{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,26]],"date-time":"2026-03-26T10:56:31Z","timestamp":1774522591580,"version":"3.50.1"},"publisher-location":"Cham","reference-count":40,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783031902512","type":"print"},{"value":"9783031902529","type":"electronic"}],"license":[{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025]]},"DOI":"10.1007\/978-3-031-90252-9_10","type":"book-chapter","created":{"date-parts":[[2025,4,24]],"date-time":"2025-04-24T20:03:20Z","timestamp":1745525000000},"page":"153-174","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Scalable and\u00a0Interpretable Identification of\u00a0Minimal Undesignable RNA Structure Motifs with\u00a0Rotational Invariance"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-4804-0825","authenticated-orcid":false,"given":"Tianshuo","family":"Zhou","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0009-0004-3351-7097","authenticated-orcid":false,"given":"Apoorv","family":"Malik","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0009-0008-1141-9479","authenticated-orcid":false,"given":"Wei Yu","family":"Tang","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2907-6557","authenticated-orcid":false,"given":"David H.","family":"Mathews","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6444-7045","authenticated-orcid":false,"given":"Liang","family":"Huang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,4,25]]},"reference":[{"issue":"1","key":"10_CR1","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/1471-2105-8-34","volume":"8","author":"R Aguirre-Hern\u00e1ndez","year":"2007","unstructured":"Aguirre-Hern\u00e1ndez, R., Hoos, H.H., Condon, A.: Computational RNA secondary structure design: empirical complexity and improved methods. BMC Bioinform. 8(1), 1\u201316 (2007)","journal-title":"BMC Bioinform."},{"issue":"5","key":"10_CR2","doi-asserted-by":"publisher","first-page":"748","DOI":"10.1016\/j.jmb.2015.11.013","volume":"428","author":"J Anderson-Lee","year":"2016","unstructured":"Anderson-Lee, J., et al.: Principles for predicting RNA secondary structure design difficulty. J. Mol. Biol. 428(5), 748\u2013757 (2016)","journal-title":"J. Mol. Biol."},{"issue":"12","key":"10_CR3","doi-asserted-by":"publisher","first-page":"2304","DOI":"10.1261\/rna.1950510","volume":"16","author":"M Andronescu","year":"2010","unstructured":"Andronescu, M., Condon, A., Hoos, H.H., Mathews, D.H., Murphy, K.P.: Computational approaches for rna energy parameter estimation. RNA 16(12), 2304\u20132318 (2010)","journal-title":"RNA"},{"issue":"11","key":"10_CR4","doi-asserted-by":"publisher","first-page":"1555","DOI":"10.1261\/rna.066324.118","volume":"24","author":"S Bellaousov","year":"2018","unstructured":"Bellaousov, S., Kayedkhordeh, M., Peterson, R.J., Mathews, D.H.: Accelerated RNA secondary structure design using preselected sequences for helices and loops. RNA 24(11), 1555\u20131567 (2018)","journal-title":"RNA"},{"issue":"1\u20132","key":"10_CR5","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1016\/0301-4622(95)00119-0","volume":"59","author":"G Benedetti","year":"1996","unstructured":"Benedetti, G., Morosetti, S.: A graph-topological approach to recognition of pattern and similarity in rna secondary structures. Biophys. Chem. 59(1\u20132), 179\u2013184 (1996)","journal-title":"Biophys. Chem."},{"issue":"3","key":"10_CR6","doi-asserted-by":"publisher","first-page":"302","DOI":"10.1089\/cmb.2019.0420","volume":"27","author":"\u00c9 Bonnet","year":"2020","unstructured":"Bonnet, \u00c9., Rzazewski, P., Sikora, F.: Designing RNA secondary structures is hard. J. Comput. Biol. 27(3), 302\u2013316 (2020)","journal-title":"J. Comput. Biol."},{"key":"10_CR7","doi-asserted-by":"publisher","unstructured":"Bose, R., Saleem, I., Mustoe, A.M.: Causes, functions, and therapeutic possibilities of RNA secondary structure ensembles and alternative states. Cell Chem. Biol. 31(1), 17\u201335 (2024). https:\/\/doi.org\/10.1016\/j.chembiol.2023.12.010, https:\/\/www.sciencedirect.com\/science\/article\/pii\/S2451945623004403","DOI":"10.1016\/j.chembiol.2023.12.010"},{"issue":"1","key":"10_CR8","doi-asserted-by":"publisher","first-page":"351","DOI":"10.1093\/nar\/26.1.351","volume":"26","author":"JW Brown","year":"1998","unstructured":"Brown, J.W.: The ribonuclease p database. Nucl. Acids Res. 26(1), 351\u2013352 (1998)","journal-title":"Nucl. Acids Res."},{"key":"10_CR9","doi-asserted-by":"crossref","unstructured":"Cannone, J.J., et al.: The comparative RNA web (CRW) site: an online database of comparative sequence and structure information for ribosomal, intron, and other RNAs. BioMed Cent. Bioinform. 3(2) (2002)","DOI":"10.1186\/1471-2105-3-2"},{"key":"10_CR10","doi-asserted-by":"publisher","unstructured":"Che\u0142kowska-Pauszek, A., Kosi\u0144ski, J.G., Marciniak, K., Wysocka, M., B\u0105kowska-\u017bywicka, K., \u017bywicki, M.: The role of rna secondary structure in regulation of gene expression in bacteria. Int. J. Mol. Sci. 22(15) (2021). https:\/\/doi.org\/10.3390\/ijms22157845, https:\/\/www.mdpi.com\/1422-0067\/22\/15\/7845","DOI":"10.3390\/ijms22157845"},{"issue":"17","key":"10_CR11","doi-asserted-by":"publisher","first-page":"3508","DOI":"10.1093\/nar\/22.17.3508","volume":"22","author":"SH Damberger","year":"1994","unstructured":"Damberger, S.H., Gutell, R.R.: A comparative database of group i intron structures. Nucl. Acids Res. 22(17), 3508\u20133510 (1994)","journal-title":"Nucl. Acids Res."},{"issue":"14","key":"10_CR12","doi-asserted-by":"publisher","first-page":"e90","DOI":"10.1093\/bioinformatics\/btl246","volume":"22","author":"C Do","year":"2006","unstructured":"Do, C., Woods, D., Batzoglou, S.: CONTRAfold: RNA secondary structure prediction without physics-based models. Bioinformatics 22(14), e90\u2013e98 (2006)","journal-title":"Bioinformatics"},{"issue":"1\u20132","key":"10_CR13","doi-asserted-by":"publisher","first-page":"1285","DOI":"10.1177\/026010608700500206","volume":"5","author":"HH Gan","year":"1987","unstructured":"Gan, H.H., et al.: Rag: rna-as-graphs database-concepts, analysis, and features. Nutr. Health 5(1\u20132), 1285\u20131291 (1987)","journal-title":"Nutr. Health"},{"issue":"11","key":"10_CR14","doi-asserted-by":"publisher","first-page":"2926","DOI":"10.1093\/nar\/gkg365","volume":"31","author":"HH Gan","year":"2003","unstructured":"Gan, H.H., Pasquali, S., Schlick, T.: Exploring the repertoire of rna secondary motifs using graph theory; implications for rna design. Nucl. Acids Res. 31(11), 2926\u20132943 (2003)","journal-title":"Nucl. Acids Res."},{"issue":"02","key":"10_CR15","doi-asserted-by":"publisher","first-page":"1350001","DOI":"10.1142\/S0219720013500017","volume":"11","author":"JA Garcia-Martin","year":"2013","unstructured":"Garcia-Martin, J.A., Clote, P., Dotu, I.: RNAiFOLD: a constraint programming algorithm for RNA inverse folding and molecular design. J. Bioinform. Comput. Biol. 11(02), 1350001 (2013)","journal-title":"J. Bioinform. Comput. Biol."},{"issue":"17","key":"10_CR16","doi-asserted-by":"publisher","first-page":"3502","DOI":"10.1093\/nar\/22.17.3502","volume":"22","author":"RR Gutell","year":"1994","unstructured":"Gutell, R.R.: Collection of small subunit (16s-and 16s-like) ribosomal RNA structures: 1994. Nucl. Acids Res. 22(17), 3502\u20133507 (1994)","journal-title":"Nucl. Acids Res."},{"key":"10_CR17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"231","DOI":"10.1007\/978-3-319-19929-0_20","volume-title":"Combinatorial Pattern Matching","author":"J Hale\u0161","year":"2015","unstructured":"Hale\u0161, J., Ma\u0148uch, J., Ponty, Y., Stacho, L.: Combinatorial RNA design: designability and structure-approximating algorithm. In: Cicalese, F., Porat, E., Vaccaro, U. (eds.) CPM 2015. LNCS, vol. 9133, pp. 231\u2013246. Springer, Cham (2015). https:\/\/doi.org\/10.1007\/978-3-319-19929-0_20"},{"issue":"14","key":"10_CR18","doi-asserted-by":"publisher","first-page":"i295","DOI":"10.1093\/bioinformatics\/btz375","volume":"35","author":"L Huang","year":"2019","unstructured":"Huang, L., et al.: Linearfold: linear-time approximate rna folding by 5\u2019-to-3\u2019dynamic programming and beam search. Bioinformatics 35(14), i295\u2013i304 (2019)","journal-title":"Bioinformatics"},{"issue":"5","key":"10_CR19","doi-asserted-by":"publisher","first-page":"1129","DOI":"10.1016\/j.jmb.2004.06.054","volume":"341","author":"N Kim","year":"2004","unstructured":"Kim, N., Shiffeldrim, N., Gan, H.H., Schlick, T.: Candidates for novel rna topologies. J. Mol. Biol. 341(5), 1129\u20131144 (2004)","journal-title":"J. Mol. Biol."},{"key":"10_CR20","doi-asserted-by":"crossref","unstructured":"Koodli, R.V., Rudolfs, B., Wayment-Steele, H.K., Designers, E.S., Das, R.: Redesigning the EteRNA100 for the Vienna 2 folding engine. BioRxiv, pp. 2021\u201308 (2021)","DOI":"10.1101\/2021.08.26.457839"},{"issue":"5","key":"10_CR21","doi-asserted-by":"publisher","first-page":"461","DOI":"10.1016\/0010-4809(89)90039-6","volume":"22","author":"SY Le","year":"1989","unstructured":"Le, S.Y., Nussinov, R., Maizel, J.V.: Tree graphs of rna secondary structures and their comparisons. Comput. Biomed. Res. 22(5), 461\u2013473 (1989)","journal-title":"Comput. Biomed. Res."},{"issue":"3","key":"10_CR22","doi-asserted-by":"publisher","first-page":"279","DOI":"10.1016\/j.sbi.2006.05.009","volume":"16","author":"NB Leontis","year":"2006","unstructured":"Leontis, N.B., Lescoute, A., Westhof, E.: The building blocks and motifs of rna architecture. Curr. Opin. Struct. Biol. 16(3), 279\u2013287 (2006)","journal-title":"Curr. Opin. Struct. Biol."},{"key":"10_CR23","doi-asserted-by":"crossref","unstructured":"Lorenz, R., et al.: ViennaRNA package 2.0. Algorithms Mol. Biol. 6(1), 1 (2011)","DOI":"10.1186\/1748-7188-6-26"},{"key":"10_CR24","doi-asserted-by":"crossref","unstructured":"Mathews, D.H., Disney, M.D., Childs, J.L., Schroeder, S.J., Zuker, M., Turner, D.H.: Incorporating chemical modification constraints into a dynamic programming algorithm for prediction of RNA secondary structure. Proc. Nat. Acad. Sci. U.S.A. 101(19), 7287\u20137292 (2004)","DOI":"10.1073\/pnas.0401799101"},{"key":"10_CR25","doi-asserted-by":"crossref","unstructured":"Portela, F.: An unexpectedly effective Monte Carlo technique for the RNA inverse folding problem. BioRxiv, p. 345587 (2018)","DOI":"10.1101\/345587"},{"issue":"2","key":"10_CR26","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1261\/rna.030049.111","volume":"18","author":"E Rivas","year":"2012","unstructured":"Rivas, E., Lang, R., Eddy, S.R.: A range of complex probabilistic models for rna secondary structure prediction that includes the nearest-neighbor model and more. RNA 18(2), 193\u2013212 (2012)","journal-title":"RNA"},{"issue":"1","key":"10_CR27","doi-asserted-by":"publisher","first-page":"148","DOI":"10.1093\/nar\/26.1.148","volume":"26","author":"M Sprinzl","year":"1998","unstructured":"Sprinzl, M., Horn, C., Brown, M., Ioudovitch, A., Steinberg, S.: Compilation of trna sequences and sequences of trna genes. Nucl. Acids Res. 26(1), 148\u2013153 (1998)","journal-title":"Nucl. Acids Res."},{"issue":"1","key":"10_CR28","doi-asserted-by":"publisher","first-page":"156","DOI":"10.1093\/nar\/26.1.156","volume":"26","author":"M Szymanski","year":"1998","unstructured":"Szymanski, M., Specht, T., Barciszewska, M.Z., Barciszewski, J., Erdmann, V.A.: 5s RRNA data bank. Nucl. Acids Res. 26(1), 156\u2013159 (1998)","journal-title":"Nucl. Acids Res."},{"key":"10_CR29","doi-asserted-by":"crossref","unstructured":"Turner, D.H., Mathews, D.H.: NNDB: the nearest neighbor parameter database for predicting stability of nucleic acid secondary structure. Nucl. Acids Res. 38(suppl_1), D280\u2013D282 (2010)","DOI":"10.1093\/nar\/gkp892"},{"key":"10_CR30","doi-asserted-by":"crossref","unstructured":"Ward, M., Courtney, E., Rivas, E.: Fitness Functions for RNA Structure Design. bioRxiv (2022)","DOI":"10.1101\/2022.06.16.496369"},{"issue":"21","key":"10_CR31","doi-asserted-by":"publisher","first-page":"4298","DOI":"10.1093\/bioinformatics\/btz222","volume":"35","author":"M Ward","year":"2019","unstructured":"Ward, M., Sun, H., Datta, A., Wise, M., Mathews, D.H.: Determining parameters for non-linear models of multi-loop free energy change. Bioinformatics 35(21), 4298\u20134306 (2019)","journal-title":"Bioinformatics"},{"issue":"10","key":"10_CR32","doi-asserted-by":"publisher","first-page":"1234","DOI":"10.1038\/s41592-022-01605-0","volume":"19","author":"HK Wayment-Steele","year":"2022","unstructured":"Wayment-Steele, H.K., et al.: Rna secondary structure packages evaluated and improved by high-throughput experiments. Nat. Methods 19(10), 1234\u20131242 (2022)","journal-title":"Nat. Methods"},{"key":"10_CR33","unstructured":"Yao, H.T.: Local decomposition in RNA structural design. Ph.D. thesis, McGill University (Canada) (2021)"},{"key":"10_CR34","doi-asserted-by":"crossref","unstructured":"Yao, H.T., Chauve, C., Regnier, M., Ponty, Y.: Exponentially few RNA structures are designable. In: Proceedings of the 10th ACM International Conference on Bioinformatics, Computational Biology and Health Informatics, pp. 289\u2013298 (2019)","DOI":"10.1145\/3307339.3342163"},{"issue":"3","key":"10_CR35","doi-asserted-by":"publisher","first-page":"439","DOI":"10.1002\/jcc.21633","volume":"32","author":"JN Zadeh","year":"2010","unstructured":"Zadeh, J.N., Wolfe, B.R., Pierce, N.A.: Nucleic acid sequence design via efficient ensemble defect optimization. J. Comput. Chem. 32(3), 439\u2013452 (2010)","journal-title":"J. Comput. Chem."},{"key":"10_CR36","doi-asserted-by":"crossref","unstructured":"Zhou, T., Dai, N., Li, S., Ward, M., Mathews, D.H., Huang, L.: RNA design via structure-aware multifrontier ensemble optimization. Bioinformatics 39(Supplement_1), i563\u2013i571 (2023)","DOI":"10.1093\/bioinformatics\/btad252"},{"key":"10_CR37","doi-asserted-by":"crossref","unstructured":"Zhou, T., Tang, W.Y., Mathews, D.H., Huang, L.: Undesignable RNA Structure Identification via Rival Structure Generation and Structure Decomposition. To appear in Proceedings of RECOMB 2024 (2024). https:\/\/arxiv.org\/pdf\/2311.08339.pdf","DOI":"10.1007\/978-1-0716-3989-4_17"},{"key":"10_CR38","doi-asserted-by":"crossref","unstructured":"Zorn, J., Gan, H.H., Shiffeldrim, N., Schlick, T.: Structural motifs in ribosomal rnas: implications for rna design and genomics. Biopolym.: Orig. Res. Biomol. 73(3), 340\u2013347 (2004)","DOI":"10.1002\/bip.10525"},{"issue":"6","key":"10_CR39","doi-asserted-by":"publisher","first-page":"747","DOI":"10.1261\/rna.069203.118","volume":"25","author":"J Zuber","year":"2019","unstructured":"Zuber, J., Mathews, D.H.: Estimating uncertainty in predicted folding free energy changes of rna secondary structures. RNA 25(6), 747\u2013754 (2019)","journal-title":"RNA"},{"issue":"1","key":"10_CR40","doi-asserted-by":"publisher","first-page":"169","DOI":"10.1093\/nar\/28.1.169","volume":"28","author":"C Zwieb","year":"2000","unstructured":"Zwieb, C., Wower, J.: tmRDB (tmRNA database). Nucl. Acids Res. 28(1), 169\u2013170 (2000)","journal-title":"Nucl. Acids Res."}],"container-title":["Lecture Notes in Computer Science","Research in Computational Molecular Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-90252-9_10","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,24]],"date-time":"2025-04-24T20:03:26Z","timestamp":1745525006000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-90252-9_10"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025]]},"ISBN":["9783031902512","9783031902529"],"references-count":40,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-90252-9_10","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025]]},"assertion":[{"value":"25 April 2025","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"Our source code is available at . Our server is available at .","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Availability"}},{"value":"RECOMB","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Research in Computational Molecular Biology","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Seoul","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Korea (Republic of)","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2025","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"26 April 2025","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"29 April 2025","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"29","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"recomb2025","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/recomb.org\/recomb2025\/index.html","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}