Quantifying the relationship between sequence and three-dimensional structure conservation in RNA
© Capriotti and Marti-Renom; licensee BioMed Central Ltd. 2010
Received: 14 December 2009
Accepted: 15 June 2010
Published: 15 June 2010
In recent years, the number of available RNA structures has rapidly grown reflecting the increased interest on RNA biology. Similarly to the studies carried out two decades ago for proteins, which gave the fundamental grounds for developing comparative protein structure prediction methods, we are now able to quantify the relationship between sequence and structure conservation in RNA.
Here we introduce an all-against-all sequence- and three-dimensional (3D) structure-based comparison of a representative set of RNA structures, which have allowed us to quantitatively confirm that: (i) there is a measurable relationship between sequence and structure conservation that weakens for alignments resulting in below 60% sequence identity, (ii) evolution tends to conserve more RNA structure than sequence, and (iii) there is a twilight zone for RNA homology detection.
The computational analysis here presented quantitatively describes the relationship between sequence and structure for RNA molecules and defines a twilight zone region for detecting RNA homology. Our work could represent the theoretical basis and limitations for future developments in comparative RNA 3D structure prediction.
The view of RNA as a simple information transfer molecule has been challenged since the discovery of ribozymes, a class of RNA with enzyme-like functions [1–3]. RNA molecules are now known to carry a large repertory of biological functions such as transfer of information, enzymatic catalysis and regulation of cellular processes . Similar to proteins, functional RNA molecules fold into specific three-dimensional conformations essential for performing their biological activity. Despite advances in characterizing the folding and unfolding of RNA molecules [5–8] and the significant increase of RNA structures deposited in the Protein Data Bank (PDB) , our knowledge of the atomic mechanism by which RNA molecules adopt their biological active structures is still limited . Nonetheless, it is common knowledge that RNA 3D structure is more conserved than RNA sequence and that such principle could be used for comparative RNA structure prediction in a similar way it is done for proteins . It was back in the eighties when Chothia and Lesk first quantified such evolutionary relationship for proteins [12–14]. Their seminal works on the relationship between protein sequence and structure conservation provided the theoretical grounds for many computational approaches in comparative protein structure and function prediction [11, 15]. Their work concluded that the overall structural changes between two homologous proteins were proportional to their sequence differences. It was then estimated that homologous proteins aligning with less than 20% sequence identity could have large structural differences . Such findings were later confirmed and expanded by several other studies [16–20].
For RNA, the axiom of "function is more conserved than structure and structure is more conserved than sequence" has been adopted since the end of the sixties  and even reinforced with the analysis of newly determined large RNA containing complexes such as the ribosome [22–29]. The wealth of new structures has prompted the development of computational methods for classifying RNA molecules [30–34], describing their structural features [35–37] assigning their functions [34, 38] comparing their structures [39–41] and predicting their structures [42–45]. For example, the relationship between sequence and structure in RNA molecules has previously been characterized for the RNA ribose zipper , the C1 region of the env HIV1 gene  and RNA loop regions [47, 48]. A new method that relies on secondary structure information to align homolog RNA sequences was also recently developed . Finally, with the aim of characterizing RNA structure diversity, Abraham and co-workers recently studied the RNA conservation at three levels: primary, secondary, and tertiary structure. The work resulted in the DARTS database , which constitutes a new classification of RNA structure after the SCOR database . However, to date no general large-scale study has systematically addressed the quantitative analysis of the relationship between sequence and structure conservation in RNA molecules. The work here introduced aims to address such gap by performing an all-against-all comparison of 451 non-identical (that is, 100% sequence identity) RNA structures from the PDB. The resulting analysis confirms in a general and quantitative manner the relationship between sequence and structure conservation in RNA molecules as well as allows the definition of a "twilight zone" for RNA homology detection.
We begin this article by describing the results of an all-against-all comparison of a non-identical RNA structure set (Results). Next, we discuss the impact that our findings could have in the development of comparative approaches for RNA structure prediction (Discussion). Finally, we end by detailing the methodology used for aligning and assessing RNA alignments (Materials and Methods).
Accurate pair-wise alignments of RNA structures
The relationship between sequence and structure conservation in RNA
As previously observed, this analysis quantitatively confirmed that RNA secondary structure largely determines tertiary structure. The relationship between secondary structure and tertiary structure conservation in RNA best fitted an exponential decay curve with a correlation coefficient of 0.73 (Figure 2C). The median of secondary structure identity (PSS) for the 589 alignments in the HA-RNA09 set was 85.7%, which agrees with previous analysis . However, there was a weaker relationship between sequence and secondary structure conservation in RNA, which could only be fitted to an exponential decay curve with a correlation coefficient of 0.37 (Figure 2D). Pairs of structures that align with relatively high sequence identity could have different secondary structures. For example, the alignment of two group I introns (1hr2 and 1x8w PDB identifiers, chains A) resulted in 75.6% sequence identity and only 54.7% secondary structure identity.
A "twilight zone" for RNA sequence alignments
Our analysis indicate that two related RNA molecules conserve a structure core of at least ~50 nucleotides, which can be superimposed within 4.0 Å RMSD. Such conserved structure core starts diverging as sequence identity decreases below 50% and becomes noteworthy (i.e., structural divergence >20%) for pairs of RNA structures that superimpose with sequence identity below 40%. Moreover, the exact relationship between sequence and structure conservation for pairs of distant RNA molecules (that is, resulting in 30 to 60% sequence identity alignments) is less evident, which results in a correlation coefficient of 0.34. Homologous pairs of RNA molecules will diverge into different structures when there is a significant decrease in the identity of their sequences. Therefore, it is more difficult to assess structure conservation based on sequence diversity in the low regime of sequence identity (i.e, <60%). Highly similar structures conserve their base pairing. The degree of conservation between tertiary and secondary structure in RNA results in a correlation of 0.73. However, the relationship between sequence and secondary structure conservation is weakly correlated, which agrees with the difficulty of predicting secondary structure from RNA sequence alone. Similar conclusions were obtained with the ARTS program, which used a >90% secondary structure identity threshold for structural classification of RNA . Our results show that for conserved RNA structure cores, high secondary structure identity implies high tertiary structure identity but not necessarily high sequence identity. This reflects the co-variation effect in RNA that requires balancing a single mutation with a second change in the based-paired nucleotide to maintain its secondary and tertiary structures.
To accurately detect a pair of related RNA structures from sequence, their alignment should result in Infernal e-values smaller than 5·10-4. This result indicate that for RNA, likewise for proteins , there is a "twilight zone" for the practical application of homology-based approaches for RNA structure prediction. Using the Infernal program with an e-value cut-off of 5·10-4, we identified 50,523 pair-wise alignments between RNA sequences from the RFam database  and known RNA structures. This represents 26.2% and 4.5% coverage of all sequences and families in the RFam database, respectively. Of those, 90.7% (45,812) were between two sequences that result in alignments above the "twilight zone" curve and represent a set of query sequences for which comparative RNA structure prediction could reliably be used.
It is important to note that our study is currently affected by two circumstances. First, the distribution of RNA structures deposited in the PDB is rather scattered. It is known that the RNA structures in the PDB do not evenly represent the entire RNA structure space. To minimize such problem, we have used a pre-selected dataset of non-identical RNA structures (identity cut-off of 100%) as well as removing alignments between a structure and its sub-structures. Moreover, such problem will become less relevant with time given the increased pace of deposition of new RNA structures in the PDB. Second, RNA motif comparison has classically been centered on small RNA fragments of about 10 to 30 nucleotides. However, given the intrinsic difficulty of discerning significant alignments from random pairs of short RNA structures or motifs, our work has focused on identifying structural cores of at least ~50 nucleotides.
Despite the increasing interest on RNA function and the accelerated deposition of RNA structures, there was a gap between the common knowledge and a quantitative analysis of the relationship between sequence and structure conservation in RNA. Here we have addressed this knowledge gap by applying our RNA alignment method  to a set of 451 non-identical RNA structures. The relationship we quantified confirms previous studies in ribosomal RNA [25, 27, 28, 53] and could prove useful to assess whether a particular alignment could be reliably used for comparative RNA structure prediction. We have quantitatively shown that: (i) there is an exponential decay relationship between sequence and structure conservation, (ii) evolution tends to conserve more structure than sequence, and (iii) there is a "twilight zone" for RNA homology detection.
Our study provides an initial assessment of the current limits of comparative modeling of RNA structures. We anticipate that our work will aid the development of new methods for RNA structure prediction from sequence. In the near future, it is expected that large-scale comparative modeling of RNA structures will extend opportunities for answering key questions about RNA evolution, such as the origin of RNA as functional molecules . We have estimated that it would be possible to model by comparative modeling segments of approximately one quarter of all RNA sequences in the RFam database. More accurate RNA sequence alignment methods, including those that explicitly use base-pairing information, will be needed to increase the coverage, diversity and accuracy of reliable comparative RNA 3D structure models. Assuming the current growth rate in the number of known RNA structures, comparative modeling will be applicable to a significant number of RNA families within the next few years and thus could play an important bridging role in understanding the atomic mechanisms of RNA folding.
Two types of RNA alignments were obtained in our experiment. First, 3D structure-based alignments, which were produced by the SARA program  and used to characterize the relationship between sequence and secondary/tertiary structure conservation in RNA. Second, sequence-based alignments, which were produced by the Infernal program  and used to characterize a "twilight zone" for RNA homology detection.
Structure-based RNA alignments
Pairs of RNA structures were aligned using the SARA program, which is based on the unit vector approach . A similar approach was previously used for protein structure alignment by the MAMMOTH program . Briefly, SARA alignments were built by the following procedure: (i) given a RNA structure with N nucleotides, for each i = 1,...,N-1 extract the vector from the i-th to the (i+1)-st selected atoms; (ii) normalize all vectors to a unit-distance, and place the tails of all normalized vectors at the origin of a unit-sphere; the resulting collection of normalized vectors is the unit-vector representation of the input RNA. In this work, SARA aligned two RNA structures by selecting only C3' atoms involved in base-pairing as computed by the 3DNA program ; (iii) calculate the Unit-vector RMS distance between two sets of unit vectors as a score for local RNA structural comparison. This is equivalent to the root mean square deviation (RMSD) between their corresponding normalized vectors after determining the rotation to minimize the RMSD ; (iv) the comparison of consecutive unit-spheres generates an all-against-all similarity scoring matrix, which is used in a dynamic programming procedure for the global alignment of two RNA structures using zero end gap penalties ; (v) the output alignment is then refined by maximizing the number of equivalent atoms or base-pairs within 3.5 Å RMSD using a variant of the MaxSub algorithm, which ensures that the best local alignment is contained in the resulting alignment [56, 60]; and (vi) three p-value and their negative logarithms are calculated to assess the statistical significance of the resulting alignment scores.
where n id is the number of identical nucleotide types aligned in the structural alignment and N is the length of the shortest of the two RNA structures.
where μ, σ are the values that best fit the extreme value distribution (Eqn. 4 and Additional file 1 Figure S1).
Sequence-based RNA alignments
To assess the limits of RNA homology detection, we used the Infernal program  to generate a set of covariance models (CMs) for each structure in the RNA09 dataset. The CMs were built using known RNA secondary structures calculated by the 3DNA program  from the 3D coordinates of the structures. An arbitrary random sequence length of 4 Mb was set to calibrate the local covariance model, which exceed the length of largest ribosomal RNA sequences in the RNA09 dataset (~2900 nt). We then performed a leave-one-out procedure removing from the RNA09 dataset one RNA entry at the time and treating it as target sequence of unknown structure. Each target was aligned with Infernal against the remaining set of CMs of known structures or templates. The size of the search space was set to 200 Mb during the search step. All other parameters in Infernal were set at their default values. The searching by Infernal returned a list of hits of each target sequence and the e-value of the statistical significance of the alignments. Infernal resulted in 2,335 top hits with e-value lower than 1.0, which where stored and used to calculate a "twilight zone" for RNA homology detection. Additionally, all the 451 covariance models generated from the RNA structures in RNA09 dataset where used to search homologous RNA sequences in the RFam database using the same Infernal-based protocol. Such analysis allowed us to assess the likely impact of comparative RNA structure prediction.
RNA structure and alignments datasets.
Number of structures
Number of alignments
We are very grateful to Dr. Baldo Oliva for fruitful discussions. MAM-R acknowledges support from the Marie Curie International Reintegration program (FP6-039722), the Generalitat Valenciana (GV/2007/065), and the Spanish Ministerio de Ciencia e Innovación (BIO2007/66670). EC acknowledges support from the Marie Curie International Outgoing Fellowship program (PIOF-GA-2009-237225).
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