Algorithmes de prediction et de recherche de multi-structures d'ARN

16 Chapter 1. Background – RNAs, non-coding RNAs, and bioinformatics
for secondary structure prediction maximizing the number of base pairs was introduced later, in
1978, by Nussinov et al. [84]. Base pair maximization is a very simple model and does not take
into account full energy parameters. The same year, Waterman and Smith [125] presented a
method to predict the MFE structure through a simple nearest-neighbor model. In 1981, Zuker
and Stiegler [134] proposed a more elaborated dynamic programming algorithm, predicting the
MFE structure. Later in the 1980’s, these folding algorithms were applied on the Turner energy
model [131].
mfold/unafold [132] and RNAfold [51] are some popular implementations of these algorithms.
For a sequence of length n, they run in time O(n 3 ) (or even O(n 4 ) if one takes into account interior
loops of any size) and space O(n 2 ). Detailed analysis of suboptimal predictions, especially
for mfold/unafold, will be done in Chapter 3. Recently, some optimizations in average less time
and space have been proposed [8].
1.2.4 Structure prediction, beyond the MFE structure
Most of the time, computing the MFE structure is not enough:
• Even if the Turner model is well established, this empiric thermodynamic data can be incomplete:
slight changes in the thermodynamic model could produce very different foldings
with similar energy levels;
• The Nearest Neighbor model does not allow for pseudoknots and base triplets, and it
does not reflect the interactions of the RNA with other molecules in the cell. Thus the
projection of a real RNA structure on its secondary component may not be optimal;
• In the cell, RNA molecules do not take only the most stable structure, but they seem to
rapidly change their conformation between structures with similar free energies. These
changes can be induced by the interaction of the RNA with other molecules, and mostly
concern their 3D structure. Some RNAs, including several mRNAs in their untranslated
region, have even been shown to bear conformational switching in their secondary structure.
Thus the MFE structure is not sufficient to fully understand the folding possibilities of an
RNA. Instead of getting the optimal structure, a complete backtracking through the dynamic
programming table can generate all suboptimal secondary structures within a given threshold
from minimum free energy. Being able to compute alternative structures may also be useful
in designing RNA sequences which not only have low folding energy, but whose folding landscape
would suggest rapid and robust folding. Such suboptimal backtracking is implemented in
RNAsubopt [127] using Waterman and Byers algorithm [124], whereas mfold does not implement
this full backtrack (see Chapter 3).
However, the set of suboptimal structures is often huge : the number of such structures
is exponential in the length of the sequence. RNAshapes [105] suggests “abstract shapes” to
classify the secondary structures. During computation of the suboptimal structures, RNAshapes
partitions the folding space into sets of structures according to their shapes.
One may be interested by selecting only relevant structures, for example those corresponding
to a local minimum of energy. The goal is to keep relevant suboptimal structures in the free
energy landscape that correspond to local minima. The notions of saturated structures and
locally optimal secondary structures meet these requirements.