Transcript Molecular evolution Fredj Tekaia Institut Pasteur [email protected] Molecular evolution •The increasing available completely sequenced organisms and the importance of evolutionary processes that affect the species history,

Molecular evolution
Fredj Tekaia
Institut Pasteur
[email protected]
Molecular evolution
•The increasing available completely sequenced
organisms and the importance of evolutionary processes
that affect the species history, have stressed the interest in
studying the molecular evolution events at the sequence
level.
Plan
• Context
• selection pressure (definitions)
• Genetic code and inherent properties of codons and
amino-acids
• Estimations of synonymous and nonsynomynous
substitutions
• Codons volatility
• Applications
Evolutionary processes include:
Ancestor
Expansion*
Phylogeny*
genesis
duplication
HGT
Exchange*
species genome
HGT
loss
Deletion*
and selection
Gene tree - Species tree
•
Time
Duplication
•
Duplication
A
B
C
Species tree
Speciation
Speciation
A
A
B
C
B
Gene tree
Genomes 2 edition 2002.. T.A. Brown
C
Original version
Actual version
Hurles M (2004) Gene Duplication: The Genomic Trade in Spare Parts. PLoS Biol 2(7): e206.
Homolog - Paralog - Ortholog
O
A
A1A1
BB
11
Species-1
Homologs: A1, B1, A2, B2
B
Paralogs: A1 vs B1 and A2 vs B2
Orthologs: A1 vs A2 and B1 vs B2
AA22
BB
22
Sequence analysis
Species-2
a
S1
S2
b
Molecular evolutionary analysis
• Aim at understanding and modeling evolutionary
events;
• Evolutionary modeling extrapolates from the divergence
between sequences that are assumed homologous, the
number of events which have occurred since the genes
diverged;
• If rate of evolution is known, then a time since
divergence can be estimated.
Molecular evolution
Applications:
Molecular evolution analysis has clarified:
• the evolutionary relationships between humans and
other primates;
• the origins of AIDS;
• the origin of modern humans and population migration;
• speciation events;
• genetic material exchange between species.
• origin of some deseases (cancer, etc...)
• .....
Molecular evolution
GACGACCATAGACCAGCATAG
GACTACCATAGA-CTGCAAAG
*** ******** * *** **
GACGACCATAGACCAGCATAG
GACTACCATAGACT-GCAAAG
*** *********
*** **
Two possible
positions for the
indel
Molecular evolution
GACGACCATAGACCAGCATAG
GACTACCATAGA-CTGCAAAG
• Mutations arise due to inheritable changes in
genomic DNA sequence;
• Mechanisms which govern changes at the
protein level are most likely due to nucleotide
substitution or insertions/deletions;
• Changes may give rise to new genes which
become fixed if they give the organism an
advantage in selection;
Molecular evolution: Definitions
Purifying (negative) selection
• A consequence of gene “drift” through random
mutations, is that many mutations will have deleterious
effects on fitness.
• “Purifying selective force” prevents accumulation of
mutation at important functional sites, resulting in
sequence conservation.
-> “Purifying selection” is a natural selection against
deleterious mutations.
-> The term is used interchangeably with “negative
selection” or “selection constraints”.
Neutral theory
• Majority of evolution at the molecular level is caused by
random genetic “drift” through mutations that are
selectively neutral or nearly neutral.
• Describes cases in which selection (purifying or positive)
is not strong enough to outweigh random events.
• Neutral mutation is an ongoing process which gives rise
to genetic polymorphisms; changes in environment can
select for certain of these alleles.
Positive selection
• Positive selection is a darwinian selection fixing
advantageous mutations.
The term is used interchangeably with “molecular
adaptation” and “adaptive molecular evolution”.
• Positive selection can be shown to play a role in some
evolutionary events
• This is demonstrated at the molecular level if the rate of
nonsynonymous mutation at a site is greater than the rate
of synonymous mutation
• Most substitution rates are determined by either neutral
evolution of purifying selection against deleterious
mutations
Molecular evolution
• We observe and try to decode the process of
molecular evolution from the perspective of
accumulated differences among related genes
from one or diverse organisms.
• The number of mutations that have occurred
can only be estimated.
Real individual events are blurred by a long
history of changes.
Nucleotide, amino-acid sequences
• 3 different DNA positions but
-GGAGCCATATTAGATAGA- only one different amino acid
position:
-GGAGCAATTTTTGATAGA2 of the nucleotide substitutions
Gly Ala Ile Phe asp Arg
are therefore synonymous and
one is non-synonymous.
-> gene
Gly Ala Ile Leu asp Arg
-> protein
DNA yields more phylogenetic information than proteins. The
nucleotide sequences of a pair of homologous genes have a higher
information content than the amino acid sequences of the
corresponding proteins, because mutations that result in synonymous
changes alter the DNA sequence but do not affect the amino acid
sequence.
Kinds of nucleotide substitutions
Given 2 nucleotide sequences, we can ask how their similarities and
differences arose from a common ancestor?
Single substitution
Multiple substitution
C
A
T
A
A
A
1 change, 1 difference
2 changes, 1 difference
Parallel substitution
Convergent substitution
C
C
2 changes, no difference
C
2 change, 1 difference
Back substitution
T
A
C
G
A
C
A
Coincidental substitution
A
A
T
3 changes, no difference
C
A
2 changes, no difference
Substitution: Transition - transversion
Nucleotides are either purine or pyrimidines :
G (Guanine) and A (Adenine) are called purine;
C (Cytosine) and T (Thymine) are called pyrimidines.
A
C
G
T
transition changes one
purine for another or one
pyrimidine for another.
transversion changes a
purine for a pyrimidine or
vice versa.
transitions occur at least 2 times as frequently as transversions
Standard genetic code
•The genetic code specifies how a combination of any of
the four bases (A,G,C,T) produces each of the 20 amino
acids.
•The triplets of bases are called codons and with four
bases, there are 64 possible codons:
(43) possible codons that code for 20 amino acids (and stop
signals).
Standard genetic code
Second position
|
T
|
C
|
A
|
G
|
----+--------------+--------------+--------------+--------------+---| TTT Phe (F) | TCT Ser (S) | TAT Tyr (Y) | TGT Cys (C) | T
T | TTC
"
| TCC
"
| TAC
| TGC
| C
F
| TTA Leu (L) | TCA
"
| TAA Ter
| TGA Ter
| A T
i
| TTG
"
| TCG
"
| TAG Ter
| TGG Trp (W) | G h
r --+--------------+--------------+--------------+--------------+-- i
s
| CTT Leu (L) | CCT Pro (P) | CAT His (H) | CGT Arg (R) | T r
t C | CTC
"
| CCC
"
| CAC
"
| CGC
"
| C d
| CTA
"
| CCA
"
| CAA Gln (Q) | CGA
"
| A
P
| CTG
"
| CCG
"
| CAG
"
| CGG
"
| G P
o --+--------------+--------------+--------------+--------------+-- o
s
| ATT Ile (I) | ACT Thr (T) | AAT Asn (N) | AGT Ser (S) | T s
i A | ATC
"
| ACC
"
| AAC
"
| AGC
"
| C i
t
| ATA
"
| ACA
"
| AAA Lys (K) | AGA Arg (R) | A t
i
| ATG Met (M) | ACG
"
| AAG
"
| AGG
"
| G i
o --+--------------+--------------+--------------+--------------+-- o
n
| GTT Val (V) | GCT A la (A) | GAT A sp (D) | GGT G ly (G) | T n
G | GTC
"
| GCC
"
| GAC
"
| GGC
"
| C
| GTA
"
| GCA
"
| GAA G lu (E) | GGA
"
| A
| GTG
"
| GCG
"
| GAG
"
| GGG
"
| G
----+--------------+--------------+--------------+--------------+----
A
R
N
D
C
Q
E
G
H
I
L
K
M
F
P
S
T
W
Y
V
Ala
Arg
Asn
Asp
Cys
Gln
Glu
Gly
His
Ile
Leu
Lys
Met
Phe
Pro
Ser
Thr
Trp
Tyr
Val
Alanine
Arginine
Asparagine
Aspartic acid
Cysteine
Glutamine
Glutamic acid
Glycine
Histidi ne
Isoleucine
Leucine
Lysine
Methionine
Phenylalanine
Proline
Serine
Threonine
Tryptophan
Tyrosine
Valine
GCT GCC GCA G CG
CGT CGC CGA C GG AGA A GG
AAT AAC
GAT GAC
TGT TGC
CAA CAG
GAG GAA
GGG GG A GGT GG C
CAT CAC
ATT ATC ATA
TTA TTG CTT CTC CT A CTG
AAA AAG
ATG
TTT TTC
CCT CCC CCA CCG
TCT TCC TCA TC G AGT AGC
ACT ACC ACA ACG
TGG
TAT TAC
GTT GTC GTA GTG
chargé(basique), chargé (acidique),
hydrophile, hydrophobe
• Because there are only 20 amino acids, but 64 possible codons, the same amino
acid is often encoded by a number of different codons, which usually differ in the
third base of the triplet.
•Because of this repetition the genetic code is said to be degenerate and codons
which produce the same amino acid are called synonymous codons.
Important properties inherent to
the standard genetic code
Synonymous vs nonsynonymous substitutions
• Nondegenerate sites: are codon position where mutations always
result in amino acid substitutions.
(exp. TTT (Phenylalanyne, CTT (leucine), ATT (Isoleucine), and
GTT (Valine)).
• Twofold degenerate sites: are codon positions where 2 different
nucleotides result in the translation of the same aa, but the 2 others
code for a different aa.
(exp. GAT and GAC code for Aspartic acid (asp, D),
whereas GAA and GAG both code for Glutamic acid (glu, E)).
• Threefold degenerate site: are codon positions where changing 3
of the 4 nucleotides has no effect on the aa, while changing the
fourth possible nucleotide results in a different aa.
There is only 1 threefold degenerate site: the 3rd position of an isoleucine codon.
ATT, ATC, or ATA all encode isoleucine, but ATG encodes methionine.
Standard genetic code
• Fourfold degenerate sites: are codon positions where changing a
nucleotide in any of the 3 alternatives has no effect on the aa.
exp. GGT, GGC, GGA, GGG(Glycine);
CCT,CCC,CCA,CCG(Proline)
• Three amino acids: Arginine, Leucine and Serine are encoded by 6 different
codons:
R Arg Arginine
L Leu Leucine
S Ser Serine
CGT CGC CGA C GG AGA A GG
TTA TTG CTT CTC CT A CTG
TCT TCC TCA TC G AGT AGC
• Five amino-acids are encoded by 4 codons which differ only in the third position.
These sites are called “fourfold degenerate” sites
A
G
P
T
V
Ala
Gly
Pro
Thr
Val
Alanine
Glycine
Proline
Threonine
Valine
GCT GCC GCA G CG
GGG GGA GGT GGC
CCT CCC CCA CCG
ACT ACC ACA ACG
GTT GTC GTA GTG
Standard genetic code
• Nine amino acids are encoded by a pair of codons which differ by a transition
substitution at the third position. These sites are called “twofold degenerate” sites.
N
D
C
Q
E
H
K
F
Y
Asn
Asp
Cys
Gln
Glu
His
Lys
Phe
Tyr
Asparagine
Aspartic acid
Cysteine
Glutamine
Glutamic acid
Histidine
Lysine
Phenylalanine
Tyrosine
AAT AAC
GAT GAC
TGT TGC
CAA CAG
GAG GAA
CAT CAC
AAA AAG
TTT TTC
TAT TAC
• Isoleucine is encoded by three different codons
I
Ile Isoleucine
ATT ATC ATA
• Methionine and Triptophan are encoded by single codon
M Met Methionine
W Trp Tryptophan
ATG
TGG
• Three stop codons: TAA, TAG and TGA
Transition:
A/G; C/T
Standard Genetic Code
Nucleotide substitutions in protein coding genes can be divided into :
• synonymous (or silent) substitutions i.e. nucleotide substitutions
that do not result in amino acid changes.
• non synonymous substitutions i.e. nucleotide substitutions that
change amino acids.
• nonsense mutations, mutations that result in stop codons.
exp: Gly: any changes in 3rd position of codon results in Gly; any
changes in second position results in amino acid changes; and so is
the first position.
G Gly Glycine
exp:
GGG GGA GGT GGC
Glu GAG
AGC
Ser
Nonsynonymous/synonymous substitutions
• Estimation of synonymous and nonsynonymous substitution rates
is important in understanding the dynamics of molecular sequence
evolution.
• As synonymous (silent) mutations are largely invisible to natural
selection, while nonsynonymous (amino-acid replacing) mutations
may be under strong selective pressure, comparison of the rates of
fixation of those two types of mutations provides a powerful tool for
understanding the mechanisms of DNA sequence evolution.
• For example, variable nonsynonymous/synonymous rate ratios
among lineages may indicate adaptative evolution or relaxed
selective constraints along certain lineages.
• Likewise, models of variable nonsynonymous/synonymous rate
ratios among sites may provide important insights into functional
constraints at different amino acid sites and may be used to detect
sites under positive selection.
Codon usage
• There are 64 (43) possible codons that code for 20 amino acids
(and stop signals).
• If nucleotide substitution occurs at random at each nucleotide site,
every nucleotide site is expected to have one of the 4 nucleotides, A,
T, C and G, with equal probability.
• Therefore, if there is no selection and no mutation bias, one would
expect that the codons encoding the same amino acid are on average
in equal frequencies in protein coding regions of DNA.
• In practice, the frequencies of different codons for the same amino
acid are usually different, and some codons are used more often than
others. This codon usage bias is often observed.
• Codon usage bias is controlled by both mutation pressure and
purifying selection.
Estimating synonymous and nonsynonymous differences
• For a pair of homologous codons presenting only one nucleotide
difference, the number of synonymous and nonsynonymous
substitutions may be obtained by simple counting of silent versus
non silent amino acid changes;
• For a pair of codons presenting more than one nucleotide
difference, distinction between synonymous and nonsynonymous
substitutions is not easy to calculate and statistical estimation
methods are needed;
• For example, when there are 3 nucleotide differences between
codons, there are 6 different possible pathways between these
codons. In each path there are 3 mutational steps.
• More generally there can be many possible pathways between
codons that differ at all three positions sites; each pathway has its
own probability.
Estimating synonymous and nonsynonymous differences
• Observed nucleotide differences between 2 homologous sequences
are classified into 4 categories: synonymous transitions, synonymous
transversions, nonsynonymous transitions and nonsynonymous
transversions.
• When the 2 compared codons differ at one position, the
classification is obvious.
• When they differ at 2 or 3 positions, there will be 2 of 6
parsimonious pathways along which one codon could change into the
other, and all of them should be considered.
• Since different pathways may involve different numbers of
synonymous and nonsynonymous changes, they should be weighted
differently.
Example: 2 homologous sequences
Glu
Val
Phe
SEQ.1
GAA GTT TTT
SEQ.2
GAC GTC GTA
Asp
Val Val
•Codon 1: GAA --> GAC ;1 nuc. diff., 1 nonsynonymous difference;
•Codon 2: GTT --> GTC ;1 nuc. diff., 1 synonymous difference;
•Codon 3: counting is less straightforward:
1
TTT(F:Phe)
2
TTA(L:Leu)
GTT(V:Val)
GTA(V:Val)
Path 1 : implies 1
non-synonymous
and 1 synonymous
substitutions;
Path 2 : implies 2
non synonymous
substitutions;
Evolutionary Distance estimation between 2 sequences
The simplest problem is the estimation of the number of
synonymous (dS) and nonsynonymous (dN) substitutions per site
between 2 sequences:
• the number of synonymous (S) and nonsynonymous (N) sites in the
sequences are counted;
• the number of synonymous and nonsynonymous differences
between the 2 sequences are counted;
• a correction for multiple substitutions at the same site is applied to
calculate the numbers of synonymous (dS) and nonsynonymous
(dN) substitutions per site between the 2 sequences.
==> many estimation Methods
Evolutionary Distance estimation
In general the genetic code affords fewer opportunities for
nonsynonymous changes than for synonymous changes.
rate of synonymous >> rate of nonsynonymous substitutions.
Furthermore, the likelihood of either type of mutation is highly dependent on
amino acid composition.
For example: a protein containing a large number of leucines will contain many
more opportunities for synonymous change than will a protein with a high number
of lysines.
L Leu Leucine
TTA TTG CTT CTC CT A CTG
4forld degeneratesite
Several possible substitutions that will not change the aa Leucine
K Lys Lysine
2fold degenerate site
AAA AAG
Only one possible mutation at 3rd position that will not change Lysine
Evolutionary Distance estimation
• Fundamental for the study of protein evolution and useful for
constructing phylogenetic trees and estimation of divergence time.
Estimating synonymous and nonsynonymous substitution rates
QuickTime™ et un décompresseur TI FF (non compressé) sont requis pour v isionner cette image.
• Ziheng Yang & Rasmus Nielsen (2000)
Estimating synonymous and nonsynonymous substitution rates under
realistic evolutionary models. Mol Biol Evol. 17:32-43.
Purifying selection:
Most of the time selection eliminates deleterious mutations, keeping
the protein as it is.
Positive selection:
In few instances we find that dN (also denoted Ka) is much greater
than dS (also denoted Ks) (i.e. dN/dS >> 1 (Ka/Ks >>1 )). This is strong
evidence that selection has acted to change the protein.
Positive selection was tested for by comparing the number of nonsynonymous substitutions per
nonsynonymous site (dN) to the number of synonymous substitutions per synonymous site (dS).
Because these numbers are normalized to the number of sites, if selection were neutral (i.e., as for a
pseudogene) the dN/dS ratio would be equal to 1. An unequivocal sign of positive selection is a dN/dS
ratio significantly exceeding 1, indicating a functional benefit to diversify the amino acid sequence.
dN/dS < 0.25 indicates purifying selection;
dN/dS = 1 suggests neutral evolution;
dN/dS >> 1 indicates positive selection.
Negative (purifying) selection eliminates
mutations i.e. inhibits protein evolution.
disadvantageous
(explains why dN < dS in most protein coding regions)
Positive selection is very important for evolution of new functions
especially for duplicated genes.
(must occur early after duplication otherwise null mutations and
will be fixed producing pseudogenes).
• dN/dS (or Ka/Ks) measures selection pressure
Mutational saturation
Mutational saturation in DNA and protein sequences
occurs when sites have undergone multiple mutations
causing sequence dissimilarity (the observed differences)
to no longer accurately reflect the “true” evolutionary
distance i.e. the number of substitutions that have
actually occurred since the divergence of two sequences.
Correct estimation of the evolutionary distance is crucial.
Generally: sequences where dS > 2 are excluded to avoid
the saturation effect of nucleotide substitution.
YN00 - P13.4.C13.18.fa.paml
ns = 13 ls = 29
Estimation by the method of:
Yang & Nielsen (2000):
seq.
seq.
YALI0A0 8195g
YALI0E2 5443g
YALI0E2 5443g
………
YALI0C2 1230g
YALI0C2 1230g
YALI0C2 1230g
YALI0C2 1230g
YALI0C2 1230g
YALI0C2 1230g
YALI0C2 1230g
YALI0C2 1230g
….
YALI0C2 1230g
YALI0D1 1638g
YALI0E1 9140g
YALI0E1 9140g
YALI0A1 7963g
YALI0A1 7963g
YALI0A0 8195g
S
15.1
17.3
17.6
N
71.9
69.7
69.4
t
0.37
1.8
1.00
kappa omega dN +- SE
1.31
1.31
1.31
YALI0A1 7963g
YALI0A0 8195g
YALI0E2 5443g
YALI0A0 2783g
YALI0C2 1252g
YALI0C2 1274g
YALI0F0 9944g
YALI0A1 3497g
24.1
24.5
24.9
24.6
25.4
25.3
24.3
28.2
62.9
62.5
62.1
62.4
61.6
61.7
62.7
58.8
5.35
6.58
4.76
4.71
6.64
6.54
7.51
7.13
1.31
1.31
1.31
1.31
1.31
1.31
1.31
1.31
YALI0B0 6160g
YALI0C2 1230g
YALI0C2 1230g
YALI0D1 1638g
27.1
27.3
25.2
22.4
59.9
59.7
61.8
64.6
7.34
8.04
7.67
4.12
1.31
1.31
1.31
1.31
0.20
0.05
0.06
……
0.75
0.57
1.27
0.07 +- 0.03
0.13 +- 0.05
0.08 +- 0.03
dS +- SE
0.36 +- 0.22
2.55 +- 13.9 5
1.35 +- 0.70
3.20
1.63
1.81
1.69
1.97
2.77
2.75
2.97
3.06
++++++++-
1.06
1.43
0.57
0.81
2.27
2.21
2.93
3.38
2.19
3.19
1.33
0.55
0.86
0.79
1.29
0.95
++++++++-
1.70
6.21
0.59
0.21
0.32
0.34
1.09
0.34
…..
1.66
1.68
2.48
0.45
2.79
3.07
3.09
1.04
++++-
2.37
3.40
3.46
0.29
1.68
1.83
1.25
2.33
++++-
0.86
1.39
0.54
2.13
3.58
3.22
3.46
2.31
-> yn00 similar results than ML (Yang & Nielsen (2000))
-> advantage : easy automation for large scale comparisons;
• PAML: Phylogenetic Analysis by Maximum Likelihood (PAML)
http://abacus.gene.ucl.ac.uk/software/paml.html
Relative Rate Test
1
2
A•
3
For determining the relative rate of
substitution in species 1 and 2, we need and
outgroup (species 3).
The point in time when 1 and 2 diverged is
marked A (common ancestor of 1 and 2).
The number of substitutions between any two species is assumed to
be the sum of the number of substitutions along the branches of the
tree connecting them:
d13=dA1+dA3
d23=dA2+dA3
d12=dA1+dA2
d13, d23 and d12 are measures of the differences
between 1 and 3, 2 and 3 and 1 and 2 respectively.
dA1=(d12+d13-d23)/2
dA2=(d12+d23-d13)/2
dA1 and dA2 should be the
same (A common ancestor
of 1 and 2).
Evolution of functionally important regions over time. Immediately after a speciation event, the two copies of the
genomic region are 100% identical (see graph on left). Over time, regions under little or no selective pressure,
such as introns, are saturated with mutations, whereas regions under negative selection, such as most exons,
retain a higher percent identity (see graph on right). Many sequences involved in regulating gene expression
also maintain a higher percent identity than do sequences with no function.
COMPARATIVE GENOMICS
Webb Miller, Kateryna D. Makova, Anton Nekrutenko, and Ross C. Hardison
Annual Review of Genomics and Human Genetics
ú
Vol. 5: 15-56 (2004)
ú
ú
ú
Reference
Yang & Nielsen,
Esimating Synonymous and Nonsynonymous Substitution Rates Under
Realistic Evolutionary Models
Mol. Biol. Evol. 2000, 17:32-43
=>Other estimation Models
Evolutionary Distance estimation between 2 sequences
• Under certain conditions, however, nonsynonymous substitution may be
accelerated by positive Darwinian selection. It is therefore interesting to examine
the number of synonymous differences per synonymous site and the number of
nonsynonymous differences per nonsynonymous site.
p-distance:
• ps = Sd/S
proportion of synonymous differences ;
• pn = Nd/N
proportion of non synonymous differences;
var(ps) = ps(1-ps)/S.
var(pn) = pn(1-pn)/S.
Sd and Nd are respectively the total number of synonymous and non
synonymous differences calculated over all codons. S and N are the
numbers of synonymous and nonsynonymous substitutions.
S+N=n total number of nucleotides and N >> S.
ps is often denoted Ks and pn is denoted Ka.
Substitutions between protein sequences
p = nd/n
V(p)=p(1-p)/n
nd and n are the number of amino acid differences and the total number of
amino acids compared.
However, refining estimates of the number of substitutions that have occurred
between the amino acid sequences of 2 or more proteins is generally more
difficult than the equivalent task for coding sequences (see paths above).
One solution is to weight each amino acid substitution differently by using
empirical data from a variety of different protein comparisons to generate a
matrix as the PAM matrix for example.
Number of synonymous (ds) and non synonymous (dn)
substitutions per site
1) Jukes and Cantor, “one-parameter method” denoted “1-p” :
This model assumes that the rate of nucleotide substitution is the
same for all pairs of the four nucleotides A, T, C and G (generally not
true!).
d = -(3/4)*Ln(1-(4/3)*p) where p is either ps or pn.
2) Kimura's 2-parameter, denoted “2-p” :
The rate of transitional nucleotide substitution is often higher than
that of transversional substitution.
d = -(1/2)*Ln(1 -2*P -Q) -(1/4)*Log(1 -2*Q)
P is the proportion of transitional differences,
Q is the proportion of transversional differences
P and Q are respectively calculated over synonymous and non
synonymous differences.
Other distance models
Jukes-Cantor model :
A
T
C
G
A
l
l
l
T
l
l
l
C
l
l
l
G
l
l
l
-
l is the rate of substitution.
Tajima-Nei mod el :
A
T
C


A
g


T
g


C


G
g
, , g and d are the rates o f substituti on.
G
d
d
d
-
Kimura 2-parameters model :
A
T
C
G




A




T
 and  are the rate s o f transiti o nal




C




G
and transvertional substitutions
Tamura model :
A
T
A
(1-q
T
(1-q)
C
(1-q)
(1-q
G
(1-q
(1-q
C
q
q
q
G
q
q
q
-
Hasegaw a et al . mod el :
A
T
A
gT
T
gA
C
gA
gT
G
gA
gT
C
gC
gC
gC
G
gG
gG
gG
-
Tamura-Nei mod el :
A
T
A
gT
T
gA
C
gA
gT2
G
gA1
gT
C
gC
gC2
gC
G
gG1
gG
gG
-
 and  are the rates of tr ansitional
and transvertional substitutions
and q is the G+C content.
 and  are the rates of tr ansitional
and transvertional substitutions
and
gi
the
nucleotide
frequencies
(i=A,T,C,G).
1 and 2 are the rate s o f transiti o nal substituti ons
between purines and between pyrimidines;
 is the rate of transvertional substitutions;
and gi the nucleotide frequencies (i=A,T,C,G).
• Example: yn00 in PAML.
• Protein sequences in a family
and corresponding DNA sequences
Procedure
1. Alignment of a family protein sequences using clustalW
2. Alignment of corresponding DNA sequences using as template their
corresponding amino acid alignment obtained in step 1
3. Format the DNA alignment in yn00 format
4. Perform yn00 program (PAML package) on the obtained DNA alignment
5. Clean the yn00 output to get YN (Yang & Nielsen) estimates in a file.
Estimations with large standard errors were eliminated
6. From YN estimates extract gene pairs with w = dN/dS >= 3 and gene pairs with
w<= 0.3, respectively.
7. Genes with w>=3 are considered as candidate genes on which positive
selection may operate. Whereas genes with w<=0.3 are candidates for purifying
(negative) selection
• Most of the genes
are under purifying
selection
• Only few genes
might be under
positive selection
dN
dS
w=dN/dS
w=dN/dS >=3
m
std
n
0.90
0.6
2.96
1.3
0.34
0.32
3.6
0.57
min
Max
5085
5085
5085
0.0
0.0
0.0
4.98
6.84
4.45
10
3.0
4.45
• Codon volatility
A new concept: codons volatility
(Plotkin et al. 2004. nature 428. p.942-945).
• New method recently introduced, the utility of which is still
under debate;
• has interresting consequences on the study of codon variability;
Detecting Selection
• If a protein coding region of a nucleotide sequence has undergone
an excess number of amino-acid substitutions, then the region will
on average contain an overabundance of “volatile” codons,
compared with the genome as a whole.
• Using the concept of codon volatility, we can scan an entire
genome to find genes that show significantly more, or less, pressure
for amino-acid substitutions than the genome as a whole.
• If a gene contains many residues under pressure for aa
replacements, then the resulting codons in that gene will on
average exhibit elevated volatility.
• If a gene is under purifying selection not to change its aa, then the
resulting sequence will on average exhibit lower volatility.
Plotkin et al. Nature 428; 942-945
Codons volatility
2
2
3
3
1
4
8
7
5
6
4
1
8
5
7
6
• The codon CGA encoding arginine (R), has 8 potential ancestor codons (i.e.
non stop codon) that differ from CGA by one substitution.
• Volatility of a codon is defined as the proportion of nonsynonymous codons
over the total neighbour sense codons obtained by a single substitution.
• The volatility of CGA = 4/8.
• The volatility of AGA also encodes an arginine = 6/8.
Plotkin et al. 2004.
Nature 428. p.942-945
Codons volatility
• 22 codons have at least one synonymous with a different volatility;
•Volatility of a codon c:
v(c) = 1/n ∑{D[aacid(c) - aacid(ci)];i=1,n};
n is the number of neighbors (other than non-stop codons) that
can mutate by a single substitution.
D is the Hamming distance = 0 if the 2 aa are identical;
=1 otherwise.
• Volatility of a gene G:
v(G) = ∑{v(ck);k=1,l}; l is the number of codons in the gene G.
Codons volatility
• Volatility is used to quantify the probability that the most recent
substitution of a site caused an amino-acid change.
• Each gene’s observed volatility is compared with a bootstrap
distribution of alternative synonymous sequences, drawn
according to the background codon usage in the genome,
and its significance statistically assessed.
• Randomization procedure controls for the gene’s length and
amino-acid composition.
• The volatility of a gene G is defined as the sum of the volatility
of its codons.
Codons volatility
Volatility p-value of G:
• The observed v(G) is compared with a bootstrap distribution of
106 synonymous versions of the gene G.
• In each randomization sample, a nucleotide sequence G’ is
constructed so that it has the same translation as G but whose
codons are drawn randomly according to the relative frequencies
of synonymous codons in the whole genome.
• p-value for G = proportion of randomized samples;
so that v(G’) > v(G).
• 1-p is a p-value that tests whether a gene is significantly less
volatile than the genome as a whole.
Detecting Selection
• A p-value near zero indicates significantly elevated volatility,
whereas a p-value near one indicates significantly depressed
volatility.
• The probability that a site’s most recent substitution caused a
non-synonymous change is:
- greater for a site under positive selection;
- smaller for a site under negative (purifying) selection.
• http://www.cgr.harvard.edu/volatility
1) Paul M. Sharp
Gene "volatility" is Most Unlikely to Reveal Adaptation
MBE Advance Access published on December 22, 2004.
doi:10.1093/molbev/msi073
2) Tal Dagan and Dan Graur
The Comparative Method Rules! Codon Volatility Cannot Detect Positive Darwinian Selection Using a Single Genome Sequence
MBE Advance Access published on November 3, 2004.
doi:10.1093/molbev/msi033
-> Volatility is not adequate for
predicting selection;
3) Robert Friedman and Austin L. Hughes
Codon Volatility as an Indicator of Positive Selection: Data from Eukaryotic Genome Comparisons
MBE Advance Access originally published on November 3, 2004. This version published November 8, 2004.
doi:10.1093/molbev/msi038
-> Extreme volatility classes have
interesting properties, in terms of aa
5) Nielsen R, Hubisz MJ.
composition or codon bias;
Evolutionary genomics: Detecting selection needs comparative data.
4) Hahn MW, Mezey JG, Begun DJ, Gillespie JH, Kern AD, Langley CH, Moyle LC.
Evolutionary genomics: Codon bias and selection on single genomes.
Nature. 2005 Jan 20;433(7023):E5-6.
Nature. 2005 Jan 20;433(7023):E6.
-> Volatility may be another measure of
codon bias;
6) Chen Y, Emerson JJ, Martin TM
Evolutionary genomics: Codon volatility does not detect selection.
Nature. 2005 Jan 20;433(7023):E6-7.
7) Zhang J, 2005.
On the evolution of codon volatility
Genetics 169: 495-501.
-> Authors : some genes are under
more positive, or less negative,
8) Plotkin JB, Dushoff J, Fraser HB.
selection
than others.
Evolutionary genomics: Codon volatility does not detect selection
(reply).
Nature. 2005 Jan 20;433(7023):E7-8.
9) Plotkin JB, Dushoff J, Desai MM and Fraser HB
Synonymous codon and selection on proteins
Codon Volatility (simple substitution model):
Codons and volatility under simple substitution model
aa
A
A
A
A
R
R
R
R
R
R
N
N
D
D
C
C
Q
Q
E
E
G
G
G
G
H
H
I
I
I
L
L
L
L
L
L
K
K
M
F
F
P
P
P
P
S
S
S
S
S
S
T
T
T
T
W
Y
Y
V
V
V
V
Tot
A
GCT
GCC
GCA
GCG
CGT
CGC
CGA
CGG
AGA
AGG
AAT
AAC
GAT
GAC
TGT
TGC
CAA
CAG
GAA
GAG
GGT
GGC
GGA
GGG
CAT
CAC
ATT
ATC
ATA
TTA
TTG
CTT
CTC
CTA
CTG
AAA
AAG
ATG
TTT
TTC
CCT
CCC
CCA
CCG
TCT
TCC
TCA
TCG
AGT
AGC
ACT
ACC
ACA
ACG
TGG
TAT
TAC
GTT
GTC
GTA
GTG
R
N
3
3
3
3
D
1
1
Q
E
1
1
3
3
4
4
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
C
1
1
2
2
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
G
1
1
1
1
1
1
1
1
1
1
1
1
1
1
H
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
3
3
3
F
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
3
3
4
4
1
3
1
1
1
1
2
3
3
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
36 54 18 18 18 18 18
1
1
1
1
Y
1
2
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
36 18
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
3
3
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
V
1
1
1
1
1
1
1
1
1
3
1
1
1
1
2
2
1
1
W
1
1
1
1
1
1
T
1
1
1
1
1
1
1
1
2
1
1
S
1
1
1
1
1
1
1
1
1
1
1
1
1
2
P
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
M
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
2
1
2
2
K
1
1
1
1
2
2
2
2
1
1
1
1
L
1
1
1
1
1
1
1
1
1
I
1
1
1
1
1
1
1
1
1
1
3
3
3
3
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
3
3
3
1
1
1
1
2
2
1
27 54 18 9 18 36 54 36 9 18
3
3
3
3
36
taa
9
9
9
9
9
9
8
9
8
9
9
9
9
9
8
8
8
8
8
8
9
9
8
9
9
9
9
9
9
7
8
9
9
9
9
8
8
9
9
9
9
9
9
9
9
9
7
8
9
daa
6
6
6
6
6
6
4
5
6
7
8
8
8
8
7
7
7
7
7
7
6
6
5
6
8
8
7
7
7
5
6
6
6
5
5
7
7
9
8
8
6
6
6
6
6
6
4
5
8
Vol
0 . 67
0 . 67
0 . 67
0 . 67
0 . 67
0 . 67
0.5
0 . 56
0 . 75
0 . 78
0 . 89
0 . 89
0 . 89
0 . 89
0 . 88
0 . 88
0 . 88
0 . 88
0 . 88
0 . 88
0 . 67
0 . 67
0 . 63
0 . 67
0 . 89
0 . 89
0 . 78
0 . 78
0 . 78
0 . 71
0 . 75
0 . 67
0 . 67
0 . 56
0 . 56
0 . 88
0 . 88
1.
0 . 89
0 . 89
0 . 67
0 . 67
0 . 67
0 . 67
0 . 67
0 . 67
0 . 57
0 . 63
0 . 89
G+C
2
3
2
3
2
3
2
3
1
2
0
1
1
2
1
2
1
2
1
2
2
3
2
3
1
2
0
1
0
0
1
1
2
1
2
0
1
1
0
1
2
3
2
3
1
2
1
2
1
A+T
1
0
1
0
1
0
1
0
2
1
3
2
2
1
2
1
2
1
2
1
1
0
1
0
2
1
3
2
3
3
2
2
1
2
1
3
2
2
3
2
1
0
1
0
2
1
2
1
2
9
9
9
9
9
7
7
7
9
9
9
9
8
6
6
6
6
7
6
6
6
6
6
6
0.89
0.67
0.67
0.67
0.67
1.
0.86
0.86
0.67
0.67
0.67
0.67
2
1
2
1
2
2
0
1
1
2
1
2
1
2
1
2
1
1
3
2
2
1
2
1
RCGA
RCGG
LCTA
LCTG
STCA
GGGA
STCG
AGCT
AGCC
AGCA
AGCG
RCGT
RCGC
GGGT
GGGC
GGGG
LCTT
LCTC
PCCT
PCCC
PCCA
PCCG
STCT
STCC
TACT
TACC
TACA
TACG
VGTT
VGTC
VGTA
VGTG
LTTA
LTTG
RAGA
RAGG
IATT
IATC
IATA
YTAT
YTAC
CTGT
CTGC
QCAA
QCAG
EGAA
EGAG
KAAA
KAAG
HCAT
HCAC
NAAT
NAAC
DGAT
DGAC
FTTT
FTTC
SAGT
SAGC
MATG
WTGG
Volatility
1
Codons Volatility: Standard Genetic Code
0.9
0.8
0.7
0.6
0.5
0.4
AA_Codons
Arg
Gly
• 12 distinct volatility values
Leu
Ser
• only 4 aa contain synonymous codons (22) of different volatilities
Vol
0.5
0.56
0.57
0.63
0.67
0.71
0.75
0.78
0.86
0.88
0.89
1.
Spearman r = 0.4312
p < 0.0005
0
1
1
1
6
2
1
1
2
12
1
2
1
1
2
2
1
1
4
5
1
1
3
3
1
3
1
7
Vol
0.5
0.56
0.57
0.63
0.67
0.71
0.75
0.78
0.86
0.88
0.89
1.
0
1
1
1
1
7
2
12
2
3
1
1
6
1
1
3
3
1
2
1
1
4
5
1
Spearman r = 0.4283
p < 0.0006
3
1
1
2
QuickTime™ et un décompresseur TIFF (non compressé) sont requis pour visionner cette image.
Q uic kT ime™ et un décompres seur T IF F ( non c ompress é) sont r equis pour v isionner cet te image.
References:
• Ziheng Yang and Rasmus Nielsen (2000)
Estimating synonymous and nonsynonymous substitution rates under realistic
evolutionary models.
Mol Biol Evol. 17:32-43.
• Yang Z. and Bielawski J.P. (2000)
Statistical methods for detecting molecular adaptation
Trends Ecol Evol. 15:496-503.
• Phylogenetic Analysis by Maximum Likelihood (PAML)
http://abacus.gene.ucl.ac.uk/software/paml.html
• Plotkin JB, Dushoff J, Fraser HB (2004)
Detecting selection using a single genome sequence of M. tuberculosis and P.
falciparum. Nature 428:942-5.
• Molecular Evolution; A phylogenetic Approach
Page, RDM and Holmes, EC (Blackwell Science, 2004)
• Sharp, PM & Li WH (1987). NAR 15:p.1281-1295.
References
• Phylogeny programs :
http://evolution.genetics.washington.edu/phylip/sftware.html
• MEGA: http://www.megasoftware.net/
• PAML: http://abacus.gene.ucl.ac.uk/software/paml.html
Books:
• Fundamental concepts of Bioinformatics.
Dan E. Krane and Michael L. Raymer
• Genomes 2 edition. T.A. Brown
• Molecular Evolution; A phylogenetic Approach
Page, RDM and Holmes, EC
Blackwell Science