RNAmap2D – calculation, visualization and analysis of contact and distance maps for RNA and protein-RNA complex structures
© Pietal et al.; licensee BioMed Central Ltd. 2012
Received: 6 June 2012
Accepted: 15 December 2012
Published: 21 December 2012
The structures of biological macromolecules provide a framework for studying their biological functions. Three-dimensional structures of proteins, nucleic acids, or their complexes, are difficult to visualize in detail on flat surfaces, and algorithms for their spatial superposition and comparison are computationally costly. Molecular structures, however, can be represented as 2D maps of interactions between the individual residues, which are easier to visualize and compare, and which can be reconverted to 3D structures with reasonable precision. There are many visualization tools for maps of protein structures, but few for nucleic acids.
We developed RNAmap2D, a platform-independent software tool for calculation, visualization and analysis of contact and distance maps for nucleic acid molecules and their complexes with proteins or ligands. The program addresses the problem of paucity of bioinformatics tools dedicated to analyzing RNA 2D maps, given the growing number of experimentally solved RNA structures in the Protein Data Bank (PDB) repository, as well as the growing number of tools for RNA 2D and 3D structure prediction. RNAmap2D allows for calculation and analysis of contacts and distances between various classes of atoms in nucleic acid, protein, and small ligand molecules. It also discriminates between different types of base pairing and stacking.
RNAmap2D is an easy to use method to visualize, analyze and compare structures of nucleic acid molecules and their complexes with other molecules, such as proteins or ligands and metal ions. Its special features make it a very useful tool for analysis of tertiary structures of RNAs. RNAmap2D for Windows/Linux/MacOSX is freely available for academic users at http://iimcb.genesilico.pl/rnamap2d.html
KeywordsContact maps Distance maps RNA secondary structure RNA base pairing RNA stacking Protein-RNA complex Docking
RNAs and proteins are linear polymers composed of a limited set of building blocks (ribonucleotide and amino acid residues, respectively) that may spontaneously fold into complex three-dimensional shapes [1, 2]. In both RNA and proteins, the order of building blocks held together by covalent bonds is called the primary structure, the local conformation of the chain stabilized mostly by hydrogen bonds is the secondary structure, while the path of the chain in three dimensions (3D) resulting from various long-range interactions is the tertiary structure. It is known that many proteins and RNAs undergo conformational transitions. Macromolecules and their parts may also exhibit structural disorder, i.e. fluctuations between many different conformations [3, 4]. The functions of proteins and RNAs typically involve physical interactions with other molecules in the cell, which are dependent on the structure and plasticity of the interacting partners. Thus, the functions of proteins and RNAs alike depend on the 3D structure and dynamics of these molecules, which in turn are encoded in their linear, i.e. unidimensional (1D) sequences .
While three-dimensional macromolecular structures represent an information-rich framework for studying biological functions, visualizing and analyzing them is difficult both for humans and computer programs. Two-dimensional (2D) flat images are more readily discernible to the eye and more memorable than complex 3D images. As a matter of fact, 3D structures of macromolecules (including proteins, nucleic acids, and their complexes), can be represented as square symmetrical matrices containing data about the proximity of residue or atom pairs in the molecule . Values stored in the matrix may represent e.g. euclidean distances between particular atoms, such matrix is then called a distance map). If only binary information about residue-residue interactions is included, a matrix is called a contact map. In a contact map, a residue-residue interaction may be qualified by an euclidean distance below a given threshold or by a particular type of contact. The representation of macromolecular structure by its 2D map is independent on the coordinate frame (i.e. makes the representation invariant to rotations and translations), which makes it useful for both visualization and structure comparison. Contact maps can be also enriched with additional information, e.g. to discriminate different types of contacts or to indicate the chirality in 3D (handedness), which is otherwise lost upon the conversion to a 2D representation.
It has been demonstrated that the 3D structure of a protein (and, by analogy, any linear polymer that forms a compact structure) can be recovered from its contact map representation, with the reconstructed and original structures similar up to the resolution of the contact map representation . This rationalizes the development of computational tools for analysis and visualization of macromolecular 2D maps, as an alternative to dealing directly with 3D structures. In fact, complex structures of RNA molecules have been traditionally described as 2D diagrams, exemplified by the popular “cloverleaf” representation of the tRNA molecule. Such diagrams emphasize “orthodox” pairing of bases with their Watson-Crick edges, and with the use of additional symbols or colors they can also display other types of pairing, using the Hoogsteen and sugar edges . However, a single nucleotide residue can interact with more than one nucleotide at a time (stacking using two faces, base-pairing using three edges, and interacting with the phosphate group). In this situation secondary structure plots become illegible due to crossing of multiple lines indicating long-distance contacts. On the other hand, the same type of information can be represented (and visualized) with a square symmetrical matrix containing data about different types of interactions e.g. discriminated by the use of different colors. With only a little training, one can learn to quickly distinguish e.g. helices and complex tertiary arrangements, such as pseudoknots. Similarities between distantly related RNAs can be seen easily in contact maps, even when the 3D structures superimpose poorly.
The development of computational tools for molecular structure visualization must keep up with the growing amount of bioinformatics data and the definition of new data types. Structure visualization, analysis, and annotation tools play an increasingly important role in research, contributing significantly to understanding the biological function of macromolecules. There is a number of tools capable of calculating, displaying, and analyzing protein contact maps, including VMD , SeqX , PConPy , or CMView . While some of these methods are able to display contacts of the protein component to the nucleic acid ligand, they do not produce a 2D map if RNA structure alone is provided as input, and they do not discriminate between different types of nucleotide interactions. As more and more RNA structures are determined by experimental methods or predicted by computational techniques, it becomes increasingly important to reinforce current state-of-art 3D RNA modeling tools with 2D visualization capabilities. Thus, we developed a computer program dedicated to structural maps of RNAs and RNA-protein or ligand-complexes, with particular emphasis on visualization of different types of interactions mediated by edges or faces of nucleotide bases, i.e. pairing and stacking.
Programming language, systems, external programs
RNAmap2D was developed based on its predecessor PROTmap2D . The core programming language of RNAmap2D is Python. The program uses the Biopython  and PyCogent  libraries to handle PDB structures.
RNAmap2D is available for Linux, Windows and MacOSX. To create a Windows executable version of the program, we used the py2exe 0.6.9 tool and to build a MacOSX version, py2app 0.3.6, respectively. Hardware requirements for RNAmap2D are very modest as of 2012, i.e. 1 GHz processor and 512 MB RAM memory.
In analogy to a number of programs for determination of protein secondary structure from 3D coordinates  that differ from each other in definition of structures and algorithms for their detection, there exist various tools for determination of contacts from RNA 3D structures. We have adapted RNAmap2D to use RNAView  for base pair calculation. However, RNAView is not available for Windows, therefore we added our own procedure for calculating base/nucleotide pairs, developed in ModeRNA . For every pair of residues considered, it superimposes reference frames of all known pairs types as well as predicts the presence of H-bonds characteristic for a given pair type based on interatomic distances and angles. This makes the latter procedure sensitive to distortions of the relative conformation of the nucleotide. According to our tests this procedure agrees with RNAView in assignment of ~95% of canonical base pairs. At startup, RNAmap2D checks for the presence of the installed RNAView program, and uses it by default for base pair interactions classification, while in its absence our modules are used.
RNAmap2D requires no programming or scripting skills to make use of all of its features, regardless of the platform. The Windows and MacOSX versions require no installation, except for downloading and unpacking the distribution file. Linux distribution is a set of bytecode Python files that require the installation of all modules cited at the beginning of this section prior to the use of the program. Users are provided with a comprehensive manual and a readme file that explains all installation steps. All versions provide the same functionalities except for the above-mentioned absence of RNAView for the Windows platform.
Our program has an easy-to-use graphic user interface that allows for customizing the final contact or distance map, and by setting all the important parameters. RNAmap2D navigation scheme design allows for making a step back from the final map view to the main options panel in order to refine parameters and promptly visualize the desired output. The intermediate results of calculations are stored in the computer memory to keep the data processing time at a minimum.
Distance and contact maps can be saved and uploaded as text files in a variety of formats, including e.g. the ones used in CASP or by the PHYLIP package. Maps can be also exported and uploaded as Microsoft Office Excel™ spreadsheets. Finally, images of maps can be exported as PNG, BMP, and TIFF files.
To optimize the speed of RNAmap2D, we used C and C++ libraries that are accessible under Python: wxPython (for the graphical user interface), Numeric and NumPy (for most numeric calculations). Also, the core calculation routine in RNAmap2D is the determination of distances and contacts between atoms and residues. We used the KDTree algorithm  as implemented in Biopython, which has log-linear calculation time, fastest known to date. As an example, for a molecule of the size of 100 nucleotide residues, the calculation time reaches 1000 time units (typically below a second for obtaining a raw list of contacts from a 3D structure). It compares favorably e.g. with an alternative approach used by the PConPy program for protein contact maps  that relies on a naïve double loop for calculating a contact map. For the molecule of identical size, the calculation time would reach 4950 units, which is five times slower. This is because time complexity of most such algorithms is of the order of O(n2). Please note however, that the calculation time for RNA molecules longer than 200 bases can be quite long if no RNAView plugin is installed. Bearing this in mind, we designed an additional “no pairings (fast)” contact map calculation mode that bypasses the pairing calculation algorithm and can be used alternatively for large RNA structures, in order to obtain a raw contact map very quickly.
Results and discussion
Based on our previous experience with protein 2D map analysis and core parts of the PROTmap2D code , we developed RNAmap2D, a standalone tool for calculation, visualization and analysis of contact and distance maps of nucleic acid structures and structures of protein-nucleic acid complexes. PROTmap2D was designed to perform various tasks on proteins only. As a consequence, it has no generic or specific capabilities that could address tasks specific to nucleic acids or complexes formed by nucleic acids. Also, PROTmap2D cannot visualize contacts made by macromolecules with ligands or ions. On the other hand, the interaction of RNA with ions is essential for the formation and stability of its 3D structure , therefore RNA-ion contacts shouldn’t be neglected in structural analyses. RNAmap2D is therefore an independent program, with multiple features specific for RNA, and not simply an upgrade of PROTmap2D. Our method can serve to analyze DNA as well as RNA. However we expect that because of regularity of DNA structures, this type of nucleic acid will not be frequently analyzed on the 2D level, hence the program’s name includes only RNA as the key input molecule. For simplicity, in this article we refer mostly to RNA alone.
RNAmap2D can calculate a contact map or a distance map of an RNA structure, compare two alternative 3D models of RNA (e.g. predicted structure versus experimentally solved one). Our program can analyze an ensemble of structures (e.g. the content of a PDB file solved by the NMR method), with two alternative statistics measures. RNAmap2D is also capable of visualizing a contact map of protein-RNA complex, and a series of such models, e.g. originating from a protein-RNA docking experiment. RNAmap2D can also calculate, visualize and export RNA secondary structure in a common dot-bracket format. Secondary structure can be also imported and displayed as a 2D diagram – in this case all contacts visualized by RNAmap2D will correspond to Watson-Crick base pairs, as other types of contacts are not represented in traditional secondary structure representations.
RNAmap2D generates interactive 2D maps, with a possibility to zoom in onto particular fragments. Zooming is enabled when a user presses a mouse button over a map and drags a rectangle-shaped area. The content of this area is shown in a separate window, with a sequence ruler, range indicator and a possibility of resizing. Also, when a user hovers a mouse cursor over a specific contact, a window appears with information about the residue pair, including residue index, residue name and binary (Y/N) contact information. Additional interaction schemes specific to different tasks are available, such as color panels, fields to input certain value limits etc., which are described below in specific sections.
Output options for 2D maps include a number of image formats (BMP, GIF, JPG, PNG, TIFF), and various text formats developed initially for storing the results of comparative analyses of protein sequences and structures: CASP , EVA , PHYLIP  and CLANS . RNAmap2D can also encode maps in formats such as CSV or MS Excel™ spreadsheets, which can be easily read and analyzed with many third-party tools. The program is also capable of reading a map encoded as a text or Excel file, e.g. a file exported from RNAmap2D and edited in a third-party program.
RNA contact map
RNAmap2D works on the level of residues rather than individual atoms. A user can specify the definition of atoms used to calculate the presence of a contact: the type of atoms to be included in calculations (the options per residue are: single atoms - C1′, C4′, O5′, N1/N9 for purines and pyrimidines respectively, or multiple atoms - all or heavy/non-hydrogen), a maximal distance (in Å) between the specified atoms to form a contact, and a minimal residue separation along the sequence (e.g. to exclude contacts between consecutive residues that are connected by covalent bonds). If multiple atoms are considered, it is sufficient for any pair of atoms from two residues to fall below the distance threshold to have this residues classified as in contact; RNAmap2D does not generate a map of contacts between individual atoms, only maps information about proximal atoms on the respective residues. However individual heteroatom records found in PDB files that represent ions or ligand atoms are treated as separate residues. If the PDB file contains several models, the user can choose a specific model to be analyzed by the program. For oligomeric structures, in most analyses it is also possible to specify chain identifiers to limit the analysis to certain chains of the molecule. Auxiliary options are: graphic sequence delimiter (ruler) and grid-like lines that separate chains (chain borders).
RNA distance map
RNA secondary structure
Contact maps of complexes involving different types of molecules
Comparison of contact maps
RNAmap2D can compare two RNA structures in two modes: molecules that have an identical number of residues, or molecules that contain a common chain with residues with corresponding numbers. The input can be either a single PDB file with two models, or two separate files, e.g. a 3D model and a reference structure. The sequences do not need to be identical. Thus, it is possible to compare two models of the same RNA (even if they don’t cover the same range of residues, as long as there is some overlap), sub-structures of different molecules, e.g. homologs with similar structure but different sequence, etc.
Comparison of structural ensembles
RNAmap2D users can choose between two ways to display contacts that vary through the model ensemble file. In both cases, white fields on the map represent 100% frequency across a model set, and black fields represent no contacts. For contacts that appear only in a fraction of models, one option of visualization presents a relative frequency of contacts, where and shades of grey correspond to intermediate values (the more frequent the contact, the lighter the field). Another option is to present all “partial” contacts by one shade of grey.
In an example analysis, we have analyzed the noncanonical base pairs in a part of the 3′ UTR from turnip crinkle virus genomic RNA. This 102-nt structural element binds to the large ribosomal subunit to promote translation. The structure consists of three main helices. In the NMR structure (PDB-ID 2krl), 10 models have been deposited. RNAmap2D can be used to check e.g. whether noncanonical base pairs are maintained in all the models. We used RNAmap2D to generate a contact map for the ensemble and then colored noncanical pairs in blue. We have inspected individual pairs in the map zoomed to a fullscreen mode and generated a statistics map and exported the contact frequencies to an Excel table. In the contact map, regions that vary in the ensemble (e.g. due to increased flexibility) are immediately visible as grey areas. For instance tertiary interactions between hairpin loop 37–43 and the structure (97–101) fluctuate, and base pairing in this region is not stable. In total, we identified 15 noncanonical base pairs, of which four differ in at least one of the 10 models. The three noncanonical pairs G9-G12, G29-U55, and A70-C87 (a sugar-Hoogsteen pair) differ in only one of the models. The fourth pair, cis-Watson-Watson U67-C87, is present in four models only. It varies a lot between the models and the participating bases can also pair in the cis-Watson-Hoogsteen mode. Residues adjacent to A70 and C87 display some flexibility in the contact map as well. This pair is located in an internal loop that is important for switching between translation and replication in the virus . We conclude that RNAmap2D helps to identify regions that undergo conformational changes by highlighting them in the graphical output, and enables their quantitative examination in a tabular report.
RNAmap2D is a new tool for calculation and visualization of nucleic acid contact and distance maps. Our aim was to facilitate analyses of RNA structures that focus on type and location of short-range interactions, without taking the spatial conformation of the backbone into account. RNAmap2D is also capable of analyzing protein-nucleic acid complexes. RNAmap2D is applicable in various scenarios, ranging from comparison of RNA 2D and 3D structural predictions with each other and with the native structure, to analyses of trajectories from MD simulations of nucleic acid structures, to studies of RNA/DNA-protein and RNA/DNA-ligand interactions and analyses of macromolecular docking experiments.
PROTmap2D and RNAmap2D both provide researchers with an extensive suite of programs for analyses and visualization of macromolecular structures. RNAmap2D runs on any modern operating system, is very fast and has an intuitive interface. Both programs serve as a complete platform that supplements the existing 3D visualization tools, with sophisticated 2D map capabilities.
Availability and requirements
Project name: RNAmap2D
Project home page: http://iimcb.genesilico.pl/rnamap2d.html
Operating systems: Windows, Linux, MacOSX.
Programming languages: Python (main), C/C++ (some parts of external libraries)
Software packages (Windows, MacOSX): None
Software packages (Linux): Python 2.6, Biopython 1.42, PyCogent 1.4, wxPython 2.8.10, PIL 1.1.6, Numeric 24.2, NumPy 1.1.3, PyExcelerator 0.6.3
Other requirements: RNAView program is recommended as an optional plugin. Please refer to User’s Manual and README file for installation instructions to be found on the RNAmap2D project home page.
Hardware requirements: min. 512 MB RAM, 1GHz CPU or better (2 GB RAM and 2 GHz CPU is recommended).
License: RNAmap2D is distributed under free academic license. Please refer to the home page for the license document.
Restriction for non-academics: Users willing to use RNAmap2D for non-academic purposes should contact the corresponding author for details. Please note that this license will not affect commercial usage of RNAView. Please contact authors of RNAView for a separate license.
Python Image Library
critical assessment of techniques for protein structure prediction
The authors thank Irina Tuszynska for discussions, suggestions, and testing RNAmap2D in the context of RNA-protein docking, and also for critically proofreading the manuscript. The authors also thank Anna Philips for help in analyzing structures containing ligands and ions and with nucleotide modifications lists encoded within the RNAmap2D.
This work was supported mainly by the European Commission (initially by the FP6 grant “EURASNET”, LSHG-CT-2005-518238 and subsequently by the FP7 grant HEALTH-PROT, contract number 229676). Integration of various software tools involving protein bioinformatics in the Bujnicki laboratory in IIMCB has been supported by the EU structural funds (POIG.02.03.00-00-003/09). M.J.P was supported by European Social Fund through a Subcarpatian Doctoral Stipend Fund project. K.R. was independently supported by the German Academic Exchange Service (grant D/09/42768). J.M.B. was supported by the Foundation for Polish Science (FNP, grant TEAM/2009-4/2).
- Dill KA: Dominant forces in protein folding. Biochemistry 1990, 29(31):7133–7155. 10.1021/bi00483a001View ArticlePubMedGoogle Scholar
- Ferre-D’Amare AR, Doudna JA: RNA folds: insights from recent crystal structures. Annu Rev Biophys Biomol Struct 1999, 28: 57–73. 10.1146/annurev.biophys.28.1.57View ArticlePubMedGoogle Scholar
- Hazy E, Tompa P: Limitations of induced folding in molecular recognition by intrinsically disordered proteins. Chemphyschem 2009, 10(9–10):1415–1419.View ArticlePubMedGoogle Scholar
- Fulle S, Gohlke H: Constraint counting on RNA structures: linking flexibility and function. Methods 2009, 49(2):181–188. 10.1016/j.ymeth.2009.04.004View ArticlePubMedGoogle Scholar
- Anfinsen CB, Scheraga HA: Experimental and theoretical aspects of protein folding. Adv Protein Chem 1975, 29: 205–300.View ArticlePubMedGoogle Scholar
- Phillips DC: The development of crystallographic enzymology. Biochem Soc Symp 1970, 30: 11–28.PubMedGoogle Scholar
- Vendruscolo M, Kussell E, Domany E: Recovery of protein structure from contact maps. FoldDes 1997, 2(5):295–306.View ArticleGoogle Scholar
- Leontis NB, Westhof E: Geometric nomenclature and classification of RNA base pairs. RNA 2001, 7(4):499–512. 10.1017/S1355838201002515PubMed CentralView ArticlePubMedGoogle Scholar
- Humphrey W, Dalke A, Schulten K: VMD: visual molecular dynamics. J Mol Graph 1996, 14(1):33–38. 27–38 27–38 10.1016/0263-7855(96)00018-5View ArticlePubMedGoogle Scholar
- Biro JC, Fordos G: SeqX: a tool to detect, analyze and visualize residue co-locations in protein and nucleic acid structures. BMC Bioinforma 2005, 6: 170. 10.1186/1471-2105-6-170View ArticleGoogle Scholar
- Ho HK, Kuiper MJ, Kotagiri R: PConPy-a python module for generating 2D protein maps. Bioinformatics 2008, 24(24):2934–2935. 10.1093/bioinformatics/btn566View ArticlePubMedGoogle Scholar
- Vehlow C, Stehr H, Winkelmann M, Duarte JM, Petzold L, Dinse J, Lappe M: CMView: interactive contact map visualization and analysis. Bioinformatics 2011, 27(11):1573–1574. 10.1093/bioinformatics/btr163View ArticlePubMedGoogle Scholar
- Pietal MJ, Tuszynska I, Bujnicki JM: PROTMAP2D: visualization, comparison, and analysis of 2D maps of protein structure. Bioinformatics 2007, 23(11):1429–1430. 10.1093/bioinformatics/btm124View ArticlePubMedGoogle Scholar
- Chapman B, Chang J: Biopython: python tools for computational biology. ACM SIGBIO Newslett 2000, 20: 15–19. 10.1145/360262.360268View ArticleGoogle Scholar
- Knight R, Maxwell P, Birmingham A, Carnes J, Caporaso JG, Easton BC, Eaton M, Hamady M, Lindsay H, Liu Z, et al.: PyCogent: a toolkit for making sense from sequence. Genome Biol 2007, 8(8):R171. 10.1186/gb-2007-8-8-r171PubMed CentralView ArticlePubMedGoogle Scholar
- Martin J, Letellier G, Marin A, Taly JF, de Brevern AG, Gibrat JF: Protein secondary structure assignment revisited: a detailed analysis of different assignment methods. BMC Struct Biol 2005, 5: 17. 10.1186/1472-6807-5-17PubMed CentralView ArticlePubMedGoogle Scholar
- Yang H, Jossinet F, Leontis N, Chen L, Westbrook J, Berman H, Westhof E: Tools for the automatic identification and classification of RNA base pairs. Nucleic Acids Res 2003, 31(13):3450–3460. 10.1093/nar/gkg529PubMed CentralView ArticlePubMedGoogle Scholar
- Rother M, Rother K, Puton T, Bujnicki JM: ModeRNA: a tool for comparative modeling of RNA 3D structure. Nucleic Acids Res 2011, 39(10):4007–4022. 10.1093/nar/gkq1320PubMed CentralView ArticlePubMedGoogle Scholar
- de Berg M, Cheong O, van Kreveld M, Overmars M: Computational geometry: algorithms and applications. Third Edition edition. Berlin Heidelberg: Springer-Verlag; 2008.View ArticleGoogle Scholar
- Draper DE: A guide to ions and RNA structure. RNA 2004, 10(3):335–343. 10.1261/rna.5205404PubMed CentralView ArticlePubMedGoogle Scholar
- Orengo CA, Bray JE, Hubbard T, LoConte L, Sillitoe I: Analysis and assessment of ab initio three-dimensional prediction, secondary structure, and contacts prediction. Proteins 1999, Suppl 3: 149–170.View ArticlePubMedGoogle Scholar
- Grana O, Eyrich VA, Pazos F, Rost B, Valencia A: EVAcon: a protein contact prediction evaluation service. Nucleic Acids Res 2005, 33(Web Server issue):W347-W351.PubMed CentralView ArticlePubMedGoogle Scholar
- Felsenstein J: PHYLIP - Phylogeny inference package (version 3.2). Cladistics 1989, 5: 164–166.Google Scholar
- Frickey T, Lupas A: CLANS: a java application for visualizing protein families based on pairwise similarity. Bioinformatics 2004, 20(18):3702–3704. 10.1093/bioinformatics/bth444View ArticlePubMedGoogle Scholar
- Gruber AR, Lorenz R, Bernhart SH, Neubock R, Hofacker IL: The vienna RNA websuite. Nucleic Acids Res 2008, 36(Web Server issue):W70-W74.PubMed CentralView ArticlePubMedGoogle Scholar
- Cruz JA, Blanchet MF, Boniecki M, Bujnicki JM, Chen SJ, Cao S, Das R, Ding F, Dokholyan NV, Flores SC, et al.: RNA-puzzles: a CASP-like evaluation of RNA three-dimensional structure prediction. RNA 2012, 14(4):610–625.View ArticleGoogle Scholar
- Dibrov SM, McLean J, Parsons J, Hermann T: Self-assembling RNA square. Proc Natl Acad Sci U S A 2011, 108(16):6405–6408. 10.1073/pnas.1017999108PubMed CentralView ArticlePubMedGoogle Scholar
- Scott LG, Hennig M: RNA structure determination by NMR. Methods Mol Biol 2008, 452: 29–61. 10.1007/978-1-60327-159-2_2View ArticlePubMedGoogle Scholar
- Das R, Baker D: Automated de novo prediction of native-like RNA tertiary structures. Proc Natl Acad Sci U S A 2007, 104(37):14664–14669. 10.1073/pnas.0703836104PubMed CentralView ArticlePubMedGoogle Scholar
- Sharma S, Ding F, Dokholyan NV: iFoldRNA: three-dimensional RNA structure prediction and folding. Bioinformatics 2008, 24(17):1951–1952. 10.1093/bioinformatics/btn328PubMed CentralView ArticlePubMedGoogle Scholar
- Rother K, Rother M, Boniecki M, Puton T, Tomala K, Lukasz P, Bujnicki JM: Template-based and template-free modeling of RNA 3D structure: Inspirations from protein structure modeling. In RNA 3D structure analysis and prediction. Edited by: Leontis NB, Westhof E. Berlin: Springer-Verlag; 2012.Google Scholar
- Tuszynska I, Bujnicki JM: DARS-RNP and QUASI-RNP: New statistical potentials for protein-RNA docking. BMC Bioinforma 2011, 12(1):348. 10.1186/1471-2105-12-348View ArticleGoogle Scholar
- Zuo X, Wang J, Yu P, Eyler D, Xu H, Starich MR, Tiede DM, Simon AE, Kasprzak W, Schwieters CD, et al.: Solution structure of the cap-independent translational enhancer and ribosome-binding element in the 3’ UTR of turnip crinkle virus. Proc Natl Acad Sci U S A 2010, 107(4):1385–1390. 10.1073/pnas.0908140107PubMed CentralView ArticlePubMedGoogle Scholar
This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.