SpringerLink
Log in

Evolution of Molecular Phenotypes - A Physicist’s View of Darwin’s Principle

  • Conference paper
Traffic and Granular Flow ’99

Abstract

The power of Darwinian evolution is based on the dichotomy of genotype and phenotype with the former being the object under variation and the latter constituting the target of selection. Only the simplest case of an evolutionary process, the optimization of RNA molecules in vitro, where phenotypes axe understood as RNA structures, can be handled explicitly. We derive a model based on differential equations with stochastic terms which includes unfolding of genotypes to yield phenotypes as well as the evaluation of the latter. The relations between genotypes and phenotypes are understood as map**s from sequence space into shape space, the space of molecular structures. Generic properties of this map are derived and analyzed for RNA secondary structures as an example. The optimization of molecular properties in populations is modeled in silico through replication and mutation in a flow reactor. The approach towards a predefined structure is monitored and reconstructed in terms of a relay series being an uninterrupted sequence of phenotypes from initial structure to target. Analysis of the molecular shapes in the relay series provides the basis for a novel definition of continuity in evolution. Discontinuities can be identified as major changes in molecular structures.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
EUR 29.95
Price includes VAT (Germany)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
EUR 85.59
Price includes VAT (Germany)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
EUR 106.99
Price includes VAT (Germany)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free ship** worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. D.R. Mills, R.L. Peterson, and S. Spiegelman, Proc. Natl. Acad. Sci. USA 58, 217–224 (1967).

    Article  Google Scholar 

  2. S. Spiegelman, Quart. Rev. Biophys. 4, 213–253 (1971).

    Article  Google Scholar 

  3. C. Flamm, W. Fontana, I.L. Hofacker, and P. Schuster, RNA, (1999).

    Google Scholar 

  4. S.R. Morgan and P.G. Higgs, J.Chem.Phys. 105, 7152–7157 (1996).

    Article  Google Scholar 

  5. E. van Nimwegen, The Statistical Dynamics of Epochal Evolution, PhD Thesis, (Universiteit Utrecht, Utrecht, NL, 1999).

    Google Scholar 

  6. S.F. Elena, V.S. Cooper, and R.E. Lenski, Science 272, 1802–1804 (1996).

    Article  Google Scholar 

  7. W. Fontana and P. Schuster, Biophys. Chem. 26, 123–147 (1987).

    Article  Google Scholar 

  8. M.A. Huynen, P.F. Stadler, and W. Fontana, Proc. Natl. Acad. Sci. USA 93, 397–401 (1996).

    Article  Google Scholar 

  9. E. van Nimwegen, J.P. Crutchfield, and M. Mitchell, Phys. Lett. A 229, 144–150 (1997).

    Article  MathSciNet  MATH  Google Scholar 

  10. W. Fontana and P. Schuster, J. Theor. Biol. 194, 491–515 (1998).

    Article  Google Scholar 

  11. W. Fontana and P. Schuster, Science 280, 1451–1455 (1998).

    Article  Google Scholar 

  12. M. Kimura, The Neutral Theory of Molecular Evolution, (Cambridge University Press, Cambridge, UK, 1983).

    Google Scholar 

  13. T. Ohta, Ann. Rev. Ecol. Syst. 23, 263–286 (1992).

    Article  Google Scholar 

  14. J.W. Drake, Proc. Natl. Acad. Sci. USA 88, 7160–7164 (1991).

    Article  Google Scholar 

  15. R.E. Lenski and M. Travisano, Proc. Natl. Acad. Sci. USA 91, 6808–6814 (1994).

    Article  Google Scholar 

  16. D. Papadopoulos, D. Schneider, J. Meier-Eiss, W. Arber, R.E. Lenski, and M. Blot, Proc. Natl. Acad. Sci. USA 96, 3807–3812 (1999).

    Article  Google Scholar 

  17. M. Kimura, Nature 217, 624–626 (1968).

    Article  Google Scholar 

  18. M. Eigen, Naturwissenschaften 58, 465–523 (1971).

    Article  Google Scholar 

  19. M. Eigen and P. Schuster, Naturwissenschaften 64, 541–565 (1977).

    Article  Google Scholar 

  20. C.J. Thompson and J.L. McBride, Math. Biosci. 21, 127–142 (1974).

    Article  MathSciNet  MATH  Google Scholar 

  21. B.L. Jones, R.H. Enns, and S.S. Rangnekar, Bull. Math. Biol. 38, 15–28 (1976).

    MATH  Google Scholar 

  22. J. Swetina and P. Schuster, Biophys. Chem. 16, 329–345 (1982).

    Article  Google Scholar 

  23. M. Nowak and P. Schuster, J. Theor. Biol. 137, 375–395 (1989).

    Article  Google Scholar 

  24. M. Eigen, J. McCaskill, and P. Schuster, Adv. Chem. Phys. 75, 149–263 (1989).

    Article  Google Scholar 

  25. I. Leuthäusser, J.Stat.Phys. 48, 343–360 (1987).

    Article  Google Scholar 

  26. N. Rohde, H. Daum, and C.K. Biebricher, J. Mol. Biol. 249, 754–762 (1995).

    Article  Google Scholar 

  27. E. Domingo, Viral Hepatitis Rev. 2, 247–261 (1996).

    Google Scholar 

  28. E. Domingo and J.J. Holland, Ann. Rev. Microbiol. 51, 151–178 (1997).

    Article  Google Scholar 

  29. E. Domingo, L. Menéndez-Arias, M.E. Quinoñes-Mateu, A. Holguín, M. Gutierrez-Rivas, M.A. Martínez, J. Quer, and J.J. Holland, Prog. Drug. Res. 48, 99–128 (1997).

    Google Scholar 

  30. R.W. Hamming, Coding and Information Theory, (Prentice Hall, Englewood Cliffs, NJ, 2nd ed., 1989).

    Google Scholar 

  31. R.W. Hamming, Bell Syst. Tech. J. 29, 147–160 (1950).

    MathSciNet  Google Scholar 

  32. J.S. McCaskill, J.Chem.Phys. 80, 5194–5202 (1984).

    Article  MathSciNet  Google Scholar 

  33. P. Schuster and J. Swetina, Bull. Math. Biol. 50, 635–660 (1988).

    MathSciNet  MATH  Google Scholar 

  34. P. Tarazona, Phys. Rev. A 45, 6038–6050 (1992).

    Article  Google Scholar 

  35. D. Alves and J.F. Fontanari, Phys. Rev. E 57, 7008–7013 (1998).

    Article  Google Scholar 

  36. P.R.A. Campos and J.F. Fontanari, Phys. Rev. E 58, 2664–2667 (1998).

    Article  Google Scholar 

  37. P.R.A. Campos and J.F. Fontanari, J. Phys. A 32, L1–L7 (1999).

    Article  Google Scholar 

  38. C. Reidys, P.F. Stadler, and P. Schuster, Bull. Math. Biol. 59, 339–397 (1997).

    Article  MATH  Google Scholar 

  39. R. Nussinov and A.B. Jacobson, Proc. Natl. Acad. Sci. USA 77, 6309–6313 (1980).

    Article  Google Scholar 

  40. M. Zuker and P. Stiegler, Nucleic Acids Research 9, 133–148 (1981).

    Article  Google Scholar 

  41. M. Zuker and D. Sankoff, Bull. Math. Biol. 46, 591–621 (1984).

    MATH  Google Scholar 

  42. I.L. Hofacker, W. Fontana, P.F. Stadler, L.S. Bonhoeffer, M. Tacker, and P. Schuster, Mh. Chemie 125, 167–188 (1994).

    Google Scholar 

  43. R.T. Batey, R.P. Rambo, and J.A. Doudna, Angew. Chem. Int. Ed. 38, 2326–2343 (1999).

    Article  Google Scholar 

  44. W. Grüner, R. Giegerich, D. Strothmann, C. Reidys, J. Weber, I.L. Hofacker, and P. Schuster, Mh. Chemie 127, 355–374 (1996).

    Google Scholar 

  45. W. Grüner, R. Giegerich, D. Strothmann, C. Reidys, J. Weber, I.L. Hofacker, and P. Schuster, Mh. Chemie 127, 375–389 (1996).

    Google Scholar 

  46. W. Fontana, D.A.M. Konings, P.F. Stadler, and P. Schuster, Biopolymers 33, 1389–1404 (1993).

    Article  Google Scholar 

  47. P. Schuster, W. Fontana, P.F. Stadler, and I.L. Hofacker, Proc. Roy. Soc. Lond. B 255, 279–284 (1994).

    Article  Google Scholar 

  48. W. Fontana, P.F. Stadler, E.G. Bornberg-Bauer, T. Griesmacher, I.L. Hofacker, M.Tacker, P. Tarazona, E.D. Weinberger, and P. Schuster, Phys. Rev. E 47, 2083–2099 (1993).

    Article  Google Scholar 

  49. I.L. Hofacker, P. Schuster, and P.F. Stadler, Discr. Appl. Math. 89, 177–207 (1998).

    MathSciNet  Google Scholar 

  50. P. Schuster, J. Biotechnol. 41, 239–257 (1995).

    Article  Google Scholar 

  51. P. Schuster, Physica D 107, 351–365 (1997).

    Article  MathSciNet  Google Scholar 

  52. C.M. Reidys, Adv. Appl. Math. 19, 360–377 (1997).

    Article  MathSciNet  MATH  Google Scholar 

  53. D.T. Gillespie, J. Comp. Phys. 22, 403–434 (1976).

    Article  MathSciNet  Google Scholar 

  54. D.T. Gillespie, J. Phys. Chem. 81, 2340–2361 (1977).

    Article  Google Scholar 

  55. W.Fontana, W. Schnabl, and P. Schuster, Phys. Rev. A 40, 3301–3321 (1989).

    Article  Google Scholar 

  56. P. Schuster and W. Fontana, Physica D 133, 427–452 (1999).

    Article  MathSciNet  MATH  Google Scholar 

  57. E. Zuckerkandl, J. Mol. Evol. 44 (Suppl. 1), S2–S8 (1997).

    Article  Google Scholar 

  58. S. Wright, The roles of mutation, inbreeding, crossbreeding and selection in evolution, In: Int. Proc. of the Sixth Int. Congress on Genetics, D.F. Jones, (Ed.), Vol. 1, pp. 356-366 (1932).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Theoretische Chemie und Molekulare Strukturbiologie, Universität Wien, Währingerstraße 17, 1090, Wien, Austria

    P. Schuster’

  2. Santa Fe Institute, 1399 Hyde Park Road, 87501, Santa Fe, NM, USA

    P. Schuster’

Authors
  1. P. Schuster’
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institut für Wirtschaft und Verkehr, Technische Universität Dresden, 01062, Dresden, Germany

    Dirk Helbing

  2. ICA 1 Universität Stuttgart, Pfaffenwaldring 57/III, 70550, Stuttgart, Germany

    Hans J. Herrmann

  3. Physik von Transport und Verkehr, Gerhard-Mercator-Universität Duisburg, Lotharstraße 1, 47048, Duisburg, Germany

    Michael Schreckenberg

  4. Theoretische Physik, Gerhard-Mercator-Universität Duisburg, Lotharstraße 1, 47048, Duisburg, Germany

    Dietrich E. Wolf

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Schuster’, P. (2000). Evolution of Molecular Phenotypes - A Physicist’s View of Darwin’s Principle. In: Helbing, D., Herrmann, H.J., Schreckenberg, M., Wolf, D.E. (eds) Traffic and Granular Flow ’99. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59751-0_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-59751-0_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-64109-1

  • Online ISBN: 978-3-642-59751-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation