{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,31]],"date-time":"2026-10-31T19:59:09Z","timestamp":1793476749506,"version":"4.5.0"},"reference-count":49,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2023,7,29]],"date-time":"2023-07-29T00:00:00Z","timestamp":1690588800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2023,7,29]],"date-time":"2023-07-29T00:00:00Z","timestamp":1690588800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100002428","name":"Austrian Science Fund","doi-asserted-by":"publisher","award":["I 4520"],"award-info":[{"award-number":["I 4520"]}],"id":[{"id":"10.13039\/501100002428","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002428","name":"Austrian Science Fund","doi-asserted-by":"publisher","award":["F 80"],"award-info":[{"award-number":["F 80"]}],"id":[{"id":"10.13039\/501100002428","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["STA 850\/48-1"],"award-info":[{"award-number":["STA 850\/48-1"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Austrian Science Fund"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Algorithms Mol Biol"],"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:sec>\n                    <jats:title>Background<\/jats:title>\n                    <jats:p>RNA features a highly negatively charged phosphate backbone that attracts a cloud of counter-ions that reduce the electrostatic repulsion in a concentration dependent manner. Ion concentrations thus have a large influence on folding and stability of RNA structures. Despite their well-documented effects, salt effects are not handled consistently by currently available secondary structure prediction algorithms. Combining Debye-H\u00fcckel potentials for line charges and Manning\u2019s counter-ion condensation theory, Einert et al. (Biophys J 100: 2745-2753, 2011) modeled the energetic contributions of monovalent cations on loops and helices.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Results<\/jats:title>\n                    <jats:p>The model of Einert et al. is adapted to match the structure of the dynamic programming recursion of RNA secondary structure prediction algorithms. An empirical term describing the salt dependence of the duplex initiation energy is added to improve co-folding predictions for two or more RNA strands. The slightly modified model is implemented in the  package in such way that only the energy parameters but not the algorithmic structure is affected. A comparison with data from the literature show that predicted free energies and melting temperatures are in reasonable agreement with experiments.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Conclusion<\/jats:title>\n                    <jats:p>The new feature in the  package makes it possible to study effects of salt concentrations on RNA folding in a systematic manner. Strictly speaking, the model pertains only to mono-valent cations, and thus covers the most important parameter, i.e., the NaCl concentration. It remains a\u00a0question for\u00a0future research to what extent unspecific effects of bi- and tri-valent cations can be approximated in a similar manner.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Availability<\/jats:title>\n                    <jats:p>Corrections for the concentration of monovalent cations are available in the  package starting from version 2.6.0.<\/jats:p>\n                  <\/jats:sec>","DOI":"10.1186\/s13015-023-00236-0","type":"journal-article","created":{"date-parts":[[2023,7,29]],"date-time":"2023-07-29T04:02:14Z","timestamp":1690603334000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Mono-valent salt corrections for RNA secondary structures in the ViennaRNA package"],"prefix":"10.1186","volume":"18","author":[{"given":"Hua-Ting","family":"Yao","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ronny","family":"Lorenz","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ivo L.","family":"Hofacker","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Peter F.","family":"Stadler","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2023,7,29]]},"reference":[{"key":"236_CR1","doi-asserted-by":"publisher","first-page":"813","DOI":"10.1146\/annurev-biochem-060409-092720","volume":"83","author":"J Lipfert","year":"2014","unstructured":"Lipfert J, Doniach S, Das RD, Herschlag D. Understanding nucleic acid-ion interactions. Annu Rev Biochem. 2014;83:813\u201341. https:\/\/doi.org\/10.1146\/annurev-biochem-060409-092720.","journal-title":"Annu Rev Biochem"},{"key":"236_CR2","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1146\/annurev.biophys.26.1.113","volume":"26","author":"P Brion","year":"1997","unstructured":"Brion P, Westhof E. Hierarchy and dynamics of RNA folding. Annu Rev Biophys Biomol Struct. 1997;26:113\u201337. https:\/\/doi.org\/10.1146\/annurev.biophys.26.1.113.","journal-title":"Annu Rev Biophys Biomol Struct"},{"key":"236_CR3","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. Nucl Acids Res. 2010;38:280\u20132. https:\/\/doi.org\/10.1093\/nar\/gkp892.","journal-title":"Nucl Acids Res"},{"key":"236_CR4","doi-asserted-by":"publisher","unstructured":"Fornace ME, Huang J, Newman CT, Porubsky NJ, Pierce MB, Pierce NA. NUPACK: Analysis and design of nucleic acid structures, devices, and systems. Technical report, chemRxiv. https:\/\/doi.org\/10.26434\/chemrxiv-2022-xv98l","DOI":"10.26434\/chemrxiv-2022-xv98l"},{"key":"236_CR5","unstructured":"Markham NR, Zuker LS, Zuker M. The UNAFold Web Server \u2013 Quikfold. http:\/\/www.unafold.org\/Dinamelt\/applications\/quickfold.php. Accessed 07 May 2023."},{"key":"236_CR6","doi-asserted-by":"publisher","first-page":"1460","DOI":"10.1073\/pnas.95.4.1460","volume":"95","author":"J SantaLucia Jr","year":"1998","unstructured":"SantaLucia J Jr. A unified view of polymer, dumbbell, and oligonucleotide DNA nearest-neighbor thermodynamics. Proc Natl Acad Sci USA. 1998;95:1460\u20135. https:\/\/doi.org\/10.1073\/pnas.95.4.1460.","journal-title":"Proc Natl Acad Sci USA"},{"issue":"16","key":"236_CR7","doi-asserted-by":"publisher","first-page":"3333","DOI":"10.1093\/bioinformatics\/bti530","volume":"21","author":"RT Koehler","year":"2005","unstructured":"Koehler RT, Peyret N. Thermodynamic properties of DNA sequences: characteristic values for the human genome. Bioinformatics. 2005;21(16):3333\u20139. https:\/\/doi.org\/10.1093\/bioinformatics\/bti530.","journal-title":"Bioinformatics"},{"key":"236_CR8","doi-asserted-by":"publisher","first-page":"4912","DOI":"10.1093\/nar\/gkl472","volume":"34","author":"ZJ Lu","year":"2006","unstructured":"Lu ZJ, Turner DH, Mathews DH. A set of nearest neighbor parameters for predicting the enthalpy change of RNA secondary structure formation. Nucleic Acids Res. 2006;34:4912\u201324. https:\/\/doi.org\/10.1093\/nar\/gkl472.","journal-title":"Nucleic Acids Res"},{"key":"236_CR9","doi-asserted-by":"publisher","first-page":"335","DOI":"10.1261\/rna.5205404","volume":"10","author":"DE Draper","year":"2004","unstructured":"Draper DE. A guide to ions and RNA structure. RNA. 2004;10:335\u201343. https:\/\/doi.org\/10.1261\/rna.5205404.","journal-title":"RNA"},{"key":"236_CR10","doi-asserted-by":"publisher","first-page":"5489","DOI":"10.1529\/biophysj.108.131813","volume":"95","author":"DE Draper","year":"2008","unstructured":"Draper DE. RNA folding: Thermodynamic and molecular descriptions of the roles of ions. Biophysical J. 2008;95:5489\u201395. https:\/\/doi.org\/10.1529\/biophysj.108.131813.","journal-title":"Biophysical J"},{"issue":"42","key":"236_CR11","doi-asserted-by":"publisher","first-page":"7477","DOI":"10.1021\/bi4008275","volume":"52","author":"Z Chen","year":"2013","unstructured":"Chen Z, Znosko BM. Effect of sodium ions on RNA duplex stability. Biochemistry. 2013;52(42):7477\u201385. https:\/\/doi.org\/10.1021\/bi4008275.","journal-title":"Biochemistry"},{"key":"236_CR12","doi-asserted-by":"publisher","DOI":"10.1038\/14940","author":"K Chin","year":"1999","unstructured":"Chin K, Sharp KA, Honig B, Pyle AM. Calculating the electrostatic properties of RNA provides new insights into molecular interactions and function. Nat Struct Biol. 1999. https:\/\/doi.org\/10.1038\/14940.","journal-title":"Nat Struct Biol."},{"key":"236_CR13","doi-asserted-by":"publisher","first-page":"1135","DOI":"10.1006\/jmbi.1999.3334","volume":"294","author":"VK Misra","year":"1999","unstructured":"Misra VK, Draper DE. The interpretation of Mg(2+) binding isotherms for nucleic acids using Poisson-Boltzmann theory. J Mol Biol. 1999;294:1135\u201347. https:\/\/doi.org\/10.1006\/jmbi.1999.3334.","journal-title":"J Mol Biol"},{"key":"236_CR14","doi-asserted-by":"publisher","first-page":"507","DOI":"10.1006\/jmbi.2002.5422","volume":"317","author":"VK Misra","year":"2002","unstructured":"Misra VK, Draper DE. The linkage between magnesium binding and RNA folding. J Mol Biol. 2002;317:507\u201321. https:\/\/doi.org\/10.1006\/jmbi.2002.5422.","journal-title":"J Mol Biol"},{"key":"236_CR15","doi-asserted-by":"publisher","first-page":"133","DOI":"10.1093\/nar\/9.1.133","volume":"9","author":"M Zuker","year":"1981","unstructured":"Zuker M, Stiegler P. Optimal computer folding of large RNA sequences using thermodynamics and auxiliary information. Nucleic Acids Res. 1981;9:133\u201348. https:\/\/doi.org\/10.1093\/nar\/9.1.133.","journal-title":"Nucleic Acids Res"},{"issue":"10","key":"236_CR16","doi-asserted-by":"publisher","first-page":"3615","DOI":"10.1529\/biophysj.106.100388","volume":"92","author":"Z-J Tan","year":"2007","unstructured":"Tan Z-J, Chen S-J. RNA helix stability in mixed $$\\text{ Na}^{+}$$\/$$\\text{ Mg}^{+}$$ solution. Biophys J. 2007;92(10):3615\u201332. https:\/\/doi.org\/10.1529\/biophysj.106.100388.","journal-title":"Biophys J"},{"issue":"2","key":"236_CR17","doi-asserted-by":"publisher","first-page":"738","DOI":"10.1529\/biophysj.108.131524","volume":"95","author":"Z-J Tan","year":"2008","unstructured":"Tan Z-J, Chen S-J. Salt dependence of nucleic acid hairpin stability. Biophys J. 2008;95(2):738\u201352. https:\/\/doi.org\/10.1529\/biophysj.108.131524.","journal-title":"Biophys J"},{"key":"236_CR18","doi-asserted-by":"publisher","first-page":"1884","DOI":"10.1261\/rna.2109105","volume":"11","author":"S Cao","year":"2005","unstructured":"Cao S, Chen S-J. Predicting RNA folding thermodynamics with a reduced chain representation model. RNA. 2005;11:1884\u201397. https:\/\/doi.org\/10.1261\/rna.2109105.","journal-title":"RNA"},{"key":"236_CR19","doi-asserted-by":"publisher","DOI":"10.1063\/1.1842059","volume":"122","author":"Z-J Tan","year":"2005","unstructured":"Tan Z-J, Chen S-JC. Electrostatic correlations and fluctuations for ion binding to a finite length polyelectrolyte. J Chem Phys. 2005;122: 044903. https:\/\/doi.org\/10.1063\/1.1842059.","journal-title":"J Chem Phys"},{"key":"236_CR20","doi-asserted-by":"publisher","first-page":"2745","DOI":"10.1016\/j.bpj.2011.04.038","volume":"100","author":"TR Einert","year":"2011","unstructured":"Einert TR, Netz RR. Theory for RNA folding, stretching, and melting including loops and salt. Biophys J. 2011;100:2745\u201353. https:\/\/doi.org\/10.1016\/j.bpj.2011.04.038.","journal-title":"Biophys J"},{"key":"236_CR21","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1007\/978-3-642-94260-0_9","volume":"24","author":"E Debye","year":"1923","unstructured":"Debye E. Peter und H\u00fcckel: Zur Theorie der Elektrolyte. Physik Z. 1923;24:185\u2013206. https:\/\/doi.org\/10.1007\/978-3-642-94260-0_9.","journal-title":"Physik Z"},{"key":"236_CR22","doi-asserted-by":"publisher","first-page":"6297","DOI":"10.1103\/PhysRevE.53.6297","volume":"53","author":"M Mazars","year":"1996","unstructured":"Mazars M. Statistical physics of the freely jointed chain. Phys Rev E. 1996;53:6297\u2013319. https:\/\/doi.org\/10.1103\/PhysRevE.53.6297.","journal-title":"Phys Rev E"},{"key":"236_CR23","doi-asserted-by":"publisher","first-page":"924","DOI":"10.1063\/1.1672157","volume":"51","author":"GS Manning","year":"1969","unstructured":"Manning GS. Limiting laws and counterion condensation in polyelectrolyte solutions I. Colligative properties. J Chem Phys. 1969;51:924\u201333. https:\/\/doi.org\/10.1063\/1.1672157.","journal-title":"J Chem Phys"},{"key":"236_CR24","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.66.011918","volume":"66","author":"K-K Kunze","year":"2002","unstructured":"Kunze K-K, Netz RR. Complexes of semiflexible polyelectrolytes and charged spheres as models for salt-modulated nucleosomal structures. Phys Rev E. 2002;66: 011918. https:\/\/doi.org\/10.1103\/PhysRevE.66.011918.","journal-title":"Phys Rev E"},{"key":"236_CR25","doi-asserted-by":"publisher","first-page":"14003","DOI":"10.1073\/pnas.06064091","volume":"103","author":"D Grilley","year":"2006","unstructured":"Grilley D, Soto AM, Draper DE. $$\\text{ Mg}^{+}$$-RNA interaction free energies and their relationship to the folding of RNA tertiary structures. Proc Natl Acad Sci USA. 2006;103:14003\u20138. https:\/\/doi.org\/10.1073\/pnas.06064091.","journal-title":"Proc Natl Acad Sci USA"},{"key":"236_CR26","doi-asserted-by":"publisher","unstructured":"Lorenz R, Bernhart SH, H\u00f6ner\u00a0zu Siederdissen C, Tafer H, Flamm C, Stadler PF, Hofacker IL. ViennaRNA Package 2.0. Alg Mol Biol 2011;6:26. https:\/\/doi.org\/10.1186\/1748-7188-6-26","DOI":"10.1186\/1748-7188-6-26"},{"key":"236_CR27","doi-asserted-by":"publisher","first-page":"1600","DOI":"10.1063\/1.1747547","volume":"18","author":"H Jacobson","year":"1950","unstructured":"Jacobson H, Stockmayer WH. Intramolecular reaction in polycondensations. I. The theory of linear systems. J Chem Phys. 1950;18:1600\u20136. https:\/\/doi.org\/10.1063\/1.1747547.","journal-title":"J Chem Phys."},{"issue":"2","key":"236_CR28","doi-asserted-by":"publisher","first-page":"513","DOI":"10.1042\/BST20120324","volume":"41","author":"SD Levene","year":"2013","unstructured":"Levene SD, Giovan SM, Hanke A, Shoura MJ. The thermodynamics of DNA loop formation, from J to Z. Biochem Soc Trans. 2013;41(2):513\u20138. https:\/\/doi.org\/10.1042\/BST20120324.","journal-title":"Biochem Soc Trans"},{"key":"236_CR29","doi-asserted-by":"publisher","first-page":"8541","DOI":"10.1093\/nar\/gkx512","volume":"45","author":"M Ward","year":"2017","unstructured":"Ward M, Datta A, Wise M, Mathews DH. Advanced multi-loop algorithms for RNA secondary structure prediction reveal that the simplest model is best. Nucleic Acids Res. 2017;45:8541\u201350. https:\/\/doi.org\/10.1093\/nar\/gkx512.","journal-title":"Nucleic Acids Res"},{"key":"236_CR30","doi-asserted-by":"publisher","first-page":"340","DOI":"10.1186\/1471-2105-9-340","volume":"9","author":"M Andronescu","year":"2008","unstructured":"Andronescu M, Bereg V, Hoos HH, Condon A. RNA STRAND: the RNA secondary structure and statistical analysis database. BMC Bioinformatics. 2008;9:340. https:\/\/doi.org\/10.1186\/1471-2105-9-340.","journal-title":"BMC Bioinformatics"},{"key":"236_CR31","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1186\/s13660-017-1317-z","volume":"2017","author":"Z-H Yang","year":"2017","unstructured":"Yang Z-H, Chu Y-M. On approximating the modified Bessel function of the second kind. J Inequal Appl. 2017;2017:41. https:\/\/doi.org\/10.1186\/s13660-017-1317-z.","journal-title":"J Inequal Appl."},{"key":"236_CR32","doi-asserted-by":"publisher","first-page":"9373","DOI":"10.1073\/pnas.83.24.9373","volume":"83","author":"SM Freier","year":"1986","unstructured":"Freier SM, Kierzek R, Jaeger JA, Sugimoto N, Caruthers MH, Neilson T, Turner DH. Improved free-energy parameters for predictions of RNA duplex stability. Proc Natl Acad Sci USA. 1986;83:9373\u20137. https:\/\/doi.org\/10.1073\/pnas.83.24.9373.","journal-title":"Proc Natl Acad Sci USA"},{"key":"236_CR33","volume-title":"Methods and programs for mathematical functions","author":"SL Moshier","year":"1989","unstructured":"Moshier SL. Methods and programs for mathematical functions. Hoboken, NJ: Prentice-Hall; 1989."},{"key":"236_CR34","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.93.025010","volume":"93","author":"E Tiesinga","year":"2021","unstructured":"Tiesinga E, Mohr PJ, Newell DB, Taylor BN. CODATA recommended values of the fundamental physical constants: 2018. Rev Mod Phys. 2021;93: 025010. https:\/\/doi.org\/10.1103\/RevModPhys.93.025010.","journal-title":"Rev Mod Phys"},{"key":"236_CR35","doi-asserted-by":"publisher","first-page":"669","DOI":"10.1016\/S0009-2614(02)01735-9","volume":"367","author":"A Catenaccio","year":"2003","unstructured":"Catenaccio A, Daruich Y, Magallanes C. Temperature dependence of the permittivity of water. Chem Phys Lett. 2003;367:669\u201371. https:\/\/doi.org\/10.1016\/S0009-2614(02)01735-9.","journal-title":"Chem Phys Lett"},{"issue":"2","key":"236_CR36","doi-asserted-by":"publisher","first-page":"175","DOI":"10.1016\/0168-1702(85)90247-3","volume":"2","author":"P Taylor","year":"1985","unstructured":"Taylor P, Rixon F, Desselberger U. Rise per base pair in helices of double-stranded rotavirus RNA determined by electron microscopy. Virus Res. 1985;2(2):175\u201382. https:\/\/doi.org\/10.1016\/0168-1702(85)90247-3.","journal-title":"Virus Res"},{"issue":"5784","key":"236_CR37","doi-asserted-by":"publisher","first-page":"755","DOI":"10.1038\/287755a0","volume":"287","author":"R Wing","year":"1980","unstructured":"Wing R, Drew H, Takano T, Broka C, Tanaka S, Itakura K, Dickerson RE. Crystal structure analysis of a complete turn of B-DNA. Nature. 1980;287(5784):755\u20138. https:\/\/doi.org\/10.1038\/287755a0.","journal-title":"Nature"},{"issue":"5","key":"236_CR38","doi-asserted-by":"publisher","first-page":"1072","DOI":"10.1016\/j.physa.2012.09.022","volume":"392","author":"Q Chi","year":"2013","unstructured":"Chi Q, Wang G, Jiang J. The persistence length and length per base of single-stranded DNA obtained from fluorescence correlation spectroscopy measurements using mean field theory. Physica A Stat Mech Appl. 2013;392(5):1072\u20139. https:\/\/doi.org\/10.1016\/j.physa.2012.09.022.","journal-title":"Physica A Stat Mech Appl"},{"issue":"12","key":"236_CR39","doi-asserted-by":"publisher","first-page":"3537","DOI":"10.1021\/bi034621r","volume":"43","author":"R Owczarzy","year":"2004","unstructured":"Owczarzy R, You Y, Moreira BG, Manthey JA, Huang L, Behlke MA, Walder JA. Effects of sodium ions on DNA duplex oligomers: improved predictions of melting temperatures. Biochemistry. 2004;43(12):3537\u201354. https:\/\/doi.org\/10.1021\/bi034621r.","journal-title":"Biochemistry"},{"key":"236_CR40","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1016\/j.chemphys.2019.01.016","volume":"521","author":"I Ferreira","year":"2019","unstructured":"Ferreira I, Jolley EA, Znosko BM, Weber G. Replacing salt correction factors with optimized RNA nearest-neighbour enthalpy and entropy parameters. Chem Phys. 2019;521:69\u201376. https:\/\/doi.org\/10.1016\/j.chemphys.2019.01.016.","journal-title":"Chem Phys"},{"issue":"2","key":"236_CR41","doi-asserted-by":"publisher","first-page":"486","DOI":"10.1093\/nar\/gkl1073","volume":"35","author":"S-I Nakano","year":"2007","unstructured":"Nakano S-I, Kirihata T, Fujii S, Sakai H, Kuwahara M, Sawai H, Sugimoto N. Influence of cationic molecules on the hairpin to duplex equilibria of self-complementary DNA and RNA oligonucleotides. Nucleic Acids Res. 2007;35(2):486\u201394. https:\/\/doi.org\/10.1093\/nar\/gkl1073.","journal-title":"Nucleic Acids Res"},{"issue":"46","key":"236_CR42","doi-asserted-by":"publisher","first-page":"14665","DOI":"10.1021\/bi961654g","volume":"35","author":"DJ Williams","year":"1996","unstructured":"Williams DJ, Hall KB. Thermodynamic comparison of the salt dependence of natural RNA hairpins and RNA hairpins with non-nucleotide spacers. Biochemistry. 1996;35(46):14665\u201370. https:\/\/doi.org\/10.1021\/bi961654g.","journal-title":"Biochemistry"},{"issue":"2","key":"236_CR43","doi-asserted-by":"publisher","first-page":"742","DOI":"10.1021\/bi00428a049","volume":"28","author":"DR Groebe","year":"1989","unstructured":"Groebe DR, Uhlenbeck OC. Thermal stability of RNA hairpins containing a four-membered loop and a bulge nucleotide. Biochemistry. 1989;28(2):742\u20137. https:\/\/doi.org\/10.1021\/bi00428a049.","journal-title":"Biochemistry"},{"issue":"42","key":"236_CR44","doi-asserted-by":"publisher","first-page":"14719","DOI":"10.1021\/bi9809425","volume":"37","author":"T Xia","year":"1998","unstructured":"Xia T, SantaLucia J Jr, Burkard ME, Kierzek R, Schroeder SJ, Jiao X, Cox C, Turner DH. Thermodynamic parameters for an expanded nearest-neighbor model for formation of RNA duplexes with Watson-Crick base pairs. Biochemistry. 1998;37(42):14719\u201335. https:\/\/doi.org\/10.1021\/bi9809425.","journal-title":"Biochemistry"},{"key":"236_CR45","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1186\/1748-7188-1-3","volume":"1","author":"SH Bernhart","year":"2006","unstructured":"Bernhart SH, Tafer H, M\u00fcckstein U, Flamm C, Stadler PF, Hofacker IL. Partition function and base pairing probabilities of RNA heterodimers. Algorithms Mol Biol. 2006;1:3. https:\/\/doi.org\/10.1186\/1748-7188-1-3.","journal-title":"Algorithms Mol. Biol."},{"key":"236_CR46","unstructured":"Lorenz R, Flamm C, Hofacker IL, Stadler PF. Efficient algorithms for co-folding of multiple RNAs. In: Ye X, Soares F, De\u00a0Maria E, G\u00f3mez\u00a0Vilda P, Cabitza F, Fred A, Gamboa H. (eds.) Biomedical Engineering Systems and Technologies. BIOSTEC 2020. Communications in Computer and Information Science, Cham: Springer, p. 1400,"},{"key":"236_CR47","doi-asserted-by":"publisher","first-page":"21022","DOI":"10.1073\/pnas.1911632116","volume":"116","author":"HT Nguyen","year":"2019","unstructured":"Nguyen HT, Hori N, Thirumalai D. Theory and simulations for RNA folding in mixtures of monovalent and divalent cations. Proc Natl Acad Sci. 2019;116:21022\u201330. https:\/\/doi.org\/10.1073\/pnas.1911632116.","journal-title":"Proc Natl Acad Sci"},{"key":"236_CR48","doi-asserted-by":"publisher","first-page":"38","DOI":"10.3389\/fchem.2016.00038","volume":"4","author":"D Bhattacharyya","year":"2016","unstructured":"Bhattacharyya D, Arachchilage GM, Basu S. Metal cations in G-quadruplex folding and stability. Front Chem Sec Chem Biol. 2016;4:38. https:\/\/doi.org\/10.3389\/fchem.2016.00038.","journal-title":"Front Chem Sec Chem Biol"},{"key":"236_CR49","doi-asserted-by":"publisher","unstructured":"Lorenz R, Bernhart SH, Qin J, H\u00f6ner\u00a0zu Siederdissen C, Tanzer A, Amman F, Hofacker IL, Stadler PF. 2D meets 4G: G-quadruplexes in RNA secondary structure prediction. IEEE Trans Comp Biol Bioinf. 2013;10:832\u2013844. https:\/\/doi.org\/10.1109\/TCBB.2013.7","DOI":"10.1109\/TCBB.2013.7"}],"container-title":["Algorithms for Molecular Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s13015-023-00236-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1186\/s13015-023-00236-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s13015-023-00236-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,7,29]],"date-time":"2023-07-29T04:03:48Z","timestamp":1690603428000},"score":1,"resource":{"primary":{"URL":"https:\/\/almob.biomedcentral.com\/articles\/10.1186\/s13015-023-00236-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7,29]]},"references-count":49,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2023,12]]}},"alternative-id":["236"],"URL":"https:\/\/doi.org\/10.1186\/s13015-023-00236-0","relation":{"has-preprint":[{"id-type":"doi","id":"10.21203\/rs.3.rs-2775511\/v1","asserted-by":"object"},{"id-type":"doi","id":"10.1101\/2023.04.07.536000","asserted-by":"object"}]},"ISSN":["1748-7188"],"issn-type":[{"value":"1748-7188","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,7,29]]},"assertion":[{"value":"4 April 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 July 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 July 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"Not applicable.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethics approval and consent to participate"}},{"value":"Not applicable.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent for publication"}},{"value":"The authors declare that they have no competing interests.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"8"}}