How to measure the topological quality of protein grammars?
  Context-free and context-sensitive formal grammars are often regarded as more appropriate to model proteins than regular level models such as finite state automata and Hidden Markov Models. In theory, the claim is well founded in the fact that many biologically relevant interactions between residues of protein sequences have a character of nested or crossed dependencies. In practice, there is hardly any evidence that grammars of higher expressiveness have an edge over old good HMMs in typical applications including recognition and classification of protein sequences. This is in contrast to RNA modeling, where CFG power some of the most successful tools. There have been proposed several explanations of this phenomenon. On the biology side, one difficulty is that interactions in proteins are often less specific and more "collective" in comparison to RNA. On the modeling side, a difficulty is the larger alphabet which combined with high complexity of CF and CS grammars imposes considerable trade-offs consisting on information reduction or learning sub-optimal solutions. Indeed, some studies hinted that CF level of expressiveness brought an added value in protein modeling when CF and regular grammars where implemented in the same framework. However, there have been no systematic study of explanatory power provided by various grammatical models. The first step to this goal is define objective criteria of such evaluation. Intuitively, a decent explanatory grammar should generate topology, or the parse tree, consistent with topology of the protein, or its secondary and/or tertiary structure. In this piece of research we build on this intuition and propose a set of measures to compare topology of the parse tree of a grammar with topology of the protein structure. 
Witold Dyrka, Fran\c{c}ois Coste, Olgierd Unold, {\L}ukasz Culer,   Agnieszka Kaczmarek
cs.FL q-bio.BM