Viral RNAs fold into more compact structures than equivalent random RNA having the same length and composition. Evolutionarily, their compactness has been connected to an evolutionary pressure to fit the RNA within the virion; structurally, it appears to be caused by a higher degree of branching in viral RNAs. To study these connections, it is generally assumed that on a large enough scale the folds of long RNAs can be mapped onto trees, and their physical size connected to some properties of the trees, from their diameter (Maximum Ladder Distance -MLD) to topological indices for branching. Comparing RNA folds of different lengths directly however, remains problematic. This is a general problem in chemistry: to compare the topological problems of two branched molecules one needs to somehow map them to trees, and then connect some topological indices to their physical properties. Topological indices however are strongly dependent on the tree size, which in turn depends both on the molecular weight and the mapping procedure. To alleviate this, we introduced a novel normalization of topological indices using estimates of their probability density functions. We determine two optimal normalized topological indices and construct a phase space that enables a robust discrimination between different architectures of branched macromolecules. In this talk I will discuss this approach in the specific setting of long RNAs.
