Sorting Cancer Karyotypes by Elementary Operations

  • Michal Ozery-Flato
  • Ron Shamir
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5267)


Since the discovery of the “Philadelphia chromosome” in chronic myelogenous leukemia in 1960, there is an ongoing intensive research of chromosomal aberrations in cancer. These aberrations, which result in abnormally structured genomes, became a hallmark of cancer. Many studies give evidence to the connection between chromosomal alterations and aberrant genes involved in the carcinogenesis process. An important problem in the analysis of cancer genomes, is inferring the history of events leading to the observed aberrations. Cancer genomes are usually described in form of karyotypes, which present the global changes in the genomes’ structure. In this study, we propose a mathematical framework for analyzing chromosomal aberrations in cancer karyotypes. We introduce the problem of sorting karyotypes by elementary operations, which seeks for a shortest sequence of elementary chromosomal events transforming a normal karyotype into a given (abnormal) cancerous karyotype. Under certain assumptions, we prove a lower bound for the elementary distance, and present a polynomial-time 3-approximation algorithm. We applied our algorithm to karyotypes from the Mitelman database, which records cancer karyotypes reported in the scientific literature. Approximately 94% of the karyotypes in the database, totalling 57,252 karyotypes, supported our assumptions, and each of them was subjected to our algorithm. Remarkably, even though the algorithm is only guaranteed to generate a 3-approximation, it produced a sequence whose length matches the lower bound (and hence optimal) in 99.9% of the tested karyotypes.


Chromosomal Aberration Cancer Genome Normal Karyotype Elementary Operation Rearrangement Event 
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  1. 1.
    NCI and NCBI’s SKY/M-FISH and CGH Database (2001),
  2. 2.
    Albertson, D.G., Collins, C., McCormick, F., Gray, J.W.: Chromosome aberrations in solid tumors. Nature Genetics 34, 369–376 (2003)CrossRefGoogle Scholar
  3. 3.
    Bourque, G., Zhang, L.: Models and methods in comparative genomics. Advances in Computers 68, 60–105 (2006)Google Scholar
  4. 4.
    Ferguson, D.O., Frederick, W.A.: DNA double strand break repair and chromosomal translocation: Lessons from animal models. Oncogene 20(40), 5572–5579 (2001)CrossRefGoogle Scholar
  5. 5.
    Hiller, B., Bradtke, J., Balz, H., Rieder, H.: CyDAS: a cytogenetic data analysis system. BioInformatics 21(7), 1282–1283 (2005), CrossRefGoogle Scholar
  6. 6.
    Höglund, M., Frigyesi, A., Säll, T., Gisselsson, D., Mitelman, F.: Statistical behavior of complex cancer karyotypes. Genes, Chromosomes and Cancer 42(4), 327–341 (2005)CrossRefGoogle Scholar
  7. 7.
    Korte, B., Vygen, J.: Combinatorial optimization: theory and algorithms. Springer, Berlin (2002)zbMATHGoogle Scholar
  8. 8.
    Mitelman, F. (ed.): ISCN: An International System for Human Cytogenetic Nomenclature. S. Karger, Basel (1995)Google Scholar
  9. 9.
    Mitelman, F., Johansson, B., Mertens, F. (eds.): Mitelman Database of Chromosome Aberrations in Cancer (2008),
  10. 10.
    Ozery-Flato, M., Shamir, R.: On the frequency of genome rearrangement events in cancer karyotypes. In: The first annual RECOMB satellite workshop on computational cancer biology (2007)Google Scholar
  11. 11.
    Radcliffe, A.J., Scott, A.D., Wilmer, E.L.: Reversals and transpositions over finite alphabets. SIAM J. Discret. Math. 19(1), 224–244 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Raphael, B.J., Volik, S., Collins, C., Pevzner, P.: Reconstructing tumor genome architectures. Bioinformatics 27, 162–171 (2003)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Michal Ozery-Flato
    • 1
  • Ron Shamir
    • 1
  1. 1.School of Computer ScienceTel-Aviv UniversityTel AvivIsrael

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