Abstract
Stochastic context-free grammar (SCFG) has been successful in modeling biomolecular structures, typically RNA secondary structure, for statistical analysis and structure prediction. Context-free grammar rules specify parallel and nested co-occurren-ces of terminals, and thus are ideal for modeling nucleotide canonical base pairs that constitute the RNA secondary structure. Stochastic grammars have been sought, which may adequately model biomolecular tertiary structures that are beyond context-free. Some of the existing linguistic grammars, developed mostly for natural language processing, appear insufficient to account for crossing relationships incurred by distant interactions of bio-residues, while others are overly powerful and cause excessive computational complexity. This paper introduces a novel stochastic grammar, called stochastic k-tree grammar (SkTG), for the analysis of context-sensitive languages. With the new grammar rules, co-occurrences of distant terminals are characterized and recursively organized into k-tree graphs. The new grammar offers a viable approach to modeling context-sensitive interactions between bioresidues because such relationships are often constrained by k-trees, for small values of k, as demonstrated by earlier investigations. In this paper it is shown, for the first time, that probabilistic analysis of k-trees over strings are computable in polynomial time n O(k). Hence, SkTG permits not only modeling of biomolecular tertiary structures but also efficient analysis and prediction of such structures.
Keywords
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Achawanantakun, R., Takyar, S., Sun, Y.: Grammar string: A novel ncRNA secondary structure representation. lifesciences society org, pp. 2–13 (2010)
Rozenknop, A.: Gibbsian context-free grammar for parsing. In: Sojka, P., Kopeček, I., Pala, K. (eds.) TSD 2002. LNCS (LNAI), vol. 2448, pp. 49–56. Springer, Heidelberg (2002)
Arnborg, S., Proskurowski, A.: Linear time algorithms for np-hard problems restricted to partial k-trees. Discrete Applied Mathematics 23(1), 11–24 (1989)
Chiang, D., Joshi, A.K., Searls, D.B.: Grammatical representations of macromolecular structure. Journal of Computational Biology 13(5), 1077–1100 (2006)
Dill, K.A., Lucas, A., Hockenmaier, J., Huang, L., Chiang, D., Josh, A.K.: Computational linguistics: A new tool for exploring biopolymer structures and statistical mechanics. Polymer 48, 4289–4300 (2007)
Ding, L., Samad, A., Li, G., Robinson, R., Xue, X., Malmberg, R., Cai, L.: Finding maximum spanning k-trees on backbone graphs in polynomial time (2013) (manuscript)
Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer (1999)
Durbin, R., Eddy, S., Krogh, A., Mitchison, G.: Biological Sequence Analysis: Probabilistic Models of Proteins and Nucleic Acids. Cambridge University Press (1998)
Hopcroft, J.E., Motwani, R., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation. Addison-Wesley (2007)
Huang, Z., Mohebbi, M., Malmberg, R., Cai, L.: RNAv: Non-coding RNA secondary structure variation search via graph homomorphism. In: Proceedings of Computational Systems Bioinformatics Conference (CSB 2010), vol. 9, pp. 56–69 (2010)
Huang, Z., Wu, Y., Robertson, J., Feng, L., Malmberg, R., Cai, L.: Fast and accurate search for non-coding RNA pseudoknot structures in genomes. Bioinforamtics 24(20), 2281–2287 (2008)
Thiim, J.F.I.M., Mardia, M., Ferkinghoff-Borg, K., Hamelryck, J.,, T.: A probabilistic model of RNA conformational space. PLoS Comput. Biol. 5(6) (2009)
Joshi, A.: How much context-sensitivity is necessary for characterizing structural descriptions. In: Dowty, D., Karttunen, L., Zwicky, A. (eds.) Natural Language Processing: Theoretical, Computational, and Psychological Perspectives, pp. 206–250. Cambridge University Press, NY (1985)
Joshi, A., Vijay-Shanker, K., Weir, D.: The convergence of mildly context-sensitive grammar formalisms. Issues in Natural Language Processing, pp. 31–81. MIT Press, Cambridge (1991)
Jurafsky, D., Wooters, C., Segal, J., Stolcke, A., Fosler, E., Tajchaman, G., Morgan, N.: Using a stochastic context-free grammar as a language model for speech recognition. In: Proceedings of International Conference on Acoustics, Speech and Signal Processing, pp. 189–192 (1995)
Klein, D., Manning, C.: Accurate unlexicalized parsing. In: Proceedings of the 41st Meeting of the Association for Computational Linguistics, pp. 423–430 (2003)
Knudsen, B., Hein, J.: Pfold: RNA secondary structure prediction using stochastic context-free grammars. Nucleic Acids Res. 31, 3423–3428 (2003)
Lari, K., Young, S.J.: The estimation of stochastic context-free grammars using the inside-outside algorithm. Computer Speech and Language 4, 35–56 (1990)
Martin, D., Sigal, R., Weyuker, E.J.: Computability, complexity, and languages: Fundamentals of theoretical computer science, 2nd edn. Morgan Kaufmann (1994)
Murzin, A.G., Brenner, S., Hubbard, T., Chothia, C.: Scop: A structural classification of proteins database for the investigation of sequences and structures. Journal of Molecular Biology 247(4), 536–540 (1995)
Nawrocki, E.P., Kolbe, D.L., Eddy, S.R.: Infernal 1.0: Inference of RNA alignments. Bioinformatics 25, 1335–1337 (2009)
Noller, H.F.: Structure of ribosomal RNA. Annual Review of Biochemistry 53, 119–162 (1984)
Patil, H.P.: On the structure of k-trees. Journal of Combinatorics, Information and System Sciences 11(2-4), 57–64 (1986)
Rivas, E., Lang, R., Eddy, S.R.: A range of complex probabilistic models for RNA secondary structure prediction that include the nearest neighbor model and more. RNA 18, 193–212 (2012)
Sakakibara, Y., Brown, M., Hughey, R., Mian, I.S., Sjolander, K., Underwood, R.C., Haussler, D.: Stochastic context-free grammars for tRNA modeling. Nucleic Acids Research 22, 5112–5120 (1994)
Salomaa, A.: Jewels of Formal Language Theory. Computer Science Press (1981)
Sánchez, I.A., Benedi, J.M., Linares, D.: Performance of a scfg-based language model with training data sets of increasing size. In: Proceedings of Conference on Pattern Recognition and Image Analysis, pp. 586–594 (2005)
Searls, D.B.: The computational linguistics of biological sequences. Artificial Intelligence and Molecular Biology, pp. 47–120 (1993)
Searls, D.B.: Molecules, languages and automata. In: Sempere, J.M., García, P. (eds.) ICGI 2010. LNCS, vol. 6339, pp. 5–10. Springer, Heidelberg (2010)
Sergio Caracciolo, S., Masbaum, G., Sokal, A., Sportiello, A.: A randomized polynomial-time algorithm for the spanning hypertree problem on 3-uniform hypergraphs. CoRR abs/0812.3593 (2008)
Song, Y., Liu, C., Huang, X., Malmberg, R., Xu, Y., Cai, L.: Efficient parameterized algorithms for biopolymer structure-sequence alignment. IEEE/ACM Transactions on Computational Biology and Bioinformatics 3(4), 423–431 (2006)
Srebro, N.: Maximum likelihood bounded tree-width Markov networks. Artificial Intelligence 143(2003), 123–138 (2003)
Uemura, Y., Hasegawa, A., Kobayashi, S., Yokomori, T.: Tree adjoining grammars for RNA structure prediction. Theoretical Computer Science 210, 277–303 (1999)
Vijay-Shanker, K., Weir, D.: The equivalence of four extensions of context-free grammars. Mathematical Systems Theory 27(6), 511–546 (1994)
Waters, C.J., MacDonald, B.A.: Efficient word-graph parsing and search with a stochastic context-free grammar. In: Proceedings of IEEE Workshop on Automatic Speech Recognition and Understanding, pp. 311–318 (1997)
Xu, J., Berger, B.: Fast and accurate algorithms for protein side-chain packing. Journal of the ACM 53(4), 533–557 (2006)
Xu, Y., Liu, Z., Cai, L., Xu, D.: Protein structure prediction by protein threading. In: Computational Methods for Protein Structure Prediction and Modeling, pp. 389–430. Springer I&II (2006)
Progress, Y.Z.: challenges in protein structure prediction. Current Opinions in Structural Biology 18(3), 342–348 (2008)
Weinberg, Z., Ruzzo, L.: Faster genome annotation of non-coding RNA families without loss of accuracy. In: Proceedings of Conference on Research in Computational Molecular Biology (RECOMB 2004), pp. 243–251 (2004)
Zimand, M.: The complexity of the optimal spanning hypertree problem. Technical Report, University of Rochester. Computer Science Department (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Ding, L., Samad, A., Xue, X., Huang, X., Malmberg, R.L., Cai, L. (2014). Stochastic k-Tree Grammar and Its Application in Biomolecular Structure Modeling. In: Dediu, AH., Martín-Vide, C., Sierra-Rodríguez, JL., Truthe, B. (eds) Language and Automata Theory and Applications. LATA 2014. Lecture Notes in Computer Science, vol 8370. Springer, Cham. https://doi.org/10.1007/978-3-319-04921-2_25
Download citation
DOI: https://doi.org/10.1007/978-3-319-04921-2_25
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-04920-5
Online ISBN: 978-3-319-04921-2
eBook Packages: Computer ScienceComputer Science (R0)