Prediction of RNA secondary structure, including pseudoknotting, by computer simulation

Abstract

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.

An approximation of loop free energy values of RNA H-pseudoknots

“…The nearest-neighbor and hairpin loop values were taken from the updated set of parameters by D+ Turner and coworkers (http://www+ibc+wustl+edu/;zuker/rna/energy/index+shtml)+ When the stems contained bulges or internal loops, the loop and mismatch contributions were also taken into account+ For plant viral RNAs, we used the parameters for 25 8C, for animal RNAs, those for 37 8C+ For computer-assisted structure predictions, two algorithms, implemented in the package STAR, were used as described by Abrahams et al+ (1990) and Gultyaev et al+ (1995)+ …”

“…Of course, the rough estimation presented does not take into account many additional effects that could be sequence-dependent+ NMR studies of a few pseudoknot structures provide evidence for loop interactions with helical grooves, which may diminish destabilizing energies (Kolk et al+, 1998)+ Possible positive enthalpic contributions in the loops were also suggested (Wyatt et al+, 1990)+ This means that a logarithmic approximation of the size dependence for loop entropies could be rather simplistic+ Also, the coefficient in the formula may slightly differ from 1+75, derived for loop closure by a base pair (Fisher, 1966), due to different excluded volume and end-to-end distance effects in pseudoknot loops+ Such effects are difficult to estimate because they should depend on a complex interplay between loop and stem dimensions, but they do not seem to lead to a considerable variation in the coefficient values+ As RNA pseudoknots are tertiary structure elements, Mg 2ϩ ion binding could be specific, with significant stabilizing effects (Puglisi et al+, 1991) and complex concentration dependence (Theimer et al+, 1998)+ Another important contribution to the stability is the stacking at the junctions between the coaxial stems, which could be influenced by some distortions+ On the other hand, even in bent pseudoknots an unpaired nucleotide at the junction is stacked with neighboring bases (Shen & Tinoco, 1995)+ Thus some deficiencies in our approximations could compensate for each other+ Without taking into account stabilizing or destabilizing sequence-specific energy contributions, we believe that the proposed parameters are valid with an accuracy of about 61 kcal/mol and could be used as rough approximations of pseudoknot stabilities and for computer predictions of structures+ Applying these parameters in the program STAR for RNA structure prediction (Abrahams et al+, 1990;Gultyaev et al+, 1995) did not result in an overrepresentation of pseudoknots in the predictions+ Although this is indirect evidence, it indicates that the proposed values do not overestimate pseudoknot stabilities significantly+ Compared to the previous estimate of the single value of 4+2 kcal/mol for all pseudoknot loops (Abrahams et al+, 1990), the current approximation suggests smaller or equal energies for short loops and greater values for large sizes, as expected+ Thus this approximation can improve the prediction programs, being able to predict proven pseudoknots without incorrectly predicted pseudoknotting due to possible un-derestimation of destabilizing effects in the loops by pseudoknot-including algorithms (Abrahams et al+, 1990;Gultyaev, 1991;Gultyaev et al+, 1995)+ Presumably, future experiments will improve these parameters and provide an opportunity to speculate about energies of more complicated pseudoknotted structures+…”

“…RNA pseudoknots are widely occurring structural motifs and were shown to be essential for various RNA functions (for reviews, see Pleij, 1994;Deiman & Pleij, 1997)+ Therefore, elucidation of structural features of pseudoknots and reliable prediction of pseudoknotting using sequence data are very important for understanding structure-function relationships in many RNA molecules+ While thermodynamic parameters for the structural elements of "classical" RNA secondary structure are measured or estimated with reasonable accuracy Xia et al+, 1998), there is no systematic study available of pseudoknot thermodynamics+ Experimental measurements of thermodynamic parameters for some model pseudoknots have shown them to be only marginally more stable than the secondary structures involved and to be strongly dependent on ionic environment (Wyatt et al+, 1990;Theimer et al+, 1998)+ Also, the conformational transitions in pseudoknots may involve intermediate steps, mainly constituent hairpins, so that it is rather difficult to determine a contribution of pseudoknot loops to the stability of structures, especially because any pseudoknot contains at least two loops+ For classical RNA secondary structure, the lack of detailed data on loop thermodynamics has been compensated by extrapolations optimized by estimates of success of predictions that used various sets of parameters (Jaeger et al+, 1989;Mathews et al+, 1998)+ In the case of pseudoknots, optimization of parameters using computer predictions faces the problem that the most frequently used approach to predict RNA secondary structure by free energy minimization does not include them (Zuker, 1989)+ Here we present an attempt to estimate the pseudoknot free energy parameters, based on the general theory of polymer loop thermodynamics+ The free energy values are adjusted to be consistent with available data on experimentally and/or phylogenetically proven pseudoknots+ The suggested set of parameters can be used for estimates of pseudoknot stabilities and in the folding algorithms (e+g+, Abrahams et al+, 1990;Gultyaev et al+, 1995;van Batenburg et al+, 1995) that allow pseudoknotting+…”

Computational methods in noncoding RNA research

“…Both impose restrictions on the kind of pseudoknots found in order to reduce the theoretical complexity of the problem, PKNOTS being more general (time complexity of O(n 6 ) and memory complexity of O(n 4 )) and pknotsRG more restrictive (O(n 4 ) for time and O(n 2 ) for memory). 1 …”

“…Abrahams et al [1] developed an algorithm that first finds all possible helices, then incrementally builds the final structure by selecting, at each step, the helix that minimizes the free energy of the current structure, allowing the introduction of pseudoknots. Schmitz and Steger developed a similar algorithm [129], but allowing the removal of current helices of the structure when the newly formed structure leads to pseudoknots or overlaps (bases participating in different helices).…”