RNA molecules are sequences of nucleotides that serve as more than mere intermediaries between DNA and proteins, e.g., as catalytic molecules. Computational prediction of RNA secondary structure is among the few structure prediction problems that can be solved satisfactorily in polynomial time. Most work has been done to predict structures that do not contain pseudoknots. Allowing pseudoknots introduces modeling and computational problems. In this paper we consider the problem of predicting RNA secondary structures with pseudoknots based on free energy minimization. We first give a brief comparison of energy-based methods for predicting RNA secondary structures with pseudoknots. We then prove that the general problem of predicting RNA secondary structures containing pseudoknots is NP complete for a large class of reasonable models of pseudoknots.

Sequences of 3279 sequences of tRNA genes and tRNAs published up to December 1996 are included in the compilation. Alignment of the sequences, which is most compatible with the tRNA phylogeny and known three-dimensional structures of tRNA, is used. Sequences and references are available under http://www.uni-bayreuth. de/departments/biochemie/trna/

The determination of the 16S and 23S rRNA secondary structure models was initiated shortly after the first complete 16S and 23S rRNA sequences were determined in the late 1970s. The structures that are common to all 16S rRNAs and all 23S rRNAs were determined using comparative methods from the analysis of thousands of rRNA sequences. Twenty-plus years later, the 16S and 23S rRNA comparative structure models have been evaluated against the recently determined high-resolution crystal structures of the 30S and 50S ribosomal subunits. Nearly all of the predicted covariation-based base pairs, including the regular base pairs and helices, and the irregular base pairs and tertiary interactions, were present in the 30S and 50S crystal structures.

A computer program is presented which determines the secondary structure of linear RNA molecules by simulating a hypothetical process of folding. This process implies the concept of ?nucleation centres?, regions in RNA which locally trigger the folding. During the simulation, the RNA is allowed to fold into pseudoknotted structures, unlike all other programs predicting RNA secondary structure. The simulation uses published, experimentally determined free energy values for nearest neighbour base pair stackings and loop regions, except for new extrapolated values for loops larger than seven nucleotides. The free energy value for a loop arising from pseudoknot formation is set to a single, estimated value of 4.2 kcal/mole. Especially in the case of long RNA sequences, our program appears superior to other secondary structure predicting programs described so far, as tests on tRNAs, the LSU intron of Tetrahymena thermophila and a number of plant viral RNAs show. In addition, pseudoknotted structures are often predicted successfully. The program is written in mainframe APL and is adapted to run on IBM compatible PCs, Atari ST and Macintosh personal computers. On an 8 MHz 8088 standard PC without coprocessor, using STSC APL, it folds a sequence of 700 nucleotides in one and a half hour.