(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* = (

*m*_{x,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

*Z*_{k} 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* = Σ

_{S} E(

*S*)⋅

*exp*(−

*E*(

*S*)/

*RI*)/

*Z*, the latter which can be computed by the method of or by the classical statistical mechanics formula

.

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