Base-pair Ambiguity and the Kinetics of RNA Folding

The route to folding for a large non-coding RNA molecule is full of kinetic traps---energetically favorable pairings of nucleotide sequences that are not part of the active structure. Yet many of these molecules spontaneously fold to a native structure when placed in a suitable chemical environment at an appropriate temperature. Levinthal9s convincing arguments (aka Levinthal9s paradox) about proteins apply to RNA molecules as well, perhaps even more compellingly: arrival to thermal equilibrium should take a great deal more time than the biological lifetime of the organism. Evidently, mechanisms have evolved that contribute to a directed and efficient folding process, and quite possibly the active configuration is not at all like a sample from an equilibrium distribution, but rather a metastable state, provided only that it will typically last long enough for its purpose. Based on the number of possible Watson-Crick or G·U wobble pairings at each location, we introduce various measures of the difficulty in reaching a stable configuration, whether or not it is a true equilibrium. We call these measures "ambiguity indexes,99 and focus on two, each of which is a function of both the primary and any given proposed secondary structure. Comparing families of RNA molecules that appear in ribonucleoproteins ("bound99 molecules) to RNA molecules that do not operate as nucleoproteins ("unbound99 molecules), we find that the unbound molecules have systematically lower ambiguity indexes, provided that the indexes are computed using the comparative-analysis structure (also known as the "gold standard99). The effect largely disappears when the indexes are based, instead, on the so-called minimum-free energy (MFE) structures. Since MFE structures are derived from an approximation of the equilibrium distribution, we interpret these and other related results as evidence for metastable but not necessarily thermal equilibrium secondary structure.