Efficient Algorithms for Probing the RNA Mutation Landscape
Figure 5
Complete mutation landscape of Hepatitis C virus stem-loop IV (HCV SLIV).
(A) Mutation profile of HCV SLIV, averaged over all 110 seed sequences from Rfam, which depicts the probability of mutation of a residue at a level k (i.e. among all k-point mutants). This profile corresponds to a 37×37 matrix M = (mx,y), where x denotes the position within the input HCV SLIV sequence (x-axis) and y denotes the mutation level or number of mutations (y-axis). Mutation frequency computed from sampled structures is represented as a gray level: probability of 1 is depicted as black while probability of 0 is depicted as white, and values of y increase from bottom to top. Sequence logo and the consensus secondary structure from the Rfam seed alignment appear below the mutation profile. (B) Superposition of k-superoptimal free energy and k-mutant ensemble free energy, as computed by RNAmutants; the x-axis represents the number of mutations and the y-axis represents free energy in kcal/mol. Note that the k-mutant ensemble free energy −RI ln Zk is lower than the k-superoptimal free energy, a situation analogous to the fact that the ensemble free energy −RI⋅ln Z is lower than the minimum free energy in the output of RNAfold. This may seem paradoxical, unless one realizes that ensemble free energy is not the same as the mean free energy μ = ΣS E(S)⋅exp(−E(S)/RI)/Z, the latter which can be computed by the method of [53] or by the classical statistical mechanics formula [33].