A reliable sequence alignment method based on probabilities of residue correspondences

ProbPFP: a multiple sequence alignment algorithm combining hidden Markov model optimized by particle swarm optimization with partition function

BACKGROUND

During procedures for conducting multiple sequence alignment, that is so essential to use the substitution score of pairwise alignment. To compute adaptive scores for alignment, researchers usually use Hidden Markov Model or probabilistic consistency methods such as partition function. Recent studies show that optimizing the parameters for hidden Markov model, as well as integrating hidden Markov model with partition function can raise the accuracy of alignment. The combination of partition function and optimized HMM, which could further improve the alignment's accuracy, however, was ignored by these researches.

RESULTS

A novel algorithm for MSA called ProbPFP is presented in this paper. It intergrate optimized HMM by particle swarm with partition function. The algorithm of PSO was applied to optimize HMM's parameters. After that, the posterior probability obtained by the HMM was combined with the one obtained by partition function, and thus to calculate an integrated substitution score for alignment. In order to evaluate the effectiveness of ProbPFP, we compared it with 13 outstanding or classic MSA methods. The results demonstrate that the alignments obtained by ProbPFP got the maximum mean TC scores and mean SP scores on these two benchmark datasets: SABmark and OXBench, and it got the second highest mean TC scores and mean SP scores on the benchmark dataset BAliBASE. ProbPFP is also compared with 4 other outstanding methods, by reconstructing the phylogenetic trees for six protein families extracted from the database TreeFam, based on the alignments obtained by these 5 methods. The result indicates that the reference trees are closer to the phylogenetic trees reconstructed from the alignments obtained by ProbPFP than the other methods.

CONCLUSIONS

We propose a new multiple sequence alignment method combining optimized HMM and partition function in this paper. The performance validates this method could make a great improvement of the alignment's accuracy.

How sequence alignment scores correspond to probability models

MOTIVATION

Sequence alignment remains fundamental in bioinformatics. Pair-wise alignment is traditionally based on ad hoc scores for substitutions, insertions and deletions, but can also be based on probability models (pair hidden Markov models: PHMMs). PHMMs enable us to: fit the parameters to each kind of data, calculate the reliability of alignment parts and measure sequence similarity integrated over possible alignments.

RESULTS

This study shows how multiple models correspond to one set of scores. Scores can be converted to probabilities by partition functions with a 'temperature' parameter: for any temperature, this corresponds to some PHMM. There is a special class of models with balanced length probability, i.e. no bias toward either longer or shorter alignments. The best way to score alignments and assess their significance depends on the aim: judging whether whole sequences are related versus finding related parts. This clarifies the statistical basis of sequence alignment.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Bioinformatics applications on Apache Spark

With the rapid development of next-generation sequencing technology, ever-increasing quantities of genomic data pose a tremendous challenge to data processing. Therefore, there is an urgent need for highly scalable and powerful computational systems. Among the state-of–the-art parallel computing platforms, Apache Spark is a fast, general-purpose, in-memory, iterative computing framework for large-scale data processing that ensures high fault tolerance and high scalability by introducing the resilient distributed dataset abstraction. In terms of performance, Spark can be up to 100 times faster in terms of memory access and 10 times faster in terms of disk access than Hadoop. Moreover, it provides advanced application programming interfaces in Java, Scala, Python, and R. It also supports some advanced components, including Spark SQL for structured data processing, MLlib for machine learning, GraphX for computing graphs, and Spark Streaming for stream computing. We surveyed Spark-based applications used in next-generation sequencing and other biological domains, such as epigenetics, phylogeny, and drug discovery. The results of this survey are used to provide a comprehensive guideline allowing bioinformatics researchers to apply Spark in their own fields.

QuickProbs 2: Towards rapid construction of high-quality alignments of large protein families

The ever-increasing size of sequence databases caused by the development of high throughput sequencing, poses to multiple alignment algorithms one of the greatest challenges yet. As we show, well-established techniques employed for increasing alignment quality, i.e., refinement and consistency, are ineffective when large protein families are investigated. We present QuickProbs 2, an algorithm for multiple sequence alignment. Based on probabilistic models, equipped with novel column-oriented refinement and selective consistency, it offers outstanding accuracy. When analysing hundreds of sequences, Quick-Probs 2 is noticeably better than ClustalΩ and MAFFT, the previous leaders for processing numerous protein families. In the case of smaller sets, for which consistency-based methods are the best performing, QuickProbs 2 is also superior to the competitors. Due to low computational requirements of selective consistency and utilization of massively parallel architectures, presented algorithm has similar execution times to ClustalΩ, and is orders of magnitude faster than full consistency approaches, like MSAProbs or PicXAA. All these make QuickProbs 2 an excellent tool for aligning families ranging from few, to hundreds of proteins.

Efficient representation of uncertainty in multiple sequence alignments using directed acyclic graphs

BACKGROUND

A standard procedure in many areas of bioinformatics is to use a single multiple sequence alignment (MSA) as the basis for various types of analysis. However, downstream results may be highly sensitive to the alignment used, and neglecting the uncertainty in the alignment can lead to significant bias in the resulting inference. In recent years, a number of approaches have been developed for probabilistic sampling of alignments, rather than simply generating a single optimum. However, this type of probabilistic information is currently not widely used in the context of downstream inference, since most existing algorithms are set up to make use of a single alignment.

RESULTS

In this work we present a framework for representing a set of sampled alignments as a directed acyclic graph (DAG) whose nodes are alignment columns; each path through this DAG then represents a valid alignment. Since the probabilities of individual columns can be estimated from empirical frequencies, this approach enables sample-based estimation of posterior alignment probabilities. Moreover, due to conditional independencies between columns, the graph structure encodes a much larger set of alignments than the original set of sampled MSAs, such that the effective sample size is greatly increased.

CONCLUSIONS

The alignment DAG provides a natural way to represent a distribution in the space of MSAs, and allows for existing algorithms to be efficiently scaled up to operate on large sets of alignments. As an example, we show how this can be used to compute marginal probabilities for tree topologies, averaging over a very large number of MSAs. This framework can also be used to generate a statistically meaningful summary alignment; example applications show that this summary alignment is consistently more accurate than the majority of the alignment samples, leading to improvements in downstream tree inference. Implementations of the methods described in this article are available at http://statalign.github.io/WeaveAlign .

Effective alignment of RNA pseudoknot structures using partition function posterior log-odds scores

Background

RNA pseudoknots play important roles in many biological processes. Previous methods for comparative pseudoknot analysis mainly focus on simultaneous folding and alignment of RNA sequences. Little work has been done to align two known RNA secondary structures with pseudoknots taking into account both sequence and structure information of the two RNAs.

Results

In this article we present a novel method for aligning two known RNA secondary structures with pseudoknots. We adopt the partition function methodology to calculate the posterior log-odds scores of the alignments between bases or base pairs of the two RNAs with a dynamic programming algorithm. The posterior log-odds scores are then used to calculate the expected accuracy of an alignment between the RNAs. The goal is to find an optimal alignment with the maximum expected accuracy. We present a heuristic to achieve this goal. The performance of our method is investigated and compared with existing tools for RNA structure alignment. An extension of the method to multiple alignment of pseudoknot structures is also discussed.

Conclusions

The method described here has been implemented in a tool named RKalign, which is freely accessible on the Internet. As more and more pseudoknots are revealed, collected and stored in public databases, we anticipate a tool like RKalign will play a significant role in data comparison, annotation, analysis, and retrieval in these databases.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-015-0464-9) contains supplementary material, which is available to authorized users.

RNA structural alignments, part II: non-Sankoff approaches for structural alignments

In structural alignments of RNA sequences, the computational cost of Sankoff algorithm, which simultaneously optimizes the score of the common secondary structure and the score of the alignment, is too high for long sequences (O(L (6)) time for two sequences of length L). In this chapter, we introduce the methods that predict the structures and the alignment separately to avoid the heavy computations in Sankoff algorithm. In those methods, neither of those two prediction processes is independent, but each of them utilizes the information of the other process. The first process typically includes prediction of base-pairing probabilities (BPPs) or the candidates of the stems, and the alignment process utilizes those results. At the same time, it is also important to reflect the information of the alignment to the structure prediction. This idea can be implemented as the probabilistic transformation (PCT) of BPPs using the potential alignment. As same as for all the estimation problems, it is important to define the evaluation measure for the structural alignment. The principle of maximum expected accuracy (MEA) is applicable for sum-of-pairs (SPS) score based on the reference alignment.

MSARC: Multiple sequence alignment by residue clustering

Background

Progressive methods offer efficient and reasonably good solutions to the multiple sequence alignment problem. However, resulting alignments are biased by guide-trees, especially for relatively distant sequences.

Results

We propose MSARC, a new graph-clustering based algorithm that aligns sequence sets without guide-trees. Experiments on the BAliBASE dataset show that MSARC achieves alignment quality similar to the best progressive methods.

Furthermore, MSARC outperforms them on sequence sets whose evolutionary distances are difficult to represent by a phylogenetic tree. These datasets are most exposed to the guide-tree bias of alignments.

Availability

MSARC is available at http://bioputer.mimuw.edu.pl/msarc

Probabilistic approaches to alignment with tandem repeats

Background

Short tandem repeats are ubiquitous in genomic sequences and due to their complex evolutionary history pose a challenge for sequence alignment tools.

Results

To better account for the presence of tandem repeats in pairwise sequence alignments, we propose a simple tractable pair hidden Markov model that explicitly models their presence. Using the framework of gain functions, we design several optimization criteria for decoding this model and describe resulting decoding algorithms, ranging from the traditional Viterbi and posterior decoding to block-based decoding algorithms tailored to our model. We compare the accuracy of individual decoding algorithms on simulated and real data and find that our approach is superior to the classical three-state pair HMM.

Conclusions

Our study illustrates versatility of pair hidden Markov models coupled with appropriate decoding criteria as a modeling tool for capturing complex sequence features.

Sequence alignment by passing messages

Background

Sequence alignment has become an indispensable tool in modern molecular biology research, and probabilistic sequence alignment models have been shown to provide an effective framework for building accurate sequence alignment tools. One such example is the pair hidden Markov model (pair-HMM), which has been especially popular in comparative sequence analysis for several reasons, including their effectiveness in modeling and detecting sequence homology, model simplicity, and the existence of efficient algorithms for applying the model to sequence alignment problems. However, despite these advantages, pair-HMMs also have a number of practical limitations that may degrade their alignment performance or render them unsuitable for certain alignment tasks.

Results

In this work, we propose a novel scheme for comparing and aligning biological sequences that can effectively address the shortcomings of the traditional pair-HMMs. The proposed scheme is based on a simple message-passing approach, where messages are exchanged between neighboring symbol pairs that may be potentially aligned in the optimal sequence alignment. The message-passing process yields probabilistic symbol alignment confidence scores, which may be used for predicting the optimal alignment that maximizes the expected number of correctly aligned symbol pairs.

Conclusions

Extensive performance evaluation on protein alignment benchmark datasets shows that the proposed message-passing scheme clearly outperforms the traditional pair-HMM-based approach, in terms of both alignment accuracy and computational efficiency. Furthermore, the proposed scheme is numerically robust and amenable to massive parallelization.

Multiple sequence alignment using Probcons and Probalign

Sequence alignment remains a fundamental task in bioinformatics. The literature contains programs that employ a host of exact and heuristic strategies available in computer science. Probcons was the first program to construct maximum expected accuracy sequence alignments with hidden Markov models and at the time of its publication achieved the highest accuracies on standard protein multiple alignment benchmarks. Probalign followed this strategy except that it used a partition function approach instead of hidden Markov models. Several programs employing both strategies have been published since then. In this chapter we describe Probcons and Probalign.

Multiple protein sequence alignment with MSAProbs

Multiple sequence alignment (MSA) generally constitutes the foundation of many bioinformatics studies involving functional, structural, and evolutionary relationship analysis between sequences. As a result of the exponential computational complexity of the exact approach to producing optimal multiple alignments, the majority of state-of-the-art MSA algorithms are designed based on the progressive alignment heuristic. In this chapter, we outline MSAProbs, a parallelized MSA algorithm for protein sequences based on progressive alignment. To achieve high alignment accuracy, this algorithm employs a hybrid combination of a pair hidden Markov model and a partition function to calculate posterior probabilities. Furthermore, we provide some practical advice on the usage of the algorithm.

Heuristic alignment methods

Computation of multiple sequence alignment (MSA) is usually formulated as a combinatory optimization problem of an objective function. Solving the problem for virtually all sensible objective functions is known to be NP-complete implying that some heuristics must be adopted. Several general strategies have been proven effective to obtain accurate MSAs in reasonable computational costs. This chapter is devoted to a brief summary of most successful heuristic approaches.

The four ingredients of single-sequence RNA secondary structure prediction. A unifying perspective

Any method for RNA secondary structure prediction is determined by four ingredients. The architecture is the choice of features implemented by the model (such as stacked basepairs, loop length distributions, etc.). The architecture determines the number of parameters in the model. The scoring scheme is the nature of those parameters (whether thermodynamic, probabilistic, or weights). The parameterization stands for the specific values assigned to the parameters. These three ingredients are referred to as "the model." The fourth ingredient is the folding algorithms used to predict plausible secondary structures given the model and the sequence of a structural RNA. Here, I make several unifying observations drawn from looking at more than 40 years of methods for RNA secondary structure prediction in the light of this classification. As a final observation, there seems to be a performance ceiling that affects all methods with complex architectures, a ceiling that impacts all scoring schemes with remarkable similarity. This suggests that modeling RNA secondary structure by using intrinsic sequence-based plausible "foldability" will require the incorporation of other forms of information in order to constrain the folding space and to improve prediction accuracy. This could give an advantage to probabilistic scoring systems since a probabilistic framework is a natural platform to incorporate different sources of information into one single inference problem.

Fighting against uncertainty: an essential issue in bioinformatics

Many bioinformatics problems, such as sequence alignment, gene prediction, phylogenetic tree estimation and RNA secondary structure prediction, are often affected by the 'uncertainty' of a solution, that is, the probability of the solution is extremely small. This situation arises for estimation problems on high-dimensional discrete spaces in which the number of possible discrete solutions is immense. In the analysis of biological data or the development of prediction algorithms, this uncertainty should be handled carefully and appropriately. In this review, I will explain several methods to combat this uncertainty, presenting a number of examples in bioinformatics. The methods include (i) avoiding point estimation, (ii) maximum expected accuracy (MEA) estimations and (iii) several strategies to design a pipeline involving several prediction methods. I believe that the basic concepts and ideas described in this review will be generally useful for estimation problems in various areas of bioinformatics.

A classification of bioinformatics algorithms from the viewpoint of maximizing expected accuracy (MEA)

Many estimation problems in bioinformatics are formulated as point estimation problems in a high-dimensional discrete space. In general, it is difficult to design reliable estimators for this type of problem, because the number of possible solutions is immense, which leads to an extremely low probability for every solution-even for the one with the highest probability. Therefore, maximum score and maximum likelihood estimators do not work well in this situation although they are widely employed in a number of applications. Maximizing expected accuracy (MEA) estimation, in which accuracy measures of the target problem and the entire distribution of solutions are considered, is a more successful approach. In this review, we provide an extensive discussion of algorithms and software based on MEA. We describe how a number of algorithms used in previous studies can be classified from the viewpoint of MEA. We believe that this review will be useful not only for users wishing to utilize software to solve the estimation problems appearing in this article, but also for developers wishing to design algorithms on the basis of MEA.

A range of complex probabilistic models for RNA secondary structure prediction that includes the nearest-neighbor model and more

The standard approach for single-sequence RNA secondary structure prediction uses a nearest-neighbor thermodynamic model with several thousand experimentally determined energy parameters. An attractive alternative is to use statistical approaches with parameters estimated from growing databases of structural RNAs. Good results have been reported for discriminative statistical methods using complex nearest-neighbor models, including CONTRAfold, Simfold, and ContextFold. Little work has been reported on generative probabilistic models (stochastic context-free grammars [SCFGs]) of comparable complexity, although probabilistic models are generally easier to train and to use. To explore a range of probabilistic models of increasing complexity, and to directly compare probabilistic, thermodynamic, and discriminative approaches, we created TORNADO, a computational tool that can parse a wide spectrum of RNA grammar architectures (including the standard nearest-neighbor model and more) using a generalized super-grammar that can be parameterized with probabilities, energies, or arbitrary scores. By using TORNADO, we find that probabilistic nearest-neighbor models perform comparably to (but not significantly better than) discriminative methods. We find that complex statistical models are prone to overfitting RNA structure and that evaluations should use structurally nonhomologous training and test data sets. Overfitting has affected at least one published method (ContextFold). The most important barrier to improving statistical approaches for RNA secondary structure prediction is the lack of diversity of well-curated single-sequence RNA secondary structures in current RNA databases.

Conotoxin protein classification using free scores of words and support vector machines

Background

Conotoxin has been proven to be effective in drug design and could be used to treat various disorders such as schizophrenia, neuromuscular disorders and chronic pain. With the rapidly growing interest in conotoxin, accurate conotoxin superfamily classification tools are desirable to systematize the increasing number of newly discovered sequences and structures. However, despite the significance and extensive experimental investigations on conotoxin, those tools have not been intensively explored.

Results

In this paper, we propose to consider suboptimal alignments of words with restricted length. We developed a scoring system based on local alignment partition functions, called free score. The scoring system plays the key role in the feature extraction step of support vector machine classification. In the classification of conotoxin proteins, our method, SVM-Freescore, features an improved sensitivity and specificity by approximately 5.864% and 3.76%, respectively, over previously reported methods. For the generalization purpose, SVM-Freescore was also applied to classify superfamilies from curated and high quality database such as ConoServer. The average computed sensitivity and specificity for the superfamily classification were found to be 0.9742 and 0.9917, respectively.

Conclusions

The SVM-Freescore method is shown to be a useful sequence-based analysis tool for functional and structural characterization of conotoxin proteins. The datasets and the software are available at http://faculty.uaeu.ac.ae/nzaki/SVM-Freescore.htm.

Generalized centroid estimators in bioinformatics

In a number of estimation problems in bioinformatics, accuracy measures of the target problem are usually given, and it is important to design estimators that are suitable to those accuracy measures. However, there is often a discrepancy between an employed estimator and a given accuracy measure of the problem. In this study, we introduce a general class of efficient estimators for estimation problems on high-dimensional binary spaces, which represent many fundamental problems in bioinformatics. Theoretical analysis reveals that the proposed estimators generally fit with commonly-used accuracy measures (e.g. sensitivity, PPV, MCC and F-score) as well as it can be computed efficiently in many cases, and cover a wide range of problems in bioinformatics from the viewpoint of the principle of maximum expected accuracy (MEA). It is also shown that some important algorithms in bioinformatics can be interpreted in a unified manner. Not only the concept presented in this paper gives a useful framework to design MEA-based estimators but also it is highly extendable and sheds new light on many problems in bioinformatics.

Effect of using suboptimal alignments in template-based protein structure prediction

Computational protein structure prediction remains a challenging task in protein bioinformatics. In the recent years, the importance of template-based structure prediction is increasing because of the growing number of protein structures solved by the structural genomics projects. To capitalize the significant efforts and investments paid on the structural genomics projects, it is urgent to establish effective ways to use the solved structures as templates by developing methods for exploiting remotely related proteins that cannot be simply identified by homology. In this work, we examine the effect of using suboptimal alignments in template-based protein structure prediction. We showed that suboptimal alignments are often more accurate than the optimal one, and such accurate suboptimal alignments can occur even at a very low rank of the alignment score. Suboptimal alignments contain a significant number of correct amino acid residue contacts. Moreover, suboptimal alignments can improve template-based models when used as input to Modeller. Finally, we use suboptimal alignments for handling a contact potential in a probabilistic way in a threading program, SUPRB. The probabilistic contacts strategy outperforms the partly thawed approach, which only uses the optimal alignment in defining residue contacts, and also the re-ranking strategy, which uses the contact potential in re-ranking alignments. The comparison with existing methods in the template-recognition test shows that SUPRB is very competitive and outperforms existing methods.

MSAProbs: multiple sequence alignment based on pair hidden Markov models and partition function posterior probabilities

MOTIVATION

Multiple sequence alignment is of central importance to bioinformatics and computational biology. Although a large number of algorithms for computing a multiple sequence alignment have been designed, the efficient computation of highly accurate multiple alignments is still a challenge.

RESULTS

We present MSAProbs, a new and practical multiple alignment algorithm for protein sequences. The design of MSAProbs is based on a combination of pair hidden Markov models and partition functions to calculate posterior probabilities. Furthermore, two critical bioinformatics techniques, namely weighted probabilistic consistency transformation and weighted profile-profile alignment, are incorporated to improve alignment accuracy. Assessed using the popular benchmarks: BAliBASE, PREFAB, SABmark and OXBENCH, MSAProbs achieves statistically significant accuracy improvements over the existing top performing aligners, including ClustalW, MAFFT, MUSCLE, ProbCons and Probalign. Furthermore, MSAProbs is optimized for multi-core CPUs by employing a multi-threaded design, leading to a competitive execution time compared to other aligners.

AVAILABILITY

The source code of MSAProbs, written in C++, is freely and publicly available from http://msaprobs.sourceforge.net.

Improving pairwise sequence alignment accuracy using near-optimal protein sequence alignments

Background

While the pairwise alignments produced by sequence similarity searches are a powerful tool for identifying homologous proteins - proteins that share a common ancestor and a similar structure; pairwise sequence alignments often fail to represent accurately the structural alignments inferred from three-dimensional coordinates. Since sequence alignment algorithms produce optimal alignments, the best structural alignments must reflect suboptimal sequence alignment scores. Thus, we have examined a range of suboptimal sequence alignments and a range of scoring parameters to understand better which sequence alignments are likely to be more structurally accurate.

Results

We compared near-optimal protein sequence alignments produced by the Zuker algorithm and a set of probabilistic alignments produced by the probA program with structural alignments produced by four different structure alignment algorithms. There is significant overlap between the solution spaces of structural alignments and both the near-optimal sequence alignments produced by commonly used scoring parameters for sequences that share significant sequence similarity (E-values < 10^-5) and the ensemble of probA alignments. We constructed a logistic regression model incorporating three input variables derived from sets of near-optimal alignments: robustness, edge frequency, and maximum bits-per-position. A ROC analysis shows that this model more accurately classifies amino acid pairs (edges in the alignment path graph) according to the likelihood of appearance in structural alignments than the robustness score alone. We investigated various trimming protocols for removing incorrect edges from the optimal sequence alignment; the most effective protocol is to remove matches from the semi-global optimal alignment that are outside the boundaries of the local alignment, although trimming according to the model-generated probabilities achieves a similar level of improvement. The model can also be used to generate novel alignments by using the probabilities in lieu of a scoring matrix. These alignments are typically better than the optimal sequence alignment, and include novel correct structural edges. We find that the probA alignments sample a larger variety of alignments than the Zuker set, which more frequently results in alignments that are closer to the structural alignments, but that using the probA alignments as input to the regression model does not increase performance.

Conclusions

The pool of suboptimal pairwise protein sequence alignments substantially overlaps structure-based alignments for pairs with statistically significant similarity, and a regression model based on information contained in this alignment pool improves the accuracy of pairwise alignments with respect to structure-based alignments.

Parameters for accurate genome alignment

Background

Genome sequence alignments form the basis of much research. Genome alignment depends on various mundane but critical choices, such as how to mask repeats and which score parameters to use. Surprisingly, there has been no large-scale assessment of these choices using real genomic data. Moreover, rigorous procedures to control the rate of spurious alignment have not been employed.

Results

We have assessed 495 combinations of score parameters for alignment of animal, plant, and fungal genomes. As our gold-standard of accuracy, we used genome alignments implied by multiple alignments of proteins and of structural RNAs. We found the HOXD scoring schemes underlying alignments in the UCSC genome database to be far from optimal, and suggest better parameters. Higher values of the X-drop parameter are not always better. E-values accurately indicate the rate of spurious alignment, but only if tandem repeats are masked in a non-standard way. Finally, we show that γ-centroid (probabilistic) alignment can find highly reliable subsets of aligned bases.

Conclusions

These results enable more accurate genome alignment, with reliability measures for local alignments and for individual aligned bases. This study was made possible by our new software, LAST, which can align vertebrate genomes in a few hours http://last.cbrc.jp/.

Finite-temperature local protein sequence alignment: percolation and free-energy distribution

Sequence alignment is a tool in bioinformatics that is used to find homological relationships in large molecular databases. It can be mapped on the physical model of directed polymers in random media. We consider the finite-temperature version of local sequence alignment for proteins and study the transition between the linear phase and the biologically relevant logarithmic phase, where the free energy grows linearly or logarithmically with the sequence length. By means of numerical simulations and finite-size-scaling analysis, we determine the phase diagram in the plane that is spanned by the gap costs and the temperature. We use the most frequently used parameter set for protein alignment. The critical exponents that describe the parameter-driven transition are found to be explicitly temperature dependent. Furthermore, we study the shape of the (free-) energy distribution close to the transition by rare-event simulations down to probabilities on the order 10(-64). It is well known that in the logarithmic region, the optimal score distribution (T=0) is described by a modified Gumbel distribution. We confirm that this also applies for the free-energy distribution (T>0). However, in the linear phase, the distribution crosses over to a modified Gaussian distribution.

Predictions of RNA secondary structure by combining homologous sequence information

Motivation: Secondary structure prediction of RNA sequences is an important problem. There have been progresses in this area, but the accuracy of prediction from an RNA sequence is still limited. In many cases, however, homologous RNA sequences are available with the target RNA sequence whose secondary structure is to be predicted.

Results: In this article, we propose a new method for secondary structure predictions of individual RNA sequences by taking the information of their homologous sequences into account without assuming the common secondary structure of the entire sequences. The proposed method is based on posterior decoding techniques, which consider all the suboptimal secondary structures of the target and homologous sequences and all the suboptimal alignments between the target sequence and each of the homologous sequences. In our computational experiments, the proposed method provides better predictions than those performed only on the basis of the formation of individual RNA sequences and those performed by using methods for predicting the common secondary structure of the homologous sequences. Remarkably, we found that the common secondary predictions sometimes give worse predictions for the secondary structure of a target sequence than the predictions from the individual target sequence, while the proposed method always gives good predictions for the secondary structure of target sequences in all tested cases.

Availability: Supporting information and software are available online at: http://www.ncrna.org/software/centroidfold/ismb2009/.

Contact:hamada-michiaki@aist.go.jp

Supplementary information:Supplementary data are available at Bioinformatics online.

Profile conditional random fields for modeling protein families with structural information

A statistical model of protein families, called profile conditional random fields (CRFs), is proposed. This model may be regarded as an integration of the profile hidden Markov model (HMM) and the Finkelstein-Reva (FR) theory of protein folding. While the model structure of the profile CRF is almost identical to the profile HMM, it can incorporate arbitrary correlations in the sequences to be aligned to the model. In addition, like in the FR theory, the profile CRF can incorporate long-range pair-wise interactions between model states via mean-field-like approximations. We give the detailed formulation of the model, self-consistent approximations for treating long-range interactions, and algorithms for computing partition functions and marginal probabilities. We also outline the methods for the global optimization of model parameters as well as a Bayesian framework for parameter learning and selection of optimal alignments.

Exact calculation of distributions on integers, with application to sequence alignment

Computational biology is replete with high-dimensional discrete prediction and inference problems. Dynamic programming recursions can be applied to several of the most important of these, including sequence alignment, RNA secondary-structure prediction, phylogenetic inference, and motif finding. In these problems, attention is frequently focused on some scalar quantity of interest, a score, such as an alignment score or the free energy of an RNA secondary structure. In many cases, score is naturally defined on integers, such as a count of the number of pairing differences between two sequence alignments, or else an integer score has been adopted for computational reasons, such as in the test of significance of motif scores. The probability distribution of the score under an appropriate probabilistic model is of interest, such as in tests of significance of motif scores, or in calculation of Bayesian confidence limits around an alignment. Here we present three algorithms for calculating the exact distribution of a score of this type; then, in the context of pairwise local sequence alignments, we apply the approach so as to find the alignment score distribution and Bayesian confidence limits.

Genome-wide searching with base-pairing kernel functions for noncoding RNAs: computational and expression analysis of snoRNA families in Caenorhabditis elegans

Despite the accumulating research on noncoding RNAs (ncRNAs), it is likely that we are seeing only the tip of the iceberg regarding our understanding of the functions and the regulatory roles served by ncRNAs in cellular metabolism, pathogenesis and host-pathogen interactions. Therefore, more powerful computational and experimental tools for analyzing ncRNAs need to be developed. To this end, we propose novel kernel functions, called base-pairing profile local alignment (BPLA) kernels, for analyzing functional ncRNA sequences using support vector machines (SVMs). We extend the local alignment kernels for amino acid sequences in order to handle RNA sequences by using STRAL's; scoring function, which takes into account sequence similarities as well as upstream and downstream base-pairing probabilities, thus enabling us to model secondary structures of RNA sequences. As a test of the performance of BPLA kernels, we applied our kernels to the problem of discriminating members of an RNA family from nonmembers using SVMs. The results indicated that the discrimination ability of our kernels is stronger than that of other existing methods. Furthermore, we demonstrated the applicability of our kernels to the problem of genome-wide search of snoRNA families in the Caenorhabditis elegans genome, and confirmed that the expression is valid in 14 out of 48 of our predicted candidates by using qRT-PCR. Finally, highly expressed six candidates were identified as the original target regions by DNA sequencing.

Unifying evolutionary and thermodynamic information for RNA folding of multiple alignments

Computational methods for determining the secondary structure of RNA sequences from given alignments are currently either based on thermodynamic folding, compensatory base pair substitutions or both. However, there is currently no approach that combines both sources of information in a single optimization problem. Here, we present a model that formally integrates both the energy-based and evolution-based approaches to predict the folding of multiple aligned RNA sequences. We have implemented an extended version of Pfold that identifies base pairs that have high probabilities of being conserved and of being energetically favorable. The consensus structure is predicted using a maximum expected accuracy scoring scheme to smoothen the effect of incorrectly predicted base pairs. Parameter tuning revealed that the probability of base pairing has a higher impact on the RNA structure prediction than the corresponding probability of being single stranded. Furthermore, we found that structurally conserved RNA motifs are mostly supported by folding energies. Other problems (e.g. RNA-folding kinetics) may also benefit from employing the principles of the model we introduce. Our implementation, PETfold, was tested on a set of 46 well-curated Rfam families and its performance compared favorably to that of Pfold and RNAalifold.

The whole alignment and nothing but the alignment: the problem of spurious alignment flanks

Pairwise sequence alignment is a ubiquitous tool for inferring the evolution and function of DNA, RNA and protein sequences. It is therefore essential to identify alignments arising by chance alone, i.e. spurious alignments. On one hand, if an entire alignment is spurious, statistical techniques for identifying and eliminating it are well known. On the other hand, if only a part of the alignment is spurious, elimination is much more problematic. In practice, even the sizes and frequencies of spurious subalignments remain unknown. This article shows that some common scoring schemes tend to overextend alignments and generate spurious alignment flanks up to hundreds of base pairs/amino acids in length. In the UCSC genome database, e.g. spurious flanks probably comprise >18% of the human-fugu genome alignment. To evaluate the possibility that chance alone generated a particular flank on a particular pairwise alignment, we provide a simple 'overalignment' P-value. The overalignment P-value can identify spurious alignment flanks, thereby eliminating potentially misleading inferences about evolution and function. Moreover, by explicitly demonstrating the tradeoff between over- and under-alignment, our methods guide the rational choice of scoring schemes for various alignment tasks.

Estimating quality of template-based protein models by alignment stability

The error in protein tertiary structure prediction is unavoidable, but it is not explicitly shown in most of the current prediction algorithms. Estimated error of a predicted structure is crucial information for experimental biologists to use the prediction model for design and interpretation of experiments. Here, we propose a method to estimate errors in predicted structures based on the stability of the optimal target-template alignment when compared with a set of suboptimal alignments. The stability of the optimal alignment is quantified by an index named the SuboPtimal Alignment Diversity (SPAD). We implemented SPAD in a profile-based threading algorithm and investigated how well SPAD can indicate errors in threading models using a large benchmark dataset of 5232 alignments. SPAD shows a very good correlation not only to alignment shift errors but also structure-level errors, the root mean square deviation (RMSD) of predicted structure models to the native structures (i.e. global errors), and local errors at each residue position. We have further compared SPAD with seven other quality measures, six from sequence alignment-based measures and one atomic statistical potential, discrete optimized protein energy (DOPE), in terms of the correlation coefficient to the global and local structure-level errors. In terms of the correlation to the RMSD of structure models, when a target and a template are in the same SCOP family, the sequence identity showed a best correlation to the RMSD; in the superfamily level, SPAD was the best; and in the fold level, DOPE was best. However, in a head-to-head comparison, SPAD wins over the other measures. Next, SPAD is compared with three other measures of local errors. In this comparison, SPAD was best in all of the family, the superfamily and the fold levels. Using the discovered correlation, we have also predicted the global and local error of our predicted structures of CASP7 targets by the SPAD. Finally, we proposed a sausage representation of predicted tertiary structures which intuitively indicate the predicted structure and the estimated error range of the structure simultaneously.

Memory-efficient dynamic programming backtrace and pairwise local sequence alignment

Motivation: A backtrace through a dynamic programming algorithm's intermediate results in search of an optimal path, or to sample paths according to an implied probability distribution, or as the second stage of a forward–backward algorithm, is a task of fundamental importance in computational biology. When there is insufficient space to store all intermediate results in high-speed memory (e.g. cache) existing approaches store selected stages of the computation, and recompute missing values from these checkpoints on an as-needed basis.

Results: Here we present an optimal checkpointing strategy, and demonstrate its utility with pairwise local sequence alignment of sequences of length 10 000.

Availability: Sample C++-code for optimal backtrace is available in the Supplementary Materials.

Contact:leen@cs.rpi.edu

Supplementary information:Supplementary data is available at Bioinformatics online.

A probabilistic model of local sequence alignment that simplifies statistical significance estimation

Sequence database searches require accurate estimation of the statistical significance of scores. Optimal local sequence alignment scores follow Gumbel distributions, but determining an important parameter of the distribution (λ) requires time-consuming computational simulation. Moreover, optimal alignment scores are less powerful than probabilistic scores that integrate over alignment uncertainty (“Forward” scores), but the expected distribution of Forward scores remains unknown. Here, I conjecture that both expected score distributions have simple, predictable forms when full probabilistic modeling methods are used. For a probabilistic model of local sequence alignment, optimal alignment bit scores (“Viterbi” scores) are Gumbel-distributed with constant λ = log 2, and the high scoring tail of Forward scores is exponential with the same constant λ. Simulation studies support these conjectures over a wide range of profile/sequence comparisons, using 9,318 profile-hidden Markov models from the Pfam database. This enables efficient and accurate determination of expectation values (E-values) for both Viterbi and Forward scores for probabilistic local alignments.

Sequence database searches are a fundamental tool of molecular biology, enabling researchers to identify related sequences in other organisms, which often provides invaluable clues to the function and evolutionary history of genes. The power of database searches to detect more and more remote evolutionary relationships – essentially, to look back deeper in time – has improved steadily, with the adoption of more complex and realistic models. However, database searches require not just a realistic scoring model, but also the ability to distinguish good scores from bad ones – the ability to calculate the statistical significance of scores. For many models and scoring schemes, accurate statistical significance calculations have either involved expensive computational simulations, or not been feasible at all. Here, I introduce a probabilistic model of local sequence alignment that has readily predictable score statistics for position-specific profile scoring systems, and not just for traditional optimal alignment scores, but also for more powerful log-likelihood ratio scores derived in a full probabilistic inference framework. These results remove one of the main obstacles that have impeded the use of more powerful and biologically realistic statistical inference methods in sequence homology searches.

Measuring global credibility with application to local sequence alignment

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 (1−α)%, 0≤α≤1, credibility limit is the minimum Hamming distance radius of a hyper-sphere containing (1−α)% of the posterior distribution. 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 (i.e., the alignment that maximizes the likelihood) and the centroid estimator (i.e., the alignment that minimizes the mean Hamming distance from the posterior weighted ensemble of alignments) 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.

Sequence alignment is the cornerstone capability used by a multitude of computational biology applications, such as phylogeny reconstruction and identification of common regulatory mechanisms. Sequence alignment methods typically seek a high-scoring alignment between a pair of sequences, and assign a statistical significance to this single alignment. However, because a single alignment of two (or more) 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 (i.e., the alignment that is in the center of the posterior distribution of alignments), 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.

Centroid estimation in discrete high-dimensional spaces with applications in biology

Maximum likelihood estimators and other direct optimization-based estimators dominated statistical estimation and prediction for decades. Yet, the principled foundations supporting their dominance do not apply to the discrete high-dimensional inference problems of the 21st century. As it is well known, statistical decision theory shows that maximum likelihood and related estimators use data only to identify the single most probable solution. Accordingly, unless this one solution so dominates the immense ensemble of all solutions that its probability is near one, there is no principled reason to expect such an estimator to be representative of the posterior-weighted ensemble of solutions, and thus represent inferences drawn from the data. We employ statistical decision theory to find more representative estimators, centroid estimators, in a general high-dimensional discrete setting by using a family of loss functions with penalties that increase with the number of differences in components. We show that centroid estimates are obtained by maximizing the marginal probabilities of the solution components for unconstrained ensembles and for an important class of problems, including sequence alignment and the prediction of RNA secondary structure, whose ensembles contain exclusivity constraints. Three genomics examples are described that show that these estimators substantially improve predictions of ground-truth reference sets.

Searching for evolutionary distant RNA homologs within genomic sequences using partition function posterior probabilities

Background

Identification of RNA homologs within genomic stretches is difficult when pairwise sequence identity is low or unalignable flanking residues are present. In both cases structure-sequence or profile/family-sequence alignment programs become difficult to apply because of unreliable RNA structures or family alignments. As such, local sequence-sequence alignment programs are frequently used instead. We have recently demonstrated that maximal expected accuracy alignments using partition function match probabilities (implemented in Probalign) are significantly better than contemporary methods on heterogeneous length protein sequence datasets, thus suggesting an affinity for local alignment.

Results

We create a pairwise RNA-genome alignment benchmark from RFAM families with average pairwise sequence identity up to 60%. Each dataset contains a query RNA aligned to a target RNA (of the same family) embedded in a genomic sequence at least 5K nucleotides long. To simulate common conditions when exact ends of an ncRNA are unknown, each query RNA has 5' and 3' genomic flanks of size 50, 100, and 150 nucleotides. We subsequently compare the error of the Probalign program (adjusted for local alignment) to the commonly used local alignment programs HMMER, SSEARCH, and BLAST, and the popular ClustalW program with zero end-gap penalties. Parameters were optimized for each program on a small subset of the benchmark. Probalign has overall highest accuracies on the full benchmark. It leads by 10% accuracy over SSEARCH (the next best method) on 5 out of 22 families. On datasets restricted to maximum of 30% sequence identity, Probalign's overall median error is 71.2% vs. 83.4% for SSEARCH (P-value < 0.05). Furthermore, on these datasets Probalign leads SSEARCH by at least 10% on five families; SSEARCH leads Probalign by the same margin on two of the fourteen families. We also demonstrate that the Probalign mean posterior probability, compared to the normalized SSEARCH Z-score, is a better discriminator of alignment quality. All datasets and software are available online.

Conclusion

We demonstrate, for the first time, that partition function match probabilities used for expected accuracy alignment, as done in Probalign, provide statistically significant improvement over current approaches for identifying distantly related RNA sequences in larger genomic segments.

A fast structural multiple alignment method for long RNA sequences

BACKGROUND

Aligning multiple RNA sequences is essential for analyzing non-coding RNAs. Although many alignment methods for non-coding RNAs, including Sankoff's algorithm for strict structural alignments, have been proposed, they are either inaccurate or computationally too expensive. Faster methods with reasonable accuracies are required for genome-scale analyses.

RESULTS

We propose a fast algorithm for multiple structural alignments of RNA sequences that is an extension of our pairwise structural alignment method (implemented in SCARNA). The accuracies of the implemented software, MXSCARNA, are at least as favorable as those of state-of-art algorithms that are computationally much more expensive in time and memory.

CONCLUSION

The proposed method for structural alignment of multiple RNA sequences is fast enough for large-scale analyses with accuracies at least comparable to those of existing algorithms. The source code of MXSCARNA and its web server are available at http://mxscarna.ncrna.org.

Rfold: an exact algorithm for computing local base pairing probabilities

MOTIVATION

Base pairing probability matrices have been frequently used for the analyses of structural RNA sequences. Recently, there has been a growing need for computing these probabilities for long DNA sequences by constraining the maximal span of base pairs to a limited value. However, none of the existing programs can exactly compute the base pairing probabilities associated with the energy model of secondary structures under such a constraint.

RESULTS

We present an algorithm that exactly computes the base pairing probabilities associated with the energy model under the constraint on the maximal span W of base pairs. The complexity of our algorithm is given by O(NW2) in time and O(N+W2) in memory, where N is the sequence length. We show that our algorithm has a higher sensitivity to the true base pairs as compared to that of RNAplfold. We also present an algorithm that predicts a mutually consistent set of local secondary structures by maximizing the expected accuracy function. The comparison of the local secondary structure predictions with those of RNALfold indicates that our algorithm is more accurate. Our algorithms are implemented in the software named 'Rfold.'

AVAILABILITY

The C++ source code of the Rfold software and the test dataset used in this study are available at http://www.ncrna.org/software/Rfold/.

RNA Sampler: a new sampling based algorithm for common RNA secondary structure prediction and structural alignment

MOTIVATION

Non-coding RNA genes and RNA structural regulatory motifs play important roles in gene regulation and other cellular functions. They are often characterized by specific secondary structures that are critical to their functions and are often conserved in phylogenetically or functionally related sequences. Predicting common RNA secondary structures in multiple unaligned sequences remains a challenge in bioinformatics research.

METHODS AND RESULTS

We present a new sampling based algorithm to predict common RNA secondary structures in multiple unaligned sequences. Our algorithm finds the common structure between two sequences by probabilistically sampling aligned stems based on stem conservation calculated from intrasequence base pairing probabilities and intersequence base alignment probabilities. It iteratively updates these probabilities based on sampled structures and subsequently recalculates stem conservation using the updated probabilities. The iterative process terminates upon convergence of the sampled structures. We extend the algorithm to multiple sequences by a consistency-based method, which iteratively incorporates and reinforces consistent structure information from pairwise comparisons into consensus structures. The algorithm has no limitation on predicting pseudoknots. In extensive testing on real sequence data, our algorithm outperformed other leading RNA structure prediction methods in both sensitivity and specificity with a reasonably fast speed. It also generated better structural alignments than other programs in sequences of a wide range of identities, which more accurately represent the RNA secondary structure conservations.

AVAILABILITY

The algorithm is implemented in a C program, RNA Sampler, which is available at http://ural.wustl.edu/software.html

T-Pile--a package for thermodynamic calculations for biomolecules

Molecular dynamics and Monte Carlo, usually conducted in canonical ensemble, deliver a plethora of biomolecular conformations. Proper analysis of the simulation data is a crucial part of biophysical and bioinformatics studies. Sequence alignment problem can be also formulated in terms of Boltzmann distribution. Therefore tools for efficient analysis of canonical ensemble data become extremely valuable. T-Pile package, presented here provides a user-friendly implementation of most important algorithms such as multihistogram analysis and reweighting technique. The package can be used in studies of virtually any system governed by Boltzmann distribution.

AVAILABILITY

T-Pile can be downloaded from: http://biocomp.chem.uw.edu.pl/services/tpile. These pages provide a comprehensive tutorial and documentation with illustrative examples of applications.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Murlet: a practical multiple alignment tool for structural RNA sequences

MOTIVATION

Structural RNA genes exhibit unique evolutionary patterns that are designed to conserve their secondary structures; these patterns should be taken into account while constructing accurate multiple alignments of RNA genes. The Sankoff algorithm is a natural alignment algorithm that includes the effect of base-pair covariation in the alignment model. However, the extremely high computational cost of the Sankoff algorithm precludes its application to most RNA sequences.

RESULTS

We propose an efficient algorithm for the multiple alignment of structural RNA sequences. Our algorithm is a variant of the Sankoff algorithm, and it uses an efficient scoring system that reduces the time and space requirements considerably without compromising on the alignment quality. First, our algorithm computes the match probability matrix that measures the alignability of each position pair between sequences as well as the base pairing probability matrix for each sequence. These probabilities are then combined to score the alignment using the Sankoff algorithm. By itself, our algorithm does not predict the consensus secondary structure of the alignment but uses external programs for the prediction. We demonstrate that both the alignment quality and the accuracy of the consensus secondary structure prediction from our alignment are the highest among the other programs examined. We also demonstrate that our algorithm can align relatively long RNA sequences such as the eukaryotic-type signal recognition particle RNA that is approximately 300 nt in length; multiple alignment of such sequences has not been possible by using other Sankoff-based algorithms. The algorithm is implemented in the software named 'Murlet'.

AVAILABILITY

The C++ source code of the Murlet software and the test dataset used in this study are available at http://www.ncrna.org/papers/Murlet/.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Probabilistic sequence alignments: realistic models with efficient algorithms

Alignment algorithms usually rely on simplified models of gaps for computational efficiency. Based on correspondences between alignments and structural models for nucleic acids, and using methods from statistical mechanics, we show that alignments with realistic laws for gaps can be computed with fast algorithms. Improved performances of probabilistic alignments with realistic models of gaps are illustrated. By contrast with optimization-based alignments, such improvements with realistic laws are not observed. General perspectives for biological and physical modelings are mentioned.

Robust prediction of consensus secondary structures using averaged base pairing probability matrices

MOTIVATION

Recent transcriptomic studies have revealed the existence of a considerable number of non-protein-coding RNA transcripts in higher eukaryotic cells. To investigate the functional roles of these transcripts, it is of great interest to find conserved secondary structures from multiple alignments on a genomic scale. Since multiple alignments are often created using alignment programs that neglect the special conservation patterns of RNA secondary structures for computational efficiency, alignment failures can cause potential risks of overlooking conserved stem structures.

RESULTS

We investigated the dependence of the accuracy of secondary structure prediction on the quality of alignments. We compared three algorithms that maximize the expected accuracy of secondary structures as well as other frequently used algorithms. We found that one of our algorithms, called McCaskill-MEA, was more robust against alignment failures than others. The McCaskill-MEA method first computes the base pairing probability matrices for all the sequences in the alignment and then obtains the base pairing probability matrix of the alignment by averaging over these matrices. The consensus secondary structure is predicted from this matrix such that the expected accuracy of the prediction is maximized. We show that the McCaskill-MEA method performs better than other methods, particularly when the alignment quality is low and when the alignment consists of many sequences. Our model has a parameter that controls the sensitivity and specificity of predictions. We discussed the uses of that parameter for multi-step screening procedures to search for conserved secondary structures and for assigning confidence values to the predicted base pairs.

AVAILABILITY

The C++ source code that implements the McCaskill-MEA algorithm and the test dataset used in this paper are available at http://www.ncrna.org/papers/McCaskillMEA/.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Probalign: multiple sequence alignment using partition function posterior probabilities

MOTIVATION

The maximum expected accuracy optimization criterion for multiple sequence alignment uses pairwise posterior probabilities of residues to align sequences. The partition function methodology is one way of estimating these probabilities. Here, we combine these two ideas for the first time to construct maximal expected accuracy sequence alignments.

RESULTS

We bridge the two techniques within the program Probalign. Our results indicate that Probalign alignments are generally more accurate than other leading multiple sequence alignment methods (i.e. Probcons, MAFFT and MUSCLE) on the BAliBASE 3.0 protein alignment benchmark. Similarly, Probalign also outperforms these methods on the HOMSTRAD and OXBENCH benchmarks. Probalign ranks statistically highest (P-value < 0.005) on all three benchmarks. Deeper scrutiny of the technique indicates that the improvements are largest on datasets containing N/C-terminal extensions and on datasets containing long and heterogeneous length proteins. These points are demonstrated on both real and simulated data. Finally, our method also produces accurate alignments on long and heterogeneous length datasets containing protein repeats. Here, alignment accuracy scores are at least 10% and 15% higher than the other three methods when standard deviation of length is >300 and 400, respectively.

AVAILABILITY

Open source code implementing Probalign as well as for producing the simulated data, and all real and simulated data are freely available from http://www.cs.njit.edu/usman/probalign

MUMMALS: multiple sequence alignment improved by using hidden Markov models with local structural information

We have developed MUMMALS, a program to construct multiple protein sequence alignment using probabilistic consistency. MUMMALS improves alignment quality by using pairwise alignment hidden Markov models (HMMs) with multiple match states that describe local structural information without exploiting explicit structure predictions. Parameters for such models have been estimated from a large library of structure-based alignments. We show that (i) on remote homologs, MUMMALS achieves statistically best accuracy among several leading aligners, such as ProbCons, MAFFT and MUSCLE, albeit the average improvement is small, in the order of several percent; (ii) a large collection (>10 000) of automatically computed pairwise structure alignments of divergent protein domains is superior to smaller but carefully curated datasets for estimation of alignment parameters and performance tests; (iii) reference-independent evaluation of alignment quality using sequence alignment-dependent structure superpositions correlates well with reference-dependent evaluation that compares sequence-based alignments to structure-based reference alignments.