A topological model of cell division: structure of the computer program.

The general structure of a computer program (CD3D) simulating division in a sheet of cells is presented. The program is based on a topological representation of cell division previously developed by the authors, and the biological background to the model is discussed. The computer modelling of the various elements of the model (i.e. vertices, edges and meshes) is described, and an annotated description of the subroutines making up the program is given in an Appendix. Although the program and model are specifically designed to represent cell division processes, the graph framework may have applicability in other biological subject areas where dynamic relationships between elements are involved.

Computer modelling of cell division during development using a topological approach.

Development in multicellular animals consists of a constant progression of cell division, differentiation and morphogenesis. Our understanding of the relationship between division and the acquisition of shape and form is not well understood, and this paper describes a computer representation of cell division processes with possible applications to the modelling of developmental events. This representation is not itself a model in the true sense, but is a scaffolding onto which a set of model assumptions and parameters can be built. We discuss one such set of assumptions, used to model cell sorting, describe the extension of the framework to represent sheets of cells in three dimensions, and make some observations on the incorporation of mechanical forces into the representation.

Computer simulation of compartment maintenance in the Drosophila wing imaginal disc.

A new method for modelling cell division is reported which uses a cellular representation based on graph theory. This allows us to model the adjacencies of non-regular dividing cells accurately, avoiding the rigid geometrical constraints present in earlier simulations. We use this system to simulate compartment boundary maintenance in the Drosophila wing imaginal disc. We show that a boundary of minimum length between two growing polyclones of cells could depend on sorting between cells in the different polyclones. We also investigate the response of the model to differential cell division rates within polyclones. This is the first demonstration that cell sorting can generate a smooth boundary in a dividing cell mass. We suggest that biological analogs of our computer sorting rules are responsible for the similar straight polyclone borders seen in the real wing disc. A possible strategy for showing the existence of these analogs is also given.