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[1] Substitution matrices – Sequence analysis 2006

Substitution Matrices

Introduction to bioinformatics 2007

Lecture 8

CENTR

FORINTEGRATIVE

BIOINFORMATICSVU

E

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[2] Substitution matrices – Sequence analysis 2006

Sequence AnalysisFinding relationships between genes and gene products of different species, including those at large evolutionary distances

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[3] Substitution matrices – Sequence analysis 2006

ArchaeaDomain 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.

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[4] Substitution matrices – Sequence analysis 2006

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 primitive and do not have a nucleus.

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[5] Substitution matrices – Sequence analysis 2006

Example of nucleotide sequence database entry for Genbank

LOCUS DRODPPC 4001 bp INV 15-MAR-1990DEFINITION D.melanogaster decapentaplegic gene complex (DPP-C), complete cds.ACCESSION M30116KEYWORDS .SOURCE D.melanogaster, cDNA to mRNA.ORGANISM Drosophila melanogaster

Eurkaryote; mitochondrial eukaryotes; Metazoa; Arthropoda;Tracheata; Insecta; Pterygota; Diptera; Brachycera; Muscomorpha;Ephydroidea; Drosophilidae; Drosophilia.

REFER�ENCE 1 (bases 1 to 4001)AUTHORS Padgett, R.W., St Johnston, R.D. and Gelbart, W.M.TITLE A transcript from a Drosophila pattern gene predicts a protein

homologous to the transforming growth factor-beta familyJOURNAL Nature 325, 81-84 (1987)MEDLINE 87090408

COMMENT The initiation codon could be at either 1188-1190 or 1587-1589FEATURES Location/Qualifiers

source 1..4001/organism=“Drosophila melanogaster”/db_xref=“taxon:7227”

mRNA <1..3918/gene=“dpp”/note=“decapentaplegic protein mRNA”/db_xref=“FlyBase:FBgn0000490”

gene 1..4001/note=“decapentaplegic”/gene=“dpp”/allele=“”/db_xref=“FlyBase:FBgn0000490”

CDS 1188..2954/gene=“dpp”/note=“decapentaplegic protein (1188 could be 1587)”/codon_start=1/db_xref=“FlyBase:FBgn0000490”/db_xref=“PID:g157292”/translation=“MRAWLLLLAVLATFQTIVRVASTEDISQRFIAAIAPVAAHIPLASASGSGSGRSGSRSVGASTSTALAKAFNPFSEPASFSDSDKSHRSKTNKKPSKSDANR……………………LGYDAYYCHGKCPFPLADHFNSTNAVVQTLVNNMNPGKVPKACCVPTQLDSVAMLYLNDQSTBVVLKNYQEMTBBGCGCR”

BASE COUNT 1170 a 1078 c 956 g 797 tORIGIN

1 gtcgttcaac agcgctgatc gagtttaaat ctataccgaa atgagcggcg gaaagtgagc61 cacttggcgt gaacccaaag ctttcgagga aaattctcgg acccccatat acaaatatcg

121 gaaaaagtat cgaacagttt cgcgacgcga agcgttaaga tcgcccaaag atctccgtgc181 ggaaacaaag aaattgaggc actattaaga gattgttgtt gtgcgcgagt gtgtgtcttc241 agctgggtgt gtggaatgtc aactgacggg ttgtaaaggg aaaccctgaa atccgaacgg301 ccagccaaag caaataaagc tgtgaatacg aattaagtac aacaaacagt tactgaaaca361 gatacagatt cggattcgaa tagagaaaca gatactggag atgcccccag aaacaattca421 attgcaaata tagtgcgttg cgcgagtgcc agtggaaaaa tatgtggatt acctgcgaac481 cgtccgccca aggagccgcc gggtgacagg tgtatccccc aggataccaa cccgagccca541 gaccgagatc cacatccaga tcccgaccgc agggtgccag tgtgtcatgt gccgcggcat601 accgaccgca gccacatcta ccgaccaggt gcgcctcgaa tgcggcaaca caattttcaa

………………………….3841 aactgtataa acaaaacgta tgccctataa atatatgaat aactatctac atcgttatgc3901 gttctaagct aagctcgaat aaatccgtac acgttaatta atctagaatc gtaagaccta3961 acgcgtaagc tcagcatgtt ggataaatta atagaaacga g

//

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[6] Substitution matrices – Sequence analysis 2006

Example of protein sequence database entry forSWISS-PROT (now UNIPROT)

ID DECA_DROME STANDARD; PRT; 588AA.AC P07713;DT 01-APR-1988 (REL. 07, CREATED)DT 01-APR-1988 (REL. 07, LAST SEQUENCE UPDATE)DT 01-FEB-1995 (REL. 31, LAST ANNOTATION UPDATE)DE DECAPENTAPLEGIC PROTEIN PRECURSOR (DPP-C PROTEIN).GN DPP.OS DROSOPHILA MELANOGASTER (FRUIT FLY).OC EUKARYOTA; METAZOA; ARTHROPODA; INSECTA; DIPTERA.RN [1]RP SEQUENCE FROM N.A.RM 87090408RA PADGETT R.W., ST JOHNSTON R.D., GELBART W.M.;RL NATURE 325:81-84 (1987)RN [2]RP CHARACTERIZATION, AND SEQUENCE OF 457-476.RM 90258853RA PANGANIBAN G.E.F., RASHKA K.E., NEITZEL M.D., HOFFMANN F.M.;RL MOL. CELL. BIOL. 10:2669-2677(1990).CC -!- FUNCTION: DPP IS REQUIRED FOR THE PROPER DEVELOPMENT OF THECC EMBRYONIC DOORSAL HYPODERM, FOR VIABILITY OF LARVAE AND FOR CELLCC VIABILITY OF THE EPITHELIAL CELLS IN THE IMAGINAL DISKS.CC -!- SUBUNIT: HOMODIMER, DISULFIDE-LINKED.CC -!- SIMILARITY: TO OTHER GROWTH FACTORS OF THE TGF-BETA FAMILY.DR EMBL; M30116; DMDPPC.DR PIR; A26158; A26158.DR HSSP; P08112; 1TFG.DR FLYBASE; FBGN0000490; DPP.DR PROSITE; PS00250; TGF_BETA.KW GROWTH FACTOR; DIFFERENTIATION; SIGNAL.FT SIGNAL 1 ? POTENTIAL.FT PROPEP ? 456FT CHAIN 457 588 DECAPENTAPLEGIC PROTEIN.FT DISULFID 487 553 BY SIMILARITY.FT DISULFID 516 585 BY SIMILARITY.FT DISULFID 520 587 BY SIMILARITY.FT DISULFID 552 552 INTERCHAIN (BY SIMILARITY).FT CARBOHYD 120 120 POTENTIAL.FT CARBOHYD 342 342 POTENTIAL.FT CARBOHYD 377 377 POTENTIAL.FT CARBOHYD 529 529 POTENTIAL.SQ SEQUENCE 588 AA; 65850MW; 1768420 CN;

MRAWLLLLAV LATFQTIVRV ASTEDISQRF IAAIAPVAAH IPLASASGSG SGRSGSRSVGASTSTAGAKA FNRFSEPASF SDSDKSHRSK TNKKPSKSDA NRQFNEVHKP RTDQLENSKNKSKQLVNKPN HNKMAVKEQR SHHKKSHHHR SHQPKQASAS TESHQSSSIE SIFVEEPTLVLDREVASINV PANAKAIIAE QGPSTYSKEA LIKDKLKPDP STYLVEIKSL LSLFNMKRPPKIDRSKIIIP EPMKKLYAEI MGHELDSVNI PKPGLLTKSA NTVRSFTHKD SKIDDRFPHHHRFRLHFDVK SIPADEKLKA AELQLTRDAL SQQVVASRSS ANRTRYQBLV YDITRVGVRGQREPSYLLLD TKTBRLNSTD TVSLDVQPAV DRWLASPQRN YGLLVEVRTV RSLKPAPHHHVRLRRSADEA HERWQHKQPL LFTYTDDGRH DARSIRDVSG GEGGGKGGRN KRHARRPTRRKNHDDTCRRH SLYVDFSDVG WDDWIVAPLG YDAYYCHGKC PFPLADHRNS TNHAVVQTLVNNMNPGKBPK ACCBPTQLDS VAMLYLNDQS TVVLKNYQEM TVVGCGCR

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[7] Substitution matrices – Sequence analysis 2006

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.

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[8] Substitution matrices – Sequence analysis 2006

Scoring matrices for nucleotide sequences

• Can be more complicated:• taking into account

transitions and transversions(e.g. Kimura model)

• Can be simple:• e.g. positive value

for match and zero for mismatch.

• frequencies of mutation are equal for all bases.

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[9] Substitution matrices – Sequence analysis 2006

Scoring matrices for nucleotide sequences

• Kimura• Simple model

1000G

0100T

0010C

0001A

GTCA

purines pyrimidines

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[10] Substitution matrices – Sequence analysis 2006

What is better to align?DNA or protein sequences?

1. Many mutations within DNA are synonymous ⇒ divergence overestimation

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[11] Substitution matrices – Sequence analysis 2006

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, frameshiftsnormally result in stretches of highly unlikely amino acids.

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[12] Substitution matrices – Sequence analysis 2006

So?Rule of thumb:

⇒ if ORF exists, then align at protein level

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[13] Substitution matrices – Sequence analysis 2006

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. non functional proteins)

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[14] Substitution matrices – Sequence analysis 2006

Scoring matrices for amino acid sequences

Main chain

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[15] Substitution matrices – Sequence analysis 2006

Example: Cysteines are very common in metal binding motifs

cysteine

histidineZn

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[16] Substitution matrices – Sequence analysis 2006

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 bychance.

• 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.

← sequences have common ancestor← sequences are aligned by chance)|,Pr(

)|,Pr(

Ryx

Myx

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[17] Substitution matrices – Sequence analysis 2006

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:

• Target probabilityIf 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:

ii yi

xi

qqRyx ∏∏=)|,Pr(SKVVSRAA

SKVVSRAA

ii yxi

pMyx ∏=)|,Pr(

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[18] Substitution matrices – Sequence analysis 2006

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).

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[19] Substitution matrices – Sequence analysis 2006

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)

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[20] Substitution matrices – Sequence analysis 2006

Formulas• Odds-ratio of two probabilities

ii

ii

ii

ii

yxi

yxi

yi

xi

yxi

qq

p

qq

p

Ryx

Myx

∏∏

=∏∏∏

=)|,Pr(

)|,Pr(

• Log-odds probability of an alignment being random is therefore given by

∑

=

ii

ii

yx

yx

qq

p

Ryx

Myxlog

)|,Pr(

)|,Pr(log

∑=∏ iixx loglog

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[21] Substitution matrices – Sequence analysis 2006

Logarithmic functionsLogarithms 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

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[22] Substitution matrices – Sequence analysis 2006

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 to that expected by chance

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[23] Substitution matrices – Sequence analysis 2006

Alignment score• The alignment score S is given by the sum of all

amino acid pair substitution scores:

( ))|,Pr(

)|,Pr(log,

Ryx

MyxyxsS

iii ==∑

• Where the substitution score for any amino acid pair [a,b] is given by:

( )ba

ab

qq

pbas log, =

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[24] Substitution matrices – Sequence analysis 2006

Alignment score• The total score of an alignment:

• would be:

),()1(),(),( TSsFAsVEsS +++= γ

EAASVF-T

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[25] Substitution matrices – Sequence analysis 2006

Empirical matrices• Are based on surveys of actual amino

acid substitutions among related proteins

• Most widely used: PAM and BLOSUM

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[26] Substitution matrices – Sequence analysis 2006

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.

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[27] Substitution matrices – Sequence analysis 2006

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.

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[28] Substitution matrices – Sequence analysis 2006

• Step 2. The target matrix was then converted to frequencies by dividing each cell (a,b) over the sum of all other substitutions of a.

• Step 3. The target matrix was normalized so that the expected number of substitutions covered 1% of the protein (PAM-1).

• Step 4. Determine the final substitution matrix.

∑=c

ac

ab

A

Aab )|Pr(

)1,|Pr( =tab

bba

ab

q

tabP

qq

ptbas

),|(loglog)|,( ==

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[29] Substitution matrices – Sequence analysis 2006

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

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[30] Substitution matrices – Sequence analysis 2006

But there is a whole series of matrices: PAM10 … PAM250• These matrices are extrapolated from PAM1 matrix

(by matrix multiplication)

• 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

A R N D C Q E G H I L K M F P S T W Y V

A 2

R -2 6

N 0 0 2

D 0 -1 2 4

C -2 -4 -4 -5 4

Q 0 1 1 2 -5 4

E 0 -1 1 3 -5 2 4

G 1 -3 0 1 -3 -1 0 5

H -1 2 2 1 -3 3 1 -2 6

I -1 -2 -2 -2 -2 -2 -2 -3 -2 5

L -2 -3 -3 -4 -6 -2 -3 -4 -2 2 6

K -1 3 1 0 -5 1 0 -2 0 -2 -3 5

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 9

P 1 0 -1 -1 -3 0 -1 -1 0 -2 -3 -1 -2 -5 6

S 1 0 1 0 0 -1 0 1 -1 -1 -3 0 -2 -3 1 3

T 1 -1 0 0 -2 -1 0 0 -1 0 -2 0 -1 -2 0 1 3

W -6 2 -4 -7 -8 -5 -7 -7 -3 -5 -2 -3 -4 0 -6 -2 -5 17

Y -3 -4 -2 -4 0 -4 -4 -5 0 -1 -1 -4 -2 7 -5 -3 -3 0 10V 0 -2 -2 -2 -2 -2 -2 -1 -2 4 2 -2 2 -1 -1 -1 0 -6 -2 4

A R N D C Q E G H I L K M F P S T W Y V

A 2

R -2 6

N 0 0 2

D 0 -1 2 4

C -2 -4 -4 -5 4

Q 0 1 1 2 -5 4

E 0 -1 1 3 -5 2 4

G 1 -3 0 1 -3 -1 0 5

H -1 2 2 1 -3 3 1 -2 6

I -1 -2 -2 -2 -2 -2 -2 -3 -2 5

L -2 -3 -3 -4 -6 -2 -3 -4 -2 2 6

K -1 3 1 0 -5 1 0 -2 0 -2 -3 5

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 9

P 1 0 -1 -1 -3 0 -1 -1 0 -2 -3 -1 -2 -5 6

S 1 0 1 0 0 -1 0 1 -1 -1 -3 0 -2 -3 1 3

T 1 -1 0 0 -2 -1 0 0 -1 0 -2 0 -1 -2 0 1 3

W -6 2 -4 -7 -8 -5 -7 -7 -3 -5 -2 -3 -4 0 -6 -2 -5 17

Y -3 -4 -2 -4 0 -4 -4 -5 0 -1 -1 -4 -2 7 -5 -3 -3 0 10V 0 -2 -2 -2 -2 -2 -2 -1 -2 4 2 -2 2 -1 -1 -1 0 -6 -2 4

A R N D C Q E G H I L K M F P S T W Y V

A 2

R -2 6

N 0 0 2

D 0 -1 2 4

C -2 -4 -4 -5 4

Q 0 1 1 2 -5 4

E 0 -1 1 3 -5 2 4

G 1 -3 0 1 -3 -1 0 5

H -1 2 2 1 -3 3 1 -2 6

I -1 -2 -2 -2 -2 -2 -2 -3 -2 5

L -2 -3 -3 -4 -6 -2 -3 -4 -2 2 6

K -1 3 1 0 -5 1 0 -2 0 -2 -3 5

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 9

P 1 0 -1 -1 -3 0 -1 -1 0 -2 -3 -1 -2 -5 6

S 1 0 1 0 0 -1 0 1 -1 -1 -3 0 -2 -3 1 3

T 1 -1 0 0 -2 -1 0 0 -1 0 -2 0 -1 -2 0 1 3

W -6 2 -4 -7 -8 -5 -7 -7 -3 -5 -2 -3 -4 0 -6 -2 -5 17

Y -3 -4 -2 -4 0 -4 -4 -5 0 -1 -1 -4 -2 7 -5 -3 -3 0 10V 0 -2 -2 -2 -2 -2 -2 -1 -2 4 2 -2 2 -1 -1 -1 0 -6 -2 4

A R N D C Q E G H I L K M F P S T W Y V

A 2

R -2 6

N 0 0 2

D 0 -1 2 4

C -2 -4 -4 -5 4

Q 0 1 1 2 -5 4

E 0 -1 1 3 -5 2 4

G 1 -3 0 1 -3 -1 0 5

H -1 2 2 1 -3 3 1 -2 6

I -1 -2 -2 -2 -2 -2 -2 -3 -2 5

L -2 -3 -3 -4 -6 -2 -3 -4 -2 2 6

K -1 3 1 0 -5 1 0 -2 0 -2 -3 5

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 9

P 1 0 -1 -1 -3 0 -1 -1 0 -2 -3 -1 -2 -5 6

S 1 0 1 0 0 -1 0 1 -1 -1 -3 0 -2 -3 1 3

T 1 -1 0 0 -2 -1 0 0 -1 0 -2 0 -1 -2 0 1 3

W -6 2 -4 -7 -8 -5 -7 -7 -3 -5 -2 -3 -4 0 -6 -2 -5 17

Y -3 -4 -2 -4 0 -4 -4 -5 0 -1 -1 -4 -2 7 -5 -3 -3 0 10V 0 -2 -2 -2 -2 -2 -2 -1 -2 4 2 -2 2 -1 -1 -1 0 -6 -2 4

X X =Multiply Matrices N times to make PAM ‘ N’; then take the Log

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[31] Substitution matrices – Sequence analysis 2006

PAM numbers vs. observed am.ac. mutational rates

2080250

2575200

6040110

505080

752530

9911

10000

Sequence Identity (%)

Observed Mutation Rate (%)

PAM Number

Note Think about intermediate “substitution” steps …

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[32] Substitution matrices – Sequence analysis 2006

The PAM250 matrixA 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 5

H -1 2 2 1 -3 3 1 -2 6

I -1 -2 -2 -2 -2 -2 -2 -3 -2 5

L -2 -3 -3 -4 -6 -2 -3 -4 -2 2 6

K -1 3 1 0 -5 1 0 -2 0 -2 -3 5

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 9

P 1 0 -1 -1 -3 0 -1 -1 0 -2 -3 -1 -2 -5 6

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 -2 0 -1 -3 0 1 3

W -6 2 -4 -7 -8 -5 -7 -7 -3 -5 -2 -3 -4 0 -6 -2 -5 17

Y -3 -4 -2 -4 0 -4 -4 -5 0 -1 -1 -4 -2 7 -5 -3 -3 0 10

V 0 -2 -2 -2 -2 -2 -2 -1 -2 4 2 -2 2 -1 -1 -1 0 -6 -2 4

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 0 -1 -6 -4 -2 2 3

A R N D C Q E G H I L K M F P S T W Y V B Z

W- R exchange is too large (due to paucity of data)

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[33] Substitution matrices – Sequence analysis 2006

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 thePAM matrix series: “best” for general alignment.

• PAM250 is the traditionally most popular matrix:“best” for detecting distant sequence similarity.

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[34] Substitution matrices – Sequence analysis 2006

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

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[35] Substitution matrices – Sequence analysis 2006

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 freqsThen: Log-odds matrix.

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[36] Substitution matrices – Sequence analysis 2006

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.

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[37] Substitution matrices – Sequence analysis 2006

The Blocks databaseGapless alignment blocks

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[38] Substitution matrices – Sequence analysis 2006

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 sequencesLow number - distant sequences

• BLOSUM62 is the most popular: best for general alignment.

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[39] Substitution matrices – Sequence analysis 2006

The log-odds matrix for BLOSUM62

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[40] Substitution matrices – Sequence analysis 2006

PAM versus BLOSUM• Based on an explicit

evolutionary model

• Derived from small, closely related proteins with ~15% divergence

• Higher PAM numbers to detect more remote sequence similarities

• Errors in PAM 1 are scaled 250X in PAM 250

• Based on empirical frequencies

• Uses much larger, more diverse set of protein sequences (30-90% ID)

• Lower BLOSUM numbers to detect more remote sequence similarities

• Errors in BLOSUM arise from errors in alignment

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[41] Substitution matrices – Sequence analysis 2006

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.

∑= )/(log2 jiijij ppssH

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[42] Substitution matrices – Sequence analysis 2006

• Recent evolution → identity matrix

• Ancient evolution → convergence to

random model

Evolution and Matrix “landscape”

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[43] Substitution matrices – Sequence analysis 2006

Specialized matrices• Several other aa exchange matrices have been

constructed, for situations in which non-standard amino acid frequencies occur

• Secondary structure based exchange matrix (Lüthy R, McLachlan AD, Eisenberg D, Proteins 1991; 10(3):229-39)

HE

C

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[44] Substitution matrices – Sequence analysis 2006

Specialized matrices• Transmembrane specific substitution matrices:

• PHAT (Ng P, Henikoff J, Henikoff S, Bioinformatics 2000;16(9):760-766)Built from predicted hydrophobic and transmembraneregions of the blocks database

• BATMAS(Sutormin RA, Rakhmaninova AB, Gelfand S, Proteins 2003; 51(1):85-95)Derived from predicted TM-kernels of bacterial proteins

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[45] Substitution matrices – Sequence analysis 2006

A note on reliability • All these matrices are designed using

standard evolutionary models.

• Circular problem

• It is important to understand that evolution is not the same for all proteins, not even for the same regions of proteins.

matrixalignment

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[46] Substitution matrices – Sequence analysis 2006

…• 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.

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[47] Substitution matrices – Sequence analysis 2006

Pair-wise alignment quality versus sequence identity

• Vogt et al., JMB 249, 816-831,1995

Twilight zone

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[48] Substitution matrices – Sequence analysis 2006

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.

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[49] Substitution matrices – Sequence analysis 2006

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.