Evolution of Molecules

  • Peter Schuster
Conference paper
Part of the International Academy of Quantum Molecular Science book series (QUCH, volume 4)


Capability of self-replication is a unique feature of polynucleotides. Their properties represent the ultimate molecular basis of biochemical and biological evolution. The kinetics of self-replication can be approached theoretically by means of ordinary differential equations (O.D.E.). Depending on the nature of the mechanism of replication we are dealing with O.D.E.’s which have different properties. Template induced replication leads to competition between polynucleotide sequences. Stable mutant distributions called “quasispecies” are formed, when the mechanism of replication is accurate enough. The two most important features of Darwinian evolution variability through mutations and optimization of the replication rate through selection can be observed at the molecular level already. By means of higher order terms competition can be suppressed provided some conditions are fulfilled. Then, the replicating elements cooperate. A rigorous proof has been presented which relates cooperation to the formation of a closed loop of catalytic interactions. Such a closed positive feedback loop has been called a “hypercycle”. Cooperation of replicating elements allows to develop new properties of the system. These new properties are established on the expenses of global optimization. Second order catalysis hinders the system to approach the global optimum of the rate of replication.


Replication Process Autocatalytic Process Mass Action Kinetic Master Sequence Catalytic Interaction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Batschelet, E., Domingo, E. and Weissmann, C. (1976) Gene 1, 127CrossRefGoogle Scholar
  2. Biebricher, C.K., Eigen, M. and Luce, R.(1981),J.Mol.Biol. 148,369 and 391CrossRefGoogle Scholar
  3. Biebricher, C.K., Diekmann, S. and Luce, R. (1982) J.Mol.Biol. 154, 629CrossRefGoogle Scholar
  4. Clarke, B.L. (1980) Adv.Chem.Phys. 43, 1CrossRefGoogle Scholar
  5. Dawkins, R . (1976) The selfish Gene. Oxford Univ.Press, OxfordGoogle Scholar
  6. Dawkins,R.(1982). The extended phenotype. W.H. Freeman, OxfordGoogle Scholar
  7. Domingo, E., Flavell, R.A. and Weissmann, C. (1976) Gene 1, 3CrossRefGoogle Scholar
  8. Domingo, E., Sabo, D., Taniguchi, T. and Weissman,C.(1978) Cell 13, 735CrossRefGoogle Scholar
  9. Domingo, E., Davilla, M. and Ortin, J. (1980) Gene 11, 333CrossRefGoogle Scholar
  10. Eigen, M. (1971) Naturwissenschaften 58, 465CrossRefGoogle Scholar
  11. Eigen, M and Schuster, P. (1979) The Hypercycle, Springer Verlag, BerlinGoogle Scholar
  12. Eigen, M. and Schuster, P. (1982), J.Mol.Evol.. in pressGoogle Scholar
  13. Eigen, M., Gardiner, W., Schuster, P. and Winkler-Oswatitsch, R., (1981) Sci.Am. 244 (4), 88CrossRefGoogle Scholar
  14. Epstein, I.R. and Eigen, M. (1979) Biophys.Chem. 10, 153CrossRefGoogle Scholar
  15. Feinberg, M. (1977) Mathematical aspects of mass action kinetics. In Chemical reactor theory (L.Lapidus, N.R.Amundson, eds.)pp. 1–78 Prentice Hall Inc., Englewood Cliffs, N.J.Google Scholar
  16. Fields, S. and Winter, G. (1981) Gene 15, 207CrossRefGoogle Scholar
  17. Fisher, R.A. (1930) The genetic theory of natural selection, Clarendon Press, OxfordGoogle Scholar
  18. Hofbauer, J., Schuster, P. and Sigmund, K. and Wolff, R., (1980) SIAM J.Appl.Math. 38, 282CrossRefGoogle Scholar
  19. Hofbauer, J., Schuster, P. and Sigmund, K. (1981) J.Math.Biol. 11, 155CrossRefGoogle Scholar
  20. Jones, B.L. (1978) J.Math,Biol. 6, 169CrossRefGoogle Scholar
  21. Jones, B.L., Enns, R.H. and Ragnekar, S.S. (1976) Bull.Math.Biol. 38, 12Google Scholar
  22. Kornberg, A. (1980) DNA Replication. W.H.Freeman, San FranciscoGoogle Scholar
  23. Küppers, B.O .(1980) Bull.Math.Biol. 41, 803Google Scholar
  24. Lohrmann, R., Bridson, P.K., and Orgel, L.E. (1980) Science 208, 1464CrossRefGoogle Scholar
  25. Ortin, J., Najera, R., Lopez, C., Davilla, M. and Domingo, E. (1980) Gene 11, 319CrossRefGoogle Scholar
  26. Schuster, P. (1981a) Prebiotic Evolution. In Biochemical Evolution ( H.Gutfreund, ed.) pp. 15–87, Cambridge University Press, Cambridge, U.K.Google Scholar
  27. Schuster, P. (1981b) Selection and evolution in molecular systems. In Nonlinear Phenomena in Physics and Biology ( R.H.Enns, B.L.Jones, R.M.Miura and S.S.Rangnekar, eds.) pp. 485–548. Plenum Publ.Co., New York.Google Scholar
  28. Schuster, P., Sigmund, K. and Wolff, R. (1979) J.Diff.Equs. 32, 357Google Scholar
  29. Spiegelman,S. (1971) Quart,Rev.Biophys. 4, 213Google Scholar
  30. Swetina, J. and Schuster, P. (1982), Biophys.Chem., in pressGoogle Scholar
  31. Thompson, C.J. and McBride, J.L. (1974) Math. Biosc. 21, 127CrossRefGoogle Scholar

Copyright information

© D. Reidel Publishing Company 1983

Authors and Affiliations

  • Peter Schuster
    • 1
  1. 1.Institut für Theoretische Chemie und StrahlenchemieUniversität WienWienAustria

Personalised recommendations