Combining overlap and containment for gene assembly in ciliates

Gene assembly in ciliates 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 to also represent containment, it is possible to define an equivalent 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 often less involved to study than its corresponding string rewriting system. We illustrate this by giving characterizations of the ‘power’ of both types of graph rewriting rules. Also, a first step is made towards a characterization of the “extended overlap graphs”.