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.
This work was partly done while the authors visited the group of Prof. Peter Widmayer at ETH Zurich.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
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)
Anfinsen, C.B.: Principles that govern the folding of protein chains. Science 181(4096), 223–230 (1973)
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)
Atkins, J., Hart, W.E.: On the intractability of protein folding with a finite alphabet of amino acids. Algorithmica 25, 279–294 (1999)
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)
Chan, H.S., Dill, K.A.: The protein folding problem. Physics today, 24–32 (1993)
Chandra, V., DattaSharma, A., Kumar, V.S.A.: The algorithmics of folding proteins on lattices. Discrete Applied Mathematics 127, 145–161 (2003)
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)
Dill, K.A.: Theory for the folding and stability of globular proteins. Biochemistry 24, 1501 (1985)
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)
Greenberg, H.J., Hart, W.E., Lancia, G.: Opportunities for combinatorial optimization in computational biology. INFORMS Journal of Computing (to appear)
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)
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)
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)
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)
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)
Nayak, A., Sinclair, A., Zwick, U.: Spatial Codes and the hardness of string folding problems. Journal of Computational Biology 6(1), 13–36 (1999)
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)
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Böckenhauer, HJ., Bongartz, D. (2004). Protein Folding in the HP Model on Grid Lattices with Diagonals. In: Fiala, J., Koubek, V., Kratochvíl, J. (eds) Mathematical Foundations of Computer Science 2004. MFCS 2004. Lecture Notes in Computer Science, vol 3153. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-28629-5_15
Download citation
DOI: https://doi.org/10.1007/978-3-540-28629-5_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22823-3
Online ISBN: 978-3-540-28629-5
eBook Packages: Springer Book Archive