Affiliations: Computational Biomodeling Laboratory, Turku Centre for Computer Science, Åbo Akademi University, Turku, Finland. sepinoud.azimi@abo.fi | Department of Mathematics, University of Turku, Turku, Finland. tero.harju@utu.fi | Computational Biomodeling Laboratory, Turku Centre for Computer Science, Åbo Akademi University, Turku, Finland. miika.langille@gmail.com | Computational Biomodeling Laboratory, Turku Centre for Computer Science, Åbo Akademi University, Turku, Finland. ion.petre@abo.fi | Computational Systems Biology Laboratory, University of Helsinki, Helsinki, Finland. vladimir.rogojin@helsinki.fi
Note: [] Address for correspondence: Computational Biomodeling Laboratory, Turku Centre for Computer Science, Åbo Akademi University, Turku 20520, Finland
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.
Keywords: Directed overlap-inclusion graphs, gene assembly in Ciliates, simple operations
