Cross-species sequence comparison holds much promise for improving computational prediction of CRMs, for elucidating their binding site composition, and for understanding how they evolve. Current methods for analyzing orthologous CRMs from multiple species rely upon sequence alignments produced by off-the-shelf alignment algorithms, which do not exploit the presence of binding sites in the sequences. We present here a unified probabilistic framework, called MORPH, that integrates the alignment task with binding site predictions, allowing more robust CRM analysis in two species. The framework sums over all possible alignments of two sequences, thus accounting for alignment ambiguities in a natural way. We perform extensive tests on orthologous CRMs from two moderately diverged species Drosophila melanogaster and D. mojavensis, to demonstrate the advantages of the new approach. We show that it can overcome certain computational artifacts of traditional alignment tools and provide a different, likely more accurate, picture of cis-regulatory evolution than that obtained from existing methods. The burgeoning field of cis-regulatory evolution, which is amply supported by the availability of many related genomes, is currently thwarted by the lack of accurate alignments of regulatory regions. Our work will fill in this void and enable more reliable analysis of CRM evolution.The discovery and analysis of  cis-regulatory modules. A major roadblock in such an analysis has been the fact that traditional alignment methods are not very accurate for regulatory sequences. This is partly because the alignment is performed independently from the binding site predictions and turnover analysis. This article describes a new computational method to compare and align two orthologous regulatory sequences. It uses a unified probabilistic framework to perform alignment and binding site prediction simultaneously, rather than one after the other. Predictions of binding sites and their evolutionary relationships are obtained after summing over all possible alignments, making them robust to alignment ambiguities. The method can also be used to predict new cis-regulatory modules. The article presents extensive applications of the method on synthetic as well as real data. These include the analysis of over 200 cis-regulatory modules in D. melanogaster and their orthologs in D. mojavensis. This analysis reveals a significantly greater degree of conservation of binding sites between these two species than will be inferred from existing alignment tools.Interspecies comparison of regulatory sequences is a major focus in the bioinformatics community today. There is extensive ongoing effort toward measuring the extent and patterns of binding site turnover in  The natural response to this challenge has been the proposal of probabilistic alignment methods that can, for example, provide a confidence value on any two bases being aligned (orthologous) without committing to any single “best” alignment. We shall see below some of the successful manifestations of this idea.Two-sequence alignment has been an indispensable tool in the bioinformatician's repertoire for nearly two decades now ,2. With cis-regulatory modules or CRMs  by scanning for statistically significant clusters of transcription factor binding sites, which in turn are detected by sequence similarity to a priori known “motifs.” Discovery of CRMs has played a key role in understanding gene regulation in metazoa, especially the fruitfly [A somewhat orthogonal line of research with respect to noncoding sequence analysis has been the search for fruitfly  and the fruitfly . Althougfruitfly ,6, it wafruitfly ,8. The afruitfly  how the fruitfly ) in its http://veda.cs.uiuc.edu/Morphalign/supplement/ (http://rd.plos.org. pcbi_0030216_0001).Here, we combine the two seemingly separate ideas mentioned above—probabilistic alignment of two sequences and probabilistic analysis of CRMs—into an integrated probabilistic framework. The new framework provides a robust way to compare CRMs across moderate evolutionary distances at which sequence-level regulatory changes are prominent and tractable. We implement efficient procedures for learning the parameters of the model, based on the expectation-maximization (E-M) technique. Two programs with related but somewhat distinct functionalities are made available: (1) the “MorphMS” program predicts CRMs located within a pair of orthologous sequences, whereas (2) the Morphalign program constructs an alignment of two given sequences and uses a novel display format to point out the ambiguities in the alignment as well as the locations of putative binding sites. Both programs require as input a set of transcription factor binding motifs that the user is interested in. All parameters of the model, except for the length of CRMs to be predicted by MorphMS, can be automatically learned from the data. The alignments produced by the Morphalign program are viewable in the highly portable HTML format, and both MorphMS and Morphalign are available for download as source code  binding site prediction accuracy, as compared to an HMM-based program  alignment accuracy on m (Stubb ) that woSequence alignment is an intensely researched topic with several major achievements, and we refer the reader to  for a reAnother class of probabilistic methods, called statistical alignment, uses an evolutionarily motivated stochastic process of indels (insertions and deletions) to construct the maximum-likelihood alignment. Earlier work in this class, including TKF91 model  and its cis-regulatory sequences from two species. As mentioned above, Stubb first finds the optimal scoring alignment using a standard alignment program such as LAGAN [Our previously published probabilistic method called Stubb  comes clas LAGAN , and fixcis-regulatory sequences while constructing sequence alignment at the same time, an objective that overlaps with ours. It first scans the given pair of orthologous sequences to find all putative binding sites, and then applies the Smith-Waterman dynamic programming algorithm to the sequences of binding sites. That is, the binding sites are the basic units (symbols) to be aligned, not nucleotides. The alignment parameters, in particular the penalty for changed spacing between two adjacent pairs of aligned binding sites, are estimated from external data. Our probabilistic framework MORPH offers several important advantages over such a method: (1) the uncertainty in assigning binding sites is handled by using a probabilistic model for CRM, so no cutoff is needed for determining binding sites; (2) the parameters in the model are automatically estimated; and (3) the ambiguity in alignment as well as binding site annotation can be precisely quantified using probabilities (see below). Additionally, MORPH simultaneously considers both background sequences and binding sites for alignment, unlike EEL, which ignores the non-site sequences.One of the first attempts to couple alignment with binding site predictions was made in the program CONREAL . This prWe begin by describing the probabilistic process (the “MORPH” model) that generates two orthologous sequences (CRMs), given a set of transcription factor binding motifs in the form of their PWMs . A PWM sHere, we provide an informal description of the MORPH model, and leave the detailed description for Materials and Methods. At the outer level of the model, we use a first-order Markov process with three states: Match, Delete, and Insert. The Match state corresponds to aligned positions and emits two equal-length strings (one for each species). The Delete and Insert states correspond to unaligned positions in either species and emit a string that will be appended to the first or second species' sequence, respectively. Thus, this outer level of the model generates alignments with blocks of aligned positions separated by unaligned strings in either or both species.The string emitted in any of the three states of the above process is chosen by another probabilistic process, which models the interspersed arrangement of binding sites and non-binding “background” sequence in the CRMs. This process first chooses a particular motif and samples a string from the probability distribution prescribed by that motif (PWM). In the Match state, the sampled string is “evolved” using an evolutionary model to obtain two related strings that are then emitted. The motif choices available include all input PWMs as well as a single-column “background” PWM that models random sequence.The model parameters include all transition probabilities among the Match, Insert, and Delete states, as well as the transition probabilities into each motif state. These parameters are trained using an E-M strategy employing dynamic programming for efficient calculations. For the two evolutionarily related strings emitted from a Match state, there is a model parameter representing evolutionary divergence of the species. This is either user-specified , were set to be equal and to range between 0.2 and 0.8, in increments of 0.1. The parameter μ, which is related to the length distribution of aligned blocks, was varied between 0.05 and 0.20, in increments of 0.05. For each combination of μI (μD) and μ, called an “experiment set,” we obtained ten pairs of sequences.We first performed extensive experiments with synthetic datasets, where “orthologous CRMs” were generated artificially. Testing on synthetic data has become a common practice in evaluation of bioinformatics algorithms today, offering the following advantages: (1) the correct answers are known in synthetic data, (2) the datasets are created with complete control over different aspects of the signal strength, and (3) large numbers of datasets can be obtained. Therefore, synthetic datasets allow us to evaluate and compare various algorithms, and gain insights into how such comparisons depend on different aspects of the data. Here, we obtained synthetic “orthologous CRMs” by sampling from the MORPH probabilistic model. A set of seven PWMs, corresponding to transcription factors involved in early development in φ (evolutionary divergence) parameter being known and all other parameters learned from the data. The Morphalign program computes a global alignment of two sequences using the MORPH framework. In this exercise, we configured it to report the maximum likelihood (Viterbi) alignment . The alignment parameters  and motif transition probabilities (ip) are automatically learned by Morphalign for each sequence pair. I = μD = 0.2, and different values of μ. We see a clear and consistent improvement in alignment accuracy (both sensitivity and specificity) when using Morphalign (and PWM knowledge), compared to LAGAN, with the improvement being more pronounced as the aligned blocks get shorter (larger μ). The same trend is seen for other values of μI ( = μD) (unpublished data). This test therefore shows us how we may get more accurate alignments of orthologous regulatory sequences if we know the relevant binding site motifs and exploit them within the MORPH framework. We also repeated these tests on synthetic datasets generated by a simple evolutionary model that is different from the MORPH probabilistic model. We find again, as shown in the Supplementary Materials at ((http://rd.plos.org. pcbi_0030216_0001), that the Morphalign program provides significantly greater sensitivity and specificity of alignments than LAGAN run with default parameters. Details of the new simulation program, which is based on the Dawg program [http://rd.plos.org. pcbi_0030216_0001).In the first analysis, we evaluated the accuracy of computed alignments by comparing them with the true alignments. For each of the ten sequence pairs in an experiment set, we counted what percentage of the truly aligned positions are aligned by the computed alignment, thus obtaining an “alignment sensitivity” that ranges between 0% (worst) to 100% (best). An “alignment specificity” was similarly computed. These two scores were computed for the popular alignment tool LAGAN, as well as for the Morphalign program, with PWMs and the  program , are alsI = μD = 0.2 and different values of μ. We find a clear and consistent improvement in binding site prediction using Morphalign, in terms of both sensitivity and specificity. Morphalign's specificity is always significantly better, and so is its sensitivity. These results remain practically unchanged for other values of μI ( = μD) (unpublished data). This analysis provides a compelling demonstration of the advantage of using the Morphalign program for binding site prediction from orthologous CRMs.In the second analysis, we investigated whether use of the probabilistic model of alignment improves binding site prediction over that from using a fixed alignment, as in Stubb . Given tDrosophila genomes (http://rana.lbl.gov/drosophila/) and the recent publication of the largest database of experimentally validated CRMs  among the newly sequenced Drosophila genomes. These two species are expected to exhibit common modes of cis-regulation, using highly conserved transcription factors and DNA binding affinities (“motifs”). At the same time, they are diverged enough (∼40 Myr) to demonstrate substantial evolutionary flux at the binding site level.  has opes et al.  and Embes et al. , both ofila CRMs , and is D. melanogaster CRMs from the REDfly database, spanning a broad spectrum of biological processes. For each CRM, we included 1-Kbp flanking sequence on either side, and extracted the ortholog of this entire sequence from D. mojavensis.  We also collected a set of 53 PWMs from FlyReg [We collected a set of 208 experimentally verified m FlyReg . Our goaIt is expected that any given CRM is regulated by a small subset of the 53 motifs, but such information is not available for most of the CRMs. Therefore, we decided to use all 53 motifs in our initial analysis. As such, false positives are inevitable during binding site prediction, and more specific information about transcription factors (such as genetic information on transcription factor–gene regulatory interactions) is necessary to deal with these. A researcher interested in analyzing a specific class of CRMs, e.g., those involved in anterior–posterior patterning of the embryo  slides a window of length 500 bp (in shifts of 250 bp) on the input sequence, and, for each position of this sliding window, reports two log-likelihood ratio (LLR) scores. The LLR1 score compares the likelihood (of the sequence data) under the MORPH model to the likelihood under a null model in which only the background PWM is used. The LLR2 score uses a null model in which the Match state is not allowed, which means that the two orthologous sequences are assumed to be generated independently. To examine whether the LLR1 and LLR2 scores are able to discriminate CRMs, we considered all 208 CRMs as the “positive” class of sequences, and collected equally many length-matched sequences (and their orthologs) from randomly selected noncoding regions of the genome, forming the “negative” class. We then asked how well the positive class can be discriminated from the negative class, based on these scores. In order to test the advantage offered by the MORPH framework, we also used the LLR1 score computed by the Stubb program. We chose to compare MORPH performance with Stubb because (1) Stubb's probabilistic framework is very similar to MORPH, except that Stubb relies on a “hard” alignment, and (2) Stubb has been shown to improve CRM prediction using two fruitfly genomes over its single-species version . We alsoion of K A. Thus, Next, we investigated the accuracy of binding site predictions. Our synthetic data results have shown how MORPH can predict binding sites with added sensitivity and specificity, in comparison to Stubb. In the current dataset, MorphMS predicted many more sites than Stubb (unpublished data). However, it was not possible to directly assess which of the methods is more accurate, since far too few binding sites have been experimentally identified in these 208 CRMs. Nevertheless, we can get a high-level insight into performance by framing the evaluation in a classification setting, as follows. The idea is that the “better method” will predict more sites in CRMs compared to random genomic segments, to the extent that this differential prediction of binding sites may allow us to classify CRMs from random sequences. Hence, we considered the total number of binding sites predicted by each method in each sequence, and tested which method is better at discriminating the positive class (CRMs) from the negative class (random genomic sequences) based on these total site counts. We note that this is only an indirect way to assess binding site prediction accuracy, and does not allow us to evaluate individual site predictions. http://rd.plos.org. pcbi_0030216_0001 for lists of these CRMs and motifs.) For each dataset, the Morphalign program  was used to align and predict binding sites in the D. melanogaster and D. mojavensis orthologs of each CRM.  We analyzed the results of this exercise with respect to insights it provides about evolution of CRMs, and how such insights differ from traditional methods of evolutionary sequence comparison. The complete set of alignments for both sets is available online , and will be a valuable resource for biologists studying the evolution of these important sets of CRMs, or of CRMs in general.The above analysis was performed on CRMs spanning many different pathways, using a very broad collection of motifs, to get a relatively unbiased view of MORPH performance. We next show results from two specific developmental pathways. We collected two sets of CRMs from REDfly: “BLASTODERM.A-P,” a set of 54 CRMs regulating anterior–posterior segmentation at the blastoderm stage, and “MESODERM,” a set of 46 CRMs involved in mesoderm specification. For each set, we also collected a set of motifs (PWMs) for transcription factors believed to be involved in that pathway—a collection of ten and 18 motifs for the BLASTODERM.A-P and MESODERM sets, respectively.  were aligned with marginal probability above a threshold of 0.1 to two or more positions in the second species (D. mojavensis). This measure, which we call the alignment ambiguity fraction, is shown in D. mojavensis aligned to the same position in D. melanogaster) and tandem repeat positions of the CRMs . Of the 43 CRMs in BLASTODERM.A-P that had over 10% alignment ambiguity, 14 CRMs had a significant overlap of ambiguously aligned and tandem repeat positions. Similar results were found in the MESODERM set. This provides statistical evidence that short tandem repeats play a large role in creating alignment ambiguities in CRMs.A distinct difference of Morphalign alignments from traditional (non-probabilistic) alignment programs is that ambiguities in the alignment are explicitly pointed out. To quantify this aspect, we asked what fraction of the positions in one species ( program ), using a in one species aligned to two different positions b and c in the second species, with b and c being separated by a large distance.) For this, we looked at contiguous stretches of ten or more ambiguously aligned positions (in one species), and measured the distance between their two aligned regions in the other species. Twenty percent of such cases had separation more than 10 bp . This suggests that these alignment ambiguities are the result of mechanisms other than tandem repeats, or that insertions have happened since the tandem repeat was created that have significantly separated the alternative alignable regions.Although the above observation points to short repeats as a source of alignment ambiguity, we also found ambiguously aligned positions separated by relatively large distances within the CRM. , but have been aligned with several gaps in the no-motifs version. D. melanogaster being aligned to a weaker match in D. mojavensis, as per the Morphalign program. These seemingly orthologous DStat sites are not aligned by the no-motifs version of the program. Thus, manual inspection suggests that Morphalign, using motif information, is able to identify  orthologous binding sites even when its no-motifs version cannot.We also compared the Morphalign alignments to those obtained by running the same program without any motifs, i.e., a probabilistic alignment program that does not predict binding sites in the process of alignment. This differs from LAGAN in its probabilistic nature and the fact that alignment parameters are learned automatically from the data. A question that many researchers are interested in is the evolutionary dynamics of binding sites in CRMs: to what extent are binding sites conserved between species, and how do their evolutionary rates compare to various “neutral” rates? An indispensable component of such studies is the alignment of orthologous CRMs, to find conserved and non-conserved binding sites. Typically, this step is done using traditional alignment programs such as LAGAN, which is acknowledged to be a weak link in the analysis, and is sometimes supplemented with a manually performed realignment step. Morphalign, with its integrated view of binding site prediction and evolutionary events (indels and substitutions), is therefore likely to help produce a different and perhaps more accurate picture of binding site evolution. Here, we present evidence that the picture presented by Morphalign alignments is indeed very different from what LAGAN alignments suggest.D. melanogaster BLASTODERM.A-P set, and asked how many of these sites were (1) aligned to a D. mojavensis site also above the PWM match threshold , (2) aligned to a site below threshold, and (3) unaligned. We examined these numbers using Morphalign alignment, as well as with LAGAN alignments that used a wide range of gap penalties. There is an expected tradeoff between sensitivity and specificity here: LAGAN alignments with a high gap penalty will tend to produce more aligned regions, and hence align more binding sites (of D. melanogaster), but at the cost of aligning sites that are not “truly” orthologous. One way to control for this is to compare alignments that overall align similar fractions of the CRMs (or numbers of binding sites), and then check what fraction of the aligned binding sites are conserved  in the second species. If we assume that most alignable binding sites are functional in both species , the better alignment should have more of its aligned binding sites conserved. Indeed, D. melanogaster sites aligned. Only the LAGAN run with the lowest gap penalty (green diamond) agreed with Morphalign (red circle) with respect to this measurement. However, as D. mojavensis, whereas LAGAN  had only 55 of the 160 aligned sites conserved in the second species, suggesting a much higher rate of binding site loss or gain. Another way to look at these results is simply to count what fraction of the sites aligned by a program were conserved: although Morphalign finds this fraction to be 53%, the LAGAN runs across the spectrum of gap penalties projected a value of 28%–34% .We used a well-characterized PWM of the Bicoid transcription factor, predicted all binding sites above a threshold in the Having shown that Morphalign gives a different picture of binding site evolution, we investigated whether this is justified. We therefore analyzed some specific examples and found that the difference is in part due to the ability of Morphalign to overcome some alignment errors. The next snapshot , bottom,cis-regulatory evolution. We have used synthetic data to showcase the potential advantages of the new framework, in improving alignment as well as binding site prediction accuracy. We have demonstrated that CRM prediction is greatly improved with the new method over existing methods that use two-species data. We present the results of using our new motif-aware alignment tool on two well-established regulatory networks in Drosophila. These are publicly available via a Web interface. We have used these alignments to demonstrate that the new framework highlights ambiguities in the alignments, and produces alignments that are significantly different from those using a traditional alignment program like LAGAN, or even a motif-agnostic version of the same probabilistic framework. Finally, we have demonstrated that our proposed method paints a very different picture of binding site evolution, namely, one with significantly less loss or gain of functionality among aligned binding sites than projected by motif-agnostic methods. We have showcased specific examples of why this difference arises, and found the common source to be local misalignments by the traditional methods, which are not aware of the locations of potential binding sites. It is easy to appreciate that such traditional methods will always make arbitrary decisions when there are two alternative alignments with the same score, and if a pair of orthologous binding sites falls at the positions of alignment ambiguity, they may be misaligned. When we use motif information, our decision is no longer arbitrary  approaches to two distinct problems: sequence alignment and CRM analysis. Our implementation of this framework is available as source code, and will particularly help researchers studying The Insert and Delete states of the MORPH model are somewhat misleading in their names. These states emit not only the evolutionary insertions and deletions that happened between the species, but also the orthologous regions that are so diverged that they are better left unaligned. It may be beneficial to model these two types of sequences (indels and orthologous but highly diverged) separately, since they may have distinct statistical properties. This is an interesting direction for future work.It is worth discussing here the two LLR scores (LLR1 and LLR2) reported by the MorphMS program. The LLR2 score contrasts the MORPH model with a null model in which the sequences are assumed unrelated, and thus implements a “homology testing” approach. This is akin to methods designed for identifying conserved noncoding sequences, such as phastCons  and ReguDrosophila genomes will prove to be an invaluable resource for studies on binding site turnover, such as the recent work of Moses et al. [An obvious line of future research is to combine pairwise alignments into a multiple alignment of three or more species. We may adopt ideas of consistency-based clustering  in mergis et al. . This, iWe first describe the probabilistic process (MORPH model) for generation of two orthologous CRMs using given PWM motifs.Alignment states. The main states of the model are Start, Stop, Match, Delete, and Insert. Of these, the first two, i.e., Start and Stop states, have no emissions, the Match state emits two strings of the same length, the Delete state emits a string to be appended only to S1, and the Insert state emits a string to be appended only to S2. For clarity of exposition, we illustrate the HMM as in D probability of continuing generation of unaligned sequence in S1, whereas the Insert state has μI probability of staying put. From the Start state, there is a μS probability that unaligned sequences will be generated before the first aligned block is formed. τ2 is the termination probability from the Pre-Match state. We can now form the transition probability matrix for the main five states of the HMM, Start, STop, Match, Delete, and Insert, as shown in 1, τ2, μS, μD, μI, and μ are parameters of the model that will be trained from the data, as described later.The edges in Motif states and emission probabilities. Once in a Match, Delete, or Insert state, the process transitions to one of several available “motif” states in order to decide which string to emit  For motif states in Delete or Insert states, the emission probability distribution is directly prescribed by the respective PWM: the probability that state W emits a string s of length l (where l must be the length of PWM W) is W emits strings s and t, each of length l (where l must be the length of PWM W) is given by:jk is the Kronecker delta and φ is the neutral substitution probability between the two species. This model was used in our earlier work [W. to emit B. The avier work ,37 and iier work  with equ1p, 2p,…, Kp, bp} are parameters of the model, with the constraint φ in Equation 1 is related to the expected conservation level in aligned sites. For an aligned position whose emission probabilities in each species are given by the probability distribution fα, we expect (from Equation 1) φ as a neutral substitution probability, here it is the effective neutral substitution probability, conditional on the fact that the site survived during evolution and was therefore aligned. We prefer to interpret φ simply as a parameter that controls what fraction of aligned positions are expected to be conserved.The motif transition probabilities {1, τ2, μS, μD, μI, μ, and all pi's. That is, the algorithm attempts to learn the values of these parameters, collectively referred to as Θ, so as to maximize the probability of generating the sequence data S given Θ.  Let T be a particular “path” in the generative process, i.e., a sequence of states that were visited in the generation of S. T is “hidden” information, hence the likelihood has to be computed by summing over all possible T. In other words, we have to find Θ that maximizes W1, W2,…, WK, Wb} are known parameters of the model, and are left out of this expression for clarity.) We use an E-M approach to maximize Pr(S|Θ). This is an iterative update algorithm that is guaranteed to improve the likelihood Pr(S|Θ) in every iteration, until convergence to a local optimum. In our case, the E-M strategy is implemented by adapting the popular Baum-Welch algorithm for HMMs [L2Klmax), where L is the length of the sequence(s), K is the number of input PWMs, and lmax is the length of the longest PWM.We employ rigorous maximum likelihood estimation of the model parameters τfor HMMs ,39. AdapOur implementation of the MORPH probabilistic framework allows some additional features that the user may find useful.Background. The user may specify separate background sequences for the two species, for the purpose of training the background motif Wb.This is motivated by the common observation that orthologous genes may have very different nucleotide composition in their respective regulatory regions. If this option is exercised, the evolutionary model specified by Equation 1 (for background positions) is no longer time reversible. The joint probability of seeing base s in species 1 and base t in species 2 is now given by W(1) and W(2) are the background PWMs in the two species. Also, the user may specify the “Markov order” of the background, in order to capture neighboring nucleotide dependencies in typical sequences. For example, a first-order Markov background captures dinucleotide frequencies.Special Match state. The user has the option of specifying that the Match state only emit non-background sites, i.e., when in the Match state, the motif transition probability for Wb is zero. For other PWMs, motif transition probabilities , is user-specified.  We proThe current implementation aligns a typical CRM of approximate length 1,000 in a few minutes, running on a single processor workstation.m. It then computes two LLRs, by comparing this maximum likelihood Pr(S|Θm) to the likelihood under two suitable null models.The MorphMS program is designed for CRM prediction from two-species data. Given two orthologous sequences, it scans one of the sequences with a fixed-length window (in fixed-length shifts), and for each such window, computes the boundaries of its orthologous window in the other sequence by using a standard alignment tool. Thus, a “hard” alignment is used in this first step of detecting “orthologous window pairs,” after which the alignment information is discarded. For each window pair, MorphMS uses the MORPH model to compute the maximum likelihood parameters Θpi, except that for the background, are zero. That is, the first null model is the maximum likelihood model in the absence of motifs. The score LLR1 therefore captures whether we can better explain the data by allowing it to contain binding sites for the given transcription factors.In the first score, called LLR1, the null model is the maximum likelihood model under the constraint that all motif transition probabilities In the second score, called LLR2, the null model includes all motif transition probabilities as learnable parameters, but requires that the Match state is not visited, i.e., the entire data is generated by a single visit to the Delete state, followed by a single visit to the Insert state. The LLR2 score measures how much of an improvement (to the likelihood) comes from allowing the data to contain aligned sites. For example, a window pair that was erroneously marked as orthologous, and in reality consists of two completely unrelated sequences each containing binding site clusters, will not receive a high LLR2 score.In summary, the LLR1 score accounts for binding sites, whereas LLR2 accounts for alignment. The MorphMS program reports the LLR1 and LLR2 scores for every window pair, and leaves the analysis of these scores to the user. Each of these scores, being an LLR, is comparable across window pairs, implying that the user may choose the top scoring window pairs as CRM predictions.Morphalign is a pairwise alignment program for orthologous CRMs that uses known PWM motifs and the MORPH probabilistic framework. It is very similar to the MorphMS program, except that it processes the entire input sequence instead of sliding a window, and produces a graphical output at the end. It uses potential binding sites to impose a higher-order structure on the sequences and performs alignment on this higher-order structure. All possible parses of each sequence into their higher-order structure are considered and weighted probabilistically, as described in “Alignment and Regulatory Evolution in Two Specific Pathways” in The Morphalign program comes with a graphical visualization tool that produces an HTML file (with embedded JavaScript code) that may be viewed through any browser, making the visualization highly portable. The most likely alignment (Viterbi solution of the HMM in the MORPH framework) or the maximum expected accuracy alignment (explained below) forms the backbone of the display, and is displayed in the usual alignment format with gaps and nucleotides. For any pair of positions (in the two sequences), their marginal alignment probability is shown (if above some threshold) by a colored line whose thickness is proportional to the probability. This allows nonaligned positions  to be flagged as being potentially orthologous. The alignment display is annotated by presence of potential binding sites. The marginal probability of a binding site for any particular transcription factor at any particular position is shown by colored (blue) bars at the appropriate position, as shown in The user has two options regarding how to display the backbone of the alignment . The Viterbi option uses the maximum likelihood path through the HMM and the Match states that this path goes through, to decide this backbone. Another option, which we have found useful in practice, is to vertically line up all those pairs of positions whose marginal alignment probabilities have the largest sum. This is called the maximum expected accuracy alignment .Synthetic data experiments. The MORPH probabilistic process was sampled from, with parameter values τ1 = 0.005, τ2 = 0.005, and φ = 0.5. This resulted in sequences of median length 487 bp. PWMs corresponding to Drosophila transcription factors Bicoid, Hunchback, Knirps, Kruppel, Tailless, and Caudal and the TorRE binding factor were used in the sequence generation process. (PWM lengths varied between 9 and 15.) LAGAN was run with its default parameters, as was done in the evaluations performed by Pollard et al. [φ = 0.5. Each of these two programs outputs, for every position in a sequence, a “marginal probability” that an occurrence of a binding site begins at that position. We used a threshold of 0.1 on this marginal probability to predict binding sites.d et al. . MorphalD. melanogaster and D. mojavensis comparisons. We started with a complete list of 284 nonredundant (and nonoverlapping) CRMs from the REDfly database [D. mojavensis. We used a set of 53 PWMs based on the FlyReg database [http://rana.lbl.gov/~dan/matrices.html). These were all motifs that were based on at least five verified binding sites from the FlyReg database.database , and retdatabase  and the Short tandem repeats in CRMs were predicted by running the Tandem Repeat Finder (TRF) program of Benson  with parAll runs of Morphalign on the real datasets were done so as to output the maximum expected accuracy alignments , rather than the maximum likelihood (Viterbi) alignment.Binding sites for the Bicoid transcription factor (“Morphalign Presents a Different Picture of Binding Site Loss and Gain” in


Fast Statistical Alignment program is based on pair hidden Markov models which approximate an insertion/deletion process on a tree and uses a sequence annealing algorithm to combine the posterior probabilities estimated from these models into a multiple alignment. FSA uses its explicit statistical model to produce multiple alignments which are accompanied by estimates of the alignment accuracy and uncertainty for every column and character of the alignment—previously available only with alignment programs which use computationally-expensive Markov Chain Monte Carlo approaches—yet can align thousands of long sequences. Moreover, FSA utilizes an unsupervised query-specific learning procedure for parameter estimation which leads to improved accuracy on benchmark reference alignments in comparison to existing programs. The centroid alignment approach taken by FSA, in combination with its learning procedure, drastically reduces the amount of false-positive alignment on biological data in comparison to that given by other methods. The FSA program and a companion visualization tool for exploring uncertainty in alignments can be used via a web interface at http://orangutan.math.berkeley.edu/fsa/, and the source code is available at http://fsa.sourceforge.net/.We describe a new program for the alignment of multiple biological sequences that is both statistically motivated and fast enough for problem sizes that arise in practice. Our  Biological sequence alignment is one of the fundamental problems in comparative genomics, yet it remains unsolved. Over sixty sequence alignment programs are listed on Wikipedia, and many new programs are published every year. However, many popular programs suffer from pathologies such as aligning unrelated sequences and producing discordant alignments in protein (amino acid) and codon (nucleotide) space, casting doubt on the accuracy of the inferred alignments. Inaccurate alignments can introduce large and unknown systematic biases into downstream analyses such as phylogenetic tree reconstruction and substitution rate estimation. We describe a new program for multiple sequence alignment which can align protein, RNA and DNA sequence and improves on the accuracy of existing approaches on benchmarks of protein and RNA structural alignments and simulated mammalian and fly genomic alignments. Our approach, which seeks to find the alignment which is closest to the truth under our statistical model, leaves unrelated sequences largely unaligned and produces concordant alignments in protein and codon space. It is fast enough for difficult problems such as aligning orthologous genomic regions or aligning hundreds or thousands of proteins. It furthermore has a companion GUI for visualizing the estimated alignment reliability. The field of biological sequence alignment is very active, with numerous new alignment programs developed every year in response to increasing demand driven by rapidly-dropping sequencing costs. The list of approximately 60 sequence alignment programs on the wikipedia compilation provides a lower bound on the number of available tools and illustrates the confusing choice facing biologists who seek to select the “best” program for their studies. Nevertheless, the ClustalW program A key issue in understanding the popularity of ClustalW is to recognize that it is difficult to benchmark alignment programs. Alignments represent homology relationships among the nucleotides, or amino acids, of the genomes of extant species, and it is impossible to infer the evolutionary history of genomes with absolute certainty. Comparisons of alignment programs therefore rely on databases of structural alignments for proteins and RNA or on gene loci or simulated data for DNA. Each type of benchmark is vulnerable to manipulation and furthermore may not represent the problem setups which are most relevant to biologists. The result is that biologists are confronted with many programs and publications, but it is frequently unclear which approach will give the best results for the everyday problems which they seek to address.Adding to the difficulty of selecting software tools is the blur between programs and ideas. Developers of alignment programs make choices about the objective functions to optimize, the statistical models to use, and the parameters for these models, but the relative impact of individual choices is rarely tested In lieu of these issues, biologists have favored the conservative approach of using the tried and trusted ClustalW program, although they frequently use it in conjunction with software which allows for manual editing of alignments We therefore approached the alignment problem with the following goals in mind:An approach which seeks to maximize the expected alignment accuracy. Our approach seeks to find the alignment with minimal expected distance to the true alignment of the input sequences, where the true alignment is treated as a random variable, with the probability of each true alignment determined under a statistical model. Explicitly incorporating a statistically-motivated objective function, this “expected accuracy” approach to alignment allows us to visualize alignments according to estimates of different quality measures, including their expected accuracy, sensitivity, specificity, consistency and certainty. We therefore offer biologists a way to compare alignments that allows them to quantitatively judge differences in alignment quality when they are performing manual edits.A method which is robust to variation in evolutionary parameters. We sought a method which is robust to phenomena such as sequences of differing evolutionary distances and base composition. While “phylogenetic alignment” methods seek to accomplish this by explicitly modeling alignments on trees Robust results when faced with the wide range of alignment problems encountered today. We sought to create a single program which is capable of achieving high accuracies on protein, RNA and DNA sequences without additional input from, e.g., database homology searches. We additionally sought to make our approach fast enough for large-scale problems such as aligning many sequences or orthologous regions of genomes. Creation of a modular code base so that future improvements in one aspect of alignment could easily be incorporated into our approach. In particular, we aimed to create a collaborative infrastructure so that “bioinformaticians with expertise in developing software for comparing genomic DNA sequences [can] pool their ideas and energy to produce a compact tool set that serves a number of needs of biomedical researchers” The “distance-based” approach to sequence alignment, proposed in We have implemented our approach in FSA, a new alignment program described below. We give an overview of the structure of FSA and explain the details of its components below. input to FSA is a set of protein, RNA or DNA sequences. These sequences are assumed to be homologous, although FSA is robust to non-homologous sequence. The output of FSA is a global alignment of the input sequences which is a  optima of the expected accuracy under FSA's statistical model.The FSA first performs pairwise comparisons of the input sequences to determine the posterior probabilities that individual characters are aligned . While the number of possible pairwise comparisons is quadratic in the number of sequences being aligned, giving unfavorable runtimes for datasets of many sequences, FSA overcomes this problem by reducing the number of pairs of sequences that are compared. This is accomplished using a randomized approach inspired by the Erdös-Rényi theory of random graphs, thereby drastically reducing the computational cost of multiple alignment.After obtaining pairwise estimates of homology at the single-character level, FSA uses the sequence annealing technique The architecture of FSA reflects the inherent modularity of the distance-based approach to alignment. FSA's inference engine uses the flexible HMMoC code-generation tool Each of these components can be improved independently of the others, allowing for rapid future improvements in distance-based alignment. For example, FSA's entire statistical model could easily be altered to incorporate position-specific features or completely replaced with a discriminative or hybrid generative-discriminative model.The components described here correspond roughly to the simplest mode of operation for FSA, outlined in bold in FSA accepts FASTA-format input files and produces alignments in multi-FASTA or Stockholm format. The server also outputs PHYLIP and ClustalW formatted files.Distance-based alignment, relying on pairwise estimations of homology, operates on the posterior probability distributions that characters in two sequences are aligned. FSA uses the standard three or five-state pair hidden Markov model (Pair HMM) shown in The standard Forward-Backward algorithm on a Pair HMM has time complexity After calculating the posterior probabilities of alignment for characters in all sequence pairs, After estimating these posterior probabilities and sorting them, FSA creates a multiple alignment with the sequence annealing technique The distance fraction of positions for which they make identical homology statements. In contrast with traditional measures of sensitivity and specificity, accuracy takes into account all positions, rather than just those that are predicted to have a homolog. The alignment with the minimum expected distance to the truth is equivalent to the alignment with the maximum expected accuracy,The posterior probabilities over alignments Using this expected accuracy as an objective function for a greedy maximization, sequence annealing begins with the null alignment  and merges single columns  according to the corresponding expected increase in “The mathematics of distance-based alignment” in In FSA's definition of an alignment, an alignment consists solely of a specification of homology. This definition differs from the standard definition of a multiple alignment, which implies an evolutionary history of substitution and indel events. For example, FSA  considers the two alignments shown in This is problematic for comparative genomics analyses which use an alignment to infer evolutionary parameters such as indel frequencies across a clade. In order to output a single global alignment from which such evolutionary parameters can be inferred, we choose a topological ordering of the alignment POSET which corresponds to a maximum-parsimony interpretation of indel events. FSA outputs the global alignment with the minimum number of “gap openings” across the individual sequences  can give misleading results. Nonetheless, sequence alignment algorithms traditionally use a single model for all sequences.In order to overcome these difficulties, FSA uses “query-specific learning,” wherein a different model is learned for each pairwise comparison (the “query”). This is done in a completely unsupervised framework: FSA uses an unsupervised Expectation Maximization (EM) algorithm to estimate transition (gap) and emission (substitution) probabilities of the Pair HMM on the fly.aligned sequences; in contrast, we empirically observe good results with as little input data as two unaligned DNA or RNA sequences of length 60 nucleotides or four unaligned protein sequences of length 266 amino acids. These figures correspond to observing each of the independent parameters of a substitution matrix four times.Despite its unsupervised nature, FSA's query-specific learning needs remarkably little sequence data to effectively learn parameters. Standard alignment algorithms estimate parameters from thousands or tens of thousands of pairs of 2−1) = 15 free parameters, FSA can learn a different emission distribution for every pairwise comparison of all but the shortest RNAs or DNAs . In contrast, emission matrices over aligned amino acids have (202−1) = 3,999 free parameters, thereby preventing FSA from learning independent models for each pair of proteins. FSA therefore learns a single emission matrix using an all-pairs comparison for protein sequences.While FSA learns distinct transition parameters for every pair of query sequences regardless of the sequence composition, it uses different learning strategies for nucleotide and amino acid emission matrices. Because a pair emission matrix over aligned nucleotides has only  using a weak Dirichlet regularizer (prior) when estimating both transition and emission probabilities, and (2) terminating parameter learning before the EM algorithm converges. By default the Dirichlet emission priors are scaled such that total number of pseudocounts for aligned characters is equal to the number of free parameters in a symmetric pair emission matrix. As is the case for other machine-learning algorithms, it can be shown that termination before convergence of query-specific learning is equivalent to a form of regularization .If there is insufficient sequence data for effective learning, then FSA does not estimate parameters and instead uses default parameters to construct an alignment. The default parameters values, as well as seeds used for the learning algorithm, are discussed in While FSA can align hundreds or thousands of sequences on a single computer, it can handle truly large-scale problems by running in a parallelized mode on a computer cluster. FSA's distance-based approach to alignment gives the multiple alignment a natural independence structure: each pairwise alignment is independent of all other pairs, allowing dramatic runtime reduction by distributing the individual pairwise computations to different processors.Two factors were considered for the parallelization of FSA : (1) communication overhead between nodes, and (2) workload distribution over the different processors. For example, distributing jobs in very small batches may reduce processor idle time but lead to high overhead; in contrast, using large batches may increase idle time but minimize overhead. FSA's parallelization mode uses the “Fixed-Size Chunking” strategy described in While the pairwise comparisons can be naturally parallelized, sequence annealing does not have the same obvious independencies. Therefore, even when running in parallelized mode, FSA performs sequence annealing on a single node. The parallelization of the annealing step is a future aim for this project. A schematic of the current parallelization strategy is given in As a greedy algorithm, sequence annealing is only guaranteed to find a local optima of the expected accuracy. FSA therefore uses an iterative refinement strategy after sequence annealing terminates to locally improve the alignment. For each round of iterative refinement, FSA looks at every character's position in the multiple alignment and sees whether the objective function can be improved by moving it to another position . FSA assembles a list of such candidate character shifts, orders the list by the expected change in the objective function, and then performs the shifts. Iterative refinement terminates when there are no candidate shifts which improve the objective function.FSA's included GUI permits the user to visually assess alignment quality under FSA's statistical model according to estimates of different measures, including expected accuracy, sensitivity, specificity, consistency and certainty. This permits biologists and bioinformaticians to incorporate reliability measures into downstream analyses, such as evolutionary rate measurements and phylogenetic reconstruction. Incorporating such information can produce distinctly different results. For example, over-aligned non-conserved sequence can cause a systematic bias towards long branch lengths; this can be ameliorated by incorporating the expected accuracy statistics produced by FSA into reconstruction algorithms. FSA's GUI can color alignments according to five different measures of alignment quality, which are approximated under its statistical model. Characters Accuracy: The expected accuracy with which Sensitivity: The expected sensitivity with which Specificity: The expected specificity with which Certainty: The certainty with which Consistency: The consistency of the many pairwise comparisons used to construct the multiple alignment and the implied optimality of the alignment of See The GUI also provides a visual and statistical guide when manually editing alignments.We benchmarked FSA against databases of multiple alignments compiled from reference structural alignments, including protein databases  sequence. This is a realistic setup for biologists who might want to decide whether a sequence is orthologous to a particular protein family. With the exception of FSA, the tested alignment programs suffered a false-positive rate increased by over 25% on this BAliBASE 3+fp dataset, indicating that they aligned the random sequence with the homologous set. In contrast, FSA left the random sequence unaligned and had an essentially-unchanged false-positive rate.BRAliBase 2.1 was assembled from the RFAM The Consan mix80 dataset of alignments of Small and Large Subunit ribosomal RNAs, assembled from the European Ribosomal RNA database Drosophila DNA sequences. FSA produced higher-accuracy alignments than the other programs on the two Drosophila datasets and only Pecan gave better alignments of the mammalian sequences.Drosophila described in Drosophila genomic alignments were created by parameterizing the DAWG and simgenome programs using whole-genome alignments produced by Pecan for The simulated alignments of nonfunctional DNA sequences from nine mammals  were created by Blanchette et al. FSA's strong performance on all three datasets of simulated long DNA sequences indicate that it is a useful and accurate tool for genomic alignment.In order to further test the appropriateness of using popular alignment programs to detect homology between sequences, we conducted a large-scale random-sequence experiment. We generated datasets of random sequences to simulate unrelated protein, short DNA, and genomic (long) DNA sequences. The results, shown in Saccharomyces cerevisiae identified as having orthologs in the six related yeast species S. paradoxus, S. mikatae, S. kudriavzevii, S. bayanus, S. castellii, and S. kluyveri Click here for additional data file.


Homology modeling is the most commonly used technique to build a three-dimensional model for a protein sequence. It heavily relies on the quality of the sequence alignment between the protein to model and related proteins with a known three dimensional structure. Alignment quality can be assessed according to the physico-chemical properties of the three dimensional models it produces.In this work, we introduce fifteen predictors designed to evaluate the properties of the models obtained for various alignments. They consist of an energy value obtained from different force fields  computed on residue selected around misaligned regions. These predictors were evaluated on ten challenging test cases. For each target, all possible ungapped alignments are generated and their corresponding models are computed and evaluated.The best predictor, retrieving the structural alignment for 9 out of 10 test cases, is based on the ANOLEA atomistic mean force potential and takes into account residues around misaligned secondary structure elements. The performance of the other predictors is significantly lower. This work shows that substantial improvement in local alignments can be obtained by careful assessment of the local structure of the resulting models. The three-dimensional structure of proteins is central to many applications, such as structure-function studies, site-directed mutagenesis, or structure based design of active compounds. Since the creation of the Protein Data Bank To this day, homology modeling methods represent one of the most reliable approache to generate a structural model for a protein sequence http://protein.bio.puc.cl/cardex/software/index.html) is an atom-based MFP, where only non-local interactions are taken into account.The local sequence identity is usually variable along the alignment between the target and its template. This often leads to situations where two regions of the alignment are easy to align, but are separated by a short stretch where the sequence identity is locally low, and for which a relatively small number of alternative alignments have to be considered. It was proposed to evaluate these alternative alignments through their corresponding homology models Scoring schemes relying on physics-based energies haves been used to discriminate between native and near-native structures A recent benchmark involving physics-based scoring functions, MFP and machine learning based approaches pointed out that structural information is very informative when evaluating the quality of an alignment In order to evaluate the quality of models, fifteen predictors were defined in this article. Each of them consists in an energy function computed on a wide or narrow residue selection around misaligned regions. For each alternative alignment, the MODELLER program Five energies functions were investigated: the standard CHARMM energy Three different residue selections around the misaligned region were investigated, taking into account either all the residues of the model, or the residues contained in the misaligned region plus their close neighbors, or the residues in the misaligned regions belonging to a secondary structure element plus their close neighbors.The fifteen predictors were assessed on ten challenging local alignments optimization problems of both α helix and β sheets, among which challenging CASP cases with no sequence identity between the template and the target. The best predictor was able to retrieve the structural alignment for 9 out of the 10 test cases. It is based on the ANOLEA energy computed on a subset of residues around the misaligned secondary structure element. The success rate of predictors based on ProsaII is at most 60%, and predictors based on the CHARMM 19 or 22 energies, with or without the solvation free energy, remain lower than 30%.In what follows, we first describe the ten local alignments optimization problems selected to assess our method. Second, the generation and scoring of alignments is presented step by step. Third, the performance of the various predictors is presented and detailed for a challenging CASP5 target. Finally, the physical ground of this approach is discussed.The main steps of our approach are outlined in ab initio methods For each test case (see below), the structural alignment between the target and the template was computed using the MALIGN3D routine in the MODELLER. This alignment was used as a reference to which the alternative alignments are compared. An initial sequence-based sequence alignment was computed with T-Coffee The residues in the ROI were grouped in one ungapped mobile block of residues containing the misaligned SSE and its adjacent loops, if any. All possible ungapped alignments were generated by shifting this block along the template sequence , with thFrom each of the alternative alignments explored by the sliding window search described above, 100 models were built by the MODEL homology modeling routine of MODELLER 6.2. Disulfide bonds were explicitly defined, and default parameters were used. To build models, MODELLER satisfies spatial restraints derived from the sequence alignment between the target and its templates. The optimization is based on MD simulations; different models can be generated using different random seeds for the assignment of the initial random velocities.2) that were present during the entire minimization.Each model generated by MODELLER was energy minimized using the CHARMM program with the CHARMM19 force field The models obtained after energy minimization were evaluated by means of various “predictors”. A predictor is defined as an energy function combined with a selection of residue. First, the different energy terms are calculated for each selected residue taking into account the complete environment, and then the sum of the energy of the selected subset of residues (see below) is assigned to the model. When all models generated for a given alignment have been evaluated, the predictor score distribution of the formers is assigned to the latter. When all alternative alignments have been evaluated, a statistical assessment is performed to compare the distribution of their predictor scores.A total of fifteen different, yet closely related, predictors were assessed, taking into account five different energy functions  and three different selections of residues  corresponding to wide or narrow region around the misaligned SSE, see below.Five different energy types were used to evaluate the structural models.The CHARMM program was used to compute the energy of the selected residues using the CHARMM19 or the CHARMM 22 force field. The electrostatic contribution was computed in three different ways: 1) using a distance-independent dielectric value of 1 (vacuum), referred to as CDIE ε = 1, 2) using a distance-dependent dielectric value (simple electrostatic screening), referred to as RDIE ε = 4, and 3) using the Generalized Born using Molecular Volume analytical method 2 (electrostatic solvation energy), referred to as GBMV2 below.The ProsaII MFP Similarly, the ANOLEA MFP was used to compute the energy of the selected residues using the recommended averaging over five contiguous residues.Three different residue selections were assessed, from wider to narrower around the ROI.All selection takes into account all residues of the model.First, the ROI selection contains two subsets of residues. The first subset contains all residues of the ROI. The second subset contains all the residues surrounding the first subset with a maximum distance threshold between heavy atoms. The optimal distance threshold was investigated  was used to carry out the tests.A statistical analysis of the distributions of predictor scores was carried out to check whether the score distributions of the predictors computed for each alignment are significantly different. A Kolmogorov-Smirnov test showed that distributions were not normal and a Bartlett's test revealed that their variances are also different (data not shown). The conditions were not met to use a Student's t-test and a non-parametric rank-based Wilcoxon test was performed instead, using a confidence threshold α of 0.05. The statistical package R . Proteins with various folds were selected: α helices (α), only β-strands (β) and both α and β (α/β). We chose a CASP1 target: the human eosinophil-derived neurotoxin (EDN) This article addresses the question of the local optimization of the sequence alignment between a target sequence and its corresponding template, a critical problem in homology modeling. This optimization was carried out by generating all possible ungapped alignments, for which a score is assigned according to the quality of their corresponding models. This score is based on different subsets of particular pair wise energy types, termed “predictors”. The method is outlined in A single ROI was selected for hBAFF (strand D), EDN (helix 1), T0141 (strand 10), T0143 (helix 6), T0151 (strand 7) and T0169 (strand 5). Two ROI distant in the sequence space were independently refined for 1flp (helix 7 then helix 1) and T0178 (strand 8 and helix 7). The alignment search space for each test case is reported in The structural variability between 100 models computed from the structural alignment using MODELLER and energy minimized using CHARMM is illustrated for the 1flp helix 1 test case, using the per residue backbone RMSD after optimal superimposition of the entire structure . As expeThe energy of minimized models is, as expected, both much lower and less variable, as illustrated in ANOLEA/SSE predictor from minimized models , whereas it was not retrieved when non minimized models were used. For other test cases, the removal of this minimization step lead to less discriminative , or even wrong predictions (data not shown). This supports that energy minimized models not only help in reducing the variance of the energy but also change the predictor landscape, allowing better predictions to be made. The energy of models was thus always minimized before evaluation by the predictors.The correct alignment for 1flp helix 1  was obtaThe results obtained with the fifteen predictors over the entire test set are summarized in Predictions based on the CHARMM 19 and 22 force field  show that the different level of approximation to treat the solvent has little impact, with a maximum success rate of 30%, whatever the residues selections taken into account. Due to the poor performance of these predictors, the p-values are not reported in All, 50% for ROI and 50% for SSE.The reliability of ProsaII-based predictors is marginally impacted by the subset of residues taken into account, as reflected by their success rates: 60% for All, 50% for ROI, and 90% for SSE. The ANOLEA/SSE predictor is thus the most reliable predictor among the fifteen predictors tested.In contrast, the success rate of ANOLEA-based predictors increase as the subset of residues taken into account is narrowed around the SSE: 40% for Optimization of the selection of neighborsROI and SSE include neighboring residues , T0143 and T0178 (strand 8). Associated p-values range from 3.8⋅10−2 to 1.3⋅10−13. The structural alignment was ambiguously identified for 1flp (helix 7), T0141 and T0169, as reflected by not statistically significant p-values. The prediction is wrong for EDN, T0151 and T0178 (helix 7).The ANOLEA/ROI predictor is better than the All predictor, with associated p-values for successful prediction ranging from 3.0⋅10−2 to 4.2⋅10−32. Compared to the ANOLEA/All predictor, these lower p-values reflect a higher confidence as the residues selection is narrowed around the ROI.The performance of the ANOLEA/SSE predictor are given in −2 to 2.2⋅10−32. Among the three ANOLEA-based predictors, ANOLEA/SSE was found to be the most successful, and also lead systematically to statistically more significant p-values.The prediction results for the 8 iterations. Even though only a limited number of test cases was addressed in this article, this probability is low enough to clearly state that the ANOLEA/SSE performs better than ProsaII/SSE.If Anolea/SSE and ProsaII/SSE predictors have had the same performance level, the probability to obtain such a result by chance  was estimated to 2.7% by a two-tails bootstrap with 10ANOLEA/All, the ANOLEA/ROI or the ANOLEA/SSE predictors  .As expected, the closer to the structural alignment, the lower the RMSD to the X-ray structure of the resulting model. ALL, ROI, SSE), 4) the alignments are ranked by statistically comparing the predictor score distributions of the corresponding models.The method presented in this paper makes use of structural information to refine misaligned regions between a sequence to model (the target) and its template. An exhaustive list of alternative ungapped alignments is generated, and their likelihood is evaluated in the structure space, using the following steps: 1) an ensemble of 100 models are generated from each alternative alignment using the MODELLER program, 2) each model is energy minimized with the CHARMM program, 3) the model quality is evaluated by predictor scores obtained using different pair wise energy functions  computed on various residue selections around the misaligned region . The good performance obtained with of the SSE subset of residue comes from its ability to limit the impact of the high variability inherent to homology modeling techniques.The results of SSE predictor compared to All and ROI predictors comes as an illustration of this general principle.These data suggest that the conformation of a SSE in its local protein environment does correspond to a local minimum of its free energy. Although this result is somewhat intuitive, it is not an universal property; the conformation of particular regions of a protein might be constrained by the rest of the fold so that the minimum free energy conformation of the total protein results in SSE conformations that are driven away from their local minima. Experimental evidences also support this idea; pieces of a cleaved protein can recombine via non covalent interactions to form a structure with properties very similar to the native ones, while the separated fragments alone are devoid of any structure and function The alignment between a target and its template is a current bottleneck in homology modeling approaches, and methodological improvements are needed to overcome this limitation, especially when sequence identity is low. Although energy-based methods are widely used to tackle this problem, they are currently limited by their accuracy. This study shows that a small number of high-quality, all atom, and minimized models are sufficient to reliably evaluate a single alignment when using a sensitive and accurate scoring function. The reliability of the prediction is greatly enhanced by considering only the SSE to optimize and its interaction with residues of adjacent SSEs only, neglecting the loops, whose large structural variability adds noise and impairs the prediction based on the total energyANOLEA/SSE predictor (for scoring) and a genetic algorithm (for sampling) is currently under investigation.The method proposed in this article is able to discriminate the structural alignment from several alternatives. Its success mainly depends on the template quality in the ROI and its surrounding. If the orientation, length and environment of misaligned secondary structure are similar between the target and the template, the approach has shown to be very efficient. The proposed sampling method explores the free energy landscape of a SSE with the assumption that no gaps are present. A full alignment optimization combining an enhanced variant of the


Short loops can be predicted with high accuracy using structural fragments from other, not necessairly homologous proteins, or by various minimization methods. For longer loops multiscale approaches employing coarse-grained de novo modeling tool. Loops of various length, from 4 to 25 residues, were modeled assuming an ideal target-template alignment of the remaining portions of the protein. It has been shown that classical modeling with MODELLER is usually better for short loops, while coarse-grained de novo modeling is more effective for longer loops. Even very long missing fragments in protein structures could be effectively modeled. Resolution of such models is usually on the level 2-6 Å, which could be sufficient for guiding protein engineering. Further improvement of modeling accuracy could be achieved by the combination of different methods. In particular, we used 10 top ranked models from sets of 500 models generated by MODELLER as multiple templates for CABS modeling. On average, the resulting molecular models were better than the models from individual methods.For a representative set of protein structures of various structural classes test predictions of loop regions have been performed using MODELLER, ROSETTA, and a CABS coarse-grained Accuracy of protein modeling, as demonstrated for the problem of loop modeling, could be improved by the combinations of different modeling techniques. The evolutionary methods are essential for the derivation of statistical potentials for de novo modeling and/or are employed in various strategies for extracting structure building blocks from known protein structures [Comparative modeling remains the most dependable and routinely used method for protein structure prediction ,2. The a biology ,4. Most ructures ,6.Classical homology modeling consists of three steps. First, a template for modeling needs to be identified and sequence alignment between the template and target sequences has to be generated. Usually, template identification is performed by certain standard tools, such as PSI-BLAST, and the resulting alignment is subsequently rectified by other tools and eventually by manual expert corrections. Remote templates can also be identified by FR procedures . With thIn the second stage the aligned fragments of templates are used to generate the corresponding fragments of the target structure. In the simplest case of a single template only, this step reduces to mere copying the template coordinates according to the alignment. In the case of multiple templates a consensus scaffold could be built, for instance via the distribution of the spatial restrains read from the templates, as it is implemented in the MODELLER method . The keyThe third, and final, stage of modeling is structure refinement which involves repacking the side chains and energy minimization of the entire structure .The above scheme, or its variants, of comparative modeling remains the best choice when significant fragments of the alignment are error-free, which is usually the case in the range of high level sequence similarity . In the "twilight zone" of low sequence similarity the alignments contain significant errors. These could be sometimes corrected by building a multi-template consensus modeling scaffold . AlternaIn this paper we address the issue of loop modeling, separating it from the alignment problem. The test set of proteins with missing loops consists of two sub-sets. The first subset, containing missing loops of 4-12 residues, has been taken from a recent work by Rossi, et al., excluding the cases of incomplete chains in the corresponding PDB entries . The worFor a representative test set of protein structures with missing loop fragments the loop reconstruction procedure was executed using MODELLER, ROSETTA, CABS and the MODELLER-CABS hybrid modeling pipeline. The test set is summarized in Table Using MODELLER, we generated 500 examples of individual loop regions, which were subsequently ranked by the DOPE statistical potential . Top ranα traces only. Corresponding data for all atom structures are essentially the same. The plots in Figure The statistics of the results is shown in Figure Figure The loop modeling exercise described in this paper separates the two fundamental problems of comparative modeling: target-template alignment and modeling of missing fragments. Ideal alignments have been assumed and the excised loops reconstructed and compared with the native structures (cRMSD of the reconstructed loops after the superposition of the fixed parts of templates and models). As expected, MODELLER and ROSETTA proved to be more accurate for short loops, while CABS models were better for longer loops  MODELLER models are used as templates for CABS, allows for meaningful loop modeling for a broad range of loop length. The hybrid MODELLER-CABS method takes advantage of the local accuracy of MODELLER structures and the efficient sampling of local free-energy minima by CABS. The hybrid-CABS method described in this work extends the applicability range of protein comparative modeling. Further increase of accuracy for large loops will require better ranking of resulting models. Model-ranking in the range of moderate- and low-resolution computational structures remains a challenging problem for the entire structure-prediction field. In this case, a small step in this direction was performed by a combination of different modeling techniques.In this work we have shown that The dataset employed in this work is summarized in Table All loops were first modeled using MODELLER, version 9v5, and the model-loop procedure . The 500α-Cα bond. The Cα pseudo atoms are restricted to vertices of regular cubic lattice with the lattice spacing equal to 0.61 Å. Due to allowed fluctuations of the Cα-Cα distance around the canonical value of 3.78 Å the set of possible representations of this virtual bond consists of 800 lattice vectors. Thus, serious lattice artifacts could be safely ignored. The accuracy of the Cα-trace projection onto this lattice is in the order of 0.35 Å. On the other hand, lattice representation smoothens the model energy landscape and speeds -up computation by using pre-computed local conformational transitions which require simple references to hashing tables instead of computing trigonometric transformations, as would be necessary in an otherwise equivalent continuous space model. Coordinates of other pseudo-atoms are off-lattice and are defined in the reference frame provided by the Cα trace. Again, these coordinates are pre-computed and stored in simple reference tables, in which the two indices  encode the conformation of three consecutive alpha carbons. It is assumed that coordinates of such fragments define positions of the side chain for the central residue.CABS is a versatile modeling tool, based on the coarse graining of polypeptide conformational space and knowledge-based force field. Applications of CABS include protein structure prediction (from comparative to template-free modeling), prediction of protein folding mechanisms and flexible modeling of macromolecular assemblies ,23,24,26α moves, two, three and four Cα fragment transitions and small displacements of larger (4-22 residue) fragments. Update of a single Cα position involves side chain updates of the central and two neighboring residues. The sampling scheme could be executed within a classical Metropolis Monte Carlo scheme  or using a Replica Exchange (REMC) protocol when equilibrium data are required only, as in the case of the present work.Conformational updates include various local transformations, controlled by a pseudo random mechanism. There are single Cβ atoms, generic (sequence independent) short-range protein-like biases, making the model chain behaving like a generic polypeptide chain, sequence-dependent short-range statistical potential, context-specific pairwise interactions of the side chain united atoms, with repulsive and attractive square-well potential, and finally, a model of main-chain cooperative hydrogen bond networks. The details of the force field could be found in earlier publications and the numerical data for the histogram-type potentials are available from the authors' homepage http://biocomp.chem.uw.edu.pl.The force field of CABS consist of several types of potentials, including the hard-core excluded volume of the main chain and CCABS allows for very straightforward implementation of restraints of various types. These may include soft biases towards predicted secondary structures and theoretically predicted side chain contacts, distance restraints read from templates for comparative modeling, restraints derived from sparse NMR data, etc.First, the template proteins (with excised loop fragments) are projected onto the CABS lattice, and the loop fragments are added in a random fashion. Then, the non-loop fragments of the original structures are used to read several hundreds of distance restraints, similarly to the procedures used in comparative modeling with CABS . SubsequAnalysis of preliminary modeling results led to an interesting observation: The distribution of the accuracy of the models generated by MODELLER and ROSETTA was significantly broader than the distribution of the quality of models generated by CABS.The reason is that the models generated by MODELLER and ROSETTA are independent of one another, while the models from CABS are highly correlated along the simulation pseudo-trajectory. Consequently, the best models (among the 500 generated by MODELLER or ROSETTA) are usually considerably better than the top-ranked models. Unfortunately, the selection of the best models from a large set of decoys remains an unsolved problem for each of these methods. Taking the above into consideration, we designed a hybrid modeling pipeline that should take advantages of these methods. Namely, top ranked models from MODELLER (top 10) were used as structural templates for the derivation of distance restrains (including loop fragments) for modeling with CABS. It was expected that better local geometry of MODELLER structures and their diversity should improve sampling with CABS. The result of such an approach are reported as the CABS-hybrid simulations. Medoids  were reported as the top ranked models. A similar modeling strategy was designed for a combination of ROSETTA and CABS. The accuracy of such an approach is similar to the accuracy of the aformentioned MODELLER-CABS hybrid. Since MODELLER is computationally less expensive than ROSETTA we present a benchmark only for the later combination.AK conceived the use of a combination of modeling techniques. MJ performed simulations and analysis of the results. AK drafted the manuscript and both authors read and approved the final version of the manuscript.Student t-test. Results from two sample paired t-test of Table Click here for fileLoop benchmark test set. Database of 186 experimentally derived protein loop models used in the simulations.Click here for file


A phylogeny is the evolutionary history of a group of organisms. To date, sequence data is still the most used data type for phylogenetic reconstruction. Before any sequences can be used for phylogeny reconstruction, they must be aligned, and the quality of the multiple sequence alignment has been shown to affect the quality of the inferred phylogeny. At the same time, all the current multiple sequence alignment programs use a guide tree to produce the alignment and experiments showed that good guide trees can significantly improve the multiple alignment quality.We devise a new algorithm to simultaneously align multiple sequences and search for the phylogenetic tree that leads to the best alignment. We also implemented the algorithm as a C program package, which can handle both DNA and protein data and can take simple cost model as well as complex substitution matrices, such as PAM250 or BLOSUM62. The performance of the new method are compared with those from other popular multiple sequence alignment tools, including the widely used programs such as ClustalW and T-Coffee. Experimental results suggest that this method has good performance in terms of both phylogeny accuracy and alignment quality.We present an algorithm to align multiple sequences and reconstruct the phylogenies that minimize the alignment score, which is based on an efficient algorithm to solve the median problems for three sequences. Our extensive experiments suggest that this method is very promising and can produce high quality phylogenies and alignments. Multiple sequence alignment is one of the most fundamental and important issues in computational biology, and its applications include homologous genes identification, protein structure prediction and phylogenetic reconstruction. The most popular and commonly used approach for multiple sequence alignment is progressive alignment. Basically, it works by aligning the two closest sequences first and adding the remaining sequences one by one until all sequences have been aligned. ClustalW ,2 is oneOn the other hand, phylogeny is the evolutionary history among organisms. To date, sequence data is still the most used data type for phylogenetic reconstruction, and Maximum Parsimony (MP) and Maximum Likelihood (ML) are commonly used as the optimization criteria for reconstructing phylogenies. The most common approach for phylogenetic analysis is usually a two-step process: first, the input DNA or protein sequences are aligned with a multiple sequence alignment program, such as ClustalW and T-Coffee; then, the phylogeny will be inferred from the alignment using tools such as PAUP and RAxML. Generally speaking, most phylogenetic reconstruction methods assume a fixed alignment of the input sequences, which is known to have impact on the accuracy of the inferred phylogeny ,7. A settree alignment, which is motivated by the fact that in most cases the sequences are not independent of each other but rather related by a evolutionary tree ;• the insertion/deletion length frequencies are set as , which control the probabilities for gaps of lengths from 1 to 7;• two groups of the insertion/deletion threshold are tested: 0.001 and 0.005;• three substitution rates are tested: 0.1, 0.2 and 0.3;• four different expected sequence lengths are tested: 200, 400, 800 and 1000.We test trees of 10 taxa for each setting of parameters. For each category, we generate 100 dataset and report the average results. Since speed is a major concern here, we use only MSAM-H with the fast heuristic median solver. The results are shown in Figure From these figures, we find that for datasets produced in this experiment, MSAM-H outperforms POY, Clustal+PAUP and T-Coffee+PAUP in most of the categories, especially when the substitution rate is increased (sequences are more distant). We also need to point out that the topology accuracy error rate decreases with the increase of input sequence length; the error rate also increases with the increase of indel rate, because for these datasets the alignment is more difficult.This experiment suggests that even MSAM-H can produce better results than phylogenetic methods using prior knowledge of alignment. The average time for MSAM-H to iteratively score a given tree is less than one second for 200 characters, less than 10 seconds for 800 characters, and less than 25 seconds for 1000 characters. The scoring procedure convergence quickly and all trees require fewer than five iterations to score. On the other hand, the hill-climbing tree search procedure will stop with fewer than 1000 trees being examined. In short, the time used by MSAM-H on 10 taxa ranges from several minutes to an hour. Although more taxa will surely require more time, as we mentioned above, this obstacle can be overcome by using other methods developed in the phylogeny research community.We compare the alignments produced by MSAM with those obtained by POY, ClustalW and T-Coffee. We also report the score from MSAM-H. In this experiment, we use the same datasets created in the previous experiments, and the final tree alignments are produced on the best trees found in the previous section. We test ClustalW and T-Coffee with their default parameters and for MSAM and MSAM-H we use the common parameters of match cost 0, mis-match penalty 1, gap opening penalty 3, and gap extension 1. For POY, We used a testing script similar to that suggested by the authors. The alignments are then assessed using bali_score, a program provided by BAliBASE  to compaTable O(n3).In terms of running time, ClustalW is always the fastest, followed by MSAM-H, POY and T-COFFEE. Among all these programs, the execution time of MSAM is the longest, largely due to its exact median computation procedure, which has time complexity of We have presented an algorithm to align multiple sequences and reconstruct the phylogenies that minimize the alignment score. This method is based on efficient algorithms to solve the median problem of three sequences. For more sequences, our method overcomes various computational problems in tree scoring and tree searching. Our extensive experiments suggest that this method is very promising and can produce high quality phylogenies and alignments.Further improvements are needed, however. We need to find a better method to produce the final alignment with respect to the best tree, and use more complex methods to search through the tree space. More experiments are necessary as well. For example, we plan to compare MSAM with other phylogeny tools such as Maximum Likelihood methods and Bayesian methods.The authors declare that they have no competing interests.All authors contribute to the development and implementation of the algorithms, and FY and JS are in charge of conducting simulations and analyzing results.