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A '''multiple sequence alignment''' ('''MSA''') is a [[sequence alignment]] of three or more [[biological sequence]]s, generally [[protein]], [[DNA]], or [[RNA]]. In many cases, the input set of query sequences are assumed to have an [[evolutionary]] relationship by which they share a linkage and are descended from a common ancestor. From the resulting MSA, sequence [[homology (biology)|homology]] can be inferred and [[molecular phylogeny|phylogenetic analysis]] can be conducted to assess the sequences' shared evolutionary origins. Visual depictions of the alignment as in the image at right illustrate [[mutation]] events such as point mutations (single [[amino acid]] or [[nucleotide]] changes) that appear as differing characters in a single alignment column, and insertion or deletion mutations ([[indel]]s or gaps) that appear as hyphens in one or more of the sequences in the alignment. Multiple sequence alignment is often used to assess sequence [[conservation (genetics)|conservation]] of [[protein ___domain]]s, [[tertiary structure|tertiary]] and [[secondary structure|secondary]] structures, and even individual amino acids or nucleotides.
Multiple sequence alignment also refers to the process of aligning such a sequence set. Because three or more sequences of biologically relevant length can be difficult and are almost always time-consuming to align by hand, computational [[algorithm]]s are used to produce and analyze the alignments. MSAs require more sophisticated methodologies than [[sequence alignment|pairwise alignment]] because they are more [[Computational complexity theory|computationally complex]]. Most multiple sequence alignment programs use [[heuristic]] methods rather than [[global optimization]] because identifying the optimal alignment between more than a few sequences of moderate length is prohibitively computationally expensive. On the other hand, heuristic methods generally fail to give guarantees on the solution quality, with heuristic solutions shown to be often far below the optimal solution on benchmark instances. <ref name="thompson2011">{{cite journal | doi = 10.1371/journal.pone.0018093|vauthors= Thompson JD, Linard B, Lecompte O, Poch O | year = 2011 | title = A comprehensive benchmark study of multiple sequence alignment methods: current challenges and future perspectives
==Algorithm==
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===Dynamic programming and computational complexity===
A direct method for producing an MSA uses the [[dynamic programming]] technique to identify the globally optimal alignment solution. For proteins, this method usually involves two sets of parameters: a [[gap penalty]] and a [[substitution matrix]] assigning scores or probabilities to the alignment of each possible pair of amino acids based on the similarity of the amino acids' chemical properties and the evolutionary probability of the mutation. For nucleotide sequences, a similar gap penalty is used, but a much simpler substitution matrix, wherein only identical matches and mismatches are considered, is typical. The scores in the substitution matrix may be either all positive or a mix of positive and negative in the case of a global alignment, but must be both positive and negative, in the case of a local alignment.<ref>{{cite web | title=Help with matrices used in sequence comparison tools | publisher=European Bioinformatics Institute | url=http://www.ebi.ac.uk/help/matrix.html | accessdate=March 3, 2010 | url-status=dead |
For ''n'' individual sequences, the naive method requires constructing the ''n''-dimensional equivalent of the matrix formed in standard pairwise [[sequence alignment]]. The search space thus increases exponentially with increasing ''n'' and is also strongly dependent on sequence length. Expressed with the [[big O notation]] commonly used to measure [[Computational complexity theory|computational complexity]], a [[Naïve algorithm|naïve]] MSA takes ''O(Length<sup>Nseqs</sup>)'' time to produce. To find the global optimum for ''n'' sequences this way has been shown to be an [[NP complete|NP-complete]] problem.<ref name="wang">{{cite journal | doi = 10.1089/cmb.1994.1.337 |vauthors=Wang L, Jiang T | year = 1994 | title = On the complexity of multiple sequence alignment
==Alignment methods==
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A set of methods to produce MSAs while reducing the errors inherent in progressive methods are classified as "iterative" because they work similarly to progressive methods but repeatedly realign the initial sequences as well as adding new sequences to the growing MSA. One reason progressive methods are so strongly dependent on a high-quality initial alignment is the fact that these alignments are always incorporated into the final result — that is, once a sequence has been aligned into the MSA, its alignment is not considered further. This approximation improves efficiency at the cost of accuracy. By contrast, iterative methods can return to previously calculated pairwise alignments or sub-MSAs incorporating subsets of the query sequence as a means of optimizing a general [[objective function]] such as finding a high-quality alignment score.<ref name="mount"/>
A variety of subtly different iteration methods have been implemented and made available in software packages; reviews and comparisons have been useful but generally refrain from choosing a "best" technique.<ref name="hirosawa">{{cite journal |vauthors=Hirosawa M, Totoki Y, Hoshida M, Ishikawa M | year = 1995 | title = Comprehensive study on iterative algorithms of multiple sequence alignment
Another iterative program, DIALIGN, takes an unusual approach of focusing narrowly on local alignments between sub-segments or [[sequence motif]]s without introducing a gap penalty.<ref name="brudno">{{cite journal | vauthors = Brudno M, Chapman M, Göttgens B, Batzoglou S, Morgenstern B | title = Fast and sensitive multiple alignment of large genomic sequences | journal = BMC Bioinformatics | volume = 4
A third popular iteration-based method called [[MUSCLE (alignment software)|MUSCLE]] (multiple sequence alignment by log-expectation) improves on progressive methods with a more accurate distance measure to assess the relatedness of two sequences.<ref name="edgar">{{cite journal | doi = 10.1093/nar/gkh340 | author = Edgar RC | year = 2004 | title = MUSCLE: multiple sequence alignment with high accuracy and high throughput
===Consensus methods===
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[[Hidden Markov model]]s are probabilistic models that can assign likelihoods to all possible combinations of gaps, matches, and mismatches to determine the most likely MSA or set of possible MSAs. HMMs can produce a single highest-scoring output but can also generate a family of possible alignments that can then be evaluated for biological significance. HMMs can produce both global and local alignments. Although HMM-based methods have been developed relatively recently, they offer significant improvements in computational speed, especially for sequences that contain overlapping regions.<ref name="mount" />
Typical HMM-based methods work by representing an MSA as a form of [[directed acyclic graph]] known as a partial-order graph, which consists of a series of nodes representing possible entries in the columns of an MSA. In this representation a column that is absolutely conserved (that is, that all the sequences in the MSA share a particular character at a particular position) is coded as a single node with as many outgoing connections as there are possible characters in the next column of the alignment. In the terms of a typical hidden Markov model, the observed states are the individual alignment columns and the "hidden" states represent the presumed ancestral sequence from which the sequences in the query set are hypothesized to have descended. An efficient search variant of the dynamic programming method, known as the [[Viterbi algorithm]], is generally used to successively align the growing MSA to the next sequence in the query set to produce a new MSA.<ref name="hughey">{{cite journal |vauthors=Hughey R, Krogh A | year = 1996 | title = Hidden Markov models for sequence analysis: extension and analysis of the basic method
Several software programs are available in which variants of HMM-based methods have been implemented and which are noted for their scalability and efficiency, although properly using an HMM method is more complex than using more common progressive methods. The simplest is [http://sourceforge.net/projects/poamsa/files/ POA] (Partial-Order Alignment)<!--this download link is temporary, remember to replace when it's fixed-->;<ref name="grasso">{{cite journal | doi = 10.1093/bioinformatics/bth126 |vauthors=Grasso C, Lee C | year = 2004 | title = Combining partial order alignment and progressive multiple sequence alignment increases alignment speed and scalability to very large alignment problems
SAM has been used as a source of alignments for [[protein structure prediction]] to participate in the [[CASP]] structure prediction experiment and to develop a database of predicted proteins in the [[yeast]] species ''[[S. cerevisiae]]''. [[HHpred / HHsearch|HHsearch]]<ref>{{ cite journal| author = Söding J | title = Protein homology detection by HMM-HMM comparison| journal = Bioinformatics| year = 2005| volume = 21| issue = 7| pages = 951–960| pmid = 15531603| doi = 10.1093/bioinformatics/bti125| citeseerx = 10.1.1.519.1257}}</ref> is a software package for the detection of remotely related protein sequences based on the pairwise comparison of HMMs. A server running HHsearch ([[HHpred / HHsearch|HHpred]]) was by far the fastest of the 10 best automatic structure prediction servers in the CASP7 and CASP8 structure prediction competitions.<ref>{{ cite journal|vauthors=Battey JN, Kopp J, Bordoli L, Read RJ, Clarke ND, Schwede T | title = Automated server predictions in CASP7| journal = Proteins | year = 2007 | volume = 69 | issue = Suppl 8 | pages = 68–82 | pmid = 17894354| doi = 10.1002/prot.21761 }}</ref>
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Most multiple sequence alignment methods try to minimize the number of [[Indel|insertions/deletions]] (gaps) and, as a consequence, produce compact alignments. This causes several problems if the sequences to be aligned contain non-[[Homology (biology)#Sequence homology|homologous]] regions, if gaps are informative in a [[phylogeny]] analysis. These problems are common in newly produced sequences that are poorly annotated and may contain [[Frameshift|frame-shifts]], wrong [[Protein ___domain|domains]] or non-homologous [[RNA splicing|spliced]] [[exons]]. The first such method was developed in 2005 by Löytynoja and Goldman.<ref name="Loytynoja-2005">{{Cite journal | last1 = Loytynoja | first1 = A. | title = An algorithm for progressive multiple alignment of sequences with insertions | doi = 10.1073/pnas.0409137102 | journal = Proceedings of the National Academy of Sciences | volume = 102 | issue = 30 | pages = 10557–10562 | year = 2005 | pmid = 16000407| pmc = 1180752| bibcode = 2005PNAS..10210557L }}</ref> The same authors released a software package called ''PRANK'' in 2008.<ref name="Loytynoja-2008">{{cite journal | vauthors = Löytynoja A, Goldman N | title = Phylogeny-aware gap placement prevents errors in sequence alignment and evolutionary analysis | journal = Science | volume = 320 | issue = 5883 | pages = 1632–5 | date = June 2008 | pmid = 18566285 | doi = 10.1126/science.1158395 | bibcode = 2008Sci...320.1632L | s2cid = 5211928 }}</ref> PRANK improves alignments when insertions are present. Nevertheless, it runs slowly compared to progressive and/or iterative methods which have been developed for several years.
In 2012, two new phylogeny-aware tools appeared. One is called ''PAGAN'' that was developed by the same team as PRANK.<ref name="Loytynoja-2012">{{cite journal | vauthors = Löytynoja A, Vilella AJ, Goldman N | title = Accurate extension of multiple sequence alignments using a phylogeny-aware graph algorithm | journal = Bioinformatics | volume = 28 | issue = 13 | pages = 1684–91 | date = July 2012 | pmid = 22531217 | pmc = 3381962 | doi = 10.1093/bioinformatics/bts198 }}</ref> The other is ''ProGraphMSA'' developed by Szalkowski.<ref name="Szalkowski-2012">{{cite journal | vauthors = Szalkowski AM | title = Fast and robust multiple sequence alignment with phylogeny-aware gap placement | journal = BMC Bioinformatics | volume = 13
===Motif finding===
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===Genetic algorithms and simulated annealing===
Standard optimization techniques in computer science — both of which were inspired by, but do not directly reproduce, physical processes — have also been used in an attempt to more efficiently produce quality MSAs. One such technique, [[genetic algorithm]]s, has been used for MSA production in an attempt to broadly simulate the hypothesized evolutionary process that gave rise to the divergence in the query set. The method works by breaking a series of possible MSAs into fragments and repeatedly rearranging those fragments with the introduction of gaps at varying positions. A general [[objective function]] is optimized during the simulation, most generally the "sum of pairs" maximization function introduced in dynamic programming-based MSA methods. A technique for protein sequences has been implemented in the software program SAGA (Sequence Alignment by Genetic Algorithm)<ref name="notredame2">{{cite journal | vauthors = Notredame C, Higgins DG | title = SAGA: sequence alignment by genetic algorithm | journal = Nucleic Acids Res. | volume = 24 | issue = 8 | pages = 1515–24 | date = April 1996 | pmid = 8628686 | pmc = 145823 | doi = 10.1093/nar/24.8.1515}}</ref> and its equivalent in RNA is called RAGA.<ref name="notredame3">{{cite journal | doi = 10.1093/nar/25.22.4570 |vauthors=Notredame C, O'Brien EA, Higgins DG | year = 1997 | title = RAGA: RNA sequence alignment by genetic algorithm
The technique of [[simulated annealing]], by which an existing MSA produced by another method is refined by a series of rearrangements designed to find better regions of alignment space than the one the input alignment already occupies. Like the genetic algorithm method, simulated annealing maximizes an objective function like the sum-of-pairs function. Simulated annealing uses a metaphorical "temperature factor" that determines the rate at which rearrangements proceed and the likelihood of each rearrangement; typical usage alternates periods of high rearrangement rates with relatively low likelihood (to explore more distant regions of alignment space) with periods of lower rates and higher likelihoods to more thoroughly explore local minima near the newly "colonized" regions. This approach has been implemented in the program MSASA (Multiple Sequence Alignment by Simulated Annealing).<ref name="kim">{{cite journal |vauthors=Kim J, Pramanik S, Chung MJ | year = 1994 | title = Multiple sequence alignment using simulated annealing
=== Mathematical programming and exact solution algorithms ===
[[Mathematical programming]] and in particular [[Mixed integer programming]] models are another approach to solve MSA problems. The advantage of such optimization models is that they can be used to find the optimal MSA solution more efficiently compared to the traditional DP approach. This is due in part, to the applicability of decomposition techniques for mathematical programs, where the MSA model is decomposed into smaller parts and iteratively solved until the optimal solution is found. Example algorithms used to solve mixed integer programming models of MSA include [[branch and price]] <ref name="althaus2006">{{cite journal | doi = 10.1007/s10107-005-0659-3 |vauthors=Althaus E, Caprara A, Lenhof HP, Reinert K | year = 2006 | title = A branch-and-cut algorithm for multiple sequence alignment | journal = Mathematical Programming | volume = 105 | issue = 2–3| pages = 387–425
===Simulated quantum computing===
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The necessary use of heuristics for multiple alignment means that for an arbitrary set of proteins, there is always a good chance that an alignment will contain errors. For example, an evaluation of several leading alignment programs using the [[List of sequence alignment software#Benchmarking|BAliBase benchmark]] found that at least 24% of all pairs of aligned amino acids were incorrectly aligned.<ref name="nuin2006">{{cite journal |vauthors=Nuin PA, Wang Z, Tillier ER |year=2006 |title=The accuracy of several multiple sequence alignment programs for proteins |journal=BMC Bioinformatics |doi=10.1186/1471-2105-7-471 |pmid=17062146 |volume=7 |pmc=1633746 |pages=471}}</ref> These errors can arise because of unique insertions into one or more regions of sequences, or through some more complex evolutionary process leading to proteins that do not align easily by sequence alone. As the number of sequence and their divergence increases many more errors will be made simply because of the heuristic nature of MSA algorithms. [[List of alignment visualization software|Multiple sequence alignment viewers]] enable alignments to be visually reviewed, often by inspecting the quality of alignment for annotated functional sites on two or more sequences. Many also enable the alignment to be edited to correct these (usually minor) errors, in order to obtain an optimal 'curated' alignment suitable for use in phylogenetic analysis or comparative modeling.<ref>{{cite web | title=Manual editing and adjustment of MSAs | publisher=European Molecular Biology Laboratory | year=2007 | url=http://www.embl.de/~seqanal/MSAcambridgeGenetics2007/MSAmanualAdjustments/MSAmanualAdjustments.html | accessdate=March 7, 2010 | archive-url=https://web.archive.org/web/20150924000135/http://www.embl.de/~seqanal/MSAcambridgeGenetics2007/MSAmanualAdjustments/MSAmanualAdjustments.html | archive-date=September 24, 2015 | url-status=dead }}</ref>
However, as the number of sequences increases and especially in genome-wide studies that involve many MSAs it is impossible to manually curate all alignments. Furthermore, manual curation is subjective. And finally, even the best expert cannot confidently align the more ambiguous cases of highly diverged sequences. In such cases it is common practice to use automatic procedures to exclude unreliably aligned regions from the MSA. For the purpose of phylogeny reconstruction (see below) the Gblocks program is widely used to remove alignment blocks suspect of low quality, according to various cutoffs on the number of gapped sequences in alignment columns.<ref name="castresana2000">{{cite journal | vauthors = Castresana J | title = Selection of conserved blocks from multiple alignments for their use in phylogenetic analysis | journal = Mol. Biol. Evol. | volume = 17 | issue = 4 | pages = 540–52 | date = April 2000 | pmid = 10742046 | doi = 10.1093/oxfordjournals.molbev.a026334 | doi-access = free }}</ref> However, these criteria may excessively filter out regions with insertion/deletion events that may still be aligned reliably, and these regions might be desirable for other purposes such as detection of positive selection. A few alignment algorithms output site-specific scores that allow the selection of high-confidence regions. Such a service was first offered by the SOAP program,<ref name="loytynojaMilinkovitch2001">{{cite journal | vauthors = Löytynoja A, Milinkovitch MC | title = SOAP, cleaning multiple alignments from unstable blocks | journal = Bioinformatics | volume = 17 | issue = 6 | pages = 573–4 | date = June 2001 | pmid = 11395440 | doi = 10.1093/bioinformatics/17.6.573 | doi-access = free }}</ref> which tests the robustness of each column to perturbation in the parameters of the popular alignment program CLUSTALW. The T-Coffee program<ref name=poirotOTooleNotredame2003>{{cite journal | vauthors = Poirot O, O'Toole E, Notredame C | title = Tcoffee@igs: A web server for computing, evaluating and combining multiple sequence alignments | journal = Nucleic Acids Res. | volume = 31 | issue = 13 | pages = 3503–6 | date = July 2003 | pmid = 12824354 | pmc = 168929 | doi = 10.1093/nar/gkg522 }}</ref> uses a library of alignments in the construction of the final MSA, and its output MSA is colored according to confidence scores that reflect the agreement between different alignments in the library regarding each aligned residue. Its extension, [http://tcoffee.crg.cat/tcs TCS] : ('''T'''ransitive '''C'''onsistency '''S'''core), uses T-Coffee libraries of pairwise alignments to evaluate any third party MSA. Pairwise projections can be produced using fast or slow methods, thus allowing a trade-off between speed and accuracy.<ref name=TCS2014MBE>{{cite journal|last=Chang|first=JM|author2=Di Tommaso, P | author3 = Notredame, C|title=TCS: A New Multiple Sequence Alignment Reliability Measure to Estimate Alignment Accuracy and Improve Phylogenetic Tree Reconstruction.|journal=Molecular Biology and Evolution|date=Jun 2014|volume=31|issue=6|pages=1625–37|doi=10.1093/molbev/msu117|pmid=24694831|url=http://mbe.oxfordjournals.org/content/31/6/1625|doi-access=free}}</ref><ref name=TCS_2015_NAR>{{cite journal | vauthors = Chang JM, Di Tommaso P, Lefort V, Gascuel O, Notredame C | title = TCS: a web server for multiple sequence alignment evaluation and phylogenetic reconstruction | journal = Nucleic Acids Res. | volume = 43 | issue = W1 | pages = W3–6 | date = July 2015 | pmid = 25855806 | pmc = 4489230 | doi = 10.1093/nar/gkv310 }}</ref> Another alignment program that can output an MSA with confidence scores is FSA,<ref name=bradley2009>{{cite journal | vauthors = Bradley RK, Roberts A, Smoot M, Juvekar S, Do J, Dewey C, Holmes I, Pachter L | title = Fast statistical alignment | journal = PLOS Comput. Biol. | volume = 5 | issue = 5 | pages = e1000392 | date = May 2009 | pmid = 19478997 | pmc = 2684580 | doi = 10.1371/journal.pcbi.1000392 | bibcode = 2009PLSCB...5E0392B }}</ref> which uses a statistical model that allows calculation of the uncertainty in the alignment. The HoT (Heads-Or-Tails) score can be used as a measure of site-specific alignment uncertainty due to the existence of multiple co-optimal solutions.<ref name=landanGraur2008>{{cite book | vauthors = Landan G, Graur D | title = Biocomputing 2008 | chapter = Local reliability measures from sets of co-optimal multiple sequence alignments | journal = Pac Symp Biocomput
There are free programs available for visualization of multiple sequence alignments, for example [[Jalview]] and [[UGENE]].
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