A computational model for cell differentiation

In this paper, we present a word set generating mechanism, called cell-differentiation system, inspired by the tissue process formation in multicellular organisms, which might model some properties of evolving communities of living cells at the syntactical level. The tools utilized to model these biological phenomena belong to the formal language theory. In this context chromosomal mutations are defined as operations on strings and the differentiation according to the control of gene expression is represented by some random-context conditions in formal languages. In the presented formal framework we prove that in a simplified form of this formalism, with only one cell-type which is regular, one single cell and no mitosis involved, the problem of establishing whether or not the set of vectors of integers indicating the number of cells in each population, is finite, linear or semilinear, is recursively undecidable. However, one can algorithmically decide whether or not a cell-differentiation system of finite cell-type can produce a specific generation of cells.