Generic properties of combinatory maps: Neutral networks of RNA secondary structures

Bulletin of Mathematical Biology

Volumn 59, Issue 2, 1997, Pages 339-397

  Reidys, Christian ^a,b   Stadler, Peter F ^a,c   Schuster, Peter ^a,c,d  

^a SANTA FE INSTITUTE   (United States)

^b LOS ALAMOS NATIONAL LABORATORY   (United States)

^c UNIVERSITY OF VIENNA   (Austria)

^d FRITZ LIPMANN INSTITUTE   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

FUNGAL RNA; PHENYLALANINE TRANSFER RNA; RNA;

ARTICLE; CHEMICAL STRUCTURE; CHEMISTRY; CHROMOSOME MAP; CONFORMATION; GENETICS; MATHEMATICS; MOLECULAR EVOLUTION; MOLECULAR GENETICS; MUTATION; NUCLEOTIDE SEQUENCE; POINT MUTATION; PROBABILITY; RNA SEQUENCE; RNA STRUCTURE; SACCHAROMYCES CEREVISIAE; STATISTICAL MODEL; THEORY;

EID: 0031105866     PISSN: 00928240     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02462007     Document Type: Article

References (50)

1. Ajtai, M., J. Komlós and E. Szemerédi. 1982, Largest random component of a k-cube. Combinatorica 2, 1-7.
2. Bollobás, B. 1985. Random Graphs. London: Academic Press.
3. Bonhoeffer, S. and P. F. Stadler. 1993. Error threshold on complex fitness landscapes. J. Theor. Biol. 164, 359-372.
4. Buckley, F. and F. Harrary. 1990. Distances in Graphs. Reading, MA: Addison-Wesley.
5. Derrida, B. and L. Peliti. 1991. Evolution in a flat fitness landscape. Bull. Math. Biol. 53, 355-382.
6. Eigen, M. 1971. Self-organization of matter and the evolution of biological macromolecules. Naturwissenschaften 58, 465-523.
7. Eigen, M., J. McCaskill and P. Schuster. 1989. The molecular quasispecies. Adv. Chem. Phys. 75, 149-263.
8. Eigen, M. and P. Schuster. 1977. The hypercycle. A principle of natural self-organization. Part A: emergence of the hypercycle. Naturwissenschaften 64, 541-565.
9. Fontana, W., T. Griesmacher, W. Schnabl, P. F. Stadler and P. Schuster. 1991. Statistics of landscapes based on free energies, replication and degradation rate constants of RNA secondary structures. Mh. Chem. 122, 795-819.
10. Fontana, W., W. Schnabl and P. Schuster. 1989. Physical aspects of evolutionary optimization and adaptation. Phys. Rev. A 40, 3301-3321.
11. Fontana, W. and P. Schuster. 1987. A computer model of evolutionary optimization. Biophys. Chem. 26, 123-147.
12. Fontana, W., D. A. M. Konings, P. F. Stadler and P. Schuster. 1993a. Statistics of RNA secondary structures. Biopolymers 33, 1389-1404.
13. Fontana, W., P. F. Stadler, E. G. Bornberg-Bauer, T. Griesmacher, I. L. Hofacker, M. Tacker, P. Tarazona, E. D. Weinberger and P. Schuster. 1993b. RNA folding and combinatory landscapes. Phys. Rev. E 47, 2083-2099.
14. Freier, S., R. Kierzek, J. Jaeger, N. Sugimoto, M. Caruthers, T. Neilson and D. Turner. 1986. Improved free-energy parameters for predictions of RNA duplex stability. Proc. Natl. Acad. Sci. USA 83, 9373-9377.
15. Grüner, W., R. Giegerich, D. Strothmann, C. Reidys, J. Weber, I. L. Hofacker, P. F. Stadler and P. Schuster. 1996a. Analysis of RNA sequence structure maps by exhaustive enumeration. I. Neutral networks. Mh. Chem. 127, 355-374.
16. Grüner, W., R. Giegerich, D. Strothmann, C. Reidys, J. Weber, I. L. Hofacker, P. F. Stadler and P. Schuster. 1996b. Analysis of RNA sequence structure maps by exhaustive enumeration. II. Structure of neutral networks and shape space covering. Mh. Chem. 127, 375-389.
17. Hamming, R. W. 1950. Error detecting and error correcting codes. Bell Syst. Tech. J. 29, 147-160.
18. Harper, L. 1966. Minimal numberings and isoperimetric problems on cubes. Theory of Graphs, International Symposium. Rome.
19. Hofacker, I. L. 1994. A Statistical Characterization of the Sequence to Structure Mapping in RNA. Ph.D. thesis, Universität Wien.
20. Hofacker, I. L., W. Fontana, P. F. Stadler, S. Bonhoeffer, M. Tacker and P. Schuster. 1994. Fast folding and comparison of RNA secondary structures. Mh. Chem. 125, 167-188.
21. Hofacker, I. L., P. Schuster and P. F. Stadler. 1996. Combinatorics of RNA secondary structures. Preprint.
22. Hogeweg, P. and B. Hesper. 1984. Energy directed folding of RNA sequences. Nucleic Acids Res. 12, 67-74.
23. Huynen, M. A., P. F. Stadler and W. Fontana. 1996. Smoothness within ruggedness: the role of neutrality in adaptation. Proc. Natl. Acad. Sci. USA 93, 397-401.
24. Kesten, H. 1982. Percolation Theory for Mathematics. Boston, MA: Birkhäuser.
25. Kimura, M. 1983. The Neutral Theory of Molecular Evolution. Cambridge: Cambridge University Press.
26. Konings, D. and P. Hogeweg. 1989. Pattern analysis of RNA secondary structure. Similarity and consensus of minimal-energy folding. J. Mol. Biol. 207, 597-614.
27. Li, H., R. Helling, C. Tang and N. Wingreen. 1996. Emergence of preferred structures in a simple model of protein folding. Science 273, 666-669.
28. Martinez, H. 1984. An RNA folding rule. Nucleic Acids Res. 12, 323-335.
29. McCaskill, J. 1990. The equilibrium partition function and base pair binding probabilities for RNA secondary structure. Biopolymers 29, 1105-1119.
30. Nowak, M. and P. Schuster. 1989. Error thresholds of replication in finite populations. Mutation frequencies and the onset of Muller's ratchet. J. Theor. Biol. 137, 375-395.
31. Nussinov, R., G. Piecznik, J. Griggs and D. Kleitman. 1978. Algorithms for loop matching. SIAM J. Appl. Math. 35, 68-82.
32. Reidys, C. 1995. Neutral Networks of RNA Secondary Structures. Ph.D. thesis, Friedrich-Schiller-Universität Jena.
33. Reidys, C., C. V. Forst and P. Schuster. 1996. Replication on neutral networks of RNA secondary structures. Preprint.
34. Riordan, J. 1978. An Introduction to Combinatorial Analysis. Princeton, NJ: Princeton University Press.
35. Salser, W. 1977. Globin messenger RNA sequences - analysis of base-pairing and evolutionary implications. Cold Spring Harbor Symp. Quant. Biol. 42, 985.
36. Sankoff, D., G. Leduc, N. Antoine, B. Paquin, B. F. Lang and R. Cedergren. 1992. Gene comparisons for phylogenetic inference: evolution of the mitochondrial genome. Proc. Natl. Acad. Sci. USA 89, 6575-6579.
37. Schuster, P. 1995a. Artificial life and molecular evolutionary biology. In Advances in Artificial Life, F. Morán, A. Moreno, J. J. Morelo and P. Chacón (Eds). Lecture Notes in Artificial Intelligence, Vol. 929, pp. 3-19. Berlin: Springer-Verlag.
38. Schuster, P. 1995b. How to search for RNA structures. Theoretical concepts in evolutionary biotechnology. J. Biotechnol. 41, 239-257.
39. Schuster, P., W. Fontana, P. F. Stadler and K. L. Hofacker. 1994. From sequences to shapes and back: a case study in RNA secondary structures. Proc. Roy. Soc. (London) B 255, 279-284.
40. Schuster, P. and P. F. Stadler. 1994. Landscapes: complex optimization problems and biopolymer structures. Computers Chem. 18, 295-314.
41. Serre, J.-P. 1977. Linear Representations of Finite Groups. Berlin: Springer.
42. Shapiro, B. A. 1988. An algorithm for comparing multiple RNA secondary structures. CABIOS 4, 381-393.
43. Shapiro, B. A. and K. Zhang. 1990. Comparing multiple RNA secondary structures using tree comparisons. CABIOS 6, 309-318.
44. Stauffer, D. 1985. Introduction to Percolation Theory. London: Taylor and Francis.
45. Tacker, M., W. Fontana, P. F. Stadler and P. Schuster. 1994. Statistics of RNA melting kinetics. Eur. Biophys. J. 23, 29-38.
46. Tacker, M., P. F. Stadler, E. G. Bornberg-Bauer, K. L. Hofacker and P. Schuster. 1996. Algorithm independent properties of RNA secondary structure predictions. Eur. Biophys. J. 25, 115-130.
47. Turner, D. H., N. Sugimoto and S. Freier. 1988. RNA structure prediction. Annual Review of Biophysics and Biophysical Chemistry 17, 167-192.
48. Waterman, M. S. 1978. Secondary structure of single-stranded nucleic acids. Adv. in Math. 1, 167-212.
49. Zuker, M. and D. Sankoff. 1984. RNA secondary structures and their prediction. Bull. Math. Biol. 46, 591-621.
50. Zuker, M. and P. Stiegler. 1981. Optimal computer folding of larger RNA sequences using thermodynamics and auxiliary information. Nucleic Acids Res. 9, 133-148.