Complete Suboptimal Folding of RNA and the Stability of Secondary Structures

Stefan Wuchty, Walter Fontana, Ivo L. Hofacker and Peter Schuster

An algorithm is presented for generating rigorously all suboptimal secondary structures between the minimum free energy and an arbitrary upper limit. The algorithm performs particularly well in the vicinity of the minimum free energy. This enables the efficient approximation of statistical quantities, such as the partition function or measures for structural diversity. The density of states at low energies and its associated structures are crucial in assessing from a thermodynamic point of view how well defined the ground state is. We demonstrate this by exploring the role of base modification in tRNA secondary structures, both at the level of individual sequences from E. coli and by comparing artificially generated ensembles of modified and unmodified sequences with the same tRNA structure. The two major conclusions are that (1) base modification considerably sharpens the definition of the ground state structure by constraining energetically adjacent structures to be similar to the ground state, and (2) sequences whose ground state structure is thermodynamically well defined show a significant tendency to buffer single point mutations. This can have evolutionary implications, since selection pressure to improve the definition of ground states with biological function may result in increased neutrality.

Keywords: RNA secondary structure, suboptimal folding, density of states, tRNA, modified bases, thermodynamic stability of structure, mutational buffering, neutrality, dynamic programming