No abstract

We survey in this paper the main differences among three variants of an intramolecular model for gene assembly: the general, the simple, and the elementary models. We present all of them in terms of sorting signed permutations and compare their behavior with respect to: (i) completeness, (ii) confluence (with the notion defined in three different setups), (iii) decidability, (iv) characterization of the sortable permutations in each model, (v) sequential complexity, and (vi) experimental validation.

No abstract

The simple intramolecular model for gene assembly in ciliates consists of three molecular operations based on local DNA manipulations. It was shown to predict correctly the assembly of all currently known ciliate gene patterns. Mathematical models in terms of signed permutations and signed strings proved limited in capturing some of the combinatorial details of the simple gene assembly process. A different formalization in terms of overlap-inclusion graphs, recently introduced by Brijder and Hoogeboom, proved well-suited to describe two of the three operations of the model and their combinatorial properties. We introduce in this paper an extension of the framework of Brijder and Hoogeboom in terms of directed overlap-inclusion graphs where more of the linear structure of the ciliate genes is described. We investigate a number of combinatorial properties of these graphs, including a necessary property in terms of forbidden induced subgraphs.