Biomedical Engineering Reference
In-Depth Information
thermodynamics are absorbance melting curves and microcalorimetry; see (118)
for a review.
Recently, algorithms have been described that are able to deal with certain
classes of pseudo-knotted structures, however, at considerable computational
cost (1,36,86,114). Alternatively, heuristics such as genetic algorithms can be
used (81). A common problem of all these approaches is the still very limited
information about the energetics of pseudo-knots (44,66).
3.
NEUTRAL NETWORKS IN THE SEQUENCE SPACE
A more detailed analysis of functional classes of RNAs shows that their
structures are very well conserved while at the same time there may be little
similarity at the sequence level, indicating that the structure has actual impor-
tance for the function of the molecule. In order to understand the evolution of
functional RNAs one therefore has to understand the relation between sequence
(genotype) and structure (phenotype). Although qualitatively there is ample evi-
dence for neutrality in natural evolution as well as in experiments under con-
trolled conditions in the lab, very little is known about regularities in general
genotype-phenotype relations. In the RNA case, however, the phenotype can be
approximated by the minimum free energy structure of RNA; see e.g. (121) for a
recent review. This results in a complex, highly nonlinear genotype-phenotype
map, which, however, is still computable. This simplifying assumption is met
indeed by RNA evolution experiments in vitro (5) as well as by the design of
RNA molecules through artificial selection (147).
There is ample evidence for redundancy in genotype-phenotype maps
f
in
the sense that many genotypes cannot be distinguished by an evolutionarily
relevant coarse-grained notion of phenotypes, which, in turn, gives rise to fitness
values that cannot be faithfully separated through selection. Regarding the fold-
ing algorithms as a map
f
that assigns a structure
s
=
f
(
x
) to each sequence
x
, we
can phrase our question more precisely: we need to know how the set of se-
quences
f
-1
(
s
) that folds into a given structure
s
is embedded in the sequence
space (where the genotypes are interpreted as nodes and all Hamming distance-
one neighbors are connected by an edge). The subgraphs of the sequence space
that are defined by the sets
f
-1
(
s
) are called
neutral networks
(122).
The most important global characterization of neutral networks is its aver-
age fraction of neutral neighbor
M
, usually called the (degree of) neutrality.
Neglecting the influence of the distribution of neutral sequences over the se-
quence space, the degree of neutrality will increase with size of the pre-image.
Generic properties of neutral networks (108) are readily derived by means of a
random graph model. Theory predicts a phase transition-like change in the ap-
pearance of neutral networks with increasing degree of neutrality at a critical
value:
