Skip to main content
SpringerLink
Log in

Mathematical Programming Formulations for Problems in Genomics and Proteomics

  • Chapter
Data Mining in Biomedicine

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 7))

  • 1366 Accesses

Abstract

Computational biology problems generally involve the determination of discrete structures over biological configurations determined by genomic or proteomic data. Such problems present great opportunities for application of mathematical programming techniques. We give an overview of formulations employed for the solution of problems in genomics and proteomics. In particular, we discuss mathematical programming formulations for string comparison and selection problems, with high applicability in biological data processing.

Supported in part by the Brazilian Federal Agency for Post-Graduate Education (CAPES) - Grant No. 1797-99-9.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. V. Bafna and P.A. Pevzner. Genome rearrangements and sorting by reversals. SIAM Journal on Computing, 25(2):272–289, 1996.

    Article  Google Scholar 

  2. J. Borneman, M. Chroback, G. D. Vedova, A. Figueroa, and T. Jiang. Probe selection algorithms with applications in the analysis of microbial communities. Bioinformatics, 17:S39–S48, 2001.

    PubMed  Google Scholar 

  3. A. Caprara. Sorting by reversals is difficult. In Proceedings of the First Annual International Conference on Computational Colecular Biology, pages 75–83. ACM Press, 1997.

    Google Scholar 

  4. A. Caprara. On the tightness of the alternating-cycle lower bound for sorting by reversals. Journal of Combinatorial Optimization, 3:149–182, 1999.

    Article  Google Scholar 

  5. A. Caprara and G. Lancia. Structural alignment of large-size proteins via lagrangian relaxation. In Proceedings of the Sixth Annual International Conference on Computational Biology, pages 100–108. ACM Press, 2002.

    Google Scholar 

  6. A. Caprara, G. Lancia, and S. K. Ng. A column-generation based branch-and-bound algorithm for sorting by reversals. In M. Farach, S. Roberts, M. Vingron, and M. Waterman, editors, Mathematical Support for Molecular Biology, volume 47 of DIMACS series in Discrete Mathematics and Theoretical Computer Science, pages 213–226. The American Mathematical Society, 1999.

    Google Scholar 

  7. M.A. Dayhoff, R.M. Schwartz, and B.C. Orcutt. A model of evolutionary change in proteins. In Atlas of Protein Sequence and Structure, chapter 5, pages 345–352. National Biomedical Research Foundation, Washington, DC, 1978.

    Google Scholar 

  8. R.F. Doolittle, M.W. Hunkapiller, L.E. Hood, S.G. Devare, K.C. Robbins, S.A. Aaronson, and H.N. Antoniades. Simian sarcoma virus onc gene, v-sis, is derived from the gene (or genes) encoding a platelet-derived growth factor. Science, 221:275–277, 1983.

    Article  PubMed  CAS  Google Scholar 

  9. N. Franklin. Conservation of genome form but not sequence in the transcription antitermination determinants of bacteriophages λ, φ21 and P22. Journal of Molecular Evolution, 181:75–84, 1985.

    CAS  Google Scholar 

  10. H.J. Greenberg, W.E. Hart, and G. Lancia. Opportunities for combinatorial optimization in computational biology. INFORMS Journal on Computing, 16(3):211–231, 2004.

    Article  Google Scholar 

  11. M. Held and R.M. Karp. The traveling salesman problem and minimum spanning trees: Part II. Mathematical Programming, 1:6–25, 1971.

    Article  Google Scholar 

  12. S. Henikoff and J.G. Henikoff. Amino acid substitution matrices from protein blocks. In Proceedings of the National Academy of Sciences, volume 89, pages 10915–10919, 1992.

    Article  CAS  Google Scholar 

  13. X. Huang and W. Miller. A time efficient, linear space local similarity algorithm. Advances in Applied Mathematics, 12:337–357, 1991.

    Article  Google Scholar 

  14. J. Kececioglu and D. Sankoff. Exact and approximation algorithms for sorting by reversals, with application to genome rearrangement. Algorithmica, 13:180–210, 1995.

    Article  Google Scholar 

  15. G._W. Klau, S. Rahmann, A. Schliep, M. Vingron, and K. Reinert. Optimal robust non-unique probe selection using integer linear programming. Bioinformatics, 20:il86–il93, 2004.

    Article  Google Scholar 

  16. G. Lancia, R. Carr, B. Walenz, and S. Istrail. Optimal PDB structure alignments: a branch-and-cut algorithm for the maximum contact map overlap problem. In Proceedings of the 5th RECOMB, pages 193–201, 2001.

    Google Scholar 

  17. K. Lanctot, M. Li, B. Ma, S. Wang, and L. Zhang. Distinguishing string selection problems. Information and Computation, 185(1):41–55, 2003.

    Article  Google Scholar 

  18. C. Lemmen and T. Lengauer. Computational methods for the structural alignment of molecules. Journal of Computer-Aided Molecular Design, 14:215–232, 2000.

    Article  PubMed  CAS  Google Scholar 

  19. V.I. Levenshtein. Binary codes capable of correcting deletions, insertions and reversals. Soviet Physics Doklady, 6:707–710, 1966.

    Google Scholar 

  20. C.N. Meneses, Z. Lu, C.A.S. Oliveira, and P.M. Pardalos. Optimal solutions for the closest string problem via integer programming. INFORMS Journal on Computing, 16(4):419–429, 2004.

    Article  Google Scholar 

  21. C.N. Meneses, C.A.S. Oliveira, and P.M. Pardalos. Optimization techniques for string selection and comparison problems in genomics. IEEE Engineering in Biology and Medicine Magazine, 24(3):81–87, 2005.

    Article  Google Scholar 

  22. G.L. Nemhauser and L.A. Wolsey. Integer and Combinatorial Optimization. Wiley Interscience Series in Discrete Mathematics and Optimization. Wiley and Sons, 1988.

    Google Scholar 

  23. P.M. Pardalos. Applications of global optimization in molecular biology. In C. Carlsson and I. Eriksson, editors, Global & Multiple Criteria Optimization and Information Systems Quality, pages 91–102. Abo Akademis Tryckeri, Finland, 1998.

    Google Scholar 

  24. A.D. Sharrocks. The design of primers for PCR. In H.G. Griffin and A.M Griffin, editors, PCR Technology, Current Innovations, pages 5–11. CRC Press, London, 1994.

    Google Scholar 

  25. M. Vendruscolo, E. Kussell, and E. Domany. Recovery of protein structure from contact maps. Folding and Design, 2:295–306, 1997.

    Article  PubMed  CAS  Google Scholar 

  26. J. Xu, M. Li, D. Kim, and Y. Xu. RAPTOR: Optimal protein threading by linear programming. Journal of Bioinformatics and Computational Biology, 1(1):95–117, 2003.

    Article  PubMed  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Industrial and Systems Engineering, University of Florida, 303 Weil Hall, Gainesville, FL, 32611, USA

    Cláudio N. Meneses & Panos M. Pardalos

  2. School of Industrial Engineering and Management, Oklahoma State University, Stillwater, OK, USA

    Carlos A. S. Oliveira

Authors
  1. Cláudio N. Meneses
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Carlos A. S. Oliveira
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Panos M. Pardalos
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. University of Florida, Gainesville, FL

    Panos M. Pardalos

  2. Florida State University, Tallahassee, FL

    Vladimir L. Boginski

  3. Dash Optimization, Englewood Cliffs, NJ

    Alkis Vazacopoulos

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Meneses, C.N., Oliveira, C.A.S., Pardalos, P.M. (2007). Mathematical Programming Formulations for Problems in Genomics and Proteomics. In: Pardalos, P.M., Boginski, V.L., Vazacopoulos, A. (eds) Data Mining in Biomedicine. Springer Optimization and Its Applications, vol 7. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-69319-4_16

Download citation

Publish with us

Policies and ethics

Search

Navigation