Monatshefte für Chemie / Chemical Monthly

, Volume 122, Issue 10, pp 795–819 | Cite as

Statistics of landscapes based on free energies, replication and degradation rate constants of RNA secondary structures

  • Walter Fontana
  • Thomas Griesmacher
  • Wolfgang Schnabl
  • Peter F. Stadler
  • Peter Schuster
Anorganische Und Physikalische Chemie


RNA secondary structures are computed from primary sequences by means of a folding algorithm which uses a minimum free energy criterion. Free energies as well as replication and degradation rate constants are derived from secondary structures. These properties can be understood as highly sophisticated functions of the individual sequences whose values are mediated by the secondary structures. Such functions induce complex value landscapes on the space of sequences. The landscapes are analysed by random walk techniques, in particular autocorrelation functions and correlation lengths are computed. Free energy landscapes were found to be of AR(1) type. The rate constant landscapes, however, turned out to be more complex. In addition, gradient and adaptive walks are performed in order to get more insight into the complex structure of the landscapes.


RNA secondary structures RNA free energies Value landscapes Autocorrelation functions Correlation lengths 

Statistik von Landschaften aus freien Energien, Replikations- und Abbaugeschwindigkeitskonstanten von RNA-Sekundärstrukturen


RNA-Sekundärstrukturen werden aus den Primärsequenzen mit Hilfe eines Computeralgorithmus berechnet, welcher einem Kriterium minimaler freier Energien folgt. Freie Energien, Replikations- oder Abbaugeschwindigkeitskonstanten werden aus den Sekundärstrukturen berechnet. Man kann daher diese Eigenschaften als komplizierte Funktionen der Sequenzen auffassen, deren Zahlenwerte durch Vermittlung der Sekundärstrukturen erhalten werden. Diese Funktionen induzieren hochkomplexe Bewertungslandschaften im Raum der Sequenzen. Die Landschaften werden mit Hilfe von Irrflugtechniken analysiert. Im einzelnen werden Autokorrelationsfunktionen und Korrelationslängen berechnet. Die freien Energie-Landschaften sind vom AR(1) Typ. Die von den Reaktionsgeschwindigkeitskonstanten abgeleiteten Landschaften stellten sich hingegen als komplexer heraus. Zusätzlich werden die Bewertungslandschaften auch noch mit Hilfe vonGradient undAdaptive Walks untersucht, um mehr Einblick in ihre komplexe Struktur zu gewinnen.


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  1. [1]
    Horwitz M. S. Z., Dube D. K., Loeb L. A. (1989) Genome31: 112Google Scholar
  2. [2]
    Joyce G. F. (1989) Gene82: 83Google Scholar
  3. [3]
    Tuerk C., Gold L. (1990) Science249: 505Google Scholar
  4. [4]
    Ellington A. D., Szostak J. W. (1990) Nature346: 818Google Scholar
  5. [5]
    Husimi Y., Keweloh C. (1987) Rev. Sci. Instrum.58: 1109Google Scholar
  6. [6]
    Biebricher C. K. (1988) Cold Spring Harbor Symp. Quant. Biol.52: 299Google Scholar
  7. [7]
    Spiegelman S. (1971) Quart. Rev. Biophys.4: 213Google Scholar
  8. [8]
    Eigen M. (1986) Chemica Scripta26B: 13Google Scholar
  9. [9]
    Kauffman S. A. (1986) J. Theor. Biol.119: 1Google Scholar
  10. [10]
    Lerner R. A., Tramontano A. (1988) Sci. Am.258/3: 42Google Scholar
  11. [11]
    Schulz P., Lerner R. A. (in press) At the cross-roads of chemistry and immunology: Catalytic antibodies. ScienceGoogle Scholar
  12. [12]
    Wright S. (1932) Proceedings of the Sixth International Congress on Genetics1: 356Google Scholar
  13. [13]
    Kauffman S. A., Levin S. (1987) J. theor. Biol.128: 11Google Scholar
  14. [14]
    Kauffman S. A. (1989) Adaptation on rugged fitness landscapes. In: Stein D. (ed.) Complex Systems (SFI Studies in the Science of Complexity). Addison-Wesley Longman, Redwood City, CA, pp. 527–618Google Scholar
  15. [15]
    Macken C. A., Perelson A. S. (1989) Proc. Natl. Acad. Sci. USA86: 6191Google Scholar
  16. [16]
    Fontana W., Schuster P. (1987) Biophys. Chem.26: 123Google Scholar
  17. [17]
    Fontana W., Schnabl W., Schuster P. (1989) Phys. Rev. A40: 3301Google Scholar
  18. [18]
    Schuster P. (1991) Complex optimization in an artificial RNA world. In: Farmer D., Langton C., Rasmussen S., Taylor C. (eds.) Artificial Life II (SFI Studies in the Sciences of Complexity, Vol. XII). Addison-Wesley Longman, Redwood City, CAGoogle Scholar
  19. [19]
    Eigen M., McCaskill J., Schuster P. (1988) J. Phys. Chem.92: 6881Google Scholar
  20. [20]
    Schuster P., Swetina J. (1988) Bull. Math. Biol.50: 635Google Scholar
  21. [21]
    Eigen M., McCaskill J., Schuster P. (1989) Adv. Chem. Phys.75: 149Google Scholar
  22. [22]
    Biebricher C. K., Eigen M., Gardiner jr., W. A. (in press) Quantitative analysis of selection and mutation in self-replicating RNA. In: Peliti L. (ed.) Biologically Inspired Physics (NATO Advanced Study Series)Google Scholar
  23. [23]
    Jaeger J. A., Turner D. H., Zuker M. (1989) Proc. Natl. Acad. Sci. USA86: 7706Google Scholar
  24. [24]
    Fontana W., Konings D. A. M., Schuster P. (1991) Statistics of RNA Secondary Structures (Preprint)Google Scholar
  25. [25]
    Sankoff D., Morin A.-M., Cedergren R. J. (1978) Can. J. Biochem.56: 440Google Scholar
  26. [26]
    Cech T. R. (1988) Gene73: 259Google Scholar
  27. [27]
    Le S.-Y., Zuker M. (1990) J. Mol. Biol.216: 729Google Scholar
  28. [28]
    Zuker M., Sankoff D. (1984) Bull. Math. Biol.46: 591Google Scholar
  29. [29]
    Zuker M. (1989) Science244: 48Google Scholar
  30. [30]
    Jaeger J. A., Turner D. H., Zuker M. (1990) Methods in Enzymology183: 281Google Scholar
  31. [31]
    McCaskill J. S. (1990) Biopolymers29: 1105Google Scholar
  32. [32]
    Hamming R. W. (1989) Coding and Information Theory, 2nd Ed. Prentice-Hall, Englewood Cliffs, NJ, pp. 44–47Google Scholar
  33. [33]
    Maynard Smith J. (1970) Nature225: 563Google Scholar
  34. [34]
    Shapiro B. A. (1988) CABIOS4: 387Google Scholar
  35. [35]
    Shapiro B. A., Zhang K. (1990) CABIOS6: 309Google Scholar
  36. [36]
    Sankoff D., Kruskal J. B. (1983) Time Warps, String Edits, and Macromolecules: The Theory and Practice of Sequence Comparison. Addison-Wesley, ReadingGoogle Scholar
  37. [37]
    Tai K.-C. (1979) J. Ass. Computing Machinery26: 422Google Scholar
  38. [38]
    Hogeweg P., Hesper B. (1984) Nucleic Acids Research12: 67Google Scholar
  39. [39]
    Konings D. A. M. (1989) Pattern Analysis of RNA Secondary Structure (Proefschrift) Rijksuniversiteit te UtrechtGoogle Scholar
  40. [40]
    Konings D. A. M., Hogeweg P. (1989) J. Mol. Biol.207: 597Google Scholar
  41. [41]
    Fontana W., Konings D. A. M., Stadler P. F., Schuster P. (1991) Quantitative comparison and Statistics of RNA Secondary Structures (Preprint)Google Scholar
  42. [42]
    Karlin S., Taylor H. M. (1975) A First Course in Stochastic Processes, 2nd Ed. Academic Press, New York, pp. 455–461Google Scholar
  43. [43]
    Weinberger E. D. (1990) Biol. Cybern.63: 325Google Scholar
  44. [44]
    Sherrington D., Kirkpatrick S. (1975) Phys. Rev. Lettes35: 1792Google Scholar
  45. [45]
    Stadler P. F., Schnabl W. (1991) The Landscape of the Traveling Salesman Problem (Preprint)Google Scholar
  46. [46]
    Freier S. M., Kierzek R., Jaeger J. A., Sugimoto N., Caruthers M. H., Neilkson T., Turner D. H. (1986) Proc. Natl. Acad. Sci. USA83: 9373Google Scholar
  47. [47]
    Fontana W., Stadler P. F., Griesmacher T., Weinberger E. D., Schuster P. (1991) Statistical Properties of RNA Free Energy Landscapes. A Study by Random Walk Techniques (Preprint)Google Scholar

Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Walter Fontana
    • 2
    • 3
  • Thomas Griesmacher
    • 1
  • Wolfgang Schnabl
    • 1
  • Peter F. Stadler
    • 1
  • Peter Schuster
    • 1
    • 3
  1. 1.Institut für Theoretische ChemieUniversität WienWienAustria
  2. 2.Los Alamos National LaboratoryUSA
  3. 3.Santa Fe InstituteUSA

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