A Toy Model for the Generation of Homochirality during Polymerization

  • 150 Accesses

  • 83 Citations


This article examines a toy model of polymerization which though artificial and unphysical has some interesting chiral features. Two key elements, enantiomeric cross inhibition and chiral feedback, are shown to lead to bifurcation, so that the end product can become homo-chiral. We find that the bifurcation is driven by the cross-inhibition but is not strongly dependant on its strength, which for perfect feedback fidelity mainly determines the time scale. We also find that bifurcation with a high degree of chiral polarization remains even when the fidelity of the chiral feedback is substantially less than unity. For small values of the feedback fidelity the polarization drops below unity and at a critical value falls sharply to zero in a `phase transition'. The value at which this happens depends on the cross-inhibition in a complex way. By comparing the behaviour of polymers differing only in their final length, N, we find that the bifurcation process is enhanced as N increases. The symmetry breaking which we find is clearly a particular manifestation of general bifurcation theory. In addition it has the specific interest that, at least in our model, long homochiral polymers are possible even in the presence of substantial enantiomeric cross-inhibition.

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


  1. Avetisov, V. and Goldanskii, V.: 1996, Mirror Symmetry-breaking at the Molecular Level, Proc. Natl. Acad. Sci. U.S.A. 93, 11435-11442.

  2. Avetisov, V. A. et al.: 1985, Strong Mirror-symmetry Violation as a Necessary Condition for Selfreplication.

  3. Avetisov, V. A. et al.: 1991, Handedness, Origin of Life and Evolution, Physics Today, July, pp. 33-41.

  4. Avetisov, V. A. and Goldanskii, V. I.: 1993, Chirality and the Equation of the 'Biological Big Bang', Phys. Lett. A 172, 407-410.

  5. Avetisov, V. A. and Goldanskii, V. I.: 1997, Kinetic Aspects of Enantioselective Processes, Chem. Phys. Reports 16, 1399-1426.

  6. Avetisov, V. A. and Goldanskii, V. I.: 1991, Homochirality and Stereospecific Activity: Evolutionary Aspects, Biosystems 25, 141-149.

  7. Bada, J. L. and Miller, S. L.: 1987, Racemization and the Origin of Optically Active Organic Compounds in Living Organisms, Biosystems 20, 21-26.

  8. Cattani, M. and Tomé, T.: 1993, Chiral-Symmetry-Breaking in Non-Equilibrium Chemical Systems: The Racemization Influence, Origin of Life 23, 125–136.

  9. Frank, F.: 1953, On Spontaneous Asymmetric Synthesis, Biochim. Biophys. Acta 11, 459-464.

  10. Goldanskii, V. I. et al.: 1986, Chiral Purity of Nucleotides as a Necessary Condition for Complementarity, FEBS Lett. 207, 181.

  11. Goldanskii, V. I. et al.: 1987, On the Decisive Role of Chiral Purity in the Origination of the Biosphere and in Its Possible Destruction, Comments Mol. Cell. Biophys. 4, 79.

  12. Goldanskii, V. I. and Kuzmin, V.: 1988, Spontaneous Mirror Symmetry Breaking in Nature and the Origin of Life, Z. Phys. Chem., (Leipzig), 269, 216-274.

  13. Goldanskii, V. I. and Kuzmin, V. V.: 1989, Spontaneous Breaking of Mirror Symmetry in Nature and Origin of Life, Sov. Phys. Uspekhi 32, 1-29.

  14. Gutman, I. et al.: 1988, The Origin of Biomolecular Chirality: The Generalized Frank Model with Arbitrary Initial Conditions, Chem. Phys. Lett. 144, 187–190.

  15. Joyce, G. F. et al.: 1984, Chiral Selection in Poly(C)-directed Synthesis of Oligo(G), Nature 310, 602.

  16. Klemm, A.: 1985, Mono-and Bistable Mixtures of Interacting Antipodes, Z. Naturforsch. A. 40, 1231–1234.

  17. Kondepudi, D. K. and Nelson, G. W.: 1983, Chiral Symmetry Breaking in Nonequilibrium Systems, Phys. Rev. Lett. 50, 1023-1026.

  18. Kondepudi, D. K. and Nelson, G.W.: 1984, Chiral Symmetry Breaking in Nonequilibrium Chemical Systems: Time Scales for Chiral Selection, Phys. Lett. A 106, 203-206.

  19. Lins, R. D. et al.: 1996, Plural Origins of the Molecular Homochirality in Our Biota, Z. Naturforsch. 51c, 70-74.

  20. Soai, K. et al.: 1995, Asymmetric Autocatalysis and Amplification of Enantiometric Excess of a Chiral Molecule, Nature 378, 767-768.

  21. Soares, T. A. et al.: 1997, Plural Origins of the Molecular Homochirality in our Biota.2.I The Relative Stabilities of Homochiral and Mixed Oligoribotides and Peptides, Z. Naturforsch. 52c: 89-96.

  22. Szathmari, J.: 1985, Chemical Amplification Through Competitive Autocatalysis, Orig of Life 16, 165–167.

Download references

Author information

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Sandars, P.G.H. A Toy Model for the Generation of Homochirality during Polymerization. Orig Life Evol Biosph 33, 575–587 (2003) doi:10.1023/A:1025705401769

Download citation

  • DNA polymerization
  • enantiomeric cross-inhibition
  • origin of homochirality