Because sequence alignment is arguably the most extensively used procedure in computational biology, we employ it here to make these general concepts more concrete. The maximum similarity estimator  and the centroid estimator  are used to demonstrate the application of Bayesian credibility limits to alignment estimators. Application of Bayesian credibility limits to the alignment of 20 human/rodent orthologous sequence pairs and 125 orthologous sequence pairs from six Shewanella species shows that credibility limits of the alignments of promoter sequences of these species vary widely, and that centroid alignments dependably have tighter credibility limits than traditional maximum similarity alignments.Computational biology is replete with high-dimensional (high-D) discrete prediction and inference problems, including sequence alignment, RNA structure prediction, phylogenetic inference, motif finding, prediction of pathways, and model selection problems in statistical genetics. Even though prediction and inference in these settings are uncertain, little attention has been focused on the development of global measures of uncertainty. Regardless of the procedure employed to produce a prediction, when a procedure delivers a single answer, that answer is a point estimate selected from the solution ensemble, the set of all possible solutions. For high-D discrete space, these ensembles are immense, and thus there is considerable uncertainty. We recommend the use of Bayesian credibility limits to describe this uncertainty, where a  sequences is a point estimate, it may not be representative of the entire set (ensemble) of possible alignments of those sequences; thus, there may be considerable uncertainty associated with any one alignment among an immense ensemble of possibilities. To address the uncertainty of a proposed alignment, we used a Bayesian probabilistic approach to assess an alignment's reliability in the context of the entire ensemble of possible alignments. Our approach performs a global assessment of the degree to which the members of the ensemble depart from a selected alignment, thereby determining a credibility limit. In an evaluation of the popular maximum similarity alignment and the centroid alignment , we find that the centroid yields tighter credibility limits (on average) than the maximum similarity alignment. Beyond the usual interest in putting error limits on point estimates, our findings of substantial variability in credibility limits of alignments argue for wider adoption of these limits, so the degree of error is delineated prior to the subsequent use of the alignments. For example, in RNA secondary structure prediction, the challenge is to select a specific set of base pairs from a combinatorially large collection, as a prediction of the secondary structure of an RNA polymer, given its sequence. Similarly, in pathway inference, the challenge is to select a set of graph edges to connect genes or their products (nodes) from a combinatorially large collection of possible edge sets, based on gene expression or other data. Model selection problems for studying diseases stemming from mutlifactorial inheritance are becoming increasing common in the post-genome era. In these studies, the ultimate goal is to identify the combinations of genes responsible for inheritance components of disease etiology based on genetic and/or other post-genome data. In motif finding, the challenge is to select a single member of a large ensemble of possible combinations of motif sites in a set of sequences. Procedures that select the single best scoring solution, such as maximum similarity, maximum likelihood, maximum http://www.ncbi.nlm.nih.gov/BLAST/) and optimization http://fasta.bioch.virginia.edu/fasta_www2/) alike, typically report the selected alignment, and a statistical score that assesses how likely an alignment with a score as good or better could have emerged by chance, under a specified null distribution . While methods that assign the significance of alignments under a null distribution have been well studied, assessments of the uncertainty of a proposed alignment, defining the confidence in this alignment and assessing its overall reliability, have received considerably less attention.Sequence alignment is a typical example and is arguably the most important high-D discrete prediction problem for biology. Because it is the cornerstone capability used by a multitude of computational biology applications, we employ sequence alignment to make these general concepts concrete. Sequence alignment methods commonly focus on identifying the highest scoring alignment between two sequences, and assessing the statistical significance of this alignment m and n have k represents the number of matches in the alignment 29 possible local alignments. The question addressed here is: How, based on the available data, should we articulate the overall uncertainty of a selected estimating alignment (how well does it represent the large ensemble of possible solutions), and thus assess the reliability of this alignment?Regardless of the alignment procedure employed, when a single alignment is chosen for the comparison of two (or more) sequences, it is a point estimate  selected from a large ensemble of all possible alignments. For example, two sequences of length i,j) is assessed by comparing the score of the optimal alignment to the score of this alignment under the constraint that positions i and j do not align The traditional approach to address the reliability of a single alignment is to evaluate the optimal alignment in the context of a set of near-optimal alignments. Near-optimal or suboptimal alignment analysis involves evaluating residue alignment consistency over the set of defined near-optimal alignments With this in mind, these near-optimal alignment and model-based methods have offered significant improvements in reliability for tasks such as structural alignment. However, these methods are focused on delineating the reliability/uncertainty of the individual components of an estimated alignment, not the reliability of an estimated alignment in the context of the entire alignment space. There are methods to assess the accuracy of an alignment in the prediction of a ground-truth standard such as an alignment based on crystal structures The introduction of probabilistic alignment methods In discrete spaces, how strongly does the available data recommend a single chosen estimate?When the data provide weak evidence for any single estimate, what criteria can be used to judge the credibility of an estimate, and what are reasonable limits in the degree of variation within the ensemble from this estimate that are consistent with the data?How can we identify the single estimate that best represents the ensemble of alignments and that is consistent with the data?We suggest the following answers to these questions:The strength of the recommendation of the data for any specific estimate is equal to its posterior probability under the assumed probabilistic model.A credibility limit is the radius of the smallest hyper-sphere around a proposed estimate that contains a specified proportion of the probability mass of the posterior distribution, where the radius is measured by the number of elements by which two solutions differ. The size of this limit characterizes an estimate's credibility.The estimate with the minimum credibility limit best represents the ensemble.a-posteriori Viterbi solutions) are optimal under a zero/one-loss function, there is no principled reason to expect them to have tight credibility limits and, thus, to have high credibility. Below we compare the credibility limits for centroid alignments to those for maximum similarity alignments.To address these questions and test our proposed answers, we employ a Bayesian probabilistic approach. In the A statistical model that yields a probability distribution over an ensemble of solutions is essential for the characterization of uncertainty. Specifically, we are interested in using the data, in combination with any parameters that have been specified, to assign “posterior” probabilities to the members of the ensemble. We call these posterior probabilities because they are assigned after considering the implications of the data, the posterior weighted ensemble. Because in high-D settings it is often impossible to characterize the entire immense ensemble of solutions, it is common practice to employ representative samples from the posterior distributions to draw inferences or make predictions A be a matrix that characterizes an alignment whose -entry is defined as:I≤J. Because a residue cannot align with more than one other residue, two constraints must be satisfied, i,jA+k,lA≤1, i≤k, l≤j. Let Θ be a matrix of residue pair similarities, such as one of the BLOSUM λo, λe) be the probability of opening and extending a gap, respectively.A probabilistic alignment model from which samples can be drawn can be described as follows. An alignment describes a set of aligned residues and associated insertion and deletion events. For a pair of sequences, R(1) and R(2), are seen as random variables, and the remaining terms are deterministic variables with perhaps unknown values. In maximum likelihood estimation, the values of these unknowns, which maximize the likelihood, are the maximum likelihood estimates. Typically, the user must set specific parameter values for the scoring matrix Θ0 and gap probabilities Λ0 to find the most probable alignment A* over all possible alignments:Most sequence alignment methods optimize an objective function that can be described, based on a probabilistic model, as a log-likelihood 0, and gap penalties, Λ0:A* to the sum of these joint likelihoods over all alignments. It approaches a value of 1 when a single alignment dominates all others.To capture the entire alignment space in a probabilistic manner, the problem of alignment can be formulated as a Bayesian inference problem Given that the number of possible alignments for even small biopolymer sequences is immense, it is not feasible to calculate the probability of all alignments in a brute force manner. However, we can almost always use the recursive relationships that are fundamental to dynamic programming (DP) to draw guaranteed representative samples from the solution ensemble In this section, we describe procedures for finding credibility limits and mean distances for the sequence alignment problem. We begin by examining the distribution function of the distances of the ensemble members from a proposed estimate. Basic to this perspective are two concepts: 1) given the available data, the solution space is inherently uncertain; and 2) a proposed estimate is a point estimate  that is intended to represent the entire ensemble Ak)( and Am) and R(2), of length I and J, the Hamming distance is simply the number of aligned positions that differ between Ak)( and Am). For alignments, this distance is simply the sum of the differences in two binary matrices of size (I×J). When ensemble members are binary objects, the Hamming distances are also equal to distances on other scales MA, the MS alignment, and CA, the EC alignment.A simple measure of the difference between two members of a discrete ensemble  is the Hamming distance. For two alignments, iD = D be the distance of the ith member, iA, of the ensemble from a proposed estimating alignment, xA, where X is a categorical variable indicating the estimator . We then rank the ensemble members by their distances from xA, and let d(1−α) is the (1−α)th quantile. Now the credibility limit at (1−α) is dα), from the estimate xA.Rank these alignments by their distance, d̂α)th quantile in this sample is our estimator of dα) is known, and the maximum length of an alignment in the ensemble is the length of the shorter of the two sequences (I). Thus, the maximum Hamming distances between an estimating alignment and the longest member of the ensemble is (LE+I). However, in our studies, we found that using this sum as a normalizing factor was misleading for cases in which the posterior space of alignments tended to be dominated by shorter local alignments. For example, the local alignments of the randomly shuffled sequences described in the LE+I) as the normalizing constant in this case produced normalized distances that were not close to one, even when there were no base pairs in common between a sampled alignment and the estimating alignment. To adjust these differences, we used the length of the longest sampled alignment, LS, as the second term in our normalizing sum, and the normalizing distance between the estimating alignment xA and the thi alignment in the sample is S indicates the set of sampled alignments. Using this normalization factor yields normalizing distances with values between zero and one. A perfect match would yield an ND score of zero, and in the case where the longest sampled alignment has no base pairings in common with the estimating alignment, the ND score would be one. We define the credibility of the alignment at (1−α) to be NDα) possible alignments, except in the unusual event that this single alignment alone has high probability. In fact, the most probable alignment, the MS alignment, often has very small probability. For example, in this study, the probabilities of the MS alignments ranged from 10As Carvalho and Lawrence In contrast, centroid alignments garner information from the complete ensemble of alignments, because these alignments minimize the expected Hamming distance from the complete posterior weighted ensemble of alignments. Centroid alignments correspond directly to the reliable alignments of Miyazawa with a cut off 0.5 Shewanella. All sequence pairs were evaluated using BALSA To assess the credibility measures and estimators described above, we examine the local alignments of sequences from (1) 20 orthologous genes between human and rodent, and (2) 24 orthologous genes between six species of cis-regulatory modules http://www.repeatmasker.org/). For the local alignments of the 20 gene pairs and the 20 intergenic regions, we examined the credibility limits associated with two estimating alignments: the MS, and the EC. Specifically, we examined the 95% quantiles of the normalized distances (ND), computed based on the distances between these estimating alignments from the 1000 sampled alignments from the posterior alignment distribution. ND95) versus the EC 95% credibility limits (EC ND95) for the local alignments of the genes and the intergenic regions. For contrast, the genes were randomly shuffled, and 95% credibility limits were defined for these non-related sequence pair alignments.The 20 orthologous genes for human/rodent are specifically up-regulated in human skeletal muscle tissue, and their upstream sequences have been used in previous studies to locate First, notice that the credibility limits for the gene sequence alignments are small, and the difference between the EC and MS is negligible. These genes are so highly conserved that the majority of the posterior distribution falls along a small set of paths with high probability, thus creating high correlation between the EC and MS. Alternatively, when the gene sequences are shuffled, the hyper-sphere surrounding 95% of the posterior distribution is very large because the probability of aligning any two residues is essentially random. This results in extremely large credibility limits with high deviation in the distance of the ensemble from the EC and MS. The intergenic regions are less conserved than the genes and, thus, are intermediate between these two extremes. Notice that the credibility limits are often surprisingly large, with normalized distances over 50% for 18 of the 20 MS alignments, and for 17 of the 20 EC alignments. This indicates that we have confidence in less than half the predicted aligned base pairs. As the plot shows, there is considerable variation in the credibility limits over the 20 examples when either the EC or MS limit is used. The credibility limits for the EC range from 29% of maximal to nearly 91%, while the MS limits range from 37% to almost 100% of maximal. This result highlights the need to report credibility limits for every sequence pair. We also see that for all but one of the sequence pairs, the MS credibility limits are greater than those for the EC. Furthermore, for 11 of the 20 upstream sequence pairs, the MS credibility limits were more than 600 base pairs larger than EC credibility limits. Thus while the differences in ND95) for the EC and MS are shown as bars, and the values are given in th percentile alignment differs from the EC estimator by 270 of a possible 1556 base pairs that could potentially differ (ND95 = 0.29), while the MS is about 20% larger with an ND95 = 0.37. Of the 20 promoter sequence pairs, there are 11 in which the two credibility limits are markedly different . ND95 values; for example, the alignment in ND95 = 0.72 for the EC, and ND95 = 0.77 for the MS alignment. Because the centroid estimator is the closest feasible alignment to the mean, for this sequence pair the mean and the mode are close, as is typical of symmetric distributions Taken together, the differences between the 20 MS normalized distances and 20 EC normalized distances in Shewanella for which full genome sequence data are available: 1) S. denitrificans OS217 (DENI), 2) S. loihica PV-4 (SPV4), 3) S. oneidensis MR-1 (SONE), 4) S. putrefaciens CN-32 (CN32), 5) Shewanella sp. MR-4 (SMR4), and 6) Shewanella sp. MR-7 (SMR7). We chose SMR4 as our base species, aligning orthologous sequences from each of the other five to the region from SMR4. Starting with SMR4, the species in order of increasing evolutionary distance are SMR4>SMR7>SONE>CN32>SPV4∼DENI. As before, we examined the 95% quantiles of the normalized distances, computed based on the distances between the estimating alignments and the sampled ensemble of alignments drawn from the posterior alignment distribution. ND95 versus the EC ND95 values for each of 24 randomly selected orthologous regions, for the pairwise comparison of SMR4 to each of the five species at varying evolutionary distances .We also examined the credibility limits for the MS and EC estimators for local alignments of orthologous pairs of intergenic regions (up to 500 bp upstream of orthologous genes) from six species of ND95 and MS ND95<0.05), but there are also three pairs whose alignments cannot be trusted (EC ND95 and MS ND95>0.6), and the remainder are scattered over the full range in between.The two species SMR4 and SMR7 are very closely related, having been isolated from samples taken at different depths  from a single location (latitude and longitude) in the Black Sea a priori which sequences it would be most beneficial to align. The tight credibility limits shown in ND95 values for the EC and MS alignments indicate that alignment of SPV4 or DENI sequences would not contribute to a meaningful evaluation of the SMR4_0576 promoter region. Unfortunately, not all alignments of promoter regions from SMR4 with the promoter sequences of orthologous genes in SONE and CN32 are reliable. For example, as We further evaluated the findings shown in Shewanella species. Specifically, alignment of orthologous promoters can substantially increase the power of motif finding, if the alignments can be trusted. However, the findings shown in These findings of large differences in the reliability of alignments within species pairs have had a substantial practical impact on our studies of phylogenetic motif finding using these reliably aligned with any single residue in the other sequence is excluded from the centroid alignment. Aligning any such residues to any bases in the other sequence would only increase the average distance of the centroid alignment from the posterior distribution of alignments. In addition, with probabilistic alignment, we return marginal probabilities of all residue pairs. Therefore, to display all the features of this alignment, we employ 1) a traditional dash to represent gaps, 2) a dot to represent residues that cannot be reliably aligned and are thus ignored in the alignment, and 3) a gradient color scheme  to show the base pair alignment probabilities, where red indicates high probability for that residue pair, green indicates probabilities nearing 50%, and the ignored region is grayed out to further differentiate those residues for which the variability in alignments is too great to permit marginal pair probabilities of 0.5 or greater. The use of heat maps or other means to visually illustrate confidence in the individual alignment of individual pairs of bases must accommodate a different feature for centroid alignments. Specifically, EC alignments have a feature not present in standard alignments, in that they allow stretches of sequence in the middle of an alignment to remain unaligned in a manner analogous to those regions at the ends of local alignments. That is, a residue in one sequence that cannot be Because prediction and estimation involve making inferences about unknown quantities based on the available data, they are inevitably uncertain. Thus, when a specific value is reported as a point estimate, it is common in many fields to simultaneously report a confidence limit or a credibility limit, which is the Bayesian analog. Such limits are all too often absent in computational biology. Here, to promote their broader adoption, we describe a method for estimating credibility limits and illustrate these concepts using sequence alignment. These credibility limits are derived from the empirical distribution function of the Hamming distance from the estimator to the members of the ensemble of solutions, or more accurately, a representative sample of the ensemble of solutions. The 95% credibility limit of a proposed estimate describes the posterior distribution by indicating the normalized Hamming distance containing 95% of the probability mass of the posterior distribution. The existence of these limits begs the question: What estimation procedure will yield tight credibility limits? We advocate the use of recently developed centroid estimators that minimize the expected Hamming distance to address this question.While it is reasonable to expect centroid estimators to produce tighter credibility limits, it is not a guaranteed product of this procedure, because the centroid is the estimator that minimizes the average differences from the posterior ensemble, while the credibility limits are based on a quantile. Nevertheless, our finding of tighter credibility limits for EC alignments compared to MS alignments should come as no surprise, since the well-known zero/one loss risk associated with the latter estimators provides no principled reason to expect that such estimators will be near the center of the posterior distribution of alignments. On the other hand, centroid alignments, which are the alignment nearest to the multivariate mean of the posterior distribution, are centered in the posterior distribution Shewanella species highlight the need for assessing the overall reliability of sequence alignments. Without such limits, there is little to distinguish alignments that vary greatly from one another in their reliability. Furthermore, our findings indicate that centroid estimators have promising potential to improve sequence alignment. For example, for over half of the human/rodent non-coding sequence pairs (each of ∼3000 bases) in our sample, the EC and MS alignments differ by more than 600 base pairs, and similar relative differences are observed in Shewanella alignments. While we report here on the credibility of nucleotide sequence alignments, they are equally applicable and valuable for protein sequence alignments.Our findings of 1) high variability in the credibility limits in the alignments of promoter sequences of 20 human/rodent sequence pairs and 2) similar high variability among 4 of the 5 pairs of In some discrete high-D inference problems, the posterior ensemble of solutions may not only be asymmetric, but also it may be multimodal, as has been reported for RNA secondary structures As mentioned above, the probabilistic model used is a Smith-Waterman recursive DP algorithm whose Viterbi alignment corresponded exactly to the MS alignment reported here. Thus, differences in credibility limits reported here are solely the result of the differences in the estimation procedures. In addition, the alignment that minimizes expected Hamming distance loss and also follows the requirement concerning adjacent gaps in the two sequences are available using a DP algorithm While we believe this evidence supports reconsideration of the maximum scoring alignment paradigm, stronger evidence for reconsideration has been in the literature for over a decade. In 1995, Miyazawa n and m, the time complexity is O(n*m) for both the optimization and Bayesian algorithms. Running times to obtain credibility limits in a recursive setting will generally be longer than times required to obtain optimal estimates because a back-trace step must be executed only once to obtain the optimal, while it must be employed multiple times to draw samples. However, this sampling will not generally greatly increase overall running times, because back-trace recursions are usually of a lower time complexity than their forward steps. For example, for local alignments the time complexity of the back-trace recursions is only O). For problems not open to recursive solutions, MCMC algorithms are commonly employed, using procedures like simulated annealing. Credibility limits and centroids also can be obtained using MCMC sampling with run times that may be less than those for optimizations We also note that the time complexity of algorithms for obtaining centroid alignments and credibility limits is not different from those of more traditional optimization based methods. When recursions can be employed to obtain optimal solutions via DP, analogous recursions are frequently available for associated probabilistic models, and stochastic back-trace procedures can be employed to draw samples from the posterior ensemble of solutions Shewanella sp. MR-4 and MR-7 in Shewanella pairs. In our on-going work with Shewanella, we have found 1329 orthologous genes that were present in all six species and computed the 95% credibility limits for both the MS and EC, for all the promoters from SMR4 aligned with the orthologous sequences from each of the remaining 5 strains. The EC ND95 credibility limits were smaller than the MS ND95 limits in 6078 (91.55%) of these 6645 sequence pairs  reported here for individual sequence pairs.The findings reported in this paper are for pairwise alignments. When multiple alignments are employed, we expect credibility limits to narrow because of the increased size of the data sets; however, we caution that the alignment space grows rapidly with increasing sequences in an alignment. Therefore, these limits may or may not shrink as quickly as expected. Furthermore, it is important to keep in mind that the credibility limits reported here are sampling estimates of true 95% quantiles, but with samples of 1000 the error bars on these estimates are 95%±1.35%. All the estimates in this work are based on a local probabilistic alignment model. While local alignment is the most common procedure, other probabilistic alignment procedures, or local alignments with other parameter settings Beyond the usual interest in putting error limits on point estimates, our findings of substantial variability in credibility limits of alignments argues for wider adoption of these limits, so that the degree of error is delineated prior to the subsequent use of the alignments. From a practical prospective, when credibility alignments are tight, those using these alignments in subsequent procedures can be confident in the input alignments and know the limited degree to which input alignment may vary. The absence of such limits may well lead to a false sense of confidence in subsequent findings, especially when credibility limits are wide, and/or seriously limit an investigator's ability to determine the source of difficulties or inconsistencies in subsequent procedures that depend on these unreliable alignments. In practice, knowing early in a study that alignments required for subsequent results are unreliable  might well lead an investigator to reconsider his/her plans. For example, in studies of phylogenetic tree reconstruction when it is known that input alignments are reliable, investigators' conclusions about phylogenetic relationships will be bolstered; whereas, prior knowledge that input alignments are unreliable will motivate serious investigators to revise their study design or, after the fact, permit reviewers to raise legitimate questions about the studies conclusions.ND95 values for any proposed estimate given a procedure for drawing samples from the posterior distribution. We caution that while the Hamming distance will be appropriate in many of these areas, it may not be as appropriate in some of these settings. Regardless of the distance measure used, the proposed procedure will return credibility limits for an estimator when a representative sample can be obtained. We believe the use of confidence or credibility limits is long overdue throughout the full spectrum of discrete high-D inference problems encountered in computational biology. These limits have a number of valuable uses, including gauging the degree by which solutions might depart from their estimated value, appraising the overall credibility of a prediction, and comparing the performance of alternative estimators in cases where a “gold standard” is not available.While the results presented here concern only sequence alignment, the procedures described are generally applicable to point estimates for high-D discrete spaces; this includes many major inference problems in computational biology, such as pathway prediction in systems biology, the prediction of phylogenetic trees, the reconstruction of ancestral states, the delineation of alternate splice forms, and prediction of RNA secondary structures. For any of these problems, the algorithm given in the Table S1Gene, ND95, and P-Quantile information on all 20 sequence pairs.(0.04 MB DOC)Click here for additional data file.


A major computational challenge in the genomic era is annotating structure/function to the vast quantities of sequence information that is now available. This problem is illustrated by the fact that most proteins lack comprehensive annotations, even when experimental evidence exists. We previously theorized that embedded-alignment profiles  provide a quantitative method that is capable of relating the structural and functional properties of proteins, as well as their evolutionary relationships. A key feature of alignment profiles lies in the interoperability of data format . Indeed, we have demonstrated that the Position Specific Scoring Matrices (PSSMs) are an informative M-dimension that is scored by quantitatively measuring the embedded or unmodified sequence alignments. Moreover, the information obtained from these alignments is informative, and remains so even in the “twilight zone” of sequence similarity (<25% identity)  One of the major challenges faced by biologists comes to this question: how to identify the relation between highly divergent protein sequences. Although numerous methods e.g.,  have beeembedded-alignment profiles present a protein as a vector where each entry quantifies the existence of alignments with a PSSM A phylogenetic profile represents a protein as a vector where each entry quantifies the existence of the protein in a different genomes Then, each of these modified query sequences is aligned by rps-BLAST against the parent profile, from which a seed is taken. Due to the “hit and the extension of the hit” approach of BLAST algorithm, the embedded “seed” creates a consistent initiation site that allows rps-BLAST to extend an alignment even between highly divergent sequences. The idea is summarily depicted in equences .Adaptive GDDA-BLAST is termed for its adaptive nature, and exploits similarities among embedded sequences to adaptively avoid expensive computations. Instead of inserting a seed into every position of a query sequence, Adaptive GDDA-BLAST embeds a seed at the query positions where the seed is likely to be extended to an alignment (see the Method section for details).Despite the great potential of the embedded alignment strategies in answering a diverse set of biological questions, their computational costs are prohibitively expensive, a problem that arises out of the current method of generating and analyzing embedded sequences. As proteins range in length from tens of amino acids to <8000, the proteomic scale studies using GDDA-BLAST are prohibitive in nature. To address this challenge, in this paper, we propose a novel sequence alignment algorithm that is as sensitive as GDDA-BLAST but is orders of magnitude faster. To compare GDDA-BLAST and Adaptive GDDA-BLAST in terms of execution time, we ran both methods with the 602 query sequences and the 51 target sequences randomly chosen from the SABmark twilight zone set TP is the number of true positives, TN is the number of true negatives and FP is the number of false positives. To calculate the sensitivity at different false positive rates for each query, we used the sequences with k highest Pearson's correleation coefficient for the query, while increasing k from 1 up to 40. As shown in To see if Adaptive GDDA-BLAST alignments could be used to encode informative alignment profiles for proteins, we took on the challenge of detecting structural homology in highly divergent protein sequences. For the test, we used 534 sequences from 61 fold groups in SABmark Twilight zone set. As employing 23,511 NBCI CDD PSSMs as a measuring PSSM set, each of 534 queries was encoded in an alignment profile. In this test, 60% coverage and 10% pairwise identity thresholds were used for filtering alignments. We used the Pearson's correleration coefficient to measure the similarity between two alignment profiles. We performed Receiver Operating Characteristic (ROC) curve analysis We performed analyses on a structurally resolved  transmembrane protein called Bovine Rhodopsin (PDB: 1F88) in order to determine the information contained in a pure population of embedded alignments 10).Our perfomance was evaluated against rps-BLAST and the TMHMM. TMHMM is a HMM-based method designed to predict transmembrane helices in proteins 10) and (3) the positional data correspond with the results obtained from TMHMM, even when tested with the expanded ILB DB under the highest statistical limit of rps-BLAST. In all cases, correlation exists between the curves obtained from the positional data and the known structural elements.It is resonable to consider that the amino-acids within transmembrane spanning helicies will be more conserved than the intervening loop residues. The support for this hypothesis is presented in inset). Both rps-BLAST and Adaptive GDDA-BLAST detect these smaller helices while Adaptive GDDA-BLAST has the highest signal. Another region of interest is contained between aa 91 and 111 which is a loop in the crystal structure, but is predicted to be a short helix by rps-BLAST and Adaptive GDDA-BLAST. We expect that this loop may be a bent-helix similar to other regions in the protein under native conditions.While both of TMHMM and Adaptive GDDA-BLAST do not accurately model the whole crystal structure, we observe interesting features. For example, several of the membrane-spanning helices are interrupted by loop regions that are not identified by TMHMM. Indeed, the C-terminus of 1F88 (aa 288–348) contains 3 small helices, the last of which is a bent-helix that is believed to be parallel to the membrane inset. BTo further show the utility of Adaptive GDDA-BLAST, we did the same analysis on a structurally resolved Ankyrin-repeat protein called Human Ankyrin-R (PDB: 1N11) X and the query sequence be Y. The length of sequence X is denoted as |X|. Assume that |X| and |Y| are n and m, respectively. A subsequence of X and Y, is represented as X|Y. Two subsequences that are aligned are represented within . For example, Let the target sequence be X as a “seed,” denoted by S, to every position of p% of X  of a target be used as seed. If so, for a target of 100 amino acid long (|X| = 100), 10 residues (k = 10) of N- or C- terminal of the target are selected as a seed. Thus, N- and C-terminal seeds can be represented as t is the number of target sequences. Moreoever, the same procedure needs to be repeated for a total number of queries.An embedded (chimera) sequence is generated by embedding either the N- or C-terminal portions of tion of  . Each chps-BLAST . For eaconly by the position of the seed, implying that for two subsequent chimeras, a considerable part of the computation is recyclable. In the Adaptive GDDA-BLAST approach, we re-use the outputs from each step of rps-BLAST for efficiency purposes. For clarity, we hereunder define the outputs of each step. In the first step of rps-BLAST, we find hits between w is a word size, is denoted as GE starting pair to distinguish it from the embedded seed of GDDA-BLAST.Note that chimera sequences differ Since a seed provides an exact match, it is very likely that the GE starting pair exists in an HSP that includes the seed. Moreover, we are only interested in the alignments that include the seed, since the other alignments are locatable through the conventional methods using the original query sequence. This limits the search space of rps-BLAST. For example, when a seed is inserted at the position 0 of a query sequence, our search space will be the region in gray, as shown in Because chimeras are essentially the same sequence if the seeds are excluded, most of their hits are conserved. Therefore, the hits between X and Y are resuable in computation of the alignments of any chimera sequences. Consider a chimera, C(q). Let Lemma 1.not interested in the hits of lemma 1-(a)  , since tma 1-(a)  for aligrps-BLAST performs ungapped extension on neighboring hits, resulting in HSPs. Similar as in Observation 2, we define the relation between an HSP of X-Y . For each hit, to generate an HSP, the ungapped extension is performed until the score drops below a threshold (HSP drop-off score). When a new HSP is constructed, the hits involved in the HSP are removed to prevent subsequent HSPs from extending over to them. This ensures that all local alignments produced later are not overlapped. We keep only the HSPs with scores larger than the threshold (minimum HSP score). Gapped extension is then performed for each HSP to generate partial alignments.The local alignments are found, as follows: First, the hits between the query and the target sequence are found. A hit consists of three consecutive residues with a score larger than a threshold . The minimum partial alignment length is proportionally determined to the length of the target sequence. Since a partial alignment is a locally most optimal alignment, it is not likely that a seed is extended further than the end position of the partial alignment. In the final step, a final alignment is chosen based on the the coverage of the alignment over the target sequence. This pre-filtered partial alignments are capable of removing the seed-inserting positions where a seed is not expendable to the final alignments with sufficient coverage.We keep only the partial alignments whose lengths are greater than the threshold , the maximum gap G(S)  is computed, as follows: GOP and GEP indicate a gap opening penalty and a gap extension penalty, respectively. Given a query sequence Y and a partial alignment  For N-terminal seed: q is computed in connection with the original query sequence positions. For example, if the N-terminal seed is inserted at the beginning of the query, then q is Given a seed q identified in Step 2, we perform an alignment with the seed S inserted in its corresponding position to generate the final alignments. The final alignments are generated by running dynamic programming, starting at the end position of the seed, For each query position a represents the alignment length at position Since we work with highly divergent sequences that produce low-identity alignments, it is reasonable to consider the following scenario: a longer alignment with a lower score can be biologically more meaningful than a shorter alignment with a higher score coverage and pairwise identity. Given an alignment , then the alignment is returned to the user.Not all alignments produced from the previous step are informative. In this step, we prune out the insignificant alignments using the metrics, % Both GDDA-BLAST and Adaptive GDDA-BLAST were implemented in C, and compiled for both Linux and Windows environments. GDDA-BLAST utilizes rps-BLAST in NCBI BLAST 2.2.15 package to compute the alignments. In order to validate the approach, we tested both GDDA-BLAST and Adaptive GDDA-BLAST in terms of the execution time and the accuracy. The execution time experiment was conducted on a dedicated machine with 1.8GHz Intel Core−3 and –h 10−6). Among the returned sequences, we filtered out any redundant sequences and the sequences whose pairwise identities to a query were more than 90%. For PSSM generation for those expanded sequences, PSI-BLAST (with the option of –h 10−6) was run again. All PSSMs used in this study will be provided upon request.To generate a PSSM set for a specific protein function or structure fold, we first collected the protein sequences, which were known to be related to the function or structure of our interest. For the PSSM set, we generated, using PSI-BLAST, PSSMs with the collected sequences or the sequences expanded from them. For expansion, each collected sequence is searched against NCBI NR database by PSI-BLAST , 0.0005 e-value threshold to include sequences for a profile construction at each iteration (-h option), and 1000 e-value threshold for returned alignment in the final iteration (-e option). For each query, all sequences that were aligned with the query out of 533 other sequences were sorted by their e-values. In case of SAM-T2K, In this study, we provide the supporting evidence for the following theories of ours: (1) that sequence embedding amplifies the low-identity alignments, and that these alignments are distinct from those derived through simple scaling of the e-value thresholds,; (2) that the low-identity alignments contain the information on protein structure/function; and (3) that PSSM libraries that are constructed from keyword searches of the CDD database, expanded using PSI-BLAST and then made into a specific database, can be used to classify proteins based on their structure/function. Several implications ensue from these findings.How to biologically characterize the membrane-spanning proteins is a challenging problem. Likewise, the structural studies on this protein class are fraught with artifacts introduced by crystallization and/or lack of appropriate co-factors . Our results demonstrate that signals derived through Adaptive GDDA-BLAST could provide the structural information distinct from Markov Models of the transmembrane regions. Due to non-native conditions, it is still tantalizing to consider that these measurements may isolate potential discrepancies in protein structure.The outstanding merit underlying the alignment profiles is centered on the successful construction of PSSMs representative of specific folds and/or activities. Indeed, the results from our present and companion studies Our results support the idea that statistical thresholds are often too stringent in domain detection algorithms. Through this study, it was found that additional information contained in alignments well below accepted statistical thresholds is also useable to identify domain boundaries and secondary structural elements. However, the finding was not applicable, when this same data were hierarchically clustered. Further analysis with a sufficiently large data set is required to identify and optimize the multiple variables that can identify highly divergent, yet informative alignments. Nevertheless, we propose that there is a wealth of information below statistical values, which is valuable to reserachers in annotating protein structure/function.In conclusion, we propose that future works be aimed at (1) creating comprehensive and refined PSSM libraries and (2) exploring sequence embedding at the level of the PSSM COBBLER  and withFigure S1Performance comparisons of different settings for GDDA-BLAST and Adaptive GDDA-BLAST. (a) Fold recognition performance of GDDA-BLAST when using different coverage threshold (with pairwise identity 10% threshold). It shows that %coverage is helpful to filter out noisy embedded alignments (no coverage threshold vs. 60% coverage thresholds). (b) Fold recognition performance of Adaptive GDDA-BLAST when using different distance metrics. Mutual information is estimated as described in [32]. 534 sequences of 61 SCOP fold groups from SABmark Twilight zone bechmark set. To calculate the sensitivity at different false positive rates, top-k sequences with the highest similarity to each 534 queries are considered as increasing k from 1.(0.41 MB EPS)Click here for additional data file.


Slow-fast analysis is a simple and effective method to reduce the influence of substitution saturation, one of the causes of phylogenetic noise and long branch attraction (LBA) artifacts. In several steps of increasing stringency, the slow-fast analysis omits the fastest substituting alignment positions from the analysed dataset and thus increases its signal/noise ratio.Our program SlowFaster automates the process of assessing the substitution rate of the alignment positions and the process of producing new alignments by deleting the saturated positions. Its use is very simple. It goes through the whole process in several steps: data input – necessary choices – production of new alignments.SlowFaster is a user-friendly tool providing new alignments prepared with slow-fast analysis. These data can be used for further phylogenetic analyses with lower risk of long branch attraction artifacts. The long branch attraction (LBA) artifact  still rea priori defined monophyletic groups). Several new alignments are then created, which contain only positions with a substitution rate lower than several thresholds, ranging from maximum to minimum rate. Thus the signal/noise ratio of the alignments successively increases, however, on the expense of amount of positions included in the alignment. Technically, the Slow-Fast method needs some input tree topology to work with. The topology must be provided by primary phylogenetic analysis of the dataset or by another independent method. This topology is needed for recognition of some monophyletic groups . Maximum parsimony is then used to determine the number of changes for each position within the monophyletic subgroups. Substitution rates assigned to positions are thus independent from interrelationships among the monophyletic groups, and therefore, these interrelationships may in turn be investigated without the fear of circularity. When each position is assigned its number of changes, those with the highest substitution rate are gradually omitted from new alignments. The following phylogenetic analyses of these new datasets (starting from the dataset containing the positions with the highest substitution rate) then provide results based on decreasing number of sequence data, however, with decreasing risk of artefactual groupings of long branches. There are several good examples of successful use of slow-fast analysis, see e.g. , [GenBank:EF209017], [GenBank:EF209018], [GenBank:EF209019] and [GenBank:EF209020], respectively.As an example, we analysed an alignment of 34 SSU rDNA sequences of 31 isolates of See e.g. ,16 for aThe alignment was prepared with ClustalX  and ambiBlastocystis isolates. This arrangement was enabled by the fact that we were mostly interested in resolving the two nodes represented in the input tree by trichotomies. Assigning substitution rates to alignment positions was thus independent from the true topology of these nodes. When the Blastocystis-containing subgroup was chosen in the tree window of SlowFaster program, new datasets in NEXUS format were created by clicking the "New alignments" button. Also, alignments of the same length as these new datasets, but shortened by random deletion of positions, were prepared by checking the "jackknives" checkbox on the program screen. These were used to test whether the loss of informative positions influences decrease of bootstrap support of the resulting tree topology more than shortening the datasets itself. We did not use the "Weights" feature of the program. When this checkbox is checked, the algorithm will assign different weights to changes within different chosen monophyletic groups. Changes within smaller groups would have assigned greater weight . The impact of large monophyla is then not dominant just because they contain more taxa.At this time, our SlowFaster program was employed to perform the slow-fast analysis. First, the alignment used in our analyses was loaded via the "Load alignment" button. Then the tree topology shown in fig. Blastocystis. All other alignments were analysed phylogenetically by all four methods  and topologies of the 32 resulting trees were bootstrapped.The maximum number of observed changes in a position of our alignment was 9. Thus, nine new alignments were created. They were labeled BlastoS8 down to BlastoS0, where the number is the threshold. BlastoS0 alignment was of course of no use in this particular case  as it contained only those positions that did not change during the evolution of It is highly probable that in some point of the slow-fast analysis, the profit from diminishing noise is lower than the loss from diminishing information. To roughly estimate the effect of the lack of information, we used average values of bootstraps as a measure of reliability of the alignments . We founBlastocystis (1b). In the original alignment, the former topology was very well supported by MP and LD, the latter was weakly supported by ML and MD. As the most saturated positions were deleted from alignment, the bootstrap support for topology "1a" decreased slightly in MP, but increased strikingly in MD and slightly in ML analysis (BlastoS1 not taken into account). The slow-fast analysis thus supports the "1a" topology. The second unresolved node concerned a branch of four reptile/amphibian isolates. Either it was basal to two major branches of mostly mammal/bird isolates , or it grouped with one of them . After the slow-fast method was applied, both LD and MD favored the first possibility with reasonable bootstrap support for S3 and S2 datasets. However, MP and ML were unable to decide on the two possibilities. We conclude that the "2b" topology is probably correct, although the certainty is not high. For other nodes, decrease/increase of their bootstrap support from datasets S3 and S2 is marked in fig. Results concerning the two unresolved trichotomies are shown in Table tocystis b. In theBlastocystis SSU rDNA tree it was able to make a choice among competing hypotheses and add more confidence in some other cases. Our software automates quite time-consuming slow-fast analysis.Overall, the slow-fast analysis, provided by the program SlowFaster, proved to be a useful tool to solve uncertain phylogenies by increasing the signal/noise ratio. In the Project name: SlowFasterProject home page: Operating system: MS WindowsProgramming language: Borland DelphiAny restrictions to use by non-academics: noneThe software can be accessed through the project home page and its current version is included with the manuscript as an additional file.MK and JF designed the program and contributed bug fixes. MK developed the source code. IC and MU collected the data used as example and analysed them together with MK. These three authors contributed to writing the manuscript. All authors read and approved the final manuscript.SlowFaster. This is the executable file of the application.Click here for fileSource code. Zip archive containing Delphi source code of the program and additional Delphi files.Click here for fileSample data. Zip archive containing sample data – alignments in Phylip, FASTA and NEXUS format and tree files in Newick format.Click here for file


Two problems complicate the study of selection in viral genomes: Firstly, the presence of genes in overlapping reading frames implies that selection in one reading frame can bias our estimates of neutral mutation rates in another reading frame. Secondly, the high mutation rates we are likely to encounter complicate the inference of a reliable alignment of genomes. To address these issues, we develop a model that explicitly models selection in overlapping reading frames. We then integrate this model into a statistical alignment framework, enabling us to estimate selection while explicitly dealing with the uncertainty of individual alignments. We show that in this way we obtain un-biased selection parameters for different genomic regions of interest, and can improve in accuracy compared to using a fixed alignment.We run a series of simulation studies to gauge how well we do in selection estimation, especially in comparison to the use of a fixed alignment. We show that the standard practice of using a ClustalW alignment can lead to considerable biases and that estimation accuracy increases substantially when explicitly integrating over the uncertainty in inferred alignments. We even manage to compete favourably for general evolutionary distances with an alignment produced by GenAl. We subsequently run our method on HIV2 and Hepatitis B sequences.We propose that marginalizing over all alignments, as opposed to using a fixed one, should be considered in any parametric inference from divergent sequence data for which the alignments are not known with certainty. Moreover, we discover in HIV2 that double coding regions appear to be under less stringent selection than single coding ones. Additionally, there appears to be evidence for differential selection, where one overlapping reading frame is under positive and the other under negative selection. A step towards this is our attempt to develop a method which can deal with the vast amount of viral data, as well as the complexity of viral genomes and their high divergence and subsequent unreliability of alignment.In the past few years we have witnessed an explosion in the viral genomic data available. GenBank alone holds over 80,000 close to complete viral genomes, and numbers are rising fast. For example, since the submission of the first SARS genome in May 2003, over 140 more have been published. With this genomic data at hand we hope to finally be able to tackle our understanding of viruses. Mechanisms of selection, that is to say the rate Several papers ,13-16,18de novo detection of overlapping genes  with (0 ≤ k < |P|) gets assigned to a certain 'region-type' r, with (r ≤ R), where regions of the same type are assumed to evolve in a similar way.To be able to calculate the probability of a certain alignment between E we use a model very similar to the one in de Groot et al.  – an array consisting of the degeneracy annotation of a nucleotide for each of the three reading frames. In our example in Figure A and B. This results in an annotation of  for our nucleotide C in the overlap, meaning that we have a degeneracy annotation of 2 and 1 with respect to gene A and B respectively.We model the evolution of our sequences according to the Hein & Støvlbæk  model. WUsing this degeneracy annotation we incorporate the concept of selection factors into our framework: transitions and transversions occur according to the Kimura  model, ax in a region of type r in S1 with degeneracy-type array t. Then our factors will be given by Fr ts and Fr tv, for a transition and a transversion respectively. Within each region, we assign a selection factor to each gene within it, that is to say if gene A and gene B overlap in region r, we have selection factors r respectively in gene A and B only. In the case of a mutation causing a non-synonymous substitution in both genes, we would let it have selection factor F2 ts = B. A transversion however would be multiplied by the selection factor F2 tv = A and gene B. If we were to assume independence between genes, the probability of a mutation causing a non-synonymous change in both genes would be given by fAB = fA·fB.Consider a nucleotide t1, t2, t3] in region r an identity, transition and transversion after time τ are given by exp Qr(t)τ where Qr(t) is the appropriate instantaneous Kimura rate matrix:The probabilities of observing at a site of degeneracy  mutating into nucleotide y.with We would like to note that even though our alignment model does assume independence of sites, we model a local dependency in our evolutionary model by conditioning our emission probabilities on the nucleotide context in the ancestral sequence. An undoubtable improvement would be to model the dependency as continuous throughout the evolutionary process . HoweverTo compute the probability of an alignment we use a simple indel model with Match, Insert and Delete states. We have as alignment parameters a gap-opening, a gap-extension and a transition probability from any state to the end state. All other state transition probabilities may be derived from these. The Insert and Delete states emit a nucleotide from a uniform distribution, aligned to a gap. In the Match state nucleotide pairs are emitted according to our above model.probabilistic alignment, which instead of producing an 'optimal' alignment, handles the set of all possible alignments and their likelihood. It computes posterior probabilities for each state at every nucleotide position. We thus are considering all possible sequence alignments and weighing them appropriately , accordely , we may rewrite the emission term of the log likelihood log L as follows:As shown in Figure R + 2 emission parameters a and b we now find the maximum likelihood estimates using the Newton-Raphson iteration method. We may do this by taking the explicit derivatives of the likelihood function, possible because of the simple substitution model used. If we had opted for a more complicated model, we would need optimization methods that did not rely on derivatives and would subsequently be slower, though the estimation would still be possible. Once the change in log-likelihood between two iterations has fallen below some given threshold, we take the likelihood to have converged. We then generate a new emission matrix E to be fed back into our alignment procedure in order to generate new posterior probabilities.For this function of the 3Once the likelihood function has converged below some set threshold, we output the final set of estimated selection parameters. We may also, if desired, construct an alignment, either using the Viterbi path or posterior decoding.We would like to be able to apply our method to multiple sequences, thus extrapolating more information where possible. We could of course devise a multiple alignment indel model, and develop a new likelihood function from which to maximize over all tree branches simultaneously. This however would be of computational much higher demand, runtime increasing exponentially with the addition of each new sequence. Instead, we therefore opt to work with a multiple pairwise alignment under the assumption of a star shaped tree, with the reference sequence as the root in the star topology. This implies viewing the evolution of the pairwise sequences as independent, which is an approximation which we wish to address in future work. This merely requires per additional sequence an extra transition and transversion parameter, since selection is acting on the gene in the ancestor and we assume this to be constant over all branches. The modification to our program is thus trivial, with only a linear increase in runtime.A and its N descendants D1, ..., DN, together with the seed parameters for the selection factors R on each region R as well as n transition and transversion parameters n respectively.As an input we have, for lack of better terminology, the ancestral sequence N pairwise alignments between the ancestor A and its N descendants. Each one of these obtains a likelihood function log L as given in equation 6. Now we create a new likelihood function log L* which is the sum of the N log likelihoods. If t in region r between the ancestral sequence A and its nth descendant, then our assumption of independence implies thatWe then build a set of N sequences under our model. Note here, that the probabilities P are dependent on the sequence-dependent transition and transversion rates n and the selection factors R which in turn are not dependent on n, since we are assuming selection to occur on the gene in the ancestral sequence.is the full likelihood of observing all Maximizing this new log likelihood function, we proceed as above and estimate a new set of selection factors and a set of sequence specific transition and transversion rates, from which we may generate a new set of pairwise statistical alignments.


Phylogenetic simulation of promoter evolution were used to analyze functional site turnover in regulatory sequences. The phenomenon of functional site turnover has important implications for the study of regulatory region evolution, such as for promoter sequence alignments and transcription factor binding site (TFBS) identification. At present, it remains difficult to estimate TFBS turnover rates on real genomic sequences, as reliable mappings of functional sites across related species are often not available. As an alternative, we introduce a flexible new simulation system, Phylogenetic Simulation of Promoter Evolution (PSPE), designed to study functional site turnovers in regulatory sequences.Using PSPE, we study replacement turnover rates of different individual TFBSs and simple modules of two sites under neutral evolutionary functional constraints. We find that TFBS replacement turnover can happen rapidly in promoters, and turnover rates vary significantly among different TFBSs and modules. We assess the influence of different constraints such as insertion/deletion rate and translocation distances. Complementing the simulations, we give simple but effective mathematical models for TFBS turnover rate prediction. As one important application of PSPE, we also present a first systematic evaluation of multiple sequence aligners regarding their capability of detecting TFBSs in promoters with site turnovers.PSPE allows researchers for the first time to investigate TFBS replacement turnovers in promoters systematically. The assessment of alignment tools points out the limitations of current approaches to identify TFBSs in non-coding sequences, where turnover events of functional sites may happen frequently, and where we are interested in assessing the similarity on the functional level. PSPE is freely available at the authors' website. With the increasing availability of genome sequences, phylogenetic footprinting appeared to offer a very promising approach for identifying cis-elements -1 and [λDel (L + u - 1)]-1, respectively, where L is the sequence length, u is the mean length of deletion segments, and λIns and λDel are Poisson rates of insertion and deletion, respectively.PSPE is based on Dawg , an earlPSPE models InDel length by one of three commonly used distributions: geometric, negative binomial, and Zipf's law distributions. We used the simple geometric distribution for InDel length in this study.To address TFBS turnover at different distances, we simulated sequence evolution at each of 15 different divergence distances: 0.01, 0.05, 0.1, 0.25, 0.5, 0.75, 1.0, 1.25, 1.5, 1.75, 2.0, 2.5, 3.0, 4.0, and 5.0, measured in the number of substitutions per site. These distances should cover the divergence between most currently sequenced genomes used in comparative genomics studies. To study the effect of different InDel rates on TFBS conservation between human and mouse, we performed simulations at ten different InDel rates measured by the number of InDels per substitution: 0, 0.01, 0.025, 0.05, 0.075, 0.1, 0.125, 0.15, 0.175, 0.2, with, for example, 0 meaning no InDel, and 0.2 meaning one InDel every five substitutions. For studying the effects of restricted translocation distances on the RTRs, we compared RTRs of each TFBS at 12 different maximal translocation distances: 0, 5, 10, 20, 30, 40, 50, 75, 100, 150, 200, and 300 bases.To estimate parameters of our RTR models, we did a non-linear least-squares regression analysis on the observed turnover data from simulation. We used the Gauss-Newton algorithm for the non-linear least-squares fitting, which minimizes the sum-of-squares error. We performed this analysis in R.We selected five alignment tools, CLUSTALW, DIALIGN, AVID/MAVID, LAGAN/MLAGAN, and MUSCLE, to assess their capability of detecting functional sites. The criteria for our selection were: either widely used or shown good performance in other studies for aligning DNA sequences; capable of aligning multiple sequences in a reasonable amount of time; free availability and easy installation in the Linux operating system; and strict co-linearity for global alignment. Many excellent alignment tools were not evaluated because: they did not meet one of the above criteria; their algorithms were similar to one of five tools we selected; and/or they did not show a significantly different performance in other evaluations. For example, ACANA , BLASTZ CLUSTALW (v1.83) is one of the best-known MSA tools and is based on a progressive method, which first aligns the most similar sequences and then successively adds more distant sequences or groups to the alignment until all sequences are aligned together. CLUSTALW employs the Needleman-Wunsch pair-wise alignment algorithm for calculating similarities between sequences and constructing a phylogenetic guide tree. We ran CLUSTALW with its default settings.DIALIGN (v2.2.1) is an anchor-based MSA tool for both DNA and protein sequences. Different from other alignment tools, DIALIGN assembles alignments by finding consistent segments exhibiting statistically significant similarity, and does not align regions showing no significant similarity. Therefore, strictly speaking, DIALIGN is a local alignment tool that produces a full global alignment only for sequences with high similarity. Recent studies ,28,79 suAVID (v2.1) is a pair-wise global alignment tool that is capable of aligning very large genomics sequences. Its employs an anchor-based approach and uses a suffix tree algorithm for identifying potential anchoring regions between sequences. MAVID (v2.0.4) is a progressive MSA tool and is the direct extension of AVID. To speed up the alignment process, MAVID does not directly align two intermediate alignments or groups; instead, it first infers the common ancestral sequence of each alignment by maximum likelihood, and then uses AVID to align two ancestral sequences. We used AVID for two-species alignments, and MAVID for three or more species. CLUSTALW at default settings was used as the tree building tool for MAVID.LAGAN/MLAGAN (v1.21) is a suite of programs for aligning DNA sequences. As an anchor-based pair-wise alignment tool, LAGAN first identifies anchoring regions by chaining similar neighboring words found in a local alignment process, and subsequently aligns other regions by the Needleman-Wunsch algorithm to form a global alignment. MLAGAN is a progressive multiple sequence alignment tool based on LAGAN pair-wise alignments. Similar to CLUSTALW in scoring multiple sequence alignments, it uses the sum-of-pairs approach for scoring substitutions and a consensus-based method for scoring gaps. Since MLAGAN does not build a phylogenetic tree, which is a required input, we provided it with the phylogenetic tree from our simulation. In this study, LAGAN was used for two-species alignments and MLAGAN for three or more species. Both tools were run with default settings.diags option for anchoring alignment and maxiters option to limit the number of refinement iterations to two.MUSCLE (v3.6) is a relatively new MSA tool for both DNA and protein sequences based on an improved progressive approach. Like CLUSTALW and T-COFFEE, MUSCLE is based on a progressive approach, and uses the sum-of-pairs scoring scheme for multiple alignments, but it differs from other progressive tools by allowing changes of both the phylogenetic tree and the alignment in intermediate steps in an iterative refining process. MUSCLE was shown to perform better than T-COFFEE and POA in aligning benchmark protein sequences ,81. BecaThe benchmark sequence datasets were simulated by the PSPE system. PSPE sequence simulation can be generally divided into two separate steps. In the first step, PSPE generates ancestral promoter sequences with different functional TFBSs  is defined as the proportion of functional sites correctly aligned with respect to a simulated TFBS map, averaged over all different pairs in a multiple sequence alignment, and can be calculated by:TFBS detection accuracy /2 is the number of different sequence pairs, and L is the total length of functional sites . aij has a value of 1 if the bases at the jth position of functionally homologous binding sites in a sequence pair i are aligned to each other and 0 otherwise. Since all our simulated sequences contain the same set of TFBSs, L is the same for all alignments.where The overall alignment sensitivity is the fraction of correctly aligned bases not considering gaps, averaged over all different pairs in a tool alignment:ki is the total number of positions for which bases are aligned to bases in the ith pair-wise alignment from a simulated alignment. cij has a value of 1 if the jth position was aligned correctly in any given pair of sequences i in the tool alignment, and 0 otherwise.where Overall alignment specificity is the fraction of correctly aligned bases among those that are aligned to gaps in a simulated alignment, averaged over all different pairs in a tool alignment:gi is the total number of positions, where bases in one sequence aligned to gaps in the other sequence in the ith pair-wise alignment of a simulated alignment; cij has a value of 1 if the jth position aligned correctly, and 0 otherwise.where TFBS sensitivity is the fraction of correctly aligned bases, among those in functional sites of ancestral sequences and not aligned to a gap in a simulated alignment, averaged over all different pairs in a tool alignment:li is the total number of positions in functional sites of ancestral sequences, where bases in one sequence aligned to bases from the other sequence in the ith pair-wise alignment of a simulated alignment; cij has a value of 1 if the jth position aligned correctly, and 0 otherwise. In case of no replacement turnovers of TFBSs, TFBS sensitivity is equal to TFBS detection accuracy.where TFBS specificity is the fraction of correctly aligned bases, among those in functional sites of ancestral sequences and aligned to gaps in a simulated alignment, averaged over all different pairs in a tool alignment:L is total length of all functional sites in the ancestral sequence.where In this paper, we mostly use detection accuracy and TFBS sensitivity. The former refers to the fraction of functional sites in the 'descendants' aligned to each other, the latter to the fraction of sites corresponding to the location of the TFBS in the 'ancestral' sequence that are correctly aligned to each other.GTR, general time reversible; HKY, Hasegawa-Kishino-Yano; InDel, insertion/deletion; MSA, multiple sequence alignment; PSPE, Phylogenetic Simulation of Promoter Evolution; PWM, position weight matrix; RTR, replacement turnover rate; TFBS, transcription factor binding site; TSS, transcription start site.WH, JN and UO contributed to the conception and design of this study. WH developed PSPE, performed analyses, and drafted the initial manuscript. WH and UO provided the interpretation of results. All authors contributed to writing and critically revising the manuscript. All authors read and approved the final manuscript.The following additional data are available with the online version of this paper. Additional data file Additional results of turnover simulations varying the binding site strength and GC content of the background sequences, and information on the E2F promoter data set.Click here for fileAdditional evaluations of alignment algorithms on sequence sets simulated with a phylogenetic tree with a star topology.Click here for file