We consider in this paper the assembly of micronuclear genes in stichotrichous ciliates to their macronuclear form. We represent the micronuclear genes and all their intermediate forms from micro-to macro-as signed permutations, where integer i stands for the i-th MDS of the macronuclear gene and ī stands for the inverted form of that MDS; the macronuclear assembled gene is represented as the sorted permutation 1 2... n, while its micronuclear form is an arbitrary signed permutation. We focus on the elementary gene assembly model consisting of two operations on signed permutations: eh elementary hairpin inverting and ed elementary double recombination; gene assembly is modeled in this framework as a permutation sorting process. The general problem we investigate is to give a characterization of all signed permutations that can be sorted by the elementary operations. We make progress towards a full solution for this problem by relating sequences of eh and ed operations applicable to a given permutation to paths in the dependency graph associated to that permutation.
Read full abstract