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C E N T R E F O R I N T E G R A T I V E B I O I N F O R M A T I C S V U Introduction to bioinformatics 2008 Lecture 7 Substitution Matrices And Multiple Sequence Alignment (I) [1] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U Sequence Analysis Finding relationships between genes and gene products of different species, including those at large evolutionary distances Many evolutionary biologists do not like talking about prokaryotes and eukaryotes anymore [2] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U Archaea Domain Archaea is mostly composed of cells that live in extreme environments. While they are able to live elsewhere, they are usually not found there because outside of extreme environments they are competitively excluded by other organisms. Species of the domain Archaea are •not inhibited by antibiotics, •lack peptidoglycan in their cell wall (unlike bacteria, which have this sugar/polypeptide compound), •and can have branched carbon chains in their membrane lipids of the phospholipid bilayer. [3] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U Archaea (Cnt.) • It is believed that Archaea are very similar to prokaryotes (e.g. bacteria) that inhabited the earth billions of years ago. It is also believed that eukaryotes evolved from Archaea, because they share many mRNA sequences, have similar RNA polymerases, and have introns. • Therefore, it is generally assumed that the domains Archaea and Bacteria branched from each other very early in history, after which membrane infolding* produced eukaryotic cells in the archaean branch approximately 1.7 billion years ago. There are three main groups of Archaea: 1. extreme halophiles (salt), 2. methanogens (methane producing anaerobes), 3. and hyperthermophiles (e.g. living at temperatures >100º C!). *Membrane infolding is believed to have led to the nucleus of eukaryotic cells, which is a membrane-enveloped cell organelle that holds the cellular DNA. Prokaryotic cells are more C E N T R E F O R I N T E G R A T I V E primitive and do not have a nucleus. [4] Substitution matrices – Sequence analysis 2006 B I O I N F O RM A T I C S V U Example of nucleotide sequence database entry for Genbank LOCUS DEFINITION ACCESSION KEYWORDS SOURCE ORGANISM REFER ENCE AUTHORS TITLE JOURNAL MEDLINE COMMENT FEATURES source mRNA gene CDS BASE COUNT ORIGIN DRODPPC 4001 bp INV 15-MAR-1990 D.melanogaster decapentaplegic gene complex (DPP-C), complete cds. M30116 . D.melanogaster, cDNA to mRNA. Drosophila melanogaster Eurkaryote; mitochondrial eukaryotes; Metazoa; Arthropoda; Tracheata; Insecta; Pterygota; Diptera; Brachycera; Muscomorpha; Ephydroidea; Drosophilidae; Drosophilia. 1 (bases 1 to 4001) Padgett, R.W., St Johnston, R.D. and Gelbart, W.M. A transcript from a Drosophila pattern gene predicts a protein homologous to the transforming growth factor-beta family Nature 325, 81-84 (1987) 87090408 The initiation codon could be at either 1188-1190 or 1587-1589 Location/Qualifiers 1..4001 /organism=“Drosophila melanogaster” /db_xref=“taxon:7227” <1..3918 /gene=“dpp” /note=“decapentaplegic protein mRNA” /db_xref=“FlyBase:FBgn0000490” 1..4001 /note=“decapentaplegic” /gene=“dpp” /allele=“” /db_xref=“FlyBase:FBgn0000490” 1188..2954 /gene=“dpp” /note=“decapentaplegic protein (1188 could be 1587)” /codon_start=1 /db_xref=“FlyBase:FBgn0000490” /db_xref=“PID:g157292” /translation=“MRAWLLLLAVLATFQTIVRVASTEDISQRFIAAIAPVAAHIPLA SASGSGSGRSGSRSVGASTSTALAKAFNPFSEPASFSDSDKSHRSKTNKKPSKSDANR …………………… LGYDAYYCHGKCPFPLADHFNSTNAVVQTLVNNMNPGKVPKACCVPTQLDSVAMLYL NDQSTBVVLKNYQEMTBBGCGCR” 1170 a 1078 c 956 g 797 t 1 gtcgttcaac agcgctgatc gagtttaaat ctataccgaa atgagcggcg gaaagtgagc 61 cacttggcgt gaacccaaag ctttcgagga aaattctcgg acccccatat acaaatatcg 121 gaaaaagtat cgaacagttt cgcgacgcga agcgttaaga tcgcccaaag atctccgtgc 181 ggaaacaaag aaattgaggc actattaaga gattgttgtt gtgcgcgagt gtgtgtcttc 241 agctgggtgt gtggaatgtc aactgacggg ttgtaaaggg aaaccctgaa atccgaacgg 301 ccagccaaag caaataaagc tgtgaatacg aattaagtac aacaaacagt tactgaaaca 361 gatacagatt cggattcgaa tagagaaaca gatactggag atgcccccag aaacaattca 421 attgcaaata tagtgcgttg cgcgagtgcc agtggaaaaa tatgtggatt acctgcgaac 481 cgtccgccca aggagccgcc gggtgacagg tgtatccccc aggataccaa cccgagccca 541 gaccgagatc cacatccaga tcccgaccgc agggtgccag tgtgtcatgt gccgcggcat 601 accgaccgca gccacatcta ccgaccaggt gcgcctcgaa tgcggcaaca caattttcaa …………………………. 3841 aactgtataa acaaaacgta tgccctataa atatatgaat aactatctac atcgttatgc 3901 gttctaagct aagctcgaat aaatccgtac acgttaatta atctagaatc gtaagaccta 3961 acgcgtaagc tcagcatgtt ggataaatta atagaaacga g // [5] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U Example of protein sequence database entry for SWISS-PROT (now UNIPROT) ID AC DT DT DT DE GN OS OC RN RP RM RA RL RN RP RM RA RL CC CC CC CC CC DR DR DR DR DR KW FT FT FT FT FT FT FT FT FT FT FT SQ DECA_DROME STANDARD; PRT; 588AA. P07713; 01-APR-1988 (REL. 07, CREATED) 01-APR-1988 (REL. 07, LAST SEQUENCE UPDATE) 01-FEB-1995 (REL. 31, LAST ANNOTATION UPDATE) DECAPENTAPLEGIC PROTEIN PRECURSOR (DPP-C PROTEIN). DPP. DROSOPHILA MELANOGASTER (FRUIT FLY). EUKARYOTA; METAZOA; ARTHROPODA; INSECTA; DIPTERA. [1] SEQUENCE FROM N.A. 87090408 PADGETT R.W., ST JOHNSTON R.D., GELBART W.M.; NATURE 325:81-84 (1987) [2] CHARACTERIZATION, AND SEQUENCE OF 457-476. 90258853 PANGANIBAN G.E.F., RASHKA K.E., NEITZEL M.D., HOFFMANN F.M.; MOL. CELL. BIOL. 10:2669-2677(1990). -!- FUNCTION: DPP IS REQUIRED FOR THE PROPER DEVELOPMENT OF THE EMBRYONIC DOORSAL HYPODERM, FOR VIABILITY OF LARVAE AND FOR CELL VIABILITY OF THE EPITHELIAL CELLS IN THE IMAGINAL DISKS. -!- SUBUNIT: HOMODIMER, DISULFIDE-LINKED. -!- SIMILARITY: TO OTHER GROWTH FACTORS OF THE TGF-BETA FAMILY. EMBL; M30116; DMDPPC. PIR; A26158; A26158. HSSP; P08112; 1TFG. FLYBASE; FBGN0000490; DPP. PROSITE; PS00250; TGF_BETA. GROWTH FACTOR; DIFFERENTIATION; SIGNAL. SIGNAL 1 ? POTENTIAL. PROPEP ? 456 CHAIN 457 588 DECAPENTAPLEGIC PROTEIN. DISULFID 487 553 BY SIMILARITY. DISULFID 516 585 BY SIMILARITY. DISULFID 520 587 BY SIMILARITY. DISULFID 552 552 INTERCHAIN (BY SIMILARITY). CARBOHYD 120 120 POTENTIAL. CARBOHYD 342 342 POTENTIAL. CARBOHYD 377 377 POTENTIAL. CARBOHYD 529 529 POTENTIAL. SEQUENCE 588 AA; 65850MW; 1768420 CN; MRAWLLLLAV LATFQTIVRV ASTEDISQRF IAAIAPVAAH IPLASASGSG SGRSGSRSVG ASTSTAGAKA FNRFSEPASF SDSDKSHRSK TNKKPSKSDA NRQFNEVHKP RTDQLENSKN KSKQLVNKPN HNKMAVKEQR SHHKKSHHHR SHQPKQASAS TESHQSSSIE SIFVEEPTLV LDREVASINV PANAKAIIAE QGPSTYSKEA LIKDKLKPDP STYLVEIKSL LSLFNMKRPP KIDRSKIIIP EPMKKLYAEI MGHELDSVNI PKPGLLTKSA NTVRSFTHKD SKIDDRFPHH HRFRLHFDVK SIPADEKLKA AELQLTRDAL SQQVVASRSS ANRTRYQBLV YDITRVGVRG QREPSYLLLD TKTBRLNSTD TVSLDVQPAV DRWLASPQRN YGLLVEVRTV RSLKPAPHHH VRLRRSADEA HERWQHKQPL LFTYTDDGRH DARSIRDVSG GEGGGKGGRN KRHARRPTRR KNHDDTCRRH SLYVDFSDVG WDDWIVAPLG YDAYYCHGKC PFPLADHRNS TNHAVVQTLV NNMNPGKBPK ACCBPTQLDS VAMLYLNDQS TVVLKNYQEM TVVGCGCR [6] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U Definition of substitution matrix • Two-dimensional matrix with score values describing the probability of one amino acid or nucleotide being replaced by another during sequence evolution. [7] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U Scoring matrices for nucleotide sequences • Can be simple: • e.g. positive value for match and zero for mismatch. • frequencies of mutation are equal for all bases. [8] Substitution matrices – Sequence analysis 2006 • Can be more complicated: • taking into account transitions and transversions (e.g. Kimura model) C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U Scoring matrices for nucleotide sequences • Simple model A C T G A 1 0 0 0 C 0 1 0 0 T 0 0 1 0 G 0 0 0 1 • Kimura purines [9] Substitution matrices – Sequence analysis 2006 pyrimidines C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U What is better to align? DNA or protein sequences? 1. Many mutations within DNA are synonymous divergence overestimation [10] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U 2. Evolutionary relationships can be more accurately expressed using a 20×20 amino acid exchange table 3. DNA sequences contain non-coding regions, which should be avoided in homology searches. 4. Still an issue when translating into (six) protein sequences through a codon table. 5. Searching at protein level: frameshifts can occur, leading to stretches of incorrect amino acids and possibly elongation. However, frameshifts normally result in stretches of highly unlikely amino acids. [11] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U So? Rule of thumb: if ORF exists, then align at protein level [12] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U Scoring matrices for amino acid sequences • Are complicated, scoring has to reflect: • Physio-chemical properties of aa’s • Likelihood of residues being substituted among truly homologous sequences • Certain aa with similar properties can be more easily substituted: preserve structure/function • “Disruptive” substitution is less likely to be selected in evolution (e.g. rendering non-functional proteins) [13] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U Scoring matrices for amino acid sequences Main chain [14] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U Example: Cysteines are very common in metal binding motifs cysteine Zn histidine [15] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U Now let’s think about alignments • Lets consider a simple alignment: ungapped global alignment of two (protein) sequences, x and y, of length n. • In scoring this alignment, we would like to assess whether these two sequences have a common ancestor, or whether they are aligned by chance. Pr( x, y | M ) Pr( x, y | R) sequences have common ancestor sequences are aligned by chance • We therefore want our amino acid substitution table (matrix) to score an alignment by estimating this ratio (= improvement over random). • In brief, each substitution score is the log-odds probability that amino acid a could change (mutate) into amino acid b through evolution, based on the constraints of our evolutionary model. [16] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U Target and background probabilities • Background probability If qa is the frequency of amino acid a in one sequence and qb is the frequency of amino acid b in another sequence, then the probability of the alignment being random is given by: Pr( x, y | R) qxi q yi i i A A R S V V K S • Target probability If pab is now the probability that amino acids a and b have derived from a common ancestor, then the probability that the alignment is due to common ancestry is is given by: Pr( x, y | M ) pxi yi i [17] Substitution matrices – Sequence analysis 2006 A A R S V V K S C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U Source of target and background probabilities: high confidence alignments • Target frequencies • The “evolutionary true” alignments allow us to get biologically permissible amino acid mutations and derive the frequencies of observed pairs. These are the TARGET frequencies (20x20 combinations). • Background frequencies • The BACKGROUND frequencies are simply the frequency at which each amino acid type is observed in these “trusted” data sets (20 values). [18] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U Log-odds • Substitution matrices apply logarithmic conversions to describe the probability of amino acid substitutions • The converted values are the so-called log-odds scores • So they are simply the logarithmic ratios of the observed mutation frequency divided by the probability of substitution expected by random chance (target – background) [19] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U Formulas • Odds-ratio of two probabilities pxi yi pxi yi Pr( x, y | M ) i i Pr( x, y | R) qxi q yi qxi q yi i i i • Log-odds probability of an alignment being random is therefore given by p xi yi Pr( x, y | M ) log log qx q y Pr( x, y | R) i i log x log x i i [20] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U Logarithmic functions Logarithms to various bases: red is to base e, green is to base 10, and purple is to base 1.7. Each tick on the axes is one unit. Logarithms of all bases pass through the point (1, 0), because any number raised to the power 0 is 1, and through the points (b, 1) for base b, because any number raised to the power 1 is itself. The curves approach the y axis but do not reach it, due to the singularity of a logarithm at x = 0. http://en.wikipedia.org/wiki/Logarithm [21] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U So… for a given substitution matrix: • a positive score means that the frequency of amino acid substitutions found in the high confidence alignments is greater than would have occurred by random chance • a zero score … that the freq. is equal to that expected by chance • a negative score … that the freq. is less than that expected by chance [22] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U Alignment score • The alignment score S is given by the sum of all amino acid pair substitution scores: Pr( x, y | M ) S sxi , yi log Pr( x, y | R) i • Where the substitution score for any amino acid pair [a,b] is given by: pab sa, b log qa qb [23] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U Alignment score • The total score of an alignment: EAAS VF-T • would be: S s( E ,V ) s( A, F ) (1) s( S , T ) [24] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U Empirical matrices • Are based on surveys of actual amino acid substitutions among related proteins • Most widely used: PAM and BLOSUM [25] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U The PAM series • The first systematic method to derive amino acid substitution matrices was done by Margaret Dayhoff et al. (1978) Atlas of Protein Structure. • These widely used substitution matrices are frequently called Dayhoff, MDM (Mutation Data Matrix), or PAM (Point Accepted Mutation) matrices. • Key idea: trusted alignments of closely related sequences provide information about biologically permissible mutations. [26] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U The PAM design • Step 1. Dayhoff used 71 protein families, made hypothetical phylogenetic trees and recorded the number of observed substitutions (along each branch of the tree) in a 20x20 target matrix. [27] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U • Step 2. The target matrix was then converted to frequencies by dividing each cell (a,b) by the sum of all other substitutions of a. Aab Pr(b | a) Aac c • Step 3. The target matrix was normalized so that the expected number of substitutions covered 1% of the protein (PAM-1). Pr(b | a, t 1) • Step 4. Determine the final substitution matrix. pab P(b | a, t ) s (a, b | t ) log log qa qb qb [28] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U PAM units • One PAM unit is defined as 1% of the amino acids positions that have been changed • E.g. to construct the PAM1 substitution table, a group of closely related sequences with mutation frequencies corresponding to one PAM unit is chosen. One PAM corresponds to about 1 million years of evolutionary time. [29] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U But there is a whole series of matrices: PAM10 … PAM250 • These matrices are extrapolated from PAM1 matrix (by matrix multiplication) A R N A 2 R -2 6 0 0 2 0 -1 2 N D C Q E G D 0 C Q I L K M P S 1 2 -5 4 3 -5 2 W Y V A 0 1 -2 3 5 -2 6 0 0 2 0 -1 2 G 6 5 2 3 M -1 0 -2 -3 -5 -1 -2 -3 -2 2 4 0 6 F -4 -4 -4 -6 -4 -5 -5 -5 -2 1 2 -5 0 0 -5 1 0 -2 0 -1 -1 X 6 0 -2 -3 5 9 P 1 0 -1 -1 -3 0 -2 -3 -1 -2 -5 S 1 0 1 0 0 -1 0 1 -1 -1 -3 0 -2 -3 1 3 1 -1 0 0 -2 -1 0 0 -1 0 -1 -2 0 1 0 -2 2 -4 -7 -8 -5 -7 -7 -3 -5 -2 -3 -4 6 3 W -6 0 -6 -2 -5 17 Y V -3 -4 -2 -4 0 -4 -4 -5 0 -1 -1 -4 -2 7 -5 -3 -3 0 -2 -2 -2 -2 -2 -2 -1 -2 4 2 -2 2 -1 -1 -1 0 0 -6 10 -2 4 N 2 R E 1 -3 -1 1 -3 -2 -3 -3 -4 -6 -2 -3 -4 -2 -1 R A Q 4 0 2 -1 -2 -2 -2 -2 -2 -2 -3 -2 L T T C K 1 F N 1 2 H D 1 1 -3 -1 I G 4 0 -1 H E 4 -2 -4 -4 -5 D 0 C Q I L K M P S 1 2 -5 4 3 -5 2 W Y V A 0 1 -2 3 5 -2 6 0 0 2 0 -1 2 G 6 5 2 3 M -1 0 -2 -3 -5 -1 -2 -3 -2 2 4 0 6 F -4 -4 -4 -6 -4 -5 -5 -5 -2 1 2 -5 0 0 -5 1 0 -2 0 -1 -1 X 6 0 -2 -3 5 9 P 1 0 -1 -1 -3 0 -2 -3 -1 -2 -5 S 1 0 1 0 0 -1 0 1 -1 -1 -3 0 -2 -3 1 3 1 -1 0 0 -2 -1 0 0 -1 0 -1 -2 0 1 0 -2 2 -4 -7 -8 -5 -7 -7 -3 -5 -2 -3 -4 6 3 W -6 0 -6 -2 -5 17 Y V -3 -4 -2 -4 0 -4 -4 -5 0 -1 -1 -4 -2 7 -5 -3 -3 0 -2 -2 -2 -2 -2 -2 -1 -2 4 2 -2 2 -1 -1 -1 0 0 -6 10 -2 4 N 2 R E 1 -3 -1 1 -3 -2 -3 -3 -4 -6 -2 -3 -4 -2 -1 R A Q 4 0 2 -1 -2 -2 -2 -2 -2 -2 -3 -2 L T T C K 1 F N 1 2 H D 1 1 -3 -1 I G 4 0 -1 H E 4 -2 -4 -4 -5 D 0 C Q I L K M P S 1 2 -5 4 3 -5 2 W Y V A 0 1 -2 3 5 -2 6 0 0 2 0 -1 2 G 6 5 2 3 M -1 0 -2 -3 -5 -1 -2 -3 -2 2 4 0 6 F -4 -4 -4 -6 -4 -5 -5 -5 -2 1 2 -5 0 0 -5 1 0 -2 0 -1 -1 6 0 -2 -3 9 P 1 0 -1 -1 -3 0 -2 -3 -1 -2 -5 S 1 0 1 0 0 -1 0 1 -1 -1 -3 0 -2 -3 1 3 1 -1 0 0 -2 -1 0 0 -1 0 -1 -2 0 1 0 -2 = 5 2 -4 -7 -8 -5 -7 -7 -3 -5 -2 -3 -4 6 3 W -6 0 -6 -2 -5 17 Y V -3 -4 -2 -4 0 -4 -4 -5 0 -1 -1 -4 -2 7 -5 -3 -3 0 -2 -2 -2 -2 -2 -2 -1 -2 4 2 -2 2 -1 -1 -1 0 0 -6 10 -2 4 N 2 R E 1 -3 -1 1 -3 -2 -3 -3 -4 -6 -2 -3 -4 -2 -1 R A Q 4 0 2 -1 -2 -2 -2 -2 -2 -2 -3 -2 L T T C K 1 F N 1 2 H D 1 1 -3 -1 I G 4 0 -1 H E 4 -2 -4 -4 -5 D 0 C Q 1 1 2 -5 4 1 3 -5 2 1 -3 -1 I 2 G H I L K M P S 1 -3 -1 0 1 -3 1 -2 3 W Y V 5 6 5 -2 -3 -3 -4 -6 -2 -3 -4 -2 2 -1 3 M -1 0 -2 -3 -5 -1 -2 -3 -2 2 4 0 6 F -4 -4 -4 -6 -4 -5 -5 -5 -2 1 2 -5 0 0 -5 1 0 -2 0 -1 -1 6 0 -2 -3 5 9 P 1 0 -1 -1 -3 S 1 0 1 0 0 -1 0 1 -1 -1 -3 0 -2 -3 1 3 1 -1 0 0 -2 -1 0 0 -1 0 -1 -2 0 1 T T 4 0 2 -1 -2 -2 -2 -2 -2 -2 -3 -2 L K 1 F 4 0 -1 H E 4 -2 -4 -4 -5 0 -2 -3 -1 -2 -5 0 -2 2 -4 -7 -8 -5 -7 -7 -3 -5 -2 -3 -4 6 3 W -6 0 -6 -2 -5 17 Y V -3 -4 -2 -4 0 -4 -4 -5 0 -1 -1 -4 -2 7 -5 -3 -3 0 -2 -2 -2 -2 -2 -2 -1 -2 4 2 -2 2 -1 -1 -1 0 0 -6 10 -2 4 Multiply Matrices N times to make PAM ‘N’; then take the Log • So: a PAM is a relative measure of evolutionary distance • 1 PAM = 1 accepted mutation per 100 amino acids • 250 PAM = 250 mutations per 100 amino acids, so 2.5 accepted mutations per amino acid [30] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U PAM numbers vs. observed am.ac. mutational rates PAM Number Observed Mutation Rate (%) Sequence Identity (%) 0 0 100 1 1 99 30 25 75 80 50 50 110 40 60 200 75 25 250 80 20 Note Think about intermediate “substitution” steps … [31] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U The PAM250 matrix A 2 R -2 6 N 0 0 2 D 0 -1 2 4 C -2 -4 -4 -5 12 Q 0 1 1 2 -5 4 E 0 -1 1 3 -5 2 4 G 1 -3 0 1 -3 -1 0 2 1 -3 1 -2 H -1 2 3 5 6 I -1 -2 -2 -2 -2 -2 -2 -3 -2 5 L -2 -3 -3 -4 -6 -2 -3 -4 -2 2 1 0 -5 1 0 -2 W- R exchange is too large (due to paucity of data) 6 K -1 3 M -1 0 -2 -3 -5 -1 -2 -3 -2 2 4 0 6 F -4 -4 -4 -6 -4 -5 -5 -5 -2 1 2 -5 0 5 9 P 1 0 -1 -1 -3 S 1 0 1 0 0 -1 0 1 -1 -1 -3 0 -2 -3 1 2 T 1 -1 0 0 -2 -1 0 0 -1 0 -1 -3 0 1 W -6 0 -1 -1 0 -2 -3 0 -2 -3 -1 -2 -5 0 -2 2 -4 -7 -8 -5 -7 -7 -3 -5 -2 -3 -4 Y -3 -4 -2 -4 0 -4 -4 -5 0 -1 -1 -4 -2 0 -6 -2 -5 17 7 -5 -3 -3 B 0 -1 2 3 -4 1 2 0 1 -2 -3 1 -2 -5 -1 0 0 -5 -3 -2 2 Z 0 0 1 3 -5 3 3 -1 2 -2 -3 0 -2 -5 0 -1 -6 -4 -2 2 A R N D Q E H I L K 2 -1 -1 -1 0 10 0 -2 -2 -2 -2 -2 -2 -1 -2 G 2 -2 3 V C 4 6 M F 0 P [32] Substitution matrices – Sequence analysis 2006 S 0 -6 -2 T W 4 Y V 3 B Z C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U PAM model • The scores derived through the PAM model are an accurate description of the information content (or the relative entropy) of an alignment (Altschul, 1991). • PAM1 corresponds to about 1 million years of evolution. • PAM120 has the largest information content of the PAM matrix series: “best” for general alignment. • PAM250 is the traditionally most popular matrix: “best” for detecting distant sequence similarity. [33] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U Summary Dayhoff’s PAM-matrices • Derived from global alignments of closely related sequences. • Matrices for greater evolutionary distances are extrapolated from those for smaller ones. • The number with the matrix (PAM40, PAM100) refers to the evolutionary distance; greater numbers are greater distances. • Attempts to extend Dayhoff's methodology or re-apply her analysis using databases with more examples: • Jones, Thornton and coworkers used the same methodology as Dayhoff but with modern databases (CABIOS 8:275) • Gonnett and coworkers (Science 256:1443) used a slightly different (but theoretically equivalent) methodology [34] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U The BLOSUM series • BLOSUM stands for: BLOcks SUbstitution Matrices • Created by Steve Henikoff and Jorja Henikoff (PNAS 89:10915). • Derived from local, un-gapped alignments of distantly related sequences. • All matrices are directly calculated; no extrapolations are used. • Again: compare observed freqs of each pair to expected freqs Then: Log-odds matrix. [35] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U The Blocks database • The Blocks Database contains multiple alignments of conserved regions in protein families. • Blocks are multiply aligned un-gapped segments corresponding to the most highly conserved regions of proteins. • The blocks for the BLOCKS database are made automatically by looking for the most highly conserved regions in groups of proteins represented in the PROSITE database. These blocks are then calibrated against the SWISS-PROT database to obtain a measure of the random distribution of matches. It is these calibrated blocks that make up the BLOCKS database. • The database can be searched to classify protein and nucleotide sequences. [36] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U The Blocks database Gapless alignment blocks [37] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U The BLOSUM series • BLOSUM30, 35, 40, 45, 50, 55, 60, 62, 65, 70, 75, 80, 85, 90. • The number after the matrix (BLOSUM62) refers to the minimum percent identity of the blocks (in the BLOCKS database) used to construct the matrix (all blocks have >=62% sequence identity); • No extrapolations are made in going to higher evolutionary distances • High number - closely related sequences Low number - distant sequences • BLOSUM62 is the most popular: best for general alignment. [38] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U The log-odds matrix for BLOSUM62 [39] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U PAM versus BLOSUM • Based on an explicit evolutionary model • Based on empirical frequencies • Derived from small, closely related proteins with ~15% divergence • Uses much larger, more diverse set of protein sequences (30-90% ID) • Higher PAM numbers to detect more remote sequence similarities • Lower BLOSUM numbers to detect more remote sequence similarities • Errors in PAM 1 are scaled 250X in PAM 250 • Errors in BLOSUM arise from errors in alignment [40] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U Comparing exchange matrices • To compare amino acid exchange matrices, the "Entropy" value can be used. This is a relative entropy value (H) which describes the amount of information available per aligned residue pair. H sij log 2 (sij / pi p j ) [41] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U Evolution and Matrix “landscape” • Recent evolution identity matrix [42] Substitution matrices – Sequence analysis 2006 • Ancient evolution convergence to random model C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U A note on reliability • All these matrices are designed using standard evolutionary models. • Circular problem alignment matrix • It is important to understand that evolution is not the same for all proteins, not even for the same regions of proteins. [43] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U … • No single matrix performs best on all sequences. Some are better for sequences with few gaps, and others are better for sequences with fewer identical amino acids. • Therefore, when aligning sequences, applying a general model to all cases is not ideal. Rather, re-adjustment can be used to make the general model better fit the given data. [44] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U Pair-wise alignment quality versus sequence identity • Vogt et al., JMB 249, 816-831,1995 Pairwise alignments were made of sequence pairs for which the ‘true’alignment was known from 3Dstructural information, so the correctness of the alignments could be checked Twilight zoneanalysis 2006 [45] Substitution matrices – Sequence C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U Take-home messages - 1 • If ORF exists, then align at protein level. • Amino acid substitution matrices reflect the log-odds ratio between the evolutionary and random model and can therefore help in determining homology via the alignment score. • The evolutionary and random models depend on generalized data sets used to derive them. This not an ideal solution. [46] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U Take-home messages - 2 • Apart from the PAM and BLOSUM series, a great number of further matrices have been developed. • Matrices have been made based on DNA, protein structure, information content, etc. • For local alignment, BLOSUM62 is often superior; for distant (global) alignments, BLOSUM50, GONNET, or (still) PAM250 work well. • Remember that gap penalties are always a problem: unlike the matrices themselves, there is no formal way to calculate their values -- you can follow recommended settings, but these are based on trial and error and not on a formal framework. [47] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U C E N T R E F O R I N T E G R A T I V E B I O I N F O R M A T I C S V U Introduction to bioinformatics 2008 Multiple Sequence Alignment (I) [48] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U Biological definitions for related sequences Homologues are similar sequences in two different organisms that have been derived from a common ancestor sequence. Homologues can be described as either orthologues or paralogues. Orthologues are similar sequences in two different organisms that have arisen due to a speciation event. Orthologs typically retain identical or similar functionality throughout evolution. Paralogues are similar sequences within a single organism that have arisen due to a gene duplication event. Xenologues are similar sequences that do not share the same evolutionary origin, but rather have arisen out of horizontal transfer events through symbiosis, viruses, etc. Vertical transfer is caused by (normal) heredity [49] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U So this means … Source: http://www.ncbi.nlm.nih.gov/Education/BLASTinfo/Orthology.html [50] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U Information content of a multiple alignment • Sequences can be conserved across species and perform similar or identical functions – hold information about which regions have high mutation rates over evolutionary time and which are evolutionarily conserved – identification of regions or domains that are critical to functionality • Sequences can be mutated or rearranged to perform an altered function – which changes in the sequences have caused a change in the functionality [51] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U Multiple alignment idea • Take three or more related sequences and align them so that the greatest number of similar characters are aligned in the same column of the alignment. Ideally, the sequences are orthologous, but often include paralogues. [52] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U Scoring a multiple alignment • You can score a multiple alignment by taking all the pairs of aligned sequences and add up the pairwise scores: Sa,b = s(a , b ) - l i j k Nk gp(k ) •This is referred to as the Sumof-Pairs score [53] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U Multiple sequence alignment Why? • It is the most important means to assess relatedness of a set of sequences • Gain information about the structure/function of a query sequence (conservation patterns) • Construct a phylogenetic tree • Putting together a set of sequenced fragments (Fragment assembly) • Many bioinformatics methods depend on it (e.g. secondary/tertiary structure prediction) [54] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U Information content of a multiple alignment [55] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U What to ask yourself • How do we get a multiple alignment? (three or more sequences) • What is our aim? –Do we go for max accuracy? –Least computational time? –Or the best compromise? • What do we want to achieve each time? [56] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U Multiple alignment methods Multi-dimensional dynamic programming > extension of pairwise sequence alignment. Progressive alignment > incorporates phylogenetic information to guide the alignment process Iterative alignment > correct for problems with progressive alignment by repeatedly realigning subgroups of sequence [57] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U Exhaustive & Heuristic algorithms • Exhaustive approaches – Examine all possible aligned positions simultaneously – Look for the optimal solution by (multi-dimensional) DP – Very (very) slow • Heuristic approaches • Strategy to find a near-optimal solution (by using rules of thumb) • Shortcuts are taken by reducing the search space according to certain criteria • Much faster [58] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U Simultaneous multiple alignment Multi-dimensional dynamic programming Combinatorial explosion DP using two sequences of length n n2 comparisons Number of comparisons increases exponentially i.e. nN where n is the length of the sequences, and N is the number of sequences Impractical even for small numbers of short sequences [59] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U Sequence-sequence alignment by Dynamic Programming sequence sequence [60] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U Multi-dimensional dynamic programming (Murata et al., 1985) Sequence 2 Sequence 1 [61] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U The MSA approach Lipman et al. 1989 • Key idea: restrict the computational costs by determining a minimal region within the n-dimensional matrix that contains the optimal path [62] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U The MSA method in detail Let’s consider 3 sequences Calculate all pair-wise alignment scores by Dynamic programming 3. Use the scores to predict a tree 4. Produce a heuristic multiple align. based on the tree (quick & dirty) 5. Calculate maximum cost for each sequence pair from multiple alignment (upper bound) & determine paths with < costs. 6. Determine spatial positions that must be calculated to obtain the optimal alignment (intersecting areas or ‘hypersausage’ around matrix diagonal) 7. Perform multi-dimensional DP Note Redundancy caused by highly correlated sequences is avoided 1. 2. 1. 2. [63] Substitution matrices – Sequence analysis 2006 3.1 3 4.2 5. 1 . . 3 1 2 1 3 1 3 2 2 . . . 1 3 6. . C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U 2 3 The DCA (Divide-and-Conquer) approach Stoye et al. 1997 • Each sequence is cut in two behind a suitable cut position somewhere close to its midpoint. • This way, the problem of aligning one family of (long) sequences is divided into the two problems of aligning two families of (shorter) sequences. • This procedure is re-iterated until the sequences are sufficiently short. • Optimal alignment by MSA. • Finally, the resulting short alignments are concatenated. [64] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U So in effect … [65] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U Multiple alignment methods Multi-dimensional dynamic programming > extension of pairwise sequence alignment. Progressive alignment > incorporates phylogenetic information to guide the alignment process Iterative alignment > correct for problems with progressive alignment by repeatedly realigning subgroups of sequence [66] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U The progressive alignment method Underlying idea: usually we are interested in aligning families of sequences that are evolutionary related. Principle: construct an approximate phylogenetic tree for the sequences to be aligned and than to build up the alignment by progressively adding sequences in the order specified by the tree. But before going into details, some notices of multiple alignment profiles … [67] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U Making a guide tree 1 2 1 Score 1-2 Score 1-3 3 4 5 Score 4-5 Similarity criterion Scores 5× 5 Pairwise alignments (allagainstall) Similarity matrix Guide tree [68] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U Progressive multiple alignment 1 2 1 Score 1-2 Score 1-3 3 4 5 Score 4-5 Scores 5× 5 Scores to distances Guide tree [69] Substitution matrices – Sequence analysis 2006 Similarity matrix Iteration possibilities Multiple alignment C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U General progressive multiple alignment technique (follow generated tree)Align these two d 1 3 1 3 2 5 These two are aligned 1 3 2 5 root 1 3 2 5 [70] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U PRALINE progressive strategy d 1 3 1 3 2 1 3 2 5 4 1 3 2 5 4 N T R E F O R I N(sequence-sequence, T E G R A T I V E At each step, Praline checks which of the pair-wiseC Ealignments B I O I N F O RM A T I C S V U sequence-profile, profile-profile) [71] Substitution matrices – Sequence analysis 2006has the highest score – this one gets selected Progressive alignment strategy All individual pairwise alignment and construction of distance matrix A B C D E A A — B C D B 11 — C 20 30 D 27 36 9 — E 30 33 20 27 E — — Calculating a guide tree; C & D the closest pair; A & B the next closest pair Figure adapted from Xiong, J. “Essential Bioinformatics” [72] Substitution matrices – Sequence analysis 2006 A C B D C D A B E Aligning C/D and A/B separately Cusing dynamic E N T R E F O R I N T E G R A T programming B I O I N F O R M A T I V E I C S V U But how can we align blocks of sequences ? A B C D E C D ? A B • The dynamic programming algorithm performs well for pairwise alignment (two axes). • So we should try to treat the blocks as a “single” sequence … [73] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U How to represent a block of sequences ? • Historically: consensus sequence single sequence that best represents the amino acids observed at each alignment position. • Modern methods: alignment profile representation that retains the information about frequencies of amino acids observed at each alignment position. [74] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U Consensus sequence Sequence 1 F A T N M G T S D P P T H T R L R K L V S Q Sequence 2 F V T N M N N S D G P T H T K L R K L V S T Consensus F * T N M * * S D * P T H T * L R K L V S * • Problem: loss of information • For larger blocks of sequences it “punishes” more distant members [75] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U Alignment profiles • Advantage: full representation of the sequence alignment (more information retained) • Not only used in alignment methods, but also in sequence-database searching (to detect distant homologues) • Also called PSSM (Position-specific scoring matrix) [76] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U Multiple alignment profiles Core region Gapped region Core region frequencies i A C D W Y - fA.. fA.. fA.. fC.. fC.. fC.. fD.. fD.. fD.. fW.. fW.. fW.. fY.. fY.. fY.. Gapo, gapx Gapo, gapx Gapo, gapx Position-dependent gap penalties [77] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U Profile building Example: each aa is represented as a frequency and gap penalties as weights. i A 0.5 C 0 D 0 W 0 Y 0.5 0.3 0.1 0 0.3 0.3 0 0.5 0.2 0.1 0.2 Gap penalties 1.0 0.5 1.0 Position dependent gap penalties C E N T R E F O R I N T E G R A T I V E [78] Substitution matrices – Sequence analysis 2006 B I O I N F O RM A T I C S V U Profile-sequence alignment sequence ACD……VWY [79] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U Sequence to profile alignment A A V V L 0.4 A 0.2 L 0.4 V Score of amino acid L in a sequence that is aligned against this profile position: Score = 0.4 * s(L, A) + 0.2 * s(L, L) + 0.4 * s(L, V) [80] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U Profile-profile alignment profile A C D . . Y profile ACD……VWY [81] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U Profile to profile alignment 0.4 A 0.75 G 0.2 L 0.25 S 0.4 V Match score of these two alignment columns using the a.a frequencies at the corresponding profile positions: Score = 0.4*0.75*s(A,G) + 0.2*0.75*s(L,G) + 0.4*0.75*s(V,G) + + 0.4*0.25*s(A,S) + 0.2*0.25*s(L,S) + 0.4*0.25*s(V,S) s(x,y) is value in amino acid exchange matrix (e.g. PAM250, Blosum62) for amino acid pair (x,y) [82] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U So, for scoring profiles … Think of sequence-sequence alignment. Same principles but more information for each position. Reminder: The sequence pair alignment score S comes from the sum of the positional scores M(aai,aaj) (i.e. the substitution matrix values at each alignment position minus penalties if applicable) Profile alignment scores are exactly the same, but the positional scores are more complex [83] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U General function for profile-profile scoring Profile 1 A C D . . Y Profile 2 A C D . . Y At each position (column) we have different residue frequencies for each amino acid (rows) SO: Instead of saying S=M(aa1, aa2) (one residue pair) For comparing two profile positions we take: 20 20 S faai faaj M(aai , aaj ) i j [84] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U Progressive alignment strategy 1. 2. 3. 4. Perform pair-wise alignments of all of the sequences (all against all); Use the alignment scores to make a similarity (or distance) matrix Use that matrix to produce a guide tree; Align the sequences successively, guided by the order and relationships indicated by the tree. Methods: Biopat (Hogeweg and Hesper 1984 -- first integrated method ever) MULTAL (Taylor 1987) DIALIGN (1&2, Morgenstern 1996) PRRP (Gotoh 1996) ClustalW (Thompson et al 1994) PRALINE (Heringa 1999) T Coffee (Notredame 2000) POA (Lee 2002) MUSCLE (Edgar 2004) PROBSCONS (Do, 2005) [85] Substitution matrices – Sequence analysis 2006 C E N T R E F O R I N T E G R A T I V E B I O I N F O RM A T I C S V U