in the attainment of constant sizes and shapes: the Entelechia model.

The Entelechia model is a generative model of morphogenesis where individual cells exhibit surface labels that express scalar difference and planar polarity along two orthogonal axes X and Y. The amount of surface label depends on the level of Martial (M) gene product within each cell. The model assumes that the confrontation of cells on both sides of compartment borders causes an increase in their level of M gene expression. The resulting disparity between the M value of border cells and that of their neighbors induces the latter to divide. After each division the daughter cells increase their own M value, and allocate to the best matching value position. The increase in M value at the borders therefore extends through the anlage in a cascade of proliferation. The Entelechia condition is reached when the border cells attain the species-specific maximal M values, and the value differences between adjacent cells become indistinguishable. Computer simulations reveal that this model accounts for a variety of observations made on imaginal discs, e.g., 1) each disc attains a constant size in terms of number of cells, independently of the growing conditions; 2) clonal restrictions separate populations of cells which proliferate by intercalar growth; 3) dissociated cells are capable of reconstructing original patterns upon reaggregation, and 4) genetic mosaics of morphogenetic mutations show local effects that may differ depending on the position of the mutant cells in the growing anlage.