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Background  Analysis of genomes evolving via block-interchange events leads to a combinatorial problem of sorting by block-interchanges, which has been studied recently to evaluate the evolutionary relationship in distance between two biological species since block-interchange can be considered as a generalization of transposition. However, for genomes consisting of multiple chromosomes, their evolutionary history should also include events of chromosome fusions and fissions, where fusion merges two chromosomes into one and fission splits a chromosome into two.    Results  In this paper, we study the problem of genome rearrangement between two genomes of circular and multiple chromosomes by considering fusion, fission and block-interchange events altogether. By use of permutation groups in algebra, we propose anO    MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBamrtHrhAL1wy0L2yHvtyaeHbnfgDOvwBHrxAJfwnaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaWaaeGaeaaakeaaimaacqWFoe=taaa@383D@    ( n  2 ) time algorithm to efficiently compute and obtain a minimum series of fusions, fissions and block-interchanges required to transform one circular multi-chromosomal genome into another, where  n  is the number of genes shared by the two studied genomes. In addition, we have implemented this algorithm as a web server, called FFBI, and have also applied it to analyzing by gene orders the whole genomes of three human  Vibrio  pathogens, each with multiple and circular chromosomes, to infer their evolutionary relationships. Consequently, our experimental results coincide well with our previous results obtained using the chromosome-by-chromosome comparisons by landmark orders between any two  Vibrio  chromosomal sequences as well as using the traditional comparative analysis of 16S rRNA sequences.    Conclusion  FFBI is a useful tool for the bioinformatics analysis of circular and multiple genome rearrangement by fusions, fissions and block-interchanges.

Analysis of circular genome rearrangement by fusions, fissions and block-interchanges