  Background: Genotype-phenotype maps provide a meaningful filtration of
sequence space and RNA secondary structures are particular such phenotypes.
Compatible sequences i.e.~sequences that satisfy the base pairing constraints
of a given RNA structure play an important role in the context of neutral
networks and inverse folding. Sequences satisfying the constraints of two
structures simultaneously are called bicompatible and phenotypic change,
induced by erroneously replicating populations of RNA sequences, is closely
connected to bicompatibility. Furthermore, bicompatible sequences are relevant
for riboswitch sequences, beacons of evolution, realizing two distinct
phenotypes.
  Results: We present a full loop energy model Boltzmann sampler of
bicompatible sequences for pairs of structures. The novel dynamic programming
algorithm is based on a topological framework encapsulating the relations
between loops. We utilize our sequence sampler to study the energy spectra and
density of bicompatible sequences, the rankings of the structures and key
properties for evolutionary transitions.
  Conclusion: Our analysis of riboswitch sequences shows that key properties of
bicompatible sequences depend on the particular pair of structures. While there
always exist bicompatible sequences for random structure pairs, they are less
suited to facilitate transitions. We show that native riboswitch sequences
exhibit a distinct signature with regards to the ranking of their two
phenotypes relative to the minimum free energy, suggesting a new criterion for
identifying native sequences and sequences subjected to evolutionary pressure.
