Scoring a multiple alignment Sum of pairsStarTree A A C CA A A A A A A CC CC

Sum of Pairs AAA AAC ACC A A A AA 10α A A A CA + (6α - 4β) A A C CA + (4α - 6β) = 20α - 10β

Sum-of-Pairs Scoring Function Score of multiple alignment = ∑ i <j score(S i,S j ) where score(S i,S j ) = score of induced pairwise alignment

Induced Pairwise Alignment S 1 S - T I S C T G - S - N I S 2 L - T I – C N G S S - N I S 3 L R T I S C S G F S Q N I Induced pairwise alignment of S 1, S 2 : S 1 S T I S C T G - S N I S 2 L T I – C N G S S N I

Star alignment Heuristic method for multiple sequence alignments Select a sequence c as the center of the star For each sequence x 1, …, x k such that index i  c, perform a Needleman-Wunsch global alignment Aggregate alignments with the principle “once a gap, always a gap.”

Choosing a center Try them all and pick the one which is most similar to all of the sequences Let S(x i,x j ) be the optimal score between sequences x i and x j. Calculate all O(k 2 ) alignments, and choose as x c the sequence x i that maximizes the following Σ S(x i,x j ) j ≠ i

Star alignment example s2s2 s1s1 s3s3 s4s4 S 1 : MPE S 2 : MKE S 3 : MSKE S 4 : SKE MPE | MKE MSKE | || M-KE SKE || MKE MPE MKE M-PE M-KE MSKE M-PE M-KE MSKE S-KE

Analysis Assuming all sequences have length n O(k 2 n 2 ) to calculate center Step i of iterative pairwise alignment takes O((i·n)·n) time two strings of length n and i·n O(k 2 n 2 ) overall cost

ClustalW Most popular multiple alignment tool today ‘W’ stands for ‘weighted’ (d ifferent parts of alignment are weighted differently). Three-step process 1.) Construct pairwise alignments 2.) Build Guide Tree ( by Neighbor Joining method ) 3.) Progressive Alignment guided by the tree - The sequences are aligned progressively according to the branching order in the guide tree

Step 1: Pairwise Alignment Aligns each sequence again each other giving a similarity matrix Similarity = exact matches / sequence length (percent identity) v 1 v 2 v 3 v 4 v 1 - v v v (.17 means 17 % identical)

Step 2: Guide Tree Create Guide Tree using the similarity matrix ClustalW uses the neighbor-joining method Guide tree roughly reflects evolutionary relations

Step 2: Guide Tree (cont’d) v1v3v4v2v1v3v4v2 Calculate: v 1,3 = alignment (v 1, v 3 ) v 1,3,4 = alignment((v 1,3 ),v 4 ) v 1,2,3,4 = alignment((v 1,3,4 ),v 2 ) v 1 v 2 v 3 v 4 v 1 - v v v

Step 3: Progressive Alignment Start by aligning the two most similar sequences Following the guide tree, add in the next sequences, aligning to the existing alignment Insert gaps as necessary FOS_RAT PEEMSVTS-LDLTGGLPEATTPESEEAFTLPLLNDPEPK-PSLEPVKNISNMELKAEPFD FOS_MOUSE PEEMSVAS-LDLTGGLPEASTPESEEAFTLPLLNDPEPK-PSLEPVKSISNVELKAEPFD FOS_CHICK SEELAAATALDLG----APSPAAAEEAFALPLMTEAPPAVPPKEPSG--SGLELKAEPFD FOSB_MOUSE PGPGPLAEVRDLPG-----STSAKEDGFGWLLPPPPPPP LPFQ FOSB_HUMAN PGPGPLAEVRDLPG-----SAPAKEDGFSWLLPPPPPPP LPFQ.. : **. :.. *:.* *. * **: Dots and stars show how well-conserved a column is.

ClustalW: another example S 1 ALSK S 2 TNSD S 3 NASK S 4 NTSD

ClustalW example S 1 ALSK S 2 TNSD S 3 NASK S 4 NTSD S1S1 S2S2 S3S3 S4S4 S1S S2S2 083 S3S3 07 S4S4 0 Distance Matrix All pairwise alignments

ClustalW example S 1 ALSK S 2 TNSD S 3 NASK S 4 NTSD S1S1 S2S2 S3S3 S4S4 S1S S2S2 083 S3S3 07 S4S4 0 Distance Matrix S3S3 S1S1 S2S2 S4S4 Rooted Tree All pairwise alignments Neighbor Joining

ClustalW example S 1 ALSK S 2 TNSD S 3 NASK S 4 NTSD S1S1 S2S2 S3S3 S4S4 S1S S2S2 083 S3S3 07 S4S4 0 1.Align S 1 with S 3 2.Align S 2 with S 4 3.Align (S 1, S 3 ) with (S 2, S 4 ) Distance Matrix S3S3 S1S1 S2S2 S4S4 Rooted Tree Multiple Alignment Steps All pairwise alignments Neighbor Joining

ClustalW example S 1 ALSK S 2 TNSD S 3 NASK S 4 NTSD S1S1 S2S2 S3S3 S4S4 S1S S2S2 083 S3S3 07 S4S4 0 1.Align S 1 with S 3 2.Align S 2 with S 4 3.Align (S 1, S 3 ) with (S 2, S 4 ) Distance Matrix Multiple Alignment Steps All pairwise alignments Neighbor Joining -ALSK NA-SK -TNSD NT-SD -ALSK -TNSD NA-SK NT-SD Multiple Alignment S3S3 S1S1 S2S2 S4S4 Rooted Tree

Progressive alignment Find seq Build guide tree Create intmdt ali most similar to each other

Other progressive approaches PILEUP Similar to CLUSTALW Uses UPGMA to produce tree

Problems with progressive alignments Depend on pairwise alignments If sequences are very distantly related, much higher likelihood of errors Care must be made in choosing scoring matrices and penalties

Iterative refinement in progressive alignment Another problem of progressive alignment: Initial alignments are “frozen” even when new evidence comes Example: x:GAAGTT y:GAC-TT z:GAACTG w:GTACTG Frozen! Now clear that correct y = GA-CTT

Evaluating multiple alignments Balibase benchmark (Thompson, 1999) De-facto standard for assessing the quality of a multiple alignment tool Manually refined multiple sequence alignments Quality measured by how good it matches the core blocks Another benchmark: SABmark benchmark Based on protein structural families

Scoring multiple alignments Ideally, a scoring scheme should Penalize variations in conserved positions higher Relate sequences by a phylogenetic tree Tree alignment Usually assume Independence of columns Quality computation Entropy-based scoring Compute the Shannon entropy of each column Sum-of-pairs (SP) score

Multiple Alignments: Scoring Number of matches (multiple longest common subsequence score) Entropy score Sum of pairs (SP-Score)

Multiple LCS Score A column is a “match” if all the letters in the column are the same Only good for very similar sequences AAA AAT ATC

Entropy Define frequencies for the occurrence of each letter in each column of multiple alignment p A = 1, p T =p G =p C =0 (1 st column) p A = 0.75, p T = 0.25, p G =p C =0 (2 nd column) p A = 0.50, p T = 0.25, p C =0.25 p G =0 (3 rd column) Compute entropy of each column AAA AAT ATC

Entropy: Example Best case Worst case

Multiple Alignment: Entropy Score Entropy for a multiple alignment is the sum of entropies of its columns:  over all columns -  X=A,T,G,C p X logp X

Entropy of an Alignment: Example column entropy: -( p A logp A + p C logp C + p G logp G + p T logp T ) Column 1 = -[1*log(1) + 0*log0 + 0*log0 +0*log0] = 0 Column 2 = -[( 1 / 4 )*log( 1 / 4 ) + ( 3 / 4 )*log( 3 / 4 ) + 0*log0 + 0*log0] = -[ ( 1 / 4 )*(-2) + ( 3 / 4 )*(-.415) ] = Column 3 = -[( 1 / 4 )*log( 1 / 4 )+( 1 / 4 )*log( 1 / 4 )+( 1 / 4 )*log( 1 / 4 ) +( 1 / 4 )*log( 1 / 4 )] = 4* -[( 1 / 4 )*(-2)] = +2.0 Alignment Entropy = = AAA ACC ACG ACT

Representing a profile as a logo Contribution of each residue to a position Phosphate binding pattern from Prosite: [LIVMF]-[GSA]-x(5)-P-x(4)-[LIVMFYW]-x-[LIVMF]-x-G-D-[GSA]-[GSAC]

Multiple Alignment Induces Pairwise Alignments Every multiple alignment induces pairwise alignments x:AC-GCGG-C y:AC-GC-GAG z:GCCGC-GAG Induces: x: ACGCGG-C; x: AC-GCGG-C; y: AC-GCGAG y: ACGC-GAC; z: GCCGC-GAG; z: GCCGCGAG

Sum of Pairs (SP) Scoring SP scoring is the standard method for scoring multiple sequence alignments. Columns are scored by a ‘sum of pairs’ function using a substitution matrix (PAM or BLOSUM) Assumes statistical independence for the columns, does not use a phylogenetic tree.

Sum of Pairs Score(SP-Score) Consider pairwise alignment of sequences a i and a j imposed by a multiple alignment of k sequences Denote the score of this suboptimal (not necessarily optimal) pairwise alignment as s*(a i, a j ) Sum up the pairwise scores for a multiple alignment: s(a 1,…,a k ) = Σ i,j s*(a i, a j )

Computing SP-Score Aligning 4 sequences: 6 pairwise alignments Given a 1,a 2,a 3,a 4 : s(a 1 …a 4 ) =  s*(a i,a j ) = s*(a 1,a 2 ) + s*(a 1,a 3 ) + s*(a 1,a 4 ) + s*(a 2,a 3 ) + s*(a 2,a 4 ) + s*(a 3,a 4 )

SP-Score: Example a1.aka1.ak ATG-C-AAT A-G-CATAT ATCCCATTT Pairs of Sequences A AA 11 1 G CG 1  Score=3 Score = 1 –  Column 1 Column 3 May also calculate the scores column by column:

Example Compute Sum of Pairs Score of the following multiple alignment with match = 3, mismatch = -1, S(X,-) = -1, S(-,-) = 0 X: G T A C G Y: T G C C G Z: C G G C C W: C G G A C Sum of pairs = = 10

Multiple alignment tools Clustal W (Thompson, 1994) Most popular PRRP (Gotoh, 1993) HMMT (Eddy, 1995) DIALIGN (Morgenstern, 1998) T-Coffee (Notredame, 2000) MUSCLE (Edgar, 2004) Align-m (Walle, 2004) PROBCONS (Do, 2004)

from: C. Notredame, “Recent progresses in multiple alignment: a survey”, Pharmacogenomics (2002) 3(1)

Useful links

Was the quagga (now extinct) more like a zebra or a horse? The quagga was an African animal that is now extinct. It looked partly like a horse, and partly like a zebra. In 1872, the last living quagga was photographed (above). Mitochondrial DNA was obtained from a museum specimen of a quagga and sequenced. Perform a multiple sequence alignment of quagga (Equus quagga boehmi), horse (Equus caballus), and zebra (Equus burchelli) mitochondrial DNA. To which animal was the quagga more closely related?

For the Entrez search Equus quagga boehmi, there is only one mitochondrial DNA sequence (mitochondrial D-loop, AF499309). From Entrez nucleotide the accession numbers are AY (horse) and AF (zebra). The sequences are: >gi| |gb|AY | Equus caballus haplotype be1 mitochondrial D-loop, complete sequence GATTTCTTCCCCTAAACGACAACAATTTACCCTCATGTGCTATGTCAGTATCAGATTATACCCCCACATA ACACCATACCCACCTGACATGCAATATCTTATGAATGGCCTATGTACGTCGTGCATTAAATTGTCTGCCC CATGAATAATAAGCATGTACATAATATCATTTATCTTACATAAGTACATTATATTATTGATCGTGCATAC CCCATCCAAGTCAAATCATTTCCAGTCAACACGCATATCACAGCCCATGTTCCACGAGCTTAATCACCAA GCCGCGGGAAATCAGCAACCCTCCCAACTACGTGTCCCAATCCTCGCTCCGGGCCCATCCAAACGTGGGG GTTTCTACAATGAAACTATACCTGGCATCTGGTTCTTTCTTCAGGGCCATTCCCACCCAACCTCGCCCAT TCTTTCCCCTTAAATAAGACATCTCGATGGACTAATGACTAATCAGCCCATGCTCACACATAACTGTGAT TTCATGCATTTGGTATCTTTTTATATTTGGGGATGCTATGACTCAGCTATGGCCGTCAAAGGCCTCGACG CAGTCAATTAAATTGAAGCTGGACTTAAATTGAACGTTATTCCTCCGCATCAGCAACCATAAGGTGTTAT TCAGTCCATGGTAGCGGGACATAGGAAACAAGTGCACCTGTGCACCTACCCGCGCAGTAAGCAAGTAATA TAGCTTTCTTAATCAAACCCCCCCTACCCCCCATTAAACTCCACATATGTACATTCAACACAATCTTGCC AAACCCCAAAAACAAGACTAAACAATGCACAATACTTCATGAAGCTTAACCCTCGCATGCCAACCATAAT AACTCAACACACCTAACAATCTTAACAGAACTTTCCCCCCGCCATTAATACCAACATGCTACTTTAATCA ATAAAATTTCCATAGACAGGCATCCCCCTAGATCTAATTTTCTAAATCTGTCAACCCTTCTTCCCC >gi| |gb|AF | Equus burchellii isolate Be1 mitochondrial D-loop, partial sequence GCTCCACCGTCAACACCCAAAGCTGAAATTCTACTTAAACTATTCCTTGATTTCCTCCCCTAAACGACAA CAATTCACCCTCATGTACTATGTCAGTATTAAAATACATCCTATGTAGCATTATACAGTTCAACATATAA TACCCTGTTAACATCCTATGTACATCGTGCATTAAATTGTT >gi| |gb|AF | Equus quagga boehmi isolate Bo1 mitochondrial D-loop, partial sequence GCTCCACCGTCAACACCCAAAGCTGAAATTCTACTTAAACTATTCCTTGATTTCCTCCCCTAAACGACAA CAGTTCACCCTCATGTACTATGTCAGTATTAAAATACATCCTATGTAGTATTATACAGTTCAACATATAA TACCCTGTTAACATCCTATGTACGTCGTGCATTAGATTGTT

The portion of the multiple sequence alignment in (excluding additional nonoverlapping horse sequence) is as follows: gi| |gb|AF | GCTCCACCGTCAACACCCAAAGCTGAAATTCTACTTAAACTATTCCTTGA 50 [zebra] gi| |gb|AF | GCTCCACCGTCAACACCCAAAGCTGAAATTCTACTTAAACTATTCCTTGA 50 [quagga] gi| |gb|AY | GA 2 [horse] ** gi| |gb|AF | TTTCCTCCCCTAAACGACAACAATTCACCCTCATGTACTATGTCAGTATT 100 gi| |gb|AF | TTTCCTCCCCTAAACGACAACAGTTCACCCTCATGTACTATGTCAGTATT 100 gi| |gb|AY | TTTCTTCCCCTAAACGACAACAATTTACCCTCATGTGCTATGTCAGTATC 52 **** ***************** ** ********** ************ gi| |gb|AF | AAAATACATCCT-ATGTAGCATTATACA-GTTCAACATATAATACCCTGT 148 gi| |gb|AF | AAAATACATCCT-ATGTAGTATTATACA-GTTCAACATATAATACCCTGT 148 gi| |gb|AY | AGATTATACCCCCACATAACACCATACCCACCTGACATGCAATATCTTAT 102 * * ** * ** * ** * **** **** **** * * * gi| |gb|AF | TAACATCCTATGTACATCGTGCATTAAATTGTT gi| |gb|AF | TAACATCCTATGTACGTCGTGCATTAGATTGTT gi| |gb|AY | GAATGGCCTATGTACGTCGTGCATTAAATTGTCTGCCCCATGAATAATAA 152 ** ********* ********** ***** Visual inspection of the alignment can give you a clue that the quagga DNA is closely related to zebra DNA: [1] the internal gaps in the alignment suggest that horse DNA (on the bottom row) is an outlier, and [2] positions that are not conserved (i.e. positions lacking an asterisk) also consistently show that horse DNA differs while quagga and zebra sequences match each other. The pairwise alignment scores also show clearly that the quagga is closer to a zebra: Sequence 1: gi| |gb|AY | 976 bp [horse] Sequence 2: gi| |gb|AF | 181 bp [zebra] Sequence 3: gi| |gb|AF | 181 bp [quagga] Start of Pairwise alignments Aligning... Sequences (1:2) Aligned. Score: 56 Sequences (1:3) Aligned. Score: 55 Sequences (2:3) Aligned. Score: 97 Finally a PubMed search with the terms quagga, horse and zebra links to an article suggesting that zebra and quagga shared a common ancestor several million years ago.article