Formal systems for gene assembly in ciliates

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 formalize 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.

Gene assembly in stichotrichous ciliates happening during sexual reproduction is one of the most involved DNA manipulation processes occurring in biology. This biological process is of high interest from the computational and mathematical points of view due to its close analogy with such concepts and notions in theoretical computer science as permutation and linked list sorting and string rewriting. Studies on computational properties of gene assembly in ciliates represent a good example of interdisciplinary research contributing to both computer science and biology. We review here a number of general results related both to the development of different computational methods enhancing our understanding on the nature of gene assembly, as well as to the development of new biologically motivated computational and mathematical models and paradigms. Those paradigms contribute in particular to combinatorics, formal languages and computability theories.

Lecture Notes in Computer Science, 2004

Two models for gene assembly in ciliates have been proposed and investigated in the last few years. The DNA manipulations postulated in the two models are very different: one model is intramolecular -a single DNA molecule is involved here, folding on itself according to various patterns, while the other is intermolecular -two DNA molecules may be involved here, hybridizing with each other. Consequently, the assembly strategies predicted by the two models are completely different. Interestingly however, the final result of the assembly (including the assembled gene) is always the same. We compare in this paper the two models for gene assembly, formalizing both in terms of pointer reductions. We also discuss invariants and universality results for both models.

The intramolecular model for gene assembly in ciliates considers three operations, ld, hi, and dlad that can assemble any gene pattern through folding and recombination: the molecule is folded so that two occurrences of a pointer (short nucleotide sequence) get aligned and then the sequence is rearranged through recombination of pointers. In general, the sequence rearranged by one operation can be arbitrarily long and consist of many coding and non-coding blocks. We consider in this paper simple variants of the three operations, where only one coding block is rearranged at a time. We characterize in this paper the gene patterns that can be assembled through these variants. Our characterization is in terms of signed permutations and dependency graphs. Interestingly, we show that simple assemblies possess rather involved properties: a gene pattern may have both successful and unsuccessful assemblies and also more than one successful assembling strategy.

Vol 1: Algorithms and Complexity & Vol 2: Formal Models and Semantics, 2004

Festschrift in Honor of Gabriel Thierrin, 2001

Ciliates (an ancient group of single cell organisms) have two sorts of nuclei with different functionalities: the micronucleus and the macronucleus. After the cell mating the micronuclear genes are converted into the macronuclear genes in the process called gene assembly. This is one of the most complex examples of DNA processing known in any organisms, and it is fascinating from the computational point of view. This paper continues the investigation of gene assembly in the framework of three molecular operations: ld-excision, hi-excision/reinsertion, and dlad-excision/reinsertion. In general, for a given micronuclear gene there exists many strategies for using these three operations to accomplish gene assembly. Since it is not known yet which strategies are actually used by ciliates, it is important to study the invariants of gene assembly, i.e., those properties of gene assembly that are common to all these strategies. A macronuclear gene (before its excision and capping with telomeres) can be assembled either in a linear or in a circular molecule. We prove in this paper that the circularity property (whether or not a given gene will be assembled in a circular molecule) is an invariant. We give a simple decision algorithm for the circularity property, and discuss a number of other related invariants.

Theoretical Computer Science, 2004

We investigate families of languages deÿned by closure under operations generalized from models of gene descrambling in stichotrichous ciliates. We speciÿcally consider languages that are closed under the synchronized insertion and deletion operations as well as languages closed under the hairpin inversion (hi) operation. Biologically, this studies sets of genes that cannot be further descrambled. In addition, we show that every trio closed under hairpin inversion is also closed under the double loop with alternating direct pointers (dlad)-excision/reinsertion bio-operation.

Lecture Notes in Computer Science, 2006

The intramolecular model for gene assembly in ciliates considers three operations, ld, hi, and dlad that can assemble any gene pattern through folding and recombination: the molecule is folded so that two occurrences of a pointer (short nucleotide sequence) get aligned and then the sequence is rearranged through recombination of pointers. In general, the sequence rearranged by one operation can be arbitrarily long and consist of many coding and non-coding blocks. We consider in this paper some simpler variants of the three operations, where only one coding block is rearranged at a time. We characterize in this paper the gene patterns that can be assembled through these variants. Our characterization is in terms of signed permutations and dependency graphs. Interestingly, we show that simple assemblies possess rather involved properties: a gene pattern may have both successful and unsuccessful assemblies and also more than one successful assembling strategy.

Mathematical Structures in Computer Science, 2002

Ciliates have d e v eloped a unique nuclear dualism -two n uclei of di erent functionality: the germline micronucleus and the somatic macronucleus. The way that ciliates assemble the macronuclear genes after cell mating constitutes one of the most intricate DNA processings in living organisms. This processing is also very interesting from the computational point of view. In this paper, we i n vestigate the operations of loop excision and hairpin excision/reinsertion used in the assembly process. In particular, we consider three levels of formalization of this process, culminating in graph reduction systems.

Natural Computing Series, 2006

The intramolecular model for gene assembly in ciliates considers three operations, ld, hi, and dlad that can assemble any micronuclear gene pattern through folding and recombination: the molecule is folded so that two occurrences of a pointer (short nucleotide sequence) get aligned and then the sequence is rearranged through recombination of pointers. In general, the sequence rearranged by one operation can be arbitrarily long and may consist of many coding and non-coding blocks. We consider in this paper some restricted variants of the three operations, where only one coding block is rearranged at a time. We present in this paper the molecular model of these simple operations. We also introduce a mathematical model for the simple operations, on three levels of abstractions: MDS descriptors, signed permutations, and signed double occurrence strings. Interestingly, we show that simple assemblies possess rather involved properties: a gene pattern may have both successful and unsuccessful assemblies and also more than one successful strategy.

2011

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.

Int'l J. of Communications, Network and …, 2012

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Micronuclear genes in stichotrichous ciliates are broken into blocks separated by noncoding sequences, sometimes with the blocks in a shuffled order, some even inverted. During reproduction, all blocks are assembled in the correct order and orientation. This process is possible due to the special structure of micronuclear genes: each coding block M ends with a short nucleotide sequence (called pointer) that is repeated at the beginning of the coding block that should follow M in the assembled gene. Many of the pointers have multiple occurrences along both strands of the gene. This yields a very high number of pointer-induced possible divisions into coding and noncoding blocks.