Structural alignment is an important step in protein comparison. Well-established methods exist for solving this problem under the assumption that the structures under comparison are considered as rigid bodies. However, proteins are flexible entities often undergoing movements that alter the positions of domains or subdomains with respect to each other. Such movements can impede the identification of structural equivalences when rigid aligners are used.Rapid Alignment of Proteins in terms of Domains) for the three-dimensional alignment of protein structures in the presence of conformational changes. The flexible aligner is coupled to a genetic algorithm for the identification of structurally conserved regions. RAPIDO is capable of aligning protein structures in the presence of large conformational changes. Structurally conserved regions are reliably detected even if they are discontinuous in sequence but continuous in space and can be used for superpositions revealing subtle differences.We introduce a new method called RAPIDO (RAPIDO is more sensitive than other flexible aligners when applied to cases of closely homologues proteins undergoing large conformational changes. When applied to a set of kinase structures it is able to detect similarities that are missed by other alignment algorithms. The algorithm is sufficiently fast to be applied to the comparison of large sets of protein structures. When comparing structures of related proteins with different amino-acid sequences it is necessary to first perform a structural alignment, i.e. to define an equivalence map between the residues in the different structures based on their relative position in space. Once structures have been successfully aligned in three dimensions, similarities and differences can be studied in order to understand function and behaviour of the molecules under consideration.It has been demonstrated that the problem of defining an equivalence map for residues in protein structures has no unique optimal solution  and thatAlignment methods can be classified based on whether the two structures to be aligned are considered as rigid bodies or whether internal flexibility between domains or subdomains is accommodated in the alignment. Methods belonging to the group of 'rigid aligners' are SSAP , CE 9],,9], ProSAs it is well known, protein molecules are flexible entities with internal movements ranging from the displacement of individual atoms to movements of entire domains or subdomains ,24. LargThe molecular chaperon GroEL is an interesting case of protein molecules exhibiting pronounced molecular flexibility between structurally conserved domains. By comparison of crystal structures of different functional states, the GroEL molecule can be divided into three domains  separated by hinge regions . Due to In recent years, tools for the flexible alignment of protein structures have been introduced. These tools find an equivalence map between the residues of two molecular structures even when substantial intramolecular movements occur around molecular hinges. The regions between hinge points are commonly considered as rigid bodies and the alignment is usually optimized to minimize the number of hinges. The group of 'flexible aligners' includes, FlexProt  and FATCHowever, in alignments of molecules such as GroEL where the polypeptide chain folds back onto itself Figure  and therRapid Alignment of Proteins in terms of Domains). RAPIDO is capable of aligning related protein molecules in the presence of large conformational differences while at the same time groups of equivalent parts of the polypeptide that are distant in sequence but nevertheless form spatially continuous domains are identified correctly as such. As a first step RAPIDO creates an equivalence map between the two structures by taking into account flexibility, with a procedure that is similar to the one used by FATCAT [structurally conserved regions that can be continuous in space but not in sequence . The result of the procedure is a description of a protein in terms of structurally conserved regions connected by localized hinges or by flexible linker regions. We have chosen the standard parameter settings for RAPIDO such that more emphasis is placed on the geometric similarity of the structurally conserved regions (as reflected in low RMSDs) than on their size . With this choice, the resulting structurally conserved regions will have a high level of similarity allowing their usage for robust coordinate-based structure superpositions.Here we introduce a new algorithm for the flexible structural alignment of proteins called RAPIDO 2. Chaining of the MFPs through a graph-based algorithm3. Refinement of the alignment4. Identification of rigid bodiesi-th residue in structure X (X = A or X = B) is represented by the coordinates of its Cα atom and will be indicated by xi (ai and bi respectively).In the remainder of this section we will refer to two structures being compared as structures A and B. The fragment as an ungapped stretch of residues and a matching fragments pair (MFP) as a pair of structurally similar fragments of the same length in two structures being compared. The search for MFPs is in fact implemented in a number of alignment tools as the initial step [matching fragment pairs (MFPs) here, have been named aligned fragment pairs (AFPs) in other publications [matching fragment pairs in order to clarify that in a later stage of the alignment algorithm, a subset of the matching fragment pairs forming the initial set is selected to assemble the actual alignment, and the selected MFPs thus become aligned fragment pairs.We define a ial step ,18,26,30ications ,18,30. Iα-atoms of the two fragments (eq. 1 in the Methods section).While many algorithms use the RMSD to measure the similarity between two fragments ,26,30, wmL (mL = 8 in the implementation) is performed, followed by a clustering step in which overlapping MFPs are joined to form longer ones.At first an exhaustive search for MFPs of length weight function for the edges, the problem of finding the best alignment is translated into the problem of identifying the longest path on a graph. We solve this problem by applying a dynamic programming algorithm for the identification of the longest path. The alignment obtained in this way is a preliminary alignment that is then refined (details on the refinement process can be found in the Methods section) resulting in the raw alignment.The MFPs identified in the first step constitute a set of potential building blocks for the final alignment from which, in the second step, a subset of MFPs representing a structural alignment is assembled. This is done by casting the problem into a graph representation to which a standard algorithm for identification of the longest path is applied. The MFPs are represented as vertices of a graph and two MFPs (e.g. two vertices) are connected by an edge if they are topologically ordered, i.e. if they are composed of two pairs of fragments that appear in the same order in the two residue sequences. Every path in the graph represents a possible alignment and by choosing an appropriate aligned residues for which distances between Cα-atoms are identical within a tolerance as structurally conserved regions. These subsets can be identified using a genetic algorithm operating on scaled difference distance matrices [i with a B-value of Bi is replaced by an analogous quantity Once the raw alignment has been calculated, the algorithm performs a search for structurally conserved regions. Structurally conserved regions relate to conformationally invariant regions detected in different conformations of the same molecule as described in . Conformmatrices ,31,32. Ik and η have been empirically optimized to 0.4 Å and 2/3. where the constants The algorithm searches iteratively for structurally conserved regions in analogy to the approach presented in ). AligneTo characterize the agreement between two structures after the equivalent residues have been divided into structurally conserved and flexible regions, separate least-square superpositions are performed for the different structurally conserved regions.RMSDf) as the standard RMSD calculated for all pairs of equivalent Cα-atoms after separate least-squares superposition for the different structurally conserved regions.Based on this superposition allowing flexibility between conserved parts of a three-dimensional structure, we define the 'flexible RMSD'  and we compare the results of RAPIDO with those obtained by FATCAT  and Flex1byu, [1rrp, [Ran is a small GTPase belonging to the Ras superfamily that plays an important role in several nuclear functions, including nucleocytoplasmic transport, cell-cycle progression and nuclear envelope assembly . Here we1byu, ); the se, [1rrp, ).The RAPIDO alignment shows that major parts of the two structures are very similar. 182 residues are aligned, 158 of which are assigned to two rigid bodies. The first rigid body covers more than 70% (140 residues) of the entire protein, can be superposed with an RMSD of 0.76 Å . The separation between the two rigid bodies is similar in the three alignments but the RMSD for the superposition of the single rigid regions is higher in FATCAT and FlexProt alignments than in the RAPIDO alignment. This is due to the fact that in these two aligners all aligned residues are used for the superposition while RAPIDO distinguishes between structurally conserved and flexible aligned residues and uses only the residues in structurally conserved regions to perform the superposition. In fact, in the FATCAT and FlexProt align fragments the SWITCH I and II loops are attributed to the first equivalent region yielding an RMSD for the superposition of this first rigid part of 1.51 Å for FATCAT and 2.87 Å for FlexProt. The unstructured loop connecting the main body and the C-terminal helix is partly assigned to the first equivalent region and partly to the second adding to the increased RMSD-values for the respective superpositions.Although, for this case, the alignments are mostly equivalent, the one provided by RAPIDO highlights the different conformations of three important functional elements corresponding to the SWITCH I and II loops and to the C-terminal loop and produces an accurate superposition of the two structures in which these differences can be clearly analyzed.Escherichia coli  with onid 1WE3, ).The structural alignment produced by RAPIDO covers 98% of the molecule , with a flexible RMSD of 0.88 Å. Four structurally conserved regions are identified Figures  and 3e cThe alignment produced by FATCAT has approximately the same length (518 residues) and a flexible RMSD of 2.45 Å. Two hinges are identified and the structure is divided into the three regions shown in Figure FlexProt creates an alignment of 513 residues with a flexible RMSD of 2.87 Å. Three hinge-points dividing the structure in four fragments are identified. As in the FATCAT alignment, the apical domain is kept separate from the rest of the structure. Even if the C-terminal parts of the hinge and equatorial domains are separated by a hinge point, their N-terminal counterparts are kept together including the stem loop. In general, the alignments produced by FATCAT and FlexProt tend to underestimate the number of hinges for this pair of structures and cannot be used to highlight the difference between the equatorial and hinge domains, nor the different conformation of the stem loop.A correct delineation of the domains is of particular interest in this case. In fact, the identified domains can be used as rigid bodies for the interpretation of low-resolution electron density maps for GroEL in different functional states as determined by electron microscopy. In this way, they allow to derive conclusions at the atomic level from lower resolution data .Protein kinases are multi-domain proteins catalyzing the phosphorylation of proteins and play important roles in controlling many cellular processes (chapter 13 in ). The prWe used RAPIDO to perform an all-against-all alignment for 68 structures of human protein kinases . For comparison, for every pair of structures, an alignment was also determined using DaliLite Ver. 2.4.4 .Alignments produced by RAPIDO and DALI are compared in Figure 1AD5, [1FMK, [1K9A, [1OPK, [Three of these cases , c-Src , [1FMK, ), Csk fr, [1K9A, ) and c-A, [1OPK, ). In the1ad5) and Csk (PDB id 1k9a). Although the positions and orientations of the SH2 and SH3 domains with respect to the protein kinase domain are substantially different in the two structures , MAPK P38 (1P38), Src (1FMK), IGF1 receptor (1JQH), EGFR (1M17), HGFR (1R0P) and JAK3 (1YVJ), the algorithm implemented in DALI can cope with many cases of different relative domain orientation. However for the cases marked in Figure 1FMK and 1R0P), parts of the small lobe are in fact included in the alignment but at the cost of a very large RMSD between the equivalent atoms  range from 0.5 sec to 1.5 s for pairs of structures between 200 and 400 residues. Without pre-processing, execution time ranges between 1.5 and 4 s for the same structures (CPU-times for iMac with an Intel Core 2 Duo processor at 2.4 GHz and 2 GB of memory running under MAC OS X version 10.4).Typical execution times with the inclusion of the pre-processing step . A distance between the two fragments, S, is calculated as:An MFP composed of two stretches of residues of length whereα-atoms of residues u and v in structure X.is the element of the distance matrix between the CS* of MFPs of length greater than or equal to mL for which S is lower than a threshold mS. Even if the number of possible fragments, S* is computationally too expensive. To reduce the complexity of this step, we thus first search for all MFPs of fixed length mL and distance S lower than a threshold mS. Then we identify groups of overlapping MFPs and test whether groups of MFPs can be merged into one larger MFP. If the score for the merged MFP is lower than the chosen threshold mS, it is kept. Technically, the merging step consists of extending a randomly chosen MFP downstream with overlapping MFPs until the score of the merged MFP becomes greater than the threshold mS. In the current implementation of the algorithm, mL = 8 and mS = 3.0.In the first step, the algorithm builds the list F1 and F2 are connected by an edge if they can be chained, i.e. if and only if F1 <<F2 according to the following definition and F2 ≡  be two MFPs. Then, F1 <<F2(F1 is less than F2) if and only ifV, E) where V is the set of vertices and E is the set of edges of the graph:This is a partial order relation and it can be demonstrated that the graph induced by the previous relation is a Directed Acyclic Graph (DAG). This graph can be formally described by the couple  connecting two MFPs is assigned a weight w which is given by the sum of two terms:A path through this graph is a coherent sequence of matching pairs that can be read as an alignment between the two structures. To optimize the structural alignment, we associate a weight to every edge in the graph. An edge  provides a measure of the local similarity of the matching pair F2. Given the measure of the distance introduced in eq. 1, we can use it to score the similarity between two fragments simply by subtracting it to the value of the ms thresholdThe first term S = 0) and decreases for fragments that are increasingly different. The term wF is calculated as the score of F2 (Sc(F2)) multiplied by its length L2. In case of an overlap between F1 and F2, we consider only the length of the non overlapping part of F2 which is L1-L2+i2-i1This function reaches a maximum if the two fragments are exactly identical , is a penalization term given by the sum of two contributions: the first penalizing the presence of gaps and the second taking into account the mutual displacement of the two MFPs F1 and F2 in the two structures:The second term, wGP is the gap penalty (set to -0.5 in the current implementation). The term P) penalizes the chaining of two MFPs that are displaced with respect to one another in the two structures.P) term, let us consider the case of an alignment including two α-helices. If the two helices have different relative positions in the two structures, the score for their alignment will be penalized by the P) term. The different relative positions can have two different reasons: Either one of the structure undergoes a conformational change moving the two helices with respect to one another  or one of the two helices in one structure is in fact not structurally equivalent to its counterpart in the other structure . In the first case, both the helices will be part of larger fragments that are structurally equivalent and the penalization introduced by the inclusion of the two helices in the alignment should be balanced by the positive contribution of the MFPs stably surrounding the two helices. If the two helices are not structurally equivalent, then the surrounding MFPs will also not be structurally equivalent thus not giving rise to balancing contributions to the score effectively leading to elimination of the two helices from the alignment.For illustrating the function of the Df is defined as a measure of the displacement in space of the two matching fragments and is calculated using difference distances between the two fragments. In case the two fragments F1 ≡  and F2 ≡  have the same length L = L1 = L2, then Df is calculated asTo achieve the required behaviour of the score, L is the minimum between L1 and L2 we select in the longest fragment the subfragment of length L yielding to the maximum value of Df.otherwise if P is a truncated linear function calculated asGP = -0.5, PC = -5.0, mC1 = 1.0, mC2 = 4.0. This choice leads to preference for short gaps and longer aligned fragments with fewer hinge regions.In the current implementation the parameters are empirically set to 'longest path' in the weighted graph and is calculated using a dynamic programming algorithm. Since the graph is a DAG the longest path can be calculated in time O(V+E) [V is the number of MFPs and E is the number of edges between them. The number of edges is O(V2) in the worst case and the number of matching fragments is potentially O(L2), with L being the average length of the two residue sequences. This means that the worst case complexity of the overall algorithm is O(L4). Nevertheless, the number of matching fragments is usually much less than L2 and several heuristics can be used to considerably speed up the algorithm.After weights have been assigned to all edges, the best alignment between the two structures can be seen as a e O(V+E)  where V Df. This can happen either when the two matching fragments are located on the two sides of a hinge point or if they belong to unrelated and locally similar stretches of residues. The first case can be distinguished from the second by considering that in the case of an hinge point a pair of chained fragments with an high value of Df will be followed by a sequence of MFPs with lower values. Therefore correct alignments are likely to contain a lower number of chained MFPs with a high value of Df. Therefore, for each vertex a counter (CH) for the number of times the Df term is greater than mC2 on the longest path that reaches that vertex, is stored. A maximum threshold for CH is fixed in the algorithm (MH) and the algorithm discards paths leading to a value of CH that is higher than this threshold. In the current implementation, this threshold is fixed to 5. As a result, the alignment provided by the algorithm can cross a hinge point a number of times that must be less than MH. This heuristic was already used by Ye et al. [An additional issue is taken into account while calculating the best alignment. As discussed above, a strong displacement between two MFPs is identified by a higher value of e et al. .The initial alignment obtained after the chaining of MFPs can be used as a basis for finding additional residue equivalences that can only be detected by checking their consistency with the initial alignment.At first, for every gap between aligned fragments, the intervening residues are systematically checked to verify if their inclusion is consistent with the rest of the alignment.For all the aligned fragments, small shifts along the sequence  are tested in order to correct small offsets in the alignment of periodic structures such as helices that can sometimes occur due to the high local similarity.Finally, aligned fragments in the vicinity of the N and C-termini are inspected and eventually removed if showing insufficient quality of the alignment.Technically, all checks are done by evaluating whether or not addition/removal of an equivalent pair of residues improves the scoring function of the genetic algorithm on the error scaled difference distance matrix between the two structures (for details on the scoring function see Schneider ).Low limit. This parameter controls whether or not different distances measured between pairs of equivalent atoms are considered as identical within error. It corresponds to the εl parameter in [The only adjustable parameter of the aligner is the meter in  and is sIn order speed up RAPIDO for aligning structures with very similar sequences, a pre-processing step exploiting the fact that sequences can be aligned much more quickly than structures was added to the scheme described above. An initial sequence alignment is in fact performed for all pairs of structures to be aligned. If this sequence alignment reveals a sufficient similarity of the primary sequences (see below), the sequence-based equivalence map is used as a starting point for a preliminary search for rigid bodies. The rigid bodies found are retained and stored as MFPs to be later used by the RAPIDO aligner algorithm. The non-rigid and/or not aligned parts of the two structures are scanned for MFPs using the standard approach described above. The set of MFPs used for the next step of the algorithm (the merging of MFPs) is then created by combining the MFPs from the two sources.Technically the sequence alignment is carried out using the Smith-Waterman dynamic programming algorithm  where a This step is particularly useful in cases like the alignment of structures of GroEL from different organisms, where the time for computation is reduced by 80% using the pre-processing. For the human kinase dataset the pre-processing step is useful in 66% of the alignments (1496 out of 2278) and the computation time is reduced by 70% on the average., [-90 were retained and manually pruned to select only structures with a sequence identity greater than 98%. With this method, for every sequence from the Human Kinome Database, all structures in the PDB that represent the respective protein were identified. For protein kinase sequences with more than one corresponding in the PDB, we then randomly selected one representative structure. The final dataset is composed of 68 structures, resulting in a total of 2278 all-against-all pairwise alignments. The PDB ids of the 68 selected structures and details about the sequence alignments are listed in additional file All sequences of human protein kinase domains as defined in the Human Kinome database  were us,  with the, . All hitRM conceived and implemented the aligner algorithm, compiled the hinge motions dataset, performed the tests, validated the results and drafted the manuscript. BB compiled the kinase structure dataset and validated the results on that dataset. TRS conceived, designed and coordinated the study and finalized the manuscript. All authors contributed to the discussion of the ideas behind the study. They all read and approved the final manuscript.Comparison between DALI and RAPIDO on the human kinase structures dataset.Click here for fileresults on Fischer's dataset.Click here for fileList of the structures included in the Dataset of human kinase structures.Click here for file


Protein structural alignment provides a fundamental basis for deriving principles of functional and evolutionary relationships. It is routinely used for structural classification and functional characterization of proteins and for the construction of sequence alignment benchmarks. However, the available techniques do not fully consider the implications of protein structural diversity and typically generate a single alignment between sequences.We have taken alternative protein crystal structures and generated simulation snapshots to explicitly investigate the impact of structural changes on the alignments. We show that structural diversity has a significant effect on structural alignment. Moreover, we observe alignment inconsistencies even for modest spatial divergence, implying that the biological interpretation of alignments is less straightforward than commonly assumed. A salient example is the GroES 'mobile loop' where sub-Ångstrom variations give rise to contradictory sequence alignments..A comprehensive treatment of ambiguous alignment regions is crucial for further development of structural alignment applications and for the representation of alignments in general. For this purpose we have developed an on-line database containing our data and new ways of visualizing alignment inconsistencies, which can be found at  Sequence comparison has become a major tool for biological research in the post-genomic era, forming the basis for functional annotation, classification, and analysis of evolutionary relationships. At the residue level, however, the relation between sequence, structure and function can often be obscure, and examples abound of proteins with a clear functional and homologous relationship but sharing negligible similarity at the sequence level.i.e. where alignment ambiguity does not occur and hence can be trusted. The general problem of uncertainty in sequence alignment has recently been discussed by Wong et al. [Structural alignment therefore is the method of choice for reliable homology assessment and derived features like functional classification and phylogeny. This importance is reflected in the number of tools available for structural alignment, such as DALI , SSAP 22, STRUCTg et al. . Due to g et al. ,17. An ag et al. , but comRecent structural alignment methods have started to place emphasis on dealing with structural flexibility, such as FATCAT , MultiPrTo further elucidate the effect of structural diversity on structural alignment, we prepared two distinct comprehensive sets of alternative structures for proteins from the HOMSTRAD database of homologous protein families. The first set comprises proteins for which alternative crystal structures are available. The other set is derived from molecular dynamics simulations to explore a more extensive spectrum of possible structures. An overview of our analysis procedure is outlined in Figure Our main results show that in many cases structural variation strongly affects structural alignments, even for highly similar sequences. Moreover, the derived alignment appears to be highly sensitive to even small conformational changes of the proteins. The uncertainty in pairing up structural equivalent residues makes it difficult to determine which alignment alternative would describe most closely the functional relationship between the proteins. To address this issue, we show how alternative alignment visualizations may be used to exploit the information contained within variable alignment regions.The relation between the variation of the alternative structures (RMSD) and the corresponding alignment similarity (SP score) is shown in Figure E. coli GroES  for which 3309 snapshot structures could be made and 565 proteins (divided over 395 families) for which we found in total 2998 alternative crystal structures with redundant sequences. A full list of all aligned structures and relevant details is provided in additional file All authors designed the research, analyzed the results and wrote the paper. WP and KAF performed the research. All authors read and approved the final manuscript.Figure S1: Combined effects of structural variation and sequence variation on the alignment.Click here for fileTable S1: Molecular Dynamics simulation set-up.Click here for fileTable S2: Details of aligned Crystal Structures (a) and Simulation Snapshots (b).Click here for file


DIALIGN-T is a reimplementation of the multiple-alignment program DIALIGN. Due to several algorithmic improvements, it produces significantly better alignments on locally and globally related sequence sets than previous versions of DIALIGN. However, like the original implementation of the program, DIALIGN-T uses a a straight-forward greedy approach to assemble multiple alignments from local pairwise sequence similarities. Such greedy approaches may be vulnerable to spurious random similarities and can therefore lead to suboptimal results. In this paper, we present DIALIGN-TX, a substantial improvement of DIALIGN-T that combines our previous greedy algorithm with a progressive alignment approach.DIRM-BASE 1. IRMBASE 2 and DIRMBASE 1 are constructed by implanting highly conserved motives at random positions in long unalignable sequences.Our new heuristic produces significantly better alignments, especially on globally related sequences, without increasing the CPU time and memory consumption exceedingly. The new method is based on a guide tree; to detect possible spurious sequence similarities, it employs a vertex-cover approximation on a conflict graph. We performed benchmarking tests on a large set of nucleic acid and protein sequences For protein benchmarks we used the benchmark database BALIBASE 3 and an updated release of the database IRMBASE 2 for assessing the quality on globally and locally related sequences, respectively. For alignment of nucleic acid sequences, we used BRAliBase II for global alignment and a newly developed database of locally related sequences called On BALIBASE3, our new program performs significantly better than the previous program DIALIGN-T and outperforms the popular global aligner CLUSTAL W, though it is still outperformed by programs that focus on global alignment like MAFFT, MUSCLE and T-COFFEE. On the locally related test sets in IRMBASE 2 and DIRM-BASE 1, our method outperforms all other programs while MAFFT E-INSi is the only method that comes close to the performance of DIALIGN-TX. Each possible fragment is given a score that is related to the P values used by BLAST [consistent set of fragments from all possible sequence pairs, maximizing the total score of these fragments. Gaps are not penalized. Here, consistency means that a set of fragment alignments can be included into one single alignment without contradictions, see for example [DIALIGN is a widely used software for multiple alignment of nucleic acid and protein sequences ,2 that cby BLAST ,4, and t example  for a moscoring scheme or objective function. Instead of summing up substitution scores for aligned residues and subtracting gap penalties, the score of an alignment is based on P-values of local sequence similarities. Only those parts of the sequences are aligned that share some statistically significant similarity, unrelated parts of the sequences remain unaligned. This way, the method can produce global as well as local alignments of the input sequences, whatever seems more appropriate. Combining local and global alignment features is particularly important if genomic sequences are aligned where islands of conserved homologies may be separated by non-related parts of the sequences. Thus, DIALIGN has been used for comparative genomics [The main difference between DIALIGN and more traditional alignment approaches is the underlying genomics , for exagenomics -9.pairwise alignments can be calculated efficiently in the segment-based approach. In DIALIGN, this is done by a space-efficient fragment-chaining algorithms [multiple alignments. Thus, heuristics must be used if more than two sequences are to be aligned. All previous versions of DIALIGN used a greedy algorithm for multiple alignment. In an initial step, optimal pairwise alignments are calculated for all possible pairs of input sequences. Since these pairwise alignments are completely independent of each other, they can be calculated on parallel processors [consistent set of fragments involving all pairs of sequences – provided they are consistent with the previously included fragments.As with traditional objective functions for sequence alignment, numerically optimal gorithms ,11. Howeocessors . FragmenInteger Linear Programming [The greedy algorithm used in DIALIGN is vulnerable to spurious random similarities. It has been shown, that the numerical score of alignments produced by this heuristic can be far below the optimum ,13. Consgramming .S = {s1, . . ., sk} of input sequences where li is the length of sequence si. A fragment f is a pair of two equal-length segments from two different input sequences. Thus, a fragment represents a local pairwise gap-free alignment of these two sequences. Each possible fragment f is assigned a weight score w(f) which, in our approach, depends on the probability P(f) of random occurrence of such a fragment. More precisely, if f is a local alignment of sequences si and sj, then P (f) is the probability of finding a fragment of the same length as f with at least the same sum of matches or similarity values for amino acids in random sequences of length li and lj, respectively. For protein alignment, a standard substitution matrix is used. Let F be the set of all possible fragments. The optimization problem is then to find a consistent set A ⊂ F of fragments with maximum total weight, i.e. a consistent set A maximizingFormally, we consider the following optimization problem: we are given a set consistent if all fragments can be included into one single alignment, see [A are allowed to overlap if different pairs of sequences are involved. That is, if two fragments f1, f2∈ A involve sequence pairs si, sj and sj, sk, respectively, then f1 and f2 are allowed to overlap in sequence sj. If two fragments involve the same pair of sequences, no overlap is allowed. It can be shown that the problem of finding an optimal consistent set A of fragments is NP-complete . Therefore, we are motivated in finding intelligent approximations that deliver a good tradeoff between alignment quality and CPU time.A set of fragments is called ent, see . FragmenF' ⊂ F and we will first search for a consistent subset A ⊂ F' with maximum total score. As in previous versions of DIALIGN, we use pairwise optimal alignments as a filter. In other words, the set F' is defined as the set of all fragments contained in any of the optimal pairwise alignments of the sequences in our input data set. Here, we also restrict the length of fragments using some suitable constant.To decrease the computational complexity of this problem, we restrict ourselves to a reduced subset greedy approach. We call this approach a direct greedy approach, as opposed to the progressive greedy approach that we introduce in this paper. A modification of this 'direct greedy' approach was also used in our reimplementation DIALIGN-T. Here, we considered not only the weight scores of individual fragments  but als weights  for detaguide tree for the set of input sequences based on their pairwise similarity scores. The sequences are then aligned in the order defined by the guide tree. We divide the set of fragments contained in the respective optimal pairwise alignments into two subsets F0 and F1 where F0 consists of all fragments with weight scores below the average fragment score in all pairwise alignments, and F1 consists of the fragments with a weight above or equal to the average weight. In a first step, the set F1 is used to calculate an initial multiple alignment A1 in a 'progressive' manner. The low-scoring fragments from set F0 are added later to A1 in a 'direct' greedy way, provided they are consistent with A1. In addition, we construct an alternative multiple alignment A0 using the 'direct' greedy approach implemented in previous versions of DIALIGN and DIALIGN-T, respectively. The program finally returns either A0 or A1, depending on which one of these two alignments has the highest score.To overcome the difficulties of a 'direct' greedy algorithm for multiple alignment, we combined greedy features with a 'progressive' alignment approach -20. RougR for pairs of cluster . Initially, each cluster Ci consists of one sequence si only. The similarity R between clusters Ci and Cj (or leaves i and j in our tree) is defined to be the score of the optimal pairwise alignment of si and sj according to our objective function, i.e. the sum of the weights of the fragments in an optimal chain of fragments for these two sequences. In every step, we merge the two sequence clusters Ci and Cj with the maximum similarity value R into a new cluster. Whenever a new cluster Cp is created by merging clusters q and r (or a node p in the tree is created with children q and r), we define the similarity between p and all other remaining clusters m to beTo construct a guide tree for the progressive alignment algorithm, we use straight-forward hierarchical clustering. Here, we use a weighted combination of complete-linkage and average-linkage clustering based on pairwise similarity values The choice of this function has been inspired by MAFFT ,22; it aS is constructed bottom-up along the guide tree. Thus, the crucial step is to combine two sub-alignments represented by nodes q and r in our tree whenever a new node p is created. In the traditional 'progressive' alignment approach, this is done by calculating a pairwise alignment of profiles, but this procedure cannot be directly adapted to our segment-based approach. Let Aq and Ar be the existing subalignments of the sequences in clusters Cq and Cr, respectively, at the time where these clusters are merged to a new cluster Cp. Let Fq, r be the set of all fragments f ∈ F connecting one sequence from cluster Cq with another sequence from cluster Cr. Now, our main goal is to find a subset Fp⊂ Fq,r with maximum total weight score that is consistent with the existing alignments Aq and Ar. In other words, we are looking for a subset Fp⊂ Fq, r with maximum total weight such thatThe final multiple alignment of our input sequence set p.describes a valid multiple sequence alignment of the sequence set represented by node Aq and Ar are merged, every single fragment f ∈ Fq,r is consistent with the existing  alignments Aq and Ar and therefore consistent with the set of all fragments accepted so far. Only groups of at least two fragments from Fq,r can lead to inconsistencies with the previously accepted fragments. Thus, there are different subtypes of consistency conflicts in Fq,r that may arise when Aq and Ar are fixed. There are pairs, triples or, in general, l-tuples of fragments of Fq,r that give rise to a conflict in the sense that the conflict can be resolved by removing exactly one fragment of such a conflicting l-tuple. Statistically, pairs of conflicting fragments are the most frequent type of conflict, so we will take care of them more intelligently rather than using only a greedy method. Since in our approach, the length of fragments is limited, we can easily determine in constant time for any pair of fragments  if the setIt is easy to see that at this time, before clusters f1 and f2. Here, the data structures described in [f1, f2) would take O(|f1| × |f2|) time where |f| is the length of a fragment f .is consistent, i.e. if it forms a valid alignment, or if there is a pairwise conflict between ribed in  are usedGq,r that has a weighted node nf for every fragment f ∈ Fq,r. The weight w(nf) of node nf is defined to be the weight score w(f) of f, and for any two fragments f1, f2 there exists an edge connecting pairwise conflict between f1 and f2, i.e. if the set Aq∪ Ar∪ {f1, f2} is inconsistent. We are now interested in finding a good subset of Fq,r that does not contain any pairwise conflicts in the above sense. The optimum solution would be obtained by removing a minimal weighted vertex cover from Gq,r. Since the weighted vertex cover problem is NP-complete we apply the 2-approximation given by Clarkson [C, the algorithm iteratively adds the node v with the maximum valueThis gives rise to a conflict graph Clarkson . This alC. For any edge  that connects a node u with v the weight w(u) is updated toto u, v) is deleted. This iteration is followed as long as there are edges left.and the edge . However, after subtracting the set C from Fq, r, the algorithm may detect that fragment f2 is part of a larger inconsistent group, and f2 is removed as well. In this case, it may be possible to include f1 again into the alignment. Therefore, our algorithm reconsiders in a final step the set C to see if some of the previously excluded fragments can now be reincluded into the alignment. This is again done using our 'direct' greedy method.Note that it is ribed in . A conseconsistency frontiers or consistency boundaries, respectively, that are used to check for consistency as these features have been described elsewhere [PAIRWISE_ALIGNMENT  that takes two sequences si and sj and  an existing consistent set of fragments A as input and calculates an optimal alignment of si and sj under the side constraint that this alignment is consistent with A and that only those positions in the sequences are aligned that are not yet aligned by a fragment from A. Note that in DIALIGN, an alignment is defined as an equivalence relation on the set of all sequence positions, so a consistent set of fragments corresponds to an alignment. Therefore, we do not formally distinguish between alignments and sets of fragments.In the previous section, we discussed all ingredients that are necessary to give a high-level description of our algorithm to compute a multiple sequence alignment. For clarity, we omit algorithmical details and data structures such as the lsewhere . We use GREEDY_ALIGNMENT  takes an alignment A and a set of fragments F' as arguments and returns a new alignment A' ⊃ A by adding fragments from the set F' in a 'directly' greedy fashion. For details on these subroutines see also [BUILD_UPGMA (F') that takes a set F' of fragments as arguments and returns a tree and a subroutine MERGE that takes the parent node p and the set of fragments F' as argument and returns an alignment of the set of sequences represented by node p. Those two subroutines are described in the previous two subsections. A pseudo-code description of the complete algorithm for multiple alignment is given in Figure A has been constructed by removing inconsistent fragments from the set F' of the fragments that are part of the respective optimal pairwise alignments, this procedure is repeated until no new fragments can be found. In the second and subsequent iteration steps, only those parts of the sequences are considered that are not yet aligned and optimal pairwise alignments are calculated under the consistency constraints imposed by the existing alignment A.Next, a subroutine see also . Furtheranchor points the same way DIALIGN 2.2 does [N-local-decoding approach [Beside the above described improvements of the optimization algorithm, we incorporated new features into DIALIGN-TX that were already part of the original implementation of DIALIGN. DIALIGN-TX now supports 2.2 does ,15. Anch2.2 does ,6, or toapproach ,27 or otT in order to exclude low-scoring fragments from the alignment. Following an approach proposed in [T and with lower values in subsequent iteration steps. By default, in the first iteration step of our algorithm, we use a value of T = -log2(0.5) for the pairwise alignment phase, while in all subsequent iteration steps, a value of T = 0 is usedd. With a user-specified threshold of T = 2 for the first iteration step, the threshold value remains -log2 (0.5) in all subsequent steps, and with a chosen threshold value of T = 1, the value for the subsequent iteration steps is set to -log2 (0.75).DIALIGN-TX also now comes with an option to specify a threshold parameter posed in , the aliO(l3) time if l is the (maximum) length of the two sequences since all possible fragments are to be considered. If the length of fragments is bounded by a constant L, the complexity is reduced to O(l2 × L). In practice, however, it is not meaningful to consider all possible fragments. Our algorithm processes fragments starting at a pair of positions i and j, respectively, with increasing fragment length. To reduce the number of fragments considered, our algorithm stops processing longer fragments starting at i and j if the previously visited short fragments starting at the same positions have low scores. More precisely, we consider the average substitution score of aligned amino acids or the average number of matches for DNA or RNA alignment, respectively, to decide if further fragments starting at i and j are considered.An optimal pairwise alignment in the sense of our fragment-based approach is a chain of fragments with maximum total weight score. Calculating such an optimal alignment takes fast mode. This option uses a lower threshold value for the average subsitution scores or number of matches. By default, during the pairwise alignment phase, fragments under consideration are extended until their average substitution score is at least 4 for amino acids (note that our BLOSUM62 matrix has 0 for the lowest score possible) and 0.25 for nucleotides, respectively. With the fast mode option, this threshold is increased by 0.25 which has the effect that the extension of fragments during the pairwise alignment phase is interrupted far more often than by default. This option, however, reduces the sensitivity of the program. We observed speed-ups up to factor 10 on various benchmark data when using this option while the alignment quality was still reasonably high, in the sense that the average sum-of-pair score and average column score on our benchmarks deteroriated around 5% – 10% only. We recommend to use this option for large input data containing sequences that are not too distantly related. Hence, this option is not advisable for strictly locally related sequences where we observed a reduction of the alignment quality almost down to a score of zero. However in the latter case this option is not necessary since the original similarity score thresholds of 4 and 0.25, respectively, are effective enough to prevent DIALIGN-TX of unnecessarily looking at too many spurious fragments.To reduce the run time for pairwise alignments, we implemented an option called In order to evaluate the improvements of the new heuristics we had several benchmarks on various reference sets and compared DIALIGN-TX with its predecessor DIALIGN-T 0.2.2 , DIALIGNs cases the occurrence of a motive in a sequence has been omitted randomly, whereby s is the number of sequences in the sequence family. The results on IRMBASE 2 and DIRMBASE 1 now tell us how the alignment programs perform in cases when it is unknown if every motive occurs in every sequence thus providing a more realistic basis for assessing the alignment quality on locally related sequences compared to the situation in the old IRMBASE 1 where every motive always occurred in every sequence.The benchmarks on locally related sequence sets were run on IRMBASE 2 for proteins and DIRMBASE 1 for DNA sequences, which have been constructed in a very similar way as IRMBASE 1  by implaEach reference set in IRMBASE 2 and DIRMBASE 1 consists of 48 sequence families, 24 of which contain ROSE motifs of length 30 while the remaining families contain motifs of length 60. 16 sequence families in each of the reference sets consist of 4 sequences each, another 16 families consist of 8 sequences while the remaining 16 families consist of 16 sequences. In ref1, random sequences of length 400 are added to the conserved ROSE motif while for ref2 and ref3, random seqences of length 500 are added. In ref4 random sequences of length 600 are added.sum-of-pair score where the percentage of correctly aligned pairs of residues is taken as a quality measure for alignments. In addition, we used the column score where the percentage of correct columns in an alignment is the criterion for alignment quality. Both scoring schemes were restricted to core blocks within the reference sequences where the 'true' alignment is known. For IRMBASE 2 and DIRMBASE 1, the core blocks are defined as the conserved ROSE motifs. To compare the output of different programs to the respective benchmark alignments, we used C. Notredame's program aln_compare [For both BAliBASE and IRMBASE, we used two different criteria to evaluate multi-alignment software tools. We used the _compare .all other comparisons DIALIGN-TX is significantly superior to the other programs with respect to the Wilcoxon Matched Pairs Signed Rank Test [The quality results of our benchmarks of DIALIGN-TX and various alignment programs on the local aligment databases can be found in Tables ank Test . DIALIGNOn IRMBASE 2 our new program DIALIGN-TX is around 1.64 times slower compared to DIALIGN-T however it is still faster than DIALIGN 2.2, on DIRM-BASE 1 we observed that DIALIGN-TX is 4.26 times slower than DIALIGN-T (which is due to the reduced sensitivity in DIALIGN-T 0.2.2) and we also see that DIALIGN-TX is around 2.04 slower than DIALIGN 2.2. Although IRMBASE 2 and DIRMBASE 1 are constructed in a similar way we see that T-COFFEE and PROBCONS behave quite well on the protein alignments whereas the perform very poorly in the DNA case while the other methods ranked mostly equal in the protein and DNA case. Overall, we conclude from our benchmarks that DIALIGN-TX is the dominant program on locally related sequence protein and DNA families that consist of closely related motives embedded in long unalignable sequences.The results of our benchmark on the global alignment databases are listed in the Tables We have a slightly different picture in the RNA case we examined using BRAliBase II benchmark database that has an even stronger global character and is the only benchmark database that we used that does not come with core blocks. DIALIGN-TX significantly outperforms POA and all other versions of DIALIGN approach whereas it is still inferior to the global methods CLUSTAL W2, MAFFT, MUSCLE and PROBCONSRNA. The difference between T-COFFEE and DIALIGN-TX on BRAliBase II is quite small, i.e. T-COFFEE outperforms DIALIGN-TX only on the SPS whereas there is no significant different on the CS. Since MAFFT and PROBCONSRNA have been trained on BRAliBase II the dominance of those methods  is not very surprising. Regarding CPU time DIALIGN-TX is approximately 1.7 times slower than DIALIGN-T 0.2.2 and DIALIGN 2.2 on BRAliBase II.weight scores. Some modifications have been introduced, such as overlap weights [In this paper, we introduced a new optimization algorithm for the segment-based multiple-alignment problem. Since the first release of the program DIALIGN in 1996, a 'direct' greedy approach has been used where local pairwise alignments (fragments) are checked for consistency one-by-one to see if they can be included into a valid multiple alignment. In this approach, the order in which fragments are checked for consistency is basically determined by their individual  weights . Neverth weights ,5, Pöhleprogressive approach to multiple alignment introduced in the 1980s for the classical multiple-alignment problem [The optimization method that we introduced herein is inspired by the so-called  problem . We adapglobal alignment, we also used a benchmark database with simulated local homologies. The test results on these data confirm some of the known results on the performance of multiple-alignment programs. On the globally related sequence sets from BAliBASE and BRALIBASE, the segment-based approach is outperformed by classical, strictly global alignment methods. However, even on these data, we could achieve a considerable improvement with the new optimization algorithm used in DIALIGN-TX. On the simulated local homologies, our method clearly outperforms other alignment approaches, and again the new algorithm introduced in this paper achieved significantly better results than older versions of DIALIGN. Among the methods for global multiple alignment, the program MAFFT [To test our method, we used standard benchmark databases for multiple alignment of protein and nucleic-acid sequences. Since these databases are heavily biased towards am MAFFT ,22 perfoWe will conduct further studies to investigate to what extent the optimization algorithms used in the different versions of DIALIGN can be improved and which alternative algorithms can be applied to the optimization problem given by the segment-based alignment approach.GOBICS) Göttingen Bioinformatics Compute Server (at [DIALIGN-TX is online available at BICS) at  The progARS conceived the new methods, implemented the program, constructed IRM-BASE 2 and DIRMBASE 1, did the evaluation and wrote parts of the manuscript, MK and BM supervised the work, provided resources and wrote parts of the manuscript. All authors read and approved the final manuscript.


Identification of RNA homologs within genomic stretches is difficult when pairwise sequence identity is low or unalignable flanking residues are present. In both cases structure-sequence or profile/family-sequence alignment programs become difficult to apply because of unreliable RNA structures or family alignments. As such, local sequence-sequence alignment programs are frequently used instead. We have recently demonstrated that maximal expected accuracy alignments using partition function match probabilities  are significantly better than contemporary methods on heterogeneous length protein sequence datasets, thus suggesting an affinity for local alignment.We create a pairwise RNA-genome alignment benchmark from RFAM families with average pairwise sequence identity up to 60%. Each dataset contains a query RNA aligned to a target RNA (of the same family) embedded in a genomic sequence at least 5K nucleotides long. To simulate common conditions when exact ends of an ncRNA are unknown, each query RNA has 5' and 3' genomic flanks of size 50, 100, and 150 nucleotides. We subsequently compare the error of the Probalign program  to the commonly used local alignment programs HMMER, SSEARCH, and BLAST, and the popular ClustalW program with zero end-gap penalties. Parameters were optimized for each program on a small subset of the benchmark. Probalign has overall highest accuracies on the full benchmark. It leads by 10% accuracy over SSEARCH (the next best method) on 5 out of 22 families. On datasets restricted to maximum of 30% sequence identity, Probalign's overall median error is 71.2% vs. 83.4% for SSEARCH . Furthermore, on these datasets Probalign leads SSEARCH by at least 10% on five families; SSEARCH leads Probalign by the same margin on two of the fourteen families. We also demonstrate that the Probalign mean posterior probability, compared to the normalized SSEARCH Z-score, is a better discriminator of alignment quality. All datasets and software are available online.We demonstrate, for the first time, that partition function match probabilities used for expected accuracy alignment, as done in Probalign, provide statistically significant improvement over current approaches for identifying distantly related RNA sequences in larger genomic segments. The importance of RNA within cellular machinery and regulation is well established ,2. Conseoptimal local alignments, with BLAST sacrificing sensitivity for speed. Conversely, the maximal expected accuracy approach is based on suboptimal alignments. Here, sequences are aligned using posterior/match probabilities within pairwise alignments. These probabilities can be computed using partition function dynamic programming matrices, introduced by Miyazawa [SSEARCH and BLAST both search for Miyazawa  and lateMiyazawa ,14, or pMiyazawa . PartitiMiyazawa , MAFFT [Miyazawa , and MUSMiyazawa ,18) on tMiyazawa , HOMSTRAMiyazawa , and OXBMiyazawa ).While Probalign was designed for global alignment, its performance on datasets of heterogeneous length  suggestsWe specifically omit INFERNAL from this investigation for several reasons. First, and most importantly, (as discussed above) the utility of profile-sequence and structure-sequence alignment methods is limited by experimental data. At large evolutionary distances and with unalignable genomic flanks surrounding the query, which is the particular focus of this study, obtaining reliable RNA family alignments is considerably difficult. Second, the cmsearch program of the INFERNAL suite is, in part, used for constructing RFAM families from which we construct our benchmark. Additional sequences found using INFERNAL were added to the RFAM seed alignments . FinallyWe find Probalign to have overall highest accuracies on the full benchmark. It leads by 10% accuracy over SSEARCH (the next best method) on 5 out of 22 families. On datasets restricted to maximum of 30% sequence identity, Probalign's overall median error is 71.2% vs. 83.4% for SSEARCH (the next best method). This difference has Friedman rank test P-value less than 0.05. Furthermore, on these datasets, Probalign leads SSEARCH by at least 10% on five families whereas SSEARCH leads Probalign by the same margin on two families out of a total of fourteen. We also demonstrate that the Probalign mean posterior probability, compared to the normalized SSEARCH Z-score, is a better discriminator of alignment quality. The Probalign mean posterior probability has Receiver Operator Characteristic (ROC) area under curve of 0.834 compared to 0.806 of the normalized SSEARCH Z-score.Note that the performance of RNA homology search programs was examined previously by Freyhult et. al. . Their bWe computed the mean error of each method within each RNA family by averaging over all pairwise alignment scores belonging to that family. We then computed the overall error of each method as the average score across all families.The full benchmark containing query RNAs with flanks constitute 13,716 datasets. We exclude HMMER when unalignable flanks are present since these will only confound the model. Table Table Column two of the table lists the Probalign and SSEARCH error on datasets restricted to maximum 30% sequence identity. There are fourteen families containing datasets that satisfy this criterion. Out of the total fourteen, Probalign leads by at least 10% on five families whereas SSEARCH leads Probalign by at least same margin on two families.In Table In order to compare the programs against HMMER, we separate from the benchmark those datasets with no query RNA flanks . Each of these query RNAs can be used to specify a model in HMMER since misleading flanks are now absent. From Table distinct RFAM families . The size of the false dataset is 13,716, exactly the same as the real dataset used above. Concatenating the real and false datasets results in 27,432 target-query pairs that were subsequently aligned using both methods. An alignment on a false positive dataset or an alignment with 100% error on the benchmark is classified as a false positive. An alignment on the benchmark with less than 100% error is classified as a true positive. A good discriminator would have a high value on alignments with high accuracy and low value on alignments with 100% error on benchmark datasets or on the false positive dataset. In this case we are interested in the quality of the Probalign mean column posterior probability and the SSEARCH normalized Z-score as alignment discriminators.In order for the evaluated methods to be of practical utility in ncRNA searches, alignments found when there is no target-query match , should be of poorer quality than the alignments above where target-query matches were always present. To assess the discriminative ability of Probalign and SSEARCH (the two best scoring methods above), we generated a false dataset of query-target pairs where the query and target were randomly selected from ad hoc threshold. For example, we may choose to classify all alignments above 0.5 Probalign mean column posterior probability to be correct hits and incorrect otherwise. In order to eliminate the arbitrariness of such a definition, we employ Receiver Operating Characteristic (ROC) analysis. Along the ROC curve, true and false positive prediction values are plotted for a series of less stringent thresholds. The further the ROC curve is to the left, the better the method is; the diagonal indicates a method based on random guesses. As can be clearly seen in Figure In order to evaluate a discriminator, we need to set an The current Probalign implementation is not as sophisticated as its SSEARCH counterpart, and therefore is much slower in comparison to the SSEARCH time. However, in practice it never takes more than a few seconds on any of our datasets. The average Probalign running time on the benchmark is 5.4 seconds compared to 0.04 seconds of SSEARCH, 0.5 seconds of ClustalW, 0.003 seconds of BLAST, and 0.14 seconds of HMMER (hmmsearch). These running times were computed on 2.4 GHz AMD Opteron 64 bit machines.A standard technique for discovering new RNAs, in the absence of queries, is to align genomic fragments and search the alignment for significant structural conservation. QRNA  RNAz 2727 and MSSeveral improvements are currently underway to Probalign. A full Probalign-local implementation would include a Smith-Waterman implemenation of posterior probability local alignment, as done in the Proda  program.1/2) with a 1.5 factor slowdown using memory reduction techniques used for HMM-based alignment programs [In big-O notation Probalign's worst-case running time and memory requirements for pairwise alignment is O(mn) where m and n are the lengths of the input sequences. Probalign's memory requirements can be improved to O has been shown to be a better indicator of alignment quality than the standard SSEARCH Z-score.We began by extracting all 26 RFAM  seed aliFor each of the initial 26 RFAM seed multiple alignments, we randomly select a maximum of 350 pairwise alignments. In families where there are less than 350 total pairs, we consider them all.query and the aligned homologous RNA is the target "hidden" in the genome. In order to make our dataset challenging enough, we exclude datasets where the genomic sequence is shorter than 5000 nucleotides.Every RNA sequence in RFAM seed is cross-linked to a genomic sequence in EMBL . For eacThe attached genomic flanks may contain additional related RNAs of the same family as the query and the target (to which the flanks were attached). This means that two different correct alignments are possible. To keep things simple, we exclude such datasets and ensure that each query-target alignment is unique. For each dataset we built a profile from the RFAM family alignment annotated with consensus secondary structure using the cmbuild program of the INFERNAL suite. We then ran the cmsearch program of the INFERNAL suite on the genomic sequence of the dataset and excluded it entirely from the benchmark if more than one hit above a bit score of 30 was reported.The pruning process yielded a total of 3,429 pairwise alignments distributed  among 22 RNA families. As mentioned earlier, all the datasets in four families failed to meet our length and uniqueness criteria just described. This subsequently leaves us with 22 families in the end. The 22 families and their characteristics can be found in Additional file To simulate practical conditions where the exact 5' and 3' ends of ncRNAs are unknown, we took each dataset in our benchmark and produced three similar versions. However, in each of the three versions we added real 5' and 3' genomic flanks of size 50, 100, and 150 nucleotides to the query RNA of each dataset. By cross-referencing each RNA sequence to the original genomic version in EMBL we were able to obtain proper real genomic flanks and hence did not need to simulate artificial ones. Subsequently, the size of our benchmark increased four-fold from 3,429 to 13,716. We remove gaps from each alignment and use the flanked query and target genomic sequences as input to each program.The full benchmark is available online . Also avWe used a subset of the benchmark with query RNA flanks of size 100 nucleotides for training the program parameters. For each of the 22 divergent families we selected 25 random datasets. If the family contained a total of less than 25 pairwise alignments we included all in the training set. The final training set contained 498 pairwise alignments and can be found on the website for this paper .match partition function matrix: Z-matrices also need to be set appropriately in line with the two changes. However, since we use zero end-gaps, this is automatically taken care of. We direct the reader to Additional file We used a modified version of the Probalign beta 1.0 program more attuned to local alignment. We make two modifications to the partition function matrices. They follow from analogous standard dynamic programming recursions for local alignment and can also be found in Muckstein et. al. . First, We use the bl2seq program (current version 2.2.16) of the NCBI BLAST suite in our experiments. In our terminology we use BLAST to represent the bl2seq program of the suite. BLAST returns local alignments that may not include the entire query. In order to measure the error correctly, we require the entire query aligned to the genomic sequence (see Prediction Error Subsection below). We accomplish this by extending the local alignment in either direction until the full query is aligned to the genomic sequence. We also evaluate only the highest E-value BLAST hit. We actually tested the performance of the second hit outputted on each dataset and found that it had much worse error than the first. This is expected since each pairwise alignment in our benchmark is unique. We optimize BLAST gap parameters using both its default scoring matrix (+3/-1) and +5/-4 (the same one as used in SSEARCH). In order to avoid excessive scenarios where BLAST does not return an alignment, we set the minimum word size to 4. We use the +5/-4 matrix for BLAST since it performs better than the default (both with optimized parameters) on our training benchmark.We use the current SSEARCH release version 3.4t26 in our experiments. SSEARCH is a local alignment program and may not contain the entire query aligned to the genome (necessary for correct error computation). This problem can be fixed using the same BLAST treatment described above. With the -a option, however, SSEARCH returns alignments of both query and genome sequence in their entirety. In this case we find the accuracies to match those calculated otherwise, which is by fixing the alignments if necessary. Thus, without loss of any accuracy we run SSEARCH with -a enabled. We optimize the SSEARCH gap open and gap extension penalty parameters on the training benchmark. Like BLAST, we also found the second SSEARCH hit to be significantly much worse off than the first one.We use ClustalW version 1.83 for our experiments. ClustalW, like Probalign, returns one global alignment of the complete query against the genomic sequence. We set the terminal gap (end-gap) penalties to zero. We optimize ClustalW gap parameters on the default ClustalW scoring matrix of +10/-9 and the SSEARCH +5/-4. However, the ClustalW default matrix optimal gap parameters perform better than the optimized +5/-4 matrix.We use HMMER version 2.3.2 in our experiments, the most current at the time of writing this paper. HMMER is designed for profile-based search that requires family alignments. Since we are interested in studying query RNA genomic search, particularly for divergent and hard cases where family alignments are not reliable, we use the single sequence RNA query for constructing the HMMER model. We use the hmmbuild program of the HMMER suite to build local alignment models (with the -f and -s options) and global alignment models (with the -g option). We then use the hmmsearch program on the training benchmark and each of the three models to search the genomic sequence for homologs of the query RNA. We find the local alignment -f and -s models to be equally the best performing and use -f in our experiments. Like BLAST and SSEARCH, HMMER local alignments may not contain the full query aligned to the genome. Therefore, we fix it in the same manner described above in the BLAST option.Table P(xi ~ yj) is the posterior probability of the ith nucleotide of sequence x aligning to the jth nucleotide of sequence y. More details about how this is computed and the Probalign method in general can be found in Additional file The Probalign mean posterior probability is defined by Equation 1. The SSEARCH Z-score and E-value are standard statistical measures of alignment reliability ,33. The In order to measure the prediction accuracy of the above two measures we created a set of false positives. For each dataset in our benchmark, we create a false positive one by replacing the genomic sequence with one selected from a different random dataset. Now, each false positive dataset contains a query RNA and a genomic sequence containing a target RNA from a different family. We expect any alignment reliability measure to have a low value on these datasets. We make these datasets available online .We are interested in finding out how much of the target RNA (which lies in the genomic sequence) is aligned to the query, excluding the query flanks. As described above, for BLAST, SSEARCH, and HMMER, all of which return local alignments, we extend the query-genome alignment in both directions until the entire query, but not its flanks, is matched to the genomic sequence. This improves sequence coverage, reduces the false negative rate, and also allows a fair comparison to Probalign and ClustalW, both of which return global alignments of the entire sequences. For each method, we take the part of the genomic sequence aligned to the query in its alignment, and measure the false positive as the number of nucleotides in this region that are not in the target RNA. Similarly, we measure the false negatives as the number of nucleotides in the target RNA that are not in the genomic region aligned to the query . See Figure Statistically significant performance differences between the various alignment methods are calculated using the Friedman rank test . This isWe conduct an ROC analysis  to studyRoshan conceived of the study and developed the benchmark. Livesay and Chikkagoudar contributed to the execution of the study and writing of the paper. All authors have read and approved the final version of the manuscript.Supplementary material. Characteristics of RNA families used in this study, detailed description of Probalign, and command line parameters of programs used.Click here for file


The dynamic motions of many proteins are central to their function. It therefore follows that the dynamic requirements of a protein are evolutionary constrained. In order to assess and quantify this, one needs to compare the dynamic motions of different proteins. Comparing the dynamics of distinct proteins may also provide insight into how protein motions are modified by variations in sequence and, consequently, by structure. The optimal way of comparing complex molecular motions is, however, far from trivial. The majority of comparative molecular dynamics studies performed to date relied upon prior sequence or structural alignment to define which residues were equivalent in 3-dimensional space.Here we discuss an alternative methodology for comparative molecular dynamics that does not require any prior alignment information. We show it is possible to align proteins based solely on their dynamics and that we can use these dynamics-based alignments to quantify the dynamic similarity of proteins. Our method was tested on 10 representative members of the PDZ domain family.As a result of creating pair-wise dynamics-based alignments of PDZ domains, we have found evolutionarily conserved patterns in their backbone dynamics. The dynamic similarity of PDZ domains is highly correlated with their structural similarity as calculated with Dali. However, significant differences in their dynamics can be detected indicating that sequence has a more refined role to play in protein dynamics than just dictating the overall fold. We suggest that the method should be generally applicable. It is well established that conformational flexibility plays a key role in the biochemical functions of proteins ,2. ProteMolecular Dynamics (MD) simulations can be used effectively to explore the conformational energy landscape accessible to proteins ,11 givinet al. [et al. [et al. [If the dynamics of non-identical proteins is compared, a mapping between the different structures is often required. Therefore a common point of previous comparative MD studies of homologous proteins is that they use prior sequence or structure alignments to find residue equivalencies between the proteins. For example, to compare the fluctuation of different cold-active enzymes, Spiwok et al.  used str [et al.  performe [et al.  who simu [et al.  and the  [et al. . In thesNevertheless, if dynamically equivalent regions do not match to sequentially and structurally similar regions, alignments can mislead the comparison of protein motions. Recently, Zen et al ,22 develet al. [The method is tested on members of the PDZ domain family. PDZ (post-synaptic density-95/discs large/zonula occludens-1) domains are common protein-protein interaction domains , most ofet al.  have proi and residue j are fluctuating relative to each other byWe introduce a novel way to characterize the backbone dynamics of proteins. The underlying idea is that in a moving protein each residue is fluctuating relative to all other residues, therefore a detailed description of motion should capture all inter-residue fluctuations. While static structures are often characterized by the matrix of inter-residue distances (i.e. the distance matrix), this representation is not applicable for a moving protein in which inter-residue distances are constantly changing. It is possible, however, to characterize the relative motion of any two residues by the distribution of their distance over time. We measure the extent to which residue Fij is calculated as the standard deviation of the distribution of Dij (distance of the two residues) in the whole conformational ensemble generated by MD simulation. In this initial investigation we only consider distances between Cα atoms, but the technique can easily be extended to a more detailed description of each amino acid residue. The standard deviation of the distance distribution reflects how much the two residues fluctuate relative to each other. Fij values are calculated for each residue pair and are collected into a matrix denoted by F, which we will refer to as the Dynamic Fingerprint Matrix (DFM). Similarly to a distance matrix that characterizes a single conformation, a dynamic fingerprint matrix characterizes an ensemble of conformations.  aligns residue α (k) of protein A with residue β (k) of protein B. Thus each pairwise alignment can be characterized by an  pair. Let FA and FB be the DFMs of the two proteins. The  alignment define a submatrix of size of |α|×|α| of both DFMs. The  entries of the two submatrices are given byWhere a prior alignment is known, the comparison of DFMs is straightforward. Given a pairwise sequence alignment of protein A and B, let α and β be the index vectors of the aligned residues of sequence A and B, respectively. That is, the i, j) entries of the two submatrices are considered equivalent as they describe the fluctuations of equivalent pairs of residues.Note that the two submatrices describe the pairwise fluctuations of the aligned residues only. The  alignment as:where each pair of equivalent matrix entries are compared one-by-one and their contribution to the overall score is given bywhereis the relative difference of the two equivalent matrix entries.s is an S-shaped logistic function that assigns positive score (s+) to highly similar matrix entries and negative score (s-) to highly dissimilar entries  over which s turns negative. The relationship between t and parameter ω of s is discussed in Additional file s less dependent on the cut-off parameter t. Since s is associated with a match column pair in the alignment, it will be referred to as the Pairwise Match Score (PMS) of columns i and j. pair corresponding to the maximal similarity score. Let  be the pair of index vectors for which SAB is maximal. SAB is then called the dynamic similarity score of protein A and B and is simply denoted by SAB. The sequence alignment problem is hereby transformed into a matrix alignment problem. Structural alignment algorithms Dali [SAB we employ a simulated annealing protocol (see Methods).In the previous section we have introduced how to compare the DFMs of two proteins using a prior sequence/structural alignment. Our main goal, however, is to find the optimal alignment of two proteins based on solely their DFMs. Note that it is the opposite strategy of previous comparative MD studies which relied upon prior alignments. We aim to find the hms Dali  and MatAhms Dali  aim to si, the sum of PMS scores with respect to all other match columns will be referred to as the Single Match Score (SMS):Although the PMS scores concerning a given match column depend on the other match columns in the alignment, it is useful to compare the total contributions of each individual column to the alignment score. For match column In other words, the SMS of a match column is the score by which the total alignment score decreases in case of removing that match from the alignment. Matches of negative SMS values are beneficial to remove in optimizing the alignment. Hence the optimal dynamics-based alignment contains only positions of non-negative SMS values. Either studying a prior  or a dynamics-based alignment, the SMS-profile represents our confidence in each aligned pairs of residues.et al [Before we discuss the comparative analysis, we first demonstrate that the DFM protocol is appropriate by characterizing the dynamics of the third PDZ domain (PDZ3) of PSD-95 (Postsynaptic Density Protein 95) from Rattus norvegicus. PSD-95 plays an important role in controlling synaptic strength and plasticity in the central nervous system . The 110et al  who perfkth row of the DFM as the dynamic profile of residue k. The dynamic profile of Phe325, for example, shows us that it is the β1/β2 loop and the α2-helix which fluctuates the most relative to this residue  alignment. In this case, the motion of the subsets of residues defined by the prior alignment is compared. To test this option, we used the Needleman-Wunsch alignment as a prior alignment, which resulted in a dynamic similarity score of -132.8. The optimal similarity score found for this example is 1307.3, and the extreme non-optimality of the sequence based alignment score illustrates that conserved sequence positions can match dynamically dissimilar subsets of residues. Accordingly, 46 per cent of the columns of the collapsed Needleman-Wunsch alignment have negative SMS. The less-matching region  appears to be the α2-helix, explaining why this region is excluded from the optimized DFM-alignment.p-value of 9·10-11 using the significance analysis framework described in Methods. Likewise the alignment algorithm has found significant dynamic similarities between other pairs of PDZ domains. The p-values are summarized in Table p-value < 0.05) dynamics.The dynamic similarity score of the PDZ domain of nNOS and PDZ3 of PSD-95 is S = 1307.3, which was converted to a 1be9, 1qau, 1qav, 1ihj and 2f0a) that are better-connected in the dynamic similarity graph. Out of the 10 possible links between these structures 8 are present in the graph. Two additional links are found between 2f0a/1x5r and 1ihj/1fc6. Three structures , however, do not have significant dynamic similarity with any other structures. Looking for structural explanations for these differences, we examined the pairwise Dali Z-scores between the 10 domains  appears to be fully connected in the graph, while two additional links are found between 1fc6/1y8t and 1ihj/1fc6. Two domains (1k32 and 2i6v) are not linked to any other structures.It is interesting to note that the dynamic similarity shows differences between different structures. We can see a cluster of five proteins (1x5r) between the well-connected clusters in the two graphs suggests a topology-preserving mapping between the structure space and dynamics space of PDZ domains. There appears to be a strong correlation (0.82) between the raw dynamic similarity scores and Dali Z-scores considering all 45 protein pairs  are from multicellular organisms (metazoa), while the other 4 proteins are from unicellular species. The structural difference between PDZ domains from simple and complex organisms is well-known. First recognized by o et al.  and exemo et al. ,42, PDZ MD simulations are subject to sampling problems. In order to assess whether the simulations have run long enough to provide a reasonable picture of the dynamics we examined the convergence of the DFM patterns. We ran five 20 ns simulations of the same protein (PSD-95 PDZ3) using different random seeds for the initial atomic velocities. The similarities of each pairs of DFMs resulted from the different MD runs were measured by the matrix alignment algorithm. Naturally, the five DFMs were not perfectly the same, but the similarity between each pair was highly significant  that still allows for significant differences in dynamics to be apparent. This may explain why methods such as elastic network models seem to work for predicting large-scale conformational changes, but that the detailed differences between protein motions can still be significant. With respect to the PDZ domains we have shown that the majority of motions within the protein are similar, but additionally that we can detect differences (located at the binding interface) that are significantly different and could not be detected by the usual sequence or structure based alignment methods. We have developed a method for measuring dynamic similarity between proteins with a simple algorithm. As the method is capable of detecting precise differences in the dynamics between structures it could also be used to assess the influence of ligand-binding on the dynamics of protein structure. We are currently exploring that aspect as well as developing further improvements on the algorithm.+ and Cl- ions to a concentration of 150 mM. After 200 ps of restrained MD, 20 ns of unrestrained MD was performed with the GROMACS software package [We carried out all-atom MD simulations of 10 representative members of the PDZ domain family  in a reasonable time, we have developed a heuristics approach based on the multiple restart Simulated Annealing (SA) method. The algorithm performs an MCMC (Markov chain Monte Carlo) search in the space of  pairs. The Markov chain starts from a random initial alignment, and in each step the alignment is modified by inserting or removing one residue pair. We use the Metropolis acceptance criterion [To find a good approximation for the global maximum of riterion  to decidriterion . The whoTo assess the statistical significance of dynamic similarity scores between PDZ domains, we have performed 20 ns MD simulations of 12 evolutionarily and functionally unrelated proteins of different sizes referred to as the Reference Set  and σ(L) functions, where μ is the location parameter, σ is the scale parameter of the Extreme Value Distribution and L = LALB is the product of the two sequence lengths.Since the optimal alignment score of two proteins is the maximum of the scores of their possible alignments, it follows a type I Extreme Value Distribution, as shown in Additional file μ (L) and σ(L) in a wider interval, not only the full DFMs but their submatrices of different sizes were also aligned. A total number of 2970 dynamic alignments were performed. Regression lines were fitted to the measured points of μ (L) and σ(L) and are used to approximate the parameters of the background distribution (Additional file p-value of a dynamic alignment of protein A and B is therefore given byTo measure L = LALB, and LA and LB are the lengths of protein A and B, respectively. (For a more detailed explanation of the applied significance analysis framework, see Additional file p = 0.05 to detect significant dynamic similarities between proteins.where PDZ: post-synaptic density-95/discs large/zonula occludens-1; DFM: dynamics fingerprint matrix.JH and PCB designed the research. MM performed the research. MM, RL and PCB analyzed the data. MM, RL and PCB wrote the paper. All authors read and approved the final manuscript.Supplementary Information. Contains detailed information about the actual algorithms employed, data sets used, and extended interpretation of the data presented in the main manuscript.Click here for file