{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,12]],"date-time":"2026-03-12T01:09:54Z","timestamp":1773277794135,"version":"3.50.1"},"reference-count":28,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2016,10,19]],"date-time":"2016-10-19T00:00:00Z","timestamp":1476835200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2016,10,19]],"date-time":"2016-10-19T00:00:00Z","timestamp":1476835200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DBI-1262439"],"award-info":[{"award-number":["DBI-1262439"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["BMC Bioinformatics"],"abstract":"<jats:title>Abstract<\/jats:title><jats:sec>\n                <jats:title>Background<\/jats:title>\n                <jats:p>RNA inverse folding is the problem of finding one or more sequences that fold into a user-specified target structure <jats:italic>s<\/jats:italic><jats:sub>0<\/jats:sub>, i.e. whose minimum free energy secondary structure is identical to the target <jats:italic>s<\/jats:italic><jats:sub>0<\/jats:sub>. Here we consider the ensemble of all RNA sequences that have low free energy with respect to a given target <jats:italic>s<\/jats:italic><jats:sub>0<\/jats:sub>.<\/jats:p>\n              <\/jats:sec><jats:sec>\n                <jats:title>Results<\/jats:title>\n                <jats:p>We introduce the program , which computes the <jats:italic>dual partition function<\/jats:italic><jats:italic>Z<\/jats:italic><jats:sup>\u2217<\/jats:sup>, defined as the sum of Boltzmann factors exp(\u2212<jats:italic>E<\/jats:italic>(<jats:bold>a,s<\/jats:bold><jats:sub>0<\/jats:sub>)\/<jats:italic>RT<\/jats:italic>) of all RNA nucleotide sequences <jats:bold>a<\/jats:bold> compatible with target structure <jats:italic>s<\/jats:italic><jats:sub>0<\/jats:sub>. Using , we efficiently sample RNA sequences that approximately fold into <jats:italic>s<\/jats:italic><jats:sub>0<\/jats:sub>, where additionally the user can specify IUPAC sequence constraints at certain positions, and whether to include dangles (energy terms for stacked, single-stranded nucleotides). Moreover, since we also compute the <jats:italic>dual partition function<\/jats:italic><jats:italic>Z<\/jats:italic><jats:sup>\u2217<\/jats:sup>(<jats:italic>k<\/jats:italic>) over all sequences having GC-content <jats:italic>k<\/jats:italic>, the user can require that all sampled sequences have a precise, specified GC-content.<\/jats:p>\n                <jats:p>Using <jats:italic>Z<\/jats:italic><jats:sup>\u2217<\/jats:sup>, we compute the <jats:italic>dual expected energy<\/jats:italic> \u2329<jats:italic>E<\/jats:italic><jats:sup>\u2217<\/jats:sup>\u232a, and use it to show that natural RNAs from the  12.0 database have <jats:italic>higher<\/jats:italic> minimum free energy than expected, thus suggesting that functional RNAs are under evolutionary pressure to be only marginally thermodynamically stable.<\/jats:p>\n                <jats:p>We show that <jats:italic>C. elegans<\/jats:italic> precursor microRNA (pre-miRNA) is significantly <jats:italic>non-robust<\/jats:italic> with respect to mutations, by comparing the robustness of each wild type pre-miRNA sequence with 2000 [resp. 500] sequences of the same GC-content generated by , which approximately [resp. exactly] fold into the wild type target structure. We confirm and strengthen earlier findings that precursor microRNAs and bacterial small noncoding RNAs display plasticity, a measure of structural diversity.<\/jats:p>\n              <\/jats:sec><jats:sec>\n                <jats:title>Conclusion<\/jats:title>\n                <jats:p>We describe , which rapidly computes the <jats:italic>dual partition function<\/jats:italic><jats:italic>Z<\/jats:italic><jats:sup>\u2217<\/jats:sup> and samples sequences having low energy with respect to a target structure, allowing sequence constraints and specified GC-content. Using different inverse folding software, another group had earlier shown that pre-miRNA is mutationally robust, even controlling for compositional bias. Our opposite conclusion suggests a cautionary note that computationally based insights into molecular evolution may heavily depend on the software used.<\/jats:p>\n                <jats:p>C\/C++-software for  is available at <jats:ext-link xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" ext-link-type=\"uri\" xlink:href=\"http:\/\/bioinformatics.bc.edu\/clotelab\/RNAdualPF\">http:\/\/bioinformatics.bc.edu\/clotelab\/RNAdualPF<\/jats:ext-link>.<\/jats:p>\n              <\/jats:sec>","DOI":"10.1186\/s12859-016-1280-6","type":"journal-article","created":{"date-parts":[[2016,10,19]],"date-time":"2016-10-19T02:10:24Z","timestamp":1476843024000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["RNAdualPF: software to compute the dual partition function with sample applications in molecular evolution theory"],"prefix":"10.1186","volume":"17","author":[{"given":"Juan Antonio","family":"Garcia-Martin","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Amir H.","family":"Bayegan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ivan","family":"Dotu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peter","family":"Clote","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2016,10,19]]},"reference":[{"issue":"17","key":"1280_CR1","doi-asserted-by":"publisher","first-page":"6593","DOI":"10.1073\/pnas.0510600103","volume":"103","author":"E Borenstein","year":"2006","unstructured":"Borenstein E, Ruppin E. Direct evolution of genetic robustness in microRNA. Proc Natl Acad Sci. 2006; 103(17):6593\u2013598. doi:10.1073\/pnas.0510600103.","journal-title":"Proc Natl Acad Sci"},{"key":"1280_CR2","doi-asserted-by":"publisher","first-page":"26","DOI":"10.1186\/1748-7188-6-26","volume":"6","author":"R Lorenz","year":"2011","unstructured":"Lorenz R, Bernhart SH, Honer Zu Siederdissen C, Tafer H, Flamm C, Stadler PF, Hofacker IL. ViennaRNA Package 2.0. Algorithms Mol Biol. 2011; 6:26. doi:10.1186\/1748-7188-6-26.","journal-title":"Algorithms Mol Biol"},{"issue":"1","key":"1280_CR3","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/1471-2148-12-52","volume":"12","author":"G Rodrigo","year":"2012","unstructured":"Rodrigo G, Fares MA. Describing the structural robustness landscape of bacterial small RNAs. BMC Evol Biol. 2012; 12(1):1\u201312. doi:10.1186\/1471-2148-12-52 2148-12-52","journal-title":"BMC Evol Biol"},{"issue":"W1","key":"1280_CR4","doi-asserted-by":"publisher","first-page":"513","DOI":"10.1093\/nar\/gkv460","volume":"43","author":"JA Garcia-Martin","year":"2015","unstructured":"Garcia-Martin JA, Dotu I, Clote P. RNAiFold 2.0: a web server and software to design custom and rfam-based RNA molecules. Nucleic Acids Res. 2015; 43(W1):513\u201321. doi:10.1093\/nar\/gkv460.","journal-title":"Nucleic Acids Res"},{"key":"1280_CR5","unstructured":"Los Alamos HIV database. 2015. http:\/\/www.hiv.lanl.gov\/. Accessed 30 Dec 2015."},{"issue":"40","key":"1280_CR6","doi-asserted-by":"publisher","first-page":"42230","DOI":"10.1074\/jbc.M404931200","volume":"279","author":"J Krol","year":"2004","unstructured":"Krol J, Sobczak K, Wilczynska U, Drath M, Jasinska A, Kaczynska D, Krzyzosiak WJ. Structural features of microRNA (miRNA) precursors and their relevance to mirna biogenesis and small interfering RNA\/short hairpin RNA design. J Biol Chem. 2004; 279(40):42230\u20132239. doi:10.1074\/jbc.M404931200.","journal-title":"J Biol Chem"},{"key":"1280_CR7","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1007\/BF00818163","volume":"125","author":"IL Hofacker","year":"1994","unstructured":"Hofacker IL, Fontana W, Stadler PF, Bonhoeffer LS, Tacker M, Schuster P. Fast folding and comparison of RNA secondary structures. Monatsch Chem. 1994; 125:167\u201388.","journal-title":"Monatsch Chem"},{"issue":"3","key":"1280_CR8","doi-asserted-by":"publisher","first-page":"439","DOI":"10.1002\/jcc.21633","volume":"32","author":"JN Zadeh","year":"2011","unstructured":"Zadeh JN, Wolfe BR, Pierce NA. Nucleic acid sequence design via efficient ensemble defect optimization. J Comput Chem. 2011; 32(3):439\u201352.","journal-title":"J Comput Chem"},{"issue":"2","key":"1280_CR9","doi-asserted-by":"publisher","first-page":"1350001","DOI":"10.1142\/S0219720013500017","volume":"11","author":"JA Garcia-Martin","year":"2013","unstructured":"Garcia-Martin JA, Clote P, Dotu I. RNAiFold: a constraint programming algorithm for RNA inverse folding and molecular design. J Bioinform Comput Biol. 2013; 11(2):1350001. doi:10.1142\/S0219720013500017.","journal-title":"J Bioinform Comput Biol"},{"key":"1280_CR10","doi-asserted-by":"publisher","first-page":"0","DOI":"10.1093\/nar\/gkh449","volume":"32","author":"Y Ding","year":"2004","unstructured":"Ding Y, Chan CY, Lawrence CE. Sfold web server for statistical folding and rational design of nucleic acids. Nucleic Acids Res. 2004; 32:0.","journal-title":"Nucleic Acids Res"},{"issue":"Database","key":"1280_CR11","doi-asserted-by":"publisher","first-page":"68","DOI":"10.1093\/nar\/gkt1181","volume":"42","author":"A Kozomara","year":"2014","unstructured":"Kozomara A, Griffiths-Jones S. mirbase: annotating high confidence microRNAs using deep sequencing data. Nucleic Acids Res. 2014; 42(Database):68\u201373. doi:24275495.","journal-title":"Nucleic Acids Res"},{"issue":"13","key":"1280_CR12","doi-asserted-by":"publisher","first-page":"308","DOI":"10.1093\/bioinformatics\/btt217","volume":"29","author":"V Reinharz","year":"2013","unstructured":"Reinharz V, Ponty Y, Waldispuhl J. A weighted sampling algorithm for the design of RNA sequences with targeted secondary structure and nucleotide distribution. Bioinformatics. 2013; 29(13):308\u201315.","journal-title":"Bioinformatics"},{"issue":"Database","key":"1280_CR13","doi-asserted-by":"publisher","first-page":"280","DOI":"10.1093\/nar\/gkp892","volume":"38","author":"DH Turner","year":"2010","unstructured":"Turner DH, Mathews DH. NNDB: the nearest neighbor parameter database for predicting stability of nucleic acid secondary structure. Nucleic Acids Res. 2010; 38(Database):280\u20132. doi:10.1093\/nar\/gkp892.","journal-title":"Nucleic Acids Res"},{"issue":"1","key":"1280_CR14","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/1471-2105-9-122","volume":"9","author":"AR Gruber","year":"2008","unstructured":"Gruber AR, Bernhart SH, Hofacker IL, Washietl S. Strategies for measuring evolutionary conservation of RNA secondary structures. BMC Bioinforma. 2008; 9(1):1\u201319. doi:10.1186\/1471-2105-9-122.","journal-title":"BMC Bioinforma"},{"key":"1280_CR15","doi-asserted-by":"publisher","first-page":"1105","DOI":"10.1002\/bip.360290621","volume":"29","author":"JS McCaskill","year":"1990","unstructured":"McCaskill JS. The equilibrium partition function and base pair binding probabilities for RNA secondary structure. Biopolymers. 1990; 29:1105\u20131119. doi:10.1002\/bip.360290621.","journal-title":"Biopolymers"},{"key":"1280_CR16","doi-asserted-by":"publisher","first-page":"7280","DOI":"10.1093\/nar\/gkg938","volume":"31","author":"Y Ding","year":"2003","unstructured":"Ding Y, Lawrence CE. A statistical sampling algorithm for RNA secondary structure prediction. Nucleic Acids Res. 2003; 31:7280\u2013301.","journal-title":"Nucleic Acids Res"},{"issue":"15","key":"1280_CR17","doi-asserted-by":"publisher","first-page":"1823","DOI":"10.1093\/bioinformatics\/btl194","volume":"22","author":"A Busch","year":"2006","unstructured":"Busch A, Backofen R. INFO-RNA, a fast approach to inverse RNA folding. Bioinformatics. 2006; 22(15):1823\u201331. doi:10.1093\/bioinformatics\/btl194.","journal-title":"Bioinformatics"},{"key":"1280_CR18","volume-title":"RNA Biochemistry and Biotechnology. NATO ASI Series","author":"M Zuker","year":"1999","unstructured":"Zuker M, Mathews DH, Turner DH. Algorithms and thermodynamics for RNA secondary structure prediction: A practical guide In: Barciszewski J, Clark BFC, editors. RNA Biochemistry and Biotechnology. NATO ASI Series. Dordrecht: Kluwer Academic Publishers: 1999. p. 11\u201343."},{"issue":"1","key":"1280_CR19","doi-asserted-by":"publisher","first-page":"439","DOI":"10.1093\/nar\/gkg006","volume":"31","author":"S Griffiths-Jones","year":"2003","unstructured":"Griffiths-Jones S, Bateman A, Marshall M, Khanna A, Eddy SR. Rfam: an RNA family database. Nucleic Acids Res. 2003; 31(1):439\u201341.","journal-title":"Nucleic Acids Res"},{"issue":"4","key":"1280_CR20","doi-asserted-by":"publisher","first-page":"1392","DOI":"10.1093\/nar\/gkh291","volume":"32","author":"RM Dirks","year":"2004","unstructured":"Dirks RM, Lin M, Winfree E, Pierce NA. Paradigms for computational nucleic acid design. Nucleic Acids Res. 2004; 32(4):1392\u20131403. doi:10.1093\/nar\/gkh291.","journal-title":"Nucleic Acids Res"},{"issue":"1","key":"1280_CR21","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/s12864-014-1203-8","volume":"16","author":"S Pei","year":"2015","unstructured":"Pei S, Anthony JS, Meyer MM. Sampled ensemble neutrality as a feature to classify potential structured RNAs. BMC Genomics. 2015; 16(1):1\u201312. doi:10.1186\/s12864-014-1203-8.","journal-title":"BMC Genomics"},{"issue":"5","key":"1280_CR22","doi-asserted-by":"publisher","first-page":"1104","DOI":"10.1006\/jmbi.1997.0889","volume":"267","author":"M Huynen","year":"1997","unstructured":"Huynen M, Gutell R, Konings D. Assessing the reliability of RNA folding using statistical mechanics. J Mol Biol. 1997; 267(5):1104\u201312. doi:10.1006\/jmbi.1997.0889.","journal-title":"J Mol Biol"},{"key":"1280_CR23","doi-asserted-by":"publisher","first-page":"3153","DOI":"10.1088\/0305-4470\/31\/14\/005","volume":"31","author":"SR Morgan","year":"1998","unstructured":"Morgan SR, Higgs PG. Barrier heights between ground states in a model of RNA secondary structure. J Phys A: Math Gen. 1998; 31:3153\u2013170. doi:10.1088\/0305-4470\/31\/14\/005.","journal-title":"J Phys A: Math Gen"},{"issue":"D1","key":"1280_CR24","doi-asserted-by":"publisher","first-page":"130","DOI":"10.1093\/nar\/gku1063","volume":"43","author":"EP Nawrocki","year":"2015","unstructured":"Nawrocki EP, Burge SW, Bateman A, Daub J, Eberhardt RY, Eddy SR, Floden EW, Gardner PP, Jones TA, Tate J, Finn RD. Rfam 12.0: updates to the RNA families database. Nucleic Acids Res. 2015; 43(D1):130\u20137. doi:10.1093\/nar\/gku1063.","journal-title":"Nucleic Acids Res"},{"issue":"1","key":"1280_CR25","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. Nucleic Acids Res. 1998; 26(1):148\u201353. doi:10.1093\/nar\/26.1.148.","journal-title":"Nucleic Acids Res"},{"issue":"Database","key":"1280_CR26","doi-asserted-by":"publisher","first-page":"159","DOI":"10.1093\/nar\/gkn772","volume":"37","author":"F Juhling","year":"2009","unstructured":"Juhling F, Morl M, Hartmann RK, Sprinzl M, Stadler PF, Putz J. tRNAdb 2009: compilation of tRNA sequences and tRNA genes. Nucleic Acids Res. 2009; 37(Database):159\u201362.","journal-title":"Nucleic Acids Res"},{"issue":"11","key":"1280_CR27","doi-asserted-by":"publisher","first-page":"0137859","DOI":"10.1371\/journal.pone.0137859","volume":"10","author":"JA Garcia-Martin","year":"2015","unstructured":"Garcia-Martin JA, Clote P. RNA Thermodynamic Structural Entropy. PLoS ONE. 2015; 10(11):0137859. doi:10.1371\/journal.pone.0137859.","journal-title":"PLoS ONE"},{"key":"1280_CR28","unstructured":"Garcia-Martin JA. RNA inverse folding and synthetic design. Ph.D. dissertation in Biology, Boston College. 2016. Dissertation made available on June 28, 2016 and will remain accessible indefinitely: http:\/\/hdl.handle.net\/2345\/bc-ir:106989."}],"container-title":["BMC Bioinformatics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s12859-016-1280-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1186\/s12859-016-1280-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s12859-016-1280-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,1]],"date-time":"2024-02-01T18:24:36Z","timestamp":1706811876000},"score":1,"resource":{"primary":{"URL":"https:\/\/bmcbioinformatics.biomedcentral.com\/articles\/10.1186\/s12859-016-1280-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,10,19]]},"references-count":28,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2016,12]]}},"alternative-id":["1280"],"URL":"https:\/\/doi.org\/10.1186\/s12859-016-1280-6","relation":{},"ISSN":["1471-2105"],"issn-type":[{"value":"1471-2105","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,10,19]]},"assertion":[{"value":"24 May 2016","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 September 2016","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 October 2016","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"424"}}