  Motivation: DNA data is transcribed into single-stranded RNA, which folds
into specific molecular structures. In this paper we pose the question to what
extent sequence- and structure-information correlate. We view this correlation
as structural semantics of sequence data that allows for a different
interpretation than conventional sequence alignment. Structural semantics could
enable us to identify more general embedded "patterns" in DNA and RNA
sequences. Results: We compute the partition function of sequences with respect
to a fixed structure and connect this computation to the mutual information of
a sequence-structure pair for RNA secondary structures. We present a Boltzmann
sampler and obtain the a priori probability of specific sequence patterns. We
present a detailed analysis for the three PDB-structures, 2JXV (hairpin), 2N3R
(3-branch multi-loop) and 1EHZ (tRNA). We localize specific sequence patterns,
contrast the energy spectrum of the Boltzmann sampled sequences versus those
sequences that refold into the same structure and derive a criterion to
identify native structures. We illustrate that there are multiple sequences in
the partition function of a fixed structure, each having nearly the same mutual
information, that are nevertheless poorly aligned. This indicates the
possibility of the existence of relevant patterns embedded in the sequences
that are not discoverable using alignments.
