Extending the Overlap Graph for Gene Assembly in Ciliates

Gene assembly is an intricate biological process that has been studied formally and modeled through string and graph rewriting systems. Recently, a restriction of the general (intramolecular) model, called simple gene assembly, has been introduced. This restriction has subsequently been defined as a string rewriting system. We show that by extending the notion of overlap graph it is possible to define a graph rewriting system for two of the three types of rules that make up simple gene assembly. It turns out that this graph rewriting system is less involved than its corresponding string rewriting system. Finally, we give characterizations of the ‘power’ of both types of graph rewriting rules. Because of the equivalence of these string and graph rewriting systems, the given characterizations can be carried over to the string rewriting system.