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V A= V V I I I V V V A A A L D D A A A S L V V L E I A G A S S S. use visual .net denso qr bar code implement tobuild qr barcode on .net USPS Confirm Service Barcode When performed for relate .NET QR Code d sequences, multiple alignment can help researchers identify conserved domains and other regions of interest. We can readily adapt the de nition of pairwise alignment to cover this case.

De nition 3.5 Multiple alignment. A multiple (global) alignment of k sequences, is an assignment of gap symbols into those sequences, or at their ends.

The k resulting strings are placed one above the other so that every character or gap symbol in either string is opposite a unique character or a unique gap symbol in the other string. It can be represented as a c k matrix, for some value of c, the ith row containing the ith sequence and (interspersed) gap symbols. The above de nition is of course a mathematical one.

From a biological perspective, a multiple alignment represents a hypothesis about homology of individual positions within the aligned sequences.. A L L I N T H E F A M I LY : S E Q U E N C E A L I G N M E N T Many algorithmic ideas tr QR Code 2d barcode for .NET ansfer directly from pairwise to multiple alignment. For example, we can distinguish between global and local multiple alignment, where with local alignment we allow the possibility of dropping pre xes and suf xes from each of the sequences.

This problem is related to the problem of motif nding, discussed in 10, and hence we do not discuss it here. We concentrate here on multiple global alignment. Two problems arise when extending the concepts of pairwise alignment to multiple alignment.

First, we need to be able to score multiple alignments. There are various ways of scoring multiple alignments, as this is a problem that needs to be addressed with an eye towards biology and an eye towards computational convenience. Second, we need to devise an ef cient method of nding the optimal alignment.

This is a computational question that unfortunately does not have an elegant solution as with pairwise alignment. The extension of pairwise alignment algorithms such as Needleman Wunsch or Smith Waterman to more than two sequences are straightforward, but their cost increases exponentially with k (where k is the number of sequences). This fact means that there is an exponential cost in the number of sequences being aligned, limiting the use of these algorithms to very few sequences.

A number of heuristics have been proposed to nd approximate solutions, none of which guarantees nding the optimal multiple alignment. The simplest ones are greedy algorithms, that start with a pairwise alignment and iteratively add the other sequences. Usually they use an initial step of clustering the sequences, so that one rst merges the closest sequences, and then gradually adds the ones that are less and less similar.

In the next chapter we will address a hidden Markov model approach to multiple alignment . A very popular and ef cient heuristic algorithm for multiple alignment is CLUSTAL, originally developed by Desmond Higgins and Paul Sharp at Trinity College, Dublin in 1988 and extended by Higgins, Julie Thompson, and Toby Gibson into the current version, CLUSTALW. The basic idea behind CLUSTAL is to break down the multiple alignment problem into multiple computationally familiar pairwise alignment problems.

First, CLUSTAL clusters the sequences together by rough similarity, and then starts doing pairwise alignments of the most similar sequences, moving out to eventually include all of the sequences. Example 3.4 Multiple alignment.

A multiple alignment of human, sheep, and cow homeodomains (accession numbers: AAH07284, AAX39333, AAP41546). Note that in this case, due to the high level of conservation of these domains, no gaps were needed to align them. In most real applications, gaps would be present in a multiple alignment.


NET put of the freely available CLUSTALW package showing a multiple alignment of fragments of various PAX genes as well as the amount of similarity at each position is shown in Figure 3.3. Pointers to the online software packages and relative literature can be found in Section 3.

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