A generalized affine gap model significantly improves protein sequence alignment accuracy

Sequence alignment underpins common tasks in molecular biology, including genome annotation, molecular phylogenetics, and homology modeling. Fundamental to sequence alignment is the placement of gaps, which represent character insertions or deletions. We assessed the ability of a generalized affine gap cost model to reliably detect remote protein homology and to produce high-quality alignments. Generalized affine gap alignment with optimal gap parameters performed as well as the traditional affine gap model in remote homology detection. Evaluation of alignment quality showed that the generalized affine model aligns fewer residue pairs than the traditional affine model but achieves significantly higher per-residue accuracy. We conclude that generalized affine gap costs should be used when alignment accuracy carries more importance than aligned sequence length.     

Approximate p-values for local sequence alignments: numerical studies.

Siegmund and Yakir (2000) have given an approximate p-value when two independent, identically distributed sequences from a finite alphabet are optimally aligned based on a scoring system that rewards similarities according to a general scoring matrix and penalizes gaps (insertions and deletions). The approximation involves an infinite sequence of difficult-to-compute parameters. In this paper, it is shown by numerical studies that these reduce to essentially two numerically distinct parameters, which can be computed as one-dimensional numerical integrals. For an arbitrary scoring matrix and affine gap penalty, this modified approximation is easily evaluated. Comparison with published numerical results show that it is reasonably accurate.     

Statistical evaluation and comparison of a pairwise alignment algorithm that a priori assigns the number of gaps rather than employing gap penalties

MOTIVATION: Although pairwise sequence alignment is essential in comparative genomic sequence analysis, it has proven difficult to precisely determine the gap penalties for a given pair of sequences. A common practice is to employ default penalty values. However, there are a number of problems associated with using gap penalties. First, alignment results can vary depending on the gap penalties, making it difficult to explore appropriate parameters. Second, the statistical significance of an alignment score is typically based on a theoretical model of non-gapped alignments, which may be misleading. Finally, there is no way to control the number of gaps for a given pair of sequences, even if the number of gaps is known in advance. RESULTS: In this paper, we develop and evaluate the performance of an alignment technique that allows the researcher to assign a priori set of the number of allowable gaps, rather than using gap penalties. We compare this approach with the Smith-Waterman and Needleman-Wunsch techniques on a set of structurally aligned protein sequences. We demonstrate that this approach outperforms the other techniques, especially for short sequences (56-133 residues) with low similarity (<25%). Further, by employing a statistical measure, we show that it can be used to assess the quality of the alignment in relation to the true alignment with the associated optimal number of gaps. AVAILABILITY: The implementation of the described methods SANK_AL is available at http://cbbc.murdoch.edu.au/ CONTACT: matthew@cbbc.murdoch.edu.au.     

Distribution of Indel lengths

Protein sequence alignment has become a widely used method in the study of newly sequenced proteins. Most sequence alignment methods use an affine gap penalty to assign scores to insertions and deletions. Although affine gap penalties represent the relative ease of extending a gap compared with initializing a gap, it is still an obvious oversimplification of the real processes that occur during sequence evolution. To improve the efficiency of sequence alignment methods and to obtain a better understanding of the process of sequence evolution, we wanted to find a more accurate model of insertions and deletions in homologous proteins. In this work, we extract the probability of a gap occurrence and the resulting gap length distribution in distantly related proteins (sequence identity < 25%) using alignments based on their common structures. We observe a distribution of gaps that can be fitted with a multiexponential with four distinct components. The results suggest new approaches to modeling insertions and deletions in sequence alignments.     

Revisiting gap locations in amino acid sequence alignments and a proposal for a method to improve them by introducing solvent accessibility

In comparative modeling, the quality of amino acid sequence alignment still constitutes a major bottleneck in the generation of high quality models of protein three-dimensional (3D) structures. Substantial efforts have been made to improve alignment quality by revising the substitution matrix, introducing multiple sequences, replacing dynamic programming with hidden Markov models, and incorporating 3D structure information. Improvements in the gap penalty have not been a major focus, however, following the development of the affine gap penalty and of the secondary structure dependent gap penalty. We revisited the correlation between protein 3D structure and gap location in a large protein 3D structure data set, and found that the frequency of gap locations approximated to an exponential function of the solvent accessibility of the inserted residues. The nonlinearity of the gap frequency as a function of accessibility corresponded well to the relationship between residue mutation pattern and residue accessibility. By introducing this relationship into the gap penalty calculation for pairwise alignment between template and target amino acid sequences, we were able to obtain a sequence alignment much closer to the structural alignment. The quality of the alignments was substantially improved on a pair of sequences with identity in the "twilight zone" between 20 and 40%. The relocation of gaps by our new method made a significant improvement in comparative modeling, exemplified here by the Bacillus subtilis yitF protein. The method was implemented in a computer program, ALAdeGAP (ALignment with Accessibility dependent GAp Penalty), which is available at http://cib.cf.ocha.ac.jp/target_protein/.     

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.     

Scoring profile-to-profile sequence alignments

Sequence alignment profiles have been shown to be very powerful in creating accurate sequence alignments. Profiles are often used to search a sequence database with a local alignment algorithm. More accurate and longer alignments have been obtained with profile-to-profile comparison. There are several steps that must be performed in creating profile-profile alignments, and each involves choices in parameters and algorithms. These steps include (1) what sequences to include in a multiple alignment used to build each profile, (2) how to weight similar sequences in the multiple alignment and how to determine amino acid frequencies from the weighted alignment, (3) how to score a column from one profile aligned to a column of the other profile, (4) how to score gaps in the profile-profile alignment, and (5) how to include structural information. Large-scale benchmarks consisting of pairs of homologous proteins with structurally determined sequence alignments are necessary for evaluating the efficacy of each scoring scheme. With such a benchmark, we have investigated the properties of profile-profile alignments and found that (1) with optimized gap penalties, most column-column scoring functions behave similarly to one another in alignment accuracy; (2) some functions, however, have much higher search sensitivity and specificity; (3) position-specific weighting schemes in determining amino acid counts in columns of multiple sequence alignments are better than sequence-specific schemes; (4) removing positions in the profile with gaps in the query sequence results in better alignments; and (5) adding predicted and known secondary structure information improves alignments.     

Local sequence alignments with monotonic gap penalties.

MOTIVATION: Sequence alignments obtained using affine gap penalties are not always biologically correct, because the insertion of long gaps is over-penalised. There is a need for an efficient algorithm which can find local alignments using non-linear gap penalties. RESULTS: A dynamic programming algorithm is described which computes optimal local sequence alignments for arbitrary, monotonically increasing gap penalties, i.e. where the cost g(k) of inserting a gap of k symbols is such that g(k) >/= g(k-1). The running time of the algorithm is dependent on the scoring scheme; if the expected score of an alignment between random, unrelated sequences of lengths m, n is proportional to log mn, then with one exception, the algorithm has expected running time O(mn). Elsewhere, the running time is no greater than O(mn(m+n)). Optimisations are described which appear to reduce the worst-case run-time to O(mn) in many cases. We show how using a non-affine gap penalty can dramatically increase the probability of detecting a similarity containing a long gap. AVAILABILITY: The source code is available to academic collaborators under licence.     

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.     

Generalized affine gap costs for protein sequence alignment

Based on the observation that a single mutational event can delete or insert multiple residues, affine gap costs for sequence alignment charge a penalty for the existence of a gap, and a further length-dependent penalty. From structural or multiple alignments of distantly related proteins, it has been observed that conserved residues frequently fall into ungapped blocks separated by relatively nonconserved regions. To take advantage of this structure, a simple generalization of affine gap costs is proposed that allows nonconserved regions to be effectively ignored. The distribution of scores from local alignments using these generalized gap costs is shown empirically to follow an extreme value distribution. Examples are presented for which generalized affine gap costs yield superior alignments from the standpoints both of statistical significance and of alignment accuracy. Guidelines for selecting generalized affine gap costs are discussed, as is their possible application to multiple alignment. Proteins 32:88–96, 1998. Published 1998 Wiley-Liss, Inc.

1 This article is a US government work and, as such, is in the public domain in the United States of America.

     

Local multiple alignment by consensus matrix

A new algorithm for aligning several sequences based on thecalculation of a consensus matrix and the comparison of allthe sequences using this consensus matrix is described. Thisconsensus matrix contains the preference scores of each nucleotideøaminoacid and gaps in every position of the alignment. Two modificationsof the algorithm corresponding to the evolutionary and functionalmeanings of the alignment were developed. The first one solvesthe best-fitting problem without any penalty for end gaps andwith an internal gap penalty function independent on the gaplength. This algorithm should be used when comparing evolutionary-relatedproteins for identifying the most conservative residues. Theother modification of the algorithm finds the most similar segmentsin the given sequences. It can be used for finding those partsof the sequences that are responsible for the same biologicalJunction. In this case the gap penalty function was chosen tobe proportional to the gap length. The result of aligning aminoacid sequences of neutral proteases and a compilation of 65allosteric effectors and substrates of PEP carboxylase are presented.     

Spatial distribution pattern of soil seed bank in canopy gaps of various sizes in temperate secondary forests, Northeast China

To promote the natural regeneration of secondary forests under gap disturbance is one of important approaches for realizing their restoration and sustainable management. However, soil seed bank, one of regeneration strategies, is poorly understood in gaps of secondary forests. Objectives of the study were to evaluate the effects of sizes of experimentally created gaps on seed distribution in soil, and of seed banks on vegetation recovery at early formation stage of gaps in temperate secondary forests, Northeast China. It was found that with increasing gap size, species richness in the seed bank significantly increased (r?=?0.691, P?<?0.05, n?=?10), but correspondence in species-composition of seed reservoir between gaps and canopies adjacent to gaps decreased (r?=??0.83, P?<?0.01, n?=?10). Gap size and soil depth and their two-way interactions had significant differences on the distribution of seed bank density (F?=?4.101, P?<?0.05; F?=?34.483, P?<?0.01; F?=?5.232, P?<?0.01, respectively). The Sokal and Sneath similarity indices in species-composition between extant and potential (seed bank) vegetation were generally low, ranging from 0.06 (interior of large gaps) to 0.24 (canopies adjacent to large gaps). From the view of seed bank to restore temperate secondary forests, establishment of medium-sized artificial gaps (i.e., gap size with 500–150 m²) could be more feasible for seed invasion. To conclude, the regeneration potential out of soil seed banks is limited, and the restoration of gaps at early formation stage may be mostly dependent on other reproductive strategies (e.g., vegetative propagation of species).     

Matt: local flexibility aids protein multiple structure alignment

Even when there is agreement on what measure a protein multiple structure alignment should be optimizing, finding the optimal alignment is computationally prohibitive. One approach used by many previous methods is aligned fragment pair chaining, where short structural fragments from all the proteins are aligned against each other optimally, and the final alignment chains these together in geometrically consistent ways. Ye and Godzik have recently suggested that adding geometric flexibility may help better model protein structures in a variety of contexts. We introduce the program Matt (Multiple Alignment with Translations and Twists), an aligned fragment pair chaining algorithm that, in intermediate steps, allows local flexibility between fragments: small translations and rotations are temporarily allowed to bring sets of aligned fragments closer, even if they are physically impossible under rigid body transformations. After a dynamic programming assembly guided by these “bent” alignments, geometric consistency is restored in the final step before the alignment is output. Matt is tested against other recent multiple protein structure alignment programs on the popular Homstrad and SABmark benchmark datasets. Matt's global performance is competitive with the other programs on Homstrad, but outperforms the other programs on SABmark, a benchmark of multiple structure alignments of proteins with more distant homology. On both datasets, Matt demonstrates an ability to better align the ends of α-helices and β-strands, an important characteristic of any structure alignment program intended to help construct a structural template library for threading approaches to the inverse protein-folding problem. The related question of whether Matt alignments can be used to distinguish distantly homologous structure pairs from pairs of proteins that are not homologous is also considered. For this purpose, a p-value score based on the length of the common core and average root mean squared deviation (RMSD) of Matt alignments is shown to largely separate decoys from homologous protein structures in the SABmark benchmark dataset. We postulate that Matt's strong performance comes from its ability to model proteins in different conformational states and, perhaps even more important, its ability to model backbone distortions in more distantly related proteins.     

Predicting and improving the protein sequence alignment quality by support vector regression

Background  

For successful protein structure prediction by comparative modeling, in addition to identifying a good template protein with known structure, obtaining an accurate sequence alignment between a query protein and a template protein is critical. It has been known that the alignment accuracy can vary significantly depending on our choice of various alignment parameters such as gap opening penalty and gap extension penalty. Because the accuracy of sequence alignment is typically measured by comparing it with its corresponding structure alignment, there is no good way of evaluating alignment accuracy without knowing the structure of a query protein, which is obviously not available at the time of structure prediction. Moreover, there is no universal alignment parameter option that would always yield the optimal alignment.     

The identification of complete domains within protein sequences using accurate E-values for semi-global alignment

The sequencing of complete genomes has created a pressing need for automated annotation of gene function. Because domains are the basic units of protein function and evolution, a gene can be annotated from a domain database by aligning domains to the corresponding protein sequence. Ideally, complete domains are aligned to protein subsequences, in a ‘semi-global alignment’. Local alignment, which aligns pieces of domains to subsequences, is common in high-throughput annotation applications, however. It is a mature technique, with the heuristics and accurate E-values required for screening large databases and evaluating the screening results. Hidden Markov models (HMMs) provide an alternative theoretical framework for semi-global alignment, but their use is limited because they lack heuristic acceleration and accurate E-values. Our new tool, GLOBAL, overcomes some limitations of previous semi-global HMMs: it has accurate E-values and the possibility of the heuristic acceleration required for high-throughput applications. Moreover, according to a standard of truth based on protein structure, two semi-global HMM alignment tools (GLOBAL and HMMer) had comparable performance in identifying complete domains, but distinctly outperformed two tools based on local alignment. When searching for complete protein domains, therefore, GLOBAL avoids disadvantages commonly associated with HMMs, yet maintains their superior retrieval performance.     

DbClustal: rapid and reliable global multiple alignments of protein sequences detected by database searches

DbClustal addresses the important problem of the automatic multiple alignment of the top scoring full-length sequences detected by a database homology search. By combining the advantages of both local and global alignment algorithms into a single system, DbClustal is able to provide accurate global alignments of highly divergent, complex sequence sets. Local alignment information is incorporated into a ClustalW global alignment in the form of a list of anchor points between pairs of sequences. The method is demonstrated using anchors supplied by the Blast post-processing program, Ballast. The rapidity and reliability of DbClustal have been demonstrated using the recently annotated Pyrococcus abyssi proteome where the number of alignments with totally misaligned sequences was reduced from 20% to <2%. A web site has been implemented proposing BlastP database searches with automatic alignment of the top hits by DbClustal.     

Transmembrane Protein Alignment and Fold Recognition Based on Predicted Topology

Background

Although Transmembrane Proteins (TMPs) are highly important in various biological processes and pharmaceutical developments, general prediction of TMP structures is still far from satisfactory. Because TMPs have significantly different physicochemical properties from soluble proteins, current protein structure prediction tools for soluble proteins may not work well for TMPs. With the increasing number of experimental TMP structures available, template-based methods have the potential to become broadly applicable for TMP structure prediction. However, the current fold recognition methods for TMPs are not as well developed as they are for soluble proteins.

Methodology

We developed a novel TMP Fold Recognition method, TMFR, to recognize TMP folds based on sequence-to-structure pairwise alignment. The method utilizes topology-based features in alignment together with sequence profile and solvent accessibility. It also incorporates a gap penalty that depends on predicted topology structure segments. Given the difference between α-helical transmembrane protein (αTMP) and β-strands transmembrane protein (βTMP), parameters of scoring functions are trained respectively for these two protein categories using 58 αTMPs and 17 βTMPs in a non-redundant training dataset.

Results

We compared our method with HHalign, a leading alignment tool using a non-redundant testing dataset including 72 αTMPs and 30 βTMPs. Our method achieved 10% and 9% better accuracies than HHalign in αTMPs and βTMPs, respectively. The raw score generated by TMFR is negatively correlated with the structure similarity between the target and the template, which indicates its effectiveness for fold recognition. The result demonstrates TMFR provides an effective TMP-specific fold recognition and alignment method.     

The First Identification of Carbohydrate Binding Modules Specific to Chitosan

Two carbohydrate binding modules (DD1 and DD2) belonging to CBM32 are located at the C terminus of a chitosanase from Paenibacillus sp. IK-5. We produced three proteins, DD1, DD2, and tandem DD1/DD2 (DD1+DD2), and characterized their binding ability. Transition temperature of thermal unfolding (T_m) of each protein was elevated by the addition of cello-, laminari-, chitin-, or chitosan-hexamer (GlcN)₆. The T_m elevation (ΔT_m) in DD1 was the highest (10.3 °C) upon the addition of (GlcN)₆ and was markedly higher than that in DD2 (1.0 °C). A synergistic effect was observed (ΔT_m = 13.6 °C), when (GlcN)₆ was added to DD1+DD2. From isothermal titration calorimetry experiments, affinities to DD1 were not clearly dependent upon chain length of (GlcN)_n; ΔG_r° values were −7.8 (n = 6), −7.6 (n = 5), −7.6 (n = 4), −7.6 (n = 3), and −7.1 (n = 2) kcal/mol, and the value was not obtained for GlcN due to the lowest affinity. DD2 bound (GlcN)_n with the lower affinities (ΔG_r° = −5.0 (n = 3) ∼ −5.2 (n = 6) kcal/mol). Isothermal titration calorimetry profiles obtained for DD1+DD2 exhibited a better fit when the two-site model was used for analysis and provided greater affinities to (GlcN)₆ for individual DD1 and DD2 sites (ΔG_r° = −8.6 and −6.4 kcal/mol, respectively). From NMR titration experiments, (GlcN)_n (n = 2∼6) were found to bind to loops extruded from the core β-sandwich of individual DD1 and DD2, and the interaction sites were similar to each other. Taken together, DD1+DD2 is specific to chitosan, and individual modules synergistically interact with at least two GlcN units, facilitating chitosan hydrolysis.     

BALSA: Bayesian algorithm for local sequence alignment

The Smith–Waterman algorithm yields a single alignment, which, albeit optimal, can be strongly affected by the choice of the scoring matrix and the gap penalties. Additionally, the scores obtained are dependent upon the lengths of the aligned sequences, requiring a post-analysis conversion. To overcome some of these shortcomings, we developed a Bayesian algorithm for local sequence alignment (BALSA), that takes into account the uncertainty associated with all unknown variables by incorporating in its forward sums a series of scoring matrices, gap parameters and all possible alignments. The algorithm can return both the joint and the marginal optimal alignments, samples of alignments drawn from the posterior distribution and the posterior probabilities of gap penalties and scoring matrices. Furthermore, it automatically adjusts for variations in sequence lengths. BALSA was compared with SSEARCH, to date the best performing dynamic programming algorithm in the detection of structural neighbors. Using the SCOP databases PDB40D-B and PDB90D-B, BALSA detected 19.8 and 41.3% of remote homologs whereas SSEARCH detected 18.4 and 38% at an error rate of 1% errors per query over the databases, respectively.     

lra: A long read aligner for sequences and contigs

It is computationally challenging to detect variation by aligning single-molecule sequencing (SMS) reads, or contigs from SMS assemblies. One approach to efficiently align SMS reads is sparse dynamic programming (SDP), where optimal chains of exact matches are found between the sequence and the genome. While straightforward implementations of SDP penalize gaps with a cost that is a linear function of gap length, biological variation is more accurately represented when gap cost is a concave function of gap length. We have developed a method, lra, that uses SDP with a concave-cost gap penalty, and used lra to align long-read sequences from PacBio and Oxford Nanopore (ONT) instruments as well as de novo assembly contigs. This alignment approach increases sensitivity and specificity for SV discovery, particularly for variants above 1kb and when discovering variation from ONT reads, while having runtime that are comparable (1.05-3.76×) to current methods. When applied to calling variation from de novo assembly contigs, there is a 3.2% increase in Truvari F1 score compared to minimap2+htsbox. lra is available in bioconda (https://anaconda.org/bioconda/lra) and github (https://github.com/ChaissonLab/LRA).