Text Algorithms (4AP) Biological measures of similarity. Jaak Vilo 2008 fall. MTAT Text Algorithms. Complete genomes

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1 Text Algorithms (4AP) Biological measures of similarity Jaak Vilo 2008 fall Jaak Vilo MTAT Text Algorithms 1 Complete genomes Lecture 1, Tuesday April 1, 2003 Serafim Batzoglou 1

2 Evolution Lecture 1, Tuesday April 1, 2003 Serafim Batzoglou W. Gilbert NATURE 349: For 15 years, the DNA databases have grown by 60 per cent a year, a factor of ten every five years. The human genome project will continue and accelerate this rate of increase. Thus I expect that sequence data for all of the model organisms and half of the total knowledge of the human organism will be available in five to seven years, and all of it by the end of the decade.... To use this flood of knowledge, which will pour across the computer networks of the world, biologists not only must become computer literate, but also change their approach to the problem of understanding life. 2

3 Technology Review, Oct 6, Dot plot Methods Needleman Wunsch (global alignment) Affine gap penalties Smith Waterman (lovcal alignment) Affine gap penalties BLAST BLAT, 3

4 Dot plots Lecture notes on Dot plot (Benjamin Corum) Brian Golding, McMaster Univ. (course outline) Dot plot: black if ai=bi, white otherwise 4

5 5 matches 8 matches 5

6 8 positions, 1 mismatch Priit Adler: 10,2 Priit Adler: 6

7 Evolution at the DNA level C ACGGTGCAGTCACCA ACGTTGCAGTCCACCA SEQUENCE EDITS Lecture 1, Tuesday April 1, 2003 REARRANGEMENTS Evolutionary Rates next generation OK OK OK X X Lecture 1, Tuesday April 1, 2003 Still OK? 7

8 Sequence conservation implies function Interleukin region in human and mouse Lecture 1, Tuesday April 1, 2003 Sequence Alignment AGGCTATCACCTGACCTCCAGGCCGATGCCC TAGCTATCACGACCGCGGTCGATTTGCCCGAC -AGGCTATCACCTGACCTCCAGGCCGA--TGCCC--- TAG-CTATCAC--GACCGC--GGTCGATTTGCCCGAC Definition Given two strings x = x 1 x 2...x M, y = y 1 y 2 y N, an alignment is an assignment of gaps to positions 0,, N in x, and 0,, N in y, so as to line up each sequence with either a letter, or a gap in the other sequence letter in one Lecture 1, Tuesday April 1,

9 What is a good alignment? Alignment: The best way to match the letters of one sequence with those of the other How do we define best? Alignment: A hypothesis that the two sequences come from a common ancestor through sequence edits Parsimonious explanation: Find the minimum number of edits that transform one sequence into the other Lecture 1, Tuesday April 1, 2003 Serafim Batzoglou Scoring Function Sequence edits: Mutations ti Insertions Deletions Scoring Function: Match: +m Mismatch: -s Gap: -d AGGCCTC AGGACTC AGGGCCTC AGG.CTC Score F = (# matches) m - (# mismatches) s (#gaps) d Lecture 1, Tuesday April 1,

10 How do we compute the best alignment? AGTGCCCTGGAACCCTGACGGTGGGTCACAAAACTTCTGGA AGTGACCTGGGAAGACCCTGACCCTGGG GTCACAAAACTC Too many possible alignments: O( 2 M+N ) Lecture 1, Tuesday April 1, 2003 Three Main Steps 1. Assign similarity scores A numerical value (score) is assigned to every cell in the array depending on similarity/dissimilarity il it i il it Similarity scores may be simple, or related to chemical similarities or frequency of observed substitutions 2. Score paths through array For each cell want to know the maximum possible score for an alignment ending at that point Cumulative score by adding in a path through the matrix Searches subrow and subcolumn for the highest score Gap penalty independent d of the length of the gap The best match is the pathway with the highest score Maximum match = largest number of amino acids of one protein that can be matched with those of another protein while allowing for all possible deletions 3. Construct an alignment 10

11 1. Values are assigned to each matching pair of residues based upon a similarity matrix. Here the matrix is the simplest: match = 1 mismatch = 0 More complex similarity matrices, such as PAM or BLOSUM, may be used. Assign Relative Values 2. Rlti Relative values are then assigned dto each cell of the array, based upon the maximum scoring pathway through the array. * Search subrow and subcolumn to assign the score for each cell. Each cell is assigned the highest possible score based upon it's own score + the highest score in the diagonal preceeding it. * Gaps are allowed and gap penalties may be assigned. In this example there are no gap penalties. 11

12 Pathfinding 3 Alignments producing a maximum match are constructed 3. Alignments producing a maximum match are constructed. * The maximum match score will always be in the outermost row or column. * A maximum alignment can be constructed by following the maximum scores in each row backwards from the outermost maximum score. * The two equal maximal alignments resulting from this example are displayed below the array. * These alignments are global every nucleotide or amino acid must be included in the alignment. This algorithm therefore misses many motif or domain similarities. 12

13 affine gaps : 1 longer is more likely than (n) = d + (n 1) e gap gap open extend To compute optimal alignment, many small gaps (n) At position i,j, need to remember best score if gap is open best score if gap is not open d e F(i, j): G(i, j): score of alignment x 1 x i to y 1 y j if x i aligns to y j score if x i, or y j, aligns to a gap Lecture 2, Thursday April 3,

14 Scoring the gaps more accurately Current model: (n) Gap of length incurs penalty n n d However, gaps usually occur in bunches Convex gap penalty function: (n) ( ) (n): for all n, (n + 1) (n) (n) (n 1) Lecture 2, Thursday April 3, 2003 Needleman Wunsch with affine gaps Initialization: F(i, 0) = d + (i 1) e F(0, j) = d + (j 1) e Iteration: F(i, j) = max F(i 1, j 1) + s(x i, y j ) G(i 1, j 1) + s(x i, y j ) Termination: G(i, j) = max same F(i 1, j) d F(i, (,j 1) d G(i, j 1) e G(i 1, j) e Lecture 2, Thursday April 3,

15 Needleman, S. B., Wunsch, C. D., J. Mol. Biol. (1970) 48: (from Aoife McLysaght and NCBI workshop slides) General algorithm for sequence comparison Fundamental principle to calculate the alignment score S(i,j) you only need to enumerate and score all ways in which one aligned pair can be added to a shorter alignment to produce an alignment of the first i residues of seq1 and the first j residues of seq2 (dynamic programming) Allpossible pairs are represented by a two dimensional array, and all possible comparisons are represented by pathways through this array Global alignments... i.e. every residue of the two sequences has to participate therefore will not detect motif or active site homology alone Global vs local alignment Global alignment methods give the optimal end to end alignment between two sequences. However, homologous sequences may share similarity in a sub region of the sequence. In trying to choose the optimal end to end alignment, global alignments can fail to pick up local homology. Local alignment methods will return alignments with high scoring regional homology. 15

16 Global vs local alignment Needleman and Wunsch ("Global" Alignment) Usesa global alignmentalgorithm algorithm, meaningthat: a. the full sequence must be aligned. b. gaps at the end of the sequence are penalized as much as internal gaps. Smith Waterman ("Local" Alignment) Uses a local alignment algorithm, meaning that: a. it searches for both full and partial sequence matches. b. gaps at the end of the sequence essentially have a penalty of zero. The local alignment problem Given two strings x = x 1 x M, y = y 1 y N Find substrings x, y whose similarity (optimal global alignment value) is maximum e.g. x = aaaacccccgggg y = cccgggaaccaacc Lecture 2, Thursday April 3,

17 Why local alignment Genes are shuffled between genomes Portions of proteins (domains) are often conserved Lecture 2, Thursday April 3, 2003 The Smith Waterman algorithm Idea: Ignore badly aligning regions Modifications to Needleman Wunsch: Initialization: F(0, j) = F(i, 0) = 0 0 Iteration: F(i, j) = max F(i 1, j) d F(i, j 1) d F(i 1, j 1) + s(x i, y j ) Lecture 2, Thursday April 3,

18 The Smith Waterman algorithm Termination: 1. If we want the best local alignment F OPT = max i,j F(i, j) 2. If we want all local alignments scoring > t Lecture 2, Thursday April 3, 2003 For all i, j find F(i, j) > t, and trace back General gap dynamic programming Initialization: same Iteration: F(i 1, j 1) + s(x i, y j ) F(i, j) = max max k=0 i 1 F(k,j) (i k) max k=0 j 1 F(i,k) (j k) Termination: same Running Time: O(N 2 M) Space: O(NM) (assume N>M) Lecture 2, Thursday April 3,

19 Smith, T. F., Waterman, M. S., J. Mol. Biol. (1981) 147: Based on N W Algorithm Instead of looking at each sequence in its entirety, this compares segments of all possible lengths and chooses whichever optimise the similarity measure (local alignments) Comparing two sequences A (=a 1 a 2 a 3... a n ) and B (=b 1 b 2 b 3... b m ) H ij =max{h i 1, j 1 +s(a i,b j ), max{h i k,j W k }, max{h i, j l W l }, 0} H ij is the maximum similarity of two segments ending in a i and b j respectively. Including the alternative that the similarity score be zero in the expression for H ij allows the local alignment to restart at any pair of aligned residues. In addition, it makes the calculation much more sensitive to the precise match and mismatch scores and gap penalties. Smith Waterman Uses a local alignment algorithm, meaning that: a. it searches for both full and partial sequence matches. b. gaps at the end of the sequence essentially have a penalty of zero. Assigns a score to each pair of bases Uses similarity scores only Uses positive scores for related residues Uses negative scores for substitutions and gaps Initializes edges of the matrix with zeros As the scores are summed in the matrix, ti any score bl below 0 is recorded ddas 0. Begins the trace back at the maximum value found anywhere in the matrix Continues until the score falls to 0. 19

20 Scoring metrics are of two types: Distance (cost) Scores The distance between identical residues must be 0. The distance, or cost, for aligning two non identical residues must be greater than 0 (i.e. negative distances are not allowed). Similarity Scores Identical or similar residues have positive scores Dissimilar residues can have 0 or even negative scores 20

21 Smith Waterman example Penalties Assigning values in the S W 2 dimensional array requires the use of gap penalties. In this example scores are derived from a simple similarity matrix plus a gap initiation and gap extension penalty as follows: Match = + 1 MisMatch = 1/3 Gap = (1 + 1/3k*) (* where k = number of residues included in gap) All cell values start at zero and are not allowed to fall below zero (so a new ( alignment path can begin at any point). Assigns value to cell based upon value of cell plus the highest value in subrow, subcolumn or direct diagonal (as shown) when gap penalties are taken into account. 21

22 Relative values in adjacent cells of a path can rise, stay the same or fll fall. Alignments can begin and end anywhere in the sequence, not just the final row or column. The value in any cell is the highest score for an alignment of any length ending at that cell. * The alignment for the path shown in red in the 2-dimensional array to the right is displayed below. 22

23 * The alignment for the path shown in red in the 2-dimensional array to the right is displayed below. The alignment for the path shown in red in the 2-dimensional i array to the right is displayed below. 23

24 Alignment Scores: The higher the score... the better the alignment. Alignment Scores and Search Algorithms (Baylor College of Medicine) A Substitution Score is chosen for each aligned pair of letters. The set of these scores is called the substitution matrix. The matrix scores highly identical matches of bases, and also gives 'better' scores to alignments of non identical bases that are similiar in some way, and a 'worse' score to pairs that are very dissimilar. This system can preserve alignments based on function by identifying, for example, sections of the two sequences that are similarly hydrophobic, even if not identical in sequence. A gap scoring system (affine gap costs) is used to chose scores for 'gaps'. A gap is one or more adjacent nulls in one sequence aligned with letters in the other sequence. Ideally, the gap scoring system charges a large initial penality for the existence of a gap, and smaller penalitiesfor each individualresidue. Thistakes intoaccount thateach mutationalevent can insert or delete multiple residues at a time the bulk of the gap cost penalty is for the existence of the mutation itself, not the length. The alignment score is the sum of the scores specified for each of the aligned pairs of letters, and letters with nulls, in the alignment. The higher the alignment score, the better the alignment. Vaata eestikeelseid referaate: Leopold Parts Mark Tehver 24

25 Smith Waterman algorithm finds best matching substrings between two sequences It uses simple dynamic programming, except the longer gaps can be supported with affine penalty scores. Maximum is taken between 1) comparison scores for last characters plus score without the last characters 2) max for all prefixes of first sequence plus the gap cost 3) max for all prefixes of second sequence plus the gap cost The used parameters: GAP_PENALTY penalty to start a gap GAP_EXTENSION penalty to extend an existing gap MATCH_PENALTY match score MISMATCH_PENALTY mismatch score SwTable(String A, String B): table[i][0] = 0, 0 <= j <= length(b) table[0][i] = 0, 0 <= i <= length(a) for(i = 1; i <= length(a); ++i) for(j = 1; j <= length(b); ++j) maxrow = -INFINITY; maxcolumn = -INFINITY; // find the best score from column maxcolumn = max(maxcolumn, table[i - k][j] - gapscore(k)); 0 < k < i // find the best score from row maxrow = max(maxcolumn, table[i][j - k] - gapscore(k)); 0 < k < j table[i][j] = max( // new value is a max of 4: table[i-1][j-1] + letterscore(ai, Bj), maxrow, maxcolumn, 0 // no negative values ); gapscore(k) = GAP_PENALTY + GAP_EXTENSION*k letterscore(c, d) = MATCH_PENALTY, if c = d MISMATCH_PENALTY, if c!= d 25

26 Gap penalties Gaps were rather freely permitted in the overly simple implementations of the Needleman Wunsch and Smith Waterman algorithms shown above. What would happen if you feel that gaps should be rarer events in your particular protein? It is possible to assign a different weight to gaps. This can be done by subtracting from the score, some predetermined value every time a gap is required. In this case you can define a weight as W = a + bk, where k is the length of the gap. Hence you can control whether many short gaps occur or whether long gaps occur but more infrequently. Deletions do occur but when they occur it is seldom many small, short deletions but rather fewer and longer deletions. How do you choose a gap penalty? Unfortunately, there is little knowledge to help here. Most of the tests done so far depend on an empirical basis designed to achieve some end. For example, Smith and Fitch have derived (by exhaustive search) gap penalties that will best align distantly related haemoglobin genes. But there is no guarantee that these values would work well for the protein or (worse) the nucleotide sequence that you are interested in. Typical values are 0.5 < a < < b < 1.0 b < a but there is nothing special about these values other than the fact that they seem to work well for some of the common comparisons. Note that in general a > b. This corresponds with biological knowledge of how gaps are generated it is easier to generate one gap of two residues rather than two gaps of one residue since the former can be created by a single mutational event. Substitution rates Weights for different mismatches should be permitted. A transition is more likely than a transversion; a Ile Val more likely than Ile Arg change. If the two sequences have no obvious relationship at their right and left ends, then end gaps should not be penalized. Unless two sequences are known to be homologous over their entire length, a local alignment is preferable to a global alignment. An optimal alignment is by no means necessarily statistically significant. One must make some estimate of the probability that a given alignment is due to chance. An alignment demonstrates similarity, not necessarily, homology. Homology is an evolutionary inference based on examination of the similarity and its biological meaning. Sequence similarity may result from homology but it may also result from chance, convergence or analogy. 26

27 PAM: [Taken from the NCBI Glossary PAM definition]. Percent Accepted Mutation. A unit introduced by Dayhoff et al. to quantify the amount of evolutionary change in a protein sequence. 1.0 PAM unit, is the amount of evolution which will change, on average, 1% of amino acids in a protein sequence. A PAM(x) substitution matrix is a look up table in which scores for each amino acid substitution have been calculated based on the frequency of that substitution in closely related proteins that have experienced a certain amount (x) of evolutionary divergence. 27

28 BLOSUM Blocks Substitution Matrix. A substitution matrix in which scores for each position are derived from observations of the frequencies of substitutions in blocks of local alignments in related proteins. Each matrix is tailored to a particular evolutionary distance. In the BLOSUM62 matrix, for example, the alignment from which scores were derived was created using sequences sharing no more than 62% identity. Sequences more identical than 62% are represented by a single sequence in the alignment so as to avoid overweighting closely related family members. (Henikoff and Henikoff) 28

29 Homology Orthology / orthologous the same gene in different species Paralogy / Paralogous Similar gene in the same organism E.g. gene duplication Paralogous genes can evolve independently and acquire new different functions Or become redundant, and disappear 29

30 BLAST Basic Local Alignment Search Tool. (Altschul et al. J. Mol. Biol. 215(3):403 10, 10, 1990) A sequence comparison algorithm optimized for speed used to search sequence databases for optimal local alignments to a query. The initial search is done for a word of length "W" that scores at least "T" when compared to the query using a substitution matrix. Word hits are then extended in either direction in an attempt to generate an alignment with a score exceeding the threshold of "S". The "T" parameter dictates the speed and sensitivity of the search. 30

31 Indexing-based local alignment (BLAST- Basic Local Alignment Search Tool) Main idea: query 1. Construct a dictionary of all the words in the query 2. Initiate a local alignment for each word match between query and DB DB Running Time: O(MN) However, orders of magnitude faster than Smith-Waterman CS262 Lecture 3, Win06, Batzoglou Indexing-based local alignment Dictionary: All words of length k (~10) Alignment initiated between words of alignment score T (typically T = k) query Alignment: Ungapped extensions until score below statistical ti ti threshold h Output: All local alignments with score > statistical threshold CS262 Lecture 3, Win06, Batzoglou scan DB query 31

32 Indexing-based local alignment Extensions Example: k = 4 The matching word GGTC initiates an alignment Extension to the left and right with no gaps until alignment falls < C below best so far Output: GTAAGGTCC GTTAGGTCC CS262 Lecture 3, Win06, Batzoglou C C C T T C C T G G A T T G C G A A C G A A G T A A G G T C C A G T Indexing-based local alignment Extensions Gapped extensions G A A C G A A G T A A G G T C C A G T Extensions with gaps in a band around anchor Output: GTAAGGTCCAGT GTTAGGTC-AGT CS262 Lecture 3, Win06, Batzoglou C T G A T C C T G G A T T G C 32

33 Indexing-based local alignment Extensions Gapped extensions until threshold G A A C G A A G T A A G G T C C A G T Extensions with gaps until score < C below best score so far Output: GTAAGGTCCAGT GTTAGGTC-AGT CS262 Lecture 3, Win06, Batzoglou C T G A T C C T G G A T T G C Sensitivity-Speed Tradeoff X% Sensitivity long words (k = 15) short words (k = 7) Speed Sens. Speed CS262 Lecture 3, Win06, Batzoglou Kent WJ, Genome Research

34 Sensitivity-Speed Tradeoff Methods to improve sensitivity/speed 1. Using pairs of words ATAACGGACGACTGATTACACTGATTCTTAC GGCACGGACCAGTGACTACTCTGATTCCCAG 2. Using inexact words ATAACGGACGACTGATTACACTGATTCTTAC 3. Patterns non consecutive positions CS262 Lecture 3, Win06, Batzoglou GGCGCCGACGAGTGATTACACAGATTGCCAG TTTGATTACACAGAT T G TT CAC G Measured improvement CS262 Lecture 3, Win06, Batzoglou Kent WJ, Genome Research

35 Non-consecutive words Patterns Patterns increase the likelihood of at least one match within a long conserved region Consecutive Positions Non-Consecutive Positions 6 common 7 common 5 common 3 common On a 100-long 70% conserved region: Consecutive Non-consecutive Expected # hits: Prob[at least one hit]: CS262 Lecture 3, Win06, Batzoglou Advantage of Patterns 11 positions 11 positions 10 positions CS262 Lecture 3, Win06, Batzoglou 35

36 Multiple patterns TTTGATTACACAGAT T G TT CAC G T G T C CAG TTGATT A G How long does it take to search the query? K patterns Takes K times longer to scan Patterns can complement one another Computational problem: Given: a model (prob distribution) for homology between two regions Find: best set of K patterns that maximizes Prob(at least one match) Buhler et al. RECOMB 2003 CS262 Lecture 3, Win06, Batzoglou Sun & Buhler RECOMB 2004 Variants of BLAST NCBI BLAST: search the universe MEGABLAST: Optimized to align very similar sequences Works best when k = 4i 16 Linear gap penalty WU-BLAST: (Wash U BLAST) Very good optimizations Good set of features & command line arguments BLAT Faster, less sensitive than BLAST Good for aligning huge numbers of queries CHAOS Uses inexact k-mers, sensitive PatternHunter p p p p Uses patterns instead of k-mers BlastZ Uses patterns, good for finding genes Typhon Uses multiple alignments to improve sensitivity/speed tradeoff CS262 Lecture 3, Win06, Batzoglou 36

37 Example Query: gattacaccccgattacaccccgattaca (29 letters) [2 mins] Database: All GenBank+EMBL+DDBJ+PDB sequences (but no EST, STS, GSS, or phase 0, 1 or 2 HTGS sequences) 1,726,556 sequences; 8,074,398,388 total t letters >gi gb AC Oryza sativa chromosome 3 BAC OSJNBa0087C10 genomic sequence, complete sequence Length = Score = 34.2 bits (17), Expect = 4.5 Identities = 20/21 (95%) Strand = Plus / Plus Query: 4 tacaccccgattacaccccga 24 Sbjct: tacacccagattacaccccga Score = 34.2 bits (17), Expect = 4.5 Identities = 20/21 (95%) Strand = Plus / Plus Query: 4 tacaccccgattacaccccga 24 Sbjct: tacacccagattacaccccga >gi gb AC Oryza sativa chromosome 3 BAC OSJNBa0052F07 genomic sequence, complete sequence Length = Score = 34.2 bits (17), Expect = 4.5 Identities = 20/21 (95%) Strand = Plus / Plus Query: 4 tacaccccgattacaccccga 24 Sbjct: 3891 tacacccagattacaccccga 3911 CS262 Lecture 3, Win06, Batzoglou Example Query: Human atoh enhancer, 179 letters [1.5 min] Result: 57 blast hits 1. gi gb AF AF Homo sapiens ATOH1 enhanc e gi gb AC Mus musculus Strain C57BL6/J ch e gi gb AF AF Mus musculus Atoh1 enhanc e gi gb AF Gallus gallus CATH1 (CATH1) gene e gi emb AL Zebrafish DNA sequence from clo e gi gb AC Oryza sativa chromosome 10 BAC O gi ref NM_ Mus musculus suppressor of Ty gi gb BC Mus musculus, Similar to suppres gi gb AF AF Mus musculus Atoh1 enhancer sequence Length = 1517 Score = 256 bits (129), Expect = 9e-66 Identities = 167/177 (94%), Gaps = 2/177 (1%) Strand = Plus / Plus Query: 3 tgacaatagagggtctggcagaggctcctggccgcggtgcggagcgtctggagcggagca 62 Sbjct: 1144 tgacaatagaggggctggcagaggctcctggccccggtgcggagcgtctggagcggagca 1203 Query: 63 cgcgctgtcagctggtgagcgcactctcctttcaggcagctccccggggagctgtgcggc 122 Sbjct: 1204 cgcgctgtcagctggtgagcgcactc-gctttcaggccgctccccggggagctgagcggc 1262 Query: 123 cacatttaacaccatcatcacccctccccggcctcctcaacctcggcctcctcctcg 179 Sbjct: 1263 cacatttaacaccgtcgtca-ccctccccggcctcctcaacatcggcctcctcctcg 1318 CS262 Lecture 3, Win06, Batzoglou 37

38 Examples: >sp P48432 SOX2_MOUSE Transcription factor SOX 2 OS=Mus musculus GN=Sox2 PE=1 SV=2 MYNMMETELKPPGPQQASGGGGGGGNATAAATGGNQKNSPDRVKRPMNAFMVWSRGQRRK MAQENPKMHNSEISKRLGAEWKLLSETEKRPFIDEAKRLRALHMKEHPDYKYRPRRKTKT LMKKDKYTLPGGLLAPGGNSMASGVGVGAGLGGGLNQRMDSYAHMNGWSNGSYSMMQEQL GYPQHPGLNAHGAAQMQPMHRYVVSALQYNSMTSSQTYMNGSPTYSMSYSQQGTPGMALG SMGSVVKSEASSSPPVVTSSSHSRAPCQAGDLRDMISMYLPGAEVPEPAAPSRLHMAQHY QSGPVPGTAKYGTLPLSHM ctattaactt gttcaaaaaa gtatcaggag ttgtcaaggc agagaagaga gtgtttgcaa aaagggaaaa gtactttgct gcctctttaa gactagggct gggagaaaga agaggagaga gaaagaaagg agagaagttt ggagcccgag gcttaagcct ttccaaaaac taatcacaac bin/hgblat?command=start Lessons learned? New searching technique: Filter based on partial hits Refine the search on the candidate hits Statistical significance Probability of a good looking hit increases when DB grows 38

39 CS262 Lecture 3, Win06, Batzoglou Multiple alignment: find the alignment for tens, if not hundreds d or thousands of sequences Very importamt for actual biological interpretation, say describing protein families through the evolution. 39

40 Relevant Citations Needleman, S.B. and Wunsch, C.D. A general method applicable to the search for similarities in the amino acid sequence of two proteins. J Mol Biol. 48(3): (1970).PubMed: Smith, T.F. and Waterman, M.S. Identification of common molecular subsequences. J Mol Biol. 147(1):195 7 (1981). PubMed: Pearson, W.R. and Lipman, D.J. Improved tools for biological sequence comparison. Proc Natl Acad Sci U S A. 85(8): (1988). PubMed: Altschul SF, Gish W, Miller W, Myers EW, Lipman DJ. Basic local alignment search tool. J Mol Biol. 215(3): (1990). PubMed: Evolution sets restrictions on possible mutations One needs to use substitution cost matrices that somehow reflect the evolutionary distance Links Distance Measures, edited by B.Golding, Feb 1996 web (Itshack Pe`er) Sequence alignment algorithms (Benjamin Corum) And some of them with local copies: Amino acids distances Amino acids distances PAM matrices (Margaret Dayhoff) PAM units PAM matrices Amino acids distances 40

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