Multiple sequence alignment (MSA) is the process or the result of sequence alignment of three or more biological sequences, generally protein, DNA, or RNA. These alignments are used to infer evolutionary relationships via phylogenetic analysis and can highlight homologous features between sequences. Alignments highlight mutation events such as point mutations (single amino acid or nucleotide changes), insertion mutations and deletion mutations, and alignments are used to assess sequence conservation and infer the presence and activity of protein domains, tertiary structures, secondary structures, and individual amino acids or nucleotides.
Multiple sequence alignments require more sophisticated methodologies than pairwise alignments, as they are more 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. However, heuristic methods generally cannot guarantee high-quality solutions and have been shown to fail to yield near-optimal solutions on benchmark test cases.
Problem statement Given sequences , similar to the form below:
A multiple sequence alignment is taken of this set of sequences by inserting any amount of gaps needed into each of the sequences of until the modified sequences, , all conform to length and no values in the sequences of of the same column consists of only gaps. The mathematical form of an MSA of the above sequence set is shown below:
To return from each particular sequence to , remove all gaps.
Graphing approach A general approach when calculating multiple sequence alignments is to use graphs to identify all of the different alignments. When finding alignments via graph, a complete alignment is created in a weighted graph that contains a set of vertices and a set of edges. Each of the graph edges has a weight based on a certain heuristic that helps to score each alignment or subset of the original graph.
Tracing alignments When determining the best suited alignments for each MSA, a trace is usually generated. A trace is a set of realized, or corresponding and aligned, vertices that has a specific weight based on the edges that are selected between corresponding vertices. When choosing traces for a set of sequences it is necessary to choose a trace with a maximum weight to get the best alignment of the sequences.
Alignment methods There are various alignment methods used within multiple sequence to maximize scores and correctness of alignments. Each is usually based on a certain heuristic with an insight into the evolutionary process. Most try to replicate evolution to get the most realistic alignment possible to best predict relations between sequences.
Dynamic programming 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.
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, a naïve MSA takes O(LengthNseqs) time to produce. To find the global optimum for n sequences this way has been shown to be an NP-complete problem. In 1989, based on Carrillo-Lipman Algorithm, Altschul introduced a practical method that uses pairwise alignments to constrain the n-dimensional search space. 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. In 2019, Hosseininasab and van Hoeve showed that by using decision diagrams, MSA may be modeled in polynomial space complexity.
Progressive alignment construction The most widely used approach to multiple sequence alignments uses a heuristic search known as progressive technique (also known as the hierarchical or tree method) developed by Da-Fei Feng and Doolittle in 1987. Progressive alignment builds up a final MSA by combining pairwise alignments beginning with the most similar pair and progressing to the most distantly related. All progressive alignment methods require two stages: a first stage in which the relationships between the sequences are represented as a phylogenetic tree, called a guide tree, and a second step in which the MSA is built by adding the sequences sequentially to the growing MSA according to the guide tree. The initial guide tree is determined by an efficient clustering method such as neighbor-joining or unweighted pair group method with arithmetic mean (UPGMA), and may use distances based on the number of identical two-letter sub-sequences (as in FASTA rather than a dynamic programming alignment).
Progressive alignments are not guaranteed to be globally optimal. The primary problem is that when errors are made at any stage in growing the MSA, these errors are then propagated through to the final result. Performance is also particularly bad when all of the sequences in the set are rather distantly related. Most modern progressive methods modify their scoring function with a secondary weighting function that assigns scaling factors to individual members of the query set in a nonlinear fashion based on their phylogenetic distance from their nearest neighbors. This corrects for non-random selection of the sequences given to the alignment program.
Progressive alignment methods are efficient enough to implement on a large scale for many (100s to 1000s) sequences. A popular progressive alignment method has been the Clustal family. ClustalW is used extensively for phylogenetic tree construction, in spite of the author's explicit warnings that unedited alignments should not be used in such studies and as input for protein structure prediction by homology modeling. European Bioinformatics Institute (EMBL-EBI) announced that CLustalW2 will expire in August 2015. They recommend Clustal Omega which performs based on seeded guide trees and HMM profile-profile techniques for protein alignments. An alternative tool for progressive DNA alignments is multiple alignment using fast Fourier transform (MAFFT).
Another common progressive alignment method named T-Coffee is slower than Clustal and its derivatives but generally produces more accurate alignments for distantly related sequence sets. T-Coffee calculates pairwise alignments by combining the direct alignment of the pair with indirect alignments that aligns each sequence of the pair to a third sequence. It uses the output from Clustal as well as another local alignment program LALIGN, which finds multiple regions of local alignment between two sequences. The resulting alignment and phylogenetic tree are used as a guide to produce new and more accurate weighting factors.
Because progressive methods are heuristics that are not guaranteed to converge to a global optimum, alignment quality can be difficult to evaluate and their true biological significance can be obscure. A semi-progressive method that improves alignment quality and does not use a lossy heuristic while running in polynomial time has been implemented in the program PSAlign.
Iterative methods 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.
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. The software package PRRN/PRRP uses a hill-climbing algorithm to optimize its MSA alignment score and iteratively corrects both alignment weights and locally divergent or "gappy" regions of the growing MSA.Mount DM. (2004). Bioinformatics: Sequence and Genome Analysis 2nd ed. Cold Spring Harbor Laboratory Press: Cold Spring Harbor, NY. PRRP performs best when refining an alignment previously constructed by a faster method.
Another iterative program, DIALIGN, takes an unusual approach of focusing narrowly on local alignments between sub-segments or sequence motifs without introducing a gap penalty. The alignment of individual motifs is then achieved with a matrix representation similar to a dot-matrix plot in a pairwise alignment. An alternative method that uses fast local alignments as anchor points or seeds for a slower global-alignment procedure is implemented in the CHAOS/DIALIGN suite.
A third popular iteration-based method named MUSCLE (multiple sequence alignment by log-expectation) improves on progressive methods with a more accurate distance measure to assess the relatedness of two sequences. The distance measure is updated between iteration stages (although, in its original form, MUSCLE contained only 2-3 iterations depending on whether refinement was enabled).
Consensus methods Consensus methods attempt to find the optimal multiple sequence alignment given multiple different alignments of the same set of sequences. There are two commonly used consensus methods, M-COFFEE and MergeAlign. M-COFFEE uses multiple sequence alignments generated by seven different methods to generate consensus alignments. MergeAlign is capable of generating consensus alignments from any number of input alignments generated using different models of sequence evolution or different methods of multiple sequence alignment. The default option for MergeAlign is to infer a consensus alignment using alignments generated using 91 different models of protein sequence evolution.
Hidden Markov models