C. Reidys et al., GENERIC PROPERTIES OF COMBINATORY MAPS - NEUTRAL NETWORKS OF RNA SECONDARY STRUCTURES, Bulletin of mathematical biology, 59(2), 1997, pp. 339-397
Random graph theory is used to model and analyse the relationships bet
ween sequences and secondary structures of RNA molecules, which are un
derstood as mappings from sequence space into shape space. These maps
are non-invertible since there are always many orders of magnitude mor
e sequences than structures. Sequences folding into identical structur
es form neutral networks. A neutral network is embedded in the set of
sequences that are compatible with the given structure. Networks are m
odeled as graphs and constructed by random choice of vertices from the
space of compatible sequences. The theory characterizes neutral; netw
orks by the mean fraction of neutral neighbors (lambda). The networks
are connected and percolate sequence space if the fraction of neutral
nearest neighbors exceeds a threshold value (lambda > lambda). Below
threshold (lambda < lambda), the networks are partitioned into a larg
est ''giant'' component and several smaller components. Structures are
classified as ''common'' or ''rare'' according to the sizes of their
pre-images, i.e. according to the fractions of sequences folding into
them. The neutral networks of any pair of two different common structu
res almost touch each other, and, as expressed by the conjecture of sh
ape space covering sequences folding into almost all common structures
, can be found in a small ball of an arbitrary location in sequence sp
ace. The results from random graph theory are compared to data obtaine
d by folding large samples of RNA sequences. Differences are explained
in terms of specific features of RNA molecular structures. (C) 1997 S
ociety for Mathematical Biology.