Genome Halving with Double Cut and Join

Genome Halving with Double Cut and Join

10 Pages · 2007 · 174 KB · English

Introduction. In this paper we discuss a generalization of the genome halving process studied by El-Mabrouk.3 Before stating and solving the problem formally in the ensuing sections, we first give some motivation for the generalization. Models of genome rearrangement processes have permitted 

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October 3, 2007 17:37 Proceedings Trim Size: 975in x 65in apbc057a GENOME HALVING WITH DOUBLE CUT AND JOIN ROBERT WARREN AND DAVID SANKOFF University of Ottawa The genome halving problem, previously solved by ElMabrouk for inversions and re ciprocal translocations, is here solved in a more general context allowing transpositions and block interchange as well, for genomes including multiple linear and circular chro mosomes We apply this to several data sets and compare the results to the previous algorithm 1 Introduction In this paper we discuss a generalization of the genome halving process studied by ElMabrouk 3 Before stating and solving the problem formally in the ensuing sections, we rst give some motivation for the generalization Models of genome rearrangement processes have permitted di erent repertoires of operations Certainly, realistic models must account for inversion Likewise, reciprocal translocations, Robertsonian translocations and other processes of chro mosome fusion and ssion, all of which involve transferring an entire telometric (ie, sux or pre x) region of at least one chromosome, are widespread across all eukaryotic domains Other movements of chromosomal fragments, usually not involving telomeres, are widely attested, and grouped together under the label of transpositions They are produced by a variety of processes, such as gene duplication followed by the loss of the original copy, or retrotransposition, or recombination errors Of the three true movement rearrangements, a inversion, translocation and trans position, only the rst two, separately or in combination, have proved very amenable to mathematical modeling, as exempli ed by the HannenhalliPevzner formula for the edit distance between two genomes, ie, the minimum number of operations required to transform one genome into another, and the ecient algorithm for pro ducing such a series of operations No formula or ecient algorithm exists for transposition, either by itself or in combination with the other two operations Recently, Yancopoulos et al6 introduced the \double cut and join" (DCJ) op eration as the basis for generating all the movement rearrangements This allowed for the inclusion of transposition with inversion and translocation in a single model a Duplications of genes or of chromosomal segments, as well as deletions and insertions are often considered as aspects of genome rearrangement, but they are not really of the same biological nature as the movements inherent in inversion, translocation and transposition, and mathematical models of rearrangement are not easily extended to encompass them 1 October 3, 2007 17:37 Proceedings Trim Size: 975in x 65in apbc057a 2 and resulted in a simpler formula for the edit distance and a simpler algorithm for recovering a corresponding series of operations A double cut and join operation simply cuts the chromosome in two places and joins the four ends of the cut in a new way The DCJ model, however, allows for the generation of a new kind of movement operation, a generalized transposition called block interchange, which is not repre sented in the biological genome rearrangement literature, though it has long been studied in the mathematical literature on rearrangement Both transposition and block interchange can be thought of as the excision of a fragment, its circularization, together counting as one DCJ operation, followed by a second set of cuts, where the circle is not necessarily cut in the same place it was originally created through a join, and then reincorporated at a new site in the chromosome Transpositions and block interchanges thus count as two DCJ operations whereas inversions and translocations each count as one The question arises, what is the biological signi cance of these chromosomal circles? On the evolutionary level, very little is known, but circular DNA structures abound in all sorts of organisms, even eukaryotes Circular chromosomes are well known in clinical studies 4 and the process of excision, circularization, linearization and reincorporation is exactly what happens in the con guration of the immune response in higher animals Because the evolutionary consequences of block inter change could have come about in other ways, there has been no reason to look for evidence of this process or even

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