Skip to main content
Log in

Factors determining the direction of the stereoselection process in the generalized Frank model

  • Papers
  • Published:
Journal of Mathematical Chemistry Aims and scope Submit manuscript

Abstract

The Frank model for spontaneous chiral stereoselection of biomolecules is extended by taking into account the influence of electroweak effects on the rates of enantiomeric chemical reactions. Explicit analytical solutions of the respective differential 'equations are obtained, describing the behaviour of the generalized Frank model immediately after the beginning of the process, when the direction of the stereoselection is decided. The direction of the stereoselection is affected by both stochastic and deterministic factors, whose complex interrelations are examined.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. L. Pasteur, Leçons sur la Dissymètrie Molèculaire (Hachette, Paris, 1981).

    Google Scholar 

  2. G. Wald, Ann. N.Y. Acad. Sci. 69 (1957)352.

    PubMed  Google Scholar 

  3. K. Harada, Naturwiss. 57 (1970)144.

    Google Scholar 

  4. S.F. Mason, Molecular Optical Activity and the Chiral Discrimination (Cambridge University Press, Cambridge, 1982).

    Google Scholar 

  5. W. Liu, Origins of Life 12 (1982)205.

    PubMed  Google Scholar 

  6. W. Liu, Sci. Sinica 25 (1982)822.

    Google Scholar 

  7. G.F. Joyce, G.M. Visser, C.A.A. van Boeckel, J.H. van Boon, L.E. Orgel and J. van Westerenen, Nature 310 (1984)602.

    PubMed  Google Scholar 

  8. R.A. Hegstrom, Nature 315 (1985)749.

    Google Scholar 

  9. L.J. Dunne, Chem. Phys. Lett. 121 (1985)17.

    Google Scholar 

  10. B. Nordèn, J.O. Liljenzin and R.K. Tokay, J. Mol. Evol. 21 (1985)364.

    Google Scholar 

  11. A. Klemm, Z. Naturforsch. 40a (1985)1231.

    Google Scholar 

  12. A.J. MacDermott, Nature 323 (1986)16.

    PubMed  Google Scholar 

  13. A.G. Cairns-Smith, Chem. Britain 22 (1986)559.

    Google Scholar 

  14. J. Galloway, Nature 330 (1987)204.

    Google Scholar 

  15. D.K. Kondepudi and G.W. Nelson, Physica 125A (1984)465.

    Google Scholar 

  16. D.K. Kondepudi and G.W. Nelson, Nature 314 (1985)438.

    Google Scholar 

  17. D.K. Kondepudi, F. Moss and P.V.E. McClintock, Physica 21D (1986)296.

    Google Scholar 

  18. D.K. Kondepudi and M.J. Gao, Phys. Rev. A35 (1987)340.

    Google Scholar 

  19. D.K. Kondepudi, BioSystems 20 (1987)75.

    PubMed  Google Scholar 

  20. I. Gutman and A. Klemm, Z. Naturforsch. 42a (1987)899.

    Google Scholar 

  21. S.F. Mason and G.E. Tranter, Chem. Phys. Lett. 94 (1983)34.

    Google Scholar 

  22. S.F. Mason and G.E. Tranter, J, Chem. Soc. Chem. Commun. (1983)117.

  23. S.F. Mason and G.E. Tranter, Mol. Phys. 53 (1984)1091.

    Google Scholar 

  24. G.E. Tranter, Mol. Phys. 56 (1985)825.

    Google Scholar 

  25. S.F. Mason and G.E. Tranter, Proc. Roy. Soc. (London) A397 (1985)45.

    Google Scholar 

  26. G.E. Tranter, Nature 318 (1985)172.

    Google Scholar 

  27. G.E. Tranter, Chem. Phys. Lett. 115 (1985)286.

    Google Scholar 

  28. G.E. Tranter, Chem. Phys. Lett. 120 (1985)93.

    Google Scholar 

  29. G.E. Tranter, Chem. Phys. Lett. 121 (1985)339.

    Google Scholar 

  30. G.E. Tranter, J. Chem. Soc. Chem. Commun. (1986)60.

  31. K. Tennakone, Chem. Phys. Lett. 105 (1984)444.

    Google Scholar 

  32. S.F. Mason, Nature 314 (1985)400.

    Google Scholar 

  33. V. Babović, I. Gutman and S. Jokić, Z. Naturforsch. 42a (1987)1024.

    Google Scholar 

  34. I. Gutman, V. Babović and S. Jokić, Chem. Phys. Lett. 144 (1988)187.

    Google Scholar 

  35. I. Gutman, V. Babović and S. Jokić, J. Serb. Chem. Soc. 53 (1988)129.

    Google Scholar 

  36. L.D. Barron, Chem. Soc. Rev. 15 (1986)189.

    Google Scholar 

  37. J.H. Brewster, J. Chem. Educ. 63 (1986)667.

    Google Scholar 

  38. R. Janoschek, Naturwiss. Rundschau 39 (1986)327.

    Google Scholar 

  39. G.E. Tranter, Nachr. Chem. Tech. Lab. 34 (1986)866.

    Google Scholar 

  40. F.C. Frank, Biochim. Biophys. Acta 11 (1953)459.

    PubMed  Google Scholar 

  41. F.F. Seelig, J. Theor. Biol. 31 (1971)355.

    PubMed  Google Scholar 

  42. F.F. Seelig, J. Theor. Biol. 32 (1971)93.

    PubMed  Google Scholar 

  43. F.F. Seelig, J. Theor. Biol. 34 (1972)197.

    PubMed  Google Scholar 

  44. D.W. Rein, R.A. Hegstrom and P.G.H. Sandars, Phys. Lett. 71A (1979)499.

    Google Scholar 

  45. R.A. Hegstrom, D.W. Rein and P.G.H. Sandars, J. Chem. Phys. 73 (1980)2329.

    Google Scholar 

  46. J.L. Lopes,Gauge Field Theories (Pergamon, Oxford, 1981).

    Google Scholar 

  47. M. Quack, Chem. Phys. Lett. 132 (1986)147.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

received by the Publisher 20 September 1989

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gutman, I. Factors determining the direction of the stereoselection process in the generalized Frank model. J Math Chem 3, 343–355 (1989). https://doi.org/10.1007/BF01169016

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01169016

Keywords

Navigation