We investigate map D0L-systems which are models of developmental systems within the framework of formal language theory. The main result proves that D0L-systems are appropriate models not only for generating the division process of cells but also for governing their differentiation. For this purpose, we assign a “colour” to each cell type, and then generate colouring patterns for the clones obtained after any number of division steps. Our method provides an arbitrarily selected periodic colour arrangement in every step, hence it satisfies the requirement of size-independence that is essential when applications in biology are considered.
A particular case of the general model is then applied to retinal cell differentiation. With as few as nine cell labels (cellular states) and just one edge label we generate a pattern of cell types that agrees with the one in vertebrate retinal receptors, as observed experimentally by Morris [J. Comp. Neurol. 140 (1970) 359-387], within a few per cent of accuracy.
We also provide an infinite family of D0L-systems supporting Cheung’s conjecture, and raise some related open problems.