A structure alignment method based on a local geometric property is presented and its performance is tested in pairwise and multiple structure alignments. In this approach, the writhing number, a quantity originating from integral formulas of Vassiliev knot invariants, is used as a local geometric measure. This measure is used in a sliding window to calculate the local writhe down the length of the protein chain. By encoding the distribution of writhing numbers across all the structures in the protein databank (PDB), protein geometries are represented in a 20-letter alphabet. This encoding transforms the structure alignment problem into a sequence alignment problem and allows the well-established algorithms of sequence alignment to be employed. Such geometric alignments offer distinct advantages over structural alignments in Cartesian coordinates as it better handles structural subtleties associated with slight twists and bends that distort one structure relative to another.The performance of programs for pairwise local alignment (TLOCAL) and multiple alignment (TCLUSTALW) are readily adapted from existing code for Smith-Waterman pairwise alignment and for multiple sequence alignment using CLUSTALW. The alignment algorithms employed a blocked scoring matrix (TBLOSUM) generated using the frequency of changes in the geometric alphabet of a block of protein structures. TLOCAL was tested on a set of 10 difficult proteins and found to give high quality alignments that compare favorably to those generated by existing pairwise alignment programs. A set of protein comparison involving hinged structures was also analyzed and TLOCAL was seen to compare favorably to other alignment methods. TCLUSTALW was tested on a family of protein kinases and reveal conserved regions similar to those previously identified by a hand alignment.These results show that the encoding of the writhing number as a geometric measure allow high quality structure alignments to be generated using standard algorithms of sequence alignment. This approach provides computationally efficient algorithms that allow fast database searching and multiple structure alignment. Because the geometric measure can employ different window sizes, the method allows the exploration of alignments on different, well-defined length scales. As the number of protein structures continues to grow, structure comparison techniques have become an increasingly crucial bioinformatics tool. Because protein structures evolve more slowly than protein sequences, structure comparison can be used to assess distant evolutionary relationships and common functions for pairs that do not have high sequence similarity (cf. ). StructRigid body superpositions with distance metrics are less than optimal because subtle twists or bends in a protein structure can have a profound influence on the scoring of the alignment. These are often corrected by considering local alignments or introducing gap penalties. Recently, a number of new algorithms have been developed that allow for the flexible alignment of local fragments ,9. A parThe use of such measures is similar in spirit to earlier work on the differential geometry of proteins  into bins and assigning each bin a letter in the alphabet. This procedure allows standard sequence alignment algorithms to be used to compare the geometric profiles. Using this approach, we have successfully "re-sequenced" all 52,087 proteins available in the PDB at the time of this work and have stored them into our own database for quick access. Using a block alignment approach identical to that used in calculating the BLOSUM substitution matrix, a scoring matrix for substitutions in the geometric alphabet was determined. Using this matrix (referred to as TBLOSUM) and our resequenced structure data bank, standard sequence alignment methods were used to perform structure alignments. To validate this approach, the performance of the local Smith-Waterman alignment (TLOCAL) and the CLUSTALW (referred to as TCLUSTALW) were used to perform high quality pairwise alignment and multiple structure alignment, respectively. This performance compares favorably with existing methods.Using a database of sequences encoded from writhing numbers and a block scoring matrix (see Methods), several test proteins were selected to optimize the performance of TLOCAL and compare it to other methods. Alignments of ten "difficult" pairs of structure  were expTable 1 shows the performance of the TLOCAL algorithm for different size windows for the ten "difficult" pairs see . This taRMSD ∝ N1/3 [Rg also scales as: Rg ∝ L1/3 where L is the protein length [reduced AFPRMSD is defined as:In Table 2, the quality of the alignments as measured by AFPRMSD is compared for TLOCAL's (window size of 5), CE and FATCAT see . Direct D ∝ N1/3 . The radn length . From tha0 to 1 Å. This quantity is now used in Tables 1-3 to compare all alignments of different lengths. In all cases, the reduced AFPRMSD shows that TLOCAL outperforms FATCAT in all cases and CE in 6 out of 10 cases [see Additional file and for simplicity we set As an additional assessment of the performance of the local topological alignment algorithm, the performance on the alignment of structures with flexible or hinged regions was determined. The difficulty in aligning proteins with hinged regions motivated the development of new structural alignment programs; FATCAT  and FlexIn addition to pairwise alignments performed by TLOCAL, the performance of the multiple structure alignment program (TCLUSTALW) was also examined. To evaluate the performance of TCLUSTALW, a family of protein kinases was aligned and the identified conserved regions were compared with those determined previously by a hand alignment. These 25 sequences include serine/threonine and tyrosine kinases provided by Scheeff and Bourne  that areThe comparison of hand alignments and those resulting from TCLUSTALW are shown side-by-side in Table 4 see . The aliIn this work, a geometric profile of an individual protein is created by calculating the writhing number of consecutive segments (sliding window) along the protein chain. The profile is then encoded into a geometric alphabet by associating a range of numerical values with different letters of the alphabet. This alphabet is determined by observing the histogram of the frequency of writhing values in all segments of all the proteins observed in the PDB. This histogram is partitioned into bins and a letter from the geometric alphabet is associated with each bin. The numerical range of the bins is adjusted so that each bin contains the same number of segments. Thus, if a segment is chosen at random, it would have an equal chance at falling into any one bin. Consequently, each letter in the "geometric alphabet" has an equal chance of occurring in a protein structure. The motivation of partitioning the histogram in this fashion is to maximize the information content of the alphabet. Other ways of encoding the writhing number could conceivably be more effective. For instance, some geometric features may be more relevant or distinctive than others and it might be important to carefully delineate the values of the writhing numbers associated with these features. Such level of detail has not been investigated to date and lacking such information, the maximum information entropy approach is taken as a good first approach to encoding the local topological information in the protein profile.A second important issue is the size of the alphabet used to encode the writhing number, a continuous variable. In principle, the smaller the bin range the greater the information content. In the limit of the bin size approaching the inherent error in the writhing number, more information will no longer be captured by decreasing the bin size. This error limit could be obtained by the propagation of the experimental error of the α-carbon atom positions used in the calculation of the writhing number. However, in mapping the structural alignment problem into a sequence alignment problem, not only is an accurate encoding required but also an accurate scoring system must be obtained. As the alphabet is expanded, more data is needed to accurately determine the values of the substitution matrix. Additionally, the programs calculating alignments will become increasingly computationally intense. There will be a trade off between increasing resolution of the bins of the histogram and the concomitant loss of scoring accuracy and increase of computation intensity. Again, these issues have not as of yet been explored in depth. Our strategy has been to adopt the twenty letter alphabet common to existing protein sequence alignment and to investigate the performance of the topological alphabet and scoring system under these familiar conditions. Keeping with these conditions, the gap penalties are treated as adjustable parameters and are generally in the range of values used for sequence alignment.Given these conditions, the structure alignment matches local geometric propensities between different proteins and aligns the topological sequence to optimize the score from these propensities. As such, no Cartesian spatial associations can be directly assigned to these alignments. This topological association rather than a direct physical association is at the heart of the method and allows the alignment to avoid the difficulties with spatial alignment of rigid bodies as exemplified by the problem with hinged proteins. While the geometric alignment method does not allow for the familiar three-dimensional viewing employed in most existing structural alignment algorithms, this approach directly addresses the deeper issue of comparing similar structural regions that are offset by intervening differences. The problem of properly assigning alignments on either side of a hinge region is then approachable by this method.Difficulties such as those presented by hinged proteins call to question the very nature of the structure alignment problem. Several authors have suggested that the alignment problem as commonly posed is not a well-defined problem and may not have an optimal solution (cf. ). AlignmTo allow comparison with methods that use distance metrics as a measure of alignment quality, we employed the device of identifying AFPs from the topological alignment and using these segments as rigid bodies for a local structural alignment. The RMSD could then be calculated from the sum of all these local alignments. Using this measure, we observe that the Smith Waterman topological alignment, TLOCAL, compares favorably with CE and with FATCAT for both "difficult" protein pairs and for hinged proteins. This demonstrates the versatility of the method in handling situations that have traditionally been problematic for structure alignment methods. Despite the good performance with the AFPRMSD distance metric, one must bear in mind that such metrics are not optimized by the topological alignment and that this method is a distinctly different from distance-based alignment methods.In addition to the versatility of handling pairwise alignments, the topological alignment method can easily be extended to areas of structural bioinformatics that have traditionally been very difficult because of their computational intensity. Two of these include fast database searching and multiple structure alignment. Our results using TCLUSTALW are particularly encouraging with the example of the alignment of TPK family members. Members of the TPK family all contain a Universal Core Domain consisting of a small, mostly β-sheeted N-terminal subdomain and a larger mostly α-helical C-terminal subdomain . Within This work shows initial encouraging results for developing a suite of structure alignment software tools based on a geometric encoding of protein structures. With a limited exploration of the parameters of the method, competitive performance of pairwise alignment has been demonstrated. Additionally, a computationally efficient and accurate multiple structure alignment has been achieved. The advantage of this method over other approaches is that it performs alignments on a well-defined length scale as dictated by the sliding window employed in generating the geometric alphabet. Current work is extending the method to rapid database searching using SBLAST, the structural equivalent of BLAST. Additional work will also focus on developing a range of substitution matrices based on different block and evolutionary models. Also, a more systematic exploration of alphabet size and segment size is currently underway. Thus, there is significant opportunity to further optimize this unique set of structural alignment software tools.n using the experimentally determined three-dimensional coordinates of the α-carbon atoms in the protein chain. These n coordinates form a piecewise linear or polygonal curve on n-1 edges, which precludes the use of the usual definition of writhing number as an integer valued quantity. The number n of α-carbons whose coordinates are used in the calculation is the window size since the writhing number is computed for each consecutive window containing n contiguous α-carbons along the protein chain. The technique used for calculating the number is adapted from previous work [r13, r14, r23, and r24, as seen in Figure r12 and r34 is right or left handed, the writhing number is positive or negative.The writhing number can be calculated for chains of arbitrary length ous work  that calWr of a segment of length N is given byTo handle polygonal curves with more than four points, the writhing numbers for all the distinct pairs of vectors are added together. Thus, the writhing number wherei,j =  + arcsin + arcsin + arcsin)·sign     (3)Ωandri,i+1 representing the vector between points i and i+1. The double summation is over all pairs of vectors with no common points and N is the number of points in the polygonal segment. In this work, segments (or window sizes) of 4, 5, 6 or 10 points (α-carbon atoms) were investigated. The right- or left-handedness of the crossing of the two segments is determined by sign ·ri,j+1). Larger positive or negative values of Wr indicate a greater degree of the curvature.with I of the alphabet. Using Shannon's definition of information entropy, IUsing Equation 2, the writhing number for each window was calculated for all PDB proteins available from the RCSB Data Bank. The frequency of occurrence of writhing numbers calculated using a sliding window of 4, 5, 6 and 10 residues is shown in Figure pi = pj, where pi is the probability that an arbitrary writhing number is assigned to the ith letter of the alphabet. Using the writhing number bins and their corresponding letters, all PDB proteins were encoded into the "geometric alphabet". The encoding of writhing numbers into a geometric alphabet ignores the identity of the amino acids themselves.the entropy function is maximized when A substitution matrix was calculated to score alphabet substitutions when comparing proteins structures encoded by the geometric alphabet. This matrix is referred to as TBLOSUM and was determined from multiple sequence alignments of closely related proteins found in the PDB. Using their SCOP classification, 44,234 proteins were grouped into 589 families as defined by their SCOP lineage (a list of these families can be obtained upon request to the authors). Only those families consisting of more than 20 members were considered. These proteins were aligned using CLUSTALW based on their original amino acid sequences using the default BLOSUM62 matrix, a gap opening penalty of 4 and a gap extension penalty of 1. Following the alignment, the geometric alphabet was superimposed upon the sequence. The statistics of geometric alphabet substitutions were determined for alignment blocks. The transitional frequencies for all possible transitions are given as:XY, assuming that alphabet pairs, X, Y, occur randomly with the members of a pair being proportional to their respective alphabet frequency. The score for any transition is the negative log-ratio of the observed frequency of the transition to the expected frequency of the transition, derived in the same manner of a BLOSUM substitution matrix:These transition frequencies for each amino acid pair are summed across all blocks for all aligned families. The frequency of members of the alphabet is obtained by simply summing over respective transition frequencies. These single alphabet frequencies are used to calculate the expected number of transition frequencies, eIf the transition between i and j occur more frequently than random, it is given a negative score. However, if the transition occurs less frequently than random, the transition is assigned a positive value. Figure Pairwise geometric alignments using the local dynamic programming algorithm TLOCAL optimize the alignment score based on the new scoring system (TBLOSUM). As previously noted, this approach to protein alignment is not intended to minimize global RMSD. Rather, it aligns regions of the proteins that show similarity in local topological profiles and does not allow a direct Cartesian rendering of the alignment. To allow for a comparison of our method with other alignment techniques, we sought a simple way to compute a RMSD for an alignment based on the topological alignment. We used the topological alignment to identify aligned fragment pairs (AFPs). The RMSD of the AFPs are computed for any pair containing at least four aligned pairs. As an example, we consider the following:VNLDW--Q-QWTWTPLDWOPQRRWSYFor the five pairs making up the first AFP and the four pairs in the third AFP, we compute a composite RMSD score, but for the single pair of Qs in the middle, no RMSD can be computed and these are not considered in our AFP RMSD calculation. The RMSD values for the AFPs are calculated using the UCSF Chimera package from the Resource for Biocomputing, Visualization, and Informatics at the University of California, San Francisco, which performs rigid translations and rotations to minimize the RMSD between the aligned residues of a pairwise alignment. We calculate RMSD for each AFP. The score for each block is squared and multiplied by its length in aligned pairs. The resulting numbers are summed and divided by the total number of aligned pairs in all the AFPs used. The square root of this number is taken as RMSD of the alignment. This procedure was applied to the CE alignments, as well as the TLOCAL alignments. One must bear in mind that CE was not designed to minimize the RMSD calculated in this fashion and is not optimized for this scoring function.All alignments were performed using open source versions of the Smith-Waterman dynamic programming algorithm and CLUSTALW. The run time for these applications do not differ from those found in sequence alignment applications. The computationally intense aspect of the work is the encoding of the PDB coordinates into a library of geometric sequences. At the time of this work, the library consisted of 52,087 proteins with a database length of 15,072,799 amino acids. For a window size of 4, cpu run time was 4.71 hours. For a window size of 10, the run time was 98.76 hours. All results were obtained on an IRIX64 server with 16 CPUs with 14G available memory and 128 M swap.AR worked on pairwise alignments and comparison to other methods. PC worked on multiple structure alignments. AR and PC worked on coding of writhe numbers and PC worked on libraries. GD provided the original impetus for the project and oversaw the project.Comparison of topological alignments for different window sizes for a group of "difficult" proteins.Click here for fileComparison of different alignment methods for "difficult" proteins.Click here for fileComparison of the effect on window size (TLOCAL) and alignment method on alignment scores for hinged proteins.Click here for fileMultiple sequence alignment of the kinase superfamily - Comparison of topological MSA with hand MSAClick here for file


Two central problems in computational biology are the determination of the alignment and phylogeny of a set of biological sequences. The traditional approach to this problem is to first build a multiple alignment of these sequences, followed by a phylogenetic reconstruction step based on this multiple alignment. However, alignment and phylogenetic inference are fundamentally interdependent, and ignoring this fact leads to biased and overconfident estimations. Whether the main interest be in sequence alignment or phylogeny, a major goal of computational biology is the co-estimation of both.We developed a fully Bayesian Markov chain Monte Carlo method for coestimating phylogeny and sequence alignment, under the Thorne-Kishino-Felsenstein model of substitution and single nucleotide insertion-deletion (indel) events. In our earlier work, we introduced a novel and efficient algorithm, termed the "indel peeling algorithm", which includes indels as phylogenetically informative evolutionary events, and resembles Felsenstein's peeling algorithm for substitutions on a phylogenetic tree. For a fixed alignment, our extension analytically integrates out both substitution and indel events within a proper statistical model, without the need for data augmentation at internal tree nodes, allowing for efficient sampling of tree topologies and edge lengths. To additionally sample multiple alignments, we here introduce an efficient partial Metropolized independence sampler for alignments, and combine these two algorithms into a fully Bayesian co-estimation procedure for the alignment and phylogeny problem.a-posteriori (MAP) phylogenetic tree, and for the posterior decoding alignment. Estimates for the evolutionary tree and multiple alignment are augmented with confidence estimates for each node height and alignment column. Our results indicate that the patterns in reliability broadly correspond to structural features of the proteins, and thus provides biologically meaningful information which is not existent in the usual point-estimate of the alignment. Our methods can handle input data of moderate size , which we analyzed overnight on a standard 2 GHz personal computer.Our approach results in estimates for the posterior distribution of evolutionary rate parameters, for the maximum Joint analysis of multiple sequence alignment, evolutionary trees and additional evolutionary parameters can be now done within a single coherent statistical framework. Two central problems in computational biology are the determination of the alignment and phylogeny of a set of biological sequences. Current methods first align the sequences, and then infer the phylogeny given this fixed alignment. Several software packages are available that deal with one or both of these sub-problems. For example, ClustalW  and T-CoThis leads on to the second issue, which is that heuristic methods are used to deal with insertions and deletions (indels), and sometimes also substitutions. This lack of a proper statistical framework makes it very difficult to accurately assess the reliability of the alignment estimate, and the phylogeny depending on it.The relevance of statistical approaches to evolutionary inference has long been recognised. Time-continuous Markov models for substitution processes were introduced more than three decades ago . InferenRao-Blackwellization [Statistical modelling and MCMC approaches have a long history in population genetic analysis. In particular, coalescent approaches to genealogical inference have been very successful, both in maximum likelihood ,20 and Blization . As a reThe only missing ingredient for a full co-estimation procedure is an alignment sampler. Unfortunately, there exists no Gibbs alignment sampler that corresponds to the analytic algorithm referred to above. In this paper we introduce a partial importance sampler to resample alignments, based on a proposal mechanism built on a partial score-based alignment procedure. This type of sampler supports the data format we need for efficient likelihood calculations, while still achieving good mixing in reasonable running time (see Results).We implemented the likelihood calculator and the alignment sampler in Java, and interfaced them with an existing MCMC kernel for phylogenetics and population genetics . We demosubstitutions, insertions and deletions of characters, approximating these as single-character processes. A sequence is represented as a string alternatingly consisting of links and characters connected by these links. This string both starts and terminates with a link. Insertions and deletions are modeled through a time-continuous birth-death process of links. When a new link is born, its associated character  is chosen from the equilibrium distribution of the substitution process.  sequences. It models three of the main processes in sequence evolution, namely 81 model . It is s81 model .) When aSince subsequences evolve independently, it is sufficient to describe the evolution of a single character-link pair. In a given finite time span, this pair evolves into a finite subsequence of characters and links. Since insertions originate from links, only the first character of this descendant subsequence may be homologous to the original character, while subsequent ones will have been inserted and therefore not be homologous to ancestral characters. The model as applied to pairwise alignments was solved analytically in , see alsBecause the TKF91 model is time reversible, the root placement does not influence the likelihood, an observation known as Felsenstein's "Pulley Principle" ). Althouhomology structure [one-state recursion. In contrast to previous approaches [tree as a parameter, and efficiently sample from tree space. The concept of homology structure referred to above is key to our algorithm, and we will presently define this concept more precisely. Let A1, A2, ...Am be sequences, related by a tree T with vertex set V. Let  denote the jth character of sequence Ai, and let  denote its k long prefix. A homology structure  on A1, ..., Am is an equivalence relation ~ on the set of all the characters of the sequences, C = {}, specifying which characters are homologous to which. The evolutionary indel process generating the homology structure on the sequences imposes constraints on the equivalence relations that may occur. More precisely, the equivalence relation ~ has the property that a total ordering, <h, exists on C such thatThe concept of tructure , also kntructure , refers tructure . By defitructure ,28), andtructure . Since oproaches ,28, the a = h b is equivalent to: a ≮h b and b ≮h a.) In particular, these conditions imply that the characters constituting a single sequence are mutually nonhomologous. The ordering <h corresponds to the ordering of columns of homologous characters in an alignment. Note that for a given homology structure, this ordering may not be unique , where s is the deterministic score and α is a scale parameter  tables are filled as for a deterministic score-based multiple alignment, starting at the tree tips and working towards the root, aligning sequences and profiles. We used linear gap penalties, and a similarity scoring matrix that was obtained by taking the log-odds of a probabilistic substitution matrix. The underlying phylogeny was used to define divergence times, and served as alignment guide tree. After filling the DP tables, we applied stochastic traceback. The probabilities for the three possible directions at each position was taken to be proportional to exp computationally simpler to use alignments, we are not aware of any efficient algorithm that can calculate such X2 and window w from a current alignment X1, we use the following Metropolis-Hastings ratio:Fortunately, we can solve both problems efficiently. We can sample alignments uniformly inside a homology structure, and at the same time sample homology structures according to their posterior probabilities. As biologically meaningful questions refer to homologies and not particular alignments, it seems reasonable to impose a simple uniform distribution over alignments within homology structures. The second problem is solved by not calculating an alignment proposal probability, but the proposal probability of the combination of an alignment and a resampling window. For a proposal of alignment H1 and H2 are homology structures corresponding to the alignments X1 and X2 respectively, |H1| and |H2| are their cardinalities , and T is the proposal probability. Using this ratio, the Markov chain will converge to the desired distribution π(X) = π(H)/|H|, since the detailed balance condition is satisfied. Indeed,where H1|, is the number of possible directed paths in the graph spanned by the one-state recursion; in other words, the number of permutations of alignment columns that result in alignments compatible with the given homology structure  given the tree and model parameters. Here A are the amino acid sequences,  is their homology structure, T is the tree including branch lengths, Q is the substitution rate matrix, and λ, μ are the amino acid insertion and deletion rates. To demonstrate the practicality of the new algorithm for likelihood calculation we undertook a Bayesian MCMC analysis of ten globin protein sequences , so that T was constrained to a molecular clock, and λ = μL/(L + 1) to make the expected sequence length under the TKF91 model agree with the observed lengths; here L is the geometric average sequence length. All other parameters were sampled under uniform priors. We assume a molecular clock to gain insight into the relative divergence times of the alpha-, beta- and myoglobin families. In doing so we incorporate insertion-deletion events as informative events in the evolutionary analysis of the globin family. The posterior density h is a complicated function defined on a space of high dimension. We summarise the information it contains by computing the expectations, over h, of various statistics of interest. We estimate these expectations by using MCMC to sample from h. Marginalizations for continuous variables can be done in a straightforward manner; see for example Figure μ parameter for two independent MCMC runs, showing excellent convergence.where a-posteriori alignment is very hard to estimate from an MCMC sample run, as there are typically far too many plausible alignments contributing to the likelihood. Indeed, we found that almost all alignments in a moderately long MCMC run (50000 samples) were unique. However, it is possible to reconstruct a reliable maximum posterior decoding [For alignments, the maximum decoding  alignmendecoding , see Figa posteriori (MAP) estimate of the phylogenetic relationships of the sequences. This example exhibits only limited uncertainty in the tree topology, however we observed an increased uncertainty for trees that included divergent sequences, such as bacterial and insect globins (results not shown).Figure μ estimates between MCMC and previous ML analyses [μ. This is probably due to the fact that no indels are apparent within any of the subfamilies despite a considerable sequence divergence. The indel rate estimated by the current cosampling procedure is greater than the estimate on a fixed multiple alignment [μ the ESSs were calculated at 5400 and 4000. We expect analyses of data sets of around 50 sequences to be readily attainable with only a few days computation.The estimated time of the most recent common ancestor of each of the alpha, beta and myoglobin families are all mutually compatible (result not shown), suggesting that the molecular clock hypothesis is at least approximately valid. Analysis of a four sequence dataset demonstrate consistency in analyses   that combines both the substitution and insertion-deletion processes in a principled way . We showOne motivation for using a fully probabilistic model, and for using a co-estimation procedure for alignments and phylogeny, is that this makes it possible to assess the uncertainties in the inferences. Fixing either the alignment or the phylogeny leads to an underestimate of the uncertainty in the other, and score-based methods give no assessment of uncertainty whatsoever.We show that the confidence estimates so obtained can contain biologically meaningful information. In the case of the multiple alignment of globin sequences, peaks in the posterior column reliabilities correspond broadly to the various conserved alpha helices that constitute the sequences see Fig. . In the At the heart of the method lies a recently introduced algorithm, termed the "indel peeling algorithm", that extends Felsenstein's peeling algorithm to incorporate insertion and deletion events under the TKF91 model . This rea-posteriori estimates of alignment, tree and parameters, and augmented these with estimates of reliability.We also developed a method for sampling multiple alignments, which is applicable for the data augmentation scheme we used for the efficient likelihood calculations. By combining the two samplers, we can co-sample alignments, evolutionary trees and other evolutionary parameters such as indel and substitution rates. The resulting samples from the posterior distribution can be summarized in traditional ways. We obtained maximum As was already mentioned in , it woul, with full installation and requirement details. The data set used in this paper is avaliable (see The BEAST package (AJ Drummond and A Rambaut), which includes the algorithm described in this paper, is available from able see IM conjectured and GL proved the one-state recursion. GL and IM independently implemented the algorithms, and wrote the paper. JLJ simplified the proof of the recursion, GL suggested to use it within an MCMC phylogeny cosampler, and IM suggested to use a Metropolised importance sampler and proved its correctness. GL and AD interfaced the Java algorithms to the BEAST phylogeny sampling package , and AD .)This XML file specifies the MCMC run for the example phylogeny and alignment co-estimation given in this paper (see Figs. Click here for file


Deluged by the rate and complexity of completed genomic sequences, the need to align longer sequences becomes more urgent, and many more tools have thus been developed. In the initial stage of genomic sequence analysis, a biologist is usually faced with the questions of how to choose the best tool to align sequences of interest and how to analyze and visualize the alignment results, and then with the question of whether poorly aligned regions produced by the tool are indeed not homologous or are just results due to inappropriate alignment tools or scoring systems used. Although several systematic evaluations of multiple sequence alignment (MSA) programs have been proposed, they may not provide a standard-bearer for most biologists because those poorly aligned regions in these evaluations are never discussed. Thus, a tool that allows cross comparison of the alignment results obtained by different tools simultaneously could help a biologist evaluate their correctness and accuracy.In this paper, we present a versatile alignment visualization system, called SinicView, , which allows the user to efficiently compare and evaluate assorted nucleotide alignment results obtained by different tools. SinicView calculates similarity of the alignment outputs under a fixed window using the sum-of-pairs method and provides scoring profiles of each set of aligned sequences. The user can visually compare alignment results either in graphic scoring profiles or in plain text format of the aligned nucleotides along with the annotations information. We illustrate the capabilities of our visualization system by comparing alignment results obtained by MLAGAN, MAVID, and MULTIZ, respectively.With SinicView, users can use their own data sequences to compare various alignment tools or scoring systems and select the most suitable one to perform alignment in the initial stage of sequence analysis. With exponentially increasing genomic sequences available in the public domain -5 comparHowever, genomic sequences can be megabase long and thus the traditional sequence alignment tools based on dynamic programming would not work efficiently due to their time and space complexities. To better tackle this problem, several tools for genomic sequence alignment have been proposed, such as pairwise sequence aligners like MUMmer , GS-Aligdirect and efficient method and can assist users to cross compare and inspect alignment results obtained by different MSA tools especially at the initial stage of sequence analysis.Although the comparison results in -31 proviEnsembl [In recent years, a number of visualization tools have been released in the public domain. These tools can be roughly divided into two categories: integrated genome/sequence browser and individual alignment result visualization. In the former category, such as UCSC ENCODE project ,33, UCSCEnsembl , ECR BroEnsembl ,37, userEnsembl . mVISTA Ensembl . rVISTA Ensembl ,41. GenoEnsembl ,43. PhylEnsembl . In geneEnsembl ,45, and Ensembl  are alsoIn this article, we present a versatile alignment visualization system, SinicView , which enables users to efficiently compare and evaluate assorted alignment results obtained by different tools. SinicView for the present calculates similarity of the alignment outputs under a fixed window using the sum-of-pairs method and provides scoring profiles of each set of aligned sequences. Other scoring matrices, such as EMBOSS DNA scoring matrix  and YASSThere are three viewing sections in SinicView: Global View, Detailed View, and Information View (including annotations and gaps.) The Global View section shows the whole percent identity plots that calculate the sum-of-pair scores based on one specified reference sequence. In the Detailed View section, the panels show the whole percent identity plots of different alignment results individually. By observing the graphical results, it is much more intuitive and straightforward to judge the consistency of the alignment results. When the sliding window is less than 100 base pairs, the Detailed View section will automatically switch from the curve-based plot to the display of the detailed alignments in a colored text format where identical characters are shown. The Information View section containing annotation and gap information is stacked beneath the Detailed View section. SinicView also provides several global comparison charts that can assist biologists to choose the best alignment result among those produced by the programs under consideration. SinicView is implemented entirely in Java language to ensure portability across major platforms and is accessible with a web browser and Internet connection. The main features of SinicView are summarized as follows:1. Visualization of the scoring distribution of alignment results in a curve-based graphic format;2. Generation of the comparison charts using stacked-bar and pie charts, which shows the distribution of the identical rates among various alignment programs for benchmarking purposes;3. Inclusion of a versatile manipulative functionality ;4. Visualization of annotation information and display of the phylogenetic trees provided by users in which the drawing tree program uses the ATVtree ;5. Visualization of detailed text alignments results;6. Capability to export the visualization results to portable image files.In what follows, we will introduce the characteristics and functionality of SinicView in more detail.SinicView offers a series of manipulative and navigational controls, such as zooming, shifting, and gap/annotation toggling. As shown in Figure SinicView can display more than one alignment result obtained by different alignment programs (either pairwise or multiple ones.) The assorted mixed-color span under the Global View panel shows among the alignment tools used the preferred aligner, which generates comparatively better results on the spot. Each of the aligners is denoted by a pre-defined color with the "performance color" label right next to the name of the tool.In the Detailed View section, the Percent Identity Plot (PIP) panels show, from top to bottom, the similarity curves of the alignment results obtained by different programs, along with the names of the alignment tools. In the Information View section, the Gap & Annotation panels (in pink and gray) display the information of annotations provided by users, and gaps of aligned sequences. The information and similarity ratios can also be displayed as the current scan-line (i.e. cursor) moves. The boxes in maroon denote the annotation area and the horizontal line represents the original sequences interleaved with inserted gaps (light gray areas.) The gap display can be toggled on or off via the checkbox on the right.reference and then calculate the sum-of-pair scores of each base pair in the reference within a fixed window. For example, each alignment result in the PIP panels at the scan-line position corresponds to human sequence, selected as the reference in Figure Because different alignment results are usually of different lengths, it is not plausible to compare these results base-pair by base-pair. In SinicView, therefore, we let users select one of input sequences as a The functionality under the "Tools" menu, called "Comparison Charts", offers two types of charts for quick-and-easy evaluation of the alignment quality. The stacked bar chart, in Figure SinicView also provides a plain-text view of the alignment results in the Detailed View section when the sliding window size is less than 100 aligned base pairs. As shown in Figure The applet version can be accessed via any JRE (Java Runtime Environment)-enabled browsers with Internet connection, thus making the installation and choosing the right platform hassle-free. However, the ease of running SinicView on-the-go cannot accommodate the bandwidth requirement in case of huge amount of sequence data involved. Hence, we have also implemented a standalone application of SinicView, which is wrapped in JRE, for off-line use.The execution procedure of the standalone SinicView is quite straightforward. Upon launch, the user will be prompted three options. The first two are to read user's Phylogenetic Tree files, an option, and MSA results from the local disk.In what follows, we will introduce two examples to demonstrate how SinicView can assist users to analyze alignment results in the initial stage of sequence comparison. The total alignment lengths in both of the examples are few hundreds of thousands of base pairs and several millions of base pairs, respectively. The conservations of the aligned sequences are different in each example. More examples can be found in .SCL gene, also known as tal-1, encodes a basic helix-loop-helix transcription factor that is pivotal for the normal development of all hematopoietic lineages, and is highly conserved between mammals and zebrafish [The Stem Cell Leukemia (SCL) gene plays a critical role in normal processes that, when disrupted, can result in leukemia. The ebrafish ,52. Prevebrafish . The aliebrafish , PipMakeebrafish , and DiAebrafish . Shah etebrafish , and demebrafish . In thisFigure The cystic fibrosis transmembrane conductance regulator (CFTR) gene is responsible for the cystic fibrosis disorder that spans approximately 190 k bp of genomic DNA and consists of 27 exons . The greFigures For comparisons of these alignments from a functional viewpoint, we downloaded the annotation of the human sequence, including exons and repeats, from the Ensembl Genome Browser . The detFigures Generally speaking, the regions aligned by TBA usually have higher identical rates than by others. As the frames shown in red in Figures Since each alignment tool has its own advantage and reveals different alignment results, we therefore wonder whether a better alignment result can be generated by hybridization of these alignment tools.SinicView is implemented totally in Java. Theoretically, it should be portable across different operating systems (OSs) and platforms. To demonstrate interoperability on real cases, we tested the applet and application versions of SinicView on different platforms and OSs. As shown in Table Besides, we also tested the loading performance of SinicView. Because the performance of an applet on the Web is strongly dependent on the network bandwidth and traffic, the estimation of loading time may not be a fair comparison. Thus, in this part we only estimated the loading performance of the standalone application of SinicView.In general, the loading performance of a Java application is dependent on the memory heap size. The default values of the initial heap size and the maximum size of a Java Virtual Machine (java_1.4.2 version or higher) are 4 M (mega) bytes and 64 M bytes, respectively. These values can be adjusted by the following command in the terminal mode:java -Xms64m -Xmx128m -jar SinicView.jar,where the parameters Xms64m and Xmx128m represent that the initial heap size is 64 M bytes and the maximum size is 128 M bytes, respectively. Thus, we used different input data sizes, initial heap sizes, and the maximum sizes to estimate the loading time of SinicView. As shown in Table Alu is the largest family of interspersed mobile elements (~300 bp) and propagated to more than one million copies in primate genomes. This type of repeat has been inserted into these genomes within the last 65 million year period [Alu inserted regions should not be aligned. However, other interspersed elements may possibly have been inserted into the ancestral sequence of mammalians. The regions of these repeats may be able to align together between the sequences of different mammalians, as shown in Example 2. However, these regions in the alignment results by different aligners are inconsistent. Since these repetitive elements in sequences could be detected by RepeatMasker [The eukaryotic genome is usually characterized by the presence of repetitive DNA consisting of nucleotide sequences of various lengths and compositions that occur from a few times to thousands of times in the genome either in tandem or in a dispersed fashion. The repr period . BecauseatMasker , the pooAs the comparison results using SinicView show, the alignments of sequences using different MSA tools are inconsistent. We begin to wonder whether the computational results obtained by different tools may in fact lead to different findings. For identification of alignment correlation, a need for additional checks of alignment validity by using different tools and scoring systems has been recognized in the literature . Thus, aExcept evaluation of the alignment quality by comparison charts in SinicView, how to decide on a good alignment with biological meanings may need much more experiences and knowledge. Sometimes, this judgment depends also on what kind of the biological problems users want to study. Here, we suggest some general rules for users to judge the alignments by biological meanings.In the coding regions, a triplet of adjacent nucleotides constitutes a codon. Usually, the first two nucleotides are identical between the two sequences and allow the third one to be either identical or different. Thus, when the partial alignment results reveal the two-out-of-three regularity for each triplet, it may imply that the aligned regions are potential coding regions. This alignment result should be more biologically meaningful than those without the two-out-of-three regularity.From molecular evolutionary viewpoint, nature prefers inserting or deleting considerable consecutive nucleotides together to interspersed individual nucleotides . Thus, aIf one of the alignment sequences has been annotated, the information is definitely useful for users to judge the alignment results by different aligners.It is not easy to promote newly developed tools because users usually cannot directly compare the new tools with the traditional ones. With SinicView, users can compare the alignment results obtained by different tools and select an appropriate one for further analysis. Thus, if the new tool can align more regions than those by the old ones and can also indicate their statistical significances, it will be welcomed and better received by the community. We would like to make SinicView available to the community of computational biologists. In addition to helping the user find a most appropriate alignment tool to use, SinicView may also be used to check whether previously obtained alignment results by different tools are worth a re-investigation, and see if this revisit of alignment results would lead to different conclusions.The capability of fine-tuning parameters relevant to the alignment process will be made available in a user-friendly interface. Furthermore, the ability to allow plug-ins of more alignment programs, in addition to the currently pre-selected ones, such as ClustalW, MAVID, MLAGAN, and GS-Aligner, will inevitably broaden the usage of SinicView. The issue of the compatibility of the input and output formats for each alignment tool also needs to be resolved. For example, both MAVID and MLAGAN require the phylogenetic tree data as input, but ClustalW does not. The ordering of the outputs of these aforementioned tools is usually switched without notice. Thus, to be able to work under a unified comparison framework requires further processing of these outputs. Besides, identifying a standard-bearer mechanism is still a challenge in entrusting existing alignment programs. So far, we have used the "sum-of-pairs" method to define the "identical rate" in each alignment result. In the future, we may provide other criteria for users to use to measure their alignment results, in addition to what have been already provided in SinicView.Deluged by the increasing number of completed genomic sequences, biologists have encountered a challenge of aligning more and much longer sequences from divergent species. Thus, the need to align longer sequences, like mega base-pair sequences or even genome-scale sequences, and evaluate the alignment results becomes more urgent. In this paper, we have presented a visualization tool for comparison of multiple sequence alignment programs. With a standard simple protocol for the input/output format, it is quite easy for users to upload their own alignment programs to SinicView. The performance of SinicView depends on the system's internal memory. In a 64 M RAM JAVA environment, SinicView can load and visualize several mega bases alignment results. Users can easily perform sequence alignment by employing multiple alignment tools and visualize the results on the fly by SinicView. More information can be found at .Project name: 1. Development of Novel Large-scale Sequence Alignment and Visualization Tools and Their Applications to Bioinformatics2. Development of a web-based personalized research environment for study of computational and evolutionary genomicsProject home page: Operating system(s): Window XP, Sun OS 5.7 Sparc, Mac OS 10.4.2 Tiger, and Linux Fedora Core 3Programming language: JavaOther requirements: Java 1.4.2 or higherLicense: Any restrictions to use by non-academics: free downloads and usage for academics only.SinicView: Sequence-aligning INnovative and Interactive Comparison VIEWerJRE: Java Runtime EnvironmentSCL: Stem Cell LeukemiaCFTR: Cystic Fibrosis Transmembrane Conductance RegulatorArthur Chun-Chieh Shih and D.T. Lee contributed the original idea, developed the system organization, and drafted the paper. Laurent Lin supervised the system implementation and also drafted some parts of the paper. Chin-Lin Peng, Yu-Wei Wu, Chun-Yi Wong, Meng-Yuan Chou, and Tze-Chang Shiao implemented the codes. Shiang-Heng Chen and Mu-Fen Hsieh implemented some partial codes before leaving their positions.


The need to compare protein profiles frequently arises in various protein research areas: comparison of protein families, domain searches, resolution of orthology and paralogy. The existing fast algorithms can only compare a protein sequence with a protein sequence and a profile with a sequence. Algorithms to compare profiles use dynamic programming and complex scoring functions.We developed a new algorithm called PHOG-BLAST for fast similarity search of profiles. This algorithm uses profile discretization to convert a profile to a finite alphabet and utilizes hashing for fast search. To determine the optimal alphabet, we analyzed columns in reliable multiple alignments and obtained column clusters in the 20-dimensional profile space by applying a special clustering procedure. We show that the clustering procedure works best if its parameters are chosen so that 20 profile clusters are obtained which can be interpreted as ancestral amino acid residues. With these clusters, only less than 2% of columns in multiple alignments are out of clusters. We tested the performance of PHOG-BLAST vs. PSI-BLAST on three well-known databases of multiple alignments: COG, PFAM and BALIBASE. On the COG database both algorithms showed the same performance, on PFAM and BALIBASE PHOG-BLAST was much superior to PSI-BLAST. PHOG-BLAST required 10–20 times less computer memory and computation time than PSI-BLAST.Since PHOG-BLAST can compare multiple alignments of protein families, it can be used in different areas of comparative proteomics and protein evolution. For example, PHOG-BLAST helped to build the PHOG database of phylogenetic orthologous groups. An essential step in building this database was comparing protein complements of different species and orthologous groups of different taxons on a personal computer in reasonable time. When it is applied to detect weak similarity between protein families, PHOG-BLAST is less precise than rigorous profile-profile comparison method, though it runs much faster and can be used as a hit pre-selecting tool. The availability of many completely sequenced genomes provides rich material for studying protein evolution. Gene duplications, gene losses, gene acquisitions and horizontal transfer of genes make it very difficult to reconstruct the exact evolutionary history of a protein family. A widely used approach to study such history is to find orthologs and paralogs by comparing completely sequenced genomes. Orthologs are genes derived from a single ancestral gene as a result of the speciation event, while paralogs are genes that result from gene duplication events -3. How cProfiles represent a very sensitive technique to represent a protein family and to compare protein families. They were introduced by Michael Gribskov and co-workers  and theyThe efforts of several authors were directed to improve profiles by sequence weighting -12 and bThe discrete view on profiles is exemplified by the PROSITE database , which s2*m*n operations, where A is the alphabet size (for proteins A = 20), m and n are protein lengths. Fast heuristic BLAST-like procedures require a discrete alphabet and it is not possible to use them to compare a pair of profiles. If we are able somehow to convert profiles to discrete values, then we can substitute an alignment column with a symbol denoting the column type. To this end, all alignment columns from the BLOCKS database were converted to frequency distributions and a special clustering procedure was applied to them. It appeared that more than 98% of alignment columns in multiple alignments from standard databases of protein multiple alignments belong to just 20 clusters, each with its own dominating amino acid residue . Therefore, it is possible to substitute an alignment column with this dominating residue that can be also thought as the "ancestral" amino acid residue from which the alignment column evolved. In the case we cannot assign an alignment column to its "ancestral" residue, a special symbol "X" is used, denoting a "garbage" column.Existing procedures for profile-profile comparisons -22 use dWhen "ancestral" sequences are obtained it is possible to find a similarity score by applying the rigorous Smith-Waterman algorithm . But it Each alignment column from a database of multiple alignments was converted to the frequency vector using a simple formula:Ni is the number of times amino acid i occurs in the column, N is the number of sequences in the multiple alignment. Thus, we obtained the data set D of all frequency vectors computed from all alignments columns.where r:Following Shmuel Pietrokovski , we defiD, we can setup a correlation coefficient threshold rthresh and then merge clusters Ci and Cj if the distance between them is less than rthresh. Our modified "k-means" procedure will run as follows.We have chosen a variation of the classical "k-means" procedure  due to tx find all frequency vectors y such that r<rthresh. These frequency vectors will form an initial cluster. If a frequency vector is already included in an initial cluster, it is not considered as a seed for a new cluster. Compute the initial means μ1,...,μk.1. For each frequency vector x in D to the cluster Ci whose mean μi is the nearest to x.2. Assign each frequency vector 3. Recompute the means of all the clusters.Ci and Cj if r<rthresh.4. Merge clusters 5. Repeat steps 2, 3 and 4 until the number of clusters does not change.ith  sequence was included in the new alignment only if it was less than 65% identical to all previously included sequences. Thus, all sequences in the resulted multiple alignment were less than 65% identical with each other. After the extraction procedure, only alignments having at least 15 sequences were considered for to further processing to have enough statistical material. In total, 39253 alignment columns were obtained. The average number of sequences in a multiple alignment was 32. The average protein identity in a multiple alignment was 27%.To find frequency column clusters in the BLOCKS database , each blr*. The plot shows that when r*< 0.6 the number of clusters is almost constant, whereas after 0.7 the number of clusters sharply increases. In the interval 0.5<r*<0.65, the number of clusters equals 20. Fig. To test that this dependence of the number of clusters on the correlation coefficient threshold is the general feature of multiple alignments we applied the same clustering procedure to the COG  and PFAMAny clustering procedure will also attempt to create a hierarchy of clusters. It is interesting to know if there are any other subclusters inside the 20 clusters obtained by our procedure. To answer this question, we applied our procedure to all columns in the BLOCKS database that belong to the alanine cluster. Fig. fi = 1) in the 20-dimensional space, we generated 1000000 random frequency vectors and counted how many of them fell inside our 20 reference clusters. A frequency vector was considered to be inside a cluster if the correlation coefficient between it and the cluster average vector exceeded 0.5. Only 4% of frequency vectors were inside our 20 clusters, proving the fact that the 20 clusters occupy a negligible part of the total 20-dimensional frequency vector space.To evaluate the size of clusters on the simplex . Each generated sequence was considered to be an ancestral sequence, and the process of column evolution in each column of the generated sequence was modeled by random generation of 32 amino acid residues to obtain the same depth of the generated multiple alignment as the average depth of multiple alignments in our clustering procedure done on BLOCKS. Each of these 32 amino acid residues was generated from its "ancestral" residue with probabilities determined by 4 transition probability matrices , correspThe same clustering procedure was applied to randomly generated frequency vectors, and similar 20 clusters were obtained. The Pearson correlation coefficients between corresponding cluster averages from both groups of clusters is >0.99. This proves that the structure of clusters in protein multiple alignments and in the random test is basically the same.Fig. To assign columns to clusters, we weight sequences in a multiple alignment to eliminate any distortions in frequency vectors that could be caused by unequal representation of similar sequences in a multiple alignment. Then for all columns frequency vectors are calculated and the correlation coefficient is found between a frequency vector and the nearest cluster average. If this correlation coefficient exceeds a threshold value we assign a column to its nearest cluster, otherwise it is replaced with the "X" symbol.To find a similarity score between two multiple alignments, we convert both multiple alignments to "ancestral" sequences as it was described in the previous section. Then our method works in a very similar way as the BLAST  and FASTl-tuples from the query "ancestral" sequence to the hash table.1. Hash all l-tuples from the "ancestral" sequence from the database in the hash table. For each l-tuple hit increment the number of hits at a particular diagonal.2. Lookup all Nmin or more l-tuple hits for further processing. If no such diagonals are found, declare both compared multiple alignments as non-similar and quit the procedure.3. Leave only diagonals with l-tuple hit leftward until the total score becomes negative. Memorize the maximum score achieved during this extension and the left end of the segment corresponding to this score. In the same way, extend this l-tuple rightward. The result of this extension is a maximal segment pair (MSP). Choose the l-tuple which is the left most to the resulting MSP if such l-tuple can be found. Apply the same extension process to this l-tuple. Scan the diagonal from left to right until no l-tuple hits are found anymore. Thus, a diagonal with Nmin or more l-tuple hits can give one or more MSPs. For further processing, leave only MSPs exceeding some diagonal threshold score SCOREthresh. If no such MSPs are found, declare both compared multiple alignments as non-similar and quit the procedure.4. At diagonals, extend the leftmost 5. Order MSPs by their left ends belonging to one member of the pair.6. Using the following recurrent relationship, obtain the score of the maximal scoring chain of MSPs:Nmsp is the total number of MSPs, si is the score of the ith MSP, li and ri are MSPs' left and right ends in the first sequence, mi and pi are MSPs' left and right ends in the second sequence, G is the fixed gap penalty for starting a gap, g· max  is the variable gap extension penalty.where Following the above description of the algorithm, we provide a summary of all parameters that can influence the PHOG-BLAST score between any two multiple alignments:(i) Profile clusters.(ii) Substitution matrix between "ancestral" sequences.r*.(iii) Correlation coefficient threshold l.(iv) Tuple size Nmin.(v) Minimum number of tuples on one diagonal SCOREthresh.(vi) MSP score threshold G.(vii) Gap starting penalty g.(viii) Gap continuation penalty Extensive computational experiments with PHOG-BLAST allowed us to determine parameter values that provide the best PHOG-BLAST performance. For some parameters, we used traditional values. For other parameters, we had to carry out a number of computational experiments to determine their best values. To determine the best value for a parameter, we varied it over a certain interval, with all other parameter values remaining constant, and monitored the PHOG-BLAST performance.Profile clusters see  were user* that determines whether an alignment column should belong to a cluster is 0.5. It is this correlation coefficient that determines the lower cutoff point on curves showing the dependence of the number clusters on the correlation coefficient threshold employed in the clustering procedure , we used these algorithms to restore protein families in a similar fashion as we did it when compared PHOG-BLAST with PSI-BLAST. To do this test, we have randomly selected 500 PFAM alignments having at least 6 sequences from the earlier mentioned downloaded 1254 PFAM alignments. From each such PFAM alignments, we randomly selected 6 sequences, and from these sequences we made two subalignments each having 3 sequences randomly selected from this group of 6 sequences. We used COMPASS and PHOG-BLAST to find BBHs between these two databases each having 500 alignments consisting of 3 sequences. All tests were performed on 3.2 GHz Pentium 4 computer with 1 GB of RAM running Red Hat Linux 7.3. It took COMPASS 40 minutes to perform the test, while PHOG-BLAST required only 2 minutes of computation time. COMPASS was able to correctly restore 490 BBHs with no false positives, while PHOG-BLAST restored 465 BBHs with no false positives. This observation together with our experience of using PHOG-BLAST when we built the PHOG database [We developed a new algorithm for finding similarity between protein multiple alignments by finding a way to convert multiple alignments into "ancestral" sequences. The justification for this conversion was our clustering procedure done on frequency distributions and the random simulation of the column evolution. Our algorithm shows performance comparable with PSI-BLAST, or better, but it runs much faster. Our results demonstrate that despite the seeming infiniteness of column space, it is possible to split it into 20 types and to indicate their evolutionary origin. Our "ancestral" sequences are similar to consensus sequences used for representing protein multiple alignments. However, we think that our approach to convert a multiple alignment into a consensus sequence is more precise, since we have a clearer evolutionary base for such conversion. This approach helped us to develop a very precise algorithm for finding similarity between multiple alignments.In building frequency distributions we did not use pseudo-counts. Any inclusion of pseudo-counts in any form when building frequency distributions only deteriorated the performance of PHOG-BLAST. Since we found 20 condensation points in the column space, this contrasts with the approach taken in , where aOur methodology of testing profile algorithms can also provide a framework for comparing different sequence weighting methods. Within our testing framework, the smaller the number of BBHs that are not found, the better a particular sequence weighting method works.We have not found any subtypes for profile clusters. However, alignment columns that are descendents of one ancestral amino acid residue differ in the speed of evolution. When we convert columns to their clusters, fast evolving columns and slow evolving columns would acquire the same symbol. We have not so far devised any way to include this additional information into our method.Since PHOG-BLAST deals with "ancestral" sequences, and not with profiles, it can be a useful tool for fast comparing multiple alignments of protein families. This task frequently arises in different areas of comparative proteomics and protein evolution. Our accompanying paper  shows ho and requires the Java runtime environment. It is also available as an additional file with this manuscript [see PHOG-BLAST is freely available in Java programming language from ript see . The PHOIM did all computation and wrote the manuscript. AM developed the approach for this research, provided overall guidance and revised this manuscript.Average frequencies of frequency column clusters obtained from BLOCKS. Dominating amino acids are shown in bold face.Click here for filePHOG-BLASTClick here for file


Automated software tools for multiple alignment often fail to produce biologically meaningful results. In such situations, expert knowledge can help to improve the quality of alignments.semi-automatic version of the alignment program DIALIGN that can take pre-defined constraints into account. It is possible for the user to specify parts of the sequences that are assumed to be homologous and should therefore be aligned to each other. Our software program can use these sites as anchor points by creating a multiple alignment respecting these constraints. This way, our alignment method can produce alignments that are biologically more meaningful than alignments produced by fully automated procedures. As a demonstration of how our method works, we apply our approach to genomic sequences around the Hox gene cluster and to a set of DNA-binding proteins. As a by-product, we obtain insights about the performance of the greedy algorithm that our program uses for multiple alignment and about the underlying objective function. This information will be useful for the further development of DIALIGN. The described alignment approach has been integrated into the TRACKER software system.Herein, we describe a  CLUSTAL W [DIALIGN [T-COFFEE [POA [MUSCLE [PROBCONS [Multiple sequence alignment is a crucial prerequisite for biological sequence data analysis, and a large number of multi-alignment programs have been developed during the last twenty years. Standard methods for multiple DNA or protein alignment are, for example, LUSTAL W , DIALIGN[DIALIGN  and T-COT-COFFEE ; an overT-COFFEE . RecentlFEE [POA , MUSCLE  [MUSCLE  or PROBCPROBCONS . These pPROBCONS -10.automated, i.e., they construct alignments following a fixed set of algorithmical rules. Most methods use a well-defined objective function assigning numerical quality score to every possible output alignment of an input sequence set and try to find an optimal or near-optimal alignment according to this objective function. In this process, a number of program parameters such as gap penalties can be adjusted. While the overall influence of these parameters is quite obvious, there is usually no direct way of influencing the outcome of an alignment program.All of the above mentioned alignment methods are fully fail to align these regions correctly, it is desirable to have an alignment method that would accept such user-defined homology information and would then align the remainder of the sequences automatically, respecting these user-specified constraints.Automated alignment methods are clearly necessary and useful where large amounts of data are to be processed or in situations where no additional expert information is available. However, if a researcher is familiar with a specific sequence family under study, he or she may already know certain parts of the sequences that are functionally, structurally or phylogenetically related and should therefore be aligned to each other. In situations where automated programs MACAW [OWEN [et al. [et al. [Göttingen Bioinformatics Compute Server (GOBICS), we provide a user-friendly web interface where anchor points can be used to guide the multiple alignment procedure [Hox gene clusters. For these sequences, the default version of DIALIGN produces serious mis-alignments where entire genes are incorrectly aligned, but meaningful alignments can be obtained if the known gene boundaries are used as anchor points.The interactive program MACAW  can be uAW [OWEN ,13 accep [et al.  and Samm [et al. . The mul [et al. ,17 has a [et al. ,19; see  [et al. . At Göttrocedure . Herein,objective function is 'wrong' by assigning high numerical scores to biologically meaningless alignments. But it is also possible that the objective function is 'correct' – i.e. biologically correct alignments have numerically optimal scores -and the employed heuristic optimisation algorithm fails to return mathematically optimal or near-optimal alignments. The anchoring approach that we implemented can help to find out which component of our alignment program is to blame if automatically produced alignments are biologically incorrect.In addition, our anchoring procedure can be used to obtain information for the further development of alignment algorithms. To improve the performance of automatic alignment methods, it is important to know what exactly goes wrong in those situations where these methods fail to produce biologically reasonable alignments. In principle, there are two possible reasons for failures of alignment programs. It is possible that the underlying biological quality of the output alignments but can in certain situations lead to alignments with significantly higher numerical scores. This demonstrates that the heuristic optimisation procedure used in DIALIGN may produce output alignments with scores far below the optimum for the respective data set. The latter result has important consequences for the further development of our alignment approach: it seems worthwile to develop more efficient algorithms for the optimisation problem that arises in the context of the DIALIGN algorithm. In other situations, the numerical scores of biologically correct alignments turned out to be below the scores of biololgically wrong alignments returned by the non-anchored version of our program. Here, improved optimisation functions will not lead to biologically more meaningful alignments. It is therefore also promising to develop improved objective function for our alignment approach.One result of our study is that anchor points can not only improve the distantly related input sequences where homologies at the primary sequence level may be obscured by spurious random similarities. Another notorious challenge for alignment programs are duplications within the input sequences. Here, tandem duplications are particularly hard to align, see e.g. [fragment alignments or fragments [weight score to each possible fragment and tries to find a consistent collection of fragments with maximum total score. For pairwise alignment, a chain of fragments with maximum score can be identified [greedily into a resulting multiple alignment.There are many situations where automated alignment procedures can produce biologically incorrect aligments. An obvious challenge are see e.g. . Specialsee e.g. . For theragments ,16. A frentified . For mulS1,..., Sk. For simplicity, let us assume that our sequences do not share any significant similarity outside the motif. Moreover, we assume that the degree of similarity among all instances of the motif is roughly comparable. There are no difficulties if two sequences are to be aligned and the motif is duplicated in both sequences, i.e if one has instances  and  of the motif in sequence S1 and instances  and  of the same motif in sequence S2 as in Figure  to  and  to  since, for pairwise alignment, our algorithm returns a chain of fragments with maximum total score.As indicated in Figure  to  in Figure  and , and among  and , respectively. However, DIALIGN uses a greedy approach only for multiple alignment where an exact solution is not feasible, but for pairwise alignment, the program returns an optimal alignment with respect to the underlying objective function. Thus, under the above assumtion, a meaningful alignment will be produced even if  exhibits stronger similarity to  than to .Note that a strictly greedy algorithm could be confused by this situation and could align, for example, ,  occurs in S1 but only one instance of the motif, M2, is present in S2. Here, it can happen that the beginning of M2 is aligned to the beginning of  and the end of M2 is aligned to the end of  as in Figure S1, S1, S3 in Figure ,  of a motif occur in S1 while S2 and S3 each contain only one instance of the motif M2 and M3, respectively. Under the above assumptions, a biologically meaningful alignment of these sequences would certainly align S2 to S3, and both motifs would be aligned either to  or to  – depending on the degree of similarity of S2 and S3 to  and , respectively. Note that such an alignment would also receive a high numerical score since it would involve three pairwise alignments of the conserved motif. However, since the pairwise alignments are carried out independently for each sequence pair, it may happen that the first instance of the motif in sequence S1,  is aligned to M2 but the second instance, , is aligned to M3 in the respective pairwise alignments as in Figure M2 and M3 will be inconsistent with the first two pairwise alignments. Depending on the degree of similarity among the motifs, alignment of  and M3 may be rejected in the greedy algorithm, so these motifs may not be aligned in the resulting multiple alignment. It is easy to see that the resulting multiple alignment would not only be biologically questionable, but it would also obtain a numerically lower score as it would involve only two pairwise alignments of the motif.The trouble starts if a tandem duplication anchored alignment approach. Here, the user can specify an arbitrary number of anchoring points in order to guide the alignment procedure. Each anchor point consists of a pair of equal-length segments of two of the input sequences. An anchor point is therefore characterised by five coordinates: the two sequences involved, the starting positions in these sequences and the length of the anchored segments. As a sixth parameter, our method requires a score that determines the priority of an anchor point. The latter parameter is necessary, since it is in general not meaningful to use all anchors proposed by the user. It is possible that the selected anchor points are inconsistent with each other in the sense that they cannot be included in one single multiple output alignment, see [subset of the proposed anchor points.To overcome the above mentioned difficulties, and to deal with other situations that cause problems for alignment programs, we implemented a semi-automatic ent, see  for our strong anchoring option, where the specified anchor positions are necessarily aligned to each other, consistency provided. The remainder of the sequences is then aligned based on the consistency constraints given by these pre-aligned positions. This option can be used to enforce correct alignment of those parts of the sequences for which additional expert information is available. For example, we are planning to align RNA sequences by using both primary and secondary structure information. Here, locally conserved secondary structures could be used as 'strong' anchor points to make sure that these structures are properly aligned, even if they share no similarity at the primary-structure level.Our software provides two slightly different options for using anchor points. There is a weak anchoring option, where consistent anchor points are only used to constraint the output alignment, but are not necessarily aligned to each other. More precisely, if a position x in sequence Si is anchored with a position y in sequence Sj through one of the anchor points, this means that y is the only position from Sj that can be aligned to x. Whether or not x and y will actually appear in the same column of the output alignment depends on the degree of local similarity among the sequences around positions x and y. If no statistically significant similarity can be detected, x and y may remain un-aligned. Moreover, anchoring x and y means that positions strictly to the left (or strictly to the right) of x in Si can be aligned only to positions strictly to the left (or strictly to the right) of y in Sj – and vice versa. Obviously, these relations are transitive, so if position x is anchored with position y1, y1 is to the left of another position y2 in the same sequence, and y2 in turn, is aligned to a position z, then positions to the left of x can be aligned only to positions to the left of z etc. The 'weak' option may be useful if anchor points are used to reduce the program running time.In addition, we have a fragments ( = segment pairs) in the greedy procedure for multi-alignment. By transitivity, a set Anc of anchor points defines a quasi partial order relation ≤Anc on the set X of all positions of the input sequences – in exactly the same way as an alignment Ali induces a quasi partial order relation ≤Ali on X as described in [Ali as well as a set of anchor points Anc as an equivalence relation defined on the set X of all positions of the input sequences. Next, we consider the partial order relation ≤ on X that is given by the 'natural' ordering of positions within the sequences. In order-theoretical terms, ≤ is the direct sum of the linear order relations defined on the individual sequences. The partial order relation ≤Anc is then defined as the transitive closure of the union ≤ ∪ Anc. In other words, we have x ≤Anc y if and only if there is a chain x0, ..., xk of positions with x0 = x and xk = y such that for every i ∈ {1,..., k}, position xi-1 is either anchored with xi or xi-1 and xi belong to the same sequence, and xi-1 is on the left-hand side of xi in that sequence.Algorithmically, strong or weak anchor points are treated by DIALIGN in the same way as ribed in ,25. FormR on X is called consistent if all restrictions of the tansitive closure of the union ≤ ∪ R to the idividual sequences coincides with their respective 'natural' linear orderings. With the weak version of our anchored-alignment approach, we are looking for an alignment Ali wich maximum score such that the union Ali ∪ Anc is consistent. With the strong option, we are looking for a maximum-scoring alignment Ali that is a superset of Anc. With both program options, our optimisation problem is to find an alignment Ali with maximum score – under the additional constraint that the set-theoretical union Ali ∪ Anc is consistent. In the weak anchoring approach, the output alignment is Ali while with the strong option, the program returns the transitive closure of the union Ali ∪ Anc.In our set-theoretical setting, a relation Anc of anchor points is itself consistent. Since a user-defined set of anchor points cannot be expectd to be consistent, the first step in our anchoring procedure is to select a consistent subset of the anchor points proposed by the user. To this end, the program uses the same greedy approach that it applies in the optimisation procedure for multiple alignment. That is, each anchor point is associated with some user-defined score, and the program accepts input anchor points in order of decreasing scores – provided they are consistent with the previously accepted anchors.The above optimisation problem makes sense only if the set prioritise potential anchor points according to arbitrary user-defined criteria. For example, one may use known gene boundaries in genomic sequences to define anchor points as we did in the Hox gene example described below. In addition, one may want to use automatically produced local alignments as anchor points to speed up the alignment procedure as outlined in [inconsistent with those 'biologically defined' anchors or inconsistent with each other. Since anchor points derived from expert knowledge should be more reliable than anchor points identified by some software program, it would make sense to first accept the known gene boundaries as anchors and then to use the automatically created local alignments, under the condition that they are consistent with the known gene boundaries. So in this case, one could use local alignment scores as scores for the automatically created anchor points, while one would assign arbitrarily defined higher scores to the biologically verified gene boundaries.The greedy selection of anchor points makes it possible for the user to lined in . Note thHox gene clusters of vertebrates. Hox genes code for homeodomain transcription factors that regulate the anterior/posterior patterning in most bilaterian animals [ParaHox genes, arose early in metazoan history from a single ancestral "UrHox gene" [Hox genes are usually organised in tightly linked clusters such that the genes at the 5'end  determine features at the posterior part of the animal while the genes at the 3'end  determine the anterior patterns.As explained above, tandem duplications pose a hard problem for automatic alignment algorithms. Clusters of such paralogous genes are therefore particularly hard to align. As a real-life example we consider here the  animals ,27. Thisox gene" . Their eHox clusters that presumably arose through genome duplications in early vertebrate evolution and later in the actinopterygian (ray finned fish) lineage [Hox clusters of gnathostomes have a length of some 100,000nt and share besides a set of homologous genes also a substantial amount of conserved non-coding DNA [In contrast to all known invertebrates, all vertebrate lineages investigated so far exhibit multiple copies of  lineage -33. Thes lineage  for a reding DNA  that preding DNA .Hox clusters of the pufferfish Takifugu rubripes. Despite the fact that the Hox genes within a paralogy group are significantly more similar to each other than to members of other paralogy groups, there are several features that make this dataset particularly difficult and tend to mislead automatic alignment procedures: (1) Neither one of the 13 Hox paralogy groups nor the Evx gene is present in all four sequences. (2) Two genes, HoxC8a and HoxA2a are present in only a single sequence. (3) The clusters have different sizes and numbers of genes .Figure Hox genes in this example by matching blocks from one Hox gene with parts of a Hox gene from a different paralogy group. As a consequence, genes that should be aligned, such as HoxA1Oa and HoxDIOa, are not aligned with each other.We observe that without anchoring DIALIGN mis-aligns many of of the Anchoring the alignment, maybe surprisingly, increases the number of columns that contain aligned sequence positions from 3870 to 4960, i.e., by about 28%, see Table biological quality of the anchored and non-anchored alignments but also looked at their numerical scores. Note that in DIALIGN, the score of an alignment is defined as the sum of weight scores of the fragments it is composed of [below the non-anchored alignment  from three teleost fishes  yields an anchored alignment score that is some 15% above the non-anchored score.We investigated not only the posed of . For somcore blocks for which 'biologically correct' alignments are known. There are two scoring systems to evaluate the accuracy of multiple alignments on BAliBASE protein families. The BAliBASE sum-of-pairs score measures the percentage of correctly aligned pairs of amino acid residues within the core blocks. By contrast, the column score measures the percentage of correctly aligned columns in the core blocks, see [BAliBASE is a benchmark database to evaluate the performance of software programs for multiple protein alignment . The datcks, see ,10 for mnot real-world sequences, but have been artificially truncated by the database authors who simply removed non-homologous C-terminal or N-terminal parts of the sequences. Only the most recent version of BAliBASE provides the original full-length sequence sets together with the previous truncated data. Therefore, most studies based on BAliBASE have a strong bias in favour of global alignment programs such as CLUSTAL W [local sequence similarities, on the other hand, is systematically underestimated by BAliBASE. Despite this systematic error, test runs on BAliBASE can give a rough impression about the performance of multiple-alignment programs in different situations.Thus, alignment programs can be evaluated by their ability to correctly align these core blocks. BAliBASE covers various alignment situations, e.g. protein families with global similarity or protein families with large internal or terminal insertions or deletions. However, it is important to mention that most sequences in the standard version of BAliBASE are LUSTAL W ; these pDIALIGN has been shown to perform well on those data sets in BAliBASE that contain large insertions and deletions. On the other hand, it is often outperformed by global alignment methods on those data sets where homology extends over the entire sequence length but similarity is low at the primary-sequence level. For the further development and improvement of the program, it is crucial to find out which components of DIALIGN are to blame for the inferiority of the program on this type if sequence families. One possibility is that biologically meaningful alignments on BAliBASE would have high numerical scores, but the greedy heuristic used by DIALIGN is inefficient and returns low-scoring alignments that do not align the core blocs correctly. In this case, one would use more efficient optimisation strategies to improve the performance of DIALIGN on BAliBASE. On the other hand, it is possible that the scoring function used in DIALIGN assigns highest scores to biologically wrong alignments. In this case, an improved optimisation algorithm would not lead to any improvement in the biological quality of the output alignments and it would be necessary to improve the objective function used by the program.a) using the non-anchored default version of the program and (b) using the core blocks as anchor points in order to enforce biologically correct alignments of the sequences. We then compared the numerical DIALIGN scores of the anchored alignments to the non-anchored default alignments. The results of these program runs are summarised in Table below the scores of the non-anchored default alignments.To find out which component of DIALIGN is to blame for its unsatisfactory performance on some of the BAliBASE data, we applied our program to BAliBASE  anchored alignment was lower than the score of the  default alignment. The DIALIGN score of the anchored alignment was 9.82 compared with 11.99 for the non-anchored alignment, so here the score of the anchored alignment was around 18 percent below the score of the non-anchored alignment.We investigated how many anchor points were necessary to enforce a correct alignment of the three core blocks in this test example. As it turned out, it was sufficient to use one single column of the core blocks as anchor points, namely the first column of the third motif. Technically, this can be done by using three anchor points of length one each: anchor point connecting the first position of this core block in sequence 1 with the corresponding position in sequence 2, another anchor connecting sequence 1 with sequence 3 and a third anchor connecting sequence 1 with sequence 4. Although our anchor points enforced the correct alignment only for a single column, most parts of the core blocks were correctly aligned as shown in Figure RepeatMasker, they need to be taken into account in the context of phylogenetic footprinting: if a sequence motif is conserved hundreds of millions of years it may well have become a regulatory region even if it is (similar to) a repetitive sequence in some of the organisms under consideration [Evolutionarily conserved regions in non-coding sequences represent a potentially rich source for the discovery of gene regulatory regions. While functional elements are subject to stabilizing selection, the adjacent non-functional DNA evolves much faster. Therefore, blocks of conservation, so-called phylogenetic footprints, can be detected in orthologous non-coding sequences with low overall similarity by comparative genomics . Alignmederation .TRACKER [M2M3 and M2M3. Since this step is performed based on the overlap of sequence intervals without explicitly considering the sequence information at all, TRACKER is very fast as long as the number of conflicting pairwise alignments remains small. In the final step DIALIGN is used to explicitly calculate the multiple sequence alignments from the subsequences that belong to individual clusters.The phylogenetic footprinting program TRACKER  was desiTRACKER  with nonFor the initial pairwise local alignment step the search space is restricted to orthologous intergenic regions, parallel strands and chaining hits. Effectively, TRACKER thus computes alignments anchored at the genes from BLASTZ fragments.E values) reduces the CPU requirements for the DIALIGN alignment by more than an order of magnitude. While this is still much slower than TRACKER (20 min vs. 40 s) it increases the sensitivity of the approach by about 30 – 40% in the Fugu example, Table We have noticed  that DIAa) to define an meaningful objective function and (b) to design an efficient optimisation algorithm that finds optimal or at least near-optimal alignments with respect to the chosen objective function. Most multi-alignment programs are using heuristic optimisation algorithms, i.e. they are, in general, not able to find the mathematically optimal alignment with respect to the objective function. An objective function for sequence alignment should assign numerically high scores to biologically meaningful alignments. However, it is clearly not possible to find a universally applicable objective function that would give highest numerical scores to the biologically correct alignments in all possible situations. This is the main reason why alignment programs may fail to produce biologically reasonable output alignments. In fact, the impossibility to define a universal objective function constitutes a fundamental limitation for all automated alignment algorithms.Automated alignment procedures are based on simple algorithmical rules. For a given set of input sequences, they try to find an alignment with maximum score in the sense of some underlying objective function. The two basic questions in sequence alignment are therefore  The chosen objective function may not be in accordance with biology, i.e., it may assign mathematically high scores to biologically wrong alignments. In this case, even efficient optimisation algorithms would lead to meaningless alignments. (b) The mathematically optimal alignment is biologically meaningful, but the employed heuristic optimisation procedure is not able to find the alignment with highest score. For the further development of alignment algorithms, it is crucial to find out which one of these reasons is to blame for mis-alignments produced by existing software programs. If (a) is often observed for an alignment program, efforts should be made to improve its underlying objective function. If (b) is the case, the biological quality of the output alignments can be improved by using a more efficient optimisation algorithm. For DIALIGN, it is unknown how close the produced alignments come to the numerically optimal alignment – in fact, it is possible to construct example sequences where DIALIGN's greedy heuristic produces alignments with arbitrarily low scores compared with the possible optimal alignment.There are two possible reasons why automated alignment procedures may fail to produce biologically correct alignments,  correct alignment was 13% below the score of the non-anchored alignment. All sequences in Figure Hox paralogy groups, and different sequences contain different genes. For such an extreme data set, it is unlikely that any reasonable objective function would assign an optimal score to the biologically correct alignment. Here, the problem is that sequence similarity no longer coincides with biological homology. The only way of producing good alignments in such situations is to force a program to align certain known homologies to each other. With our anchoring approach we can do this, for example by using known gene boundaries as anchor points.In the Fugu example, Figure For the BAliBASE benchmark data base, the total score of the  anchored alignments was also below the score of the  non-anchored default alignments.single column using corresponding anchor points to obtain a meaningful alignment of the entire sequences where not only the one anchored column but most of the three core blocks are correctly aligned. This indicates that the correct alignment of the core blocks corresponds to a local maximum in the alignment landscape.This implies, that improved optimisation algorithms will not lead to biologically improved alignments for these sequences. In this case, however, there is some correspondence between sequence similarity and homology, so one should hope that the performance of DIALIGN on these data can be improved by to designing better objective functions. An interesting example from BAliBASE is shown in Figure HoxA cluster example the numerical score of the anchored alignment was around 15% above the score of the non-anchored alignment. This demonstrates that the greedy optimisation algorithm used by DIALIGN can lead to results with scores far below the optimal alignment. In such situations, improved optimisation algorithms may lead not only to mathematically higher-scoring alignments but also to alignments that are closer to the biologically correct alignment. We will use our anchored-alignment approach systematically to study the efficiency of objective functions and optimisation algorithms for our segment-based approach to multiple sequence alignment.In contrast, in the teleost The program is available online and as downloadable source code at Göttingen Bioinformatics Compute Server (GOBICS) .The author(s) declare that they have no competing interests.