1. Pairwise sequence
Alignment

2. Sequence Alignment
Sequence analysis is the process of making biological inferences from the known sequence of monomers in protein, DNA and RNA polymers.

3. Complete DNA Sequences
More than 400 complete genomes have been sequenced

4. Evolution

5. 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

6. Sequence Alignment | |||| ||||| ||| TGGTCACATCTGCCGC
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

7. 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

8. 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)

9. 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 A C
Insertion:
A C G C A A T T G A C

11. Seq.Align. Protein Function
More than 25% sequence identity ?
Similar 3D structure ?
Similar function ?
Similar sequences produce similar proteins

12. 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

13. 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…

14. Pairwise alignments in the 1950s
b-corticotropin (sheep)
Corticotropin A (pig)
ala gly glu asp asp glu
asp gly ala glu asp glu
CYIQNCPLG
CYFQNCPRG
Oxytocin
Vasopressin

15. 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: , 1961.

17. 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

18. 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

19. Page 54

20. 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

21. 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

22. retinol-binding protein
(NP_006735)
b-lactoglobulin
(P02754)
Page 42

23. 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.

24. Definitions
Homology
Similarity attributed to descent from a common ancestor.
Page 42

25. Definitions Homology Identity
Similarity attributed to descent from a common ancestor.
Identity
The extent to which two (nucleotide or amino acid) sequences are invariant.
RBP: RVKENFDKARFSGTWYAMAKKDPEGLFLQDNIVAEFSVDETGQMSATAKGRVRLLNNWD- 84
+ K GTW++ MA L A V T L+ W+
glycodelin: QTKQDLELPKLAGTWHSMAMA-TNNISLMATLKAPLRVHITSLLPTPEDNLEI V LHRWEN 81
Page 44

26. 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.
Page 43

27. Orthologs: members of a gene (protein) family in various organisms.
common carp
Orthologs:
members of a
gene (protein)
family in various
organisms.
This tree shows
RBP orthologs.
zebrafish
rainbow trout
teleost
African
clawed
frog
chicken
human
mouse
horse
rat
pig
cow
rabbit
10 changes
Page 43

28. Paralogs: members of a gene (protein) family within a species Page 44
apolipoprotein D
Paralogs:
members of a
gene (protein)
family within a
species
retinol-binding
protein 4
Complement
component 8
Alpha-1
Microglobulin
/bikunin
prostaglandin
D2 synthase
progestagen-
associated
endometrial
protein
neutrophil
gelatinase-
associated
lipocalin
Odorant-binding
protein 2A
Lipocalin 1
10 changes
Page 44

30. 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 lactoglobulin
Page 46

31. Definitions Similarity Identity Conservation
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.

32. 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 lactoglobulin
Identity
(bar)
Page 46

33. 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 lactoglobulin
Somewhat
similar
(one dot)
Very
similar
(two dots)
Page 46

34. 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

35. 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 lactoglobulin
Internal
gap
Terminal
gap
Page 46

36. 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.

37. 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 lactoglobulin

38. 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

39. Pairwise sequence alignment allows us
to look back billions of years ago (BYA)
Origin of
life
Earliest
fossils
Origin of
eukaryotes
Eukaryote/
archaea
Fungi/animal
Plant/animal
insects 4 3 2 1
Page 48

40. Multiple sequence alignment of
glyceraldehyde 3-phosphate dehydrogenases
fly GAKKVIISAP SAD.APM..F VCGVNLDAYK PDMKVVSNAS CTTNCLAPLA
human GAKRVIISAP SAD.APM..F VMGVNHEKYD NSLKIISNAS CTTNCLAPLA
plant GAKKVIISAP SAD.APM..F VVGVNEHTYQ PNMDIVSNAS CTTNCLAPLA
bacterium GAKKVVMTGP SKDNTPM..F VKGANFDKY. AGQDIVSNAS CTTNCLAPLA
yeast GAKKVVITAP SS.TAPM..F VMGVNEEKYT SDLKIVSNAS CTTNCLAPLA
archaeon GADKVLISAP PKGDEPVKQL VYGVNHDEYD GE.DVVSNAS CTTNSITPVA
fly KVINDNFEIV EGLMTTVHAT TATQKTVDGP SGKLWRDGRG AAQNIIPAST
human KVIHDNFGIV EGLMTTVHAI TATQKTVDGP SGKLWRDGRG ALQNIIPAST
plant KVVHEEFGIL EGLMTTVHAT TATQKTVDGP SMKDWRGGRG ASQNIIPSST
bacterium KVINDNFGII EGLMTTVHAT TATQKTVDGP SHKDWRGGRG ASQNIIPSST
yeast KVINDAFGIE EGLMTTVHSL TATQKTVDGP SHKDWRGGRT ASGNIIPSST
archaeon KVLDEEFGIN AGQLTTVHAY TGSQNLMDGP NGKP.RRRRA AAENIIPTST
fly GAAKAVGKVI PALNGKLTGM AFRVPTPNVS VVDLTVRLGK GASYDEIKAK
human GAAKAVGKVI PELNGKLTGM AFRVPTANVS VVDLTCRLEK PAKYDDIKKV
plant GAAKAVGKVL PELNGKLTGM AFRVPTSNVS VVDLTCRLEK GASYEDVKAA
bacterium GAAKAVGKVL PELNGKLTGM AFRVPTPNVS VVDLTVRLEK AATYEQIKAA
yeast GAAKAVGKVL PELQGKLTGM AFRVPTVDVS VVDLTVKLNK ETTYDEIKKV
archaeon GAAQAATEVL PELEGKLDGM AIRVPVPNGS ITEFVVDLDD DVTESDVNAA
Page 49

41. Multiple sequence alignment of human lipocalin paralogs
~~~~~EIQDVSGTWYAMTVDREFPEMNLESVTPMTLTTL.GGNLEAKVTM lipocalin 1
LSFTLEEEDITGTWYAMVVDKDFPEDRRRKVSPVKVTALGGGNLEATFTF odorant-binding protein 2a
TKQDLELPKLAGTWHSMAMATNNISLMATLKAPLRVHITSEDNLEIVLHR progestagen-assoc. endo.
VQENFDVNKYLGRWYEIEKIPTTFENGRCIQANYSLMENGNQELRADGTV apolipoprotein D
VKENFDKARFSGTWYAMAKDPEGLFLQDNIVAEFSVDETGNWDVCADGTF retinol-binding protein
LQQNFQDNQFQGKWYVVGLAGNAI.LREDKDPQKMYATIDKSYNVTSVLF neutrophil gelatinase-ass.
VQPNFQQDKFLGRWFSAGLASNSSWLREKKAALSMCKSVDGGLNLTSTFL prostaglandin D2 synthase
VQENFNISRIYGKWYNLAIGSTCPWMDRMTVSTLVLGEGEAEISMTSTRW alpha-1-microglobulin
PKANFDAQQFAGTWLLVAVGSACRFLQRAEATTLHVAPQGSTFRKLD complement component 8
Page 49

42. 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

43. Calculation of an alignment score

44. 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?

45. 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

46. Page 80

47. Dayhoff’s 34 protein superfamilies
Accepted point mutations
Protein PAMs per 100 million years
Ig kappa chain 37
Kappa casein 33
Lactalbumin
Hemoglobin a 12
Myoglobin
Insulin
Histone H
Ubiquitin
400 fold
From 1978
Page 50

48. Pairwise alignment of human (NP_005203)
versus mouse (NP_031812) ubiquitin

49. Multiple sequence alignment of
glyceraldehyde 3-phosphate dehydrogenases
fly GAKKVIISAP SAD.APM..F VCGVNLDAYK PDMKVVSNAS CTTNCLAPLA
human GAKRVIISAP SAD.APM..F VMGVNHEKYD NSLKIISNAS CTTNCLAPLA
plant GAKKVIISAP SAD.APM..F VVGVNEHTYQ PNMDIVSNAS CTTNCLAPLA
bacterium GAKKVVMTGP SKDNTPM..F VKGANFDKY. AGQDIVSNAS CTTNCLAPLA
yeast GAKKVVITAP SS.TAPM..F VMGVNEEKYT SDLKIVSNAS CTTNCLAPLA
archaeon GADKVLISAP PKGDEPVKQL VYGVNHDEYD GE.DVVSNAS CTTNSITPVA
fly KVINDNFEIV EGLMTTVHAT TATQKTVDGP SGKLWRDGRG AAQNIIPAST
human KVIHDNFGIV EGLMTTVHAI TATQKTVDGP SGKLWRDGRG ALQNIIPAST
plant KVVHEEFGIL EGLMTTVHAT TATQKTVDGP SMKDWRGGRG ASQNIIPSST
bacterium KVINDNFGII EGLMTTVHAT TATQKTVDGP SHKDWRGGRG ASQNIIPSST
yeast KVINDAFGIE EGLMTTVHSL TATQKTVDGP SHKDWRGGRT ASGNIIPSST
archaeon KVLDEEFGIN AGQLTTVHAY TGSQNLMDGP NGKP.RRRRA AAENIIPTST
fly GAAKAVGKVI PALNGKLTGM AFRVPTPNVS VVDLTVRLGK GASYDEIKAK
human GAAKAVGKVI PELNGKLTGM AFRVPTANVS VVDLTCRLEK PAKYDDIKKV
plant GAAKAVGKVL PELNGKLTGM AFRVPTSNVS VVDLTCRLEK GASYEDVKAA
bacterium GAAKAVGKVL PELNGKLTGM AFRVPTPNVS VVDLTVRLEK AATYEQIKAA
yeast GAAKAVGKVL PELQGKLTGM AFRVPTVDVS VVDLTVKLNK ETTYDEIKKV
archaeon GAAQAATEVL PELEGKLDGM AIRVPVPNGS ITEFVVDLDD DVTESDVNAA

50. From closely related protein sequences (at least 85% identity)
Dayhoff’s numbers of “accepted point mutations”:
what amino acid substitutions occur in proteins?
From closely related protein sequences (at least 85% identity)
Numbers of APM, multiplied by 10, in 1572 cases of amino acid substitutions from closely related sequences

51. The relative mutability of amino acids
Asn His 66
Ser Arg 65
Asp Lys 56
Glu Pro 56
Ala Gly 49
Thr 97 Tyr 41
Ile 96 Phe 41
Met 94 Leu 40
Gln 93 Cys 20
Val 74 Trp 18
Describes how often each amino acid is likely to change over a short evolutionary period
Page 53

52. Normalized frequencies of amino acids
Gly 8.9% Arg 4.1%
Ala 8.7% Asn 4.0%
Leu 8.5% Phe 4.0%
Lys 8.1% Gln 3.8%
Ser 7.0% Ile 3.7%
Val 6.5% His 3.4%
Thr 5.8% Cys 3.3%
Pro 5.1% Tyr 3.0%
Glu 5.0% Met 1.5%
Asp 4.7% Trp 1.0%
blue=6 codons; red=1 codon
Page 53

53. Page 54

54. Dayhoff’s PAM1 mutation probability matrix
There is 98.67%chance that A will be replaced by A over an evolutionary distance of 1 PAM
Original amino acid
Each element shows the probability that an original amino acid j (columns)will be replaced byanother amino acid i (rows) for 1% sequence divergence
Replaced amino acid

55. Dayhoff’s PAM1 mutation probability matrix
Each element of the matrix shows the probability that an original
amino acid (top) will be replaced by another amino acid (side)

56. 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.

57. Point-accepted mutations
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)

58. Dayhoff’s PAM1 mutation probability matrix
Page 55

59. Dayhoff’s PAM0 mutation probability matrix:
the rules for extremely slowly evolving proteins
Top: original amino acid
Side: replacement amino acid
Page 56

60. Dayhoff’s PAM2000 mutation probability matrix:
the rules for very distantly related proteins
PAM A
Ala R
Arg N
Asn D
Asp C
Cys Q
Gln E
Glu G
Gly
8.7%
4.1% N
4.0% D
4.7% C
3.3% Q
3.8% E
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

61. PAM250 mutation probability matrix
Top: original amino acid
Side: replacement amino acid
Page 57

62. PAM250 log odds
scoring matrix
S(a,b)= 10 log10 (Mab/Pb)
Page 58

63. 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

68. 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,
S(a,tryptophan) = 10 log10 (0.55/0.010) = 17.4
Normalized frequency of W is 0.01

69. 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

70. 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

71. PAM250 log odds
scoring matrix
Page 58

72. PAM10 log odds
scoring matrix
Page 59

73. Rat versus
mouse RBP
Rat versus
bacterial
lipocalin

74. 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, CADMVGTFTDTEDPAKFKM
btlact, 80 GECAQKKIIAEKTKIPAVFKI
** * ** **
Page 60

75. 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

76. BLOSUM Matrices 100 collapse Percent amino acid identity 62 30

77. BLOSUM Matrices 100 100 100 collapse collapse 62 62 62 collapse
Percent amino acid identity 30 30 30
BLOSUM80
BLOSUM62
BLOSUM30

78. 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

79. 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

80. 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
K I F I M K
N L F K T R
K I F K T K
K L F E S R
K I F K G R
G D E V K
G D S K K
G D P K A
G D A E R
G D A A K

81. • 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

82. 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)

86. 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

87. Blosum62 scoring matrix
Page 61

88. 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

89. Major Differences between PAM and BLOSUM

90. Point-accepted mutations
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)

91. Two randomly diverging protein sequences change
in a negatively exponential fashion
Percent identity
“twilight zone”
Evolutionary distance in PAMs
Page 62

92. 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
PAM250
Percent identity
Differences per 100 residues
“twilight zone”
PAM matrices reflect different degrees of divergence
Page 62

93. 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

94. Ancestral sequence Sequence 1 Sequence 2 ACCCTAC A no change A
C single substitution C --> A
C multiple substitutions C --> A --> T
C --> G coincidental substitutions C --> A
T --> A parallel substitutions T --> A
A --> C --> T convergent substitutions A --> T
C back substitution C --> T --> C
Sequence 1
Sequence 2
Li (1997) p.70

97. Percent identity between two proteins: What percent is significant?
100%
80%
65%
30%
23%
19%

98. 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