Skip to main content
SpringerLink
Log in

Emergence of molecular chirality due to chiral interactions in a biological environment

  • Original Paper
  • Published:
Journal of Biological Physics Aims and scope Submit manuscript

Abstract

We explore the interplay between tunneling process and chiral interactions in the discrimination of chiral states for an ensemble of molecules in a biological environment. Each molecule is described by an asymmetric double-well potential and the environment is modeled as a bath of harmonic oscillators. We carefully analyze different time-scales appearing in the resulting master equation at both weak- and strong-coupling limits. The corresponding results are accompanied by a set of coupled differential equations characterizing optical activity of the molecules. We show that, at the weak-coupling limit, chiral interactions prohibit the coherent racemization induced by decoherence effects and thus preserve the initial chiral state. At the strong-coupling limit, considering the memory effects of the environment, Markovian behavior is observed at long times.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  1. Terentjew, A.P., Klabunovskii, J.I.: The role of dissymmetry in the origin of living material. In: Florkin, M. (ed.) Aspects of the Origin of Life. Pergamon Press, New York (1960)

    Google Scholar 

  2. Mason, S.: Chem. Soc. Rev. 17, 347 (1988)

    Article  Google Scholar 

  3. Palyi, G., et al.: Progress in Biological Chirality. Elsevier, Amsterdam (2004)

    Google Scholar 

  4. Klabunovskii, E. I.: Russ. J. Org. Chem. 48, 881 (2012)

    Article  Google Scholar 

  5. Hund, W.: Z. Phys. 43, 805 (1927)

    Article  ADS  Google Scholar 

  6. Mason, S.F.: Nature 311, 19 (1984)

    Article  ADS  Google Scholar 

  7. Janoschek, J.: Chirality from Weak Boson to the A-Helix. Springer, Berlin (1991)

    Google Scholar 

  8. Barron, L.D.: Chirality at the sub-molecular level: True and false chirality. In: Lough, W.J., Wainer, I.W. (eds.) Chirality in Natural and Applied Science. Blackwell Publishing, Oxford (2002)

    Google Scholar 

  9. Letokhov, V.S.: Phys. Lett. 53A, 275 (1975)

    Article  ADS  Google Scholar 

  10. Harris, R.A., Stodolsky, L.: Phys. Lett. B 78, 313 (1978)

    Article  ADS  Google Scholar 

  11. Quack, M.: Ang. Chem. Int. Ed. Engl. 41, 4618 (2002)

    Article  Google Scholar 

  12. Wesendrup, R., et al.: J. Phys. Chem. A107, 6668 (2003)

    Article  Google Scholar 

  13. Darquié, B., et al.: Chirality 22, 870 (2010)

    Article  Google Scholar 

  14. MacDermott, A.: The weak force and SETH: the search for extra-terrestrial homochirality. In: Cline, D.B. (ed.) Physical Origin of Homochirality in Life. Woodbury (1996)

  15. Mason, S.F.: Molecular optical activity and the chiral discriminations. Cambridge (1982)

  16. Stone, A.J.: The Theory of Intermolecular Forces. Clarendon Press, Oxford (1996)

    Google Scholar 

  17. Avalos, M., et al.: Chem. Rev. 98, 2391 (1998)

    Article  Google Scholar 

  18. Breuer, H.P., Petruccione, F.: The Theory of Open Quantum Systems. Oxford University Press, Oxford (2002)

    MATH  Google Scholar 

  19. Vardi, A.: J. Chem. Phys. 112, 8743 (2000)

    Article  ADS  Google Scholar 

  20. Jona-Lasinio, G., et al.: Phys. Rev. Lett. 88, 123001 (2002)

    Article  ADS  Google Scholar 

  21. Grecchi, V., Sacchetti, A.: J. Phys. A: Math. Gen. 37, 3527 (2004)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  22. Bargueño, P., et al.: Chem. Phys. Lett. 516, 29 (2011)

    Article  ADS  Google Scholar 

  23. Gonzalo, I., Bargueño, P.: Phys. Chem. Chem. Phys. 13, 17130 (2011)

    Article  Google Scholar 

  24. Dorta-Urra, A., et al.: J. Chem. Phys. 136, 174505 (2012)

    Article  ADS  Google Scholar 

  25. Peñate-Rodriguez, H.C., et al.: Chem. Phys. Lett. 523, 49 (2012)

    Article  ADS  Google Scholar 

  26. Peñate-Rodriguez, H.C., et al.: Chirality 25, 514 (2013)

    Article  Google Scholar 

  27. Giulini, D., et al.: Decoherence and the Appearance of a Classical World in Quantum Theory. Springer, Berlin (1996)

    Book  MATH  Google Scholar 

  28. Schlosshauer, M.: Decoherence and the Quantum to Classical Transition. Springer, Berlin (2007)

    Google Scholar 

  29. Joos, E., Zeh, H.D.: Z. Phys. B 59, 223 (1985)

    Article  ADS  Google Scholar 

  30. Diosi, L.: Europhys. Lett. 30, 63 (1995)

    Article  ADS  Google Scholar 

  31. Adler, S.L.: J. Phys. A 39, 14067 (2006)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  32. Vacchini, B., Hornberger, K.: Phys. Rep. 478, 71 (2009)

    Article  MathSciNet  ADS  Google Scholar 

  33. Harris, R.A., Stodolsky, L.: J. Chem. Phys. 74, 2145 (1981)

    Article  ADS  Google Scholar 

  34. Harris, R.A., Stodolsky, L.: J. Chem. Phys. 74, 2145 (1981)

    Article  ADS  Google Scholar 

  35. Harris, R.A., Stodolsky, L.: Phys. Lett. B 116, 464 (1982)

    Article  ADS  Google Scholar 

  36. Pfeifer, P.: Rev. Phys. A 26, 701 (1982)

    Article  Google Scholar 

  37. Ghahramani, F.T., Shafiee, A.: Phys. Rev. A 88, 032504 (2013)

    Article  ADS  Google Scholar 

  38. Fain, B.: Phys. Lett. A 89, 455 (1982)

    Article  ADS  Google Scholar 

  39. Trost, J., Hornberger, K.: Phys. Rev. Lett. 103, 023202 (2009)

    Article  ADS  Google Scholar 

  40. Bahrami, M., Shafiee, A.: Comput. Theo. Chem. 978, 84 (2011)

    Article  Google Scholar 

  41. Leggett, A.J., et al.: Rev. Mod. Phys. 59, 1 (1987)

    Article  ADS  Google Scholar 

  42. Gilmore, J., McKenzie, R.H.: Chem. Phys. Lett. 421, 266 (2006)

    Article  ADS  Google Scholar 

  43. Pachon, L.A., Brumer, P.: J. Phys. Chem. Lett. 2, 2728 (2011)

    Article  Google Scholar 

  44. Fleming, G., Scholes, G., Cheng, Y.: Procedia Chem. 3, 38 (2011)

    Article  Google Scholar 

  45. Huelga, S., Plenio, M.: Procedia Chem. 3, 248 (2011)

    Article  Google Scholar 

  46. Shi, Q., Zhu, L., Chen, L.: J. Chem. Phys. 135, 044505 (2011)

    Article  ADS  Google Scholar 

  47. Lei, C., Zhang, W.: Phys. Rev. A 84, 052116 (2011)

    Article  MathSciNet  ADS  Google Scholar 

  48. Zhang, J., et al.: Phys. Rev. B 84, 214304 (2011)

    Article  ADS  Google Scholar 

  49. Cheche, T.O., Lin, S.H.: Phys. Rev. E 64, 061103 (2001)

    Article  ADS  Google Scholar 

  50. Wilhelm, F.K., Kleff, S., von Delft, J.: Chem. Phys. 296, 345 (2003)

    Article  ADS  Google Scholar 

  51. Nakajima, S.: Progr. Theor. Phys. 20, 948 (1958)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  52. Zwanzig, R.: J. Chem. Phys. 33, 1338 (1960)

    Article  MathSciNet  ADS  Google Scholar 

  53. Grifoni, M., et al.: Eur. Phys. J. B 10, 719 (1999)

    Article  ADS  Google Scholar 

  54. Silbey, R., Harris, R.A.: J. Chem. Phys. 80, 2615 (1984)

    Article  ADS  Google Scholar 

  55. Harris, R.A., Silbey, R.: J. Chem. Phys. 83, 1069 (1985)

    Article  ADS  Google Scholar 

  56. Silbey, R., Harris, R.A.: J. Phys. Chem. 93, 7062 (1989)

    Article  Google Scholar 

  57. Townes, C.H., Schawlow, A.L.: Microwave Spectroscopy. McGraw-Hill, New York (1955)

    Google Scholar 

  58. Herzberg, G.: Spectra, Molecular and Structure, Molecular. Infrared and Raman Spectra of Polyatomic Molecules. Krieger, Malabar (1991)

    Google Scholar 

  59. Weiss, U.: Quantum Dissipative Systems. World Scientific, Singapore (2008)

    Book  MATH  Google Scholar 

  60. Bahrami, M., Bassi, A.: Phys. Rev. A 84, 062115 (2011)

    Article  ADS  Google Scholar 

  61. Puri, R.P.: Mathematical Methods Of Quantum Optics. Springer, Berlin (2001)

    Book  MATH  Google Scholar 

  62. Caldeira, A.O., Leggett, A.J.: Physica A 121, 587 (1983)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  63. Mathai, A.M.: A Handbook of Generalized Special Functions for Statistical and Physical Sciences. Oxford University Press, New York (1993)

    MATH  Google Scholar 

  64. Bothma, J., Gilmore, J., McKenzie, R.H.: Modelling quantum decoherence in biomolecules. In: Abbott, D., Davis, P.C.W., Pati, A.K. (eds.) Quantum Aspects of Life. Woodbury (1996)

  65. Gilmore, J., McKenzie, R.H.: J. Phys. Condens. Matter 17, 1735 (2005)

    Article  ADS  Google Scholar 

  66. Allen, L., Eberly, J.H.: Optical Resonance and Two-Level Atoms. Wiley, New York (1975)

    Google Scholar 

  67. Laine, E-M.: Phys. Scr. T 140, 014053 (2010)

    Article  ADS  Google Scholar 

Download references

Acknowledgments

We would like to thank Dr. Mohammad Bahrami for his instructive comments, and Dr. Mohammad Arjmand for an editorial reading of the article.

Author information

Authors and Affiliations

  1. Research Group on Foundations of Quantum Theory and Information, Department of Chemistry, Sharif University of Technology, P.O.Box 11365-9516, Tehran, Iran

    Arash Tirandaz, Farhad Taher Ghahramani & Afshin Shafiee

Authors
  1. Arash Tirandaz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Farhad Taher Ghahramani
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Afshin Shafiee
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Afshin Shafiee.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tirandaz, A., Ghahramani, F.T. & Shafiee, A. Emergence of molecular chirality due to chiral interactions in a biological environment. J Biol Phys 40, 369–386 (2014). https://doi.org/10.1007/s10867-014-9356-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10867-014-9356-x

Keywords

Search

Navigation