Abstract
Transcription is the first step of gene expression, in which a particular segment of DNA is copied to RNA by the enzyme RNA polymerase (RNAP). Despite many details of the complex interactions between DNA and RNA synthesis disclosed experimentally, much of physical behavior of transcription remains largely unknown. Understanding torsional mechanics of DNA and RNAP together with its nascent RNA and RNA-bound proteins in transcription maybe the first step towards deciphering the mechanism of gene expression. In this study, based on the balance between viscous drag on RNA synthesis and torque resulted from untranscribed supercoiled DNA template, a simple model is presented to describe mechanical properties of transcription. With this model, the rotation and supercoiling density of the untranscribed DNA template are discussed in detail. Two particular cases of transcription are considered, transcription with constant velocity and transcription with torque dependent velocity. Our results show that, during the initial stage of transcription, rotation originated from the transcribed part of DNA template is mainly released by the rotation of RNAP synthesis. During the intermediate stage, the rotation is usually released by both the supercoiling of the untranscribed part of DNA template and the rotation of RNAP synthesis, with proportion depending on the friction coefficient in environment and the length of nascent RNA. However, with the approaching to the upper limit of twisting of the untranscribed DNA template, the rotation resulted from transcription will then be mainly released by the rotation of RNAP synthesis.
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References
Cooper, G.M.: The Cell: A Molecular Approach, 2nd edn. Sinauer Associates, Inc., Sunderland (2000)
Dehaseth, P.L., Zupancic, M.L., Record Jr., M.T.: RNA polymerase–promoter interactions: the comings and goings of RNA polymerase. J. Bacteriol. 180, 3019–3025 (1998)
Cheetham, G.M.T., Jeruzalmi, D., Steitz, T.A.: Structural basis for initiation of transcription from an RNA polymerase promoter complex. Nature 399, 80–83 (1999)
Watson, J.D., Baker, T.A., Bell, S.P., Gann, A.A., Levine, M., Losick, R.M.: Molecular Biology of the Gene, 7th edn. Pearson, London (2013)
Wilkins, M.H., Stokes, A.R., Wilson, H.R.: Molecular structure of deoxypentose nucleic acids. Nature 171(4356), 738–740 (1953)
Liu, L.F., Wang, J.C.: Supercoiling of the DNA template during transcription. Proc. Natl. Acad. Sci. 84(20), 7024–7027 (1987)
Giaever, G.N., Wang, J.C.: Supercoiling of intracellular DNA can occur in eukaryotic cells. Cell 55(5), 849–856 (1988)
Tsao, Y.P., Wu, H.Y., Liu, L.F.: Transcription-driven supercoiling of DNA: direct biochemical evidence from in vitro studies. Cell 56(1), 111–118 (1989)
Krasilnikov, A.S., Podtelezhnikov, A., Vologodskii, A., Mirkin, S.M.: Large-scale effects of transcriptional DNA supercoiling in vivo. J. Mol. Biol. 292(5), 1149–1160 (1999)
Harada, Y., Ohara, O., Takatsuki, A., Itoh, H., Shimamoto, N., Kinosita Jr., K.: Direct observation of DNA rotation during transcription by \(Escherichia coli\) RNA polymerase. Nature 409(6816), 113–115 (2001)
Kouzine, F., Liu, J., Sanford, S., Chung, H.J., Levens, D.: The dynamic response of upstream DNA to transcription-generated torsional stress. Nat. Struct. Mol. Biol. 11(11), 1092–1100 (2004)
Forth, S., Sheinin, M.Y., Inman, J., Wang, M.D.: Torque measurement at the single-molecule level. Ann. Rev. Biophys. 42(42), 583–604 (2013)
Ma, J., Wang, M.D.: DNA supercoiling during transcription. Biophys. Rev. 8(1), 75–87 (2016)
Rybenkov, V.V., Vologodskii, A.V., Cozzarelli, N.R.: The effect of ionic conditions on DNA helical repeat, effective diameter and free energy of supercoiling. Nucl. Acids Res. 25(7), 1412–1418 (1997)
Moroz, J.D., Nelson, P.: Torsional directed walks, entropic elasticity, and DNA twist stiffness. Proc. Natl. Acad. Sci. 94(26), 14418–14422 (1997)
Marko, F.J.: Torque and dynamics of linking number relaxation in stretched supercoiled DNA. Phys. Rev. E 76(2), 021926 (2007)
Lavelle, C.: Pack, unpack, bend, twist, pull, push: the physical side of gene expression. Curr. Opin. Genet. Dev. 25, 74–84 (2014)
Sevier, S.A., Levine, H.: Mechanical properties of transcription. Phys. Rev. Lett. 118(26), 268101 (2017)
Howard, J.: Mechanics of Motor Proteins and the Cytoskeleton. Sinauer Associates, Sunderland (2001)
Chong, S., Chen, C., Ge, H., Xie, X.S.: Mechanism of transcriptional bursting in bacteria. Cell 158(2), 314–326 (2014)
Müller, M.J.I., Klumpp, S., Lipowsky, R.: Tug-of-war as a cooperative mechanism for bidirectional cargo transport by molecular motors. Proc. Natl. Acad. Sci. 105, 4609–4614 (2008)
Kunwar, A., Mogilner, A.: Robust transport by multiple motors with nonlinear force–velocity relations and stochastic load sharing. Phys. Biol. 7(1), 16012 (2010)
Jie, J., Bai, L., Wang, M.D.: Transcription under torsion. Science 340(6140), 1580–1583 (2013)
Nicolas, D., Phillips, N.E., Naef, F.: What shapes eukaryotic transcriptional bursting? Mol. Biosyst. 13(2), 1280–1290 (2017)
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Communicated by Hal Tasaki.
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Xu, X., Zhang, Y. Theoretical Model of Transcription Based on Torsional Mechanics of DNA Template. J Stat Phys 174, 1316–1326 (2019). https://doi.org/10.1007/s10955-019-02236-0
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DOI: https://doi.org/10.1007/s10955-019-02236-0