A fast structural multiple alignment method for long RNA sequences
 Yasuo Tabei^{1, 2},
 Hisanori Kiryu^{2},
 Taishin Kin^{2} and
 Kiyoshi Asai^{1, 2}Email author
DOI: 10.1186/14712105933
© Tabei et al; licensee BioMed Central Ltd. 2008
Received: 14 September 2007
Accepted: 23 January 2008
Published: 23 January 2008
Abstract
Background
Aligning multiple RNA sequences is essential for analyzing noncoding RNAs. Although many alignment methods for noncoding RNAs, including Sankoff's algorithm for strict structural alignments, have been proposed, they are either inaccurate or computationally too expensive. Faster methods with reasonable accuracies are required for genomescale analyses.
Results
We propose a fast algorithm for multiple structural alignments of RNA sequences that is an extension of our pairwise structural alignment method (implemented in SCARNA). The accuracies of the implemented software, MXSCARNA, are at least as favorable as those of stateofart algorithms that are computationally much more expensive in time and memory.
Conclusion
The proposed method for structural alignment of multiple RNA sequences is fast enough for largescale analyses with accuracies at least comparable to those of existing algorithms. The source code of MXSCARNA and its web server are available at http://mxscarna.ncrna.org.
Background
Noncoding RNAs (ncRNAs) are transcribed RNA molecules that do not encode proteins. Their functions often depend on their 3Dstructures rather than their primary sequences. The secondary structures of RNA sequences can be identified by various methods, including minimization of the free energy [1–3]. However, it is not always possible to obtain the accurate secondary structures. More reliable predictions of the secondary structures are possible if we have a set of RNA sequences with a common secondary structure. For consensus structure prediction, RNAalifold [4], Pfold [5], and McCaskillMEA [6] are applicable only to sets of aligned RNA sequences. Multiple alignment tools that consider only sequence similarities, e.g. ClustalW [7], Dialign [8], and TCoffee [9], however, have limited accuracy for RNA sequences with low similarity.
Simultaneous prediction of the common secondary structure and optimal alignment of RNA sequences is computationally quite expensive, even if pseudoknotted structures are excluded. For example, the strict algorithm of Sankoff [10] requires O(L^{3N}) in time and O(L^{2N}) in memory for N sequences of length L. Its faster variants that restrict the distances of the base pairs in the primary sequences are proposed for pairwise alignments [11–14].
Although structural alignment of multiple RNA sequences with reasonable computational cost is difficult, several algorithms have been proposed. Hofacker et al. proposed a method for progressive multiple alignments by direct comparison of the basepairing probability matrices [12], implemented in PMmulti which was recently reimplemented in FoldalignM [15] and Locarna [16] by Torarinsson et al. and Will et al., respectively. In Stemloc, Holmes et al. incorporated a constraint approach that limits the range of structures and alignments to be considered by preprocessing the sequences [13, 14]. Siebert et al. proposed an approach distantly related to Sankoff's algorithm and implemented it in MARNA [17] that uses the structural information for pairwise alignments before combining them into multiple alignments with TCoffee [9]. Dalli et al. developed a new scoring approach, StrAl, that takes into account sequence similarities as well as basepairing probabilities [18]. Xu et al. proposed a new sampling based algorithm that finds the common structure between input sequences by probabilistically sampling aligned stems based on stem conservation calculated from intrasequence base pairing probabilities and intersequence base alignment probabilities, which was implemented in RNASampler [19]. Bauer et al. developed a graph based representation which modeled sequencestructured alignment as an integer linear program (ILP), and implemented it in RNAlara [20]. Kiryu et al. proposed a variant of Sankoff's algorithm with marked reduction of computation, which was implemented in Murlet [21]. All of these methods, however, are still too slow to apply to the RNA sequences longer than 1000 bases. Seibel et al. developed an alignment tool with an editor, which uses the secondary structure information of individual sequences to align multiple RNA sequences with low time complexities (4SALE) [22]. In order to extract the common secondary structure, it is also possible to find the structural motifs without aligning the whole sequences. For structural motif finding, Yao et al. proposed an algorithm based on covariance models (CMfinder) [23], and Hamada et al. proposed a graph mining approach (RNAmine) [24].
Here we propose a method, implemented in MXSCARNA, for fast multiple alignments of RNA sequences. This method extends our previous work in pairwise alignments (SCARNA) [25] to progressive multiple alignments with improved score functions, and simultaneously construct multiple alignments and the associated common secondary structures. The pairwise alignment in this progressive alignment is an heuristic algorithm that separately aligns 5' parts and 3' parts of the stems with rough consistency considerations.
In benchmark experiments, our method was at least as accurate as currently available stateofart multiple alignment methods, but unlike those methods, the computations were fast enough for largescale analyses, though the accuracies for the alignments of long sequences have not yet been confirmed.
Results and Discussion
Algorithm
Overview of the algorithm
The proposed method, implemented in MXSCARNA, progressively aligns multiple RNA sequences, in an extension of the pairwise structural alignment algorithm (implemented in SCARNA) of our previous work [25].
First the guide tree for the progressive alignment is built by Unweighted Pair Group Method with Arithmetic Mean (UPGMA) [26] by using the pairwise similarities of the RNA sequences. Second the basepairing probability matrices are calculated for all the RNA sequences by McCaskill's algorithm [27]. Those basepairing probabilities are used for extracting the potential stems and for the matching scores in the Dynamic Programming (DP) of the alignments. Third the RNA sequences are progressively aligned along the guide tree using SCARNA's pairwise alignment algorithm with improved score functions introduced in this paper.
At the first stage of the progressive alignment, which corresponds to the bottom level of the guide tree, the pairs of RNA sequences are aligned by engineered DP algorithm of SCARNA's pairwise alignment. The pairwise alignment is very fast because the potential stems extracted from the basepairing probability matrices are decomposed into 5' part and 3' part and those two parts are independently aligned. In each upperlevel step of the progressive alignment according to the guide tree, potential stems for groups of RNA sequences are extracted from the averaged basepairing probability matrices.
The DP algorithm of the pairwise alignment uses the approximated posterior probabilities as score functions. The approximation uses the product of the pairwise posterior probabilities of Maximum Expected Accuracy (MEA) alignments and the basepairing probabilities of the sequences. MEA alignment maximizes the expected number of positions where the two nucleotides are correctly aligned. To yield robust alignments, the pairwise posterior probabilities of MEA alignments are modified by the probability consistency transformation.
Definitions
Definition 1: Stem candidate
Given a basepairing probability matrix for an RNA sequence and a threshold τ (0 <τ < 1), stem candidate is a set of continuous base pairs of which the basepairing probabilities are greater than τ.
Definition 2: Stem fragment
Given a basepairing probability matrix for an RNA sequence, a threshold τ (0 <τ < 1), and an integer W, stem fragment is a set of continuous base pairs of length W, of which the basepairing probabilities are greater than τ.
Definition 3: Stem component
For each stem fragment, a stem component X_{ a }, either a 5' stem component or a 3' stem component, is an object that has the following properties:

p(X_{ a }): position, the position of the leftmost base of the 5' or 3' part of the stem fragment.

s(X_{ a }): sequence, the nucleotide sequence of the 5' or 3' part of the stem fragment.

c(X_{ a }): partner component, the complementary (3' or 5') stem component.

d(X_{ a }): loop distance, the distance to the complementary (3' or 5') stem component.
A stem fragment is written as [X_{ a }, X_{ a' }] by using the mutually complementary stem components, 5' stem component X_{ a }and 3' stem component X_{ a' }, which represent the 5' and 3' parts of the stem fragment. X_{ a }and X_{ a' }satisfyX_{ a }= c(X_{ a' }) and X_{ a' }= c(X_{ a }).
The loop distance d(X_{ a }) can be written asd(X_{ a }) = p(c(X_{ a }))  p(X_{ a })  W.
Definition 4: stem component sequence (SCS)
A stem component sequence (SCS) is a sorted sequence of all the stem components of an RNA sequence, in order of their positions and, if the positions are the same, according to their loop distances.
For i <j, a SCS X= X_{1}X_{2} ... X_{ m }satisfiesp(X_{ i }) <p(X_{ j }) or p(X_{ i }) = p(X_{ j }) &d(X_{ i }) <d(X_{ j }).
Definition 5: relations of stem fragments without an overlap
Two stem fragments, [X_{ a }, X_{ a' }] and [X_{ b }, X_{ b' }] of an RNA sequence are, parallel if and only ifp(X_{ a }) <p(X_{ a' }) <p(X_{ b }) <p(X_{ b' }) or p(X_{ b }) <p(X_{ b' }) <p(X_{ a }) <p(X_{ a' }),
nested if and only if p(X_{ a }) <p(X_{ b }) <p(X_{ b' }) <p(X_{ a' }) or p(X_{ b }) <p(X_{ a }) <p(X_{ a' }) <p(X_{ b' }),
pseudoknotted if and only if p(X_{ a }) <p(X_{ b }) <p(X_{ a' }) <p(X_{ b' }) or p(X_{ b }) <p(X_{ a }) <p(X_{ b' }) <p(X_{ a' }).
Definition 6: relations of overlapping stem fragments
Two stem fragments, [X_{ a }, X_{ a' }] and [X_{ b }, X_{ b' }] of an RNA sequence are, rcontinuous if and only ifr = p(X_{ b })  p(X_{ a }) = p(X_{ a' })  p(X_{ b' }),
illcontinuous if and only if X_{ a }overlaps X_{ b }and X_{ a' }overlaps X_{ b' }andp(X_{ b })  p(X_{ a }) ≠ p(X_{ a' })  p(X_{ b' }),
contradictory if and only if only one side, either 5' part or 3' part, of the stem fragments overlap.
The three possible relationships between stem fragments without an overlap: parallel, nested, and pseudoknotted, may exist in the same secondary structure of an RNA sequence. However, among the three possible relationships between overlapping stem fragments, only rcontinuous stem fragments may coexist in the same secondary structure of an RNA sequence. 1continuous, a special case of rcontinuous, means that the two stem fragments are adjacent in the RNA sequence and a part of a stem candidate with a length of W + 1 (Figure 1). As described later, two overlapping stem components in the alignment are controlled to belong to two rcontinuous stem fragments in DP.
Building stem component sequences
In a basepairing probability matrix, which is calculated by McCaskill's algorithm [27], a potential stem is located in two symmetry locations as continuous counterdiagonal positions which have high basepairing probabilities. Therefore, the stem components for each RNA sequence defined in previous section are extracted by scanning counterdiagonal windows of length W in the basepairing probability matrix and selecting the windows whose elements are greater than τ. Smaller value in W or τ increase the sensitivity of the predictions of the stems and decrease the specificity of them. W and τ are set to 2 and 0.01 respectively in all the computational experiments in this paper.
The stem components are sorted in order of their positions and loop distances to construct a stem component sequence (SCS).
For each group alignment in the progressive alignment, the average of the basepairing probability matrices is calculated directly according to the alignment of the group of RNA sequences. The stem components for the group are extracted from the averaged matrix, and the SCS is constructed by sorting the stem components.
Alignment of stem component sequences
with the initial conditions; M(0, 0) = 0, M(·, 0) = M(0, ·) = G(0, 0) = G(·, 0) = G(0, ·) = ∞.
δ_{ s }(i, j) corresponds to the incremental score for the match of the overlapping stem components, which is discussed in the next section.
The second and third terms of equation (1) keep the stem components in the adjacent DP match from overlapping in the nucleotide sequences. p_{ i }/q_{ j }are the indices (smaller than i/j) of the nearest components that do not overlap with X_{ i }/Y_{ j }(Figure 2). s(i, j) is a match score for X_{ i }and Y_{ j }, which is discussed in the next section.
Equation (2) refers only adjacent positions in DP matrix because overlaps of X_{ i }and Y_{ j }with the other stem components are permitted. Because the 5' stem components and the 3' stem components are handled independently, there is no term for bifurcation in secondary structures in equations (1) and (2).
The traceback pointer keeps the triplets, indices of X, Y, and the selection of M or G, in the recursion (1) and (2). The first term of the triplet, the index of X, can be either α_{ i }, p_{ i }, i, or i  1, and the second term of the triplet, the index of Y, can be either β_{ j }, q_{ j }, j, or j  1. In the traceback of the DP, M(i, j) and G(i, j) are used jointly to obtain the optimal path and to select M or G, which gives the maximum score of the alignment. The alignments of SCSs are constructed by selecting the stem components that appear in the path with the selected M. All of the mismatched stem components are excluded from the alignment. The algorithm makes the adjacent DP matches of stem components either not overlapping in the nucleotide sequences or consistently overlapping (1continuous) as a match of the stems longer than W. Pairwise alignment of the SCSs requires only O(XY) in time and in memory. That computational complexities are evaluated as (L^{2}) for two RNA sequences of length L because the number of the stem components is regarded as a linear function of the length of the nucleotide sequence [25].
The pairwise alignment of SCSs allows some inconsistent matches by ignoring strict treatments of the complementary components. For two stem fragments, [X_{ a }, X_{ a' }] and [Y_{ b }, Y_{ b' }], if X_{ a }matches Y_{ b }in the SCS alignment, X_{ a' }should match Y_{ b' }. Let us define such a match as leftright consistent. Because 5' stem components and 3' stem components are aligned independently, leftright consistency is not guaranteed in general. Any match which is not leftright consistent is removed as a post process. If any two of the stem components of a same SCS appear in the SCS alignment and their complementary components overlap (i.e. contradictory in Definition 6), those complementary components do not appear together in the alignment because the alignment of complementary components are controlled to be either nonoverlapping or rcontinuous. Therefore, the post process also guarantees that no pair of contradictory stem fragments appears in the alignment [25].
The score function using the MEA alignment
In our previous work [25], a function of the RIBOSUM [28] score, loop distance, basepairing probabilities, and the stacking energy were used as the score s(i, j) in recursion (1). In MXSCARNA, the score function is replaced by an approximated posterior probability according to the principle of Maximum Expected Accuracy (MEA). Recent studies have shown that the accuracy of the resulting sequence alignment and secondary structure predictions is better than that of predictions made by the conventional maximum likelihood estimation (MLE) algorithms [21, 29–32].
P(x_{ k }◇ x_{ l }x) and P(y_{ m }◇ y_{ n }y) are the basepairing probabilities that the particular positions x_{ k }and x_{ l }, y_{ m }and y_{ n }, respectively, form base pairs; these probabilities are computed by McCaskill's algorithm [27].
where S is the set of RNA sequences to be aligned. In this transformation, the probability of specific nucleotides of two sequences being aligned are replaced by the average over the products of probabilities that the two nucleotides are aligned to the same nucleotides in arbitrary third sequences. This calculation requires O(N^{3}L^{3}) in time and O(N^{2}L^{2}) in memory. The probability consistency transformations are applied twice in current implementation.
where ${{X}^{\prime}}_{i}/{{Y}^{\prime}}_{j}$ are the complementary stem components of X_{ i }/Y_{ j }.
The sum of the probabilities, not the logarithms of the probabilities, is used for the matching score, in an effort to maximize the number of correctly aligned bases including the implicit prediction of the base pairs (MEA principle).
Alignment of loop region
Computational Experiments
Datasets
To test the empirical performance of MXSCARNA, we used three datasets for the benchmark multiple alignments: an original multiple alignment dataset, the BRAlibaseII multiple alignment dataset [33], and Kiryu et al.'s multiple alignment dataset [21].
Our original dataset comprised 1669 multiple alignments of 5 sequences, the secondary structures of which have been published, obtained from the Rfam 7.0 database [34]. There are 27 families of RNA sequences in the dataset and the sequence identities varied from 35% to 100%. Sequences that included bases other than A, C, G, and U were removed because some of the alignment programs were unable to align them. The BRAlibaseII benchmark dataset included 481 multiple alignments of 5 sequences. The sequences of each multiple alignment were extracted from tRNA, Intron_gpII, 5S_rRNA, and U5 families in the Rfam 5.0 database and the signal recognition particle RNA family (SRP) in the SRPDB database [35]. Because the dataset did not include consensus secondary structure annotations to the alignments, we used the secondary structure annotations recovered by Kiryu et al. [21].
Kiryu et al.'s multiple alignment benchmark dataset was generated from selected seed alignments in the Rfam 7.0 database that have published consensus structures [21]. For each sequence family, as many as 1000 random combinations of 10 sequences were generated. The alignments whose mean pairwise sequence identity exceeded 95% and whose gap characters accounted for more than 30% of the total number of characters aligned were removed. As such, this dataset consisted of 85 multiple alignments of 10 sequences, generated from 17 sequence families, with five alignments for each. The dataset was reasonably divergent, and its mean length varied from 54 to 291 bases, and mean pairwise sequence identities varied from 40% to 94%.
Evaluation measures
where TP indicates the number of correctly predicted base pairs, TN the number of base pairs that were correctly predicted as unpaired, FP the number of incorrectly predicted base pairs, and FN the number of true base pairs that were not predicted. The term ξ accounts for predicted base pairs that were not present in the reference structure but were compatible with it. Compatible base pairs are not true positives but have to be neither inconsistent (one or both nucleotides being a part of a different base pair in the reference structure) nor pseudoknotted with respect to the reference structure [37]. In order to calculate MCC for each test alignment, the reference alignment and the "correct" consensus secondary structure are taken from the database. In order to compare the accuracies of the alignments in terms of the implicitly predicted common secondary structures, the common secondary structures for each test alignment by the alignment programs were predicted by the Pfold program [5].
Comparison of accuracies with those of other aligners
To compare the accuracies of the alignment methods we used a Linux machine with an AMD Opteron processor (2 GHz and 4 GB RAM).
Command line options for the programs in the experiments. This table summarizes multiple alignment programs and their command line options used in the paper.
Program  Command 

MXSCARNA  ./mxscarna <input_filename> 
Murlet  ./murlet max_time = 100 <input_filename> 
ProbCons  ./probcons <input_filename> 
MAFFT  ./mafft <input_filename> 
ClustalW  ./clustalw <input_filename> 
StrAl  ./stral <input_filename> 
RNASampler  perl RNASampler_driver.pl p <input_dir> q <input_filename> i 15 S 100 
RNAlara  ./lara i <input_filename> 
Locarna  ./mlocarna structlocal = false sequlocal = false <input_filename> 
FoldalignMFoldalign  perl FoldalignM_Foldalign.pl f <input_filename> 
FoldalignMMcCaskill  java FoldalignM_McCaskill <input_filename> 
MARNA  perl marna.pl g 2 <input_filename> 
PMmulti  perl pmmulti.pl <input_filename> 
stemloc  ./stemloc g m slow <input_filename> 
Accuracies for the original multiple alignment dataset. SPS and MCC values (%) for the original multiple alignment dataset are presented. Each family has 5 RNA sequences. Family: Rfam family name. %id: average sequence identity. length: average sequence length (bases) in each family. Average(all): the average SPS or MCC for all families. Average(sub): the average SPS or MCC for the subset of families with an average sequence length of less than or equal to 100 bases. Because PMmulti and Stemloc were unable to align all data, the proportion of data that was aligned is given in parentheses as no. of sequences aligned/total no. of sequences. FoldalignM consists of two modes: FoldalgnM_FoldalignM and FoldalignM_McCaskill, which are separately evaluated and indicated as FoldalignM(1) and FoldalignM(2) respectively.
SPS:Family  %id  length  MXSCARNA  Murlet  ProbCons  MAFFT  ClustalW  StrAl  RNASampler 

IRE  62  29  98  96  93  89  77  83  92 
s2m  78  43  96  96  96  96  96  96  95 
UnaL2  78  54  95  98  98  96  92  94  82 
Hammerhead_3  71  55  96  94  93  89  83  89  91 
SECIS  42  64  65  66  65  52  45  56  46 
sno_14q_I_II  71  74  90  95  96  93  93  87  71 
tRNA  48  76  87  87  87  84  76  82  87 
ctRNA_pGA1  74  80  88  86  85  88  84  86  89 
Tymo_tRNA  70  83  84  83  82  75  75  79  77 
Y  64  95  71  72  72  73  65  64  65 
SRP_bact  52  95  71  71  70  66  70  62  66 
Purine  55  100  74  77  77  78  75  81  69 
5S_rRNA  60  117  88  89  89  86  86  86  83 
S_box  66  130  79  80  78  78  68  72  67 
U4  67  141  79  81  80  79  79  78  69 
RFN  65  150  86  87  87  88  81  80  81 
5_8S_rRNA  67  154  91  93  93  90  88  89  78 
U1  60  158  81  81  79  79  79  76  74 
Telomerase_cil  56  171  48  50  49  43  38  41  37 
Lysine  50  180  78  81  79  72  70  76  72 
U2  66  185  76  76  75  71  71  73  71 
U17  75  214  91  93  93  89  89  87  81 
U3  51  246  43  44  44  47  41  40  34 
SRP_euk_arch  46  294  50  56  47  42  42  48  44 
tmRNA  46  373  48  50  50  47  46  39  42 
RnaseP_bact_b  64  387  82  80  79  78  74  74  66 
Telomerase_vert  66  463  69  70  69  69  66  64  65 
Average(all)  78  79  78  75  72  73  70  
Average(sub)  85  85  85  82  78  80  78  
SPS:Family  RNAlara  Locarna  FoldalignM(1)  FoldalignM(2)  MARNA  PMmulti  Stemloc  
IRE  85  88 (100/100)  87 (99/101)  85 (97/100)  92  90 (101/101)  87 (101/101)  
s2m  96  99 (43/50)  95 (50/50)  95 (47/50)  94  98 (44/50)  93 (50/50)  
UnaL2  93  93 (78/89)  89 (75/89)  86 (87/89)  88  87 (75/89)  75 (89/89)  
Hammerhead_3  88  80 (100/100)  79 (99/100)  77 (97/100)  89  87 (77/100)  94 (100/100)  
SECIS  48  47 (62/63)  46 (63/63)  44 (63/63)  49  39 (63/63)  60 (60/63)  
sno_14q_I_II  78  76 (98/98)  73 (98/98)  61 (97/98)  67  73 (97/98)  89 (97/98)  
tRNA  91  82 (103/103)  90 (100/103)  78 (97/103)  59  86 (103/103)  88 (103/103)  
ctRNA_pGA1  86  74 (20/28)  75 (28/28)  74 (27/28)  79  72 (20/28)  84 (28/28)  
Tymo_tRNA  79  78 (49/59)  68 (59/59)  68 (56/59)  66  71 (49/59)  57 (57/59)  
Y  56  49 (21/24)  50 (24/24)  47 (24/24)  60  43 (11/24)  68 (23/24)  
SRP_bact  63  62 (70/70)  64 (70/70)  56 (67/70)  56  61 (63/70)  60 (67/70)  
Purine  64  65 (45/45)  64 (45/45)  62 (45/45)  64  65 (45/45)  37 (45/45)  
5S_rRNA  85  
S_box  57  
U4  71  
RFN  78  
5_8S_rRNA  81  
U1  74  
Telomerase_cil  32  
Lysine  59  
U2  71  
U17  79  
U3  32  
SRP_euk_arch  42  
tmRNA  34  
RnaseP_bact_b  66  
Telomerase_vert  51  
Average(all)  68  
Average(sub)  77  74  73  69  72  73  74  
MCC:Family  %id  length  MXSCARNA  Murlet  ProbCons  MAFFT  ClustalW  StrAl  RNASampler 
IRE  62  29  90  91  75  72  65  43  89 
S2m  78  43  84  83  84  84  84  84  81 
UnaL2  78  54  52  70  51  53  51  50  51 
Hammerhead_3  71  55  99  95  93  86  72  79  96 
SECIS  42  64  76  60  55  35  23  37  73 
sno_14q_I_II  71  74  93  98  93  93  91  91  95 
tRNA  48  76  91  89  86  84  76  83  95 
ctRNA_pGA1  74  80  96  93  88  89  81  92  94 
Tymo_tRNA  70  83  87  85  75  73  72  80  90 
Y  64  95  95  85  86  83  67  83  94 
SRP_bact  52  95  81  72  54  50  58  57  83 
Purine  55  100  90  94  90  86  80  84  91 
5S_rRNA  60  117  75  79  69  70  69  70  70 
S_box  66  130  90  87  86  81  76  81  86 
U4  67  141  75  71  62  62  54  65  67 
RFN  65  150  84  83  84  84  82  83  82 
5_8S_rRNA  67  154  58  51  47  45  41  46  52 
U1  60  158  70  68  61  56  60  57  71 
Telomerase  56  171  65  41  28  21  24  31  60 
Lysine  50  180  87  90  76  66  63  71  89 
U2  66  185  73  76  58  51  62  59  77 
U17  75  214  79  80  78  76  75  72  72 
U3  51  246  46  26  22  19  46  21  39 
SRP_euk_arch  46  294  72  75  46  37  35  49  72 
tmRNA  46  373  51  54  50  49  43  42  49 
RNaseP_bact_b  64  387  73  58  63  58  53  60  37 
Telomerase  66  463  64  51  47  44  40  36  53 
Average(all)  78  74  67  63  61  63  74  
Average(sub)  86  85  77  74  68  72  86  
MCC:Family  RNAlara  Locarna  FoldalignM(1)  FoldalignM(2)  MARNA  PMmulti  Stemloc  
IRE  81  89  85  89  82  89  81  
s2m  84  83  85  86  79  85  84  
UnaL2  53  53  53  51  51  50  45  
Hammerhead_3  95  94  87  91  95  91  98  
SECIS  63  74  74  75  57  67  78  
sno_14q_I_II  92  87  92  84  81  93  85  
tRNA  95  87  95  87  67  90  95  
ctRNA_pGA1  97  95  96  96  95  94  95  
Tymo_tRNA  85  75  87  82  62  82  83  
Y  86  87  94  89  87  83  93  
SRP_bact  65  87  86  83  63  80  69  
Purine  77  89  88  88  82  86  89  
5S_rRNA  72  
S_box  72  
U4  60  
RFN  79  
5_8S_rRNA  46  
U1  60  
Telomerase  39  
Lysine  58  
U2  63  
U17  63  
U3  21  
SRP_euk_arch  42  
tmRNA  40  
RNaseP_bact_b  65  
Telomerase  28  
Average(all)  65  
Average(sub)  81  83  85  83  75  83  83 
Accuracies for the BRAlibaseII multiple alignment dataset. SPS and MCC values (%) for the BRAlibaseII multiple alignment dataset are presented. Each family has 5 RNA sequences. Family: Rfam family name. %id: average sequence identity. length: average sequence length (bases) in each family. Average(all): the results of the average value of the SPS or MCC for all families. Average(sub): the average SPS or MCC for the subset of families with an average sequence length of less than or equal to 100 bases. Because PMmulti and Stemloc were unable to align all data, the proportion of data that was aligned is given in parentheses as no. of sequences aligned/total no. of sequences. FoldalignM consists of two modes: FoldalgnM_FoldalignM and FoldalignM_McCaskill, which are separately evaluated and indicated as FoldalignM(1) and FoldalignM(2) respectively.
SPS:Family  %id  length  MXSCARNA  Murlet  ProbCons  MAFFT  ClustalW  StrAl  RNASampler  

tRNA  69  76  91  91  91  89  85  89  92  
Intron_gpII  64  80  79  80  80  77  75  79  74  
5S_rRNA  70  117  89  90  90  89  88  89  90  
U5  72  118  74  75  76  72  72  73  78  
SRP  67  300  88  88  88  87  87  86  82  
Average(all)  84  85  85  83  81  83  83  
Average(sub)  83  84  84  82  80  82  83  
SPS:Family  RNAlara  Locarna  FoldalignM(1)  FoldalignM(2)  MARNA  PMmulti  Stemloc  
tRNA  95  93 (98/98)  94 (97/98)  90 (91/98)  79 (98/98)  90 (89/98)  88 (98/98)  
Intron_gpII  75  71 (89/92)  70 (92/92)  67 (89/92)  76 (92/92)  77 (61/92)  77 (92/92)  
5S_rRNA  93  92 (89/89)  92 (88/89)  89 (89/89)  58 (78/89)  85 (89/89)  72 (89/89)  
U5  80  77 (109/109)  72 (108/109)  69 (107/109)  85 (74/109)  56 (105/109)  64 (109/109)  
SRP  82  83 (84/93)  
Average(all)  85  83  
Average(sub)  86  83  82  79  74  77  75  
MCC:Family  %id  length  MXSCARNA  Murlet  ProbCons  MAFFT  ClustalW  StrAl  RNASampler  RNAlara 
tRNA  69  76  94  92  91  90  83  88  94  93 
Intron_gpII  64  80  82  80  77  76  74  74  80  79 
5S_rRNA  70  117  71  69  67  68  67  69  69  70 
U5  72  118  80  75  70  66  66  69  77  72 
SRP  67  300  75  72  68  67  68  65  71  63 
Average(all)  80  78  75  73  72  73  78  76  
Average(sub)  82  79  76  75  72  75  80  79  
MCC:Family  Locarna  FoldalignM(1)  FoldalignM(2)  MARNA  PMmulti  Stemloc  
tRNA  92  96  92  80  93  93  
Intron_gpII  80  76  80  78  76  76  
5S_rRNA  71  72  71  59  70  68  
U5  74  70  69  60  61  78  
SRP  73  
Average(all)  78  
Average(sub)  79  79  78  69  75  79 
Accuracies for Kiryu et al.'s dataset. SPS and MCC values (%) for Kiryu et al.'s dataset are presented. Each family has 10 RNA sequences. Family: Rfam family name. %id: average sequence identity. length: average sequence length (bases) in each family. Average(all): the results of the average value of the SPS or MCC for all families. Average(sub): the average SPS or MCC for the subset of families with an average sequence length of less than or equal to 100 bases. Because PMmulti and Stemloc were unable to align all data, the proportion of data that was aligned is given in parentheses as no. of sequences aligned/total no. of sequences. FoldalignM consists of two modes: FoldalgnM_FoldalignM and FoldalignM McCaskill, which are separately evaluated and indicated as FoldalignM(1) and FoldalignM(2) respectively.
SPS:Family  %id  length(nt)  MXSCARNA  Murlet  ProbCons  MAFFT  ClustalW  StrAl  RNAlara 

UnaL2  73  54  92  95  95  91  84  86  87 
SECIS  41  64  70  73  68  44  35  59  53 
tRNA  45  73  87  90  87  76  62  75  91 
sno_14q_I_II  64  75  82  92  92  91  80  75  72 
SRP_bact  47  93  58  61  61  60  61  48  56 
THI  55  105  77  83  82  78  58  65  65 
S_box  66  107  86  88  88  82  82  77  77 
5S_rRNA  57  116  84  85  85  81  82  79  83 
Retroviral_psi  92  117  97  97  97  97  96  97  97 
RFN  66  140  89  91  90  91  83  80  86 
5_8S_rRNA  61  154  85  88  87  84  78  81  75 
U1  59  157  74  77  75  73  71  66  66 
Lysine  49  181  75  77  75  66  60  68  59 
U2  62  182  71  74  73  68  65  67  69 
Tbox  45  244  44  50  50  43  34  32  15 
IRES_HCV  94  261  96  96  96  96  96  83  96 
SRP_euk_arch  40  291  42  42  40  36  34  40  39 
Average(all)  77  80  79  74  68  69  70  
Average(sub)  82  86  85  80  73  75  77  
SPS:Family  RNASampler  Locarna  FoldalignM(1)  FoldalignM(2)  MARNA  PMmulti  Stemloc  
UnaL2  72  88  68  60  83 (5/5)  69 (5/5)  82 (5/5)  
SECIS  54  49  42  41  47 (5/5)  35 (5/5)  82 (5/5)  
tRNA  82  79  84  66  54 (5/5)  69 (5/5)  91 (5/5)  
sno_14q_I_II  64  57  45  34  49 (5/5)  39 (3/5)  77 (5/5)  
SRP_bact  54  52  55  51  43 (5/5)  36 (4/5)  47 (3/5)  
THI  68  65  65  62  62 (4/5)  58 (5/5)  71 (5/5)  
S_box  76  63  57  57  78 (5/5)  44 (5/5)  84 (5/5)  
5S_rRNA  77  79  74  70  71 (5/5)  57 (5/5)  77 (3/5)  
Retroviral_psi  96  95  91  91  96 (5/5)  87 (5/5)  75 (5/5)  
RFN  82  72  73  63  77 (5/5)  58 (4/5)  80 (5/5)  
5_8S_rRNA  69  75  56  31  64 (5/5)  58 (5/5)  73 (1/5)  
U1  63  68  50 (5/5)  
Lysine  71  55  58 (5/5)  
U2  65  64  65 (1/5)  
Tbox  32  15  22 (5/5)  
IRES_HCV  93  75  92 (3/5)  
SRP_euk_arch  33  40  37 (5/5)  
Average(all)  68  64  62  
Average(sub)  72  70  64  57  52  60  76  
MCC:Family  %id  length(nt)  MXSCARNA  Murlet  ProbCons  MAFFT  ClustalW  StrAl  RNAlara 
UnaL2  73  54  42  41  46  36  24  32  44 
SECIS  41  64  78  78  59  20  23  45  70 
tRNA  45  73  93  97  91  85  65  85  97 
sno_14q_I_II  64  75  87  91  91  91  66  75  87 
SRP_bact  47  93  66  56  46  49  54  52  69 
THI  55  105  71  70  70  62  38  48  58 
S_box  66  107  90  89  87  79  77  75  76 
5S_rRNA  57  116  75  67  62  64  53  66  69 
Retroviral_psi  92  117  86  86  86  84  86  86  86 
RFN  66  140  67  71  72  73  71  60  70 
5_8S_rRNA  61  154  38  43  35  16  14  26  33 
U1  59  157  69  61  57  56  61  52  56 
Lysine  49  181  83  81  71  33  52  61  64 
U2  62  182  74  71  56  38  39  58  68 
Tbox  45  244  72  78  80  51  41  26  0 
IRES_HCV  94  261  63  62  62  63  26  34  63 
SRP_euk_arch  40  291  70  63  40  21  23  38  33 
Average(all)  72  71  65  54  48  54  61  
Average(sub)  72  72  68  60  52  59  69  
MCC:Family  RNASampler  Locarna  FoldalignM(1)  FoldalignM(2)  MARNA  PMmulti  Stemloc  
UnaL2  51  42  57  50  36  18  39  
SECIS  78  80  75  80  40  64  77  
tRNA  94  96  95  89  51  91  98  
sno_14q_I_II  84  95  95  86  79  77  87  
SRP_bact  73  74  80  75  47  44  64  
THI  72  60  50  51  59  41  77  
S_box  86  82  83  87  83  55  88  
5S_rRNA  62  75  72  73  59  58  66  
Retroviral_psi  86  88  76  89  84  73  87  
RFN  69  69  67  70  65  58  72  
5_8S_rRNA  38  40  43  41  21  14  34  
U1  64  73  45  
Lysine  86  80  66  
U2  79  65  66  
Tbox  44  1  2  
IRES_HCV  63  47  61  
SRP_euk_arch  62  64  52  
Average(all)  70  66  54  
Average(sub)  72  73  72  72  60  54  72 
Summary of accuracies for all three datasets. The summary of SPS and MCC values (%) for all three multiple alignment datasets are presented. Average(all): the results of the average value of the SPS or MCC for all families. Average(sub): the average SPS or MCC for the subset of families. FoldalignM consists of two modes: FoldalgnM_FoldalignM and FoldalignM_McCaskill, which are separately evaluated and indicated as FoldalignM(1) and FoldalignM(2) respectively.
Dataset  MXSCARNA  Murlet  ProbCons  MAFFT  ClustalW  StrAl  RNASampler  

original dataset  Average(all)  78/78  79/74  78/67  75/63  72/61  73/63  70/74 
Average(sub)  85/86  85/85  85/77  82/74  78/68  80/72  78/86  
BRAlibaseII  Average(all)  84/80  85/78  85/75  83/73  81/72  83/73  83/78 
Average(sub)  83/82  84/79  84/76  82/75  80/72  82/75  83/80  
Kiryu et al.'s dataset  Average(all)  77/72  80/71  79/65  74/54  68/48  69/54  68/70 
Average(sub)  82/72  86/72  85/68  80/60  73/52  75/59  72/72  
RNAlara  Locarna  FoldalignM(1)  FoldalignM(2)  MARNA  PMmulti  Stemloc  
original dataset  Average(all)  68/65  
Average(sub)  77/81  74/83  73/85  69/83  72/75  73/83  74/83  
BRAlibaseII  Average(all)  85/76  83/78  
Average(sub)  86/79  83/79  82/79  79/78  74/69  77/75  75/79  
Kiryu et al.'s dataset  Average(all)  70/61  64/66  62/54  
Average(sub)  77/69  70/73  64/72  57/72  60/60  52/54  76/72 
Evaluation of new score function
In order to evaluate the performance of our new score function (4), we compared it in pairwise alignment with the previous score function of SCARNA, which is a linear combination of RIBOSUM score, stacking energy, loopdistance penalty, basepairing probability. Dowell's dataset [39], which consists of R100 dataset and percid dataset, are used for the evaluation. R100 is a dataset which consists of 100 pairwise alignments chosen randomly from tRNA and 5SrRNA families in Rfam 7.0 database [34] and percid is a balanced dataset of 100 pairwise alignments from the same families.
Accuracy of new score function. The comparison of new score function of MXSCARNA and the old one which was used in SCARNA in terms of pairwise alignment. The SPS and MCC values (%) are used as accuracy measure for alignments. R100 is a dataset which consists of 100 pairwise alignments chosen randomly from tRNA and 5SrRNA families in Rfam 7.0 database [34] and percid is a sequence identitly balanced dataset which also consists of 100 pairwise alignments from these families.
dataset  score function  SPS  MCC 

R100  MXSCARNA  90  77 
SCARNA  84  74  
percid  MXSCARNA  79  71 
SCARNA  78  69 
Time and memory
The computational complexities of the proposed method for N sequences of length L were evaluated as follows. The construction of the guide tree using the alignments of all pairs of the sequences required O(N^{2}L^{2}) in time and O(L^{2} + N^{2}) in memory. The calculation of basepairing probability matrices for N sequences by McCaskill's algorithm [27] required O(NL^{3}) in time and O(NL^{2}) in memory. The probability consistency transformation (see (3) in Method) required O(N^{3}L^{3}) in time and O(N^{2}L^{2}) in memory. Pairwise alignment of stem component sequences required O(N^{2}L^{2}) in time and memory as is explained in Method. Therefore, the total computational complexities were O(N^{3}L^{3}) in time and O(N^{2}L^{2}) in memory. For the basepairing probabilities, the computational time for each sequence can be reduced to O(LW^{2}) by restricting the maximum distance of the base pairs to a fixed constant W [40]. The computation of probability consistency transformation for a pair of sequences can also be calculated in O(L^{2}) time by restricting the effective width of transformation to a fixed value. Those reductions reduce total time complexity to O(N^{3}L^{2}). We will address those improvements in future work.
Sequence identities and alignment accuracies
Availability and requirements
Project name: ncRNA.org project;
Project home page: http://www.ncrna.org/;
Operating systems: Linux with gcc 3.0 and Cygwin with gcc 3.4;
Programming language: C++;
License: free software, except for inclusion to comertical software;
The source code of MXSCARNA and its web server, the dataset and its references are available at http://mxscarna.ncrna.org. On the web server W and τ correspond to "SCSLENGTH" and "BASEPROBTHRESHHOLD" respectively, and "BASEPAIRSCORECONST" is a parameter of McCaskillMEA [6] used for the secondary structure prediction, which controls the sensitivity and the specificity of the prediction (α in equation 4 in [6]).
Conclusion
We have developed MXSCARNA, a new structural multiple aligner of RNA sequences, which progressively applies the pairwise alignment algorithm used in SCARNA. The accuracies of MXSCARNA in terms of SPS and MCC were evaluated for three datasets: an original dataset, the BRAlibaseII benchmark multiple alignment dataset, and Kiryu et al.'s multiple alignment dataset. MXSCARNA's accuracies were at least comparable to those of current stateofart aligners. In addition, the accuracies of MXSCARNA were robust over a broad range of sequence similarities, whereas the other aligners tested showed reductions in SPS or MCC. The computational complexities of MXSCARNA were evaluated as O(N^{3}L^{3}) in time and O(N^{2}L^{2}) in memory for N sequences of length L. In the comparison of execution time for benchmark datasets, MXSCARNA was by far the fastest among the structural aligners and was fast enough for largescale analyses. MXSCARNA aligns even 5000base RNA sequences with acceptable computational costs though the accuracies of alignments for long sequences are not yet confirmed. The source code of MXSCARNA and its web server are available at the web site [41].
Declarations
Acknowledgements
This work was supported in part by a GrantinAid for Scientific Research on Priority Areas "Comparative Genomics" from the Ministry of Education, Culture, Sports, Science and Technology of Japan and by the "Functional RNA Project" funded by the New Energy and Industrial Technology Development Organization (NEDO) of Japan. The authors thank the Japan Biological Informatics Consortium (JBIC) for its support through the "Functional RNA Project" and Michiaki Hamada, Kengo Sato, and colleagues in the Computational Biology Research Center (CBRC) for useful discussions.
Authors’ Affiliations
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 MXSCARNA[http://mxscarna.ncrna.org/]
Copyright
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.