RNA Secondary Structure Prediction Via Energy Density Minimization

  • Can Alkan
  • Emre Karakoc
  • S. Cenk Sahinalp
  • Peter Unrau
  • H. Alexander Ebhardt
  • Kaizhong Zhang
  • Jeremy Buhler
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3909)


There is a resurgence of interest in RNA secondary structure prediction problem (a.k.a. the RNA folding problem) due to the discovery of many new families of non-coding RNAs with a variety of functions. The vast majority of the computational tools for RNA secondary structure prediction are based on free energy minimization. Here the goal is to compute a non-conflicting collection of structural elements such as hairpins, bulges and loops, whose total free energy is as small as possible. Perhaps the most commonly used tool for structure prediction, mfold/RNAfold, is designed to fold a single RNA sequence. More recent methods, such as RNAscf and alifold are developed to improve the prediction quality of this tool by aiming to minimize the free energy of a number of functionally similar RNA sequences simultaneously. Typically, the (stack) prediction quality of the latter approach improves as the number of sequences to be folded and/or the similarity between the sequences increase. If the number of available RNA sequences to be folded is small then the predictive power of multiple sequence folding methods can deteriorate to that of the single sequence folding methods or worse.

In this paper we show that delocalizing the thermodynamic cost of forming an RNA substructure by considering the energy density of the substructure can significantly improve on secondary structure prediction via free energy minimization. We describe a new algorithm and a software tool that we call Densityfold, which aims to predict the secondary structure of an RNA sequence by minimizing the sum of energy densities of individual substructures. We show that when only one or a small number of input sequences are available, Densityfold can outperform all available alternatives. It is our hope that this approach will help to better understand the process of nucleation that leads to the formation of biologically relevant RNA substructures.


Secondary Structure Secondary Structure Prediction Free Energy Minimization Free Energy Density Total Free Energy 
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.


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  1. 1.
    Mapping RNA Form & Function. Science 309(5740) (September 2, 2005)Google Scholar
  2. 2.
  3. 3.
    Akutsu, T.: Dynamic programming algorithms for RNA secondary structure prediction with pseudoknots. Discr. Appl. Math. 104(1-3), 45–62 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Arslan, A.N., Egecioglu, O., Pevzner, P.A.: A New Approach to Sequence Comparison: Normalized Sequence Alignment. In: Proc. RECOMB, pp. 2–11. ACM, New York (2001)Google Scholar
  5. 5.
    Bafna, V., Tang, H., Zhang, S.: Consensus Folding of Unaligned RNA Sequences Revisited. In: Miyano, S., Mesirov, J., Kasif, S., Istrail, S., Pevzner, P.A., Waterman, M. (eds.) RECOMB 2005. LNCS (LNBI), vol. 3500, pp. 172–187. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  6. 6.
    Condon, A., Davy, B., Rastegari, B., Zhao, S., Tarrant, F.: Classifying RNA pseudoknotted structures. Theor. Comput. Sci. 320(1), 35–50 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Davydov, E., Batzoglou, S.: A Computational Model for RNA Multiple Structural Alignment. In: GECCO 2004. LNCS, vol. 3103, pp. 254–269. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  8. 8.
    Gorodkin, J., Heyer, L., Stormo, G.: Finding the most significant common sequence and structure motifs in a set of RNA sequences. Nucl. Acids Res. 25(18), 3724–3732 (1997)CrossRefGoogle Scholar
  9. 9.
    Griffiths-Jones, S., Bateman, A., Marshall, M., Khanna, A., Eddy, S.: Rfam: an RNA family database. Nucl. Acids Res. 31(1), 439–441 (2003)CrossRefGoogle Scholar
  10. 10.
    Hofacker, I., Fekete, M., Stadler, P.: Secondary structure prediction for aligned RNA sequences. J. Mol. Biol. 319(5), 1059–1066 (2002)CrossRefGoogle Scholar
  11. 11.
    Ji, Y., Xu, X., Stormo, G.D.: A graph theoretical approach for predicting common RNA secondary structure motifs including pseudoknots in unaligned sequences. Bioinformatics 20(10), 1591–1602 (2004)CrossRefGoogle Scholar
  12. 12.
    Lin, G., Ma, B., Zhang, K.: Edit distance between two RNA structures. In: Proc. RECOMB, pp. 211–220. ACM, New York (2001)Google Scholar
  13. 13.
    Lyngso, R.B., Zuker, M., Pedersen, C.N.S.: Fast evaluation of internal loops in RNA secondary structure prediction. Bioinformatics 15(6), 440–445 (1999)CrossRefGoogle Scholar
  14. 14.
    Ma, B., Wang, L., Zhang, K.: Computing similarity between RNA structures. Theoretical Computer Science 276(1-2), 111–132 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Mathews, D., Sabina, J., Zuker, M., Turner, D.: Expanded sequence dependence of thermodynamic parameters improves prediction of RNA secondary structure. J. Mol. Biol. 288(5), 911–940 (1999)CrossRefGoogle Scholar
  16. 16.
    Mathews, D., Turner, D.: Dynalign: an algorithm for finding the secondary structure common to two RNA sequences. J. Mol. Biol. 317(2), 191–203 (2002)CrossRefGoogle Scholar
  17. 17.
    Nussinov, R., Jacobson, A.: Fast algorithm for predicting the secondary structure of single stranded RNA. Proc. Nat. Acad. Sci. USA 77(11), 6309–6313 (1980)CrossRefGoogle Scholar
  18. 18.
    Rivas, E., Eddy, S.R.: A dynamic programming algorithm for RNA structure prediction including pseudoknots. J. Mol. Biol. 285(5), 2053–2068 (1999)CrossRefGoogle Scholar
  19. 19.
    Sankoff, D.: Simultaneous Solution of the RNA Folding, Alignment and Protosequence Problems. SIAM J. Appl. Math. 45, 810–825 (1985)zbMATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Thompson, J., Higgins, D., Gibson, T.: Clustal-W: improving the sensitivity of progressive multiple sequence alignment through sequence weighting, position specific gap penalties and weight matrix choice. Nucl. Acids Res. 22, 4673–4680 (1994)CrossRefGoogle Scholar
  21. 21.
    Tinoco, I., Uhlenbeck, O., Levine, M.: Estimation of secondary structure in ribonucleic acids. Nature 230(5293), 362–367 (1971)CrossRefGoogle Scholar
  22. 22.
    Zuker, M., Stiegler, P.: Optimal computer folding of large RNA sequences using thermodynamics and auxiliary information. Nucleic Acids Res. 9(1), 133–148 (1981)CrossRefGoogle Scholar
  23. 23.
    Zuker, M.: On finding all suboptimal foldings of an RNA molecule. Science 244, 48–52 (1989)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Can Alkan
    • 1
  • Emre Karakoc
    • 2
  • S. Cenk Sahinalp
    • 2
  • Peter Unrau
    • 3
  • H. Alexander Ebhardt
    • 3
  • Kaizhong Zhang
    • 4
  • Jeremy Buhler
    • 5
  1. 1.Department of Genome SciencesUniversity of WashingtonUSA
  2. 2.School of Computing ScienceSimon Fraser UniversityCanada
  3. 3.Department of Molecular Biology and BiochemistrySimon Fraser UniversityCanada
  4. 4.Department of Computer ScienceUniversity of Western OntarioCanada
  5. 5.Department of Computer ScienceWashington University in St LouisUSA

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