New models and algorithms for RNA pseudoknot order assignment

Aalberts, D.P. (2005). Asymmetry in RNA pseudoknots: Observation and theory, Nucleic Acids Research33(7): 2210–2214.10.1093/nar/gki508107996715831794Search in Google Scholar

Adamiak, R., Blazewicz, J., Formanowicz, P., Gdaniec, Z., Kasprzak, M., Popenda, M. and Szachniuk, M. (2004). An algorithm for an automatic NOE pathways analysis in 2D NMR spectra of RNA duplexes, Journal of Computational Biology42(11): 163–180.10.1089/10665270477341694815072694Search in Google Scholar

Adrjanowicz, K., Kaminski, K., Tarnacka, M., Szutkowski, K., Popenda, L., Bartkowiak, G. and Paluch, M. (2016). The effect of hydrogen bonding propensity and enantiomeric composition on the dynamics of supercooled ketoprofen—Dielectric, rheological and NMR studies, Physical Chemistry Chemical Physics18(15): 10585–10593.10.1039/C6CP00578KSearch in Google Scholar

Antczak, M., Popenda, M., Zok, T., Sarzynska, J., Ratajczak, T., Tomczyk, K., Adamiak, R.W. and Szachniuk, M. (2016). New functionality of RNAComposer: Application to shape the axis of miR160 precursor structure, Acta Biochimica Polonica63(4): 737–744.10.18388/abp.2016_132927741327Search in Google Scholar

Antczak, M., Popenda, M., Zok, T., Zurkowski, M., Adamiak, R.W. and Szachniuk, M. (2018). New algorithms to represent complex pseudoknotted RNA structures in dot-bracket notation, Bioinformatics34(8): 1304–1312.10.1093/bioinformatics/btx783590566029236971Search in Google Scholar

Antczak, M., Zok, T., Popenda, M., Lukasiak, P., Adamiak, R.W., Blazewicz, J. and Szachniuk, M. (2014). RNApdbee—A webserver to derive secondary structures from PDB files of knotted and unknotted RNAs, Nucleic Acids Research42(W1): W368–W372.10.1093/nar/gku330408611224771339Search in Google Scholar

Blazewicz, J., Figlerowicz, M., Kasprzak, M., Nowacka, M. and Rybarczyk, A. (2011). RNA partial degradation problem: Motivation, complexity, algorithm, Journal of Computational Biology18(6): 821–834.10.1089/cmb.2010.015321563977Search in Google Scholar

Blazewicz, J., Frohmberg, W., Gawron, P., Kasprzak, M., Kierzynka, M., Swiercz, A. and Wojciechowski, P. (2013). DNA sequence assembly involving an acyclic graph model, Foundations of Computing and Decision Sciences38(1): 25–34.10.2478/v10209-011-0019-4Search in Google Scholar

Blazewicz, J., Kasprzak, M., Kierzynka, M., Frohmberg, W., Swiercz, A., Wojciechowski, P. and Zurkowski, P. (2018). Graph algorithms for DNA sequencing—Origins, current models and the future, European Journal of Operational Research264(3): 799–812.10.1016/j.ejor.2016.06.043Search in Google Scholar

Blazewicz, J., Szachniuk, M. and Wojtowicz, A. (2005). RNA tertiary structure determination: NOE pathways construction by tabu search, Bioinformatics21(10): 2356–2361.10.1093/bioinformatics/bti35115731205Search in Google Scholar

Bon, M., Micheletti, C. and Orland, H. (2012). McGenus: a Monte Carlo algorithm to predict RNA secondary structures with pseudoknots, Nucleic Acids Research41(3): 1895–1900.10.1093/nar/gks1204356194523248008Search in Google Scholar

Bon, M., Vernizzi, G., Orland, H. and Zee, A. (2008). Topological classification of RNA structures, Journal of Molecular Biology379(4): 900–911.10.1016/j.jmb.2008.04.03318485361Search in Google Scholar

Bron, C. and Kerbosch, J. (1973). Algorithm 457: Finding all cliques of an undirected graph, Communications of the ACM16(9): 575–577.10.1145/362342.362367Search in Google Scholar

Cheng, L., Connor, T.R., Siren, J., Aanensen, D.M. and Corander, J. (2013). Hierarchical and spatially explicit clustering of DNA sequences with BAPS software, Molecular Biology and Evolution30(5): 1224–1228.10.1093/molbev/mst028367073123408797Search in Google Scholar

Chiu, J.K.H. and Chen, Y.-P.P. (2012). Conformational features of topologically classified RNA secondary structures, PLoS ONE7(7): e39907.10.1371/journal.pone.0039907339033022792195Search in Google Scholar

Desai, N., Brown, A.A. and Ramakrishnan, V. (2017). The structure of the yeast mitochondrial ribosome, Science355(6324): 528–531.10.1126/science.aal2415529564328154081Search in Google Scholar

Gan, H.H., Pasquali, S. and Schlick, T. (2003). Exploring the repertoire of RNA secondary motifs using graph theory: Implications for RNA design, Nucleic Acids Research31(11): 2926–2943.10.1093/nar/gkg36515670912771219Search in Google Scholar

Gebert, J., Lätsch, M., Pickl, S.W., Weber, G. and Wünschiers, R. (2006). An algorithm to analyze stability of gene-expression patterns, Discrete Applied Mathematics154(7): 1140–1156.10.1016/j.dam.2004.08.011Search in Google Scholar

Giuliani, A., Krishnan, A., Zbilut, J. and Tomita, M. (2008). Proteins as networks: Usefulness of graph theory in protein science, Current Protein & Peptide Science9(1): 28–38.10.2174/13892030878356570518336321Search in Google Scholar

Kropat, E., Özmen, A., Weber, G., Meyer-Nieberg, S. and Defterli, O. (2016). Fuzzy prediction strategies for gene-environment networks—Fuzzy regression analysis for two-modal regulatory systems, RAIRO Operations Research50(2): 413–435.10.1051/ro/2015044Search in Google Scholar

Kruthika, H.A., Mahindrakar, A.D. and Pasumarthy, R. (2017). Stability analysis of nonlinear time-delayed systems with application to biological models, International Journal of Applied Mathematics and Computer Science27(1): 91–103, DOI: 10.1515/amcs-2017-0007.10.1515/amcs-2017-0007Search in Google Scholar

Kuang, R., Leslie, C.S. and Yang, A.-S. (2004). Protein backbone angle prediction with machine learning approaches, Bioinformatics20(10): 1612–1621.10.1093/bioinformatics/bth13614988121Search in Google Scholar

Kucharík, M., Hofacker, I.L., Stadler, P.F. and Qin, J. (2016). Pseudoknots in RNA folding landscapes, Bioinformatics32(2): 187–194.10.1093/bioinformatics/btv572470810826428288Search in Google Scholar

Kuppusamy, L. and Mahendran, A. (2016). Modelling DNA and RNA secondary structures using matrix insertion–deletion systems, International Journal of Applied Mathematics and Computer Science26(1): 245–258, DOI: 10.1515/amcs-2016-0017.10.1515/amcs-2016-0017Search in Google Scholar

Lai, D., Proctor, J.R., Zhu, J.Y.A. and Meyer, I.M. (2012). R-CHIE: A web server and R package for visualizing RNA secondary structures, Nucleic Acids Research40(12): e95.10.1093/nar/gks241338435022434875Search in Google Scholar

Leontis, N.B. and Zirbel, C.L. (2012). Nonredundant 3D structure datasets for RNA knowledge extraction and benchmarking, in N. Leontis and E. Westhof (Eds), Nucleic Acids and Molecular Biology, Springer Nature, Berlin/Heidelberg, pp. 281–298.10.1007/978-3-642-25740-7_13Search in Google Scholar

Leontis, N. and Westhof, E. (2012). RNA 3D Structure Analysis and Prediction, Springer, Berlin/New York, NY.10.1007/978-3-642-25740-7Search in Google Scholar

Lim, C.S. and Brown, C.M. (2018). Know your enemy: Successful bioinformatic approaches to predict functional RNA structures in viral RNAs, Frontiers in Microbiology8: 2582.10.3389/fmicb.2017.02582575854829354101Search in Google Scholar

Lu, X.-J. and Olson, W.K. (2008). 3DNA: A versatile, integrated software system for the analysis, rebuilding and visualization of three-dimensional nucleic-acid structures, Nature Protocols3(7): 1213–1227.10.1038/nprot.2008.104306535418600227Search in Google Scholar

Luby, M. (1986). A simple parallel algorithm for the maximal independent set problem, SIAM Journal on Computing15(4): 1036–1053.10.1137/0215074Search in Google Scholar

Lukasiak, P., Antczak, M., Ratajczak, T., Szachniuk, M., Popenda, M., Adamiak, R.W. and Blazewicz, J. (2015). RNAssess—A web server for quality assessment of RNA 3D structures, Nucleic Acids Research43(W1): W502–W506.10.1093/nar/gkv557448924226068469Search in Google Scholar

Magnus, M., Antczak, M., Zok, T., Wiedemann, J., Lukasiak, P., Cao, Y., Bujnicki, J.M., Westhof, E., Szachniuk, M. and Miao, Z. (2020). RNA-Puzzles toolkit: A computational resource of RNA 3D structure benchmark datasets, structure manipulation, and evaluation tools, Nucleic Acids Research48(2): 576–588.10.1093/nar/gkz1108714551131799609Search in Google Scholar

Miao, Z. and Westhof, E. (2017). RNA structure: Advances and assessment of 3D structure prediction, Annual Review of Biophysics46: 483–503.10.1146/annurev-biophys-070816-03412528375730Search in Google Scholar

Miskiewicz, J. and Szachniuk, M. (2018). Discovering structural motifs in miRNA precursors from the Viridiplantae kingdom, Molecules23(6): 1367.10.3390/molecules23061367610013529882777Search in Google Scholar

Morimura, H., Tanaka, S.-I., Ishitobi, H., Mikami, T., Kamachi, Y., Kondoh, H. and Inouye, Y. (2013). Nano-analysis of DNA conformation changes induced by transcription factor complex binding using plasmonic nanodimers, ACS Nano7(12): 10733–10740.10.1021/nn403625s24195575Search in Google Scholar

Parisien, M., Cruz, J.A., Westhof, E. and Major, F. (2009). New metrics for comparing and assessing discrepancies between RNA 3D structures and models, RNA15(10): 1875–1885.10.1261/rna.1700409274303819710185Search in Google Scholar

Pasquali, S., Gan, H. and Schlick, T. (2005). Modular RNA architecture revealed by computational analysis of existing pseudoknots and ribosomal RNAs, Nucleic Acids Research33(4): 1384–1398.10.1093/nar/gki26755295515745998Search in Google Scholar

Pillsbury, M., Orland, H. and Zee, A. (2005). Steepest descent calculation of RNA pseudoknots, Physical Review E72(1).10.1103/PhysRevE.72.01191116090005Search in Google Scholar

Popenda, L., Bielecki, L., Gdaniec, Z. and Adamiak, R.W. (2009). Structure and dynamics of adenosine bulged RNA duplex reveals formation of the dinucleotide platform in the C:G-A triple, Arkivoc2009(3): 130–144.10.3998/ark.5550190.0010.311Search in Google Scholar

Popenda, M., Miskiewicz, J., Sarzynska, J., Zok, T. and Szachniuk, M. (2020). Topology-based classification of tetrads and quadruplex structures, Bioinformatics36(4): 1129–1134.10.1093/bioinformatics/btz738703177831588513Search in Google Scholar

Pugalenthi, G., Suganthan, P.N., Sowdhamini, R. and Chakrabarti, S. (2007). SMotif: A server for structural motifs in proteins, Bioinformatics23(5): 637–638.10.1093/bioinformatics/btl67917237055Search in Google Scholar

Purzycka, K., Popenda, M., Szachniuk, M., Antczak, M., Lukasiak, P., Blazewicz, J. and Adamiak, R. (2015). Automated 3D RNA structure prediction using the RNAComposer method for riboswitches, in S.J. Chen and D.H. Burke Aguero (Eds), Methods in Enzymology, Vol. 553, Elsevier, San Diego, CA, pp. 3–34.Search in Google Scholar

Radom, M., Rybarczyk, A., Szawulak, B., Andrzejewski, H., Chabelski, P., Kozak, A. and Formanowicz, P. (2017). Holmes: A graphical tool for development, simulation and analysis of Petri net based models of complex biological systems, Bioinformatics33(23): 3822–3823.10.1093/bioinformatics/btx49228961696Search in Google Scholar

Rebis, T., Lijewski, S., Nowicka, J., Popenda, L., Sobotta, L., Jurga, S., Mielcarek, J., Milczarek, G. and Goslinski, T. (2015). Electrochemical properties of metallated porphyrazines possessing isophthaloxybutylsulfanyl substituents: Application in the electrocatalytic oxidation of hydrazine, Electrochimica Acta168: 216–224.10.1016/j.electacta.2015.03.191Search in Google Scholar

Reidys, C.M., Huang, F.W.D., Andersen, J.E., Penner, R.C., Stadler, P.F. and Nebel, M.E. (2011). Topology and prediction of RNA pseudoknots, Bioinformatics27(8): 1076–1085.10.1093/bioinformatics/btr09021335320Search in Google Scholar

Rietveld, K., Poelgeest, R.V., Pleij, C., Boom, J.V. and Bosch, L. (1982). The tRNA-like structure at the 3' terminus of turnip yellow mosaic virus RNA. Differences and similarities with canonical tRNA, Nucleic Acids Research10(6): 1929–1946.Search in Google Scholar

Rødland, E.A. (2006). Pseudoknots in RNA secondary structures: Representation, enumeration, and prevalence, Journal of Computational Biology13(6): 1197–1213.10.1089/cmb.2006.13.119716901237Search in Google Scholar

Rybarczyk, A., Hertz, A., Kasprzak, M. and Blazewicz, J. (2017). Tabu search for the RNA partial degradation problem, International Journal of Applied Mathematics and Computer Science27(2): 401–415, DOI: 10.1515/amcs-2017-0028.10.1515/amcs-2017-0028Search in Google Scholar

Saenger, W. (1984). Principles of Nucleic Acid Structure, Springer-Verlag, London.10.1007/978-1-4612-5190-3Search in Google Scholar

Sarzynska, J. and Kulinski, T. (2005). Dynamics and stability of GCAA tetraloops with 2-aminopurine and purine substitutions, Journal of Biomolecular Structure and Dynamics22(4): 425–439.10.1080/07391102.2005.1050701415588106Search in Google Scholar

Schlick, T. (2018). Adventures with RNA graphs, Methods143: 16–33.10.1016/j.ymeth.2018.03.009605191829621619Search in Google Scholar

Seetin, M. and Mathews, D. (2011). Automated RNA tertiary structure prediction from secondary structure and low-resolution restraints, Journal of Computational Chemistry32(10): 2232–2244.10.1002/jcc.21806328833421509787Search in Google Scholar

Shi, Y.-Z., Jin, L., Feng, C.-J., Tan, Y.-L. and Tan, Z.-J. (2018). Predicting 3D structure and stability of RNA pseudoknots in monovalent and divalent ion solutions, PLOS Computational Biology14(6): e1006222.10.1371/journal.pcbi.1006222600793429879103Search in Google Scholar

Simon, M. (2005). Emergent Computation. Emphasizing Bioinformatics, Springer New York, New York, NY.10.1007/b138851Search in Google Scholar

Slabinski, L., Jaroszewski, L., Rodrigues, A.P., Rychlewski, L., Wilson, I.A., Lesley, S.A. and Godzik, A. (2007). The challenge of protein structure determination-lessons from structural genomics, Protein Science16(11): 2472–2482.10.1110/ps.073037907221168717962404Search in Google Scholar

Staple, D.W. and Butcher, S.E. (2005). Pseudoknots: RNA structures with diverse functions, PLoS Biology3(6): e213.10.1371/journal.pbio.0030213114949315941360Search in Google Scholar

Sun, T.-t., Zhao, C. and Chen, S.-J. (2018). Predicting cotranscriptional folding kinetics for riboswitch, The Journal of Physical Chemistry B122(30): 7484–7496.10.1021/acs.jpcb.8b04249634527729985608Search in Google Scholar

Szachniuk, M. (2019). RNApolis: Computational platform for RNA structure analysis, Foundations of Computing and Decision Sciences44(2): 241–257.10.2478/fcds-2019-0012Search in Google Scholar

Szachniuk, M., Cola, M.C.D., Felici, G. and Blazewicz, J. (2014). The orderly colored longest path problem—A survey of applications and new algorithms, RAIRO—Operations Research48(1): 25–51.10.1051/ro/2013046Search in Google Scholar

Szachniuk, M., Cola, M.C.D., Felici, G., de Werra, D. and Blazewicz, J. (2015). Optimal pathway reconstruction on 3D NMR maps, Discrete Applied Mathematics182: 134–149.10.1016/j.dam.2014.04.010Search in Google Scholar

Szostak, N., Royo, F., Rybarczyk, A., Szachniuk, M., Blazewicz, J., del Sol, A. and Falcon-Perez, J.M. (2014). Sorting signal targeting mRNA into hepatic extracellular vesicles, RNA Biology11(7): 836–844.10.4161/rna.29305417995824921245Search in Google Scholar

Tarjan, R.E. and Trojanowski, A.E. (1977). Finding a maximum independent set, SIAM Journal on Computing6(3): 537–546.10.1137/0206038Search in Google Scholar

Vernizzi, G., Orland, H. and Zee, A. (2016). Classification and predictions of RNA pseudoknots based on topological invariants, Physical Review E94(4).10.1103/PhysRevE.94.04241027841638Search in Google Scholar

Weber, G., Defterli, O., Gök, S.Z.A. and Kropat, E. (2011). Modeling, inference and optimization of regulatory networks based on time series data, European Journal of Operational Research211(1): 1–14.10.1016/j.ejor.2010.06.038Search in Google Scholar

Weber, G., Kropat, E., Akteke-Öztürk, B. and Görgülü, Z. (2009). A survey on OR and mathematical methods applied on gene-environment networks, CEJOR17(3): 315–341.10.1007/s10100-009-0092-4Search in Google Scholar

Wiedemann, J. and Milostan, M. (2017). StructAnalyzer—A tool for sequence vs. structure similarity analysis, Acta Biochimica Polonica63(4): 753–757.Search in Google Scholar

Wiedemann, J., Zok, T., Milostan, M. and Szachniuk, M. (2017). LCS-TA to identify similar fragments in RNA 3D structures, BMC Bioinformatics18(1): 456.10.1186/s12859-017-1867-6565159829058576Search in Google Scholar

Wojciechowski, P., Frohmberg, W., Kierzynka, M., Zurkowski, P. and Blazewicz, J. (2016). G-MAPSEQ—A new method for mapping reads to a reference genome, Foundations of Computing and Decision Sciences41(2): 123–142.10.1515/fcds-2016-0007Search in Google Scholar

Zemla, A. (2003). LGA: A method for finding 3D similarities in protein structures, Nucleic Acids Research31(13): 3370–3374.10.1093/nar/gkg57116897712824330Search in Google Scholar

Zok, T., Antczak, M., Riedel, M., Nebel, D., Villmann, T., Lukasiak, P., Blazewicz, J. and Szachniuk, M. (2015). Building the library of RNA 3D nucleotide conformations using the clustering approach, International Journal of Applied Mathematics and Computer Science25(3): 689–700, DOI: 10.1515/amcs-2015-0050.10.1515/amcs-2015-0050Search in Google Scholar

Zok, T., Antczak, M., Zurkowski, M., Popenda, M., Blazewicz, J., Adamiak, R.W. and Szachniuk, M. (2018). RNApdbee 2.0: Multifunctional tool for RNA structure annotation, Nucleic Acids Research46(W1): W30–W35.Search in Google Scholar