Sequence comparison and Phylogeny

1
Sequence comparisonand Phylogeny
based on Chapter 4 Lesk, Introduction to
Bioinformatics
2
Contents

• Motivation
• Sequence comparison and alignments
• Dot plots
• Dynamic programming
• Substitution matrices
• Dynamic programming Local and global alignments
  and gaps
• BLAST
• Significance of alignments
• Multiple sequence alignments
• Phylogenetic trees

3
Motivation

• From where are we?
• Recent Africa vs. Multi-regional Hypothese
• In 1999 Encephalitis caused by the West Nile
  Virus broke out in New York. How did the virus
  come to New York?
• How did the nucleus get into the eucaryotic
  cells?
• To answer such questions we will need sequence
  comparison and phylogenetic trees

4
Sequence Similarity Searches

• Sequence similarity can be clue to common
  evolutionary ancestor
• E.g. globin genes in chimpanzees and humans
• or common function
• E.g. v-sys onco genes in simian sarcoma virus
  leading to cancer in monkeys and the seemingly
  unrelated growth stimulating hormone PDGF, which
  stimulates cell growth (first success of
  similarity idea, 1983)
• In general
• If an unknown sequences is found, deduce its
  function/structure indirectly by finding similar
  sequences, whose function/structure is known
• Assumption Evolution changes sequences slowly
  often maintaining main features of a sequences
  function/structure

5
Sequence alignment

• Substitutions, insertions and deletions can be
  interpreted in evolutionary terms
• But distinguish chance similarity and real
  biological relationship

CCGTAA
TCGTAA
CCGTAT
TCGTAC
TTGTAA
TCGTAG
TAGTAC
6
Evolution

• Convergent evolution same sequence evolved from
  different ancestors
• Back evolution - mutate to a previous sequence

CCGTAA
TCGTAA
CCGTAT
TCGTAC
TAGTAA
TCGTAG
TAGTAC
TAGTAC
CCGTAA
7
Similarity vs. Homology

• Any sequence can be similar
• Sequences homologues if evolved from common
  ancestor
• Homologous sequences
• Orthologs similar biological function
• Paralogs different biological function (after
  gene duplication), e.g. lysozyme and
  a-lactalbumin, a mammalian regulatory protein
• Assumption Similarity indicator for homology
• Note, altered function of the expressed protein
  will determine if the organism will survive to
  reproduce, and hence pass on the altered gene

8
Sequence alignments

• Given two or more sequences, we wish to
• Measure their similarity
• Determine the residue-residue correspondences
• Observe patterns of conservation and variability
• Infer evolutionary relationships

9
What is the best alignment?

• Uninformative -------gctgaacg ctataatc------
  -
• Without gaps gctgaacg ctataatc
• With gaps gctga-a--cg --ct-ataatc
• Another one gctg-aa-cg -ctataatc-
• Formally The best alignment have only a minimal
  number of mismatches (insertions, deletions,
  replace)
• We need a method to systematically explore and to
  compute alignments

10
Scores for an alignment

• Percentage of matches
• Score each match, mismatch, gap opening, gap
  extension
• Example
• match 1
• mismatch -1
• Gap opening -3
• Gap extension -1
• Uninformative 0, score -21 -------gctgaacg
  ctataatc-------
• Without gaps25,score -4 gctgaacg ctataatc
  
• With gaps 0, score -23 gctga-a--cg --ct-a
  taatc
• Another one 50, score-12 gctg-aa-cg -ctat
  aatc-

11
Scores for an alignment

• Percentage of matches
• Score each match, mismatch, gap opening, gap
  extension
• Example
• match 2
• mismatch -1
• Gap opening -1
• Gap extension -1
• Uninformative 0, score -17 -------gctgaacg
  ctataatc-------
• Without gaps25,score -2 gctgaacg ctataatc
  
• With gaps 0, score -15 gctga-a--cg --ct-a
  taatc
• Another one 50, score0 gctg-aa-cg -ctataa
  tc-

12
Dot plots
13
Dot plots

• A convenient way of comparing 2 sequences
  visually
• Use matrix, put 1 sequence on X-axis, 1 on Y-axis
• Cells with
• identical characters filled with a 1,
• non-identical with 0
• (simplest scheme - could have weights)

14
Dot plots
15
Dot plots
16
Interpreting dot plots

• What do identical sequences look like?
• What do unrelated sequences look like?
• What do distantly related sequences look like?
• What does reverse sequence look like?
• Relevant for detections of stems in RNA structure
• What does a palindrome look like?
• Relevant for restriction enzymes
• What do repeats look like?
• What does a protein with domains A and B and
  another one with domains B and C look like?

17
Dot plot for identical sequences
18
Dotplot for unrelated sequences
19
Dotplot for distantly related sequences
20
Dotplot for reverse sequences
21
Dotplot for reverse sequences

• Relevant to identify stems in RNA structures
• Plot sequence against its reverse complement

22
Palindromes and restriction enzymes

• Madam, I'm Adam
• Able was I ere I saw Elba (supposedly said by
  Napoleon)
• Doc note I dissent, a fast never prevents a
  fatness, I diet on cod.
• Because DNA is double stranded and the strands
  run antiparallel, palindromes are defined as any
  double stranded DNA in which reading 5 to 3
  both are the same
• The HindIII cutting site
• 5'-AAGCTT-3'
• 3'-TTCGAA-5'
• The EcoRI cutting site
• 5'-GAATTC-3'
• 3'-CTTAAG-5'

23
Dotplot of a Palindrome
24
Dotplot of repeats
25
Dotplot of Repeats/Palindrome
26
Dotplot for shared domain
27
Result

• Dot plot
• dorothycrowfoothodgkin
• d
• o
• r
• o
• t
• h
• y
• h
• o
• d
• g
• k
• i
• n

28
Result

• Dot plot
• dorothycrowfoothodgkin
• d
• o
• r
• o
• t
• h
• y
• h
• o
• d
• g
• k
• i
• n

29
Dotplots

• Window size 15
• Dot if
• 6 matches in window

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gtgi1942644pdb1MEG Crystal Structure Of A
Caricain D158e Mutant In Complex With E-64
Length 216 Score 271 bits (693), Expect
1e-73 Identities 142/216 (65), Positives
168/216 (77), Gaps 4/216 (1) Query 1
IPEYVDWRQKGAVTPVKNQGSCGSCWAFSAVVTIEGIIKIRTGNLNQYSE
QELLDCDRRS 60 PE VDWRKGAVTPVQGSCGSC
WAFSAV TEGI KIRTG L SEQELDCRRS Sbjct 1
LPENVDWRKKGAVTPVRHQGSCGSCWAFSAVATVEGINKIRTGKLVELSE
QELVDCERRS 60 Query 61 YGCNGGYPWSALQLVAQYGIHYRN
TYPYEGVQRYCRSREKGPYAAKTDGVRQVQPYNQGA 120
GC GGYP AL VA GIH R YPY Q CR G KT
GV VQP NG Sbjct 61 HGCKGGYPPYALEYVAKNGIHLRSKY
PYKAKQGTCRAKQVGGPIVKTSGVGRVQPNNEGN 120 Query
121 LLYSIANQPVSVVLQAAGKDFQLYRGGIFVGPCGNKVDHAVAAV--
--GYGPNYILIKNS 176 LL IA QPVSVV G
FQLYGGIF GPCG KVHAV AV G YILIKNS Sbjct
121 LLNAIAKQPVSVVVESKGRPFQLYKGGIFEGPCGTKVEHAVTAVGY
GKSGGKGYILIKNS 180 Query 177 WGTGWGENGYIRIKRGTGN
SYGVCGLYTSSFYPVKN 212 WGT WGE GYIRIKR
GNS GVCGLY SSYP KN Sbjct 181 WGTAWGEKGYIRIKRAPGN
SPGVCGLYKSSYYPTKN 216 1 lpenvdwrkk
gavtpvrhqg scgscwafsa vatveginki rtgklvelse
qelvdcerrs 61 hgckggyppy aleyvakngi
hlrskypyka kqgtcrakqv ggpivktsgv grvqpnnegn
121 llnaiakqpv svvveskgrp fqlykggife gpcgtkveha
vtavgygksg gkgyilikns 181 wgtawgekgy
irikrapgns pgvcglykss yyptkn
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• gtgi2624670pdb1AIM Cruzain Inhibited By
  Benzoyl-Tyrosine-Alanine- Fluoromethylketone
• Length 215
• Score 121 bits (303), Expect 3e-28
• Identities 78/202 (38), Positives 107/202
  (52), Gaps 13/202 (6)
• Query 2 PEYVDWRQKGAVTPVKNQGSCGSCWAFSAVVTIEGIIKI
  RTGNLNQYSEQELLDCDRRSY 61
• P VDWR GAVT VKQG CGSCWAFSA E
  L SEQ L CD
• Sbjct 2 PAAVDWRARGAVTAVKDQGQCGSCWAFSAIGNVECQWFL
  AGHPLTNLSEQMLVSCDKTDS 61
• Query 62 GCNGGYPWSALQLVAQY---GIHYRNTYPY---EGVQRY
  CRSREKGPYAAKTDGVRQVQP 115
• GCGG A Q YPY EG
  C A T V Q
• Sbjct 62 GCSGGLMNNAFEWIVQENNGAVYTEDSYPYASGEGISPP
  CTTSGHTVGATITGHVELPQD 121
• Query 116 YNQGALLYSIANQPVSVVLQAAGKDFQLYRGGIFVGPCG
  NKVDHAVAAVGYGPN----YI 171
• Q A N PVV A Y GG
  DH V VGY Y
• Sbjct 122 EAQIAAWLAV-NGPVAVAVDAS--SWMTYTGGVMTSCVS
  EALDHGVLLVGYNDSAAVPYW 178
• Query 172 LIKNSWGTGWGENGYIRIKRGT 193

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• gi7546546pdb1EF7B Chain B, Crystal
  Structure Of Human Cathepsin X
• Length 242
• Score 52.0 bits (123), Expect 2e-07
• Identities 60/231 (25), Positives 94/231
  (40), Gaps 34/231 (14)
• Query 1 IPEYVDWRQKGAV---TPVKNQ---GSCGSCWAFSAVVT
  IEGIIKIRTGNL---NQYSEQ 51
• P DWR V NQ CGSCWA
  I I S Q
• Sbjct 1 LPKSWDWRNVDGVNYASITRNQHIPQYCGSCWAHASTSA
  MADRINIKRKGAWPSTLLSVQ 60
• Query 52 ELLDCDRRSYGCNGGYPWSALQLVAQYGIHYRNTYPYEG
  VQRYCR--------SREKGPY 103
• DC C GG S QGI Y
  C K
• Sbjct 61 NVIDCGNAG-SCEGGNDLSVWDYAHQHGIPDETCNNYQA
  KDQECDKFNQCGTCNEFKECH 119
• Query 104 AAKTDGVRQVQPYN-----QGALLYSIANQPVSVVLQAA
  GKDFQLYRGGIFVGPCGNK-V 157
• A V Y AN PS A
  Y GGI
• Sbjct 120 AIRNYTLWRVGDYGSLSGREKMMAEIYANGPISCGIMAT
  ER-LANYTGGIYAEYQDTTYI 178
• Query 158 DHAVAAVGY----GPNYILIKNSWGTGWGENGYIRI---
  --KRGTGNSYGV 199

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38
Dynamic programming
39
From Dotplots to Alignments

• Obvious best alignment DOROTHYCROWFOOTHODGKIN
  DOROTHY--------HODGKIN

40
From Dotplots to Alignments

• Find best path from top left corner to bottom
  right
• Moving east corresponds to - in the second
  sequence
• Moving south corresponds to - in the first
  sequence
• Moving southeast corresponds to a match if the
  characters are the same or a mismatch otherwise
• Can we automate this?

41
From Dotplots to Alignments

• Algorithm (Dynamic Programming)
• Insert a row 0 and column 0 initialised with 0
• Starting from the top left, move down row by row
  from row 1 and
• right column by column from column 1 visiting
  each cell
• Consider
• The value of the cell north
• The value of the cell west
• The value of the cell northwest if the row/column
  character mismatch
• 1 the value of the cell northwest if the
  row/column character match
• Put down the maximum of these values as the value
  for the current cell
• Trace back the path with the highest values from
  the bottom right to the top left and output the
  alignment

42
From Dotplots to Alignments

• 0 1 2 3 4 5 6 T G C A T A0 1 A2 T3
  C4 T5 G6 A7 T

43
From Dotplots to Alignments

• 0 1 2 3 4 5 6 T G C A T A0 0 0 0 0 0 0 01
  A 02 T 03 C 04 T 05 G 06 A 07 T 0
• Insert a row 0 and column 0 initialised with 0

44
From Dotplots to Alignments

• 0 1 2 3 4 5 6 T G C A T A0 0 0 0 0 0 0 01
  A 0 0 0 0 1 1 12 T 03 C 04 T 05 G 06 A 07
  T 0

• Consider
• Value north
• Value west
• Value northwest if the row/column character
  mismatch
• 1 value northwest if the row/column character
  match
• Put down the maximum of these values for current
  celll

45
From Dotplots to Alignments

• 0 1 2 3 4 5 6 T G C A T A0 0 0 0 0 0 0 01
  A 0 0 0 0 1 1 12 T 0 1 1 1 1 2 23
  C 0 1 1 2 2 2 24 T 0 1 1 2 2 3 35
  G 0 1 2 2 2 3 36 A 0 1 2 2 3 3 47
  T 0 1 2 2 3 4 4

46
Reading the Alignment

• 0 1 2 3 4 5 6 T G C A T A0 0 0 0 0 0 0 01
  A 0 0 0 0 1 1 12 T 0 1 1 1 1 2 23
  C 0 1 1 2 2 2 24 T 0 1 1 2 2 3 35
  G 0 1 2 2 2 3 36 A 0 1 2 2 3 3 47
  T 0 1 2 2 3 4 4

-tgcat-a- at-c-tgat
47
Reading the Alignment there are more than one
possibility

• 0 1 2 3 4 5 6 T G C A T A0 0 0 0 0 0 0 01
  A 0 0 0 0 1 1 12 T 0 1 1 1 1 2 23
  C 0 1 1 2 2 2 24 T 0 1 1 2 2 3 35
  G 0 1 2 2 2 3 36 A 0 1 2 2 3 3 47
  T 0 1 2 2 3 4 4

---tgcata atctg-at-
48
FormallyLongest Common Subsequence LCS

• What is the length s(V,W) of the longest common
  subsequence of two sequencesVv1..vn and
  Ww1..wm ?
• Find sequences of indices1 i1 lt lt ik n and
  1 j1 lt lt jk msuch that vit wjt for 1
  t k
• How? Dynamic programming
• si,0 s0,j 0 for all 1 i n and 1 j m
  and
• si-1,jsi,j max si,j-1 si-1,j-1 1,
  if vi wj
• Then s(V,W) sn,m is the length of the LCS

49
Example LCS

• 0 1 2 3 4 5 6 T G C A T A0 1 A2 T3
  C4 T5 G6 A7 T

50
Example LCS

• 0 1 2 3 4 5 6 T G C A T A0 0 0 0 0 0 0 01
  A 02 T 03 C 04 T 05 G 06 A 07 T 0
• Initialisation si,0 s0,j 0 for all 1 i
  n and 1 j m and

51
Example LCS

• 0 1 2 3 4 5 6 T G C A T A0 0 0 0 0 0 0 01
  A 0 0 0 0 1 1 12 T 03 C 04 T 05 G 06 A 07
  T 0
• Computing each cell si-1,j si,j max
  si,j-1 si-1,j-1 1, if vi wj

52
Example LCS

• 0 1 2 3 4 5 6 T G C A T A0 0 0 0 0 0 0 01
  A 0 0 0 0 1 1 12 T 0 1 1 1 1 2 23
  C 0 1 1 2 2 2 24 T 0 1 1 2 2 3 35
  G 0 1 2 2 2 3 36 A 0 1 2 2 3 3 47
  T 0 1 2 2 3 4 4
• Computing each cell si-1,j si,j max
  si,j-1 si-1,j-1 1, if vi wj

53
LCS Algorithm

• Complexity
• LCS has quadratic complexity O(n m)

• LCS(V,W)
• For i 1 to n
• si,0 0
• For j 1 to m
• s0,j 0
• For i 1 to n
• For j 1 to m
• If vi wj and si-1,j-1 1 si-1,j and si-1,j-1
  1 si,j-1 Then
• si,j si-1,j-1 1
• bi,j North West
• Else if si-1,j si,j-1 Then
• si,j si-1,j
• bi,j North
• Else
• si,j si,j-1
• bi,j West
• Return s and b

54
Printing the alignment of LCS

• PRINT-LCS(b,V,i,j)
• If i0 or j0 Then Return
• If bi,j North West Then
• PRINT-LCS(V,b,i-1,j-1)
• Print vi
• Else if bi,j North Then
• PRINT-LCS(V,b,i-1,j)
• Else
• PRINT-LCS(V,b,i,j-1)

55
Rewards/Penalities

• We can use different schemes
• -1 for insert/delete/mismatch
• 1 for match
• Consider
• -1 the value of the cell north
• -1 the value of the cell west
• -1 the value of the cell northwest if the
  row/column character mismatch
• 1 the value of the cell northwest if the
  row/column character match
• Put down the maximum of these values as the value
  for the current cell

56
Reading the Alignment

• 0 1 2 3 4 5 6 T G C A T A0 0 0 0 0 0 0 01
  A 0 -1 -1 -1 1 0 12 T 0 1 0 -1 0 2 13
  C 0 0 -1 1 0 1 14 T 0 1 0 0 0 1 05
  G 0 0 2 1 0 0 06 A 0 -1 1 1 2 1 17
  T 0 1 0 0 1 3 2

---tgcata atctg-at-
57
Rewards/Penalities

• Lets refine the schemes
• Transition mutations are more common
• purinelt-gtpurine, alt-gtg
• pyrimidinelt-gtpyrimidine, tlt-gtc
• Transversions (purinelt-gtpyrimidine) are less
  common
• Use a subsitutation matrix to rate mismatches
• -2 for insert/delete
• Mismatch/match according to substitution matrix
• Consider
• -2 the value of the cell north
• -2 the value of the cell west
• Corresponding value of the substion matrix the
  value of the cell northwest
• Put down the maximum of these values as the value
  for the current cell

58
Reading the Alignment

• 0 1 2 3 4 5 6 T G C A T A0 0 0 0 0 0 0 01
  A 0 -2 0 -2 2 0 22 T 0 2 0 0 0 4 23
  C 0 0 0 2 0 2 24 T 0 2 0 0 0 2 05
  G 0 0 4 2 0 0 26 A 0 -2 2 2 4 2 27
  T 0 2 0 2 2 6 4

---tgcata atctg-at-
59
Substitution matrixes
60
How to derive a substitution matrix for amino
acids?

• Amino acids can be classified by physiochemical
  properties

61
PAM 250 matrix
Cys 12 Ser 0 2 Thr -2 1 3 Pro -3 1 0
6 Ala -2 1 1 1 2 Gly -3 1 0 -1 1 5 Asn -4
1 0 -1 0 0 2 Asp -5 0 0 -1 0 1 2 4 Glu
-5 0 0 -1 0 0 1 3 4 Gln -5 -1 -1 0 0 -1
1 2 2 4 His -3 -1 -1 0 -1 -2 2 1 1 3
6 Arg -4 0 -1 0 -2 -3 0 -1 -1 1 2 6 Lys -5
0 0 -1 -1 -2 1 0 0 1 0 3 5 Met -5 -2 -1
-2 -1 -3 -2 -3 -2 -1 -2 0 0 6 Ile -2 -1 0 -2
-1 -3 -2 -2 -2 -2 -2 -2 -2 2 5 Leu -6 -3 -2 -3
-2 -4 -3 -4 -3 -2 -2 -3 -3 4 2 6 Val -2 -1 0
-1 0 -1 -2 -2 -2 -2 -2 -2 -2 2 4 2 4 Phe -4
-3 -3 -5 -4 -5 -4 -6 -5 -5 -2 -4 -5 0 1 2 -1
9 Tyr 0 -3 -3 -5 -3 -5 -2 -4 -4 -4 0 -4 -4 -2
-1 -1 -2 7 10 Trp -8 -2 -5 -6 -6 -7 -4 -7 -7 -5
-3 2 -3 -4 -5 -2 -6 0 0 17 C S T P A
G N D E Q H R K M I L V F Y W
gt0, likely mutation 0, random mutation lt0,
unlikely
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PAM 250 Interpretation

• Immutable
• Cysteine (Avg-2.8) known to have several
  unique, indispensable functions
• attachment site of heme group in cytochrome and
  of iron sulphur FeS in ferredoxins
• Cross links in proteins such as chymotrypsin or
  ribonuclease
• Seldom without unique function
• Glycine (Avg-1.6) small size maybe advantageous
  
• Mutable
• Serine often functions in active site, but can be
  easily replaced
• Self-alignment
• Tryptophan with itself scores very high, as W
  occurs rarely

65
Point Accepted Mutations PAM

• Substitution matrix using explicit evolutionary
  model of how amino acids change over time
• Use parsimony method to determine frequency of
  mutations
• Entry in PAM matrix Likelihood ratio for
  residues a and b Probability a-b is a mutation /
  probability a-b is chance
• PAM x Two sequences V, W have evolutionary
  distance of x PAM if a series of accepted point
  mutations (and no insertions/deletions) converts
  V into W averaging to x point mutation per 100
  residues
• Mutations here mutations in the DNA
• Because of silent mutations and back mutations n
  can be gt100
• PAM 250 most commonly used

66
PAM and Sequence Similarity
67
PAM

• Dayhoff, Eck, Park A model of evolutionary
  change in proteins, 1978
• Accepted point mutation substitution of an
  amino acid accepted by natureal selection
• Assumption X replacing Y as likely as Y
  replacing X
• Used cytochrome c, hemoglobin, myoglobin, virus
  coat proteins, chymotrypsinogen, glyceraldehyde
  3-phosphate dehrydogenase, clupeine, insulin,
  ferredoxin
• Sequences which are too distantly related have
  been omitted as they are more likely to contain
  multiple mutations per site

68
PAM Step 1

• Step 1 Construct a multiple alignment
• Example
• ACGCTAFKI
• GCGCTAFKI
• ACGCTAFKL
• GCGCTGFKI
• GCGCTLFKI
• ASGCTAFKL
• ACACTAFKL

69
PAM Step 2

• Create a phylogenetic tree (parsimony method)

ACGCTAFKI A-gtG
I-gtL GCGCTAFKI ACGCTAFKL
A-gtG A-gtL C-gtS G-gtA GCGCTGFKI
GCGCTLFKI ASGCTAFKL ACACTAFKL
70
PAM Step 3

• Note, the following variables
• Residue frequency ri is the number of amino acid
  i occurring in the sequences, e.g. rA 10 and
  rG10
• Number of residues r is the number of overall
  amino acids in all sequences, e.g. r63
• Substitutability si is the number of
  substitutions in the tree involving amino acid i
  , e.g. sA4
• Substituion frequency si,j is the number of
  substitutions involving amino acid i and j (i.e.
  the number of i?j and j?i ), e.g. sA,G 3
• Number of substitutions s is the number of
  overall substitutions, s6

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PAM Step 4

• Relative mutability is the number of times the
  amino acid is substituted by any other amino acid
  in the tree divided by the total number of
  substitutions that could have affected the
  residue
• Note, it is assumed that substitutions in both
  directions are equally likely
• mi 100 x ( si x ri ) / ( 2 s x r )
• Example mA 100 x ( 4 x 10 ) / ( 2 x 6 x 63 )
  5.3

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PAM Step 5

• Compute mutation probability
• Mi,j mj x si,j / sj
• Example MG,A 5.3 x 3 / 4 3.975

73
PAM Step 6

• Finally the entry in the PAM Matrix
• Ri,j log ( Mi,j / ( ri / r ) )
• Example RG,A log ( 3.975 / (10/63) ) 1.4

74
PAM Step 6

• For the entries on the diagonal
• mj relative mutability ? 1-mj relative
  immutability
• Rj,j log ( (1-mj ) / ( rj / r ) )

75
BLOSUM

• Different approach to PAM
• BLOcks SUbstitution Matrix (based on BLOCKS
  database)
• Generation of BLOSUM x
• Group highly similar sequences and replace them
  by a representative sequences.
• Only consider sequences with no more than x
  similarity
• Align sequences (no gaps)
• For any pair of amino acids a,b and for all
  columns c of the alignment, let q(a,b) be the
  number of co-occurrences of a,b in all columns c.
• Let p(a) be the overall probability of a
  occurring
• BLOSUM entry for a,b is log2 ( q(a,b) / (
  p(a)p(b) ) )
• BLOSUM 50 and BLOSUM 62 widely used

76
LCS Algorithm (Longest Common Subsequence)
Revisited

• Algorithm (Dynamic Programming) with Substitution
  Matrix
• Insert a row 0 and column 0 initialised with 0
• Starting from the top left, move down row by row
  from row 1 and
• right column by column from column 1 visiting
  each cell
• Consider
• The value of the cell north
• The value of the cell west
• The value of the cell northwest if the row/column
  character mismatch
• s the value of the cell northwest, where s is
  the value in the subsitution matrix for the
  residues in row/column
• Put down the minimum of these values as the value
  for the current cell
• Trace back the path with the highest values from
  the bottom right to the top left and output the
  alignment

77
LCS Revisited Formally

• What is the length s(V,W) of the longest common
  subsequence of two sequencesVv1..vn and
  Ww1..wm ?
• Find sequences of indices1 i1 lt lt ik n and
  1 j1 lt lt jk msuch that vit wjt for 1
  t k
• How? Dynamic programming
• si,0 s0,j 0 for all 1 i n and 1 j m
  and
• si-1,jsi,j max si,j-1 si-1,j-1 t,
  where t is the value for vi and wj in
  the substitution matrix
• Then s(V,W) sn,m is the length of the LCS

78
Dynamic programming revisitedlocal and global
alignments and gap
79
Evolution and Alignments

• Alignments can be interpreted in evolutionary
  terms
• Identical letters are aligned. Interpretation
  part of the same ancestral sequence and not
  changed
• Non-identical letters are aligned
  (substitution)Interpretation Mutation
• GapsInterpretation Insertions and deletions
  (indels)

80
Evolution and Alignments

• Specific problems aligning DNA
• Frame shift
• DNA triplets code amino acids
• Indel of one nucleotide shifts the whole sequence
  of triplets
• Thus may have a global effect and change all
  coded amino acids
• Silent mutation
• Substitution in DNA leaves transcribed amino acid
  unchanged
• Non-sense mutation
• Substitution to stop-codon

81
Local and Global Alignments

• Global alignment (Needleham-Wunsch) algorithm
  finds overall best alignment
• Example members of a protein family, e.g.
  globins are very conserved and have the same
  length in different organisms from fruit fly to
  humans
• Local alignment (Smith-Waterman) algorithm finds
  locally best alignment
• most widely used, as
• e.g. genes from different organisms retain
  similar exons, but may have different introns
• e.g. homeobox gene, which regulates embryonic
  development occurs in many species, but very
  different apart from one region called
  homeodomain
• e.g. proteins share some domains, but not all

82
Local Alignment

• LCS s(V,W) computes globally best alignment
• Often it is better to maximise locally, i.e.
  compute maximal s(vivi , wj wi ) for all
  substrings of V and W
• Can we adapt algorithm?
• Global alignment longest path in matrix s from
  (0,0) to (n,m)
• Local alignment longest path in matrix s from
  any (i,j) to any (i,j)
• Modify definition of s adding vertex of weight 0
  from source to every other vertex, creating a
  free jump to any starting position (i,j)

83
Local Alignment

• Modify the definition of s as follows
• si,0 s0,j 0 for all 1 i n and 1 j m
  and
• 0 si-1,jsi,j max si,j-1 si-1,j-1
  t, where t is the value for vi wj in the
  substitution matrix
• Then s(V,W) max si,j is the length of the
  local LCS
• This computes longest path in edit graph
• Several local alignment may have biological
  significance (consider e.g. two multi-domain
  proteins whose domains are re-ordered

84
Aligning with Gap Penalties

• Gap is sequence of spaces in alignment
• So far, we consider only insertion and deletion
  of single nucleotides or amino acids creating
  alignments with many gaps
• So far, score of a gap of length l is l
• Because insertion/deletion of monomers is
  evolutionary slow process, large numbers of gaps
  do not make sense
• Instead whole substrings will be deleted or
  inserted
• We can generalise score of a gap to a score
  function A B l, where A is the penalty to open
  the gap and B is the penalty to extend the gap

85
Aligning with Gap Penalties

• High gap penalties result in shorter,
  lower-scoring alignments with fewer gaps and
• Lower gap penalties give higher-scoring, longer
  alignments with more gaps
• Gap opening penalty A mainly influences number of
  gaps
• Gap extension penalty B mainly influences length
  of gaps
• E.g. if interested in close relationships, then
  choose A, B above default values, for distant
  relationships decrease default values

86
Aligning with Gap Penalties

• Adapt the definition of s as follows
• s-deli,j max s-deli-1,j - B si-1,j
  (AB)
• s-insi,j max s-insi,j-1 - B si,j-1
  (AB)
• 0 s-deli,jsi,j max s-insi,j
  si-1,j-1 t, where t is the value for vi,
  wj in the substitution matrix Then s(V,W)
  max si,j is the length of the local LCS with
  gap penalties A and B

87
FASTA and BLAST
88
Motivation

• As in dotplots, the underlying data structure for
  dynamic programming is a table
• Given two sequences of length n dynamic
  programming takes time proportional to n2
• Given a database with m sequences, comparing a
  query sequence to the whole database takes time
  proportional to m n2
• What does this mean?
• Imagine you need to fill in the tables by hand
  and it takes 10 second to fill in one cell
• Assume there are 1.000.000 sequences each 100
  amino acids long
• How long does it take?

89

• 1.000.000 x 100 x 100 x 10 sec 1011 sec
  27.777.778h 1157407days 3170 years
• Even if a computer does not take 10 sec, but just
  0.1ms to fill in one cell, it would still be 12
  days.
• We cannot do something about the database size,
  but can we do something about the table size?

90
An idea Prune the search space
91
Another idea

• Did we formulate the problem correctly?
• Do we need the alignments for all sequences in
  the database?
• No, only for reasonable hits ? introduce a
  threshold
• A reasonable alignment will contain short
  stretches of perfect matches
• Find these first, then extend them to connect
  them as best possible

92
FASTA and BLAST

• FASTA and BLAST faster than dynamic programming
  (5 times and 50 times respectively)
• Underlying idea for a heuristic
• High-scoring alignments will contain short
  stretches of identical letters, called words
• FASTA and BLAST first search for matches of words
  of a given length and score threshold
• BLAST for words of length 3 for proteins and 11
  for DNA
• FASTA for words of length 2 for proteins and 6
  for DNA
• Next, matches are extended to local (BLAST) and
  global (FASTA) alignments

93
FASTA and BLAST

• More formallyIf the strings Vv1..vm and
  Ww1..wm match with at most k mismatches, then
  they share an p-tuple for p ?m/(k1)?, i.e.
  vi..vil-1 wj..wjl-1 for some 1 i,j m-p1
• FILTRATION ALGORITHM, which detects all matching
  words of length m with up to k mismatches
• Potential match detection Find all matches of
  p-tuples of V,W (can be done in linear time by
  inserting them into a hash table)
• Potential match verification Verify each
  potential match by extending it to the left and
  right until either the first k1 mismatches are
  found or the beginning or end of the sequences
  are found

94
Example for BLAST

• Search SWISSPROT for Immunoglobulin

95
Example for BLAST

• Search BLAST (www.ncbi.nlm.nih.gov/BLAST/) for
  P11912

96
Example for BLAST

• Distribution of Hits

97
Example for BLAST Top Hits

• Score E Sequences producing significant
  alignments Score E-Value gi547896spP11912C7
  9A_HUMAN B-cell antigen receptor comp... 473
  e-133 gi728993spP40293C79A_BOVIN B-cell
  antigen receptor comp... 312 3e-85
  gi126779spP11911C79A_MOUSE B-cell antigen
  receptor comp... 278 5e-75 gi728994spP40259C
  79B_HUMAN B-cell antigen receptor comp... 55
  1e-07 gi125781spP01618KV1_CANFA IG KAPPA
  CHAIN V REGION GOM 38 0.019 gi125361spP17948
  VGR1_HUMAN Vascular endothelial growth ... 37
  0.042 gi549319spP35969VGR1_MOUSE Vascular
  endothelial growth ... 36 0.052
  gi114764spP15530C79B_MOUSE B-cell antigen
  receptor comp... 36 0.064 gi1718161spP53767V
  GR1_RAT Vascular endothelial growth f... 35
  0.080 gi125735spP01681KV01_RAT Ig kappa
  chain V region S211 35 0.095
  gi1730075spP01625KV4A_HUMAN IG KAPPA CHAIN
  V-IV REGION LEN 34 0.26 gi1718188spP52583VGR2
  _COTJA Vascular endothelial growth... 33 0.28
  gi125833spP06313KV4B_HUMAN IG KAPPA CHAIN
  V-IV REGION J... 33 0.30 gi125806spP01658KV3
  F_MOUSE IG KAPPA CHAIN V-III REGION ... 33 0.30
  gi125808spP01659KV3G_MOUSE IG KAPPA CHAIN
  V-III REGION ... 33 0.30 gi1172451spQ05793PG
  BM_MOUSE Basement membrane-specific ... 33 0.33
  gi125850spP01648KV5O_MOUSE Ig kappa chain V-V
  region HP... 33 0.36 gi125830spP06312KV40_HU
  MAN Ig kappa chain V-IV region p... 33 0.38
  gi2501738spQ06639YD03_YEAST Putative 101.7
  kDa transcri... 33 0.41

98
Example for BLAST Alignment
gtgi126779spP11911C79A_MOUSE B-cell antigen
receptor complex associated protein
alpha-chain precursor (IG-alpha) (MB-1 membrane
glycoprotein) (Surface-IGM-associated protein)
(Membrane-bound immunoglobulin associated
protein) (CD79A) Length 220 Score 278 bits
(711), Expect 5e-75 Identities 150/226 (66),
Positives 165/226 (73), Gaps 6/226
(2) Query 1 MPGGPGVLQALPATIFLLFLLSAVYLGPGCQA
LWMHKVPASLMVSLGEDAHFQCPHNSSN 60 MPGG
LL LS LGPGCQAL P SL VLGEA C
N Sbjct 1 MPGG----LEALRALPLLLFLSYACLGPGCQAL
RVEGGPPSLTVNLGEEARLTC-ENNGR 55 Query 61
NANVTWWRVLHGNYTWPPEFLGPGEDPNGTLIIQNVNKSHGGIYVCRVQ
EGNESYQQSCG 120 N NTWW L N TWPP
LGPG G L VNK G CV E N SCG Sbjct
56 NPNITWWFSLQSNITWPPVPLGPGQGTTGQLFFPEVNKNTGACTG
CQVIE-NNILKRSCG 114 Query 121
TYLRVRQPPPRPFLDMGEGTKNRIITAEGIILLFCAVVPGTLLLFRKRWQ
NEKLGLDAGD 180 TYLRVR P
PRPFLDMGEGTKNRIITAEGIILLFCAVVPGTLLLFRKRWQNEK GD
D Sbjct 115 TYLRVRNPVPRPFLDMGEGTKNRIITAEGIILLFCA
VVPGTLLLFRKRWQNEKFGVDMPD 174 Query 181
EYEDENLYEGLNLDDCSMYEDISRGLQGTYQDVGSLNIGDVQLEKP
226 YEDENLYEGLNLDDCSMYEDISRGLQGTYQDVG
LIGD QLEKP Sbjct 175 DYEDENLYEGLNLDDCSMYEDISRG
LQGTYQDVGNLHIGDAQLEKP 220
99
Example for BLAST

• Lineage Report
• root
• . cellular organisms
• . . Eukaryota eukaryotes
• . . . Fungi/Metazoa group eukaryotes
• . . . . Bilateria animals
• . . . . . Coelomata animals
• . . . . . . Gnathostomata vertebrates
• . . . . . . . Tetrapoda vertebrates
• . . . . . . . . Amniota vertebrates
• . . . . . . . . . Eutheria mammals
• . . . . . . . . . . Homo sapiens (man)
  ---------------------- 473 33 hits mammals
  B-cell antigen receptor complex associated
  protein alpha-ch
• . . . . . . . . . . Bos taurus (bovine)
  ..................... 312 2 hits mammals
  B-cell antigen receptor complex associated
  protein alpha-ch
• . . . . . . . . . . Mus musculus (mouse)
  .................... 278 31 hits mammals
  B-cell antigen receptor complex associated
  protein alpha-ch
• . . . . . . . . . . Canis familiaris (dogs)
  ................. 37 1 hit mammals
  IG KAPPA CHAIN V REGION GOM
• . . . . . . . . . . Rattus norvegicus (brown rat)
  ........... 35 7 hits mammals
  Vascular endothelial growth factor receptor 1
  precursor (VE
• . . . . . . . . . . Oryctolagus cuniculus
  (domestic rabbit) . 29 1 hit mammals
  IG KAPPA CHAIN V REGION K29-213
• . . . . . . . . . Coturnix japonica
  ------------------------- 33 2 hits birds
  Vascular endothelial growth factor
  receptor 2 precursor (VE
• . . . . . . . . . Gallus gallus (chickens)
  .................. 31 4 hits birds
  CILIARY NEUROTROPHIC FACTOR RECEPTOR ALPHA
  PRECURSOR (CNTFR

100
How good is an alignment?

• Be careful Fitch/Smith found 17 alignments for
  alpha- and beta-chains in chicken haemoglobins
• Only one is the correct one (according to the
  structure)
• Given an alignment, how good is it
• Percentage of matching residues, i.e. number of
  matches divided by length of smallest sequence
• Advantage independent of sequence length
• E.g. ATC TGAT 4/6 66.67 TGCAT A
• More general also consider gaps, extensions,

101
Blast Raw Score

• R a I b X - c O - d G, where
• I is the number of identities in the alignment
  and a is the reward for each identity
• X is the number of mismatches in the alignment
  and b is the reward for each mismatch
• O is the number of gaps and c is the penalty for
  each gap
• G is the number of - characters in the
  alignment and d is the penalty for each
• The values for a,b,c,d appear at the bottom of a
  Blast report. For BLASTn they are a1, b-3, c5,
  d2

102
Example

• Query 1 atgctctggccacggcacttgcgga
• Sbjt107 atgctctggccacggatcttgtgga
• tcccagggtgatctgtgcacctgcgata 53
• tccca---tgatatgtgcacctgcgata 156
• R 1 x 46 -3 x 4 - 5 x 1 - 2 x 3 23
• So, given the scores how significant is the
  alignment?

103
Significance of an alignment

• Significance of an alignment needs to be defined
  with respect to a control population
• Pairwise alignment How can we get control
  population?
• Generate sequences randomly? ? Not a good model
  of real sequences
• Chop up both sequences and randomly reassemble
  them
• Database search How can we get control
  population?
• Control whole database
• Align sequence to control population and see how
  good result is in comparison
• This is captured by Z scores, P-values and
  E-values

104
Z-score

• Z-score normalises the score S
• Let m be mean of population and std its standard
  deviation, then Z-score (S m) / std
• Z-score of 0 ? no better than average, hence
  might have occurred by chance
• The higher the Z-score the better

105
P-value

• P-value probability of obtaining a score S
• Range 0 P 1
• Let m be the number of sequences in the control
  population with score S
• Let p be the size of the control population
• Then P-value m / p
• Rule of thumb
• P 10-100 exact match,
• 10-100 P 10-50 nearly identical (SNPs)
• 10-50 P 10-10 homology certain
• 10-5 P 10-1 usually distant relative
• P gt 10-1 probably insignificant

106
E-values

• E-value takes also the database into account
• E-value expected frequency of a score S
• Range 0 E m, where m is the size of the
  database
• Relationship to P E m P
• E values are calculated from
• the bit score
• the length of the query
• the size of the database

107
BLAST Bit score

• The bit score normalizes the raw score S to make
  score under different settings comparable
• The bit score is obtained from the raw score as
  follows
• S ( lambda x R - ln(K) ) / ( ln(2),
• where lambda 1.37 and K0.711
• Example
• S ( 1.37 x 23 - ln(0.711) ) / ln(2) 46

108
E-value

• The E-value is then calculated as follows
• E m x n x 2 -S , where
• m is the effective length of the query
• n is the effective length of the database
• S is the bit score
• (effective length takes into account that an
  alignment cannot start at the end of a sequence)
• Example
• m34 (19 nucleotides fewer than the 53 submitted)
• n5,854,611,841
• Result E0.003

109
Precision and Recall

• How good are BLAST and FASTA?
• True positives, tp hits which are biologically
  meaningful
• False positives, fp hits which are not
  biologically meaningful
• True negatives, tn non-hits which are not
  biologically meaningful
• False negatives, fn non-hits which are
  biologically meaningful
• Minimise fp and fn
• Recall tp/(tpfn) (meaningful hits / all
  meaningful)
• Precision tp/(tpfp) (meaningful hits / all
  hits)
• But since no objective data available difficult
  to judge BLAST and FASTAs sensitivity and
  specificity

110
Multiple Sequence Alignments
111
Multiple Sequence Alignment

• Align more than two sequences
• Choice of sequences
• If too closely related then large redundant
• If very distantly related then difficult to
  generate good alignment
• Additionally use colour for residues with similar
  properties
• Yellow Small polar GLy,Ala,Ser,Thr
• Green Hydrophobic Cys,Val,Ile,Leu, Pro,Phe
  ,Tyr,Met,Trp
• Magenta Polar Asn,Gln,His
• Red Negatively charged Asp,Glu
• Blue Positively charged Lys, Arg

112
Thioredoxins WCGPCK or R motif
113
Thioredoxins Gly/Pro turn
114
Thioredoxins every second hydrophobic beta
strand
115
Thioredoxins ca. every 4th hydrophobic alpha
helix
116
(No Transcript)
117
Profiles, PSI-Blast, HMM
118
Profiles

• Derive profile from multiple sequence alignment
• Useful to
• Align distantly related sequences
• Conserved regions, which may indicate active site
• Classify subfamilies within homologues
• How can profile be used to search
• Insist on profile (such as WGCPC)? Too strict
• Use frequence distribution of profile

119
Consider frequencies

• Score for
• VDFSAS 1316167167
• ADATAA 11601160
• Not good to pick up distant relationships
• Better combine with substitution matrix
• Result position specific substitution matrix

120
PSI-Blast

• Globin familiy (oxygen transport ) of proteins
  occurs in many species
• Proteins have same function and structure and
• But there are pairs of members of the family
  sharing less than 10 identical residues
• A B C
• PSI-BLAST idea score via intermediaries may be
  better than score from direct comparison

50
50
Only 10
121
PSI-BLAST

• PSI-BLAST
• 1. BLAST
• 2. Collect top hits
• 3. Build multiple sequence alignment from
  significant local matches
• 4. Build profile
• 5. Re-probe database with profile
• 6. Go back to 2.

122
PSI-BLAST

• But beware of PSI-BLAST
• False positives propagate and spread through
  iterations
• If protein A consists of domains D and E, and
  protein B of domains E and F and protein C of
  domain F, then PSI-BLAST will relate A and C
  although they do not share any domain

123
Hidden Markov Model

• Procedure to generate sequences
• State transition systems with three types of
  states
• Deletion
• Insertion
• Match, which emits residues
• Follow probability distribution for successor
  state
• Train model on multiple sequence alignment

124
Summary

• Evolutionary model Indels and substitutions
• Homologues vs. similarity
• Dot plots
• Easy visual exploration, but not scalable
• Dynamic programming
• Local, global, gaps
• Substitution matrices (PAM, BLOSUM)
• BLAST and FASTA
• Scores and significance
• Multiple Sequence Alignments
• Profiles, PSI-BLAST, HMM

125
Phylogeny
126
Motivation

• How did the nucleus get into the eucaryotic
  cells?
• From where are we?
• Recent Africa vs. Multi-regional Hypothese
• In 1999 Encephalitis caused by the West Nile
  Virus broke out in New York. How did the virus
  come to New York?

127
How did the nucleus get into the eucaryotic cells?

• Simple experiment
• Blast classes genes with related functions in
  yeast (Eucaryote)
• against Bacteria and
• against Archaea
• And count number of significant hits

128
How did the nucleus get into the eucaryotic cells?

• Mitochondria und Energy metabolism
• Significantly more hits in bacteria
• Cell organisation
• Significantly more hits in Archaea
• Fundamental Result without any experiment!

Blue Bacteria Grey Archaea
129
Phylogeny

• Taxonomists aim to classify and group organisms
• E.g. Aristoteles, De Partibus Animalium
• Ought we, for instance, to begin by discussing
  each separate species man, lion, ox, and the
  like taking each kind in hand independently of
  the rest, or ought we rather to deal first with
  the attributes which they have in common in
  virtue of some common element of their nature,
  and proceed from this as a basis for
  consideration of them separately other

130
Schools of Taxonomists

• Goal create taxonomy
• Approach
• Phenotype
• Phylogeny
• 3 schools
• Phenotype only
• Evolutionary TaxonomistsPhenotype ( Phylogeny)
  
• Cladists Phylogeny (Phenotype)

131
Practical Application Westnile virus in NY

• Westnile virus mainly in Africa
• Transmitted by insects and birds
• How did the virus get to NY in 1999
• Hundreds of DNA samples taken
• All 99.8 identical ? single entry to NY!
• Phylogenetic tree allows to deduce origin

132
Example Westnil virus in NY

• How can the trees be constructed?

133
Three Methods to Generate Phylogenetic Trees

• Distance-based
• Hierarchical clustering
• Character-based
• Parsimony
• Maximum likelihood

134
Distance-based Approach

• Single Alignment
• Score 46 matches, 3 mismatches, 1 gap, 3 gap
  extensions,
• z.B. Score 46x1 - 3x1 - 1x2 - 3x1 38
• Approach
• Define distance between two sequences, e.g.
  percentage of mismatches in their alignment
• Construct tree, which groups sequences with
  minimal distances iteratively together

135
Hierarchical Clustering
136
Hierarchical Clustering

• Given a distance matrix D(dij) with 1 i,j n
• Result A binary tree of clusters
• Init
• ToDo
• For all i in 1,, n do
• Let ti be a tree without children, i.e. a leaf
• ToDo ToDo ? ti
• Main loop
• While ToDo gt 1 do
• Find i,j such that dij is minimal
• Add a new column and row labelled k (i,j) to D
  
• For all indices h of D apart from k,i,j do
• dh,k dk,h min dh,i , dh,j // min
  single linkage
• Let tk be a new tree with children ti and tj
• ToDo ( ToDo ? tk ) - ti ,tj
• Remove columns and rows i,j from D
• Complexity O(n2)

137
Hierarchical Clustering

• How to define distance between clusters?
• Single linkage
• dh,k dk,h min dh,i , dh,j
• Example Distance (A,B) to C is 1
• Complete linkage
• dh,k dk,h max dh,i , dh,j
• Example Distance (A,B) is C is 2
• Average linkage
• dh,k dk,h 0.5 dh,i 0.5 dh,j
• Example Distance (A,B) to C is 1.5
• Are dendrograms always the same independent of
  the linkage method?

138
Parsimony-method

• Approach Generate smallest tree containing all
  the sequences as leaves

139
Parsimony

• Generate smallest tree
• Informative vs. non-informative sites
• Build pairs with fewest possible substitutions
• Example
• 3 possible trees
• ((a,b),(c,d)) or ((a,c),(b,d)) or ((a,d),(b,c))
• 1,2,3,4 are not informative
• 5,6 are informative
• 5 ((a,b),(c,d))
• 6 ((a,c),(b,d))

140
Maximum likelihood

• Assigns quantitative probabilities to mutation
  events
• Reconstructs ancestors for all nodes in the tree
• Assigns branch lengths based on probabilities of
  the mutational events
• For each possible tree topology, the assumed
  substitution rates are varied to find the
  parameters that give the highest likelihood of
  producing the observed data

141
Problems

• Character-based methods tend to be better (based
  on paleontological data)
• All make assumptions
• No back mutations
• Same evolutionary rate

142
Assessing Quality Bootstrapping

• Given a tree obtained from one of the methods
  above
• Generate Multiple Alignment
• For a number of interations
• Generate new sequences by selecting columns
  (possibly the same column more than once) form
  the multiple alignment
• Generate tree for the new sequences
• Compare this new tree with the given tree
• For each cluster in the given tree, which also
  approach in the new tree, the bootstrap value is
  increased
• Bootstrap-Value Percentage of trees containing
  the same cluster

143
From where are we?

• Recent-Africa Hypothesis
• Homo Sapiens came 100-200.000 years ago from
  Africa
• Multi-regional Hypothesis
• Ancestors of Homo Sapiens left Africa ca.
  2.000.000 years ago
• Which ones right?

144
Experiment

• Mitochondrial DNA form 53 humans in different
  regions sequenced
• Outgroup Mitochondrial DNA of chimpanzee

145
A nice phylogeny (Nature 2004)
Nature October 2004 Volume 431 No. 7012
146
Why Mitochondria?

• Simple genetic structure
• No repetitions
• No Pseudo genes
• No Introns
• No recombination

147
Molecular Clock

• Based on genetic and paleontological the most
  recent common ancestor (mrca) of chimpanzee and
  homo sapiens dates back 5.000.000 years
• Molecular clock
• ? 1.7 x10-8 nucleotide changes per site and year
• Assumption equal distribution, no silent
  mutations
• Diversity in Afrikca 3.7 x10-3 nucleotide
  changes per site and year
• Diversity outside Africa 1.7 x10-3 nucleotide
  changes per site and year
• Estimated expansion1925 generations ago ca.
  40.000 years
• Mrca of all humans 171.500 /- 50.000 years ago
• Mrca of African and non-African 52,000 /-
  27.500 years ago
• Experiment supports recent-Africa hypothesis

148
Summary

• Schools of taxonomists
• Assumptions made
• Methods
• Distance-based
• Character-based