RDMAS: a web server for RNA deleterious mutation analysis

1471-2105-7-404 1471-2105 Software RDMAS: a web server for RNA deleterious mutation analysis Shu Wenjie shuwj@bmi.ac.cn Bo Xiaochen boxc@bmi.ac.cn Liu Rujia liurj@mails.tsinghua.edu.cn Zhao Dongsheng dszhao@bmi.ac.cn Zheng Zhiqiang xyzheng@sohu.com Wang Shengqi sqwang@bmi.ac.cn

Beijing Institute of Radiation Medicine, Beijing 100850, China

Beijing Institute of Health Administration and Medicine Information, Beijing 100850, China

College of Electro-Mechanic and Automation, National University of Defense Technology, Changsha, Hunan 410073, China

Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China

BMC Bioinformatics 1471-2105 2006 7 1 404 http://www.biomedcentral.com/1471-2105/7/404 16956394 10.1186/1471-2105-7-404 19 4 2006 06 9 2006 06 9 2006 2006 Shu et al; licensee 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.

Abstract

Background

The diverse functions of ncRNAs critically depend on their structures. Mutations in ncRNAs disrupting the structures of functional sites are expected to be deleterious. RNA deleterious mutations have attracted wide attentions because some of them in cells result in serious disease, and some others in microbes influence their fitness.

Results

The RDMAS web server we describe here is an online tool for evaluating structural deleteriousness of single nucleotide mutation in RNA genes. Several structure comparison methods have been integrated; sub-optimal structures predicted can be optionally involved to mitigate the uncertainty of secondary structure prediction. With a user-friendly interface, the web application is easy to use. Intuitive illustrations are provided along with the original computational results to facilitate quick analysis.

Conclusion

RDMAS can be used to explore the structure alterations which cause mutations pathogenic, and to predict deleterious mutations which may help to determine the functionally critical regions. RDMAS is freely accessed via http://biosrv1.bmi.ac.cn/rdmas.

Background

In addition to its central role in information transfer from DNA to protein, RNA performs a remarkable range of functions 1. Large numbers of noncoding RNA (ncRNA) transcripts are being revealed 2. Exploring the role and diversity of these numerous ncRNAs now constitutes a main challenge in life science 3. In a broad sense, the list of functional ncRNAs also includes functional motifs within protein-coding genes, located mostly in the non-translated 5' or 3' regions of messenger RNAs.

Mutations in RNA genes may lead to striking alterations in RNA structures that impair functions, resulting in diseases. Mutations in some RNA regulators have been reported to be associated with neuropsychiatric disorders 4. Mutations of tRNAs in mitochondria are reported to harbor more than half of all known mitochondrial pathogenic mutations 5. Some recent researches also show that mutations in microRNA (miRNA) genes and its flanking sequences may contribute to cancer 678.

On the other hand, RNA deleterious mutations could be "beneficial" in some situation. The distribution of the recognized ribosomal functional sites and the antibiotic action sites has been found to be clearly correlated with the location of the known deleterious mutations in bacterial rRNAs. Therefore, deleterious mutations in rRNAs can serve as hallmarks of both functionally important ribosomal centers and antibiotic sites 9. In their study on influenza viruses, Herlocher et al. found a nonsense mutation on PB2 segment which causes much difference in the secondary structure responsible for cold adaptation 10, that implies that viruses with similar deleterious mutations have potential for live vaccines.

In principle, a RNA mutation could be deleterious because it disrupts a functional site involved in catalysis, ligand-binding, or interaction with proteins. Since the functions of the ncRNAs critically depend on their specific structures, nucleotide alterations which result in structure change are expected to be deleterious. From this point of view, structure analysis should help to identify deleterious mutations. Some structure based method for RNA deleterious mutation analysis have been presented 1112, which are applicable when few homologs are available. A user friendly Java application named RNAmute for RNA deleterious mutation analysis has also been reported 1314.

The RDMAS we describe here is a noncommercial web application for RNA deleterious mutation analysis. Several secondary structure comparison methods have been implemented in RDMAS to evaluate structure deleteriousness of single nucleotide substitution in RNA molecules.

Implementation

Structural dissimilarity metric

There are 3 × N possible single point mutations for a RNA molecule with N nucleotides. The deleteriousness of these mutations is analyzed in RDMAS on the basis of structure difference. The dissimilarity of secondary structures between wild-type and mutant, D(R, R^*), is used to predict the deleteriousness of mutations. Four types of metric are employed, which are:

(i) Difference between free energy of RNA secondary structures, i.e.D(R, R^*) = |E(R) - E(R^*)|, where E(·) is the free energy computation function.

(ii) Edit distance between tree or their string representations of RNA secondary structures, i.e.D(R, R^*) = ED(R, R^*), where ED(·) represents the edit distance computation functions. The structure comparisons are implemented using Vienna RNA package 1516 based on four different tree representations, including full, homeomorphically irreducible tree (HIT), coarse grained and weighted coarse representation.

(iii) Difference between topological indices of RNA structures, i.e. D(R, R^*) = |I(R) - I(R^*)|, where I(·) represents the topological index computation functions. Several topological indices defined on the RNA tree graph representation has been presented 1217181920. Suggested by Merris and tested by Barash's group, the Wiener index which has been widely used in computational biochemistry has also been introduced into RNA graph 2122 recently. There is an interesting relation 23 between the Wiener number and the Laplacian spectrum of tree graph used in RNAMute. We have also proposed and employed novel topological descriptors defined on Shapiro's coarse grained and weighted coarse grained RNA tree 24 to characterize RNA structures (details will be published elsewhere). The topological indices used in RDMAS are listed in Table 1. Detailed descriptions can be found in the online manual of the web server (Figure 1C).

Table 1

Topological indices used to measure the structural difference between RNAs in RDMAS.

Topological index

Description

λ _T

Second eigenvalue of Laplacian matrix of Shapiro's coarse grained RNA tree

λ T w MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaaiiGacqWF7oaBdaqhaaWcbaGaemivaqfabaGaem4DaChaaaaa@313C@

Second eigenvalue of Laplacian matrix of Shapiro's weighted coarse grained RNA tree

⁰ χ

Zero-order Randiæ index defined on Shapiro's coarse grained RNA tree

¹ χ

First-order Randiæ index defined on Shapiro's coarse grained RNA tree

² χ

Second-order Randiæ index defined on Shapiro's coarse grained RNA tree

⁰ χ ^w

Zero-order Randiæ index defined on Shapiro's weighted coarse grained RNA tree

¹ χ ^w

First-order Randiæ index defined on Shapiro's weighted coarse grained RNA tree

² χ ^w

Second-order Randiæ index defined on Shapiro's weighted coarse grained RNA tree

Wiener index defined on Shapiro's coarse grained RNA tree

W ^w

Wiener index defined on Shapiro's weighted coarse grained RNA tree

Balaban index defined on Shapiro's coarse grained RNA tree

J ^w

Balaban index defined on Shapiro's weighted coarse grained RNA tree

Figure 1

Web interface of RDMAS

Web interface of RDMAS. (A) Input page. (B) Output page. (C) Online manual.

(iv) Base pair distance between dot-bracket representations of RNA structures, i.e. D(R, R^*) = BP(R, R^*), where BP(·) represents the base pair distance computation function.

The secondary structure prediction in RDMAS is implemented using RNAfold and RNAsubopt 25 from the Vienna RNA package 1516. The former is a variation of the Zuker and Stiegler 2627 minimum free energy problem that extends McCaskill's algorithm 28 and computes the complete density of states of an RNA sequence at predefined energy resolution, while the latter is for the calculation of all suboptimal structures within a user defined energy range above the MFE. In order to mitigate the uncertainty of the MFE structure, suboptimal structures of mutants within 1 kcal/mol (the default setting of RNAsubopt) above the minimum free energy (MFE) are considered. Three methods are used to estimate the difference between the structures of the wild-type and possible structure set of the mutant Γ^*= {R1∗ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGsbGudaqhaaWcbaGaeGymaedabaGaey4fIOcaaaaa@2FE5@, R2∗ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGsbGudaqhaaWcbaGaeGOmaidabaGaey4fIOcaaaaa@2FE7@,…, Rn∗ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGsbGudaqhaaWcbaGaemOBa4gabaGaey4fIOcaaaaa@305A@}, where Ri∗ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGsbGudaqhaaWcbaGaemyAaKgabaGaey4fIOcaaaaa@3050@ represents the i th predicted structure of the mutant. The two extreme values, D'(R, Γ^*) = max⁡i{D(R,Ri∗)} MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaadaWfqaqaaiGbc2gaTjabcggaHjabcIha4bWcbaGaemyAaKgabeaakmaacmqabaGaemiraqKaeiikaGIaemOuaiLaeiilaWIaemOuai1aa0baaSqaaiabdMgaPbqaaiabgEHiQaaakiabcMcaPaGaay5Eaiaaw2haaaaa@3D20@ and D'(R, Γ^*) = max⁡i{D(R,Ri∗)} MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaadaWfqaqaaiGbc2gaTjabcggaHjabcIha4bWcbaGaemyAaKgabeaakmaacmqabaGaemiraqKaeiikaGIaemOuaiLaeiilaWIaemOuai1aa0baaSqaaiabdMgaPbqaaiabgEHiQaaakiabcMcaPaGaay5Eaiaaw2haaaaa@3D20@ are taken for the most optimistic and the most pessimistic estimation, respectively. The synthetic estimation is given by summing the contribution of all structures weighted by their Boltzmann probabilities, which is similar to the methods used in some research 29. In this case, the deleteriousness is given by D′(R,Γ∗)=∑i=1nwi⋅D(R,Ri∗)/∑i=1nwi MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaadaWcgaqaaiqbdseaezaafaGaeiikaGIaemOuaiLaeiilaWIaeu4KdC0aaWbaaSqabeaacqGHxiIkaaGccqGGPaqkcqGH9aqpdaaeWbqaaiabdEha3naaBaaaleaacqWGPbqAaeqaaaqaaiabdMgaPjabg2da9iabigdaXaqaaiabd6gaUbqdcqGHris5aOGaeyyXICTaemiraqKaeiikaGIaemOuaiLaeiilaWIaemOuai1aa0baaSqaaiabdMgaPbqaaiabgEHiQaaakiabcMcaPaqaamaaqahabaGaem4DaC3aaSbaaSqaaiabdMgaPbqabaaabaGaemyAaKMaeyypa0JaeGymaedabaGaemOBa4ganiabggHiLdaaaaaa@53DA@, where wi=exp⁡{−[E(Ri∗)−E(RMFE∗)]/kT} MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWG3bWDdaWgaaWcbaGaemyAaKgabeaakiabg2da9iGbcwgaLjabcIha4jabcchaWnaacmqabaWaaSGbaeaacqGHsislcqGGBbWwcqWGfbqrcqGGOaakcqWGsbGudaqhaaWcbaGaemyAaKgabaGaey4fIOcaaOGaeiykaKIaeyOeI0IaemyrauKaeiikaGIaemOuai1aa0baaSqaaiabd2eanjabdAeagjabdweafbqaaiabgEHiQaaakiabcMcaPiabc2faDbqaaiabdUgaRjabdsfaubaaaiaawUhacaGL9baaaaa@4CF6@.

Input and options

With a step-by-step style input interface (Figure 1A), the RDMAS web server is easy to use. The sequence of a RNA molecule can be input either by pasting raw sequence or by uploading sequence file in FASTA format. Multi-FASTA (MFA) format sequence file is also supported to facilitate users. The limit of sequence length is 200 bases for immediate jobs and 2,000 bases for batch jobs, which meets the need of ncRNA analysis in most cases. For batch jobs, a valid email address is required. The analysis scheme is designed to be custom-built for users. The algorithms for computing structure difference and the methods for using the sub-optimal structures can be selected by users.

Output

The intermediate result report page will be refreshed automatically every 5 seconds after immediate jobs submission. The output page (Figure 1B) of an immediate job can be seen within 1 minute. Served as an online interactive analysis interface, all the output result can be viewed as graphic representation or text list by selecting the content item and clicking the "view" button on the output page. For batch jobs, a notification email containing a URL linked to the output page will be sent to the user when the job has been completed. The URL remains valid for 48 hours.

To make the analysis results intuitive, the maximum difference in structures between the wild-type and the possible mutants at each position are extracted into a structural deleteriousness profile and plotted as waveforms (Figure 2B). The structurally important sites can be easily revealed by peaks with high structural deleteriousness on the profile. The list of the structural deleteriousness values (Figure 2D) and the corresponding dot-bracket representations of secondary structures (Figure 2E) can be displayed as plain text on the output page.

Figure 2

Analysis result of microRNA miR-21 precursor

Analysis result of microRNA miR-21 precursor. The computation is based on the weighted second-order Randiæ index ²χ^wdefined on the stem-loop graph representation. (A) Structure illustrations of the wild-type and two mutants with great deleteriousness (G5U, A17C and U38A). The mutated nucleotides are marked by red circles. (B) Structural deleteriousness profile of pre-miR-21. (C) Deleteriousness distribution histogram of pre-miR-21. (D) Structural deleteriousness of some possible mutants of pre-miR-21. (E) Secondary structures of some possible mutants of pre-miR-21.

The statistical distributions of the deleteriousness value are calculated and illustrated as histograms (Figure 2C), which may facilitate the analysis on RNA mutational robustness.

With a hyperlink located at the bottom of the output page (Figure 1B), the output page offers download of the results as a single packed file in ".gz" format for off-line analysis. In addition to the structural deleteriousness profile and deleteriousness distribution histogram (all in "PNG" image format), the secondary structure illustration of the wild-type and the mutants (all in PostScript format) are also included in the result file. The result file name is in the form "yymmddhhmmss.no", where "yy" is year, "mm" is month, "dd" is day, "hh" is hour, mm is minute, "ss" is second and "no" is serial number.

Results and discussion

Performance of the web server

To test the computational efficiency of RDMAS, 500 random sequences (listed in Additional files) with 10 different lengths were submitted. All types of structure distance measurement are used in these tests. The CUP time of these 500 tests is illustrated in Figure 3.

Figure 3

The CPU time of 10 groups of tests

The CPU time of 10 groups of tests.

Case study

By using artificial mutants, some investigations have been done on the sequence and structural requirements for miRNA processing and functions 303132. These experimental results have shown that the base-pairing at the base of the precursor stem is critical for miRNA processing, while the internal loops, terminal loops and bulges are proved to be not essential.

To demonstrate how our web application can be helpful to the analysis on deleterious mutations in ncRNAs, the precursor of human miRNA miR-21 (pre-miR-21), a stem-loop of 71 nt, has been analyzed using RDMAS. Figure 2B is the structural deleteriousness profile of pre-miR-21 computed based on the tree edit distance of HIT representation. Figure 2C is the corresponding deleteriousness distribution histogram. The structures of the wild-type and three mutants G5U, A17C and U38A are illustrated in Figure 2A. The structural deleteriousness of possible mutants and the corresponding dot-bracket representations of the structures are listed partly in Figure 2D and Figure 2E.

It is shown that most mutants in pre-miR-21 are not deleterious. The mutations opening the base of the precursor stem lead to marked difference in RNA structure, while the mutations in the terminal loop and bulge seem to be less deleterious. These results are in good accord with the main conclusions drawn in the aforementioned experimental studies.

Future works

Although the suboptimal structures of the mutant can be used in RDMAS, the structural distance measurement using multiple predicted structures is still a challenge to the present methods. Further research is needed to find approaches to measure the structural distance taking suboptimal structures of both the wild-type and the mutant into consideration at the same time.

On the basis of the criteria of conservation and compensatory co-evolution, Kondrashov presented a method using multiple homologous sequences to predict pathogenic mutations in mitochondria encoded human tRNAs 33. In some other mutation studies on ncRNAs, especially on viral and bacterial RNAs, enough amounts of homologous sequences are also available. Our further research will also focus on developing methods for RNA deleterious mutation analysis using both homologic and structural information.

Conclusion

Compared to single nucleotide mutation analysis in protein-coding gene, research on RNA mutation has been insufficient, both bioinformatics algorithms and applications are needed. Like RNAmute 13, the RDMAS we developed is a non-commercial software for RNA deleterious mutation analysis, and will be helpful both in the researches on the structure-function relationship of ncRNAs (such as functionally critical region identification) and in the RNA-targeted drug design.

Availability and requirements

Project name: RDMAS

Project home page: http://biosrv1.bmi.ac.cn/rdmas

Operating system(s): Linux, Unix (no GUI)

Programming language: C and PHP

Other requirements: Vienna RNA package

License: GPL

Restrictions to use by non-academics: on request

Authors' contributions

WS and XB designed and developed the methodology. WS and RL programmed the web application. DZ and ZZ test the software. XB wrote the manuscript. SW guided the project.

Acknowledgements

We thank the Super Biomed Computation Center at Beijing Institute of Health Administration and Medicine Information for providing computing resources. We thank Mingjing Lu (Tsinghua University) for the graphic design of the web interface. This work is supported by a grant from the Special Funds for Major State Basic Research Program of China (973 Program) (No. 2004CB518904).

RNA: Versatility in form and function Caprara MG Nilsen TW Nat Struct Mol Biol 2000 7 831 833 10.1038/82816 The Functional Genomics of Noncoding RNA Mattick JS Science 2005 309 1527 1528 10.1126/science.1117806 16141063 Fewer Genes, More Noncoding RNA Claverie JM Science 2005 309 1529 1530 10.1126/science.1116800 16141064 Expanding the 'central dogma': the regulatory role of nonprotein coding genes and implications for the genetic liability to schizophrenia Perkins DO Jeffries C Sullivan P Mol Psychiatry 2005 10 69 78 10.1038/sj.mp.4001577 15381925 MITOMAP: a human mitochondrial genome database--2004 update Brandon MC Lott MT Nguyen KC Spolim S Navathe SB Baldi P Wallace DC Nucl Acids Res 2005 33 D611 D613 540033 15608272 10.1093/nar/gki079 A MicroRNA Signature Associated with Prognosis and Progression in Chronic Lymphocytic Leukemia Calin GA Ferracin M Cimmino A Di Leva G Shimizu M Wojcik SE Iorio MV Visone R Sever NI Fabbri M Iuliano R Palumbo T Pichiorri F Roldo C Garzon R Sevignani C Rassenti L Alder H Volinia S Liu C Kipps TJ Negrini M Croce CM The New England Journal of Medicine 2005 353 1793 1801 10.1056/NEJMoa050995 16251535 MicroRNA and Lung Cancer Eder M Scherr M The New England Journal of Medicine 2005 352 2446 2448 10.1056/NEJMcibr051201 15944431 MicroRNAs as Oncogenes and Tumor Suppressors Chen CZ The New England Journal of Medicine 2005 353 1768 1771 10.1056/NEJMp058190 16251533 Deleterious mutations in small subunit ribosomal RNA identify functional sites and potential targets for antibiotics Yassin A Fredrick K Mankin AS PNAS 2005 102 16620 16625 1283848 16269538 10.1073/pnas.0508444102 Molecular and Biological Changes in the Cold-Adapted "Master Strain" A/AA/6/60 (H2N2) Influenza Virus Herlocher ML Maassab HF Webster RG PNAS 1993 90 6032 6036 46861 8327480 10.1073/pnas.90.13.6032 Detection of common motifs in RNA secondary structures Margalit H Shapiro BA Oppenheim AB Maizel JVJ Nucleic Acids Res 1989 17 4829 4845 318035 2473442 Deleterious mutation prediction in the secondary structure of RNAs Barash D Nucl Acids Res 2003 31 6578 6584 275566 14602917 10.1093/nar/gkg872 RNAmute: RNA secondary structure mutation analysis tool Churkin A Barash D BMC Bioinformatics 2006 7 221 1489952 16638137 10.1186/1471-2105-7-221 Structural Analysis of Single-Point Mutations Given an RNA Sequence: A Case Study with RNAMute Churkin A Barash D EURASIP Journal on Applied Signal Processing 2006 2006 56246 10.1155/ASP/2006/56246 Vienna RNA secondary structure server Hofacker IL Nucl Acids Res 2003 31 3429 3431 169005 12824340 10.1093/nar/gkg599 Fast folding and comparison of RNA secondary structures Hofacker IL Monatsh Chem 1994 125 167 188 10.1007/BF00818163 Second eigenvalue of the Laplacian matrix for predicting RNA conformational switch by mutation Barash D Bioinformatics 2004 20 1861 1869 10.1093/bioinformatics/bth157 14988109 A graph-topological approach to recognition of pattern and similarity in RNA secondary structures Benedetti G Morosetti S Biophys Chem 1996 59 179 184 10.1016/0301-4622(95)00119-0 8867337 Characterization and comparison of Escherichia coli transfer RNAs by graph theory based on secondary structure Bermudez CI Daza EE Andrade E J Theor Biol 1999 197 193 205 10.1006/jtbi.1998.0866 10074393 Classification of non-coding RNA using graph representations of secondary structure Karklin Y Meraz RF Holbrook SR Pac Symp Biocomput 2005 4 15 15759609 Prediction of Small RNA Conformational Switching Using Fine-Grain Graph Representations and the Wiener Index: 20050/5/16; Haifa, Israel. Avihoo A Barash D 2005 Shape Similarity Measures for the Design of Small RNA Switches A.Avihoo D.Barash. Biomolecular Structure and Dynamics 2006 24 17 24 An edge version of the matrix-tree theorem and the wiener index Merris R Linear and Multilinear Algebra 1989 25 291 296 An algorithm for comparing multiple RNA secondary structures Shapiro BA Comput Appl Biosci 1988 4 387 393 2458170 Complete suboptimal folding of RNA and the stability of secondary structures Wuchty S Fontana W Hofacker IL Schuster P Biopolymers 1999 49 145 165 10.1002/(SICI)1097-0282(199902)49:2<145::AID-BIP4>3.0.CO;2-G 10070264 Mfold web server for nucleic acid folding and hybridization prediction Zuker M Nucl Acids Res 2003 31 3406 3415 169194 12824337 10.1093/nar/gkg595 Optimal computer folding of large RNA sequences using thermodynamics and auxiliary information Zuker M Stiegler P Nucl Acids Res 1981 9 133 148 326673 6163133 The equilibrium partition function and base pair binding probabilities for RNA secondary structure McCaskill JS Biopolymers 1990 29 1105 1119 10.1002/bip.360290621 1695107 Analysis of the conformational energy landscape of human snRNA with a metric based on tree representation of RNA structures Kitagawa J Futamura Y Yamamoto K Nucl Acids Res 2003 31 2006 2013 152804 12655018 10.1093/nar/gkg288 The nuclear RNase III Drosha initiates microRNA processing Y L C A J H H C J K J Y J L P P O R S K VN K Nature 2003 425 415 419 10.1038/nature01957 14508493 Structural requirements for pre-microRNA binding and nuclear export by Exportin 5 Zeng Y Cullen BR Nucl Acids Res 2004 32 4776 4785 519115 15356295 10.1093/nar/gkh824 Sequence requirements for micro RNA processing and function in human cells Zeng Y Cullen BR RNA 2003 9 112 123 1370375 12554881 10.1261/rna.2780503 Prediction of pathogenic mutations in mitochondrially encoded human tRNAs Kondrashov FA Hum Mol Genet 2005 14 2415 2419 10.1093/hmg/ddi243 16014637