Fig. 3

Z-scores of mutational robustness (a) and of plasticity (b) are presented for the bacterial small noncoding RNA (sncRNA) collection from [3] and for C. elegans precursor microRNA (pre-miRNA) from miRBase 20. For each wild type pre-miRNA [resp. sncRNA] wild type sequence, RNAdualPF sampled 2000 [resp. 1000] sequences using the minimum free energy structure of the wild type sequence as target structure. The GC-content of the sampled sequences was either required to be exactly that of the wild type sequence, or not (default mode of RNAdualPF), as indicated in the legend. Sampled sequences were used to compute the mutational robustness and plasticity, as explained in the main text. Note that C. elegans miRNA is significantly robust if GC-content is not controlled, but significantly non-robust if GC-content of RNAdualPF samples is identical to that of wild type pre-miRNA. Similarly, bacterial sncRNAs are not significantly robust if GC-content is not controlled, but significantly non-robust when GC-content is identical to that of wild type sncRNA. For this figure, mutational robustness of RNA sequence a=a ₁,…,a _n is defined by \(1 - \frac {\langle D_{\text {\sc bp}}\rangle }{n}\), where ensemble distance D _bp(a,b) between two length n sequences a and b is defined in [14], and the average ensemble distance from all single-point mutants of a is defined by \(\langle D_{\text {\sc bp}}\rangle = \sum _{\mathbf {b}} \frac {D_{\text {\textsc {bp}}}(\mathbf {a},\mathbf {b})}{3n}\) where the sum is taken over all single-point mutants b of a. We use this notation of mutational robustness, rather than the notion defined in [3], since the latter notion is not a true metric, as explained in “Formal definitions of robustness” section. The plasticity \(P = \frac {\langle D_{\text {\sc v}}\rangle }{n/2} = \sum _{i<j}\frac {p_{i,j}(1-p_{i,j})}{n}\) is defined in [3] as normalized ensemble diversity, where ensemble diversity [14] (Vienna structural diversity) D _V is defined by Eq. (4)