Abstract
In this chapter we study the structure of neutral networks as induced subgraphs of sequence space . Since exhaustive computation of sequence to structure maps using folding algorithms is at present time only feasible for sequences of length \({<}40\), we will study the structure of neutral networks using the language of random graphs . For data on sequence to structure maps into RNA secondary structures, obtained by computer folding algorithms, see [55, 56]. In [71] data on sequence to structure maps into RNA pseudoknot structures based on cross are being presented. The above papers allow to contrast the random graph model with biophysical folding maps. Our presentation is based on the papers [105, 102, 103, 106].
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
M. Abramowitz and I.A. Stegun, editors. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. 55. NBS Applied Mathematics, Dover, NY 1964.
M. Ajtai, J. Komlós, and E. Szemerédi. Largest random component of a k-cube. Combinatorica, 2:1–7, 1982.
B. Bollobás, Y. Kohayakawa, and T. Luczak. The evolution of random subgraphs of the cube. Random Struct. Algorithms, 3:55–90, 1992.
B. Bollobás, Y. Kohayakawa, and T. Luczak. On the evolution of random boolean functions. in: P. Frankl, Z. Füredi, G. Katona, D. Miklós (eds), Extremal Probls Finite Sets, 137–156, 1992.
C. Borgs, J.T. Chayes, H. Remco, G. Slade, and J. Spencer. Random subgraphs of finite graphs: III. the phase transition for the n-cube. Combinatorica, 26:359–410, 2006.
J.D. Burtin. The probability of connectedness of a random subgraph of an n-dimensional cube. Probl Infom Transm, 13:147–152, 1977.
V.L. Emerick and S.A. Woodson. Self-splicing of the tetrahymena pre-rrna is decreased by misfolding during transcription. Biochemistry, 32:14062–14067, 1993.
P. Erdős and J. Spencer. The evolution of the n-cube. Comput. Math. Appl., 5:33–39, 1979.
C. Flamm, I.L. Hofacker, S. Maurer-Stroh, P.F. Stadler, and M. Zehl. Design of multistable RNA molecules. RNA, 7:254–265, 2001.
J.R. Fresco, A. Adains, R. Ascione, D. Henley, and T. Lindahl. Tertiary structure in transfer ribonucleic acids. Cold Spring Harbor Symp. Quant. Biol., 31:527–539, 1966.
U. Goebel and C.V. Forst. RNA pathfinder–global properties of neutral networks. Zeitschrift fuer physikalische Chemie, 216, 2002.
W. Grüner, R. Giegerich, D. Strothmann, C.M. Reidys, J. Weber, I.L. Hofacker, P.F. Stadler, and P. Schuster. Analysis of RNA sequence structure maps by exhaustive enumeration I. structures of neutral networks and shape space covering. Chem. Mon., 127:355–374, 1996.
W. Grüner, R. Giegerich, D. Strothmann, C.M. Reidys, J. Weber, I.L. Hofacker, P.F. Stadler, and P. Schuster. Analysis of RNA sequence structure maps by exhaustive enumeration II. structures of neutral networks and shape space covering. Chem. Mon., 127:375–389, 1996.
L.H. Harper. Minimal numberings and isoperimetric problems on cubes. Theory of Graphs, International Symposium, Rome, 1966.
E.R. Hawkins, Chang S.H., and W.L. Mattice. Kinetics of the renaturation of yeast trnaleu3. Biopolymers, 16:1557–1566, 1977.
F.W.D. Huang, L.Y.M. Li, and C.M. Reidys. Sequence-structure relations of pseudoknot RNA. BMC Bioinformatics, 10, Suppl 1, S39, 2009.
M.V. Meshikov. Coincidence of critical points in percolation problems. Soviet Mathematics, Doklady, 33:856–859, 1986.
M. Molloy and B. Reed. The size of the giant component of a random graph with given degree sequence. Combin. Probab. Comput., 7:295–305, 1998.
C.M. Reidys. Random induced subgraphs of generalized n-cubes. Adv. Appl. Math., 19:360–377, 1997.
C.M. Reidys. Distance in random induced subgraphs of generalized n-cubes. Combinator. Probab. Comput., 11:599–605, 2002.
C.M. Reidys. Local connectivity of neutral networks. Bull. Math. Biol., 71:265–290, 2008. in press.
C.M. Reidys. The largest component in random induced subgraphs of n-cubes. Discr. Math., 309, Issue 10:3113–3124, 2009.
C.M. Reidys, P.F. Stadler, and P.K. Schuster. Generic properties of combinatory maps and neutral networks of rna secondary structures. Bull. Math. Biol., 59(2):339–397, 1997.
E.A. Schultes and P.B. Bartels. One Sequence, Two Ribozymes: Implications for the Emergence of New Ribozyme Folds. Science, 289:448–452, 2000.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2011 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Reidys, C. (2011). Neutral networks. In: Combinatorial Computational Biology of RNA. Springer, New York, NY. https://doi.org/10.1007/978-0-387-76731-4_7
Download citation
DOI: https://doi.org/10.1007/978-0-387-76731-4_7
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-76730-7
Online ISBN: 978-0-387-76731-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)