Fast RNA Secondary Structure Prediction Using Fuzzy Stochastic Models - Biomedical Engineering Systems and Technologies - page 158

2.3 Influence of Disturbances

To get a first impression on the influence of disturbances (in the ensemble distribu-
tion for a given input sequence) on the quality of generated sample sets, we opted
for the potentially most intuitive application in this context, namely probability pro-
filing for unpaired bases within particular loop types (see, e.g., [1]). In principle, for
each nucleotide position i , 1 ≤ i ≤ n , of a given sequence of length n , one com-
putes the probabilities that i is an unpaired base within a specific loop type. These
probabilities are given by the observed frequencies in a representative statistical sam-
ple of the complete ensemble (of all possible secondary structures) for the given input
sequence.
Furthermore, in order to investigate to what extend the accuracy of predicted fold-
ings changes when different dimensions of relative disturbances are incorporated into
the needed sampling probabilities, we will additionally derive the most probable (MP)
structure in the generated samples, respectively, as prediction.
Note that for our examinations, we will exemplarily consider a well-known trusted
tRNA structure, Escherichia coli tRNA Ala , since this molecule folds into the typical
cloverleaf structure, making it very easy to judge the accuracy of the resulting profiles
and predictions.

Hpl ot M p l ot

1.0 1.0

0.8 0.8

0.6 0.6

0.4 0.4

0.2 0.2

0.0 0.0

0 10 20 30 40 50 60 70 0 10 20 30 40 50 60 70

Nucleotide Position Nucleotide Position

Ala . Hplot and Mplot display
the probability that an unpaired base lies in a hairpin and multibranched loop, respectively. All
results have been derived from samples of size 1 , 000 , generated with min hel =2 and min HL =
3 . Errors were produced with max ErrPerc =0 . 99 (thick gray lines) and fix ErrPerc =0 . 99 (thick
dotted darker gray lines). The profiles also display the respective exact results (thin black lines)
and the native folding of E.coli tRNA

Fig. 1. Loop profiles and MP predictions obtained for E.coli tRNA

Ala (black points).

Figure 1 indicates that even in the case of large relative errors, the sampled struc-
tures still exhibit the typical cloverleaf structure of tRNAs, especially for the extenu-
ated disturbance variant according to max ErrPerc which seems to have practically no
effect on the resulting sampling quality and prediction accuracy. However, Fig. 2 per-
fectly demonstrates that if the disturbances have been created by generating absolute
errors on all inside values, then - even for rather small values - the resulting samples
(and corresponding predictions as well) seem to be useless. Nevertheless, it seems rea-
sonable to believe that the inside and outside probabilities do not necessarily have to be
computed in an exact way, but it may probably suffice to only (adequately) approximate
them.