Structural alignment attempts to establish homology between two or more polymer structures based on their shape and three-dimensional conformation. This process is usually applied to protein tertiary structures but can also be used for large RNA molecules. In contrast to simple structural superposition, where at least some equivalent residues of the two structures are known, structural alignment requires no a priori knowledge of equivalent positions. Structural alignment is a valuable tool for the comparison of proteins with low sequence similarity, where evolutionary relationships between proteins cannot be easily detected by standard sequence alignment techniques. Structural alignment can therefore be used to imply evolutionary relationships between proteins that share very little common sequence. However, caution should be used in using the results as evidence for shared evolutionary ancestry because of the possible confounding effects of convergent evolution by which multiple unrelated amino acid sequences converge on a common tertiary structure.
Structural alignments can compare two sequences or multiple sequences. Because these alignments rely on information about all the query sequences' three-dimensional conformations, the method can only be used on sequences where these structures are known. These are usually found by X-ray crystallography or NMR spectroscopy. It is possible to perform a structural alignment on structures produced by structure prediction methods. Indeed, evaluating such predictions often requires a structural alignment between the model and the true known structure to assess the model's quality. Structural alignments are especially useful in analyzing data from structural genomics and proteomics efforts, and they can be used as comparison points to evaluate alignments produced by purely sequence-based bioinformatics methods.[1]
The outputs of a structural alignment are a superposition of the atomic coordinate sets and a minimal root mean square deviation (RMSD) between the structures. The RMSD of two aligned structures indicates their divergence from one another. Structural alignment can be complicated by the existence of multiple protein domains within one or more of the input structures, because changes in relative orientation of the domains between two structures to be aligned can artificially inflate the RMSD.
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The minimum information produced from a successful structural alignment is a set of superposed three-dimensional coordinates for each input structure. (Note that one input element may be fixed as a reference and therefore its superposed coordinates do not change.) The fitted structures can be used to calculate mutual RMSD values, as well as other more sophisticated measures of structural similarity such as the global distance test (GDT,[2] the metric used in CASP). The structural alignment also implies a corresponding one-dimensional sequence alignment from which a sequence identity, or the percentage of residues that are identical between the input structures, can be calculated as a measure of how closely the two sequences are related.
Because protein structures are composed of amino acids whose side chains are linked by a common protein backbone, a number of different possible subsets of the atoms that make up a protein macromolecule can be used in producing a structural alignment and calculating the corresponding RMSD values. When aligning structures with very different sequences, the side chain atoms generally are not taken into account because their identities differ between many aligned residues. For this reason it is common for structural alignment methods to use by default only the backbone atoms included in the peptide bond. For simplicity and efficiency, often only the alpha carbon positions are considered, since the peptide bond has a minimally variant planar conformation. Only when the structures to be aligned are highly similar or even identical is it meaningful to align side-chain atom positions, in which case the RMSD reflects not only the conformation of the protein backbone but also the rotameric states of the side chains. Other comparison criteria that reduce noise and bolster positive matches include secondary structure assignment, native contact maps or residue interaction patterns, measures of side chain packing, and measures of hydrogen bond retention.[3]
The most basic possible comparison between protein structures makes no attempt to align the input structures and requires a precalculated alignment as input to determine which of the residues in the sequence are intended to be considered in the RMSD calculation. Structural superposition is commonly used to compare multiple conformations of the same protein (in which case no alignment is necessary, since the sequences are the same) and to evaluate the quality of alignments produced using only sequence information between two or more sequences whose structures are known. This method traditionally uses a simple least-squares fitting algorithm, in which the optimal rotations and translations are found by minimizing the sum of the squared distances among all structures in the superposition.[4] More recently, maximum likelihood and Bayesian methods have greatly increased the accuracy of the estimated rotations, translations, and covariance matrices for the superposition.[5][6]
Algorithms based on multidimensional rotations and modified quaternions have been developed to identify topological relationships between protein structures without the need for a predetermined alignment. Such algorithms have successfully identified canonical folds such as the four-helix bundle.[7] The SuperPose method is sufficiently extensible to correct for relative domain rotations and other structural pitfalls.[8]
the optimal "threading" of a protein sequence onto a known structure and the production of an optimal multiple sequence alignment have been shown to be NP-complete.[9][10] However, this does not imply that the structural alignment problem is NP-complete. Strictly speaking, an optimal solution to the protein structure alignment problem is only known for certain protein structure similarity measures, such as the measures used in protein structure prediction experiments, GDT_TS[2] and MaxSub.[11] These measures can be rigorously optimized using an algorithm capable of maximizing the number of atoms in two proteins that can be superimposed under a predefined distance cutoff.[12] Unfortunately, the algorithm for optimal solution is not practical, since its running time depends not only on the lengths but also on the intrinsic geometry of input proteins.
Approximate polynomial-time algorithms for structural alignment that produce a family of "optimal" solutions within an approximation parameter for a given scoring function have been developed.[12][13] Although these algorithms theoretically classify the approximate protein structure alignment problem as "tractable", they are still computationally too expensive for large scale protein structure analysis. As a consequence, practical algorithms that converge to the global solutions of the alignment, given a scoring function, do not exist. Most algorithms are, therefore, heuristic, but algorithms that guarantee the convergence to at least local maximizers of the scoring functions, and are practical, have been developed.[14]
Protein structures have to be represented in some coordinate-independent space to make them comparable. This is typically achieved by constructing a sequence-to-sequence matrix or series of matrices that encompass comparative metrics: rather than absolute distances relative to a fixed coordinate space. An intuitive representation is the distance matrix, which is a two-dimensional matrix containing all pairwise distances between some subset of the atoms in each structure (such as the alpha carbons). The matrix increases in dimensionality as the number of structures to be simultaneously aligned increases. Reducing the protein to a coarse metric such as secondary structure elements (SSEs) or structural fragments can also produce sensible alignments, despite the loss of information from discarding distances, as noise is also discarded.[15] Choosing a representation to facilitate computation is critical to developing an efficient alignment mechanism.
Structural alignment techniques have been used in comparing individual structures or sets of structures as well as in the production of "all-to-all" comparison databases that measure the divergence between every pair of structures present in the Protein Data Bank (PDB). Such databases are used to classify proteins by their fold.
A common and popular structural alignment method is the DALI, or distance alignment matrix method, which breaks the input structures into hexapeptide fragments and calculates a distance matrix by evaluating the contact patterns between successive fragments.[16] Secondary structure features that involve residues that are contiguous in sequence appear on the matrix's main diagonal; other diagonals in the matrix reflect spatial contacts between residues that are not near each other in the sequence. When these diagonals are parallel to the main diagonal, the features they represent are parallel; when they are perpendicular, their features are antiparallel. This representation is memory-intensive because the features in the square matrix are symmetrical (and thus redundant) about the main diagonal.
When two proteins' distance matrices share the same or similar features in approximately the same positions, they can be said to have similar folds with similar-length loops connecting their secondary structure elements. DALI's actual alignment process requires a similarity search after the two proteins' distance matrices are built; this is normally conducted via a series of overlapping submatrices of size 6x6. Submatrix matches are then reassembled into a final alignment via a standard score-maximization algorithm - the original version of DALI used a Monte Carlo simulation to maximize a structural similarity score that is a function of the distances between putative corresponding atoms. In particular, more distant atoms within corresponding features are exponentially downweighted to reduce the effects of noise introduced by loop mobility, helix torsions, and other minor structural variations.[15] Because DALI relies on an all-to-all distance matrix, it can account for the possibility that structurally aligned features might appear in different orders within the two sequences being compared.
The DALI method has also been used to construct a database known as FSSP (Fold classification based on Structure-Structure alignment of Proteins, or Families of Structurally Similar Proteins) in which all known protein structures are aligned with each other to determine their structural neighbors and fold classification. There is an searchable database based on DALI as well as a downloadable program and web search based on a standalone version known as DaliLite.
The combinatorial extension (CE) method is similar to DALI in that it too breaks each structure in the query set into a series of fragments that it then attempts to reassemble into a complete alignment. A series of pairwise combinations of fragments called aligned fragment pairs, or AFPs, are used to define a similarity matrix through which an optimal path is generated to identify the final alignment. Only AFPs that meet given criteria for local similarity are included in the matrix as a means of reducing the necessary search space and thereby increasing efficiency.[17] A number of similarity metrics are possible; the original definition of the CE method included only structural superpositions and inter-residue distances but has since been expanded to include local environmental properties such as secondary structure, solvent exposure, hydrogen-bonding patterns, and dihedral angles.[17]
An alignment path is calculated as the optimal path through the similarity matrix by linearly progressing through the sequences and extending the alignment with the next possible high-scoring AFP pair. The initial AFP pair that nucleates the alignment can occur at any point in the sequence matrix. Extensions then proceed with the next AFP that meets given distance criteria restricting the alignment to low gap sizes. The size of each AFP and the maximum gap size are required input parameters but are usually set to empirically determined values of 8 and 30 respectively.[17] Like DALI and SSAP, CE has been used to construct an all-to-all fold classification database from the known protein structures in the PDB.
The RCSB PDB has recently released an updated version of CE and FATCAT as part of the RCSB PDB Protein Comparison Tool. It provides a new variation of CE that can detect circular permutations in protein structures.[18]
GANGSTA+ is a combinatorial algorithm for non-sequential structural alignment of proteins and similarity search in databases (http://gangsta.chemie.fu-berlin.de).[19] It uses a combinatorial approach on the secondary structure level to evaluate similarities between two protein structures based on contact maps. Different SSE assignment modes can be used. The assignment of SSEs can be performed respecting the sequential order of the SSEs in the polypeptide chains of the considered protein pair (sequential alignment) or by ignoring this order (non-sequential alignment). Furthermore, SSE pairs can optionally be aligned in reverse orientation. The highest ranking SSE assignments are transferred to the residue level by a pointmatching approach.[20] To obtain an initial common set of atomic coordinates for both proteins, pairwise attractive interactions of the C-alpha atom pairs are defined by inverse Lorentzians and energy minimized.
MAtching Molecular Models Obtained from THeory. As its name suggests, MAMMOTH was originally developed for comparing models coming from structure prediction (THeory) since it is tolerant of large unalignable regions, but it has proven to work well with experimental models, especially when looking for remote homology. Benchmarks on targets of blind structure prediction (the CASP experiment) and automated GO annotation have shown it is tightly rank correlated with human curated annotation.[21][22] A highly complete database of mammoth-based structure annotations for the predicted structures of unknown proteins covering 150 genomes facilitates genomic scale normalization.[23]
MAMMOTH-based structure alignment methods decompose the protein structure into short, seven-residue, peptides (heptapeptides) which are compared with the heptapeptides of another protein. The similarity score between two heptapeptides is calculated using a unit-vector RMS (URMS) method.[24] These scores are stored in a similarity matrix, and with a hybrid (local-global) dynamic programming the optimal residue alignment is calculated. Protein similarity scores calculated with MAMMOTH is derived from the likelihood of obtaining a given structural alignment by chance.[21]
MAMMOTH-mult is an extension of the MAMMOTH algorithm to be used to align related families of protein structures. This algorithm is very fast and produces consistent and high quality structural alignments.[25] Multiple structural alignments calculated with MAMMOTH-mult produces structurally-implied sequence alignments that can be further used for multiple-template homology modeling, HMM-based protein structure prediction, and profile-type PSI-BLAST searches.
Rapid Alignment of Proteins In terms of DOmains. RAPIDO is a web server for the 3D alignment of crystal structures of different protein molecules, in the presence of conformational changes.[26] Similar to what CE does as a first step, RAPIDO identifies fragments that are structurally similar in the two proteins using an approach based on difference distance matrices. The Matching Fragment Pairs (MFPs) are then represented as nodes in a graph which are chained together to form an alignment by means of an algorithm for the identification of the longest path on a DAG (Directed Acyclic Graph). The final step of refinement is performed to improve the quality of the alignment. After aligning the two structures the server applies a genetic algorithm for the identification of conformationally invariant regions.[27] These regions correspond to groups of atoms whose interatomic distances are constant (within a defined tolerance). In doing so RAPIDO takes into account the variation in the reliability of atomic coordinates by employing weighting-functions based on the refined B-values. The regions identified as conformationally invariant by RAPIDO represent reliable sets of atoms for the superposition of the two structures that can be used for a detailed analysis of changes in the conformation. In addition to the functionalities provided by existing tools, RAPIDO can identify structurally equivalent regions even when these consist of fragments that are distant in terms of sequence and separated by other movable domains.
SABERTOOTH uses structural profiles to perform structural alignments. The underlying structural profiles expresses the global connectivity of each residue. Despite the very condensed vectorial representation, the tool recognizes structural similarities with accuracy comparable to established alignment tools based on coordinates and performs comparably in quality.[28] Furthermore, the algorithm has favourable scaling of computation time with chain length. Since the algorithm is independent of the details of the structural representation, the framework can be generalized to sequence-to-sequence and sequence-to-structure comparison within the same setup, and it is therefore more general than other tools. SABERTOOTH can be used online at http://www.fkp.tu-darmstadt.de/sabertooth/
The SSAP (Sequential Structure Alignment Program) method uses double dynamic programming to produce a structural alignment based on atom-to-atom vectors in structure space. Instead of the alpha carbons typically used in structural alignment, SSAP constructs its vectors from the beta carbons for all residues except glycine, a method which thus takes into account the rotameric state of each residue as well as its location along the backbone. SSAP works by first constructing a series of inter-residue distance vectors between each residue and its nearest non-contiguous neighbors on each protein. A series of matrices are then constructed containing the vector differences between neighbors for each pair of residues for which vectors were constructed. Dynamic programming applied to each resulting matrix determines a series of optimal local alignments which are then summed into a "summary" matrix to which dynamic programming is applied again to determine the overall structural alignment.
SSAP originally produced only pairwise alignments but has since been extended to multiple alignments as well.[29] It has been applied in an all-to-all fashion to produce a hierarchical fold classification scheme known as CATH (Class, Architecture, Topology, Homology),[30] which has been used to construct the CATH Protein Structure Classification database.
In the TOPOFIT method,[31] of protein structures is analyzed using three-dimensional Delaunay triangulation patterns derived from backbone representation. It has been found that structurally related proteins have a common spatial invariant part, a set of tetrahedrons, mathematically described as a common spatial sub-graph volume of the three-dimensional contact graph derived from Delaunay tessellation (DT). Based on this property of protein structures we present a novel common volume superimposition (TOPOFIT) method to produce structural alignments of proteins. The superimposition of the DT patterns allows one to objectively identify a common number of equivalent residues in the structural alignment, in other words, TOPOFIT identifies a feature point on the RMSD/Ne curve, a topomax point, until which two structures correspond to each other including backbone and inter-residue contacts, while the growing number of mismatches between the DT patterns occurs at larger RMSD (Ne) after topomax point. The topomax point is present in all alignments from different protein structural classes; therefore, the TOPOFIT method identifies common, invariant structural parts between proteins. The TOPOFIT method adds new opportunities for the comparative analysis of protein structures and for more detailed studies on understanding the molecular principles of tertiary structure organization and functionality. It helps to detect conformational changes, topological differences in variable parts, which are particularly important for studies of variations in active/binding sites and protein classification.[32]
Secondary Structure Matching (SSM),[33] or PDBeFold at the Protein Data Bank in Europe uses graph matching followed by c-alpha alignment to compute alignments.
Improvements in structural alignment methods constitute an active area of research, and new or modified methods are often proposed that are claimed to offer advantages over the older and more widely distributed techniques. A recent example, TM-align, uses a novel method for weighting its distance matrix, to which standard dynamic programming is then applied.[34][35] The weighting is proposed to accelerate the convergence of dynamic programming and correct for effects arising from alignment lengths. In a benchmarking study, TM-align has been reported to improve in both speed and accuracy over DALI and CE.[34]
However, as algorithmic improvements and computer performance have erased purely technical deficiencies in older approaches, it has become clear that there is no one universal criterion for the 'optimal' structural alignment. TM-align, for instance, is particularly robust in quantifying comparisons between sets of proteins with great disparities in sequence lengths, but it only indirectly captures hydrogen bonding or secondary structure order conservation which might be better metrics for alignment of evolutionarily related proteins. Thus recent developments have focused on optimizing particular attributes such as speed, quantification of scores, correlation to alternative gold standards, or tolerance of imperfection in structural data or ab initio structural models. An alternative methodology that is gaining popularity is to use the consensus of various methods to ascertain proteins structural similarities.[36]
In choosing among modern algorithms, investigators should strongly consider the optimization for the purpose of intended application, as well as on the algorithm's penetration into the particular field so as to facilitate comparison to other authors' results. For example, MAMMOTH has been specialized for speed and correlation to human annotation,[21][22] and is thus suited for large-scale structural genomics studies: MAMMOTH has been adopted by Rosetta@home and the World Community Grid's Yeast[37] and Human[38] Proteome Folding projects because it is designed for remote structural homology detection even with relatively inaccurate or incomplete predicted structure models. The venerable DALI is perhaps the most ubiquitous in the literature and due to its integration with other European Bioinformatics Institute web-based tools, the EBI DALI is easily approached by researchers interested in singleton applications.
Historically, it was initially unclear if comparisons that preserved sequence order would be more sensitive than ones that simply compare architecture or contacts without regard to secondary segment ordering. Early versions of DALI allowed a choice of non-sequential alignment at a great cost in speed. Non-sequential methods lost favor as segment order preserving methods outperformed them in speed, quantification of high-confidence similarity scores, and amenability to adoption of rich scoring heuristics. However, in some applications, discovery of conserved but out-of-order structure motif recognition is vital and additionally some forms of experimental data collection, such as cryo-electron microscopy, generally resolve regular secondary elements but not their connection order. This has renewed interest in Non-sequential approaches. Some examples are GANGSTA+ [19] and TOPOFIT.[39]
Structural alignment techniques have traditionally been applied exclusively to proteins, as the primary biological macromolecules that assume characteristic three-dimensional structures. However, large RNA molecules also form characteristic tertiary structures, which are mediated primarily by hydrogen bonds formed between base pairs as well as base stacking. Functionally similar noncoding RNA molecules can be especially difficult to extract from genomics data because structure is more strongly conserved than sequence in RNA as well as in proteins,[40] and the more limited alphabet of RNA decreases the information content of any given nucleotide at any given position.
A recent method for pairwise structural alignment of RNA sequences with low sequence identity has been published and implemented in the program FOLDALIGN.[41] However, this method is not truly analogous to protein structural alignment techniques because it computationally predicts the structures of the RNA input sequences rather than requiring experimentally determined structures as input. Although computational prediction of the protein folding process has not been particularly successful to date, RNA structures without pseudoknots can often be sensibly predicted using free energy-based scoring methods that account for base pairing and stacking.[42]
Choosing a software tool for structural alignment can be a challenge due to the large variety of available packages that differ significantly in methodology and reliability. A partial solution to this problem was presented in [36] and made publicly accessible through the ProCKSI webserver. A more complete list of currently available and freely distributed structural alignment software can be found in structural alignment software.
Properties of some structural alignment servers and software packages are summarized and tested with examples at Structural Alignment Tools in Proteopedia.Org.
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