Download Lecture 9-11

Pairwise sequence
Alignment
Sequence Alignment
• Sequence analysis is the process of making
biological inferences from the known
sequence of monomers in protein, DNA and
RNA polymers.
Complete DNA
Sequences
More than 400
complete genomes
have been sequenced
Evolution
Sequence
alignment
• Comparing DNA/protein sequences for
– Similarity
– Homology
• Prediction of function
• Construction of phylogeny
• Shotgun assembly
– End-space-free alignment / overlap alignment
• Finding motifs
Sequence Alignment
Procedure of comparing two (pairwise) or more
(multiple) sequences by searching for a series of
individual characters that are in the same order in
the sequences
GCTAGTCAGATCTGACGCTA
| |||| ||||| |||
TGGTCACATCTGCCGC
Sequence Alignment
AGGCTATCACCTGACCTCCAGGCCGATGCCC
TAGCTATCACGACCGCGGTCGATTTGCCCGAC
-AGGCTATCACCTGACCTCCAGGCCGA--TGCCC--TAG-CTATCAC--GACCGC--GGTCGATTTGCCCGAC
Definition
Given two strings
x = x1x2...xM,
y = y1y2…yN,
an alignment is an assignment of gaps to positions
0,…, M in x, and 0,…, N in y, so as to line up each
letter in one sequence with either a letter, or a gap
in the other sequence
Sources of variation
• Nucleotide substitution
– Replication error
– Chemical reaction
• Insertions or deletions (indels)
– Unequal crossing over
– Replication slippage
• Duplication
– a single gene (complete gene duplication)
– part of a gene (internal or partial gene duplication)
• Domain duplication
• Exon shuffling
– part of a chromosome (partial polysomy)
– an entire chromosome (aneuploidy or polysomy)
– the whole genome (polyploidy)
Common mutations in DNA
Substitution:
A C G T T G A C
A C G A T G A C
Deletion:
A C G T T G A C
A C G A C
Insertion:
A C G T T G A C
A C G C A A T T G A C
Seq.Align.
Protein1
Protein Function
Protein2
More than 25%
sequence identity
?
Similar 3D structure
?
Similar function
?
Similar sequences produce similar proteins
Differing rates of DNA
evolution
• Functional/selective constraints (particular features
of coding regions, particular features in 5'
untranslated regions)
• Variation among different gene regions with
different functions (different parts of a protein may
evolve at different rates).
• Within proteins, variations are observed between
– surface and interior amino acids in proteins (order of magnitude difference in rates
in haemoglobins)
– charged and non-charged amino acids
– protein domains with different functions
– regions which are strongly constrained to preserve particular functions and regions
which are not
– different types of proteins -- those with constrained interaction surfaces and those
without
Common assumptions
• All nucleotide sites change independently
• The substitution rate is constant over time and in
different lineages
• The base composition is at equilibrium
• The conditional probabilities of nucleotide substitutions
are the same for all sites, and do not change over time
• Most of these are not true in many cases…
Pairwise alignments in the 1950s
b-corticotropin (sheep)
Corticotropin A (pig)
Oxytocin
Vasopressin
ala gly glu asp asp glu
asp gly ala glu asp glu
CYIQNCPLG
CYFQNCPRG
globins: a- b-
myoglobin
Early example of sequence
alignment: globins (1961)
H.C. Watson and J.C.
Kendrew, “Comparison
Between the Amino-Acid
Sequences of Sperm Whale
Myoglobin and of Human
Hæmoglobin.” Nature
190:670-672, 1961.
Pairwise sequence alignment is the most
fundamental operation of bioinformatics
• It is used to decide if two proteins (or genes)
are related structurally or functionally
• It is used to identify domains or motifs that
are shared between proteins
• It is the basis of BLAST searching (next week)
• It is used in the analysis of genomes
Pairwise alignment: protein sequences
can be more informative than DNA
• protein is more informative (20 vs 4 characters);
many amino acids share related biophysical properties
• codons are degenerate: changes in the third position
often do not alter the amino acid that is specified
• protein sequences offer a longer “look-back” time
• DNA sequences can be translated into protein,
and then used in pairwise alignments
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Pairwise alignment: protein sequences
can be more informative than DNA
• DNA can be translated into six potential proteins
5’ CAT CAA
5’ ATC AAC
5’ TCA ACT
5’ CATCAACTACAACTCCAAAGACACCCTTACACATCAACAAACCTACCCAC 3’
3’ GTAGTTGATGTTGAGGTTTCTGTGGGAATGTGTAGTTGTTTGGATGGGTG 5’
5’ GTG GGT
5’ TGG GTA
5’ GGG TAG
Pairwise alignment: protein sequences
can be more informative than DNA
• Many times, DNA alignments are appropriate
--to confirm the identity of a cDNA
--to study noncoding regions of DNA
--to study DNA polymorphisms
--example: Neanderthal vs modern human DNA
Query: 181 catcaactacaactccaaagacacccttacacccactaggatatcaacaaacctacccac 240
|||||||| |||| |||||| ||||| | |||||||||||||||||||||||||||||||
Sbjct: 189 catcaactgcaaccccaaagccacccct-cacccactaggatatcaacaaacctacccac 247
retinol-binding protein
(NP_006735)
b-lactoglobulin
(P02754)
Page 42
Definitions
Pairwise alignment
The process of lining up two or more sequences
to achieve maximal levels of identity
(and conservation, in the case of amino acid sequences)
for the purpose of assessing the degree of similarity
and the possibility of homology.
Definitions
Homology
Similarity attributed to descent from a common ancestor.
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Definitions
Homology
Similarity attributed to descent from a common ancestor.
Identity
The extent to which two (nucleotide or amino acid)
sequences are invariant.
RBP:
glycodelin:
26
RVKENFDKARFSGTWYAMAKKDPEGLFLQDNIVAEFSVDETGQMSATAKGRVRLLNNWD- 84
+ K ++ + + +
GTW++ MA
+
L +
A
V T +
+L+ W+
23 QTKQDLELPKLAGTWHSMAMA-TNNISLMATLKAPLRVHITSLLPTPEDNLEI V LHRWEN 81
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Definitions: two types of homology
Orthologs
Homologous sequences in different species
that arose from a common ancestral gene
during speciation; may or may not be responsible
for a similar function.
Paralogs
Homologous sequences within a single species
that arose by gene duplication.
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common carp
zebrafish
rainbow trout
teleost
Orthologs:
members of a
gene (protein)
family in various
organisms.
This tree shows
RBP orthologs.
African
clawed
frog
chicken
human
mouse
rat
horse
pig cow rabbit
10 changes
Page 43
apolipoprotein D
retinol-binding
protein 4
Complement
component 8
Alpha-1
Microglobulin
/bikunin
Paralogs:
members of a
gene (protein)
family within a
species
prostaglandin
D2 synthase
progestagenassociated
endometrial
protein
Odorant-binding
protein 2A
neutrophil
gelatinaseassociated
lipocalin
Lipocalin 1
10 changes
Page 44
Pairwise alignment of retinol-binding protein
and b-lactoglobulin
1 MKWVWALLLLAAWAAAERDCRVSSFRVKENFDKARFSGTWYAMAKKDPEG 50 RBP
. ||| |
.
|. . . | : .||||.:|
:
1 ...MKCLLLALALTCGAQALIVT..QTMKGLDIQKVAGTWYSLAMAASD. 44 lactoglobulin
51 LFLQDNIVAEFSVDETGQMSATAKGRVR.LLNNWD..VCADMVGTFTDTE 97 RBP
: | |
|
|
:: | .| . || |:
||
|.
45 ISLLDAQSAPLRV.YVEELKPTPEGDLEILLQKWENGECAQKKIIAEKTK 93 lactoglobulin
98 DPAKFKMKYWGVASFLQKGNDDHWIVDTDYDTYAV...........QYSC 136 RBP
|| ||.
|
:.|||| | .
.|
94 IPAVFKIDALNENKVL........VLDTDYKKYLLFCMENSAEPEQSLAC 135 lactoglobulin
137 RLLNLDGTCADSYSFVFSRDPNGLPPEAQKIVRQRQ.EELCLARQYRLIV 185 RBP
. |
|
| :
||
.
| || |
136 QCLVRTPEVDDEALEKFDKALKALPMHIRLSFNPTQLEEQCHI....... 178 lactoglobulin
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Definitions
Similarity
The extent to which nucleotide or protein sequences
are related. It is based upon identity plus
conservation.
Identity
The extent to which two sequences are invariant.
Conservation
Changes at a specific position of an amino acid or
(less commonly, DNA) sequence that preserve the
physico-chemical properties of the original residue.
Pairwise alignment of retinol-binding protein
and b-lactoglobulin
1 MKWVWALLLLAAWAAAERDCRVSSFRVKENFDKARFSGTWYAMAKKDPEG 50 RBP
. ||| |
.
|. . . | : .||||.:|
:
1 ...MKCLLLALALTCGAQALIVT..QTMKGLDIQKVAGTWYSLAMAASD. 44 lactoglobulin
51 LFLQDNIVAEFSVDETGQMSATAKGRVR.LLNNWD..VCADMVGTFTDTE 97 RBP
: | |
|
|
:: | .| . || |:
||
|.
45 ISLLDAQSAPLRV.YVEELKPTPEGDLEILLQKWENGECAQKKIIAEKTK 93 lactoglobulin
98 DPAKFKMKYWGVASFLQKGNDDHWIVDTDYDTYAV...........QYSC 136 RBP
|| ||.
|
:.|||| | .
.|
94 IPAVFKIDALNENKVL........VLDTDYKKYLLFCMENSAEPEQSLAC 135 lactoglobulin
Identity
(bar)
137 RLLNLDGTCADSYSFVFSRDPNGLPPEAQKIVRQRQ.EELCLARQYRLIV 185 RBP
. |
|
| :
||
.
| || |
136 QCLVRTPEVDDEALEKFDKALKALPMHIRLSFNPTQLEEQCHI....... 178 lactoglobulin
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Pairwise alignment of retinol-binding protein
and b-lactoglobulin
1 MKWVWALLLLAAWAAAERDCRVSSFRVKENFDKARFSGTWYAMAKKDPEG 50 RBP
. ||| |
.
|. . . | : .||||.:|
:
1 ...MKCLLLALALTCGAQALIVT..QTMKGLDIQKVAGTWYSLAMAASD. 44 lactoglobulin
51 LFLQDNIVAEFSVDETGQMSATAKGRVR.LLNNWD..VCADMVGTFTDTE 97 RBP
: | |
|
|
:: | .| . || |:
||
|.
45 ISLLDAQSAPLRV.YVEELKPTPEGDLEILLQKWENGECAQKKIIAEKTK 93 lactoglobulin
98 DPAKFKMKYWGVASFLQKGNDDHWIVDTDYDTYAV...........QYSC 136 RBP
|| ||.
|
:.|||| | .
.|
94 IPAVFKIDALNENKVL........VLDTDYKKYLLFCMENSAEPEQSLAC 135 lactoglobulin
Somewhat
similar
(one dot)
Very
similar
(two dots)
137 RLLNLDGTCADSYSFVFSRDPNGLPPEAQKIVRQRQ.EELCLARQYRLIV 185 RBP
. |
|
| :
||
.
| || |
136 QCLVRTPEVDDEALEKFDKALKALPMHIRLSFNPTQLEEQCHI....... 178 lactoglobulin
Page 46
Definitions
Pairwise alignment
The process of lining up two or more sequences
to achieve maximal levels of identity
(and conservation, in the case of amino acid sequences)
for the purpose of assessing the degree of similarity
and the possibility of homology.
Page 47
Pairwise alignment of retinol-binding protein
and b-lactoglobulin
1 MKWVWALLLLAAWAAAERDCRVSSFRVKENFDKARFSGTWYAMAKKDPEG 50 RBP
. ||| |
.
|. . . | : .||||.:|
:
1 ...MKCLLLALALTCGAQALIVT..QTMKGLDIQKVAGTWYSLAMAASD. 44 lactoglobulin
51 LFLQDNIVAEFSVDETGQMSATAKGRVR.LLNNWD..VCADMVGTFTDTE 97 RBP
: | |
|
|
:: | .| . || |:
||
|.
45 ISLLDAQSAPLRV.YVEELKPTPEGDLEILLQKWENGECAQKKIIAEKTK 93 lactoglobulin
98 DPAKFKMKYWGVASFLQKGNDDHWIVDTDYDTYAV...........QYSC 136 RBP
|| ||.
|
:.|||| | .
.|
94 IPAVFKIDALNENKVL........VLDTDYKKYLLFCMENSAEPEQSLAC 135 lactoglobulin
137 RLLNLDGTCADSYSFVFSRDPNGLPPEAQKIVRQRQ.EELCLARQYRLIV 185 RBP
. |
|
| :
||
.
| || |
136 QCLVRTPEVDDEALEKFDKALKALPMHIRLSFNPTQLEEQCHI....... 178 lactoglobulin
Internal
gap
Terminal
gap
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Gaps
• Positions at which a letter is paired with a null
are called gaps.
• Gap scores are typically negative.
• Since a single mutational event may cause the insertion
or deletion of more than one residue, the presence of
a gap is ascribed more significance than the length
of the gap. Thus there are separate penalties for gap
creation and gap extension.
• In BLAST, it is rarely necessary to change gap values
from the default.
Pairwise alignment of retinol-binding protein
and b-lactoglobulin
1 MKWVWALLLLAAWAAAERDCRVSSFRVKENFDKARFSGTWYAMAKKDPEG 50 RBP
. ||| |
.
|. . . | : .||||.:|
:
1 ...MKCLLLALALTCGAQALIVT..QTMKGLDIQKVAGTWYSLAMAASD. 44 lactoglobulin
51 LFLQDNIVAEFSVDETGQMSATAKGRVR.LLNNWD..VCADMVGTFTDTE 97 RBP
: | |
|
|
:: | .| . || |:
||
|.
45 ISLLDAQSAPLRV.YVEELKPTPEGDLEILLQKWENGECAQKKIIAEKTK 93 lactoglobulin
98 DPAKFKMKYWGVASFLQKGNDDHWIVDTDYDTYAV...........QYSC 136 RBP
|| ||.
|
:.|||| | .
.|
94 IPAVFKIDALNENKVL........VLDTDYKKYLLFCMENSAEPEQSLAC 135 lactoglobulin
137 RLLNLDGTCADSYSFVFSRDPNGLPPEAQKIVRQRQ.EELCLARQYRLIV 185 RBP
. |
|
| :
||
.
| || |
136 QCLVRTPEVDDEALEKFDKALKALPMHIRLSFNPTQLEEQCHI....... 178 lactoglobulin
Pairwise alignment of retinol-binding protein
from human (top) and rainbow trout (O. mykiss)
1 .MKWVWALLLLA.AWAAAERDCRVSSFRVKENFDKARFSGTWYAMAKKDP 48
::
|| || ||
.||.||. .| :|||:.|:.| |||.|||||
1 MLRICVALCALATCWA...QDCQVSNIQVMQNFDRSRYTGRWYAVAKKDP 47
.
.
.
.
.
49 EGLFLQDNIVAEFSVDETGQMSATAKGRVRLLNNWDVCADMVGTFTDTED 98
|||| ||:||:|||||.|.|.||| ||| :||||:.||.| ||| || |
48 VGLFLLDNVVAQFSVDESGKMTATAHGRVIILNNWEMCANMFGTFEDTPD 97
.
.
.
.
.
99 PAKFKMKYWGVASFLQKGNDDHWIVDTDYDTYAVQYSCRLLNLDGTCADS 148
||||||:||| ||:|| ||||||::||||| ||: |||| ..||||| |
98 PAKFKMRYWGAASYLQTGNDDHWVIDTDYDNYAIHYSCREVDLDGTCLDG 147
.
.
.
.
.
149 YSFVFSRDPNGLPPEAQKIVRQRQEELCLARQYRLIVHNGYCDGRSERNLL 199
|||:||| | || || |||| :..|:|
.|| : | |:|:
148 YSFIFSRHPTGLRPEDQKIVTDKKKEICFLGKYRRVGHTGFCESS...... 192
Pairwise sequence alignment allows us
to look back billions of years ago (BYA)
Origin of
life
4
Earliest
fossils
Origin of Eukaryote/
eukaryotes archaea
3
2
Fungi/animal
Plant/animal
1
insects
0
Page 48
Multiple sequence alignment of
glyceraldehyde 3-phosphate dehydrogenases
fly
human
plant
bacterium
yeast
archaeon
GAKKVIISAP
GAKRVIISAP
GAKKVIISAP
GAKKVVMTGP
GAKKVVITAP
GADKVLISAP
SAD.APM..F
SAD.APM..F
SAD.APM..F
SKDNTPM..F
SS.TAPM..F
PKGDEPVKQL
VCGVNLDAYK
VMGVNHEKYD
VVGVNEHTYQ
VKGANFDKY.
VMGVNEEKYT
VYGVNHDEYD
PDMKVVSNAS
NSLKIISNAS
PNMDIVSNAS
AGQDIVSNAS
SDLKIVSNAS
GE.DVVSNAS
CTTNCLAPLA
CTTNCLAPLA
CTTNCLAPLA
CTTNCLAPLA
CTTNCLAPLA
CTTNSITPVA
fly
human
plant
bacterium
yeast
archaeon
KVINDNFEIV
KVIHDNFGIV
KVVHEEFGIL
KVINDNFGII
KVINDAFGIE
KVLDEEFGIN
EGLMTTVHAT
EGLMTTVHAI
EGLMTTVHAT
EGLMTTVHAT
EGLMTTVHSL
AGQLTTVHAY
TATQKTVDGP
TATQKTVDGP
TATQKTVDGP
TATQKTVDGP
TATQKTVDGP
TGSQNLMDGP
SGKLWRDGRG
SGKLWRDGRG
SMKDWRGGRG
SHKDWRGGRG
SHKDWRGGRT
NGKP.RRRRA
AAQNIIPAST
ALQNIIPAST
ASQNIIPSST
ASQNIIPSST
ASGNIIPSST
AAENIIPTST
fly
human
plant
bacterium
yeast
archaeon
GAAKAVGKVI
GAAKAVGKVI
GAAKAVGKVL
GAAKAVGKVL
GAAKAVGKVL
GAAQAATEVL
PALNGKLTGM
PELNGKLTGM
PELNGKLTGM
PELNGKLTGM
PELQGKLTGM
PELEGKLDGM
AFRVPTPNVS
AFRVPTANVS
AFRVPTSNVS
AFRVPTPNVS
AFRVPTVDVS
AIRVPVPNGS
VVDLTVRLGK
VVDLTCRLEK
VVDLTCRLEK
VVDLTVRLEK
VVDLTVKLNK
ITEFVVDLDD
GASYDEIKAK
PAKYDDIKKV
GASYEDVKAA
AATYEQIKAA
ETTYDEIKKV
DVTESDVNAA
Page 49
Multiple sequence alignment of
human lipocalin paralogs
~~~~~EIQDVSGTWYAMTVDREFPEMNLESVTPMTLTTL.GGNLEAKVTM
LSFTLEEEDITGTWYAMVVDKDFPEDRRRKVSPVKVTALGGGNLEATFTF
TKQDLELPKLAGTWHSMAMATNNISLMATLKAPLRVHITSEDNLEIVLHR
VQENFDVNKYLGRWYEIEKIPTTFENGRCIQANYSLMENGNQELRADGTV
VKENFDKARFSGTWYAMAKDPEGLFLQDNIVAEFSVDETGNWDVCADGTF
LQQNFQDNQFQGKWYVVGLAGNAI.LREDKDPQKMYATIDKSYNVTSVLF
VQPNFQQDKFLGRWFSAGLASNSSWLREKKAALSMCKSVDGGLNLTSTFL
VQENFNISRIYGKWYNLAIGSTCPWMDRMTVSTLVLGEGEAEISMTSTRW
PKANFDAQQFAGTWLLVAVGSACRFLQRAEATTLHVAPQGSTFRKLD...
lipocalin 1
odorant-binding protein 2a
progestagen-assoc. endo.
apolipoprotein D
retinol-binding protein
neutrophil gelatinase-ass.
prostaglandin D2 synthase
alpha-1-microglobulin
complement component 8
Page 49
General approach to pairwise alignment
• Choose two sequences
• Select an algorithm that generates a score
• Allow gaps (insertions, deletions)
• Score reflects degree of similarity
• Alignments can be global or local
• Estimate probability that the alignment
occurred by chance
Calculation of an alignment score
Where we’re heading in the next 10 minutes:
creating a set of “scoring matrices” that let us
assign scores for each aligned amino acid in a
pairwise alignment.
What should the score be when a serine
matches a serine, or a threonine, or a valine?
Can we devise “lenient” scoring systems to
help us align distantly related proteins, and
more conservative scoring systems to align
closely related proteins?
lys found at 58% of arg sites
Emile Zuckerkandl and Linus Pauling (1965) considered
substitution frequencies in 18 globins
(myoglobins and hemoglobins from human to lamprey).
Black: identity
Gray: very conservative substitutions (>40% occurrence)
White: fairly conservative substitutions (>21% occurrence)
Red: no substitutions observed
Page 80
Page 80
Dayhoff’s 34 protein superfamilies
Accepted point mutations
Protein
Ig kappa chain
Kappa casein
Lactalbumin
Hemoglobin a
Myoglobin
Insulin
Histone H4
Ubiquitin
From 1978
PAMs per 100 million years
37
33
27
12
8.9
400 fold
4.4
0.10
0.00
Page 50
Pairwise alignment of human (NP_005203)
versus mouse (NP_031812) ubiquitin
Multiple sequence alignment of
glyceraldehyde 3-phosphate dehydrogenases
fly
human
plant
bacterium
yeast
archaeon
GAKKVIISAP
GAKRVIISAP
GAKKVIISAP
GAKKVVMTGP
GAKKVVITAP
GADKVLISAP
SAD.APM..F
SAD.APM..F
SAD.APM..F
SKDNTPM..F
SS.TAPM..F
PKGDEPVKQL
VCGVNLDAYK
VMGVNHEKYD
VVGVNEHTYQ
VKGANFDKY.
VMGVNEEKYT
VYGVNHDEYD
PDMKVVSNAS
NSLKIISNAS
PNMDIVSNAS
AGQDIVSNAS
SDLKIVSNAS
GE.DVVSNAS
CTTNCLAPLA
CTTNCLAPLA
CTTNCLAPLA
CTTNCLAPLA
CTTNCLAPLA
CTTNSITPVA
fly
human
plant
bacterium
yeast
archaeon
KVINDNFEIV
KVIHDNFGIV
KVVHEEFGIL
KVINDNFGII
KVINDAFGIE
KVLDEEFGIN
EGLMTTVHAT
EGLMTTVHAI
EGLMTTVHAT
EGLMTTVHAT
EGLMTTVHSL
AGQLTTVHAY
TATQKTVDGP
TATQKTVDGP
TATQKTVDGP
TATQKTVDGP
TATQKTVDGP
TGSQNLMDGP
SGKLWRDGRG
SGKLWRDGRG
SMKDWRGGRG
SHKDWRGGRG
SHKDWRGGRT
NGKP.RRRRA
AAQNIIPAST
ALQNIIPAST
ASQNIIPSST
ASQNIIPSST
ASGNIIPSST
AAENIIPTST
fly
human
plant
bacterium
yeast
archaeon
GAAKAVGKVI
GAAKAVGKVI
GAAKAVGKVL
GAAKAVGKVL
GAAKAVGKVL
GAAQAATEVL
PALNGKLTGM
PELNGKLTGM
PELNGKLTGM
PELNGKLTGM
PELQGKLTGM
PELEGKLDGM
AFRVPTPNVS
AFRVPTANVS
AFRVPTSNVS
AFRVPTPNVS
AFRVPTVDVS
AIRVPVPNGS
VVDLTVRLGK
VVDLTCRLEK
VVDLTCRLEK
VVDLTVRLEK
VVDLTVKLNK
ITEFVVDLDD
GASYDEIKAK
PAKYDDIKKV
GASYEDVKAA
AATYEQIKAA
ETTYDEIKKV
DVTESDVNAA
Dayhoff’s numbers of “accepted point mutations”:
what amino acid substitutions occur in proteins?
A
Ala
A
R
N
D
C
Q
E
G
H
R
Arg
N
Asn
D
Asp
C
Q
E
Cys
Gln related
Glu
From closely
G
Gly
protein sequences (at
least 85% identity)
30
109
17
154
0
532
33
10
0
0
93
120
50
76
0
266
0
94
831
0
422
579
10
156
162
10
30
112
21
103
226
43
10
243
23
10
Numbers of APM, multiplied by 10, in 1572 cases of amino acid substitutions from closely related sequences
The relative mutability of amino acids
Asn
Ser
Asp
Glu
Ala
Thr
Ile
Met
Gln
Val
134
120
106
102
100
97
96
94
93
74
His
Arg
Lys
Pro
Gly
Tyr
Phe
Leu
Cys
Trp
66
65
56
56
49
41
41
40
20
18
Describes how often each amino acid is likely to change over a short evolutionary period
Page 53
Normalized frequencies of amino acids
Gly
Ala
Leu
Lys
Ser
Val
Thr
Pro
Glu
Asp
8.9%
8.7%
8.5%
8.1%
7.0%
6.5%
5.8%
5.1%
5.0%
4.7%
Arg
Asn
Phe
Gln
Ile
His
Cys
Tyr
Met
Trp
4.1%
4.0%
4.0%
3.8%
3.7%
3.4%
3.3%
3.0%
1.5%
1.0%
blue=6 codons; red=1 codon
Page 53
Page 54
Dayhoff’s PAM1 mutation probability matrix
Replaced amino acid
Original amino acid
A
R
N
D
C
Q
E
G
H
I
There is
98.67%chance that
A will be replaced
by A over an
evolutionary
distance of 1 PAM
A
Ala
R
Arg
N
D
C
Asn Asp Cys
Q
Gln
E
Glu
G
Gly
H
His
I
Ile
9867
2
9
1
9913
4
10
3
8
17
21
2
6
1
0
1
10
0
0
10
3
1
9822
36
0
4
6
6
21
3
6
0
42
6
4
1
1
1
0
0
1
1
3
9
4
1
23
1
10
0
7
56
0
35
9865
4
2
3
21
1
12
11
1
3
7
9935
1
0
1
8
18
3
1
20
1
0
9912
0
2
2
3
1
2
1
2
0
0
9872
Each element shows the probability
9859
0 amino acid
6 j
53
that an original
(columns)will be replaced byanother
0
9973
0
0
amino acid i (rows) for 1% sequence
divergence
5
0
9876
27
Dayhoff’s PAM1 mutation probability matrix
A
R
N
D
C
Q
E
G
H
I
A
Ala
R
Arg
N
Asn
D
Asp
C
Cys
Q
Gln
E
Glu
G
Gly
H
His
I
Ile
9867
2
9
10
3
8
17
21
2
6
1
9913
1
0
1
10
0
0
10
3
4
1
9822
36
0
4
6
6
21
3
6
0
42
9859
0
6
53
6
4
1
1
1
0
0
9973
0
0
0
1
1
3
9
4
5
0
9876
27
1
23
1
10
0
7
56
0
35
9865
4
2
3
21
1
12
11
1
3
7
9935
1
0
1
8
18
3
1
20
1
0
9912
0
2
2
3
1
2
1
2
0
0
9872
Each element of the matrix shows the probability that an original
amino acid (top) will be replaced by another amino acid (side)
Substitution Matrix
A substitution matrix contains values proportional
to the probability that amino acid i mutates into
amino acid j for all pairs of amino acids.
Substitution matrices are constructed by assembling
a large and diverse sample of verified pairwise alignments
(or multiple sequence alignments) of amino acids.
Substitution matrices should reflect the true probabilities
of mutations occurring through a period of evolution.
The two major types of substitution matrices are
PAM and BLOSUM.
PAM matrices:
Point-accepted mutations
PAM matrices are based on global alignments
of closely related proteins.
The PAM1 is the matrix calculated from comparisons
of sequences with no more than 1% divergence.
Other PAM matrices are extrapolated from PAM1.
All the PAM data come from closely related proteins
(>85% amino acid identity)
Dayhoff’s PAM1 mutation probability matrix
A
R
N
D
C
Q
E
G
H
I
A
Ala
R
Arg
N
Asn
D
Asp
C
Cys
Q
Gln
E
Glu
G
Gly
H
His
I
Ile
9867
2
9
10
3
8
17
21
2
6
1
9913
1
0
1
10
0
0
10
3
4
1
9822
36
0
4
6
6
21
3
6
0
42
9859
0
6
53
6
4
1
1
1
0
0
9973
0
0
0
1
1
3
9
4
5
0
9876
27
1
23
1
10
0
7
56
0
35
9865
4
2
3
21
1
12
11
1
3
7
9935
1
0
1
8
18
3
1
20
1
0
9912
0
2
2
3
1
2
1
2
0
0
9872
Page 55
Dayhoff’s PAM0 mutation probability matrix:
the rules for extremely slowly evolving proteins
PAM0
A
R
N
D
C
Q
E
G
A
Ala
100%
0%
0%
0%
0%
0%
0%
0%
R
Arg
0%
100%
0%
0%
0%
0%
0%
0%
N
Asn
0%
0%
100%
0%
0%
0%
0%
0%
D
Asp
0%
0%
0%
100%
0%
0%
0%
0%
C
Cys
0%
0%
0%
0%
100%
0%
0%
0%
Q
Gln
0%
0%
0%
0%
0%
100%
0%
0%
Top: original amino acid
Side: replacement amino acid
E
Glu
0%
0%
0%
0%
0%
0%
100%
0%
G
Gly
0%
0%
0%
0%
0%
0%
0%
100%
Page 56
Dayhoff’s PAM2000 mutation probability matrix:
the rules for very distantly related proteins
PAM
A
R
N
D
C
Q
E
G
Ala
Arg
Asn
Asp
Cys
Gln
Glu
Gly
A
8.7%
8.7%
8.7%
8.7%
8.7%
8.7%
8.7%
8.7%
R
4.1%
4.1%
4.1%
4.1%
4.1%
4.1%
4.1%
4.1%
N
4.0%
4.0%
4.0%
4.0%
4.0%
4.0%
4.0%
4.0%
D
4.7%
4.7%
4.7%
4.7%
4.7%
4.7%
4.7%
4.7%
C
3.3%
3.3%
3.3%
3.3%
3.3%
3.3%
3.3%
3.3%
Q
3.8%
3.8%
3.8%
3.8%
3.8%
3.8%
3.8%
3.8%
E
5.0%
5.0%
5.0%
5.0%
5.0%
5.0%
5.0%
5.0%
G
8.9%
8.9%
8.9%
8.9%
8.9%
8.9%
8.9%
8.9%
PAM1 matrix is multiplied 2000 times by itself
Top: original amino acid
Side: replacement amino acid
PAM250 mutation probability matrix
A
R
N
D
C
Q
E
G
H
I
L
K
M
F
P
S
T
W
Y
V
A
R
N
D
C
Q
E
G
H
I
L
K
M F
P
S
T
W Y
V
13
6
9
9
5
8
9
12
6
8
6
7
7
4
11
11
11
2
4
9
3
17
4
3
2
5
3
2
6
3
2
9
4
1
4
4
3
7
2
2
4
4
6
7
2
5
6
4
6
3
2
5
3
2
4
5
4
2
3
3
5
4
8
11
1
7
10
5
6
3
2
5
3
1
4
5
5
1
2
3
2
1
1
1
52
1
1
2
2
2
1
1
1
1
2
3
2
1
4
2
3
5
5
6
1
10
7
3
7
2
3
5
3
1
4
3
3
1
2
3
5
4
7
11
1
9
12
5
6
3
2
5
3
1
4
5
5
1
2
3
12
5
10
10
4
7
9
27
5
5
4
6
5
3
8
11
9
2
3
7
2
5
5
4
2
7
4
2
15
2
2
3
2
2
3
3
2
2
3
2
3
2
2
2
2
2
2
2
2
10
6
2
6
5
2
3
4
1
3
9
6
4
4
3
2
6
4
3
5
15
34
4
20
13
5
4
6
6
7
13
6
18
10
8
2
10
8
5
8
5
4
24
9
2
6
8
8
4
3
5
1
1
1
1
0
1
1
1
1
2
3
2
6
2
1
1
1
1
1
2
2
1
2
1
1
1
1
1
3
5
6
1
4
32
1
2
2
4
20
3
7
5
5
4
3
5
4
5
5
3
3
4
3
2
20
6
5
1
2
4
9
6
8
7
7
6
7
9
6
5
4
7
5
3
9
10
9
4
4
6
8
5
6
6
4
5
5
6
4
6
4
6
5
3
6
8
11
2
3
6
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
55
1
0
1
1
2
1
3
1
1
1
3
2
2
1
2
15
1
2
2
3
31
2
7
4
4
4
4
4
4
5
4
15
10
4
10
5
5
5
7
2
4
17
Top: original amino acid
Side: replacement amino acid
Page 57
A
R
N
D
C
Q
E
G
H
I
L
K
M
F
P
S
T
W
Y
V
2
-2 6
0 0 2
0 -1 2 4
-2 -4 -4 -5 12
0 1 1 2 -5 4
0 -1 1 3 -5 2 4
1 -3 0 1 -3 -1 0 5
-1 2 2 1 -3 3 1 -2 6
-1 -2 -2 -2 -2 -2 -2 -3 -2 5
S(a,b)= 10 log10 (Mab/Pb)
-2 -3 -3 -4 -6 -2 -3 -4 -2 -2 6
-1 3 1 0 -5 1 0 -2 0 -2 -3 5
-1 0 -2 -3 -5 -1 -2 -3 -2 2 4 0 6
-3 -4 -3 -6 -4 -5 -5 -5 -2 1 2 -5 0 9
1 0 0 -1 -3 0 -1 0 0 -2 -3 -1 -2 -5 6
1 0 1 0 0 -1 0 1 -1 -1 -3 0 -2 -3 1 2
1 -1 0 0 -2 -1 0 0 -1 0 -2 0 -1 -3 0 1 3
-6 2 -4 -7 -8 -5 -7 -7 -3 -5 -2 -3 -4 0 -6 -2 -5 17
-3 -4 -2 -4 0 -4 -4 -5 0 -1 -1 -4 -2 7 -5 -3 -3 0 10
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
PAM250 log odds
scoring matrix
Page 58
Why do we go from a mutation probability
matrix to a log odds matrix?
• We want a scoring matrix so that when we do a pairwise
alignment (or a BLAST search) we know what score to
assign to two aligned amino acid residues.
• Logarithms are easier to use for a scoring system. They
allow us to sum the scores of aligned residues (rather
than having to multiply them).
Page 57
How do we go from a mutation probability
matrix to a log odds matrix?
• The cells in a log odds matrix consist of an “odds ratio”:
the probability that an alignment is authentic
the probability that the alignment was random
The score S for an alignment of residues a,b is given by:
S(a,b) = 10 log10 (Mab/pb)
As an example, for tryptophan,
Normalized frequency of W is 0.01
S(a,tryptophan) = 10 log10 (0.55/0.010) = 17.4
What do the numbers mean
in a log odds matrix?
S(a,tryptophan) = 10 log10 (0.55/0.010) = 17.4
A score of +17 for tryptophan means that this alignment
is 50 times more likely than a chance alignment of two
Trp residues.
S(a,b) = 17
Probability of replacement (Mab/pb) = x
Then
17 = 10 log10 x
1.7 = log10 x
101.7 = x = 50
Page 58
What do the numbers mean
in a log odds matrix?
A score of +2 indicates that the amino acid replacement
occurs 1.6 times as frequently as expected by chance.
A score of 0 is neutral.
A score of –10 indicates that the correspondence of two
amino acids in an alignment that accurately represents
homology (evolutionary descent) is one tenth as frequent
as the chance alignment of these amino acids.
Page 58
A
R
N
D
C
Q
E
G
H
I
L
K
M
F
P
S
T
W
Y
V
2
-2 6
0 0 2
0 -1 2 4
-2 -4 -4 -5 12
0 1 1 2 -5 4
0 -1 1 3 -5 2 4
1 -3 0 1 -3 -1 0 5
-1 2 2 1 -3 3 1 -2 6
-1 -2 -2 -2 -2 -2 -2 -3 -2 5
-2 -3 -3 -4 -6 -2 -3 -4 -2 -2 6
-1 3 1 0 -5 1 0 -2 0 -2 -3 5
-1 0 -2 -3 -5 -1 -2 -3 -2 2 4 0 6
-3 -4 -3 -6 -4 -5 -5 -5 -2 1 2 -5 0 9
1 0 0 -1 -3 0 -1 0 0 -2 -3 -1 -2 -5 6
1 0 1 0 0 -1 0 1 -1 -1 -3 0 -2 -3 1 2
1 -1 0 0 -2 -1 0 0 -1 0 -2 0 -1 -3 0 1 3
-6 2 -4 -7 -8 -5 -7 -7 -3 -5 -2 -3 -4 0 -6 -2 -5 17
-3 -4 -2 -4 0 -4 -4 -5 0 -1 -1 -4 -2 7 -5 -3 -3 0 10
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
PAM250 log odds
scoring matrix
Page 58
A
R
N
D
C
Q
E
G
H
I
L
K
M
F
P
S
T
W
Y
V
7
-10
9
-7
-9
9
-6
-17
-1
8
-10
-11
-17
-21
10
-7
-4
-7
-6
-20
9
-5
-15
-5
0
-20
-1
8
-4
-13
-6
-6
-13
-10
-7
7
-11
-4
-2
-7
-10
-2
-9
-13
10
-8
-8
-8
-11
-9
-11
-8
-17
-13
9
-9
-12
-10
-19
-21
-8
-13
-14
-9
-4
7
-10
-2
-4
-8
-20
-6
-7
-10
-10
-9
-11
7
-8
-7
-15
-17
-20
-7
-10
-12
-17
-3
-2
-4
12
-12
-12
-12
-21
-19
-19
-20
-12
-9
-5
-5
-20
-7
9
-4
-7
-9
-12
-11
-6
-9
-10
-7
-12
-10
-10
-11
-13
8
-3
-6
-2
-7
-6
-8
-7
-4
-9
-10
-12
-7
-8
-9
-4
7
-3
-10
-5
-8
-11
-9
-9
-10
-11
-5
-10
-6
-7
-12
-7
-2
8
-20
-5
-11
-21
-22
-19
-23
-21
-10
-20
-9
-18
-19
-7
-20
-8
-19
13
-11
-14
-7
-17
-7
-18
-11
-20
-6
-9
-10
-12
-17
-1
-20
-10
-9
-8
10
-5
-11
-12
-11
-9
-10
-10
-9
-9
-1
-5
-13
-4
-12
-9
-10
-6
-22
-10
R
N
D
Q
E
A
C
G
H
PAM10 log odds
scoring matrix
I
L
K
M
F
P
S
T
W Y
8
V
Page 59
Rat versus
mouse RBP
Rat versus
bacterial
lipocalin
Comparing two proteins with a PAM1 matrix
gives completely different results than PAM250!
Consider two distantly related proteins. A PAM40 matrix
is not forgiving of mismatches, and penalizes them
severely. Using this matrix you can find almost no match.
hsrbp, 136 CRLLNLDGTC
btlact,
3 CLLLALALTC
* ** * **
A PAM250 matrix is very tolerant of mismatches.
24.7% identity in 81 residues overlap; Score: 77.0; Gap frequency: 3.7%
hsrbp, 26 RVKENFDKARFSGTWYAMAKKDPEGLFLQDNIVAEFSVDETGQMSATAKGRVRLLNNWDV
btlact, 21 QTMKGLDIQKVAGTWYSLAMAASD-ISLLDAQSAPLRVYVEELKPTPEGDLEILLQKWEN
*
**** *
* *
*
** *
hsrbp, 86 --CADMVGTFTDTEDPAKFKM
btlact, 80 GECAQKKIIAEKTKIPAVFKI
**
* ** **
Page 60
BLOSUM Matrices
BLOSUM matrices are based on local alignments.
BLOSUM stands for blocks substitution matrix.
BLOSUM62 is a matrix calculated from comparisons of
sequences with no less than 62% divergence.
Page 60
BLOSUM Matrices
Percent amino acid identity
100
62
30
BLOSUM62
Percent amino acid identity
BLOSUM Matrices
100
100
100
62
62
62
30
30
30
BLOSUM80
BLOSUM62
BLOSUM30
BLOSUM Matrices
All BLOSUM matrices are based on observed alignments;
they are not extrapolated from comparisons of
closely related proteins.
The BLOCKS database contains thousands of groups of
multiple sequence alignments.
BLOSUM62 is the default matrix in BLAST 2.0.
Though it is tailored for comparisons of moderately distant
proteins, it performs well in detecting closer relationships.
A search for distant relatives may be more sensitive
with a different matrix.
Page 60
BLOSUM Scoring Matrices
•In the Dayhoff model, the scoring values are derived from
protein sequences with at least 85% identity
• Alignments are, however, most often performed on
sequences of less similarity, and the scoring matrices for
use in these cases are calculated from the 1 PAM matrix
• Henikoff and Henikoff (1992) have therefore developed
scoring matrices based on known alignments of more
diverse sequences
BLOSUM Scoring Matrices
• They take a group of related proteins and produce a set
of blocks representing this group, where a block is
defined as an ungapped region of aligned amino acids
• An example of two blocks is
KIFIMK
NLFKTR
KIFKTK
KLFESR
KIFKGR
GDEVK
GDSKK
GD PKA
G DAE R
G D AA K
• The Henikoffs used over 2000 blocks in order to derive
their scoring matrices
• For each column in each block they counted the number
of occurrences of each pair of amino acids, when all pairs
of segments were used
• Then the frequency distribution of all 210 different pairs
of amino acids were found
• A block of length w from an alignment of m sequences
makes (wm(m-1))/2 pairs of amino acids
We define
• hab as the number of occurrences of the amino acid pair
(ab)
(note that hab=hba)
• T as the total number of pairs in the alignment
where ≥ is interpreted as a total ordering over the amino
acids
• fab=hab/T (the frequency of observed pairs)
Developing Scoring Matrices for
Different Evolutionary Distances
• The procedure for developing a BLOSUM X matrix
1. Collect a set of multiple alignments
2. Find the blocks
3. Group the segments with an X% identity
4. Count the occurrences of all pairs of amino acids
5. Develop the matrix, as explained before
• BLOSUM-62 is often used as the standard for ungapped
alignments
• For gapped alignments, BLOSUM-50 is more often used
A
R
N
D
C
Q
E
G
H
I
L
K
M
F
P
S
T
W
Y
V
4
-1 5
-2 0 6
-2 -2 1 6
0 -3 -3 -3 9
-1 1 0 0 -3 5
-1 0 0 2 -4 2 5
0 -2 0 -1 -3 -2 -2 6
-2 0 1 -1 -3 0 0 -2 8
-1 -3 -3 -3 -1 -3 -3 -4 -3 4
-1 -2 -3 -4 -1 -2 -3 -4 -3 2 4
-1 2 0 -1 -1 1 1 -2 -1 -3 -2 5
-1 -2 -2 -3 -1 0 -2 -3 -2 1 2 -1 5
-2 -3 -3 -3 -2 -3 -3 -3 -1 0 0 -3 0 6
-1 -2 -2 -1 -3 -1 -1 -2 -2 -3 -3 -1 -2 -4 7
1 -1 1 0 -1 0 0 0 -1 -2 -2 0 -1 -2 -1 4
0 -1 0 -1 -1 -1 -1 -2 -2 -1 -1 -1 -1 -2 -1 1 5
-3 -3 -4 -4 -2 -2 -3 -2 -2 -3 -2 -3 -1 1 -4 -3 -2 11
-2 -2 -2 -3 -2 -1 -2 -3 2 -1 -1 -2 -1 3 -3 -2 -2
2
7
0 -3 -3 -3 -1 -2 -2 -3 -3 3 1 -2 1 -1 -2 -2 0 -3 -1 4
A R N D C Q E G H I
L K M F P S T W Y
V
Blosum62 scoring matrix
Page 61
By use of relative entropy, it can be found that PAM250
corresponds to BLOSUM-45 and PAM160 corresponds to
BLOSUM-62, and
PAM120 corresponds to BLOSUM-80
Rat versus
mouse RBP
Rat versus
bacterial
lipocalin
Page 61
Major Differences between PAM and BLOSUM
PAM
BLOSUM
Built from global alignments
Built from local alignments
Built from small amout of Data
Built from vast amout of Data
Counting is based on minimum
replacement or maximum parsimony
Perform better for finding global
alignments and remote homologs
Higher PAM series means more
divergence
Counting based on groups of
related sequences counted as one
Better for finding local alignments
Lower BLOSUM series means
more divergence
PAM matrices:
Point-accepted mutations
PAM matrices are based on global alignments
of closely related proteins.
The PAM1 is the matrix calculated from comparisons
of sequences with no more than 1% divergence.
Other PAM matrices are extrapolated from PAM1.
All the PAM data come from closely related proteins
(>85% amino acid identity)
Percent identity
Two randomly diverging protein sequences change
in a negatively exponential fashion
“twilight zone”
Evolutionary distance in PAMs
Page 62
Percent identity
At PAM1, two proteins are 99% identical
At PAM10.7, there are 10 differences per 100 residues
At PAM80, there are 50 differences per 100 residues
At PAM250, there are 80 differences per 100 residues
“twilight zone”
Differences per 100 residues
PAM250
PAM matrices reflect different degrees of divergence Page 62
PAM: “Accepted point mutation”
• Two proteins with 50% identity may have 80 changes
per 100 residues. (Why? Because any residue can be
subject to back mutations.)
• Proteins with 20% to 25% identity are in the “twilight zone”
and may be statistically significantly related.
• PAM or “accepted point mutation” refers to the “hits” or
matches between two sequences (Dayhoff & Eck, 1968)
Page 62
Ancestral sequence
ACCCTAC
A
C
C
C --> G
T --> A
A --> C --> T
C
no change
single substitution
multiple substitutions
coincidental substitutions
parallel substitutions
convergent substitutions
back substitution
Sequence 1
A
C --> A
C --> A --> T
C --> A
T --> A
A --> T
C --> T --> C
Sequence 2
Li (1997) p.70
Percent identity between two proteins:
What percent is significant?
100%
80%
65%
30%
23%
19%
An alignment scoring system is required
to evaluate how good an alignment is
• positive and negative values assigned
• gap creation and extension penalties
• positive score for identities
• some partial positive score for
conservative substitutions
• global versus local alignment
• use of a substitution matrix