Simple Gene Assembly Is Deterministic

Issue title: SPECIAL ISSUE ON TRAJECTORIES OF LANGUAGE THEORY Dedicated to the memory of Alexandru Mateescu

Article type: Research Article

Authors: Langille, Miika | Petre, Ion

Affiliations: Turku Centre for Computer Science Department of Computer Science, Åbo Akademi University Turku 20520 Finland. E-mails: miika.langille@abo.fi; ion.petre@abo.fi

Abstract: We investigate in this paper a simple intramolecular model for gene assembly in ciliates. Unlike the general intramolecular model, the folds that a micronuclear chromosome may form to assemble the genes is very restricted (minimal) here: between any two pointers there may be at most one coding block. It has been known that the general model is universal, being able to assemble any gene pattern (to sort any signed permutation). The simple model on the other hand is not universal: there exist signed permutations that cannot be sorted in this model. Remarkably though, all known micronuclear gene patterns in ciliates can indeed be assembled in the simple model. We prove in this paper that while the general model is non-deterministic, the simple model is "weakly deterministic": any gene pattern either has only successful or only unsuccessful sorting strategies. Moreover, although different strategies may lead to different permutations for the same input, these final results have the same structure.

Keywords: Gene assembly, signed permutations, simple operations, determinism

Journal: Fundamenta Informaticae, vol. 73, no. 1-2, pp. 179-190, 2006