Email updates

Keep up to date with the latest news and content from BMC Bioinformatics and BioMed Central.

This article is part of the supplement: Highlights from the Fifth International Society for Computational Biology (ISCB) Student Council Symposium

Open Access Poster presentation

PAUL: protein structural alignment using integer linear programming and Lagrangian relaxation

Inken Wohlers1*, Lars Petzold2, Francisco S Domingues3 and Gunnar W Klau1

Author Affiliations

1 Life Sciences Group, Centrum Wiskunde & Informatica, Science Park 123,1098 XG Amsterdam, the Netherlands

2 Mathematics in Life Sciences Group, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany

3 Computational Biology and Applied Algorithmics Group, Max-Planck-Institut für Informatik, 66123 Saarbrücken, Germany

For all author emails, please log on.

BMC Bioinformatics 2009, 10(Suppl 13):P2  doi:10.1186/1471-2105-10-S13-P2

The electronic version of this article is the complete one and can be found online at:

Published:19 October 2009

© 2009 Wohlers et al; licensee BioMed Central Ltd.


Protein structural alignment determines the three-dimensional superposition of protein structures by means of aligning the protein's residues. It is a basic method for identifying proteins of related structure or common evolutionary origin and for measuring three-dimensional similarity. Applications are for instance the search for proteins with similar biological function or the classification of proteins based on their structural features.


We present a structural alignment approach that computes an alignment based on the protein's inter-residue distances. Building upon work for the alignment of protein contact maps by Caprara et al. [1], we use these distances to formulate the problem as an integer linear program which is subsequently solved using Lagrangian relaxation. One advantage of the integer linear programming formulation over heuristic methods is that we compute in many cases demonstrably optimal alignments. The bottleneck of the integer linear programming approach is its computational complexity which does not allow to incorporate all inter-residue distances in the problem description. On that account we select and score inter-residue distances efficiently. We develop and optimize a scoring function inspired by Holm and Sander. [2] using a set of 200 pairwise HOMSTRAD [3] alignments with a sequence identity of less than 35%. Subsequently, we use this scoring function to assess the performance of PAUL on the more challenging SISY data set of 130 alignments [4,5] – on this data set we compare PAUL alignments to alignments computed by MATRAS [6], DALI [2], FATCAT [7], SHEBA [8], CA [9] and CE [10].

Results and conclusion

Our novel, non-heuristic structural alignment algorithm is flexible and mathematically sound. On the SISY data set PAUL alignments show higher mean and median alignment accuracies than all other methods (see Figure 1). In more than 30% of the cases, PAUL is the most accurate method. PAUL is thus competitive to other state-of-the-art algorithms and a beneficial tool for high-quality pairwise structural alignment.

thumbnailFigure 1. Box-and-whisker plots of the distributions of the percentages of alignment accuracies for the SISY set for PAUL, MATRAS, DALI, FATCAT, SHEBA, CA and CE. Additionally, the average alignment accuracies are denoted in blue.


  1. Caprara A, Carr R, Istrail S, Lancia G, Walenz B: 1001 optimal PDB structure alignments: integer programming methods for finding the maximum contact map overlap.

    J Comput Biol 2004, 11(1):27-52. PubMed Abstract | Publisher Full Text OpenURL

  2. Holm L, Sander C: Protein structure comparison by alignment of distance matrices.

    J Mol Biol 1993, 233(1):123-138. PubMed Abstract | Publisher Full Text OpenURL

  3. Mizuguchi K, Deane CM, Blundell TL, Overington JP: Homstrad: a database of protein structure alignments for homologous families.

    Protein Sci 1998, 7(11):2469-2471. PubMed Abstract | Publisher Full Text | PubMed Central Full Text OpenURL

  4. Andreeva A, Prlic A, Hubbard TJ, Murzin AG: Sisyphus-structural alignments for proteins with non-trivial relationships.

    Nucleic Acids Res 2007, (35 Database):253-259. PubMed Abstract | Publisher Full Text | PubMed Central Full Text OpenURL

  5. Mayr G, Domingues FS, Lackner P: Comparative analysis of protein structure alignments.

    BMC Struct Biol 2007, 7:50-50. PubMed Abstract | BioMed Central Full Text | PubMed Central Full Text OpenURL

  6. Kawabata T: Matras: A program for protein 3d structure comparison.

    Nucleic Acids Res 2003, 31(13):3367-3369. PubMed Abstract | Publisher Full Text | PubMed Central Full Text OpenURL

  7. Ye Y, Godzik A: Flexible structure alignment by chaining aligned fragment pairs allowing twists.

    Bioinformatics 2003, 19(Suppl 2):ii246-ii255. PubMed Abstract | Publisher Full Text OpenURL

  8. Jung J, Lee B: Protein structure alignment using environmental profiles.

    Protein Eng 2000, 13(8):535-543. PubMed Abstract | Publisher Full Text OpenURL

  9. Bachar O, Fischer D, Nussinov R, Wolfson H: A computer vision based technique for 3-D sequence-independent structural comparison of proteins.

    Protein Eng 1993, 6(3):279-288. PubMed Abstract | Publisher Full Text OpenURL

  10. Shindyalov IN, Bourne PE: Protein structure alignment by incremental combinatorial extension (CE) of the optimal path.

    Protein Eng 1998, 11(9):739-747. PubMed Abstract | Publisher Full Text OpenURL