  The prevalent method for RNA secondary structure prediction for a single
sequence is free energy minimization based on the nearest neighbor
thermodynamic model (NNTM). One of the least well-developed parts of the model
is the energy function assigned to the multibranch loops. Parametric analysis
can be performed to elucidate the dependance of the prediction on the branching
parameters used in the NNTM. Since the objective function is linear, this boils
down to analyzing the normal fans of the branching polytopes. Here we show that
because of the way the multibranch loops are scored under the NNTM, certain
branching patterns are possible for all sequences. We do this by characterizing
the dominant parts of the parameter space obtained by looking at the relevant
section of the normal fan; therefore, we conclude that the structures that are
normally found in nature are obtained for a relatively small set of parameters.
