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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 = |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 | url = | journal = PloS one | volume = 6 | issue = 3| pages = e18093| pmid = | pmc = |bibcode= }}</ref><ref name="nuin2006"
==Algorithm==
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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 | archiveurl=https://web.archive.org/web/20100311140200/http://www.ebi.ac.uk/help/matrix.html | archivedate=March 11, 2010 }}</ref>
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 | url = | journal = J Comput Biol | volume = 1 | issue = 4| pages = 337–348 | pmid = 8790475 |citeseerx=10.1.1.408.894 }}</ref><ref name="just">{{cite journal | doi = 10.1089/106652701753307511 | author = Just W | year = 2001 | title = Computational complexity of multiple sequence alignment with SP-score | url = | journal = J Comput Biol | volume = 8 | issue = 6| pages = 615–23 | pmid = 11747615 | citeseerx = 10.1.1.31.6382 }}</ref><ref name=elias>{{cite journal | journal=J Comput Biol | volume=13 | pages=1323–1339 | year=2006 | author=Elias, Isaac | title=Settling the intractability of multiple alignment | pmid=17037961 | doi =10.1089/cmb.2006.13.1323 | issue=7 | citeseerx=10.1.1.6.256 }}</ref> In 1989, based on Carrillo-Lipman Algorithm,<ref name="carrillo">{{cite journal |vauthors=Carrillo H, Lipman DJ | year = 1988 | title = The Multiple Sequence Alignment Problem in Biology | url = https://zenodo.org/record/1236134| journal = SIAM Journal on Applied Mathematics | volume = 48 | issue = 5| pages = 1073–1082 | doi=10.1137/0148063}}</ref> Altschul introduced a practical method that uses pairwise alignments to constrain the n-dimensional search space.<ref name="altschul">{{cite journal | doi = 10.1073/pnas.86.12.4412 |vauthors=Lipman DJ, Altschul SF, Kececioglu JD | year = 1989 | title = A tool for multiple sequence alignment | url = | journal = Proc Natl Acad Sci U S A | volume = 86 | issue = 12| pages = 4412–4415 | pmid = 2734293 | pmc = 287279 |bibcode=1989PNAS...86.4412L }}</ref> In this approach pairwise dynamic programming alignments are performed on each pair of sequences in the query set, and only the space near the n-dimensional intersection of these alignments is searched for the n-way alignment. The MSA program optimizes the sum of all of the pairs of characters at each position in the alignment (the so-called ''sum of pair'' score) and has been implemented in a software program for constructing multiple sequence alignments.<ref>{{cite web | title=Genetic analysis software | publisher=National Center for Biotechnology Information | url=https://www.ncbi.nlm.nih.gov/CBBresearch/Schaffer/msa.html | accessdate=March 3, 2010}}</ref> In 2019, Hosseininasab and van Hoeve showed that by using decision diagrams, MSA may be modeled in polynomial space complexity.<ref name="hosseininasab"
==Alignment methods==
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=== 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 and Reinert K| year = 2006 | title = A branch-and-cut algorithm for multiple sequence alignment | url = https://link.springer.com/article/10.1007/s10107-005-0659-3 | journal = Mathematical Programming | volume = 105 | issue = | pages = 387-425 | pmid = | pmc = }}</ref> and [[Benders decomposition]] <ref name="hosseininasab"
===Simulated quantum computing===
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