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Homochiral Growth Through Enantiomeric Cross-Inhibition

Abstract

The stability and conservation properties of a recently proposed polymerization model are studied. The achiral (racemic) solution is linearly unstable once the relevant control parameter (here the fidelity of the catalyst) exceeds a critical value. The growth rate is calculated for different fidelity parameters and cross-inhibition rates. A chirality parameter is defined and shown to be conserved by the nonlinear terms of the model. Finally, a truncated version of the model is used to derive a set of two ordinary differential equations and it is argued that these equations are more realistic than those used in earlier models of that form.

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References

  1. Avetisov, V. A. and Goldanskii, V.: 1993, Chirality and the Equation of ‘Biological Big Bang’, Phys. Lett. A172, 407–410.

  2. Bada, J. L.: 1995, Origins of Homochirality, Nature 374, 594–595.

  3. Bada, J. L., Luyendyk, B. P. and Maynard, J. B.: 1970, Marine Sediments: Dating by the Racemization of Amino Acids, Science 170, 730–732.

  4. Bailey, J.: 2001, Astronomical Sources of Circularly Polarized Light and the Origin of Homochirality, Orig. Life Evol. Biosph. 31, 167–183.

  5. Bonner, W. A.: 1999, Chirality Amplification–The Accumulation Principle Revisited, Orig. Life Evol. Biosph. 29, 615–624.

  6. Crick, F. H. C.: 1968, The Origin of the Genetic Code, J. Mol. Biol. 38, 367–379.

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

  8. 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.

  9. Haken, H.: 1983, Synergetics–An Introduction, Springer, Berlin.

  10. Hare, P. E. and Mitterer, R. M.: 1967, Nonprotein Amino Acids in Fossil Shells, Yearbook Carnegie Institution of Washington 65, 362–364.

  11. Hegstrom, R. A.: 1984, Parity Nonconservation and the Origin of Biological Chirality–Theoretical Calculations, Orig. Life 14, 405–414.

  12. Joyce, G. F., Visser, G. M., van Boeckel, C. A. A., van Boom, J. H., Orgel, L. E. and Westrenen, J.: 1984, Chiral Selection in Poly(C)-Directed Synthesis of Oligo(G), Nature 310, 602–603.

  13. Kippenhahn, R. and Weigert, A.: 1990, Stellar Structure and Evolution, Springer, Berlin.

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

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

  16. Kondepudi, D. K., Moss, F. and McClintock, P. V. E.: 1986, Observation of Symmetry Breaking, State Selection and Sensitivity in a Noisy Electron System, Physica. 21D, 296–306.

  17. Kondepudi, D. K., Kaufman, R. J. and Singh, N.: 1990, Chiral Symmetry Breaking in Sodium Chlorate Crystallization, Science 250, 975–976.

  18. Nelson, K. E., Levy, M. and Miller, S. L.: 2000, Peptide Nucleic Acids Rather than RNA may have been the First Genetic Molecule, Proc. Natl. Acad. Sci. U.S.A. 97, 3868–3871.

  19. Nielsen, P. E.: 1993, Peptide Nucleic Acid (PNA): A Model Structure for the Primordial Genetic Material, Orig. Life Evol. Biosph. 23, 323–327.

  20. Orgel, L. E.: 1968, Evolution of the Genetic Apparatus, J. Mol. Biol. 38, 381–393.

  21. Pogodina, N. V., Lavrenko, V. P., Srinivas, S. and Winter, H. H.: 2001, Rheology and Structure of Isotactic Polypropylene Near the Gel Point: Quiescent and Shear-Induced Crystallization, Polymer 42, 9031–9043.

  22. Pooga, M., Land, T. Bartfai, T. and Langel, Ü.: 2001, PNA Oligomers as Tools for Specific Modulation of Gene Expression, Biomol. Eng. 17, 183–192.

  23. Rasmussen, S., Chen, L., Nilsson, M. and Abe, S.: 2003, Bridging Nonliving and Living Matter, Artif. Life 9, 269–316.

  24. Sandars, P. G. H.: 2003, A Toy Model for the Generation of Homochirality During Polymerization, Orig. Life Evol. Biosph. 33, 575–587.

  25. Saito, Y. and Hyuga, H.: 2004, Complete Homochirality Induced by the Nonlinear Autocatalysis and Recycling, J. Phys. Soc. Jpn. 73, 33–35.

  26. Tedeschi, T., Corradini, R., Marchelli, R., Pushl, A. and Nielsen, P. E.: 2002, Racemization of Chiral PNAs During Solid-Phase Synthesis: Effect of the Coupling Conditions on Enantiomeric Purity, Tetrahedron: Asymmetry 13, 1629–1636.

  27. Wattis, J. A. D. and Coveney, P. V.: 1999, The Origin of the RNA World: A Kinetic Model, J. Phys. Chem. B 103, 4231–4250.

  28. Wattis, J. A. D. and Coveney, P. V.: 2005, Symmetry-Breaking in Chiral Polymerisation, Orig. Life Evol. Biosph. 35, this issue, 243–273.

  29. Woese, C.: 1967, The Genetic Code, Harper and Row, New York.

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Correspondence to A. Brandenburg.

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Brandenburg, A., Andersen, A.C., Höfner, S. et al. Homochiral Growth Through Enantiomeric Cross-Inhibition. Orig Life Evol Biosph 35, 225–241 (2005) doi:10.1007/s11084-005-0656-9

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Keywords

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