Thermodynamics of RNA folding. When is an RNA molecule in equilibrium?

Most computational algorithms for RNA structure prediction are based on calculation of the minimum free energy secondary structure. For some sequences the structure predicted by phylogenetic comparison has a much higher free energy than the minimum free energy structure. It is therefore possible that some sequences do not fold to their minimum free energy state, but that the structure formed is governed by the kinetics of the folding process. Here we discuss the example of tRNA, where thermodynamic analysis suggests that the molecules are in equilibrium, and the example of SV-11, where the molecule folds to a metastable state determined by the folding kinetics. We have analysed the equilibrium thermodynamic properties of the complete set of transfer RNA sequences in the tRNA database. Random sequences were also generated having the same base composition and the same length distribution as the real sequences. Within the random sample, sequences with properties comparable to real tRNA molecules are rare. Secondary structure in real tRNA melts at higher temperatures than in random sequences, and over a narrower temperature range, i.e. the melting process is more cooperative. These results suggest that evolution has selected for sequences with thermodynamic properties substantially different from those of typical random sequences. We have written a Monte-Carlo programme to simulate the kinetics of secondary structure formation. Times for reorganisation of secondary structure are extremely long, and therefore the system may remain trapped in a particular region of configuration space. The sequence SV-11 from the Qb replicase system is known experimentally to fold to a metastable structure with free energy considerably higher than the groundstate structure. Our simulations show that if folding occurs during the growth of the sequence the molecule folds to a metastable state in which it alternates between a number of closely related structures. The structure was not observed to reorganise to the groundstate even after a very long simulation. If folding occurs only after completion of the whole molecule then the groundstate structure is often formed.