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Impact of the topology of viral RNAs on their encapsulation by virus coat proteins

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Abstract

Single-stranded RNAs of simple viruses seem to be topologically more compact than other types of single-stranded RNA. It has been suggested that this has an evolutionary purpose: more compact structures are more easily encapsulated in the limited space that the cavity of the virus capsid offers. We employ a simple Flory theory to calculate the optimal amount of polymers confined in a viral shell. We find that the free energy gain or more specifically the efficiency of RNA encapsidation increases substantially with topological compactness. We also find that the optimal length of RNA encapsidated in a capsid increases with the degree of branching of the genome even though this effect is very weak. Further, we show that if the structure of the branching of the polymer is allowed to anneal, the optimal loading increases substantially.

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Notes

  1. The thickness of the ARM region depends on whether it makes contact with polyanionic cargo. See, e.g., [32].

References

  1. Chiu, W., Burnett, R.M., Garcea, R.L.: Structural Biology of Viruses, eds. Oxford University Press, Oxford (1997)

    Google Scholar 

  2. Caspar, D.L.D., Klug, A.: Physical principles in the construction of regular viruses. Quant. Biol. 27, 1–24 (1962)

    Article  Google Scholar 

  3. Fraenkel-Conrat, H., Williams, R.C.: Reconstitution of active tobacco mosaic virus from its inactive protein and nucleic acid components. Proc. Nat. Acad. Sci. USA 41, 690–698 (1955)

    Article  ADS  Google Scholar 

  4. McPherson, A.: Micelle formation and crystallization as paradigms for virus assembly. BioEssays 27, 447–458 (2005)

    Article  Google Scholar 

  5. Larson, S.B., McPherson, A.: Satellite tobacco mosaic virus RNA: structure and implications for assembly. Curr. Opin. Struck. Biol. 11, 59–65 (2001)

    Article  Google Scholar 

  6. Cuillel, M., Berthet-Colominas, C., Timmins, P.A., Zulauf, M.: Reassembly of brome mosaic virus from dissociated virus. Eur. Biophys J. 15, 169–176 (1987)

    Article  Google Scholar 

  7. Bancroft, J.B., Hiebert, E., Rees, M.W., Markham, R.: Properties of cowpea chlorotic mottle virus, its protein and nucleic acid. Virology 34, 224–239 (1968)

    Article  Google Scholar 

  8. Bancroft, J.B., Hiebert, E., Bracker, C.E.: The effects of various polyanions on shell formation of some spherical viruses. Virology 39, 924–930 (1969)

    Article  Google Scholar 

  9. Hiebert, E., Bancroft, J.B., Bracker, C.E.: The assembly in vitro of some small spherical viruses, hybrid viruses and other nucleoproteins. Virology 34, 492–508 (1968)

    Article  Google Scholar 

  10. Zlotnick, A.: To build a virus capsid: an equilibrium model of the self assembly of polyhedral protein complexes. J. Mol. Biol. 241, 59–67 (1994)

    Article  Google Scholar 

  11. Zlotnick, A., Aldrich, R., Johnson, J.M., Ceres, P., Young, M.J.: Mechanism of capsid assembly for an icosahedral plant virus. Virology 277, 450–456 (2000)

    Article  Google Scholar 

  12. Hu, Y., Zandi, R., Anavitarte, A., Knobler, C.M., Gelbart, W.M.: Packaging of a polymer by a viral capsid: the interplay between polymer length and capsid size. Biophys. J. 94, 1428–1436 (2008)

    Article  Google Scholar 

  13. Ren, Y., Wong, S.-M., Lim, L.-Y.: In vitro reassembled plant virus-like particles for loading of polyacids. J. Gen. Virol. 87, 2749–2754 (2006)

    Article  Google Scholar 

  14. Sikkema, F.D., Cornellas-Aragnones, M., Fokkink, R.G., Verduin, B.J.M., J.Cornelissen, J.L.M., Nolte, R.J.: Monodisperse polymer-virus hybrid nanoparticles. Org. Biomol. Chem. 5, 54–57 (2007)

    Article  Google Scholar 

  15. Tsvetkova, I., Chen, C., Rana, S., Kao, C., Rotello, V., Dragnea, B.: Pathway switching in templated virus-like particle assembly. Soft Matter 8, 4571–4576 (2012)

    Article  ADS  Google Scholar 

  16. Benjamin, J., Ganser-Pornillos, B.K., Tivol, W.F., Sundquist, W.I., Jensen, G.J.: Three-dimensional structure of HIV-1 virus-like particles by electron cryotomography. J. Mol. Biol. 346, 577–588 (2005)

    Article  Google Scholar 

  17. Briggs, J.A.G., Grunewald, K., Glass, B., Forster, F., Krausslich, H.-G., Fuller, S.D.: The mechanism of HIV-1 core assembly: insights from three-dimensional reconstructions of authentic virions. Structure (Lond.) 14, 15–20 (2006)

    Article  Google Scholar 

  18. Ganser, B.K., Li, S., Klishko, V.Y., Finch, J.T., Sundquist, W.I.: Assembly and analysis of conical models for the HIV-1 core. Science 283, 80–83 (1999)

    Article  ADS  Google Scholar 

  19. Nguyen, T.T., Bruinsma, R.F., Gelbart, W.M.: Continuum theory of retroviral capsids. Phys. Rev. Lett. 96, 078102 (2006)

    Article  ADS  Google Scholar 

  20. Nguyen, T.T., Bruinsma, R.F., Gelbart, W.M.: Elasticity theory and shape transitions of viral shells. Phys. Rev. E 72, 051923 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  21. Yu1, Z., Dobro, M.J., Woodward, C.L., Levandovsky, A., Danielson, C.M., Sandrin, V., Shi, J., Aiken, C., Zandi, R., Hope, T.J., Jensen, G.J.: Unclosed HIV-1 capsids suggest a curled sheet model of assembly. J. Mol. Biol. 425, 112–123 (2013)

    Article  Google Scholar 

  22. Hicks, S.D., Henley, C.L.: Irreversible growth model for virus capsid assembly. Phys. Rev. E 74, 031912 (2006)

    Article  ADS  Google Scholar 

  23. Levandovsky, A., Zandi, R.: Nonequilibirum assembly, retroviruses and conical shape. Phys. Rev. Lett. 102, 198102 (2009)

    Article  ADS  Google Scholar 

  24. Grime, J.M.A., Voth, G.A.: Early stages of the HIV-1 capsid protein lattice formation. Biophys. J. 103, 1774–1783 (2012)

    Article  ADS  Google Scholar 

  25. Bruinsma, R.F., Gelbart, W.M., Reguera, D., Rudnick, J., Zandi, R.: Viral self-assembly as a thermodynamic process. Phys. Rev. Lett. 90, 248101 (2003)

    Article  ADS  Google Scholar 

  26. Borodavka, A., Tuma, R., Stockley, P.G.: Evidence that viral RNAs have evolved for efficient, two-stage packaging. Proc. Natl. Acad. Sci. USA 109, 15769–15774 (2012)

    Article  ADS  Google Scholar 

  27. Ni, P., Wang, Z., Ma, X., Das, N.C., Sokol, P., Chiu, W., Dragnea, B., Hagan, M., Kao, C.C.: An examination of the electrostatic interactions between the N-terminal tail of the brome mosaic virus coat protein and encapsidated RNAs. J. Mol. Biol. 419, 284–300 (2012)

    Article  Google Scholar 

  28. Hagan, M.F.: A theory for viral capsid assembly around electrostatic cores. J. Chem. Phys. 130, 114902 (2009)

    Article  ADS  Google Scholar 

  29. van der Schoot, P., Bruinsma, R.: Electrostatics of an RNA virus. Phys. Rev. E 70, 061928 (2005)

    Article  Google Scholar 

  30. Belyi, V.A., Muthukumar, M.: Electrostatic origin of the genome packing in viruses. Proc. Natl. Acad. Sci. USA 103, 17174–17178 (2006)

    Article  ADS  Google Scholar 

  31. Siber, A., Zandi, R., Podgornik, R.: Thermodynamics of nanospheres encapsulated in virus capsids. Phys. Rev. E 81, 051919 (2010)

    Article  ADS  Google Scholar 

  32. Prinsen, P., van der Schoot, P., Gelbart, W.M., Knobler, C.M.: Multishell structures of virus coat proteins. J. Phys. Chem. B 114, 5522–5533 (2010)

    Article  Google Scholar 

  33. Hu, T., Zhang, R., Shklovskii, B.I.: Electrostatic theory of viral self-assembly. Physica A 387, 3059–3064 (2008)

    Article  ADS  Google Scholar 

  34. Ting, C.L., Wu, J., Wang, Z.-G.: Thermodynamic basis for the genome to capsid charge relationship in viral encapsidation. Proc. Natl. Acad. Sci. USA 108, 16985–16990 (2011)

    Article  ADS  Google Scholar 

  35. van der Schoot, P., Zandi, R.: Kinetic theory of virus capsid assembly. Phys. Biol. 4, 296–304 (2007)

    Article  ADS  Google Scholar 

  36. Zandi, R., van der Schoot, P.: Size regulation of ss-RNA viruses. Biophys. J. 96, 9–20 (2009)

    Article  Google Scholar 

  37. Šiber, A., Lošdorfer Božic, A., Podgornik, R.: Energies and pressures in viruses: contribution of nonspecific electrostatic interactions. Phys. Chem. Chem. Phys. 14, 3746–3765 (2012)

    Article  Google Scholar 

  38. Šiber, A., Podgornik, R.: Nonspecific interactions in spontaneous assembly of empty versus functional single-stranded RNA viruses. Phys. Rev. E 78, 051915 (2008)

    Article  ADS  Google Scholar 

  39. Lin, H., van der Schoot, P., Zandi, R.: Impact of charge variation on the encapsulation of nanoparticles by virus coat proteins. Phys. Biol. 9, 066004 (2012)

    Article  Google Scholar 

  40. Dobrynin, A.V., Rubinstein, M.: Theory of polyelectrolytes in solutions and at surfaces. Prog. Polym. Sci. 30, 1049–1118 (2005)

    Article  Google Scholar 

  41. Elrad, O.M., Hagan, M.F.: Encapsulation of a polymer by an icosahedral virus. Phys. Biol. 7, 045003 (2010)

    Article  Google Scholar 

  42. Lee, S.I., Nguyen, T.T.: Radial distribution of RNA genomes packaged inside spherical viruses. Phys. Rev. Lett. 100, 198102 (2008)

    Article  ADS  Google Scholar 

  43. De Gennes, P.-G.: Statistics of branching and hairpin helices for the dAT copolymer. Biopolymers 6, 715–729 (1968)

    Article  Google Scholar 

  44. Grosberg, A., Gutin, A., Shakhnovich, E.: conformational entropy of a branched polymer. Macromolecules 28, 3718–3727 (1995)

    Article  ADS  Google Scholar 

  45. Gutin, A.M., Grosberg, A.Y., Shakhnovich, E.I.: Polymers with annealed and quenched branchings belong to different universality classes. Macromolecules 26, 1293–1295 (1993)

    Article  MathSciNet  ADS  Google Scholar 

  46. Grosberg, A.Y.: Disordered polymers. Phys. Uspekhi 40, 125–158 (1997)

    Article  ADS  Google Scholar 

  47. Bundschuh, R., Hwa, T.: Statistical mechanics of secondary structures formed by random RNA sequences. Phys. Rev. E 65, 031903, 1–22 (2002)

    Google Scholar 

  48. Gopal, A., Zhou, Z.H., Knobler, C.M., Gelbart, W.M.: Visualizing large RNA molecules in solution. RNA 18, 284–299 (2012)

    Article  Google Scholar 

  49. Yoffe, A.M., Prinsen, P., Gopal, A., Knobler, C.M., Gelbart, W.M., Ben-Shaul, A.: Predicting the sizes of large RNA molecules. Biophys. J. 105, 16153–16158 (2008)

    Google Scholar 

  50. Fang, L.T., Gelbart, W.M., Ben-Shaul, A.: The size of RNA as an ideal branched polymer. J. Chem. Phys. 135, 155105 (2011)

    Article  ADS  Google Scholar 

  51. Borisov, O.V., Vilgis, T.A.: Polyelectrolyte manifolds. Europhys. Lett. 35, 327–333 (1996)

    Article  ADS  Google Scholar 

  52. Schwab, D., Bruinsma, R.: Flory theory of the folding of designed RNA molecules. J. Phys. Chem. B 113, 3880–3893 (2009)

    Article  Google Scholar 

  53. Yaman, K., Pincus, P., Solis, F., Witten, T.A.: Polymers in curved boxes. Macromolecules 30, 1173–1178 (1997)

    Article  ADS  Google Scholar 

  54. van der Spoel, D., Feenstra, K.A., Hemminga, M.A., Berendsen, H.J.C.: Molecular modeling of the RNA minding N-terminal part of Cowpea chlorotic mottle virus coat protein in solution with phosphate ions. Biophys. J. 71, 2920–2932 (1996)

    Article  Google Scholar 

  55. Moghaddam, S., Caliskan, G., Chauhan, S., Hyeon, C., Briber, R.M., Thirumalai, D., Woodson, S.A.: Metal ion dependence of cooperative collapse transitions in RNA. J. Mol. Biol. 393, 753–764 (2009)

    Article  Google Scholar 

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Authors and Affiliations

  1. Group Theory of Polymers and Soft Matter, Eindhoven University of Technology, PO Box 513, 5600 MB, Eindhoven, The Netherlands

    Paul van der Schoot

  2. Institute for Theoretical Physics, Utrecht University, Leuvenlaan 4, 3584 CE, Utrecht, The Netherlands

    Paul van der Schoot

  3. Department of Physics & Astronomy, University of California, Riverside, CA, 92521, USA

    Roya Zandi

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Correspondence to Roya Zandi.

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van der Schoot, P., Zandi, R. Impact of the topology of viral RNAs on their encapsulation by virus coat proteins. J Biol Phys 39, 289–299 (2013). https://doi.org/10.1007/s10867-013-9307-y

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