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A testable genotype-phenotype map: modeling evolution of RNA molecules

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Biological Evolution and Statistical Physics

Part of the book series: Lecture Notes in Physics ((LNP,volume 585))

Abstract

Recent experiments and progress in modelling evolution in silico converge towards a coherent view of Darwinian evolution in molecular systems. Conventional population genetics and quasi-species theory model evolution in genotype space and properties of phenotypes enter evolutionary dynamics as parameters only. RNA evolution in vitro is an appropriate basis for the development of a new and comprehensive model of evolution, which is focussed on the phenotype and its fitness relevant properties. Relation between genotypes and phenotypes are described by mappings from genotype space onto a space of phenotypes. These mappings are many-to-one and thus give ample room for neutrality. The RNA model reduces genotype-phenotype relations to a mapping from sequences into secondary structures with minimal free energies and allows to derive otherwise inaccessible quantitative results. RNA sequences that fold into the same structure form neutral networks in genotype space, which determine the course of evolution. Neutral networks are embedded in sets of compatible sequences. Intersections of these sets represent regions in sequence space where single molecules can form two or more structures. Continuity and discontinuity in evolution are defined through straightforward interpretation of computer simulations of RNA optimization. In silico evolution provides insight into the accessibility of phenotypes and demonstrate the constructive role of random genetic drift in the search for phenotypes of higher fitness. New experimental data, among them the results of genome research, will present a solid basis for test and further development of the model for phenotype evolution.

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References

  1. S. Spiegelman. An approach to the experimental analysis of precellular evolution. Quart.Rev. Biophys., 4:213–253, 1971.

    Article  CAS  Google Scholar 

  2. C. K. Biebricher and M. Eigen. Kinetics of RNA replication by Qβ replicase. In E. Domingo, J. J. Holland, and P. Ahlquist, editors, RNA Genetics I: RNAdirected Virus Replication., pages 1–21. Plenum Publishing Corporation, Boca Raton, Florida, 1987.

    Google Scholar 

  3. M. Eigen and W. C. Gardiner. Evolutionary molecular engineering based on RNA replication. Pure Appl. Chem., 56:967–978, 1984.

    Article  CAS  Google Scholar 

  4. A. Watts and G. Schwarz, editors. Evolutionary Biotechnology-From Theory to Experiment, volume 66/2–3 of Biophysical Chemistry. Elesvier, Amsterdam, 1997.

    Google Scholar 

  5. L. Gold, C. Tuerk, P. Allen, J. Binkley, D. Brown, L. Green, S. MacDougal, D. Schneider, D. Tasset, and S. R. Eddy. RNA: The shape of things to come. In R. F. Gesteland and J. F. Atkins, editors, The RNA World, pages 497–509. Cold Spring Harbor Laboratory Press, Plainview, NY, 1993.

    Google Scholar 

  6. D. S. Wilson and J. W. Szostak. In vitro selection of fuctional nucleic acids. Annu.Rev. Biochem., 68:611–647, 1999.

    Article  PubMed  CAS  Google Scholar 

  7. B. I. Dahiyat, C. A. Sarisky, and S. L. Mayo. De Novo protein design: Towards fully automated sequence selection. J. Mol. Biol., 273:789–796, 1997.

    Article  PubMed  CAS  Google Scholar 

  8. A. A. Beaudry and G. F. Joyce. Directed evolution of an RNA enzyme. Science, 257:635–641, 1992.

    Article  PubMed  CAS  Google Scholar 

  9. R. R. Breaker. In vitro selection of catalytic polynucleotides. Chem.Rev., 97:371–390, 1997.

    Article  PubMed  CAS  Google Scholar 

  10. N. Lehman and G. F. Joyce. Evolution in vitro: Analysis of a lineage of ribozymes. Current Biology, 3:723–734, 1993.

    Article  PubMed  CAS  Google Scholar 

  11. D. P. Bartel and J. W. Szostak. Isolation of new ribozymes from a large pool of random sequences. Science, 261:1411–1418, 1993.

    Article  PubMed  CAS  Google Scholar 

  12. E. Mayr and W. B. Provine, editors. The Evolutionary Synthesis. Perspectives of the Unification of Biology. Harvard University Press, Cambridge, MA, 1980.

    Google Scholar 

  13. R. A. Fisher. The Genetical Theory of Natural Selection. Oxford University Press, Oxford, UK, 1930.

    Google Scholar 

  14. M. Kimura. The Neutral Theory of Molecular Evolution. Cambridge University Press, Cambridge, UK, 1983.

    Google Scholar 

  15. J. L. King and T. H. Jukes. Non-Darwinian evolution: Random fixation of selectively neutral variants. Science, 164:788–798, 1969.

    Article  PubMed  CAS  Google Scholar 

  16. W.-H. Li and D. Graur. Fundamentals of Molecular Evolution. Sinauer Associates, Sunderland, MA, 1991.

    Google Scholar 

  17. L. H. Caporale, editor. Molecular Strategies in Biological Evolution, volume 870 of Annals New York Acad. Sci. New York Academy of Sciences, New York, 1999.

    Google Scholar 

  18. F. J. Ayala. Vagaries of the molecular clock. Proc. Natl. Acad. Sci. USA, 94:7776–7783, 1997.

    Google Scholar 

  19. D. Papadopoulos, D. Schneider, J. Meier-Eiss, W. Arber, R. E. Lenski, and M. Blot. Genomic evolution during a 10 000-generation experiment with bacteria. Proc. Natl.Acad. Sci.USA, 96:3807–3812, 1999.

    Google Scholar 

  20. M. Eigen. Selforganization of matter and the evolution of biological macromolecules. Naturwissenschaften, 58:465–523, 1971.

    Article  PubMed  CAS  Google Scholar 

  21. R. W. Hamming. Error detecting and error correcting codes. Bell Syst.Tech. J., 29:147–160, 1950.

    Google Scholar 

  22. M. Eigen and P. Schuster. The hypercycle. A principle of natural self-organization. Part A: Emergence of the hypercycle. Naturwissenschaften, 64:541–565, 1977.

    Article  PubMed  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  24. C. K. Biebricher and W. C. Gardiner. Molecular evolution of RNA in vitro. Biophys. Chem., 66:179–192, 1997.

    Article  PubMed  CAS  Google Scholar 

  25. E. Domingo. Biological significance of viral quasispecies. Viral Hepatitis Reviews, 2:247–261, 1996.

    Google Scholar 

  26. E. Domingo and J. J. Holland. RNA virus mutations and fitness for survival. Annu.Rev. Microbiol., 51:151–178, 1997.

    Article  PubMed  CAS  Google Scholar 

  27. J. W. Drake. A constant rate of spontaneous mutation in DNA-based microbes. Proc. Natl.Acad. Sci., 88:7160–7164, 1991.

    Google Scholar 

  28. J. W. Drake. Rates of spontaneous mutation among RNA viruses. Proc. Natl. Acad. Sci., 90:4171–4175, 1993.

    Google Scholar 

  29. J. W. Drake, B. Charlesworth, D. Charlesworth, and J. F. Crow. Rates of spontaneous mutation. Genetics, 148:1667–1686, 1998.

    PubMed  CAS  Google Scholar 

  30. J. W. Drake. The distribution of rates of spontaneous mutation over viruses, prokaryotes, and eukaryotes. Annals of the New York Academy of Sciences, 870:100–107, 1999.

    Article  PubMed  CAS  Google Scholar 

  31. P. F. Stadler. Landscapes and their correlation functions. J. Math. Chem., 20:1–45, 1996.

    Article  CAS  Google Scholar 

  32. P. F. Stadler. Fitness landscapes arising from the sequence-structure maps of biopolymers. J. Mol. Struct. (Theochem), 463:7–19, 1999.

    Article  CAS  Google Scholar 

  33. P. F. Stadler, R. Seitz, and G. P. Wagner. Population dependent fourier decomposition of fitness landscapes over recombination spaces: Evolvability of complex characters. Bull. Math. Biol., 62:399–428, 2000.

    Article  PubMed  CAS  Google Scholar 

  34. C. M. Reidys and P. F. Stadler. Combinatorial landscapes. SIAM Rev., 2001. In press.

    Google Scholar 

  35. B. Derrida. Random-energy model: An exactly solvable model of disordered systems. Phys. Rev. B, 24:2613–2626, 1981.

    Article  CAS  Google Scholar 

  36. C. Amitrano, L. Peliti, and M. Saber. Population dynamics in a spin-glass model of chemical evolution. J. Mol. Evol., 29:513–525, 1989.

    Article  PubMed  CAS  Google Scholar 

  37. P. Tarazona. Error threshold for molecular quasispecies as phase transitions: From simple landscapes to spin-glass models. Phys.Rev.A, 45:6038–6050, 1992.

    Article  PubMed  CAS  Google Scholar 

  38. S. A. Kauffman. The Origins of Order. Self-Organization and Selection in Evolution. Oxford University Press, Oxford, UK, 1993.

    Google Scholar 

  39. J. Swetina and P. Schuster. Self-replication with errors-A model for polynucleotide replication. Biophys. Chem., 16:329–345, 1982.

    Article  PubMed  CAS  Google Scholar 

  40. P. Schuster and J. Swetina. Stationary mutant distribution and evolutionary optimization. Bull. Math. Biol., 50:635–660, 1988.

    PubMed  CAS  Google Scholar 

  41. C. Reidys, P. F. Stadler, and P. Schuster. Generic properties of combinatory maps. Neutral networks of RNA secondary structure. Bull. Math. Biol., 59:339–397, 1997.

    Article  PubMed  CAS  Google Scholar 

  42. W. Grüner, R. Giegerich, D. Strothmann, C. Reidys, J. Weber, I. L. Hofacker, P. F. Stadler, and P. Schuster. Analysis of RNA sequence structure maps by exhaustive enumeration. I. Neutral networks. Mh.Chem., 127:355–374, 1996.

    Google Scholar 

  43. W. Grüner, R. Giegerich, D. Strothmann, C. Reidys, J. Weber, I. L. Hofacker, P. F. Stadler, and P. Schuster. Analysis of RNA sequence structure maps by exhaustive enumeration. II. Structure of neutral networks and shape space covering. Mh.Chem., 127:375–389, 1996.

    Google Scholar 

  44. 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, 47:2083–2099, 1993.

    Article  CAS  Google Scholar 

  45. 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 

  46. W. Fontana and P. Schuster. Shaping space: The possible and the attainable in RNA genotype-phenotype mapping. J. Theor. Biol., 194:491–515, 1998.

    Article  PubMed  CAS  Google Scholar 

  47. W. Fontana and P. Schuster. Continuity in evolution: On the nature of transitions. Science, 280:1451–1455, 1998.

    Article  PubMed  CAS  Google Scholar 

  48. M. A. Huynen, P. F. Stadler, and W. Fontana. Smoothness within ruggedness: The role of neutrality in adaptation. Proc. Natl.Acad. Sci.USA, 93:397–401, 1996.

    Google Scholar 

  49. E. van Nimwegen, J. P. Crutchfield, and M. Mitchell. Finite populations induce metastability in evolutionary search. Phys. Lett.A, 229:144–150, 1997.

    Article  Google Scholar 

  50. R. T. Batey, R. P. Rambo, and J. A. Doudna. Tertiary motifs in structure and folding of RNA. Angew. Chem. Int. Ed., 38:2326–2343, 1999.

    Article  Google Scholar 

  51. P. G. Higgs. RNA secondary structures-Physical and computational aspects. Quart.Rev. Biophys., 33:199–253, 2000.

    Article  CAS  Google Scholar 

  52. M. Zuker and P. Stiegler. Optimal computer folding of larger RNA sequences using thermodynamics and auxiliary information. Nucleic Acids Research, 9:133–148, 1981.

    Article  PubMed  CAS  Google Scholar 

  53. I. L. Hofacker, W. Fontana, P. F. Stadler, L. S. Bonhoeffer, M. Tacker, and P. Schuster. Fast folding and comparison of RNA secondary structures. Mh. Chem., 125:167–188, 1994.

    CAS  Google Scholar 

  54. R. Nussinov and A. B. Jacobson. Fast algorithm for predicting the secondary structure of single-stranded RNA. Proc. Natl.Acad. Sci., 77:6309–6313, 1980.

    Google Scholar 

  55. M. S. Waterman and T. H. Byers. A dynamic programming algorithm to find all solutions in a neighborhood of the optimum. Math. Biosc., 77:179–188, 1985.

    Article  Google Scholar 

  56. P. Schuster and P. F. Stadler. Discrete models of biopolymers. In M. J. C. Crabbe, M. Drew, and A. Konopka, editors, Handbook of Computational Chemistry. Marcel Dekker, New York, 2000. In press.

    Google Scholar 

  57. P. Schuster. Molecular insight into the evolution of phenotypes. In J. P. Crutch-field and P. Schuster, editors, Evolutionary Dynamics-Exploringthe Interplay of Accident, Selection, Neutrality, and Function. Oxford University Press, New York, 2001. In press.

    Google Scholar 

  58. J. Rogers and G. F. Joyce. A ribozyme that lacks cytidine. Nature, 402:323–325, 1999.

    Article  PubMed  CAS  Google Scholar 

  59. I. L. Hofacker, P. Schuster, and P. F. Stadler. Combinatorics of RNA secondary structures. Discr. Appl.Math., 89:177–207, 1999.

    Google Scholar 

  60. E. A. Schultes and D. P. Bartel. One sequence, two ribozymes: Implications for the emergence of new ribozyme folds. Science, 289:448–452, 2000.

    Article  PubMed  CAS  Google Scholar 

  61. E. H. Ekland, J. W. Szostak, and D. P. Bartel. Structurally complex and highly active RNA ligases derived from random RNA sequences. Science, 269:364–370, 1995.

    Article  PubMed  CAS  Google Scholar 

  62. A. T. Perrotta and M. D. Been. A toggle duplex in hepatitis delta virus selfcleaving RNA that stabilizes an inactive and a salt-dependent pro-active ribozyme conformation. J. Mol. Biol., 279:361–373, 1998.

    Article  PubMed  CAS  Google Scholar 

  63. W. Fontana and P. Schuster. A computer model of evolutionary optimization. Biophys. Chem., 26:123–147, 1987.

    Article  PubMed  CAS  Google Scholar 

  64. W. Fontana, W. Schnabl, and P. Schuster. Physical aspects of evolutionary optimization and adaptation. Phys.Rev.A, 40:3301–3321, 1989.

    Article  PubMed  CAS  Google Scholar 

  65. D. T. Gillespie. A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J. Comp. Phys., 22:403–434, 1976.

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  67. C. M. Reidys, C. V. Forst, and P. Schuster. Replication and mutation on neutral networks. J. Math. Biol., 63:57–94, 2001.

    Article  CAS  Google Scholar 

  68. P. Schuster and A. Wernitznig. Stochastic dynamics of neutral evolution: RNA in the flow reactor, 2001. Preprint.

    Google Scholar 

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

    Google Scholar 

  70. G. Zipf. Human Behaviour and the Principle of Least Effort. Addison-Wesley, Reading, MA, 1949.

    Google Scholar 

  71. J. Cupal, P. Schuster, and P. F. Stadler. Topology in phenotype space. In Computer Science in Biology, GCB’99 Proceedings, pages 9–15. Univ. Bielefeld, Hannover, DE, 1999.

    Google Scholar 

  72. J. Cupal, S. Kopp, and P. F. Stadler. RNA shape space topology. Artificial Life, 6:3–23, 2000.

    Article  PubMed  CAS  Google Scholar 

  73. B. M. Stadler, P. F. Stadler, G. P. Wagner, and W. Fontana. The topology ofthe possible: Formal spaces underlying patterns of evolutionary change. J. Theor. Biol., 2000. Submitted.

    Google Scholar 

  74. N. S. Goel and N. Richter-Dyn. Stochastic Models in Biology. Academic Press, New York, 1974.

    Google Scholar 

  75. S. F. Elena, V. S. Cooper, and R. E. Lenski. Punctuated evolution caused by selection of rare beneficial mutants. Science, 272:1802–1804, 1996.

    Article  PubMed  CAS  Google Scholar 

  76. H. Li, R. Helling, C. Tang, and N. Wingreen. Emergence of preferred structures in a simple model of protein folding. Science, 273:666–669, 1996.

    Article  PubMed  CAS  Google Scholar 

  77. S. Govindarajan and R. A. Goldstein. Why are some protein structures so common? Proc. Natl.Acad. Sci.,USA, 93:3341–3345, 1996.

    Google Scholar 

  78. A. Babajide, I. L. Hofacker, M. J. Sippl, and P. F. Stadler. Neutral networks in protein space: A computational study based on knowledge-based potentials of mean force. Folding and Design, 2:261–269, 1997.

    Article  PubMed  CAS  Google Scholar 

  79. S. Govindarajan and R. A. Goldstein. The foldability landscape of model proteins. Biopolymers, 42:427–438, 1997.

    Article  PubMed  CAS  Google Scholar 

  80. S. Govindarajan and R. A. Goldstein. Evolution of model proteins on a foldability landscape. Proteins, 29:461–466, 1997.

    Article  PubMed  CAS  Google Scholar 

  81. S. Gavrilets. Evolution and speciation on holey adaptive landscapes. Trends in Ecology and Evolution, 12:307–312, 1997.

    Article  Google Scholar 

  82. S. Gavrilets. Evolution and speciation in a hyperspace: The roles of neutrality, selection, mutation, and random drift. In J. P. Crutchfield and P. Schuster, editors, Evolutionary Dynamics-Exploringthe Interplay of Accident, Selection, Neutrality, and Function. Oxford University Press, New York, 2001. In press.

    Google Scholar 

  83. L. W. Ancel and W. Fontana. Plasticity, evolvability, and modularity in RNA. J. Exp. Zool. (Mol.Dev.Evol.), 288:242–283, 2000.

    Article  CAS  Google Scholar 

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  1. Institute für Theoretische Chemie und Molekulare Strukturbiologie, Universität Wien, Währingerstraβe 17, A-1090, Wien, Austria

    Peter Schuster

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

    Peter Schuster

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  1. Peter Schuster
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  1. Institute for Theoretical Physics, University of Cologne, Zülpicher Straße 77, 50937, Köln, Germany

    Michael Lässig

  2. Theory Division, MPI for Colloids and Interfaces, 14424, Potsdam, Germany

    Angelo Valleriani

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Schuster, P. (2002). A testable genotype-phenotype map: modeling evolution of RNA molecules. In: Lässig, M., Valleriani, A. (eds) Biological Evolution and Statistical Physics. Lecture Notes in Physics, vol 585. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45692-9_4

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  • DOI: https://doi.org/10.1007/3-540-45692-9_4

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