Pearson correlation between various aspects of selenocysteine insertion sequences from the seed alignment of Rfam family RF00031 [23].

For each of the 61 RNA sequences, we ran FFTbor, starting from empty initial structure , and we ran a Monte Carlo folding algorithm, developed by E. Freyhult and P. Clote (unpublished). Using the Monte Carlo algorithm, we determined the mean first passage time (MFPT), defined as the average taken over 50 runs, of the number of Monte Carlo steps taken to fold the empty structure into the MFE structure, where an absolute upper bound of 5 million steps was allowed in the simulation. From the output of FFTbor, we computed (1) the mean number () of base pairs per structure, taken over the ensemble of all secondary structures for the given sequence, (2) the standard deviation () of the number of base pairs per structure, (3) the coefficient of variation , (4) the RNA sequence length, and (5) the minimum free energy (MFE). Additionally, we computed the logarithm base 10 of mean first passage time (log10MFPT), taken over 50 Monte Carlo runs per sequence (log base 10 of the standard deviation of number of Monte Carlo steps per run was approximately 9% of log10MFPT on average). The table shows the correlation between each of these aspects. Some correlations are obvious – for example, (i) the standard deviation is highly correlated with the coefficient of variation ; (ii) the mean is negatively correlated with the coefficient of variation ; (iii) the mean is negatively correlated with the minimum free energy (MFE) – if most low energy structures in the ensemble have many base pairs, then it is likely that the minimum free energy is very low (i.e. since MFE is negative, the absolute value of MFE increases); (iv) sequence length is negatively correlated with MFE – as sequence length increases, the minimum free energy (MFE) decreases. However, it may appear surprising that (v) the mean number of base pairs per structure is independent of MFPT (correlation ), although (vi) MFE is correlated with MFPT (correlation ) – i.e. from (iii), lower MFE is correlated with a larger average number of base pairs per structure, from (vi) higher MFE is correlated with longer folding time, but from (v) the average number of base pairs per structure is independent of folding time. The most important insight from this table is that (vii) standard deviation is correlated with mean first passage time – the correlation is statistically significant, with one-tailed -value of .