Crumple: A Method for Complete Enumeration of All Possible Pseudoknot-Free RNA Secondary Structures

The computing for this project was performed at the OU Supercomputing Center for Education & Research (OSCER) at the University of Oklahoma (OU). OSCER director Henry Neeman and OSCER staff provided valuable technical expertise. The authors acknowledge and appreciate the discussions about this work with Dr. Changwook Kim, Adam Heck, Sean Lavelle, and Jui-wen Liu.Conceived and designed the experiments: SB SJS. Performed the experiments: SB JWS. Analyzed the data: SB JWS SJS. Wrote the paper: SB JWS SJS.The diverse landscape of RNA conformational space includes many canyons and crevices that are distant from the lowest minimum free energy valley and remain unexplored by traditional RNA structure prediction methods. A complete description of the entire RNA folding landscape can facilitate identification of biologically important conformations. The Crumple algorithm rapidly enumerates all possible non-pseudoknotted structures for an RNA sequence without consideration of thermodynamics while filtering the output with experimental data. The Crumple algorithm provides an alternative approach to traditional free energy minimization programs for RNA secondary structure prediction. A complete computation of all non-pseudoknotted secondary structures can reveal structures that would not be predicted by methods that sample the RNA folding landscape based on thermodynamic predictions. The free energy minimization approach is often successful but is limited by not considering RNA tertiary and protein interactions and the possibility that kinetics rather than thermodynamics determines the functional RNA fold. Efficient parallel computing and filters based on experimental data make practical the complete enumeration of all non-pseudoknotted structures. Efficient parallel computing for Crumple is implemented in a ring graph approach. Filters for experimental data include constraints from chemical probing of solvent accessibility, enzymatic cleavage of paired or unpaired nucleotides, phylogenetic covariation, and the minimum number and lengths of helices determined from crystallography or cryo-electron microscopy. The minimum number and length of helices has a significant effect on reducing conformational space. Pairing constraints reduce conformational space more than single nucleotide constraints. Examples with Alfalfa Mosaic Virus RNA and Trypanosome brucei guide RNA demonstrate the importance of evaluating all possible structures when pseduoknots, RNA-protein interactions, and metastable structures are important for biological function. Crumple software is freely available at http://adenosine.chem.ou.edu/software.html.Yeshttp://www.plosone.org/static/editorial#pee

Guide RNA Secondary Structures.

<p>A. Secondary structure proposed from chemical and enzymatic probing of RNA <i>in vitro </i><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0052414#pone.0052414-Schmid1" target="_blank">[17]</a>. In the protein-RNA crystal structure <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0052414#pone.0052414-Schumacher1" target="_blank">[36]</a>, only the first short hairpin is observed, and the second hairpin is unwound and only density for four nucleotides is observed. The structure shown in A has a predicted free energy greater than 0 kcal/mol <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0052414#pone.0052414-Mathews2" target="_blank">[15]</a>. B. Lowest energy secondary structure consistent with the given set of constraints. The predicted free energy is −1.6 kcal/mol. C. Alternative secondary structures that are consistent with the given set of constraints and that are not sampled by RNAStructure <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0052414#pone.0052414-Reuter2" target="_blank">[48]</a> or Sfold <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0052414#pone.0052414-Ding1" target="_blank">[49]</a>. Secondary structures pictures were generated with RNA Pseudoviewer <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0052414#pone.0052414-Byun1" target="_blank">[47]</a>. Experimental constraints include the following: chemically modified nucleotides A12, A13, A19, A24, A25, A27, G18, G21, G35, G40, G44 and single stranded nucleotides A12,A13,G18,U20,G40,G44.</p

Examples of Crumple Computations for Biological RNAs.

a<p>Wall time for computation in serial on a single AMD Athlon 64 X2 6400+ computer at 3.2 GHz with 4 GB RAM.</p>b<p>Wall time for parallel computations with 256 processes on the Sooner supercomputer (Intel Xeon E5405 2.0 GHz Linux MPI cluster).</p

A parallel implementation of the Wuchty algorithm with additional experimental filters to more thoroughly explore RNA conformational space.

We present new modifications to the Wuchty algorithm in order to better define and explore possible conformations for an RNA sequence. The new features, including parallelization, energy-independent lonely pair constraints, context-dependent chemical probing constraints, helix filters, and optional multibranch loops, provide useful tools for exploring the landscape of RNA folding. Chemical probing alone may not necessarily define a single unique structure. The helix filters and optional multibranch loops are global constraints on RNA structure that are an especially useful tool for generating models of encapsidated viral RNA for which cryoelectron microscopy or crystallography data may be available. The computations generate a combinatorially complete set of structures near a free energy minimum and thus provide data on the density and diversity of structures near the bottom of a folding funnel for an RNA sequence. The conformational landscapes for some RNA sequences may resemble a low, wide basin rather than a steep funnel that converges to a single structure

Ring Graph Parallelization Diagram for Crumple.

<p>Red Arrows indicate the direction of requests for work. Green arrows indicate the flow of distributed work. One node is arbitrarily selected as the first and master node.</p

Alfalfa Mosaic Virus RNA 4 Protein Binding Site.

<p>A. Secondary structure with pseudoknots as seen in the crystal structure of the RNA-protein complex <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0052414#pone.0052414-Guogas1" target="_blank">[21]</a>. B. Secondary structure without pseudoknot interactions as determined by chemical and enzymatic probing of the RNA in isolation <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0052414#pone.0052414-HouserScott1" target="_blank">[22]</a>, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0052414#pone.0052414-Quigley1" target="_blank">[23]</a>. C. Alternative AMV secondary structure containing a multibranch loop that is also consistent with the set of constraints listed in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0052414#pone-0052414-t003" target="_blank">Table 3</a> legend. Secondary structures pictures were generated with RNA Pseudoviewer <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0052414#pone.0052414-Byun1" target="_blank">[47]</a>.</p

Work Distribution in Parallel Computations.

<p>The sequence in this example is a 48-nucleotide guide RNA. The computations were done in parallel on the Sooner supercomputer (Intel Xeon E5405 2.0 GHz Linux MPI cluster).</p

Vienna RNA subopt++

<p>This package contains all parts of the code necessary to run the Vienna RNA folding programs, including the modifications made to the Wuchty algorithm for optional multibranch loops, global constraints on the minimum number and length of helices, conditional chemical probing constraints, and an energy-independent lonely pairs filter.  The starting point was the Vienna RNA websuite 1.8.3.  Refer to the Vienna website  http://www.tbi.univie.ac.at/RNA/</p> <p>for the most current version fo the Vienna RNA package and also all previous versions.  Please cite Algorithms for Molecular Biology, 6:1 26, 2011, doi:10.1186/1748-7188-6-26.</p> <p>This modified package is also available at  http://adenosine.chem.ou.edu/software.html.</p> <p>Have fun folding RNA!</p> <p> </p

Experimental Constraints Reduce the Conformation Space for Minimal Protein Binding Site of Alfalfa Mosaic Virus RNA 4.

<p><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0052414#pone-0052414-t003" target="_blank">Table 3:</a> The sequence for the AMV binding site with numbering according to (23) is 5′843AUGCUCAUGCAAAACUGCAUGAAUGCCCCUAAGGGAUGC881<b>.</b> The experimental constraints used are the following: nucleotides solvent accessible to chemical modification U872, A873; 1 nucleotide single stranded A 856; 3 nucleotides single stranded A856, A855, A854; 1 nucleotide double stranded A853; C869-G877 covary; 10 paired nucleotides A853, C852, G851, U850, A849, C848, G859, C860, A861, U862.</p