Abstract
The formula N−(C+I/2) to compute the number of Double-Cut-and-Join operations needed to transform one genome into another is both simple and easy to prove. When it was published, in 2006, we omitted all details on how it was constructed. In this chapter, we will give an elementary treatment on the intuitions and methods underlying the formula, showing that simplicity is sometimes difficult to achieve. We will also prove that this formula is one among an infinite number of candidates, and that the techniques can be applied to other genomic distances.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
Since Single-Cut-and-Join operations are sometimes less intuitive, here is a scenario that sorts genome (a b c) to genome (a c b) in four steps. Cuts are indicated by vertical bars: (a b c |)⟶(∘ a | b c ∘)⟶(∘ a ∘) (b | c)⟶(∘ a c b ∘)⟶(a c b).
References
Bergeron, A., Medvedev, P., Stoye, J.: Rearrangement models and single-cut operations. J. Comput. Biol. 17(9), 1213–1225 (2010)
Bergeron, A., Mixtacki, J., Stoye, J.: A unifying view of genome rearrangements. In: Proceedings of WABI 2006. LNBI, vol. 4175, pp. 163–173 (2006)
Dobzhansky, T., Sturtevant, A.H.: Inversions in the chromosomes of drosophila pseudoobscura. Genetics 23(1), 28–64 (1938)
Feijão, P., Meidanis, J.: SCJ: a breakpoint-like distance that simplifies several rearrangement problems. IEEE/ACM Trans. Comput. Biol. Bioinform. 8(5), 1318–1329 (2011)
Feijão, P., Meidanis, J.: Extending the algebraic formalism for genome rearrangements to include linear chromosomes. In: Proceedings of BSB 2012. LNBI, vol. 7409, pp. 13–24 (2012)
Hannenhalli, S., Pevzner, P.A.: Transforming men into mice (polynomial algorithm for genomic distance problem). In: Proceedings of FOCS 1995, pp. 581–592 (1995)
Meidanis, J., Dias, Z.: An alternative algebraic formalism for genome rearrangements. In: Comparative Genomics: Empirical and Analytical Approaches to Gene Order Dynamics, Map Alignment and the Evolution of Gene Families, pp. 213–223. Kluwer Academic, Dordrecht (2000)
Tannier, E., Zheng, C., Sankoff, D.: Multichromosomal median and halving problems under different genomic distances. BMC Bioinform. 10, 120 (2009)
Wikipedia: http://en.wikipedia.org/wiki/DNA_repair
Yancopoulos, S., Attie, O., Friedberg, R.: Efficient sorting of genomic permutations by translocation, inversion and block interchange. Bioinformatics 21(16), 3340–3346 (2005)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag London
About this chapter
Cite this chapter
Bergeron, A., Stoye, J. (2013). The Genesis of the DCJ Formula. In: Chauve, C., El-Mabrouk, N., Tannier, E. (eds) Models and Algorithms for Genome Evolution. Computational Biology, vol 19. Springer, London. https://doi.org/10.1007/978-1-4471-5298-9_5
Download citation
DOI: https://doi.org/10.1007/978-1-4471-5298-9_5
Publisher Name: Springer, London
Print ISBN: 978-1-4471-5297-2
Online ISBN: 978-1-4471-5298-9
eBook Packages: Computer ScienceComputer Science (R0)