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Bioinformatics Advance Access first published online on June 9, 2005
This version published online on June 13, 2005
Bioinformatics, doi:10.1093/bioinformatics/bti535
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© The Author (2005). Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oupjournals.org
Received May 3, 2005
Revised June 2, 2005
Accepted June 8, 2005

Article

Efficient sorting of genomic permutations by translocation, inversion & block interchange

Sophia Yancopoulos 1, Oliver Attie 2, and Richard Friedberg 3

1 Institute for Medical Research, North Shore-LIJ Health System, Manhasset, NY 11030 USA
2 Center for the Study of Gene Structure & Function, Hunter College, NY, NY, 10021 USA
3 Department of Physics, Columbia University, NY, NY 10025 USA


  Abstract

Motivation: Finding genomic distance based on gene order is a classic problem in genome rearrangements. Efficient exact algorithms for genomic distances based on inversions and/or translocations have been found but are complicated by special cases, rare in simulations and empirical data. We seek a universal operation underlying a more inclusive set of evolutionary operations and yielding a tractable genomic distance with simple mathematical form.

Results: We study a universal double-cut-and-join operation that accounts for inversions, translocations, fissions and fusions, but also produces circular intermediates which can be reabsorbed. The genomic distance, computable in linear time, is given by #(breakpoints)-#(cycles) in the comparison graph of the two genomes; #(hurdles) does not enter. Without changing this formula, we can replace generation and re-absorption of a circular intermediate by a generalized transposition, equivalent to a block interchange, with weight two. Our simple algorithm converts one multi-linear chromosome genome to another in the minimum distance.


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