Aligning multiple RNA sequences is essential for analyzing non-coding RNAs. Although many alignment methods for non-coding 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 genome-scale analyses.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 state-of-art algorithms that are computationally much more expensive in time and memory..The proposed method for structural alignment of multiple RNA sequences is fast enough for large-scale analyses with accuracies at least comparable to those of existing algorithms. The source code of MXSCARNA and its web server are available at  Non-coding RNAs (ncRNAs) are transcribed RNA molecules that do not encode proteins. Their functions often depend on their 3D-structures rather than their primary sequences. The secondary structures of RNA sequences can be identified by various methods, including minimization of the free energy -3. HowevO(LN3) in time and O(LN2) 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  by using the mutually complementary stem components, 5' stem component Xa and 3' stem component Xa', which represent the 5' and 3' parts of the stem fragment. Xa and Xa' satisfyA stem fragment is written as  and  of an RNA sequence are, parallel if and only ifTwo stem fragments,  and  of an RNA sequence are, r-continuous if and only ifTwo stem fragments,  and , if Xa matches Yb in the SCS alignment, Xa' should match Yb'. Let us define such a match as left-right consistent. Because 5' stem components and 3' stem components are aligned independently, left-right consistency is not guaranteed in general. Any match which is not left-right 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 r-continuous. Therefore, the post process also guarantees that no pair of contradictory stem fragments appears in the alignment [The pairwise alignment of SCSs allows some inconsistent matches by ignoring strict treatments of the complementary components. For two stem fragments, [lignment .s 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 [In our previous work , a functgorithms ,29-32.x and y, xi ~ yj means that xi ∈ x and yi ∈ y are aligned on the same column in the alignment, and xi ◇ xj means that xi, xj ∈ x form a base pair. For two RNA sequences, x, y and k, l ∈ {1, ···, |x|}, m, n ∈ {1, ···, |y|}, let P be the posterior probability, i.e. the sum of the probabilities that two positions of the sequences, xk and ym, xl and yn, are aligned in the alignment, and that two pairs of the nucleotides, xk and xl, ym and yn, form base pairs in the secondary structures as well; this is computed by the inside-outside algorithm of the pair Stochastic Context Free Grammar (pair SCFG) [s, but the computational costs, O(L6) in time and O(L4) in memory for sequences of length L, are impractical. We instead used the following approximated posterior probability introduced by Kiryu et al. [In the following, for nucleotide sequences ir SCFG)  for struu et al. .P(xk ◇ xl|x) and P(ym ◇ yn|y) are the base-pairing probabilities that the particular positions xk and xl, ym and yn, respectively, form base pairs; these probabilities are computed by McCaskill's algorithm [lgorithm .xk ~ ym|x, y) and xl ~ yn|x, y) are the posterior probabilities modified by probability consistency transformation [ormation , which iS 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(N3L3) in time and O(N2L2) in memory. The probability consistency transformations are applied twice in current implementation.where P is the posterior probability, i.e. the sum of the probabilities that particular positions of the two sequences, xk and zr, are aligned in some alignment; this is computed by the forward-backward algorithm of the pair Hidden Markov Model (pair HMM) [air HMM)  for pairXi/Yj.where 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).xk ~ ym|x, y), as the matching scores. The probabilities, not the logarithms of the probabilities, again are used, according to the MEA principle. The recursion is shown following.The remaining loop regions (except the selected common stems) are aligned by using the consistency-transferred posterior probabilities, Emission and transition probabilities for the pair HMM in MXSCARNA Figure  were traTo 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 , and KirOur original dataset comprised 1669 multiple alignments of 5 sequences, the secondary structures of which have been published, obtained from the Rfam 7.0 database . There aKiryu et al.'s multiple alignment benchmark dataset was generated from selected seed alignments in the Rfam 7.0 database that have published consensus structures . For eactest alignment) for the reference alignment were defined as follows. The SPS was defined as the proportion of correctly aligned nucleotide pairs:The qualities of the alignments were evaluated by the Sum-of-Pairs Score (SPS) for the accuracy of the alignments and by the Matthews Correlation Coefficient (MCC)  for the I is the number of columns in the test alignment, J is the number of columns in the reference alignment, on column i in the test alignment j in the reference alignment where 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 pseudo-knotted with respect to the reference structure [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 tructure . In ordetructure .To compare the accuracies of the alignment methods we used a Linux machine with an AMD Opteron processor (2 GHz and 4 GB RAM).We compared the performance of MXSCARNA with that of Murlet , ProbConThe results from the BRAlibaseII benchmark multiple alignment dataset are shown in Table All results are summarized in Table 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, loop-distance penalty, base-pairing probability. Dowell's dataset , which cThe SPS and MCC are shown in Table 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(N2L2) in time and O(L2 + N2) in memory. The calculation of base-pairing probability matrices for N sequences by McCaskill's algorithm [O(NL3) in time and O(NL2) in memory. The probability consistency transformation (see (3) in Method) required O(N3L3) in time and O(N2L2) in memory. Pairwise alignment of stem component sequences required O(N2L2) in time and memory as is explained in Method. Therefore, the total computational complexities were O(N3L3) in time and O(N2L2) in memory. For the base-pairing probabilities, the computational time for each sequence can be reduced to O(LW2) by restricting the maximum distance of the base pairs to a fixed constant W [O(L2) time by restricting the effective width of transformation to a fixed value. Those reductions reduce total time complexity to O(N3L2). We will address those improvements in future work.The computational complexities of the proposed method for lgorithm  requirednstant W . The comComparisons of alignment tools in regard to execution time for nucleotide sequences of various lengths are presented in Figures Alignment methods based only on sequence similarities often fail to capture common secondary structures among their alignments, especially when the similarities between sequences are low. In contrast, current alignment methods that rely on information about secondary structures tend to produce inaccurate alignments for sequences of moderate to high similarity by putting too much weight on common secondary structures. The relationships between accuracy and sequence identity for three alignment tools MXSCARNA, ProbCons, and Stemloc are shown in Figures Project name: ncRNA.org project;;Project home page: 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;. On the web server W and τ correspond to "SCSLENGTH" and "BASEPROBTHRESHHOLD" respectively, and "BASEPAIRSCORECONST" is a parameter of McCaskill-MEA [α in equation 4 in [The source code of MXSCARNA and its web server, the dataset and its references are available at kill-MEA  used forion 4 in ).O(N3L3) in time and O(N2L2) 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 large-scale analyses. MXSCARNA aligns even 5000-base 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 [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 state-of-art 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 web site .YT and KA developed the algorithm, and together they wrote the manuscript with the help of TK. YT implemented the algorithm into the software (MXSCARNA) and executed all of the computational experiments. HK contributed to the design of the new score function and closely collaborated in the computational experiments. TK helped to design the computational experiments and to write the manuscript. With the help of YT, KA organized the development of the web server. All the authors have read and approved the final version of the manuscript.


The majority of relations between proteins can be represented as a conventional sequential alignment. Nevertheless, unusual non-sequential alignments with different connectivity of the aligned fragments in compared proteins have been reported by many researchers. It is interesting to understand those non-sequential alignments; are they unique, sporadic cases or they occur frequently; do they belong to a few specific folds or spread among many different folds, as a common feature of protein structure. We present here a comprehensive large-scale study of non-sequential alignments between available protein structures in Protein Data Bank.The study has been conducted on a non-redundant set of 8,865 protein structures aligned with the aid of the TOPOFIT method. It has been estimated that between 17.4% and 35.2% of all alignments are non-sequential depending on variations in the parameters. Analysis of the data revealed that non-sequential relations between proteins do occur systematically and in large quantities. Various sizes and numbers of non-sequential fragments have been observed with all possible complexities of fragment rearrangements found for alignments consisting of up to 12 fragments. It has been found that non-sequential alignments are not limited to proteins of any particular fold and are present in more than two hundred of them. Moreover, many of them are found between proteins with different fold assignments. It has been shown that protein structure symmetry does not explain non-sequential alignments. Therefore, compelling evidences have been provided that non-sequential alignments between proteins are systematic and widespread across the protein universe.The phenomenon of the widespread occurrence of non-sequential alignments between proteins might represent a missing rule of protein structure organization. More detailed study of this phenomenon will enhance our understanding of protein stability, folding, and evolution. Protein structure comparison is a fundamental approach in many areas of biomedical studies. Its applications range from protein classification and establishing evolutionary relationship between proteins to functional prediction, molecular modeling and protein engineering. While structure comparison can be done in a number of ways, protein structure alignment is one of the major techniques used, populated today with more than 40 methods, the most complete list of which can be found at Wikipedia . These mThe key representation of such sequential alignment was introduced as a matrix approach by Needleman and Wunsch , which sUnderstanding more about these types of alignments is interesting; are they unique, sporadic cases; do they occur frequently; do they belong to a few specific folds or spread among many different folds as a common feature of protein structure. Such a large-scale study is also important for the theoretical understanding of protein organization, the evolution of proteins, and using non-sequential approach has a practical application as a designing tool in protein engineering.β-hairpin flip [Many researches have reported cases of non-sequential alignments such as circular permutations, domain or region swaps -15, and pin flip ,10. The pin flip ,17. A supin flip  states tpin flip . Many napin flip -30; thusThe appearance of similar domains/regions in different orders in sequence as a domain/region swap have been analyzed by Fliess and coworkers . Their sα-atoms in protein structures and does not assume any sequential order of residues in an alignment. Its distinctive feature is that the method does not balance between lower RMSD and a higher number of aligned positions (Ne) but rather identifies the largest group of residues which have the same neighbors in the same locations common in both compared structures, defined mathematically as a topological invariant and detected by saturation point (topomax point) in the spatial tessellation graph. Such an objective methodology provides unambiguous identification and separation of the structurally invariant parts from the variable parts by identifying a precise border between the two. Unlike all other methods , composing alignments of fragments or secondary structure elements, TOPOFIT extends an alignment pair by pair of residues; thus, is not biased by fragment choice or secondary structure element definition. The method is also computationally efficient, so that all proteins in the PDB (as of July 2005) have already been calculated, grouped into clusters and stored in the TOPOFIT-DB database [Since then several methods for protein structure alignment have been developed which can produce non-sequential alignments ,33-38 indatabase . We haveZ-score, i.e. Z-score > 3. From the experience of using T-DB we should mention that the range of Z-score values from 3 to 5 is the "twilight zone" where together with structurally significant alignments there are also trivial cases containing just one or two secondary structure elements; while alignments at Z-score > 5 typically represent high structural similarity between proteins. But to ensure the validity of this study we used an even tighter criteria: only the alignments with very high structural similarity, Z-score > 7, have been collected, resulting in total of 82,263 structurally similar protein pairs. These alignments are referred to as dataset D1. The alignments collected in the dataset D1 are considerably large in size  and represent high structural match (RMSD < 2 Å) as shown in Figure A comprehensive large-scale analysis of 8,865 non-redundant representatives from each protein cluster in TOPOFIT-DB  has beenZ-score > 7 have been used, resulting in total of 4,648 alignments. The distributions of their alignment sizes and RMSD are similar to the ones for dataset D1. These alignments will be referred to below as dataset D2.Another dataset has been collected by compiling alignments between protein families as defined by SCOP   alignments have been found in large quantities in structurally similar proteins. In other words, there are many alignments between highly structurally similar proteins for which the alignment matrix is not diagonal. The overall proportion of non-sequential alignments was estimated to be as high as 35.2%, but not lower than 17.4% when tightened thresholds have been applied  and C2-domain of synaptotagmin I (PDB-code 1rsy) is shown in Figure Rattus norvegicus). The structures are aligned at Ne = 108 and RMSD = 1.2 Å, where Ne is number of equivalent residues in alignment and RMSD is root mean square deviation between Cα-atoms of the equivalent residues; and the alignment consist of two parallel layers of 4 β-strands. In synaptotagmin one of the β-strands is located at the N-terminal end, while in phospholipase, its structural equivalent is at the C-terminal end. This β-strand is the non-sequential part of the alignment and can be seen on the alignment plot as a small fragment (in green) parallel to the long sequential alignment  in the protein sequence. An example of a circular permutation alignment for posphoinositide-specific phospholipase C delta  and ADP-dependent glucokinase from Thermococcus litoralis (PDB-code 1gc5:A) are aligned at Ne = 234 residues and RMSD of 1.7 Å. In this example, two structurally equivalent regions: 1) α-helix and 2) α-helix and β-strand are located one after another but in a different order in the sequences of the compared proteins. Most of the alignment is sequential, namely, one can produce a long sequential alignment out of the aligned residues with only a small part of it being non-sequential, either magenta or orange on the picture. It is evident that if those parts were swapped in any of the sequences then one would get a perfect sequential alignment. Based on this observation, we will call such alignments "swaps". Interestingly, the functionality of these proteins is similar and involves ATP/ADP binding. Moreover, the binding site residues are composed from the parts, which are non-sequential.Similar to the circular permutations there are also alignments with just one structurally equivalent part rearranged in the sequence, but not necessarily from N- to C-terminal. An example has already been shown in Figure Mycobacterium tuberculosis (PDB-code 1i9g:A) and zeta-crystallin from Homo sapiens (PDB-code 1yb5:A). These two structures are very similar (RMSD is 1.7 Å) with the non-sequential region found at the place where antiparallel β-strand of methyltransferase is aligned to the parallel β-strand of zeta-crystallin. There is no permutation of fragment order in these proteins; most of the alignment is sequential while the reverse part, just 10 residues, is small but noticeable. To separate such cases  from the previous alignments we will call the aligned fragments with the same direction of the polypeptide chain as the 'forward' alignment and those with the opposite direction as the 'reverse'.Another type of simple non-sequential alignment is similar to the above examples, but different in the direction of the polypeptide chain. Such alignment is observed when all the structurally aligned fragments have the same order in the sequences, but the direction of the chains in one fragment is opposite, i.e. in one protein the residues in this fragment go from N- to C-terminal, while in the other protein they go from C- to N-terminal. An example of such alignment is shown in Figure Escherichia coli (PDB-code 1kvu) andcatechol o-methylstransferase from Rattus norvegicus (PDB-code 1vid) has four non-sequential fragments, one of which is reverse. The two proteins share a large common structural part, consisting of 137 residues superimposed at RMSD of 1.7 Å. The major part of it is the long sequential alignment, while the non-sequential fragments are three secondary structural elements (α-helix and two β-strands) and an irregular fragment of four residues. Even though the number of residues in the non-sequential fragments (24 residues) is not that large, the permutation of fragments in the sequences of protein is complex, which is shown on the schematic diagram  and molybdenum cofactor biosynthetic enzyme from Escherichia coli (PDB-code 1di6:A). Both proteins belong to the α/β class, but to different folds: THDP-fold and molybdenum cofactor biosynthetic enzymes fold respectively. The core of the domains consists of five β-strands surrounded by six α-helices. In dehydrogenase all strands are parallel while in biosynthetic enzyme one of the strands (namely β5) is antiparallel. The structures are aligned with Ne = 95 residues and RMSD of 1.6 Å. The structural alignment consists of six fragments , while the others are single secondary structure elements: α-helixes or β-strands. Four parallel β-strands are well aligned, but their orders in polypeptide chain are completely different . Interestingly, the sizes of the aligned β-strands are almost the same, while the sizes of the α-helices are different, e.g. helix α6 in the dehydrogenase has an extra turn compared to the corresponding helix α2 in the biosynthetic enzyme. The longest possible sequential alignment is just 25 residues long, which is less than one third of the entire structural alignment.In the above examples there is a common feature: one can clearly identify a long sequential segment in an alignment with the non-sequential part(s) being substantially smaller than the sequential one. While alignments with such a feature occur frequently, nevertheless, we have observed many cases without a dominant sequential part. An example of such case is shown in Figure s Figure , one of α-helix bundle with several helices, where one or many of the helices can be aligned in the opposite direction. In the presented study many cases of the reverse alignments have been found. A reverse complex alignment of adenylate kinase from Methanococcus thermolithotrophicus(PDB-code 1ki9:A) and glucose/galactose-binding protein from Salmonella typhimurium (PDB-code 1gca) is shown in Figure α-helix, β-strand, β-strand, and α-helix. In both proteins the segments have long insertions: in the adenylate kinase three helices are inserted between the two aligned β-strands, while in the glucose/galactose-binding protein another domain is inserted between the second aligned β-strand and last aligned α-helix. The fourth segment represents an alignment of consecutive α-helix, β-strand, and α-helix. The remaining two segments represent an alignment of single β-strand. This is a remarkable example of how the same structure can be formed by the polypeptide chain going in opposite directions; moreover, the order of the segments forming the structure is different in both sequences.Another interesting type of alignment is a completely reverse alignment. In this type two proteins share significant structural similarity, while their sequences align in the opposite directions in all the aligned fragments. To the best of our knowledge, only one case of the reverse alignments is well-known; the General statistics on all different alignment types is shown in Table Ne < 20). Once, an alternative sequential alignment has been found the protein pair was considered to be sequential. Only those non-sequential alignments without any alternative sequential alignments have been considered as true non-sequential cases and are included in the following analysis.Non-sequential alignments can be trivial if they occur as a result of symmetry or shift in protein structure, but such cases are easily detected: in this case an alternative sequential alignment should exist. It is known that proteins with symmetries and repeats have many alternative alignments, thus, for each protein pair we have evaluated all possible alternative alignments with similar length (ΔMethods) and considering alternative alignments have been summarized in Table We have classified non-sequential alignments between proteins into three classes based on the types of alignment fragments in the alignment: forward , reverse , and mixed (different fragment types). Furthermore, each class has been subdivided into subclasses based on the pattern of fragment permutation: simple (order of fragments is not permuted), circular (cases fitting the definition of circular permutation), swaps (two fragment are swapped but is not a circular permutation), and complex . Statistics on the number of non-sequential cases using different thresholds  then it is either very simple (has no permutations) or very complex (has too many permutations) alignment. Table α, all-β, and mixture of αand β , with the majority of all-αalignments being α-helical bundles.Since all structures in SCOP are split into domains and classified, the D2 dataset is better suited for analysis of alignment distribution among protein folds. All alignments can be clearly separated into three groups by dominant type of secondary structure elements of the aligned residues: all-The following observations have been made using true non-sequential alignments: 17,428 in dataset D1 and 1,130 in dataset D2 -binding domain') being exceptional. The reason for this is the outdated version of SCOP (dataset D2), when compared to TOPOFIT-DB (dataset D1), and ambiguity in assigning SCOP folds to TOPOFIT-DB's centroids, which are not split into domains and can represent multi-domain proteins. Thus, the discrepancies in numbers are explained purely by technical rather than biological or methodological reasons and results obtained using the two datasets are consistent.Escherichia coli (PDB-code 1onr:A) and class I aldolase from Drosophila melanogaster (PDB-code 1fba:A) shown in Figure α/β-units  over 170 residues with RMSD of 3.6 Å  had been eliminated, still non-sequential alignments in symmetrical structures have been found. This points to the fact that a non-sequential alignment in a symmetrical structure is not always a trivial case. Consider as an example, the structure alignment of transaldolase B from .6 Å , we have excluded folds from the analysis where there are at least two proteins with non-sequential alignment. Thus, all potentially symmetrical folds have been excluded resulting in a new dataset (reduced dataset), where all non-sequential alignments occur only between proteins of different folds. It was found that non-sequential cases are found in 7.7% of cases of reduced dataset, which is smaller than 21.2% on the whole data set, but is still very significant. In other words, at least one third of non-sequential alignments are found in non-symmetrical structures.The previously observed results can be briefly summarized: 1) Non-sequential alignments are found in many non-symmetrical folds; 2) Non-sequential alignments are spread more or less evenly across folds, i.e. there is no specific fold(s) preferable for non-sequential alignments; 3) Up to 50% of non-sequential alignments are found for proteins with different folds; 4) The proportion of non-sequential alignments for proteins with different folds is comparable with proportions for proteins with the same fold; 5) At least one third of non-sequential alignments are found in non-symmetrical structures. Thus, the conclusion is that non-sequential alignments do occur in any class and type of protein structures and a protein structure symmetry/shift does not explain non-sequential alignments. In other words, the occurrence of non-sequential alignments is a general feature of protein structure.Methods). This was done to ensure that rank is not overestimated due to the presence of several fragments in one segment. Using this definition, it is easy to see that any alignment with n fragments can have the highest rank of n - 1, because at least one structural element is not rearranged relative to others .Non-sequential alignments can be very simple that only one fragment is non-sequential, whereas, they can be so complex that only one fragment can be put in sequential order in both sequences. In other words, we have observed very simple and complex rearrangements of structurally equivalent elements in proteins. In order to address rearrangement complexity we introduce the term "rank" of an alignment, which is the number of rearrangements of structurally equivalent parts of proteins needed to put them in sequential order in the sequences of both proteins. According to this definition, sequential alignments are represented as a single structural equivalent and thus have rank zero, while circular permutations and cases similar to the one shown in Figure Figure α-β tubulin (1jff:B and 1tub:B). Thus, we can state the absolute majority of proteins with high sequence similarity have only circular permutations cases of non-sequential alignments.It is interesting to understand whether there are any non-sequential cases in highly similar proteins, both in structure and in sequence, i.e. those that have been grouped in TOPOFIT-DB in clusters. Thus, alignments between the structures of each of 8,865 clusters have been collected for a total of 2,509,599 alignments. The analysis reveals that the absolute majority of detected non-sequential cases are circular permutations with few exceptions. Statistically, 31,358 out of 2,509,599 alignments were non-sequential, out of which 95.5%  were circular permutations, 3.5% represented alignment of different conformation of same protein, and the remaining 1% have been accounted for non-sequential alignments in only 7 protein families: fructose-1,6-bisphosphatase (1fpk:A and 1d9q:B), arrestin (1cf1:A and 1ayr:B), annexin (1hm6:A and 1hvg), aspartate/ornithine carbamoyltransferase (2atc:B and 1rac:B), 3-isopropylmalate dehydrogenase (1iso and 1hqs:A), NADH peroxidase (1f3p:A and 1nhs), In the presented study a comprehensive large-scale analysis of non-sequential alignments between all PDB structures (as of July 2005) has been performed. We have found that up to 35.2% of all significant alignments are non-sequential. Consideration of different thresholds and alternative alignments has been made to ensure robust detection of non-sequential cases. These variations in methodology revealed that non-sequential alignments are found in at least 17.4% of cases. Thus, the estimated proportion of non-sequential alignments is in the range of values between 17.4 to 35.2%, which is a significant proportion of structural relations not detected by most of the current methods.It was found that the majority (more than 50%) of the non-sequential alignments fit to the formal definition of circular permutation. It is important to stress here how this number should be understood. Often, proteins aligned in a circular way are assumed to be evolutionary related and this assumption is often encoded into an alignment method to detect such cases. There is no such assumption (of evolutionary origin) in the methodology used in this study and thus, a large number of circular alignments alone does not necessarily mean an evolutionary relationship between the compared proteins. The same way, the origin of more complex non-sequential alignments is not clear.Besides circular permutations, non-sequential alignments with a large variety of alignment patterns have been found. All possible complexities of rearrangements, various sizes and numbers of non-sequential fragments have been observed. It has been found that non-sequential alignments are not limited to proteins of any particular fold and are present in more than two hundred of different folds. Moreover, up to 50% of non-sequential alignments are found for proteins with a different fold assignment. While many of the non-sequential alignments were found for proteins with symmetrical structures, it has been shown that protein structure symmetry does not explain non-sequential alignments. Therefore, compelling evidence of different forms has been provided, confirming that non-sequential alignments between proteins are diverse and widespread across the protein universe.α-helix bundle with several helices, where one or many of the helices can be aligned in the opposite direction. The α-helix bundles have been studied experimentally and successful attempts on redesigning the four-helix bundle to have inverted helices have been reported [α-helix bundle can be theoretically extended to other protein folds with the cases of reverse alignments observed in this study. Thus, the existence of the reverse alignments for proteins of other folds can serve as the basis for new approaches in protein engineering to redesign proteins.Many cases of reverse alignments in various folds have been found in this study. To the best of our knowledge, only one case of reverse alignment is well known, the reported ,46. SuchResults and Figure The discovery of the existence of all theoretically possible complexities of fragment rearrangement in proteins is intriguing  in our understanding of protein structure organization. Finding such a rule can be a challenge for the future research, but, apparently, the existence of the non-sequential alignments is not rare effect but rather a systematic feature of all proteins. More detailed studies of these alignments will bring new insight in our understanding of protein evolution, protein stability and protein folding and functionality. As a first step toward understanding the non-sequential alignments, a testable hypothesis has been suggested, stating that the three-dimensional shape of protein structure does not depend on the order of protein fragments in the polypeptide chain.Z-scores to all other proteins in the cluster. Comparison of the centroids and proteins inside each cluster resulted in 39,276,862 structural alignments stored in the database. For this study, only centroid-centroid alignments from TOPOFIT-DB with Z-score > 7 have been used, leading to a total of 82,263 alignments.For this study the structural relations between the representative proteins from the TOPOFIT-DB  databaseZ-score > 7 have been used, leading to a total of 4,648 alignments.A second data set has been collected by comparing alignments between protein families as defined by SCOP (release 1.69). For each family the first structure, in the list of proteins assigned to the family, has been used as a representative, resulting in 2,845 representatives. 4,045,590 structural alignments have been produce and stored in TOPOFIT_DB database  by compaz, for a pair of segments x and y, as a segment located in between the two segments in either of the sequences  part of a structural alignment :1) number of segments interfering with it ;2) number of aligned residues in the interfering segments ;3) cumulative number of residues in the tested pair of segments (larger preference).Fmin.The best pair is found by comparing those values, where each next value is used only if the preceding values were equal. Segments in the best pair are combined only if the pair has no interfering segments. Otherwise, the interfering segment having a minimal number of aligned residues is removed from the structural alignment. So, on each step, the number of segments decreases by one. Steps are repeated until all segments are combined into one or the segment to remove has length more or equal then value of Fmin is not like a conventional threshold because short fragments are not simply removed from the alignment, but first are tested for the possibility of being combined with longer fragments and only upon failure are removed.The procedure considers forward and reverse segments simultaneously, however only segments of the same type (both are either forward or reverse) are being combined. Special care is taken with segments of length one; they are evaluated in pairs with both forward and reverse segments. Here it is important to stress that the minimal fragment parameter Fmin values have been calculated in order to evaluate the discrimination of noise caused by small size fragments , but the spike in the distribution at lower values has disappeared. Thus, it is evident that the noise is mostly represented by short fragments of length 1 and 2 residues. The distributions for Fmin values from 3 to 6 do not differ much, while larger Fmin values lead to significant disruptions in the shape of distributions in the region from 75 to 110. Consequently, non-sequential alignments mostly consist of aligned segments of 6 or more aligned residues. Therefore, the best signal-to-noise discrimination can be archived when the value of the Fmin parameter equals 3–6 residues. This is where the majority of the noise is filtered out while the signal  is not cut. In the overall analysis presented here, the value Fmin = 4 has been used, while additionally a tightened criteria, Fmin = 6, has been applied for cross checking.The major change in distribution occurs at Fmin parameter, detection of non-sequential cases is robust.Applying tightened criteria resulted in an 11 % decrease  in the number of non-sequential cases detected. Thus, we concluded that at selected values of the . A simple bubble sort algorithm has been used to calculate the number of permutations needed to sort the numbers in ascending order. For the alignment shown in Figure Ne of reverse segments is higher than the cumulative Ne of forward segments.The rank of an alignment is defined as the number of rearrangements of structurally equivalent parts of proteins needed to put them in sequential order in the sequences of both proteins. Technically, the rank was calculated as the number of segment permutations. In order to calculate the number of permutations in an alignment, the corresponding alignment segments have been ordered by sequence order in the first aligned protein and numbered incrementally starting from one. Then, the segments have been ordered by sequence order in the second aligned protein. In case the considered alignment is non-sequential, renumbering will permute the order of the numbers assigned. For example, the order of numbers for the alignment shown in Figure ,3,2,4. AThe non-sequential alignments were visualized and analyzed in integrated software package, Friend  with theAA did the data collection, calculations, and analysis and prepared the manuscript. VAI did design of the project, data analysis and prepared the manuscript. All authors have read and approved the final manuscript.


There is currently no way to verify the quality of a multiple sequence alignment that is independent of the assumptions used to build it. Sequence alignments are typically evaluated by a number of established criteria: sequence conservation, the number of aligned residues, the frequency of gaps, and the probable correct gap placement. Covariation analysis is used to find putatively important residue pairs in a sequence alignment. Different alignments of the same protein family give different results demonstrating that covariation depends on the quality of the sequence alignment. We thus hypothesized that current criteria are insufficient to build alignments for use with covariation analyses.We show that current criteria are insufficient to build alignments for use with covariation analyses as systematic sequence alignment errors are present even in hand-curated structure-based alignment datasets like those from the Conserved Domain Database. We show that current non-parametric covariation statistics are sensitive to sequence misalignments and that this sensitivity can be used to identify systematic alignment errors. We demonstrate that removing alignment errors due to 1) improper structure alignment, 2) the presence of paralogous sequences, and 3) partial or otherwise erroneous sequences, improves contact prediction by covariation analysis. Finally we describe two non-parametric covariation statistics that are less sensitive to sequence alignment errors than those described previously in the literature.Protein alignments with errors lead to false positive and false negative conclusions . Covariation analysis can provide a verification step, independent of traditional criteria, to identify systematic misalignments in protein alignments. Two non-parametric statistics are shown to be somewhat insensitive to misalignment errors, providing increased confidence in contact prediction when analyzing alignments with erroneous regions because of an emphasis on they emphasize pairwise covariation over group covariation. Two or more variable positions in a protein may coadapt to conserve interactions needed for proper structure or function de novo protein structure prediction and structure-function analysis Covariation statistics are often used to aid in residue contact identification, MIp and its transform, Zp, which was much more sensitive and specific than other previous non-parametric methods.Atchley et al. The goal of multiple sequence alignment is to place residues from each sequence in the protein family at homologous positions in the final sequence alignment. The multiple sequence alignment for a given protein family is usually different in the various standard collections of protein families and the disagreement between protein datasets demonstrates that all multiple sequence alignment methods produce errors. Furthermore, the placement of a gap in the protein family is an explicit acknowledgement that no homologous position exists for one or more members of the protein family. The difficulty in generating a sequence alignment is highlighted by the observation that even structure-based alignment methods disagree We observed that the same protein family often gave different numbers of covarying positions when alignments were from different sources even if the alignments contained comparable numbers of sequences. We also found that alignments generated without structural information identified fewer pairs in contact in the folded protein compared to alignments generated with structural information. These observations suggested that the quality of the alignment made a large contribution to the background covariation signal. This observation is supported by Wong et al. Zp can be used to identify systematic misalignments in protein families. Furthermore, we show that new statistics Zpx are relatively insensitive to systematic alignment errors, and are especially effective at identifying pairwise covarying residues. Significantly, these two corrections identify substantially different populations of covarying pairs with similar accuracy.Here we examine the effect of systematic misalignment on covariation scores. We demonstrate that alignment errors lead to incorrect conclusions about covariation and conservation. We show that Many commonly-used multiple sequence alignment programs use the progressive sequence alignment strategy in which the alignment and the locations of insertions and deletions are permanently fixed in the growing alignment Zp signal increased if both positions in a pair were in the misaligned segment (red) and decreased if one of the positions in the pair was in the misaligned segment and the other was outside the segment (green) when compared with the pairs unaffected by the misalignment (blue).The impact of systematic errors on the estimation of covariation was tested in an alignment of triosephosphate isomerase by randomly shifting a fraction of the sequences in one aligned segment left or right by 1 residue. We chose to shift between 0 and 30% of the sequences within the selected segment positions—a range chosen because the commonly-used multiple sequence alignment programs have between 70% and 80% accuracy Zp values were not distributed evenly among all positions in the alignment  Contacting pairs of positions in the properly aligned regions tend to be assigned Zp scores that are much higher than the mean, but often not large enough to stand out against the misaligned region. However, there is often a large difference between the score of a contacting pair and the next-highest score. 2) Noncontacting pairs tend to have small differences between consecutive scores. 3) High-scoring pairs due to misalignment tend to cluster together. Thus we introduce Zp measure  Zp values in 6-residue windows; a number were identified that had 5 or more 6-residue windows with mean local Zp scores Zp as shown in Zp scores at the conserved active site.The above analysis on modeled data suggests that if systematically misaligned protein families exist in popular datasets, they might have segments that display high local  scores  . cd00300 scores  . One popZp is sensitive to systematic misalignment errors, the contact map produced from the original cd00300 alignment contains predictions centered around the sites of misalignment and contains no useful structural information as shown in Zp:original. In contrast, Zpx produce more informative contact maps than Zp even with systematically misaligned data; however, the contact maps are largely composed of local contacts covering the secondary structure of the protein . The overlap in the 1411 total pairs is shown in Zpx, Zp identified 75%, 64% and 54% of the total pairs with 15%, 14% and 10% of the pairs being unique to each method. The pairs most likely to be in contact were pairs identified by both Zpx. These 685 pairs composed 49% of the total pairs identified with 626 in contact (91% contacting). We conclude that pairs identified by both Zpx were more likely to be in contact than if either was used by itself.We wanted to know if the three methods were identifying the same set or a different set of contacting pairs. We identified alignments in the CDD where lignment . Zp idenZpx were so effective at identifying contacting pairs. We examined this by modeling group coevolution with the simple model of in silico evolution described in the We were interested why Zp, residues that coevolve with an intermediate group size attain mean scores greater than 6, which is close to the mean Zpx show markedly lower mean scores for the intermediate sized groups of coevolving positions than for pairwise coevolving positions. The effect is similar at lower coevolution probabilities for all three methods, although it is non-linear for Zpx. We conclude that the ability of Zpx to emphasize the effect of pairwise covariation at the expense of group covariation explains in part why these two methods identify contacting pairs with greater sensitivity and specificity than other non-parametric methods.not in contact must be caused by functional constraints It is assumed that the covariation signal derived from structural and functional constraints is superimposed on the phylogenetic and stochastic signal Local covariation increases with misalignment proportionally to the amount of conservation at a position and inversely proportional to the amount of entropy. Covariation can be understood as proportionally high positional entropy relative to low joint entropy. This is related to the underlying information-theoretic values outlined in Zp when compared to other statistics outlined in this manuscript. Zpx statistics do not identify mistalignments because they filter out the misalignment covariation signal. Zp works because it transforms the covariation values based on the assumption that the background covariation is due to shared phylogeny and relative entropy — an assumption that is explicitly violated when misalignments are introduced.It is worth noting that the ability to detect misalignments is unique to Zp, Zpx were used to identify new structurally and functionally important pairs of residues. These successes demonstrate the effectiveness of increased local covariation and the new covariation statistics.The increased local covariation methods outlined in this paper have already been critical to the completion of two publications. In one Zp identified two regions of phosphoglycerate kinase which contained subclusters of residues found in completely different environments We found that flaws in the alignments themselves often result in positions having high covariation scores because of systematic misalignments. Since systematic misalignments involve several positions that are close in sequence (eg. cd00300), this could explain some of the group covarying positions that have been seen by many investigators, eg. Zp can identify misaligned regions. We found that markedly elevated local Zp values were the hallmark of misaligned regions and suggest that the investigator proceeds with caution during the analysis of positions showing this pattern of covariation. If an investigator draws conclusions from an alignment which has not been examined with increased local covariation, there is an increased risk of drawing erroneous conclusions from the alignment.The logic of building an alignment is partially circular: alignments are built in part by maximizing sequence conservation, but then are used to find conserved positions which are, in turn, identified as important. While structure-based methods are often used as the benchmark and standard for protein alignments Zpx and Zpx and Finally, we demonstrated that Zp to systematic alignment errors can be exploited to identify regions of potential misalignment. Covariation provides an independent method for verifying the quality of an alignment and should therefore be especially useful for verifying alignments built on sequence conservation alone. The cd00300 alignment showed that misalignments occur in structure-based alignment datasets; importantly, cd00300 showed that misalignments occur in functionally-important conserved regions. We recommend investigating any incidents of increased local Zp Click here for additional data file.Figure S1Zp values in cd00300, the lactate dehydrogenase superfamily. Panel A shows a histogram of the mean Zp value between all pairs of ungapped positions in a 6 residue window. Red and blue bars are positions in the alignment that are adjacent to indels. The mean entropy of the residues multiplied by −1 in the window is plotted in green below. Panel B shows the same plot from an alignment with the malate dehydrogenase sequences and partial sequences Click here for additional data file.Figure S2Positions containing gaps violate the assumption of positional homology. Strong structural conservation flanks an insertion of two residues in a surface loop. The gap region is highlighted in grey and is two residues long for the shorter sequences and four residues long for the longer sequences. Highlighted in yellow are two alternate hypotheses of the residues which are homologous to the two residues in the shorter sequences. Structurally, it is impossible to determine which two residues are homologous to the shorter gap sequences. Choosing two of the four residues in the insertion region as homologous to the shorter sequence residues will likely introduce error into the alignment.(0.13 MB PDF)Click here for additional data file.Table S1Zp score greater than or equal to 2.5 for all pairs of positions over a residue window of width 6.Alignments containing probable systematic misalignments. Table of alignments in CDD which have 5 or more peaks of mean (0.04 MB PDF)Click here for additional data file.Table S2Sequences removed from cd00300 because of poor alignment to structure alignment. Not all possibly erroneous sequences were removed in order to meet the cutoff for minimum number of sequences for covariance methods.(0.08 MB PDF)Click here for additional data file.Table S3MIp, and the analysis here suggests that cutoff is appropriate for ∼80% accuracy. Only pairs 10 or more positions apart in sequence are included to prevent proximity in sequence from biasing results.Scoring cutoffs for arbitrary accuracy in CDD alignments. CDD alignments were examined and those that contained ≥150 sequences, ≥50 nongapped positions and where each method made at least one true prediction were identified at an accuracy of 80% or higher. There were 100 such protein families and they are identified in (0.02 MB PDF)Click here for additional data file.Table S4Venn Diagram Alignments. Alignments curated according to (0.09 MB PDF)Click here for additional data file.


Conservation and variation scores are used when evaluating sites in a multiple sequence alignment, in order to identify residues critical for structure or function. A variety of scores are available today but it is not clear how different scores relate to each other.We applied 25 conservation and variation scores to alignments from the Catalytic Site Atlas (CSA). We calculated distances among scores based on correlation coefficients, and constructed a dendrogram of the scores by average linking cluster analysis. The cluster analysis showed that most scores fall into one of two groups--substitution matrix based group and frequency based group respectively. We also evaluated the scores' performance in predicting catalytic sites and found that frequency based scores generally perform best.Conservation and variation scores can be classified into mainly two large groups. When using a score to predict catalytic sites, frequency based scores that also consider a background distribution are most successful. A protein's amino acid sequence is considered to carry information about structure and function of the protein. However, it is still difficult to predict residues important for structure and function from a single sequence. One effective way of extracting such information is the comparison of homologous sequences, since proteins sharing a common ancestry often are similar in structure and function. Therefore, the residues critical for function or structure have been conserved in homologous proteins during the course of molecular evolution. In other words, we can predict the residues or alignment sites under strong constraints by comparing amino acid sequences of homologous proteins and identifying conserved alignment sites. Not only conservation, but also variability sometimes provides important information about proteins. As an example, consider a viral peptide antigen, which is a target for the immune system of the hosts. The amino acid residue at a site recognized by the immune system of hosts would change rapidly to escape an attack by the immune system. Therefore, the antigenicity-determining sites can be predicted by evaluating the variability of alignment sites.A quantitative measure for conservation or variability of alignment sites is useful for identifying sites under constraints, and various methods to quantitatively evaluate the conservation or variability of alignment sites have been developed. The methods are hereafter referred to as scoring methods or simply as scores. Such scores have been reviewed and classified based on calculation method by Valdar , althougWe present here an empirical comparison of scoring methods. We have collected programs for scoring methods--some were implemented by ourselves and others were provided by the developers. We apply the methods to a subset of the Catalytic Site Atlas , which iOne simple way of evaluating the similarity between a pair of scores is to calculate a correlation coefficient between the two scores over alignment sites in a whole dataset. However, if one score is highly affected by the number of sequences in one alignment, this simple correlation does not reflect actual similarity. We therefore first examine the dependency of each score on alignments size. Strictly speaking, we should consider effective alignment size by taking sequence weights into account. We however take a simpler way of using the number of sequences as measure of alignment size since some methods do not use sequence weights and are therefore considered to depend on alignment size directly.N and mean score is shown in Table N. This can however not explain the positive correlations. The positive correlation of Lockless99 is explained by the fact that it calculates binomial probabilities for the number of occurences of amino acids. The probabilities for k nbecome very small for increasing values of N, giving a higher conservation score .The correlations between alignment size N - 1 (since it is a summation of N - 1 terms) which did not abolish the dependency on alignment size (data not shown). The conclusion will have to be that a comparison of scores in different alignments should not be done, and we therefore adopt the procedure of calculating correlations only within alignments as described in Methods for the cluster analysis.It is not straightforward to exclude the dependencies found. For example, we divided the real-valued evolutionary trace Mihalek04 by acc). In cases where only two scoring methods are joined, we refer to it as simply the correlation coefficient (cc). Each node is labeled with the result from a bootstrap analysis, where the number is to be interpreted as the percentage of bootstrap samples that have an identical node. Generally, the dendrogram was found to be very stable by the bootstrap procedure, as can be seen by the fact that many nodes have been labeled with 100. We define two major groups (A and B) which are illustrated by squares in the dendrogram. They are clustered with bootstrap probabilities of 100% and 87% respectively.The result of the cluster analysis using average linking is shown in the dendrogram in Figure acc = 0.94 with a bootstrap probability of 100%. The internal topology of cluster A is also very stable, as can be seen on the bootstrap probabilities on the nodes internal to this cluster. This cluster holds all the scores described above as "substitution matrix scores" (see Methods), except for Mihalek07.The top node in cluster A is labeled as A0 in Figure acc ≥ 0.99. The scoring methods Karlin96 and Sander91sp are very similar already in their formulations, but we can also conclude that Pei01sp(w) is very similar in practice even though the score formulation is quite different. Hence, at least for this dataset, the weighting of Pei01sp does not make much difference. We may also note that even though Sander91sp uses sequence weights for each pair, this does not make any practical difference compared to Karlin96 and Pei01sp that do not use sequence weights at all. All these scores also use the same matrix K Min their calculations, which may explain their similarities. The other scores in cluster A are Valdar01, Thompson97 and Liu08w. Valdar01 is by its definition quite similar to Karlin96 and Sander91sp, using different sequence weighting and a different scoring matrix. Thompson97 measures the deviation from a hypothetical "consensus residue". It measures this deviation using a scoring matrix just as the other scores in cluster A, which is seen to give Thompson97 a very similar behaviour. Liu08w compares each occuring amino acid to the most common amino acid at the site, also using a similar scoring matrix.The highest correlations in cluster A are found between Karlin96, Pei01sp(w) and Sander91sp, which are all clustered at acc = 0.90 in the dendrogram in Figure cc = 0.98) between Mihalek04 and Zhang08, and they do indeed share a summation over the same phylogenetic tree. Zhang08 uses von Neumann entropy, which considers the amino acid similarities that the Shannon entropy used by Mihalek04 does not. The summation over the same phylogenetic tree seems to erase most differences between these entropies, however. We may compare this pair to their phylogeny-free counterparts Shannonw and Caffrey04w (see Subgroup B2), which show a slightly larger difference (cc = 0.96).A variety of scores are classified into cluster B, which is formed at node B0 located at Mayrose04 is the most distant relative in cluster B, even though its closest relatives are the other phylogeny-based scores. Mayrose04 is a computationally different method, but its score is also conceptually different. It uses mutation probabilities from the JTT matrix , and calcc = 0.97) with Lockless99 while correlating with cc = 0.98 to Shannon. Hence, Pei01var(w) is not as unrelated to the relative scores Lockless99, Wang06w and Capra07w as it may seem by the dendrogram. Wu70 correlates with cc = 0.99 to both Shannon and Shannonw, and we may conclude that the formulation of Wu70 is in practice very similar to an entropy. Caffrey04w is also clustered together with these "non-relative" scores, though at some distance. Wang06w and Capra07w are clustered together at cc = 0.99, which is not surprising since they are very similar by their definitions. Wang06w uses relative entropy while Capra07w uses the Jensen-Shannon divergence that has relative entropy in its definition. As mentioned above, Lockless99 is clustered together with these scores which is expected since Lockless99 is a score that also measures deviation from a background.Subgroup B2 contains scores that do not consider phylogeny in their scoring. This subgroup is vaguely divided into scores that do or do not consider background distributions, where the scores that do consider a background are located to the right of node B2. The exception to this rule is Pei01var and Pei01varw. By inspecting the correlation matrix, we could however see that Pei01var had a quite high correlation  may be interpreted as a probability that the given amino acid α will mutate to amino acid β (or be conserved if α = β). A feature of this score, which may be what makes it different from most other scores, is that rare mutations show a large relative entropy (hence a large conservation score). Mihalek et al.  as shown in Table Substitution matrix scores do not consider residues by themselves, but rather consider the mutations that have occured. Sander and Schneider  introducet al. [k. The vectors are defined in the space of amino acids using a substitution matrix. A mean vector is then calculated for the site and the final score is the average euclidean distance to the mean vector. Mihalek et al. [kn to estimate the probability kp. It then assumes a background distribution created by a substitution matrix normalized so that each row and column approximately sum to one (it is not possible to do exactly and keep a symmetric matrix). It is a score that rewards mutations (or lack of mutations) that deviate from this background. Liu and Guo [α0) in each site, and sums over comparisons of each amino acid with α0.A vectorial view was proposed by Thompson et al.  in whichk et al.  develope and Guo  introducet al. [Mihalek et al.  developeet al. . They doet al. [et al. [Zhang et al.  later in [et al.  develope [et al. , and is  [et al.  which weSeveral scoring methods are not included in this study. For example, cumulative relative entropy  and quanInteger-valued evolutionary trace and zoom methods are associated with real-valued evolutionary trace . IntegerWe do not include 3 D cluster analysis , which cet al. [Valdar  suggesteet al.  and a gaWe evaluate scores on a subset of the Catalytic Site Atlas (CSA) , compileet al. [kp.The purpose of a conservation or variation score is generally to compare sites within an alignment, and we analyze specifically this property of the scoring methods. In order to do this, we negate scores that give high scores for high variability, so that all scores can be viewed as conservation scores. Further, when comparing sites within an alignment, the scores Sander91, Shenkin91 and Gerstein95 give equal comparisons since they are all variations of a Shannon entropy. We therefore evaluate them together as a score which we name Shannon . We also evaluate the score Shannonw as suggested by Pei et al.  which usWe also show that a comparison of scoring methods other than within alignments is difficult, by evaluating how the scores depend on alignment size . We do this by, for each scoring method, calculating the Pearson correlation between alignment size and mean score on the alignment.Ci) . Hierarchical clustering is then done on the distance matrix 1 denotes a unit matrix, i.e. a matrix consisting only of ones. Since we are interested in how the scores compare sites, i.e. the ranking of sites, we use the Spearman's rank correlation which also solves possible problems with outliers and nonlinear correlations.We perform hierarchical cluster analysis on the scoring methods, in order to see how scoring methods relate to each other. For this analysis we calculate a distance between every possible pair of scoring methods. We do this by calculating a correlation matrix j is obtained by randomly picking m alignments from the original dataset  and calculating a distance matrix At each stage of the hierarchical clustering, the two closest clusters (created at earlier stages) or single units are merged into a new cluster. Above we defined the distance between units (the scoring methods) but we also have to define the distance betweeen clusters, i.e. we have to define a clustering method. We choose to mainly present average linking as clustering method, which means that clusters are joined based on the average distance between all inter-cluster pairs. Other possible methods include single linking and complete linking. In single linking the distance between two clusters is equal to the distance between the closest inter-cluster pair, while in complete linking it is equal to the distance between the most distant inter-cluster pair. Both these methods are vulnerable to outliers, since they merge clusters based only on local measures. Therefore, we mainly discuss the clustering of scoring methods based on the average linking method. For comparison, we however also perform hierarchical clustering using single and complete linking. We also perform a bootstrap procedure to determine the reliability of each node in the resulting dendrogram. One bootstrap sample We evaluate the performances of scoring methods in predicting catalytic sites in the alignments. We do this by calculating the receiver operator characteristic (ROC) curve for each score and alignment. We subsequently calculate the area under each ROC curve (AUC), and calculate an average AUC score on all alignments for each score. We also evaluate how performance depends on the size of alignment, by setting upper bounds on alignment size and evaluating AUC scores only for alignments with a size smaller than that.HT conceived the study. FJ implemented methods and performed the analysis. All authors read and approved the final manuscript.Single linking hierarchical clustering. Dendrogram created using single linking.Click here for fileComplete linking hierarchical clustering. Dendrogram created using complete linking.Click here for file


Large nucleotide sequence datasets are becoming increasingly common objects of comparison. Complete bacterial genomes are reported almost everyday. This creates challenges for developing new multiple sequence alignment methods. Conventional multiple alignment methods are based on pairwise alignment and/or progressive alignment techniques. These approaches have performance problems when the number of sequences is large and when dealing with genome scale sequences.We present a new method of multiple sequence alignment, called MISHIMA (Method for Inferring Sequence History In terms of Multiple Alignment), that does not depend on pairwise sequence comparison. A new algorithm is used to quickly find rare oligonucleotide sequences shared by all sequences. Divide and conquer approach is then applied to break the sequences into fragments that can be aligned independently by an external alignment program. These partial alignments are assembled together to form a complete alignment of the original sequences.Helicobacter pylori (about 1.7 Mb each) were successfully aligned in about 6 hours using a single PC.MISHIMA provides improved performance compared to the commonly used multiple alignment methods. As an example, six complete genome sequences of bacteria species  Alignment of vast number of nucleotide sequences is one of the central problems in current genomic studies. Sequence alignment is used in many kinds of biological studies, including phylogenetic analysis, identification of conserved domains, prediction of protein structure and database searches.Alignment of multiple sequences remains a considerable challenge in terms of computation time required to complete an alignment of a reasonably large sequence dataset. Even pairwise sequence alignment becomes hard when the sequences are very long. Most alignment algorithms use some sorts of heuristics to reduce the computation time. Every alignment method was designed with some expectations on the size of data to be analyzed and what sort of computer hardware is likely to be used. The progress in alignment techniques during the last 30 years would not be possible without the parallel constant improvement in computer technology. The alignment methods being developed these days work better than those of 20 ago partly just because they are designed to run on faster processors and use more memory.The most simple and widely used such heuristic is the method of progressive alignment , which wAn alternative approach to solve the problem of multiple sequence alignment is the iterative procedure of refining the global alignment, for example in PRRP program . Also a Another direction focuses on increasing the performance of traditional dynamic programming based methods. This includes Divide-and-Conquer techniques, implemented in DCA  and OMA Recently it became popular to locate regions of local conservations before attempting to construct the global alignment. This idea was used for pairwise alignment in MUMmer , ShuffleWhile there is considerable progress in recent multiple alignment research, it still remains a challenging problem to align multiple genomic sequences. Therefore we investigated an non-conventional heuristic approach to multiple sequence analysis, which we present in this work. A prototype of MISHIMA was briefly introduced by Kryukov and Saitou .It is believed that only a certain part of a genome is functional, and most of the genome content is never expressed or used. As a result some parts of the genome remain mostly unchanged during the evolution, while other parts quickly accumulate mutations through neutral evolution . ConservThis idea has already been implemented in other methods, in which homology was first detected by pairwise sequence comparison and the obtained information was then used to build the alignment , an ideal case for this method would be where A*N/4K = N, which means A = 4K. Thus, to have the best results with this method, the length of sequences to be analyzed should be comparable to, or shorter than 4K.Length k is a very important factor affecting the chance for a k-tuple to be useful for alignment purposes. A random sequence of length L is expected to contain L/4This is an intuitive estimation, to give some feeling of relation between the dataset size and k-tuple's k. Of course the real biological sequences, especially those that we are trying to align, are often not completely random, which suggests that longer sequences can be aligned if they contain significant homology. Therefore the capability of MISHIMA to align the real sequences should be higher than this estimate. But non-conserved intergenic regions in a genomic sequences may well be considered as random sequence, and the total size of such regions in a sequence data is a limiting factor for MISHIMA. This shows that the length k is the basic parameter affecting the performance of this method.Choosing the optimal length of a k-tuple is critical for the successful alignment. If k is too small, too many occurrences of each k-tuple will be found. Although to some extent this depends on the length of the sequences, it is difficult to predict whether the particular k is too small or not. Therefore we use all k-tuples with k from 1 to M in this method. For selecting M - the upper limit of k - we suggest to depend on the memory limitation. Most of the steps of the MISHIMA algorithm are performed in linear time, which makes it practical to use the largest M allowed by the amount of available memory.2+...+4M) bytes. This allows us to use M of 12, with the dictionary occupying less than 300 MB of RAM.We ended up using 12 bytes for each k-tuple in a dictionary. The total amount of memory required for dictionary is therefore 12*. Then the matrix of size TxT is constructed. Each cell of the matrix contains the incompatibility distance between two seeds. In the first step all of the selected T seeds are included and the matrix contains TxT distance values. Then the matrix is analyzed to find the sum of all numbers for every row. This sum corresponds to the total amount of incompatibility introduced by one seed. Now the seed which introduces the largest amount of incompatibility is removed from the set. The matrix is recalculated and the procedure iterates until no incompatibility is left unresolved. Finally only compatible seeds remain, which are used as alignment anchors. If all seeds are mutually incompatible with each other, there will be still one anchor left after removing the incompatibility. This anchor is used to divide the sequences into 2 parts, which are aligned separately.The number of anchors found in all our example datasets is included in Additional file After the dictionary step has finished and a set of non-conflicting seeds is selected, the algorithm will have a set of anchors, connecting the sequences. The sequences are then divided and regions between the anchors are aligned independently from each other. After all partial alignments are complete, they are concatenated to construct a final complete alignment.Alignment of the regions between the seeds is performed using an external aligner provided the sequences are short enough. Otherwise MISHIMA is used again (recursively) to divide the sequences into shorter parts. The depth of the recursive operation in MISHIMA can be set with the command line option '-max-depth = x'. Since MISHIMA takes a constant time for each step of finding seeds and dividing the sequences, using a limited depth may improve the performance on some datasets.The overall flow of MISHIMA algorithm is shown in Fig. The performance of MISHIMA was evaluated on several example dataset, detailed in the Results section. We used several popular aligners for comparison: CLUSTAL W, MUSCLE, MAFFT and MLAGAN. The details, including version and parameters we used with these methods, are included in Additional file ij = 100*Mij/L, where Mij is the number of alignment positions where sequences i and j have the same nucleotide (not including gaps), and L is the length of complete multiple alignment (including gaps).For assessing the alignment quality we used the sum-of-pairs alignment score , based oWhile a simulated dataset is necessary for a serious discussion of alignment quality, we believe that using the sum-of-pairs score is sufficient for evaluating MISHIMA's performance, for the following reasons: 1. Our main focus is on comparing MISHIMA+external aligner combination to external aligner alone. 2. We are mainly interested in verifying whether MISHIMA would not produce particularly big misalignments; the simplified score is sufficient for this purpose. 3. MISHIMA is targeting rather closely related sequences, which means that the correct alignments produced by almost any method will have about the same score, and misalignments will result in a noticeable score decrease.The sum-of-pairs identity score was computed for all example alignments produced by MISHIMA and other methods.Complete human mitochondrial DNA (mtDNA) genome sequences were used as an example of very closely related sequences. As of July 16, 2009, a total of 4,718 complete human mtDNA genome sequences are available in DDBJ/EMBL/GenBank International Nucleotide Sequence Database. MISHIMA was able to successfully align hundreds of such genomes. Computation results can be seen in Additional file We measured the time MISHIMA takes for aligning the whole and partial sequences and compared it with three popular aligners: CLUSTAL W, MUSCLE and MAFFT Fig. . PartialCLUSTAL W is the slowest among the compared aligners, even with [-quicktree] option, followed by MUSCLE Fig. . Fig. 2 When 400 human mtDNA sequences are compared, MAFFT set at faster option is clearly faster than MISHIMA. However, if we add [-max-depth = 1] option to MISHIMA (shown in light blue), both aligners finish in similar time. Because human mtDNA sequences are quite similar with each other, good seeds are found in abundance in the first iteration of dictionary analysis, and average block length (length of sequences between two adjacent anchor seeds) is already short enough for CLUSTAL W usage. Therefore, we recommend using this option when aligning closely related sequences, such as sequences from same species.While the performance of MISHIMA is similar to that of MAFFT, it should be noted that only high similarity regions are aligned by MISHIMA, and the lower similarity parts are aligned with an external alignment program - either CLUSTAL W or MAFFT. This means that when CLUSTAL W is used as an external aligner, the alignment quality will be close to that of the CLUSTAL W complete alignment. Fig. We also tried MLAGAN  on theseMISHIMA is powerful for aligning closely related nucleotide sequences, as shown in the above section. If more divergent sequences are compared, how does MISHIMA perform? We thus retrieved complete mtDNA genomes from various order of mammalian species. Average nucleotide difference for these datasets are within the range of 0.25-0.27.Alignment times taken by MISHIMA (with various settings), CLUSTAL W, MUSCLE, and MAFFT for aligning datasets of 50, 100 and 200 complete mtDNA sequences are shown in Table If we compare computation times shown in Table MISHIMA greatly accelerates the aligner that it is using: MISHIMA+CLUSTAL W is much faster than CLUSTAL W alone, MISHIMA+MAFFT is faster than MAFFT alone. Is this achieved by sacrificing the alignment quality? Fig. Streptococcus pyogenes as example. Each genome is about 2 MB, so the total dataset size is about 8 MB. CLUSTAL W could not produce the alignment even after 15 days, and computation was aborted. In good contrast, MISHIMA+CLUSTAL W could successfully produce the multiple alignment of these four genomes in less than three hours. In the course of alignment the dataset was separated into 485 segments, divided by 484 seeds. The average length of one segment was about 4 kb, which is much easier to align than complete sequences.We are now moving from mtDNA genome sequences to much larger bacterial genomes. We first chose 4 strains of Streptococcus pyogenes strains resulted in 3 times slower computation. As the number of iterations increased, computation time was reduced, and the computation time for the case of [-max-depth = 3] was slightly shorter than default unlimited depth , 1, 2, and 3. Computation times for each case are shown in Table Streptococcus pyogenes revealed several large insertions and deletions, some more than 10 kb long. If one is interested in quickly finding such large deletions, we recommend use of [-align-seeds-only] option, so that the external aligner is not activated. In this way only seed anchoring is conducted, which is much faster (only 27 seconds in S. pyogenes example) than producing full multiple alignment.In any case, it is clear that MISHIMA can be used to align multiple complete bacterial genomes, as long as they are closely related. The alignment of four strains of Helicobacter pylori - each about 1.7 MB. Average nucleotide difference of the dataset is 0.133. Neither CLUSTAL W, MAFFT nor MUSCLE were able to complete the alignment even after 3 days. Therefore we decided to also run tests on fragments of these genomes; we chopped 200 Kb from the beginning of every sequence, then 400 Kb, 600 Kb, and so on, until 1.6 Mb. The computation time of various methods can be seen in Fig. We then moved to a more complex dataset - 6 complete genomes of different strains of MISHIMA+MAFFT combination performed well on this dataset. Adding options [-max-depth = 1] and [-max-depth = 2] allowed to save time and improve the alignment score with this dataset.Staphylococcus aureus. CLUSTAL W, MUSCLE and MAFFT were taking too long time to align this dataset. MLAGAN was still able to produce the alignment. MISHIMA was operating with the default options in this example, using MAFFT as an external aligner. MISHIMA and MLAGAN alignment times are comparable to each other with partial datasets. When increasing the alignment length, MISHIMA+MAFFT combination becomes faster  were generated using newly built random sequence generator . We used MISHIMA with [-align-seeds-only -max-depth = 1] options. As expected, MISHIMA could not detect any seeds, which is a good indication that the data is very hard or impossible to align. Quick examination of the result confirmed that the sequences could not be aligned. MISHIMA took only 13 and 15 seconds to produce the results for 50 and 100 sequences, while CLUSTAL W took hours trying to align these random and non-homologous sequences Table .We therefore recommend to first try using MISHIMA with [-align-seeds-only -max-depth = 1] options on new data. By this way you will be able to quickly know if there are any problems with the sequences. If MISHIMA was able to find seeds and produce a rough alignment, then the sequences are fine and normal MISHIMA alignment procedure can be used. In fact, computation times using this option set for human complete mtDNA genomes are 00:00:18, 00:01:15, and 00:14:38 for 50, 100, and 200 sequences, respectively. When [-max-depth = 1] option is also activated, computation times for 200 and 400 sequences are 00:00:51 and 00:02:27, respectively. These are much shorter than MISHIMA default for producing full multiple alignments.We developed a heuristic method for multiple sequence alignment that can greatly speed up alignment of large datasets - those consisting of hundreds of sequences, as well as those with very long sequences, such as complete bacteria genomes.MISHIMA depends on either MAFFT (default option), or CLUSTAL W  for aligning the areas between the "seeds" to produce the complete alignment. However even without other programs MISHIMA can be used to quickly produce a rough alignment where only seeds are aligned. This can be very useful for quick evaluation of a new dataset before applying a more thorough alignment procedure.Given the rapidly increasing number of sequenced organisms, there is a growing interest in comparing closely related species. MISHIMA is particularly helpful for such analysis due to its ability to quickly locate homology signals.Project name: MISHIMAhttp://esper.lab.nig.ac.jp/study/mishima/Project home page: Operating system: WindowsProgramming language: C (not open source).Other requirements: For using with CLUSTAL W, CLUSTAL W version 2.0.10 or later should be installed. For using with MAFFT, MAFFT version 6.707b or later should be installed.License: Binary is free for any use.Any restrictions to use by non-academics: None.KK came up with the idea of heuristic homology search, developed the software, ran tests and drafted the manuscript. NS contributed to the design of the algorithm, did additional testing on large datasets, and improved the manuscript. Both authors read and approved the final manuscript.Index of/study/mishima/supplementary-dataClick here for file


The presence of gaps in an alignment of nucleotide or protein sequences is often an inconvenience for bioinformatical studies. In phylogenetic and other analyses, for instance, gapped columns are often discarded entirely from the alignment.MaxAlign is a program that optimizes the alignment prior to such analyses. Specifically, it maximizes the number of nucleotide (or amino acid) symbols that are present in gap-free columns – the alignment area – by selecting the optimal subset of sequences to exclude from the alignment.MaxAlign can be used prior to phylogenetic and bioinformatical analyses as well as in other situations where this form of alignment improvement is useful. In this work we test MaxAlign's performance in these tasks and compare the accuracy of phylogenetic estimates including and excluding gapped columns from the analysis, with and without processing with MaxAlign. In this paper we also introduce a new simple measure of tree similarity, Normalized Symmetric Similarity (NSS) that we consider useful for comparing tree topologies.other sequences.We demonstrate how MaxAlign is helpful in detecting misaligned or defective sequences without requiring manual inspection. We also show that it is not advisable to exclude gapped columns from phylogenetic analyses unless MaxAlign is used first. Finally, we find that the sequences removed by MaxAlign from an alignment tend to be those that would otherwise be associated with low phylogenetic accuracy, and that the presence of gaps in any given sequence does not seem to disturb the phylogenetic estimates of The MaxAlign web-server is freely available online at http://www.cbs.dtu.dk/services/MaxAlign where supplementary information can also be found. The program is also freely available as a Perl stand-alone package. A multiple alignment of nucleotide or protein sequences often forms the basis for phylogenetic analysis. In a perfect alignment, gaps correspond to insertion or deletion events, and as such should contain phylogenetic information on a par with substitutions. While some work has been done to make use of this type of data -3 there all the included taxa and one has a sufficiently long sequence. However, there are many other scenarios where the approach can be useful. For instance, it is often the case in molecular evolutionary analysis today that the focus is not on the phylogeny but on the analysis of the sequences themselves, and on properties of each position, such as the rate of evolution or the action of natural selection. In such cases keeping the sites in the analysis becomes important. The use of an automated, rapid alignment clean-up method is also clearly relevant in the case of large-scale or batch-type analyses, where phylogenies are produced from many potentially large data sets, or in the case of bioinformatical analyses not tolerant to the presence of gaps.One way around this problem is to remove particularly gap-rich sequences, thereby ending up with a dataset containing more ungapped columns. This solution is of course not meaningful if the main goal of the analysis is to infer the topology of the phylogenetic tree connecting The goal of this tool is to maximize the alignment area, defined as the number of characters that are present in gap free columns. Alignment area is thus equal to the number of sequences included in the alignment times the number of columns that have no gaps. This maximization of the alignment area is done by selectively removing sequences from the alignment. Finding the right sequences to remove, however, is not a straightforward problem .To scrutinize the performance of MaxAlign, we have analyzed very large sets of protein alignments from two different sources: (1) alignments extracted from the Pfam database, and (2)MaxAlign can use one of two different algorithms: a heuristic algorithm , and an optimal algorithm . We tested both algorithms on the full Pfam dataset. The average runtime for the heuristic was 0.6 seconds per alignment (user time) demonstrating that use of MaxAlign is not a bottleneck for data analysis. Among the 5242 alignments, the heuristic algorithm found the optimal solution in 78% of the alignments. In only 4% of the alignments, the heuristic algorithm did not find the optimal solution. The remaining alignments either could not be improved from the start (4%), or the branch and bound algorithm could not reach a solution in 2 hours . Thus, the heuristic algorithm found the best solution in 95% of the cases in which a solution was found. Moreover, analysis of the solutions in the few cases where the heuristic was not optimal showed that the alignment area of the heuristic solution was, on average, 99.0% of the optimal solution (median: 99.6%). On the whole, we therefore recommend using the heuristic algorithm of MaxAlign.The alignment area of the Pfam alignments was quite variable, with a majority (52.2%) having no gap free columns . The average number of gap free columns in the unprocessed alignments was only 19.4, and the average alignment area 1494  such that the final content of noise was approximately 10%. These datasets were then re-aligned using the program mafft with default parameters. We thenIt is an unsolved issue in phylogenetic analysis how to best deal with gaps. We touched upon this topic by investigating how MaxAlign and removal of gapped columns interfere with phylogenetic tree inference. To do so, we first simulated 1000 alignments along each of 3 trees of different shapes. From each of these synthetic alignments, we then constructed three derived data sets by (a) removing gapped columns, (b) applying MaxAlign, and (c) applying MaxAlign and removing gapped columns. For each of the resulting 12,000 synthetic alignments , we then performed maximum likelihood phylogenetic analysis using the program phyml. The accuracy of phylogenetic reconstruction was then analyzed by calculating the normalized symmetric tree similarity (see Methods) between the true tree  on one hand, and the four trees estimated by phylogenetic analysis on the other. These tree similarities were computed based on the subset of taxa shared by the original and maxaligned datasets. For the trees inferred from the original (simulated) alignment and from the original alignment excluding gaps, we also computed the similarity to the true tree based on the full set of taxa. The outcome of this comparison can be found both in figure nd and last). However, it can also be seen that applying MaxAlign decreases the accuracy only very slightly  is measured on the One reason for discarding gapped columns is that summing over all possible missing values is a time consuming step in a maximum likelihood calculation. We have evaluated how much time is saved by using MaxAlign with and without discarding columns with gaps. The results are presented in table It can be seen that either using MaxAlign or removing columns with gaps nearly halves the computer time needed to find the phylogenetic tree. Removing columns with gaps does so by preventing the summation over unknown characters as well as reducing the number of sites to be included in the analysis. MaxAlign diminishes the number of summations required and also reduces the size of the dataset, by including fewer sequences.The computer time required for these phylogenetic analyses was particularly short, as we used a very fast program (phyml), and the alignments contained few sequences. In situations using more time-consuming analyses and software, as well as larger alignments, these relative differences in computing time will have an increased impact.In the present work, we have shown how MaxAlign is helpful in "cleaning up" big alignments, and demonstrated how it may be used in connection with phylogenetic analysis. In the analysis presented above, we found that the use of MaxAlign more than halved the running time of the analysis even when gapped columns were not excluded. When gapped columns were discarded from the alignment, the output was of much higher quality if MaxAlign was first used to pre-process the data, as the number of columns included in the analysis increased immensely. We have also shown that in the conditions tested, the accuracy of the phylogenetic estimate of the tree topology increases if one includes the gapped columns. The sequences removed by MaxAlign were predominantly those associated with the highest degree of uncertainty regarding their placement in the final trees.The use of MaxAlign prior to bioinformatical and phylogenetic analyses optimizes the number of nucleotides or amino acids present in ungapped alignment columns , thereby increasing the amount of useful data and/or the speed of the analysis. Moreover, MaxAlign is also very helpful in detecting misaligned or defective sequences without requiring manual inspection. Given its very short running times and ease of use, it can without difficulty be used as a step in both automated and manual phylogenetic and bioinformatical analyses.gap pattern. In the example alignment shown in figure MaxAlign maximizes the alignment area of an alignment by removing selected sequences. It has two algorithms to do so: one heuristic and one branch-and-bound. Both are based on the concept of MaxAlign has several additional features. For example, it is possible to select a subset of sequences that should be kept in the final alignment, even if their removal would yield an improvement of the alignment area. This is done by simply adding a plus sign ("+") in front of the sequence name in the fasta file. In this way, the user can preserve key sequences in his/her analysis. Also, users interested in codon-based analyses can run MaxAlign on protein sequences and obtain their output alignments both in protein and nucleotide format .The server is freely accessible at  where a To test the relevance of MaxAlign in real biological problems, the Pfam-A Release 21.0 of full alignments  was usedTo test the ability of MaxAlign in removing non-homologous sequences from an alignment, we added noise sequences to each of the 5242 above-mentioned Pfam alignments in a ratio of 1:10. Thus, the alignments ended up containing between 33 to 550 sequences. These alignments were submitted to MaxAlign and the fraction of noise sequences removed was recorded. For each alignment, non-homologous sequences were chosen randomly from the rest of Pfam.To test the impact of MaxAlign in phylogenetic analyses, a set of benchmarking phylogenetic analyses was set up. To be certain of the true tree topology, we simulated alignments along known trees, using simprot . To ensuThe 3 trees chosen to generate the simulated alignments had very different kinds of topology, and were downloaded from the TreeFam database. Tree 1 Each simulated alignment gave rise to 4 derived datasets: the alignment after processing with MaxAlign, but keeping the gapped columns, the alignment after processing with MaxAlign and removal of gapped columns, the original alignment with the gapped columns removed and the original alignment without any processing.These datasets were then used as the basis for reconstructing the tree topology. This was done by using phyml  with theAll Pfam alignments having between 30–100 sequences  were included in this analysis, which consisted of measuring the average duration of phylogenetic analyses, in a way very similar to the one described above, apart from using real alignments instead of simulated alignments . We did not analyze computation time on the original datasets (those not processed by MaxAlign) with removal of gapped columns, as the majority of these alignments had zero columns available for the analysis.To compare the performance of the two algorithms available in MaxAlign, we applied them to the full set of 5242 Pfam alignments described above and evaluated the solutions in terms of time spent and changes in alignment area.The degree ofdissimilarity between two phylogenetic trees can be quantified using a number of different measures of tree distance. The most widely used measures are probably the symmetric distance, the quaAny branch in a phylogenetic tree can be thought of as defining a bipartition where the leaves are divided into those present on one side of the branch and those present on the other side of the branch. The symmetric distance of Robinson and Foulds is simply the number of bipartitions (branches) in tree 1 that are not present in tree 2 plus the number of bipartitions in tree 2 that are not present in tree 1. This is an intuitively understandable measure of treedissimilarity that is fairly rapid to compute.We now propose a normalized version of this distance measure: simply divide the symmetric distance between two trees by the total number of bipartitions present in the two trees. . This "Normalized Symmetric Distance" is zero when trees are identical and 1.0 when they have absolutely no bipartitions in common. From the Normalized Symmetric Distance (NSD), the corresponding "Normalized Symmetric Similarity" (NSS) can be computed simply as NSS = 1.0 – NSD. This similarity measure is 1.0 for identical trees and zero for trees without any common bipartitions.RGO had the idea for the project, designed a first version of MaxAlign and wrote the paper. PWS designed the current algorithms and implemented all the final software. AGP wrote the paper, designed and implemented all tests and supervised the project. All authors read and approved the final manuscript.MaxAlign perl script. The file contains the MaxAlign perl script that can be used at the command line.Click here for file