On the Structure of RNA Branching Polytopes

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 dependence 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.