Combinatorial Problems on Strings with Applications to Protein Folding

  • Alantha Newman
  • Matthias Ruhl
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2976)


We consider the problem of protein folding in the HP model on the 3D square lattice. This problem is combinatorially equivalent to folding a string of 0’s and 1’s so that the string forms a self-avoiding walk on the lattice and the number of adjacent pairs of 1’s is maximized. The previously best-known approximation algorithm for this problem has a guarantee of \(\frac{3}{8}=.375\) [HI95]. In this paper, we first present a new \(\frac{3}{8}\)-approximation algorithm for the 3D folding problem that improves on the absolute approximation guarantee of the previous algorithm. We then show a connection between the 3D folding problem and a basic combinatorial problem on binary strings, which may be of independent interest. Given a binary string in { a,b }*, we want to find a long subsequence of the string in which every sequence of consecutive a’s is followed by at least as many consecutive b’s. We show a non-trivial lower-bound on the existence of such subsequences. Using this result, we obtain an algorithm with a slightly improved approximation ratio of at least .37501 for the 3D folding problem. All of our algorithms run in linear time.


Lattice Point Combinatorial Problem Binary String Linear Time Algorithm Input String 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [BL98]
    Berger, B., Leighton, T.: Protein Folding in the Hydrophobic-Hydrophilic (HP) Model is NP-Complete. In: Proceedings of the 2nd Conference on Computational Molecular Biology, RECOMB (1998)Google Scholar
  2. [CGP+98]
    Crescenzi, P., Goldman, D., Papadimitriou, C., Piccolboni, A., Yannakakis, M.: On the Complexity of Protein Folding. In: Proceedings of the 2nd Conference on Computational Molecular Biology, RECOMB (1998)Google Scholar
  3. [Dil85]
    Dill, K.A.: Theory for the Folding and Stability of Globular Proteins. Biochemistry 24, 1501 (1985)CrossRefGoogle Scholar
  4. [Dil90]
    Dill, K.A.: Dominant Forces in Protein Folding. Biochemistry 29, 7133–7155 (1990)CrossRefGoogle Scholar
  5. [HI95]
    Hart, W.E., Istrail, S.: Fast Protein Folding in the Hydrophobic-hydrophilic Model within Three-eighths of Optimal. In: Proceedings of the 27th ACM Symposium on the Theory of Computing, STOC (1995)Google Scholar
  6. [New02]
    Newman, A.: A New Algorithm for Protein Folding in the HP Model. In: Proceedings of the 13th ACM-SIAM Symposium on Discrete Algorithms, SODA (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Alantha Newman
    • 1
  • Matthias Ruhl
    • 2
  1. 1.MIT Laboratory for Computer ScienceCambridge
  2. 2.IBM Almaden Research CenterSan Jose

Personalised recommendations