Simulate the Haystack and Select the Needle: RNA Pseudoknot Prediction in Two Steps

Much of RNA function is driven by base pairs that cross. As these so-called pseudoknots break the recursive decomposition that makes nested secondary-structure thermodynamics tractable, in practice simulators either forbid them entirely or limit their possible topology. Here, we separate RNA folding prediction into two steps: generation, which samples candidates with a nested thermodynamic simulator that cannot itself represent a crossing but is eminently tractable, and selection, which then chooses among them by some other criterion. This allows us to investigate whether small imperfections in physical simulators translate to candidates only a small perturbation away from the correct structures. On PseudoBase a pool generated in this way contains a structure recovering $F_1 = 0.931$ of native pairs against the best published method's $0.777$; on the harder, longer ArchiveII it contains $0.638$ against $0.536$; it finds $0.702$ of the crossing pairs. Selection, however, proves to be much harder, as real pseudoknots often rely on tertiary structure stabilization. Of the criteria we tested, external evolutionary covariation information does best, reaching $F_1 = 0.599$ on the ArchiveII database, better than any tool or method we test, though it recovers only $0.300$ of the native crossing pairs. Its advantage is in the nested scaffold, not the pseudoknot. As this evidence is not always available, we employed an RNA language model in hope it had internalised enough covariation during pretraining to be able to stand in for alignments where none exist. However, on families disjoint from its training set it does not improve on the baseline $F_1$ ($-0.013$ $[-0.066,+0.039]$). Neither does better physics solve the selection problem, as we find when introducing as a selector a novel polymer-physics free energy exact for arbitrary crossing topology. This two-step process reveals that while the answer is already in the pool, nothing we tried reliably finds it.