CIRCULARITY AND OTHER INVARIANTS OF GENE ASSEMBLY IN CILIATES
Ion Petre2001, Festschrift in Honor of Gabriel Thierrin
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Abstract
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.
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The way that ciliates transform genes from their micronuclear to the macronuclear form is very interesting (and unique), also from a computational point of view. In this paper, we describe the model of gene assembly in ciliates presented in (2), (3), and (4). Moreover, we prove that the set of three operations underlying this model is universal, in the sense
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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.
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Mathematical Structures in Computer Science, 2002
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The process of gene assembly in ciliates is a fascinating example of programmed DNA manipulations in living cells. Macronuclear genes are split into coding blocks (called MDSs), shuffled and separated by non-coding sequences to form micronuclear genes. Assembling the coding blocks from micronuclear genes to form functional macronuclear genes is facilitated by an impressive in-vivo implementation of the linked list data structure of computer science. Complexity measures for genes may be defined in many ways, including the number of MDSs, the number of loci, etc. We take a different approach in this paper and propose four complexity measures for genes in ciliates, based on the 'effort' required to assemble the gene. We consider: (a) the types of operations used in the assembly, (b) the number of operations used in the assembly, (c) the length of the molecular folds involved, and (d) the length of the shortest possible parallel assembly for that gene.
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We define three operations on strings and languages suggested by the process of gene assembly in hypotrichous ciliates. This process is considered to be a prime example of DNA computing in vivo. This paper is devoted to some computational aspects of these operations from a formal language point of view. The closure of the classes of regular and context-free languages under these operations is settled. Then, we consider the ld-macronuclear language of a given language L, which consists of all ldmacronuclear strings obtained from the strings of L by iteratively applying the loop-direct repeat-excision. Finally, we discuss some open problems and further directions of research.
Gene assembly in ciliates: formal frameworks
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This is the second part of a review of the research on formal modelling of gene assembly in ciliates. In the first part, we provided the basic biological background and introduced molecular operations in the process of gene assembly. In this part, we shall represent these operations within three formal frameworks: MDS descriptors, legal strings, and overlap graphs, corresponding to different abstraction levels which however turn out to be equivalent as far as the operational ability of gene assembly is concerned.
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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.
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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.
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