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Evolutionary dynamics and optimization

Neutral networks as model-landscapes for RNA secondary-structure folding-landscapes

  • 2. Origins of Life and Evolution
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Advances in Artificial Life (ECAL 1995)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 929))

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Abstract

We view the folding of RNA-sequences as a map that assigns a pattern of base pairings to each sequence, known as secondary structure. These preimages can be constructed as random graphs (i.e. the neutral networks associated to the structure s).

By interpreting the secondary structure as biological information we can formulate the so called Error Threshold of Shapes as an extension of Eigen's et al. concept of an error threshold in the single peak landscape [5]. Analogue to the approach of Derrida & Peliti [3] for a flat landscape we investigate the spatial distribution of the population on the neutral network.

On the one hand this model of a single shape landscape allows the derivation of analytical results, on the other hand the concept gives rise to study various scenarios by means of simulations, e.g. the interaction of two different networks [29]. It turns out that the intersection of two sets of compatible sequences (with respect to the pair of secondary structures) plays a key role in the search for “fitter” secondary structures.

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References

  1. L. W. Buss. The Evolution of Individuality. Princeton University Press, Princeton, 1987.

    Google Scholar 

  2. R. Dawkins. Replicator selection and the extended phenotype. Zeitschrift für Tierpsychologie, 47:61–76, 1978.

    Google Scholar 

  3. B. Derrida and L. Peliti. Evolution in a flat fitness landscape. Bull. Math. Biol., 53:355–382, 1991.

    Google Scholar 

  4. M. Eigen. Selforganization of matter and the evolution of biological macro-molecules. Die Naturwissenschaften, 10:465–523, 1971.

    Google Scholar 

  5. M. Eigen, J. McCaskill, and P. Schuster. The molecular Quasispecies. Adv. Chem. Phys., 75:149–263, 1989.

    Google Scholar 

  6. M. Eigen and P. Schuster. The Hypercycle: a principle of natural self-organization. Springer, Berlin, 1979 (ZBP:234.

    Google Scholar 

  7. W. Feller. An Introduction to Probability Theory and its Applications, volume I and II. John Wiley, New York, London, Sydney, 1966.

    Google Scholar 

  8. W. Fontana, T. Griesmacher, W. Schnabl, P. Stadler, and P. Schuster. Statistics of landscapes based on free energies, replication and degredation rate constants of RNA secondary structures. Monatshefte der Chemie, 122:795–819, 1991.

    Google Scholar 

  9. W. Fontana, D. A. M. Konings, P. F. Stadler, and P. Schuster. Statistics of RNA secondary structures. Biopolymers, 33:1389–1404, 1993.

    PubMed  Google Scholar 

  10. W. Fontana, W. Schnabl, and P. Schuster. Physical aspects of evolutionary optimization and adaption. Physical Review A, 40(6):3301–3321, Sep. 1989.

    Google Scholar 

  11. W. Fontana, P. F. Stadler, E. G. Bornberg-Bauer, T. Griesmacher, I. L. Hofacker, M. Tacker, P. Tarazona, E. D. Weinberger, and P. Schuster. RNA folding and combinatory landscapes. Phys. Rev. E, 47(3):2083–2099, March 1993.

    Google Scholar 

  12. C. V. Forst, C. Reidys, and P. Schuster. Error thresholds, diffusion, and neutral networks. Artificial Life, 1995. in prep.

    Google Scholar 

  13. C. V. Forst, J. Weber, C. Reidys, and P. Schuster. Transitions and evolutive optimization in Multi Shape landscapes. in prep., 1995.

    Google Scholar 

  14. D. Gillespie. Exact stochastic simulation of coupled chemical reactions. J. Chem. Phys., 81:2340–2361, 1977.

    Google Scholar 

  15. I. L. Hofacker, W. Fontana, P. F. Stadler, S. Bonhoeffer, M. Tacker, and P. Schuster. Fast folding and comparison of RNA secondary structures. Monatshefte f. Chemie, 125(2):167–188, 1994.

    Google Scholar 

  16. M. Huynen, P. F. Stadler, and W. Fontana. Evolutionary dynamics of RNA and the neutral theory. Nature, 1994. submitted.

    Google Scholar 

  17. S. Karlin and H. M. Taylor. A first course in stochastic processes. Academic Press, second edition, 1975.

    Google Scholar 

  18. M. Kimura. Evolutionary rate at the molecular level. Nature, 217:624–626, 1968.

    PubMed  Google Scholar 

  19. M. Kimura. The Neutral Theory of Molecular Evolution. Cambridge Univ. Press, Cambridge, UK, 1983.

    Google Scholar 

  20. D. R. Mills, R. L. Peterson, and S. Spiegelman. An extracellular darwinian experiment with a self-duplicating nucleic acid molecule. Proc. Nat. Acad. Sci., USA, 58:217–224, 1967.

    Google Scholar 

  21. M. Nowak and P. Schuster. Error tresholds of replication in finite populations, mutation frequencies and the onset of Muller's ratchet. Journal of theoretical Biology, 137:375–395, 1989.

    Google Scholar 

  22. C. Reidys, C. V. Forst, and P. Schuster. Replication on neutral networks of RNA secondary structures. Bull. Math. Biol., 1995. submitted.

    Google Scholar 

  23. C. Reidys, P. F. Stadler, and P. Schuster. Generic properties of combinatory maps and neutral networks of RNA secondary structures. Bulletin of Math. Biol., 1995. submitted.

    Google Scholar 

  24. P. Schuster, W. Fontana, P. F. Stadler, and I. L. Hofacker. From sequences to shapes and back: A case study in RNA secondary structures. Proc.Roy.Soc.(London)B, 255:279–284, 1994.

    Google Scholar 

  25. P. Schuster and P. F. Stadler. Landscapes: Complex optimization problems and biomolecular structures. Computers Chem., 18:295–324, 1994.

    Google Scholar 

  26. M. Tacker, W. Fontana, P. Stadler, and P. Schuster. Statistics of RNA melting kinetics. Eur. Biophys. J., 23(1):29–38, 1994.

    Google Scholar 

  27. M. Tacker, P. F. Stadler, E. G. Bornberg-Bauer, I. L. Hofacker, and P. Schuster. Robust Properties of RNA Secondary Structure Folding Algorithms. in preparation, 1993.

    Google Scholar 

  28. G. P. Wagner. What has survived of Darwin's theory? Evolutionary trends in plants, 4(2):71–73, 1990.

    Google Scholar 

  29. J. Weber, C. Reidys, and P. Schuster. Evolutionary optimization on neutral networks of RNA secondary structures. in preparation, 1995.

    Google Scholar 

  30. S. Wolfram. Mathematica: a system for doing mathematics by computer. Addison-Wesley, second edition, 1991.

    Google Scholar 

  31. S. Wright. The roles of mutation, inbreeding, crossbreeeding and selection in evolution. In D. F. Jones, editor, int. Proceedings of the Sixth International Congress on Genetics, volume 1, pages 356–366, 1932.

    Google Scholar 

  32. S. Wright. Random drift and the shifting balance theory of evolution. In K. Kojima, editor, Mathematical Topics in Population Genetics, pages 1–31. Springer Verlag, Berlin, 1970.

    Google Scholar 

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Correspondence to Christian V. Forst .

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Federico Morán Alvaro Moreno Juan Julián Merelo Pablo Chacón

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Forst, C.V., Reidys, C., Weber, J. (1995). Evolutionary dynamics and optimization. In: Morán, F., Moreno, A., Merelo, J.J., Chacón, P. (eds) Advances in Artificial Life. ECAL 1995. Lecture Notes in Computer Science, vol 929. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59496-5_294

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  • DOI: https://doi.org/10.1007/3-540-59496-5_294

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