Sequence analysis Pairwise sequence alignment

Transcription

1 UMF11 Introduction to bioinformatics, 25 Sequence analysis Pairwise sequence alignment 1. Sequence alignment Lecturer: Marina lexandersson 12 September, 25 here are two types of sequence alignments, global and local. In global alignment, the entire sequences are aligned up to both ends. Sequences that are quite similar and approximately the same length are suitable for global alignment. small example LGPSKDFGKISESREFDN LNPLERSFGKINM-RED In local alignments, segments of sequences with the highest similarity are aligned. his is used for instance when two proteins are suspected to share a common domain, or when comparing long stretches of DN. It is also usually a much more sensitive way to detect similarities between two highly diverged sequences. his is because in such cases only part of the sequence has been under strong enough selection to preserve detectable similarity; the rest will have accumulated so many mutations that they are no longer alignable FGKI FGKI It may seem that one should always use local alignments. But then it may be difficult to spot an overall similarity, so it depends on the situation. Pairwise sequence alignment can be performed using the following methods: 1. Dot matrix analysis 2. he dynamic programming algorithm 3. Pair Hidden Markov models 4. Database searches using word- or k-tuple methods, such as FS or BLS 2. Dynamic programming he dynamic programming method consists of three parts 1. he recursive relation 2. he tabular computation 3. he traceback 1

2 UMF11 Introduction to bioinformatics, Global alignment: the Needleman-Wunsch algorithm he idea of the Needleman-Wunsch algorithm is to build up an optimal alignment using previous solutions for optimal alignments of smaller subsequences he recursive relation We want to align sequences x 1x2... xn and y 1 y2... ym and start by producing an n m matrix F where F ( i, = score of optimal path of subsequences x 1...xi and y 1...y j ssume a linear gap penalty d. i 1, + s( xi, y j ) i, = max i 1, i, (match/mismatch) (gap in y) (gap in x) with F (,) =, i,) = id,, = jd. F ( i 1, F ( i, s( x i, y j ) i 1, F ( i, he tabular computation In the tabular computation we calculate the scores of each cell in F, starting with cell (,) and the boundary conditions for the first row and column. hen we calculate the scores one row at the time. In each cell we keep a pointer to the optimal previous position 2

3 UMF11 Introduction to bioinformatics, 25 i,: he traceback In the traceback we start in cell ( n, m) and follow the arrows back to (,) to achieve the optimal alignment. G G- -G G 2.2 Local alignment: the Smith-Waterman algorithm In a local alignment we are looking for the best alignment between subsequences of x and y. GGG GG he highest scoring alignment of subsequences of x and y is then called the optimal local alignment. he Smith-Waterman algorithm is very similar to the global alignment algorithm he recursive relation he recursive relation in the Needleman-Wunsch algorithm only needs a slight modification to fit our purposes 3

4 UMF11 Introduction to bioinformatics, 25 i 1, + s( xi, y j ) i 1, i, = max i, s an extra possibility, F ( i, is allowed to take the value if all other options have value less than, resulting in a matrix with all non-negative values. s a consequence the top row and the leftmost column will be filled with s, and not id and jd as before he tabular computation. s a consequence of the added possibility in the recursive relation, the top row and the leftmost column will now be filled with s, and not id and jd as before. Moreover, we only keep a pointer to the previous optimal position in cells with positive values. i,: he traceback nother difference from the global alignment case is that now an alignment can begin and end anywhere in the matrix. Instead of starting the traceback in the bottom right corner F ( n, m), we begin in the cell with the highest value of F ( i,. he traceback ends when we meet a cell with value, which corresponds to the start of the alignment. 4

5 UMF11 Introduction to bioinformatics, 25 Example 1. We want to align protein sequences seq1:hegwghee and seq2:pwhee using local alignment, with gap penalty d = 8 and the BLOSUM5 matrix (see below). H E G W G H E E P 5 5 W H E E he highest score in the matrix is 28, so that is where the traceback starts. he optimal local alignment with score 28 is thus WGHE W-HE 5

6 UMF11 Introduction to bioinformatics, Pair Hidden Markov Models (PHMMs) pair hidden Markov model consists of three states S = { M, I, D} where M = match (or mismatch) I = insertion (in seq1 => deletion in seq2) D = deletion (in seq1 => insertion in seq2) M I D he output from a PHMM is an aligned pair of sequences. In the match state, the generated output is a pair of residues, which can be identical (match), or not (mismatch). In the insertion and deletion states the generated output is one residue paired up with a gap. Example 2. ssume that we have a sequence alignment generating machine. he alignment G - - G G would then have been produced as follows M M I M D D M - G - - G 6

7 UMF11 Introduction to bioinformatics, 25 But in reality we only observe the sequences seq1:gg and seq2:g and need to determine the optimal alignment under our model, that is our PHMM. he algorithm used to find the best alignment in a PHMM is called the Viterbi algorithm. he Viterbi algorithm is a dynamic programming method similar to the Needleman-Wunsch algorithm, where we formulize the recursive relation based on the PHMM parameters, and perform the tabular computation and the traceback in the same manner. 4. Database searches With dynamical programming we're guaranteed to find the optimal alignment, but unfortunately these algorithms are usually computationally complex (in speed and memory usage). Heuristic searches are less sensitive, but pretty good still and much faster. he idea is that most good alignments have short stretches of ungapped very high scoring matches. Hence, good alignments without such a stretch are missed, but these are rather rare. 4.1 BLS (Basic Local lignment Search ool) BLS is one of the most widely used tools in bioinformatics, and perhaps in biology all together. BLS takes a query sequence (DN or protein) and searches for local alignment matches in a database. he procedure is as follows: Find all substrings of length w (w-length words) in the database that aligns with words in the query sequence, where the alignment has score higher than some threshold t. hese words are called hits. Extend each hit to see if it is contained in an alignment segment of score higher than some other threshold S. Usually w is about 3-5 for amino acids and ~ 12 for DN. Example 3. Let w = 2, t = 8 and S = 2, and use a PM12 substitution matrix. ssume we want to search a database for matches to the peptide query Query: QLNFSGW Possible w-length words ( words of length 2) of the query are: QL, LN, NF, FS, S, G, GW We match these words with words in the database sequences, but only record the matches with scores t. hus possible alignments in the database are QL QL QL QL: = 11, = 9, = 8 QL QM HL QL, QM, HL LN LN: = 9 LN LN 7

8 UMF11 Introduction to bioinformatics, 25 NF NF NF NF: NF = 12, F = 8, NY = 8 NF, F, NY and so on. hen for each database entry having one or more hits, we align the words and try to extend the alignment to see if it is part of a segment with a score S. For instance, assume there is a database entry Database entry: HLNYW his entry for instance contains the hit LN. We align the words and try to extend the alignment Q LN FSGW H LN YW In this case we get score 21 > S for the subsequences QLNFS HLNY If the database entry contains more hits, these are extended in the same manner. BLS reports the hits ordered according to score, and with the score and E-value (indicating the significance of the score). 4.2 FS For nucleotide searches FS may be more sensitive than BLS. he procedure is as follows: lookup table is created for all identical matching words of length ktup (1-2 for proteins, 4-6 for DN) between the query sequence and the database. he comparison of the query sequence and the database can be viewed as a set of dotplots, with the query as the vertical sequence and the database sequences as the horizontal. Diagonals with the largest number of words are registered. he best regions are rescored, using a scoring matrix, trying to extend the match for as long as possible and still have a score above a given threshold. Ungapped regions are joined if the total score is S. he highest scoring candidates are realigned using a dynamical programming algorithm, but restricting it to a band around the candidate match. 8

9 UMF11 Introduction to bioinformatics, Significance of scores: P-values and E-values he classical approach uses the extreme value distribution to calculate the probability that the best match from a search of N unrelated sequences has score S. If this probability is very small we don't believe that the sequences are unrelated, and so they are likely to be homologous. HSP = high scoring pair. If two random sequences of lengths n and m are aligned, the probability of finding at least one segment pair with score S is Pr(at least one HSP with score S ) 1 exp{ Knme λs } where K, λ depends on the scoring scheme. We call this probability the P-value. he expected number of segment pairs having score S in the random model is the E-value E [#HSPs with score S ] = Kmne λs. Scores are often normalized to get rid of the dependence on the scoring system S log K S' = λ log 2 and the E-value S ' mn / 2. BLS reports the normalized score and the E-value where m is the length of the query sequence, and n the length of the entire database (the sum of all sequence lengths in the database). 9

10 UMF11 Introduction to bioinformatics, 25 BLOSUM5 R N D Q E G H I L K M F P S W Y V R N D Q E G H I L K M F P S W Y W PM12 R N D Q E G H I L K M F P S W Y V R N D Q E G H I L K M F P S W Y V