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Directed Overlap-inclusion Graphs as Representations of Ciliate Genes

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Azimi S. , Harju T. , Langille M. , Petre I. , Rogojin V.

Fundamenta Informaticae

2011

tom Vol. 110, nr 1-4

29-44

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.

Computational Efficiency of Intermolecular Gene Assembly

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Ishdorj T.-O. , Loos R. , Petre I.

Fundamenta Informaticae

2008

tom Vol. 84, nr 3-4

363-373

We investigate here the computational efficiency of gene rearrangement found in ciliates (unicellular organisms). We show how the so-called guided recombination systems, which model this gene rearrangement, can be used as problem solvers. Specifically, these systems can uniformly solve SAT with time complexity O(nźm) for a Boolean formula of m clauses over n variables.