ASBP Training_Alignment and Phylogeny
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Transcript of ASBP Training_Alignment and Phylogeny
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III. Evolutionary Change in DNA Sequences
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Kinds of questions
Indentification of INDIVIDUALS does the fish in the freezer match the carcass on
the field
Detecting RELATEDNESS can kin selection (i.e. high level of relatedness)explain cooperative courtship behavior?
Assigning INDIVIDUALS to POPULATIONS do fish populations across the Bohol
Sea show sufficient differentiation to allow us to identify unknown samples to asource population with a high level of confidence?
Defining structure of POPULATIONS what forces could explain the geneticdifferentiation among populations of rabbit fish in western Philippines.
Identifying SPECIES boundaries are these two forms of rock fish a single
species or tow distinct speices
PHYLOGENETIC TREES where do whales (Cetaceans) fit in a phlogenetictreee of mammalian groups.
What is the grand arrangement of the tree of life in terms of kingdoms and phyla?
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WHY USE MOLECULAR MARKERS?
Only genetically transmitted traits are informative to phylogenyestimation
Molecular markers open the whole biological world to geneticscrutiny
Genetic markers access an almost unlimited pool of geneticvariability
Molecular data distinguishes Homology (common ancestry) fromAnalogy (convergence from different ancestors
Provides a common yardstick for measuring divergence
Facilitate Mechanistic appraisals of evolution
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PHYLOGENY and SYSTEMATICS
How are taxa arranged in thetree of life?
MORPHOLOGY
MOLECULARAPPROACHES
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0.092 0.060 0.019 0.0075
Gibbon
Orangutan
Human
Chimpanzee
Gorilla
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Terms
Nodes (terminal observed taxa; internalhypotheticalancestors)
Dichotomous or polytonous (uncertainty of relationships
or multiple simultaneous branching) Rooted vs unrooted trees
Clades and ingroups monophyly vs paraphyletic
Ingroup and outgroup
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Nucleotide Difference Between Sequences
A simple measure of the extent of sequence divergenceis p proportion of nucleotide sites at which the twosequences are different. This is estimated by:
p = nd/n
And is called the p distance. Although the overallnucleotide difference.
^
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Different types of nucleotide pairs between Xand Y
Class Nucleotide Pair
Identical nucleotidesfrequency
AA TT CC GG Total
O1 O2 O3 O4 O
Transition-type pair frequency AG GA TC CT
P11 P12 P21 P22 P
Transversion-type pairfrequency
AT TA AC CA
Q11
Q12
Q21
Q22
Q
TG GT CG GC
Q31 Q32 Q41 Q42
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Transition/ Transversion ratio
R = P / Q
R is usually 0.5 2.0 in many nuclear genes. In mtDNA it can be as highas 15.
R is subject to a large sampling error when the number of nucleotidesexamined (n) is small.
V(R) = R2 (1/nP + 1/nQ)
Assumption
P11= P12 ; P21= P22; Q11= Q12; Q 21= Q22; Q31= Q32 ;Q41= Q42
^ ^ ^
^
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Estimation of the number of substitutions
When p is large, it gives an underestimateWhy?
It does not consider backward and parallel substitutions
A number of mathematical models have beendeveloped to address this. We will discuss:
Jukes and Cantors Method
Kimuras Two-Parameter Method
Tajima and Neis MethodTamuras Method
Tamura and Neis Method
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Jukes-Cantor model
Assumes that nucleotide substitution occurs at anynucleotide site with equal frequency
Each site and nucleotide changes to one of the
remaining nucleotides with a probability of per year
Probability of change in nucleotide= rate of substitution
r = 3
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Jukes-Cantor model
A T C G
A -
T
-
C -
G -
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Consider X and Y
Let qt = proportion of identical nucleotides at time t
Let pt = 1-qt = proportion of different nucleotides
Probability that site with similar nucleotides in X and Y
at t will be remain similar by t+1:(1-r)2 or approximately 1-2r
Probability that site with different nucleotides in X and Ywill be similar by t+1:
(1-r) * 2
= 2r (1-r)/3 or approximately 2r/3
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Deriving a value for d
qt+1 = (1-2r) qt + 2r/3 (1-qt)qt+1 qt =2r/3 8r/3 qt
Using a continuous time model using dq/dtto
represent qt+1 qt
dq/dt =2r/3 8r/3 q
The solution of this equation with initial
conditions q=1 at t=0
q= 1-3/4 (1-e-8rt/3)
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Under our present model, the expected number ofnucleotide usbstituions per site (d) for the twosequences is 2rt. Therefore, d is given by:
d = -(3/4) ln [1-(4/3 p)]
where; p= 1-q is the proportion of different nucelotidesbetween X and Y. An estimate d can be obtained by
using p. The large-sample variance of d is:
V(d) = 9p(1-p)
(3-4p)2 n
^ ^
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Kimura Two Parameter model
Considers the higher rate of transitional vs trasversionalnucleotide substitution and 2
Total substitution rate per year r = + 2
C
A
T
G
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Kimura Two Parameter model
A T C G
A -
T
-
C
-
G -
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Deriving d
P = (1-2 e-4(+)t +e -8t)
Q = (1-e-8 t)
Where t is the time for transitional substitution:
d = 2rt = 2t + 4rt
= - ln (1-2P-Q)- ln (1-2Q)
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Variance of d (Kimuras model)
Variance of d is:
V(d) = 1/n [c12P + c3
2Q (c1P + c3Q)2]
Where;
c1 = 1 , c2 = 1 , and c3 = (c1 +c2)/2
1-2P-Q 1-2Q
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Notes:
In both the Kimura and Jukes Cantor models, theexpected frequencies of A,C,T and G will eventuallybecome equal to 0.25.
Both models make no assumption about the initialfrequencies. This property makes the two modelsapplicable to a wider condition than may other models.
There is no need to assume the stationarity ofnucleotide frequencies for estimating d.
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Tajima-Nei (Equal-input) model
A T C G
A - gT gC gG
T gA - gC gG
C gA gT - gG
G gA gT gC -
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Tajima-Nei (Equal-input) model
Similar model was proposed independently byFelsenstein (1981) and Tajima and Nei (1982)
It is necessary to assume stationarity of nucleotide
frequencies for estimating the number of nucleotidesubstitutions:
d = -b ln (1-p/b)
where,
b = [ 1- gi2 +p2/c]i=1
4
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And c is given by:
c = xij2
2gigj
Where xij (i
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Tamura model
In Kimuras model, the four nucleotides eventuallybecome 0.25. In real data, however, nucleotidefrequencies are rarely equal and the GC content isoften quite different from 0.5. (Drosophila for example
= 0.1) Tamuras (1992) model was developed as an extension
of Kimuras modelto the case of low or high GC content.
d = -h ln (1-P/ h-Q) () (1-h) ln (1-2Q)
Where h = 2 (1-), and is the GC content
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Tamura model
A T C G
A - 2 1 1
T 2 - 1 1
C 2 2 - 1
G 2 2 1 -
1 = gG + gC2 = gA + gT
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Tamura-Nei model
Hasegawa et al (1985) maximum likelihood method.This is a hybrid of Kimuras model, equal input model
and considers both the transition/ transversion and GC
content biases mentioned earlier. The formula for d isquite complicated but similar to Tamura and Neismodel of which it is a special case.
d = - 2gAgG ln [ 1- gR P1 1 Q]gR 2gAgG 2gR
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d = - 2gAgG ln [ 1- gR P1 1 Q]
gR 2gAgG 2gR
- 2gTgC ln [ 1- gY P2 1 Q]gY 2gTgC 2gY
- 2 [gRgY gAgGgR gTgCgR] ln [ 1 - 1 Q]
gR gY 2gRgY
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Gamma Distances
For our list of distances, the rate of nucleotidesubstitution is assumed to be the same for allnucleotide sites. In reality, this assumption rarely holds,and the rate varies from site to site.
Statistical analyses of rate substion at differentnucleotide sties suggested that the rate variationapproximately follows a gamma distribution
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Comparison of DifferentDistance Measures
0
0.5
1
1.5
2
0
0
.3
0.75
1
.2
1
.5
1
.8
Expected number of substitutions per s ite
Estimatednu
mberof
substitutions
persite
Tamura-NeiTamuraKimuraJukes-Cantorp
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Alignment of NucleotideSequences
ATGCGTCGTT
ATCCGCGAT
ATGCGTCGTTATCCG_CGAT
ATGC_GTCGTT
AT_CCG_CGAT
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Methods
Similarity index - Needleman and Wunsch (1970)
Alignment distance Sellers (1974)
E = Min w1 +w2
w1 andw2 are penalties for a mismatch and a gap (e.g 1and 4). The gap penalty is a function of the gap length.Similarly, mismatches are can be divided into
transitional and transversional mismatches and differentpenalities are given to them.
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Alignment of Multiple Sequences
Customary to use progressive alignment algorithm -pairs of sequences with small distances are first alignedand the alignment of more distantly related sequencesis done progressively for larger and larger groups.
Pairs of sequences are aligned using the progressivealignment algorithm. Groups of sequences are alignedwith each other using a profile alignment algorithm
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Handling sequence gaps in estimation ofevolutionary distances
Complete deletion delete all sites with gaps from thedata analysis. Generally desirable because differentregions of DNA sequences oftern evolve differently.
Pairwise-deletion if the number of nucloties invovledin the gap is small and gaps are distributed more orless at random, distances may be computed from pairsof sequences ignoring only those gaps that in the two
sequences compared
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ExampleA-AC-GGAT-AGGA-ATAAA
AT-CC?GATAA?GAAAC-A
ATTCC-GA/TACGATA-AGA
Differences/Comparison
Option Sequence (1,2) (1,3) (2,3)
Complete- deletion1 A C GA A GA A A A 1/10 0/10 1/10
2 A C GA A GA A C A
3 A C GA A GA A A A
Pairwise-deletion1 A-AC-GGAT-AGGA-ATAAA 2/12 3/12 3/14
2 AT-CC?GATAA?GAAAAC-A
3 ATTCC-GA?TACGATA-AGA
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Assignment:
Reading assignments
ClustalX-
http://inn-prot.weizmann.ac.i./software/ClustalX.html
http://www.biozentrum.unibas.ch/`biphit/slustal/ClustalX_help.html
Mega 2
http://www.megasoftware.net/
http://inn-prot.weizmann.ac.i./software/ClustalX.htmlhttp://www.biozentrum.unibas.ch/%60biphit/slustal/ClustalX_help.htmlhttp://www.megasoftware.net/http://www.megasoftware.net/http://www.biozentrum.unibas.ch/%60biphit/slustal/ClustalX_help.htmlhttp://inn-prot.weizmann.ac.i./software/ClustalX.htmlhttp://inn-prot.weizmann.ac.i./software/ClustalX.htmlhttp://inn-prot.weizmann.ac.i./software/ClustalX.html