Bioinformatics Integration Network
Hybridization Structure of 2 RNA Molecules
Bernhart S. , Hofacker I. L. , Schuster P.
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2 Institute for Theoretical Chemistry and Structural Biology, University of Vienna, Austria
Abstract:
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Functional RNAs and their importance for cellular processes are increasingly recognized by life scientists. Some of their functions, e.g. miRNA, are mediated by intermolecular interactions between RNA molecules. To this date, computational analysis of these interactions is heuristic or neglects the possibility to build intramolecular base pairs. We present a variant of the ViennaRNA folding algorithm that is able to deal with this problem for the thermodynamic ensemble. This enables us to predict base pair probabilities of RNA dimers. RNAcofold
In contrast to folding a single RNA molecule, cofolding of two molecules causes every loop containing the cut between the molecules to be an exterior loop, thus not contributing to the overall energy. When cofolding, we concatenate the sequences and then check whether a loop is an exterior loop or not (figure 2). Introduction
Recently, the topic of functional RNAs has risen to the attention of many geneticists. Especially the RNAi/miRNA pathway has been recognized to be important in vivo as well as in vitro4. While there is some knowledge about the targets of miRNAs on the genome, the putative weaker interactions between „non­target“ mRNA and miRNA/siRNA have been neglected. One basic problem concerning the prediction and evaluation of miRNA targets is that the algorithms used for evaluation have been designed for intramolecular folding of RNAs only. Thus, their performance in folding two Figure 2: Effect of the cut between molecules appearing in the different loop As can be seen, any loop incorporating the cut is considered to be an RNA molecules (cofolding), is questionable. types. exterior loop
Existing Algorithms either do only compute the minimum free energy of RNA dimers or fail to take Furthermore, there is an entropy penalty for the binding of two molecules.
into account intramolecular base pairs1,3. The probability to get any binding between molecules is of course dependent on their relative and absolute concentrations. It can be computed using mass action law:
Equation 1: Dimer formation
QAB, QA, QB: partition functions of dimer resp. monomers
as well as mass conservation to get the following equation system:
Figure 1: RNA secondary structure
Red: Interior loops/stacks Green: Hairpin Loops Yellow: Multiloop RNA secondary structures
Conclusion and Outlook:
RNAcofold is a program that computes the partition function and the minimum free energy of two interacting RNA molecules.
In addition, it can compute the equilibrium concentrations of RNA dimers dependent on the initial concentrations. We plan to use RNAcofold together with faster, coarse grained algorithms, like RNAduplex, to identify and evaluate target sites for miRNA/siRNA. It also can be used to design short RNA molecules that have a certain effect on the structure of other RNA molecules, and to predict the binding probability for two molecules. This can be of use for RNA probes as well as in DNA computing. The major drawback is that RNAcofold is unable to predict pseudo­knots, which putatively are of some importance for RNA interactions.
Accordingly, RNAcofold can be further improved by incorporating certain classes of pseudo­knots into the program. Equation 2: Quadratic equation system for dimer formation
A0, B0: Initial concentrations of monomers
CA, CB: Concentration of A, B
This equation system can be solved iteratively and has been shown to converge always.
An RNA secondary structure is defined as a set of Our program, RNAcofold, is able to predict the base pairs fulfilling the following conditions2:
ensemble base pair probabilities as well as the 3) Watson­Crick and GU base pairs are allowed
minimum free energy (mfe) structures. In the computation of the partition function for all possible 4) Bases take part in at most one base pair
dimers and monomers dimer concentrations are 5) If i,j and k,l form a base pair, and i<k<j, then computed from the initial concentrations. i<k<l<j must hold The RNAcofold algorithm is cubic in processor time Condition 3) excludes pseudo­knots.
quadratic in memory requirements. A simpler algorithm developed in our group, RNAduplex, neglects intramolecular base pairs. Due to its linear time complexity, it can be used for screening large databases. It provides possible binding sites, which can be further evaluated using The free energy of a secondary structure is the RNAcofold.
sum of all its loop­energies. The partition function is computed considering all possible structures The RNAcofold algorithm can still be improved by with Boltzmann weights. the consideration of intermolecular pseudo­knots which are much more frequent and important than their intramolecular counterparts. The energy of a secondary structure is computed by partitioning secondary structures into loops. A loop is a structure unit containing one or more base pairs (figure 1).
Figure 3: Output of RNAcofold: a bantam miRNA binding on its target site (ca 150 bases). Right: Dot plot. Upper right base pair probabilities. Lower left: mfe structure Left: mfe structure as predicted by RNAcofold.
The bantam miRNA is marked red.
Figure 4: Relative Concentrations of RNA dimers/monomers References:
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4. Dimitrov, R.A. and Zuker, M., Prediction of hybridization and melting for double stranded nucleic acids, Biophysical J., 2004, 87, p.215­226
5. Hofacker, I.L. et al., Fast folding and comparison of RNA secondary structures, Monatshefte Chemie, 1994, 125, p. 167­188
6. Rehmsmeier, M. et al., Fast and effective prediction of microRNA/target duplexes, RNA, 2004, 10, p. 1507­1517
7. Couzin, J., Breakthrough of the year: Small RNAs Make Big Splash, Science, 2002, 298, p. 2296­2297
Acknowledgement:
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This work is supported by the GEN­AU project Bioinformatics Integration Network (BIN).
Correspondence:
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E­mail: berni@tbi.univie.ac.at, ivo@tbi.univie.ac.at
URL: http://www.tbi.univie.ac.at