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Twist-stretch relations in nucleic acids

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Abstract

Nucleic acids are highly deformable helical molecules constantly stretched, twisted and bent in their biological functioning. Single molecule experiments have shown that double stranded (ds)-RNA and standard ds-DNA have opposite twist-stretch patterns and stretching properties when overwound under a constant applied load. The key structural features of the A-form RNA and B-form DNA helices are here incorporated in a three-dimensional mesoscopic Hamiltonian model which accounts for the radial, bending and twisting fluctuations of the base pairs. Using path integral techniques which sum over the ensemble of the base pair fluctuations, I compute the average helical repeat of the molecules as a function of the load. The obtained twist-stretch relations and stretching properties, for short A- and B-helical fragments, are consistent with the opposite behaviors observed in kilo-base long molecules.

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Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Notes

  1. This holds if, in the experimental setup, only two ends of the strands are anchored. Instead, the over-stretching transition is shifted to \(\sim 110\) pN when all four ends of the strands are anchored so that the helix is torsionally constrained.

  2. As the long term stability of physiological B-DNA is required in a multitude of applications, dehydration conditions are routinely employed e.g, in methods for digital information storage (Grass et al. 2015). On the other hand, dehydration may structurally transform DNA, unwind the helix and ultimately lead to unwanted denaturation effects (Ghoshdastidar and Senapati 2018).

  3. The presence of a hydroxyl group bound to the 2’ carbon of the ribose ring is the key reason forcing RNA to coil into the A-form (Fohrer et al. 2006)

References

  • Apostolaki A, Kalosakas G (2011) Targets of DNA-binding proteins in bacterial promoter regions present enhanced probabilities for spontaneous thermal openings. Phys Biol 8:026006

    Article  PubMed  Google Scholar 

  • Balcerak A, Trebinska-Stryjewska A, Konopinski R, Wakula M, Grzybowska EA (2019) RNA-protein interactions: disorder, moonlighting and junk contribute to eukaryotic complexity. Open Biol 9:190096

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Bao L, Zhang X, Jin L, Tan ZJ (2016) Flexibility of nucleic acids: from DNA to RNA. Chin Phys B 25:018703

    Article  Google Scholar 

  • Barbi M, Cocco S, Peyrard M (1999) Helicoidal model for DNA opening. Phys Lett A 253:358

    Article  CAS  Google Scholar 

  • Biton YY (2018) Effects of Protein-Induced Local Bending and Sequence Dependence on the Configurations of Supercoiled DNA Minicircles. J Chem Theory Comput 14:2063–2075

    Article  CAS  PubMed  Google Scholar 

  • Bongini L, Melli L, Lombardi V, Bianco P (2014) Transient kinetics measured with force steps discriminate between double-stranded DNA elongation and melting and define the reaction energetics. Nucleic Acids Res 42:3436–3449

    Article  CAS  PubMed  Google Scholar 

  • Bosaeus N, El-Sagheer AH, Brown T, Åkerman B, Nordèn B (2014) Force-induced melting of DNA-evidence for peeling and internal melting from force spectra on short synthetic duplex sequences. Nucleic Acids Res 42:8083–8091

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Calladine CR, Drew HR (1992) Understanding DNA. Academic Press, San Diego

    Google Scholar 

  • Campa A, Giansanti A (1998) Experimental tests of the Peyrard-Bishop model applied to the melting of very short DNA chains. Phys Rev E 58:3585–3588

    Article  CAS  Google Scholar 

  • Choi SR, Kim NH, Jin HS, Seo YJ, Lee J, Lee JH (2019) Base-pair opening dynamics of nucleic acids in relation to their biological function. Comput Struct Biotech J 17:797–804

    Article  CAS  Google Scholar 

  • Cloutier TE, Widom J (2004) Spontaneous sharp bending of double-stranded DNA. Mol Cell 14:355–362

    Article  CAS  PubMed  Google Scholar 

  • Cluzel P, Lebrun A, Heller C, Lavery R, Viovy JL, Chatenay D, Caron F (1996) DNA: an extensible molecule. Science 271:792–794

    Article  CAS  PubMed  Google Scholar 

  • Dauxois T, Peyrard M, Bishop AR (1993) Entropy driven DNA denaturation. Phys Rev E 47:R44–R47

    Article  CAS  Google Scholar 

  • Dickerson RE (1983) The DNA helix and how it is read. Sci Am 249:94–111

    Article  CAS  Google Scholar 

  • Drukker K, Wu G, Schatz GC (2001) Model simulations of DNA denaturation dynamics. J Chem Phys 114:579–590

    Article  CAS  Google Scholar 

  • Faustino I, Pérez A, Orozco M (2010) Toward a consensus view of duplex RNA flexibility. Biophys J 99:1876–1885

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Feynman RP, Hibbs AR (1965) Quantum mechanics and path integrals. Mc Graw-Hill, New York

    Google Scholar 

  • Fohrer J, Hennig M, Carlomagno T (2006) Influence of the 2’-hydroxyl group conformation on the stability of A-form helices in RNA. J Mol Biol 356:280–287

    Article  CAS  PubMed  Google Scholar 

  • Franklin RE, Gosling RG (1953) Molecular configuration in sodium thymonucleate. Nature 171:740–741

    Article  CAS  PubMed  Google Scholar 

  • Garai A, Saurabh S, Lansac Y, Maiti PK (2015) DNA Elasticity from Short DNA to Nucleosomal DNA. J Phys Chem B 119:11146–11156

    Article  CAS  PubMed  Google Scholar 

  • Ghoshdastidar D, Senapati S (2018) Dehydrated DNA in B-form: ionic liquids in rescue. Nucleic Acids Res 46:4344–4353

    Article  PubMed  PubMed Central  Google Scholar 

  • Gore J, Bryant Z, Nöllmann M, Le MU, Cozzarelli NR, Bustamante C (2006) DNA overwinds when stretched. Nature 442:836–839

    Article  CAS  PubMed  Google Scholar 

  • Grass RN, Heckel R, Puddu M, Paunescu D, Stark WJ (2015) Robust chemical preservation of digital information on DNA in silica with error-correcting codes. Angew Chem Int Ed 54:2552

    Article  CAS  Google Scholar 

  • Herrero-Galàn E, Fuentes-Perez ME, Carrasco C, Valpuesta JM, Carrascosa JL, Moreno-Herrero F, Arias-Gonzalez JR (2013) Mechanical identities of RNA and DNA double helices unveiled at the single-molecule level. J Am Chem Soc 135:122–131

    Article  PubMed  Google Scholar 

  • Hillebrand M, Kalosakas G, Skokos Ch, Bishop AR (2020) Distributions of bubble lifetimes and bubble lengths in DNA. Phys Rev E 102:062114

    Article  CAS  PubMed  Google Scholar 

  • Hudson WH, Ortlund EA (2014) The structure, function and evolution of proteins that bind DNA and RNA. Nat Rev Mol Cell Biol 15:749–760

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Kiianitsa K, Stasiak A (1997) Helical repeat of DNA in the region of homologous pairing. Proc Natl Acad Sci USA 94:7837–7840

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Kleinert H (2004) Path Integrals in Quantum Mechanics, Statistics, Polymer Physycs and Financial Markets, ( World Scientific Publishing, Singapore )

  • Kosikov KM, Gorin AA, Zhurkin VB, Olson WK (1999) DNA stretching and compression: large-scale simulations of double helical structures. J Mol Biol 289:1301–1326

    Article  CAS  PubMed  Google Scholar 

  • Lam PM, Zhen Y (2017) Cyclization of short DNA fragments. Phys A 482:569

    Article  CAS  Google Scholar 

  • Lankas̆ F, S̆pac̆ková N, Moakher M, Enkhbayar P, S̆poner J, (2010) A measure of bending in nucleic acids structures applied to A-tract DNA. Nucleic Acids Res 38:3414–3422

  • Le TT, Kim HD (2014) Probing the elastic limit of DNA bending. Nucleic Acids Res 42:10786–10794

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Léger JF, Romano G, Sarkar A, Robert J, Bourdieu L, Chatenay D, Marko JF (1999) Structural transitions of a twisted and stretched DNA molecule. Phys Rev Lett 83:1066

    Article  Google Scholar 

  • Liebl K, Drsata T, Lankas̆ F, Lipfert J, Zacharias M, (2015) Explaining the striking difference in twist-stretch coupling between DNA and RNA: a comparative molecular dynamics analysis. Nucleic Acid Res 43:10143–10156

  • Lionnet T, Joubaud S, Lavery R, Bensimon D, Croquette V (2006) Wringing out DNA. Phys Rev Lett 96:178102

    Article  PubMed  Google Scholar 

  • Lipfert J, Skinner GM, Keegstra JM, Hensgens T, Jager T, Dulin D, Köber M, Yu Z, Donkers SP, Chou FC, Das R, Dekker NH (2014) Double-stranded RNA under force and torque: similarities to and striking differences from double-stranded DNA. Proc Natl Acad Sci USA 111:15408–15413

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Macedo DX, Guedes I, Albuquerque EL (2014) Thermal properties of a DNA denaturation with solvent interaction. Phys A 404:234–241

    Article  CAS  Google Scholar 

  • Marko JF (2015) Biophysics of protein-DNA interactions and chromosome organization. Phys A 418:126–153

    Article  CAS  Google Scholar 

  • Noy A, Golestanian R (2012) Length scale dependence of DNA mechanical properties. Phys Rev Lett 109:228101

    Article  PubMed  Google Scholar 

  • Olsen K, Bohr J (2011) The geometrical origin of the strain-twist coupling in double helices. AIP Adv 1:012108

    Article  Google Scholar 

  • Peyrard M, Bishop AR (1989) Statistical mechanics of a nonlinear model for DNA denaturation. Phys Rev Lett 62:2755

    Article  CAS  PubMed  Google Scholar 

  • Peyrard M, Cuesta-López S, James G (2009) Nonlinear analysis of the dynamics of DNA breathing. J Biol Phys 35:73

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Romano F, Chakraborty D, Doye JPK, Ouldridge TE, Louis AA (2013) Coarse-grained simulations of DNA overstretching. J Chem Phys 138:085101

    Article  PubMed  Google Scholar 

  • Rouzina I, Bloomfield VA (2001) Force-Induced Melting of the DNA Double Helix 1. Thermodynamic analysis. Biophys J 80:882–893

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Royer A (1984) On the Fourier series representations of path integrals. J Math Phys 25:2873

    Article  Google Scholar 

  • Santosh M, Maiti PK (2009) Force induced DNA melting. J Phys Condens Matter 21:034113

    Article  PubMed  Google Scholar 

  • Singh A, Singh N (2015) Effect of salt concentration on the stability of heterogeneous DNA. Phys A 419:328–334

    Article  CAS  Google Scholar 

  • Smith S, Finzi L, Bustamante C (1992) Direct mechanical measurement of the elasticity of single DNA molecules by using magnetic beads. Science 258:1122–1126

    Article  CAS  PubMed  Google Scholar 

  • Sulaiman A, Zen FP, Alatas H, Handoko LT (2012) The thermal denaturation of the Peyrard-Bishop model with an external potential. Phys Scr 86:015802

    Article  Google Scholar 

  • Vafabakhsh R, Ha T (2012) Extreme Bendability of DNA Less than 100 Base Pairs Long Revealed by Single-Molecule Cyclization. Science 337:1097–1101

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • van Eijck L, Merzel F, Rols S, Ollivier J, Forsyth VT, Johnson MR (2011) Direct determination of the base-pair force constant of DNA from the acoustic phonon dispersion of the double helix. Phys Rev Lett 107:088102

    Article  PubMed  Google Scholar 

  • van Mameren J, Gross P, Farge G, Hooijman P, Modesti M, Falkenberg M, Wuite GJL, Peterman EJG (2009) Unraveling the structure of DNA during overstretching by using multicolor, single-molecule fluorescence imaging. Proc Natl Acad Sci USA 106:18231–18236

    Article  PubMed  PubMed Central  Google Scholar 

  • Wang JC (1979) Helical repeat of DNA in solution. Proc Natl Acad Sci USA 76:200–203

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Wang MD, Yin H, Landick R, Gelles J, Block SM (1997) Stretching DNA with optical tweezers. Biophys J 72:1335–1346

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Wartell RM, Benight AS (1985) Thermal denaturation of DNA molecules: a comparison of theory with experiment. Phys Rep 126:67–107

    Article  CAS  Google Scholar 

  • Weber G (2013) Mesoscopic model parametrization of hydrogen bonds and stacking interactions of RNA from melting temperatures. Nucleic Acids Res 41:e30

    Article  CAS  PubMed  Google Scholar 

  • Wiggins PA, Heijden TVD, Moreno-Herrero F, Spakowitz A, Phillips R, Widom J, Dekker C, Nelson PC (2006) High flexibility of DNA on short length scales probed by atomic force microscopy. Nat Nanotechnol 1:137

    Article  CAS  PubMed  Google Scholar 

  • Wu YY, Bao L, Zhang X, Tan ZJ (2015) Flexibility of short DNA helices with finite-length effect: from base pairs to tens of base pairs. J Chem Phys 142:125103

    Article  PubMed  Google Scholar 

  • Yuan C, Rhoades E, Lou XW, Archer LA (2006) Spontaneous sharp bending of DNA: role of melting bubbles. Nucleic Acids Res 34:4554–4560

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Zdravković S, Satarić MV (2001) The impact of viscosity on the DNA dynamics. Phys Scr 64:612

    Article  Google Scholar 

  • Zgarbová M, Otyepka M, Sponer J, Lankas̆ F, Jurecka P, (2014) Base pair fraying in molecular dynamics simulations of DNA and RNA. J Chem Theory Comput 10:3177–3189

  • Zhang F, Collins MA (1995) Model simulations of DNA dynamics. Phys Rev E 52:4217

    Article  CAS  Google Scholar 

  • Zhang YL, Zheng WM, Liu JX, Chen YZ (1997) Theory of DNA melting based on the Peyrard-Bishop model. Phys Rev E 56:7100–7115

    Article  CAS  Google Scholar 

  • Zhang Y, He L, Li S (2023) Temperature dependence of DNA elasticity: an all-atom molecular dynamics simulation study. J Chem Phys 158:094902

    Article  CAS  PubMed  Google Scholar 

  • Zoli M (2003) Path integral description of a semiclassical Su-Schrieffer-Heeger model. Phys Rev B 67:195102

    Article  Google Scholar 

  • Zoli M (2005) Path integral of the two dimensional Su-Schrieffer-Heeger model. Phys Rev B 71:205111

    Article  Google Scholar 

  • Zoli M (2011) Stacking interactions in denaturation of DNA fragments. Eur Phys J E 34:68

    Article  CAS  PubMed  Google Scholar 

  • Zoli M (2014) Entropic penalties in circular DNA assembly. J Chem Phys 141:174112

    Article  PubMed  Google Scholar 

  • Zoli M (2014) Twist versus nonlinear stacking in short DNA molecules. J Theor Biol 354:95–104

    Article  CAS  PubMed  Google Scholar 

  • Zoli M (2016) J- factors of short DNA molecules. J Chem Phys 144:214104

    Article  PubMed  Google Scholar 

  • Zoli M (2016) Flexibility of short DNA helices under mechanical stretching. Phys Chem Chem Phys 18:17666

    Article  CAS  PubMed  Google Scholar 

  • Zoli M (2018) Short DNA persistence length in a mesoscopic helical model. EPL - Europhys Lett 123:68003

    Article  Google Scholar 

  • Zoli M (2018) End-to-end distance and contour length distribution functions of DNA helices. J Chem Phys 148:214902

    Article  PubMed  Google Scholar 

  • Zoli M (2019) DNA size in confined environments. Phys Chem Chem Phys 21:12566

    Article  CAS  PubMed  Google Scholar 

  • Zoli M (2020) Stretching DNA in hard-wall potential channels. EPL - Europhys Lett 130:28002

    Article  CAS  Google Scholar 

  • Zoli M (2020) First-passage probability: a test for DNA Hamiltonian parameters. Phys Chem Chem Phys 22:26901

    Article  CAS  PubMed  Google Scholar 

  • Zoli M (2021) Base pair fluctuations in helical models for nucleic acids. J Chem Phys 154:194102

    Article  CAS  PubMed  Google Scholar 

  • Zoli M (2022) Non-linear Hamiltonian models for DNA. Eur Biophys J 51:431–447

    Article  CAS  PubMed  Google Scholar 

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Zoli, M. Twist-stretch relations in nucleic acids. Eur Biophys J 52, 641–650 (2023). https://doi.org/10.1007/s00249-023-01669-6

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