Biomedical Engineering Reference
In-Depth Information
1
M
=
1
,
L 1
[1]
L
cr
where L is the size of the genetic alp h abet. For example, L = 4 for the canonical
genetic alphabet {A,U,G,C} . If
then the network consists of many
isolated parts with one dominating g iant component. On the other hand, the net-
work is generically connected if
MM
<
cr
. The critical value c M is the connec-
tivity threshold. This property of neutral networks reminds one of percolation
phenomena known from different areas of physics, although the high symmetry
of the sequence space, with all points being equivalent, introduces a difference
in the two concepts.
A series of computational studies (27-30,42,43,63,122) has in the last dec-
ade drawn a rather detailed picture of the genotype-phenotype map of RNA (see
also Figure 2).
MM
>
cr
(i) More sequences than structures . For sequence spaces of chain lengths
n 10 there are orders of magnitude more sequences than structures, and hence
the map is many-to-one.
(ii) Few common and many rare structures . Relatively few common
structures are opposed by a relatively large number of rare structures, some of
which are formed by a single sequence only ("relatively" points at the fact that
the numbers of both common and rare structures increase exponentially with n ,
but the exponent for the common structures is smaller than that for the rare
ones).
(iii) Shape space covering . The distribution of neutral genotypes, which
are sequences that fold into the same structure, is approximately random
in the sequence space. As a result it is possible to define a spherical ball with
diameter d cov being much smaller than the diameter n of the sequence space,
which contains on average for every common structure at least one sequence
that folds into it.
(iv) Existence and connectivity of neutral networks . Neutral networks,
being pre-images of phenotypes or structures in the sequence space, of common
structures are connected unless specific and readily recognizable special features
of RNA structures require specific non-random distribution in the {A,U,G,C}
sequence space, ) (AUGC) . (For structures formed from sequences over a {G,C}
alphabet the connectivity threshold is higher, whereas at the same time the mean
number of neutral neighbors is smaller).
Shape space covering, item (iii) above, is a consequence of the high suscep-
tibility of RNA secondary structures to randomly placed point mutations. Com-
puter simulations (28,122) have shown that a small number of point mutations is
very likely to cause large changes in the secondary structures: mutations in 10%
of the sequence positions already lead almost surely to unrelated structures if the
mutated positions are chosen randomly. The genotype-phenotype map of RNA
 
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