Advertisement

Protein Folding in the HP Model on Grid Lattices with Diagonals

  • Hans-Joachim Böckenhauer
  • Dirk Bongartz
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3153)

Abstract

The protein folding problem, i.e., the computational prediction of the three-dimensional structure of a protein from its amino acid sequence, is one of the most important and challenging problems in computational biology. Since a complete simulation of the folding process of a protein is far too complex to handle, one tries to find an approximate solution by using a simplified, abstract model. One of the most popular models is the so-called HP model, where the hydrophobic interactions between the amino acids are considered to be the main force in the folding process, and furthermore the folding space is modelled by a two- or three-dimensional grid lattice.

In this paper, we will present some approximation algorithms for the protein folding problem in the HP model on an extended grid lattice with plane diagonals. The choice of this kind of lattice removes one of the major drawbacks of the original HP model, namely the bipartiteness of the grid which severely restricts the set of possible foldings. Our algorithms achieve an approximation ratio of \(\frac{26}{15}\approx 1.733\) for the two-dimensional and of \(\frac{8}{5}=1.6\) for the three-dimensional lattice. This improves significantly over the best previously known approximation ratios for the protein folding problem in the HP model on any lattice.

Keywords

Approximation Algorithm Approximation Ratio Hydrophobic Amino Acid Input String Contact Edge 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Agarwala, R., Batzoglou, S., Dančík, V., Decatur, S.E., Hannenhalli, S., Farach, M., Muthukrishnan, S., Skiena, S.: Local rules for protein folding on a triangular lattice and generalized hydrophobicity in the HP model. Journal of Computational Biology 4(2), 275–296 (1997)CrossRefGoogle Scholar
  2. 2.
    Anfinsen, C.B.: Principles that govern the folding of protein chains. Science 181(4096), 223–230 (1973)CrossRefGoogle Scholar
  3. 3.
    Anfinsen, C.B., Haber, E., Sela, M., White, F.H.: The kinetics of formation of native ribonuclease during oxidation of the reduced polypeptide chain. Proceedings of the National Academy of Sciences, USA 47, 1309–1314 (1961)CrossRefGoogle Scholar
  4. 4.
    Atkins, J., Hart, W.E.: On the intractability of protein folding with a finite alphabet of amino acids. Algorithmica 25, 279–294 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Berger, B., Leighton, F.T.: Protein folding in the hydrophobic-hydrophilic (HP) model is NP-complete. In: Proc. of the 2nd Annual Internat. Conference on Research in Computational Molecular Biology (RECOMB 1998), pp. 30–39 (1998)Google Scholar
  6. 6.
    Chan, H.S., Dill, K.A.: The protein folding problem. Physics today, 24–32 (1993)Google Scholar
  7. 7.
    Chandra, V., DattaSharma, A., Kumar, V.S.A.: The algorithmics of folding proteins on lattices. Discrete Applied Mathematics 127, 145–161 (2003)CrossRefMathSciNetGoogle Scholar
  8. 8.
    Crescenzi, P., Goldman, D., Papadimitriou, C., Piccolboni, A., Yannakakis, M.: On the complexity of protein folding. Journal of Computational Biology 5(3), 423–466 (1998)CrossRefGoogle Scholar
  9. 9.
    Dill, K.A.: Theory for the folding and stability of globular proteins. Biochemistry 24, 1501 (1985)CrossRefGoogle Scholar
  10. 10.
    Dill, K.A., Bromberg, S., Yue, K., Fiebig, K., Yee, D., Thomas, P., Chan, H.: Principles of protein folding – a perspective from simple exact models. Protein Science 4, 561–602 (1995)CrossRefGoogle Scholar
  11. 11.
    Greenberg, H.J., Hart, W.E., Lancia, G.: Opportunities for combinatorial optimization in computational biology. INFORMS Journal of Computing (to appear)Google Scholar
  12. 12.
    Hart, W.E., Istrail, S.: Fast protein folding in the hydrophobic-hydrophilic model within three-eights of optimal. Journal of Computational Biology 3(1), 53–96 (1996)CrossRefGoogle Scholar
  13. 13.
    Hart, W.E., Istrail, S.: Robust proofs of NP-hardness for protein folding: General lattices and energy potentials. Journal of Computational Biology 4(1), 1–22 (1997)CrossRefGoogle Scholar
  14. 14.
    Hart, W.E., Istrail, S.: Lattice and off-lattice side chain models of protein folding: linear time structure prediction better than 86% of optimal. Journal of Computational Biology 4(3), 241–259 (1997)CrossRefGoogle Scholar
  15. 15.
    Heun, V.: Approximate protein folding in the HP side chain model on extended cubic lattices. Discrete Applied Mathematics 127(1), pp. 163-177 (2003) Extended abstract In: Nešetřil, J. (ed.) ESA 1999. LNCS, vol. 1643, pp. 212–223. Springer, Heidelberg (1999)Google Scholar
  16. 16.
    Mauri, G., Piccolboni, A., Pavesi, G.: Approximation algorithms for protein folding prediction. In: Proc. of the 10th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 1999), pp. 945–946 (1999)Google Scholar
  17. 17.
    Nayak, A., Sinclair, A., Zwick, U.: Spatial Codes and the hardness of string folding problems. Journal of Computational Biology 6(1), 13–36 (1999)CrossRefGoogle Scholar
  18. 18.
    Newman, A.: A new algorithm for protein folding in the HP model. In: Proc. of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2002), pp. 876–884 (2002)Google Scholar
  19. 19.
    Ngo, J.T., Marks, J., Karplus, M.: Computational complexity, protein structure prediction, and the Levinthal paradox. In: Merz Jr., K., LeGrand, S. (eds.) The Protein Folding Problem and Tertiary Structure Prediction, pp. 433–506. Birkhäuser, Boston (1994)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Hans-Joachim Böckenhauer
    • 1
  • Dirk Bongartz
    • 1
  1. 1.Lehrstuhl für Informatik IRWTH AachenAachenGermany

Personalised recommendations