Chapter 5 Rate and Patterns of Nucleotide Substitution 1 Chau-Ti Ting [email protected] Unless...

Chapter 5Rate and Patterns of Nucleotide Substitution

1

Chau-Ti Ting

[email protected]

Unless noted, the course materials are licensed under Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Taiwan (CC BY-NC-SA 3.0)

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§ Rate of nucleotide substitution

The rate of nucleotide substitution, r, is defined as he number of substitutions per site per year. The mean rate of substitution can be calculated by dividing the number of substitutions, K, between two homologous sequences by 2T, where T is the time of divergence between the two sequences. That is

Source: Dan Graur and Wen-Hsiung Li2000. Fundamentals of Molecular Evolution., p. 100. Sinauer Associates, Inc. Sunderland, MA, USA.

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http://get.nccu.edu.tw:8080/getcdb/handle/getcdb/127023

Coding regionSynonymous versus nonsynonymousThe rate of nonsynonymous substitution is extremely variable among genes:Range: effective zero in actin 3.1x10-9 in interferon

Extreme case – ubiquitin, which is completely conserved between human and fly and which differs among animal, plant, and fungi by only 2 or 3 out of 76 amino acid residues.

In the vast majority of genes, the synonymous substitution rate greatly exceeds the nonsynonymous substitution rate.



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Transition versus transversion

At fourfold degenerate sites it is possible to compare the rate of transitional substitution and transversional substitution, since both types of substitution are synonymous.



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National Taiwan University Chau-Ti Ting

Exon Exon Exon

Intron Intron

5’ 3’

Flanking region Flanking region

GC box

CAAT boxTATA box

Transcription initiation

Initiation codon

Stop codon

AATAAA box

Transcription termination

Poly(A) site

Promoter region

GT AG

Intron

19-27 bp upstream of the transcription startpoint

TACTAAC box

30 bp upstream of the 3’ end of the intron

GT-AG rule

5’ 3’

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PseudogenesA pseudogene is a nongenic DNA segment that exhibits

a high degree of similarity to a functional gene but which contains defects, such as nonsense and frameshift mutations, that prevent it from being expressed properly.


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Noncoding region In almost all genes, the substitution rates in the 5’ and 3’ UTR are lower than those at fourfold degenerate sites.The rate in pseudogenes is slightly higher than that in the other regions.

Table 4.4 Numbers of nucleotide substitutions per site (K) between cow and goat globin genes


Source: Dan Graur and Wen-Hsiung Li2000. Fundamentals of Molecular Evolution., p. 107. Sinauer Associates, Inc. Sunderland, MA, USA. 7




Exon Exon Exon

Intron Intron

5’ 3’

Flanking region Flanking region

GC box

CAAT boxTATA box

Transcription initiation

Initiation codon

Stop codon

AATAAA box

Transcription termination

Poly(A) site

Promoter region

GT AG

Intron

19-27 bp upstream of the transcription startpoint

TACTAAC box

30 bp upstream of the 3’ end of the intron

GT-AG rule

5’ 3’

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§ Causes of Variation in Substitution RatesThe rate of substitution is determined by two factors:

(1) the rate of mutations(2) the probability of fixation of a mutation (Ch. 2)


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Functional constraintsFunctional constraints or selective constraints defines that range of alternative nucleotides that is acceptable at a site without affecting negatively the function or structure if the gene or the gene product.

Kimura has illustrate this principle by a simple model

where vT is the total mutation rate by unit time, f0 is the fraction of neutral or nearly neutral mutations and K is the substitution rate

Whenever a particularly conservative sequence is found, researchers start looking for a specific function in this region



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Patterns of substitution and replacement

The pattern of nucleotide substitution is defined as the relative frequency with which a certain nucleotide changes into another during evolution.

Pij= nij

ni

Where nij is the number of substitutions from i to j, and ni is the number of i nucleotides in the ancestral sequence



A

T

G

C


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Inferring substitutions on a specific lineageSource: Dan Graur and Wen-Hsiung Li2000. Fundamentals of Molecular Evolution., p. 125. Sinauer Associates, Inc. Sunderland, MA, USA.

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55 processed pseudogene sequences from human

Pseudogenes are expected to become rich in A and T


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Mutation maybe different between the two strands!!


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Patterns of amino acid replacement

Physicochemical distance are based on such properties of the amino acid as polarity, molecular weight, and chemical composition.

Grantham’s distance (1974, Table 4.7)conserved replacement LeuIle d=5radical replacement TrpCys d=215

typical amino acidleucins, isoleucin, glutamin, methionine

Idiosyncratic amino acidcysteine, tryptophan, tyrosine, glycine



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Wikipedia Dancojocjri 16

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Patterns of amino acid replacement

Physicochemical distance are based on such properties of the amino acid as polarity, molecular weight, and chemical composition.

Grantham’s distance (1974, Table 4.7)conserved replacement LeuIle d=5radical replacement TrpCys d=215

typical amino acidleucins, isoleucin, glutamin, methionine

Idiosyncratic amino acidcysteine, tryptophan, tyrosine, glycine



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Amino acid exchangeability


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Molecular ClockIn their comparative studies of hemoglobin and cytochrome c protein sequences from different species, Zucherkandel and Pauling (1962, 1965) and Margoliash (1963) first notice that the rates of amino acid replacement were approximately the same among various mammalian lineages.Zucherkandel and Pauling (1965) therefore proposed that for any given protein, the rate of molecular evolution is approximately constant over time in all lineage or, in other words, that there exists a molecular clock.


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If a proteins evolve at a constant rates, they can be used to determine dates of species divergence and to reconstruct phylogeny relationships among organisms.

Let us assume that the rate of nonsynonymous substitution for the chain of hemoglobin is 0.56 x 10-9 substitutions per site per year, and that -globins from rat and human differ by 0.093 substitutions per site. Then, under the molecular clock hypothesis, the divergence time between the human and rat lineages is estimated to be approximately 0.93/(2 x 0.56 x 10-9)= 80 million years ago.

Kimura (1983) – “ For each protein, the rate of evolution in terms of amino acid substitution is approximately constant per year per site for various lineage, as long as the function is and tertiary structure of the molecule remain essentially unaltered.”



Source: Motoo Kimura1983. The Neutral Theory of Molecular Evolution., p. 98. Cambridge University Press, Cambridge, USA.

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Controversies and challenges

• Classical evolutionists argued against it because the suggestion of rate constancy did not sit well with the erratic tempo of evolution at the morphological and physiological levels.

• Based on molecular clock, the estimate divergence between humans and other African apes is only 5 million years. However, the then-prevailing view among paleontologists was that human and apes diverged at least 15 million years ago.

• Extreme high rate of amino acid replacement occurred following the gene duplication that gave rise to the - and -hemoglobins, and that the high rates were due to advantageous mutations that improved the function of these globin chains.

• Protein sequence evolution often proceeds much more rapidly at times of adaptive radiation than during periods in which no speciation occurred.


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Relative Rate TestThe controversy over molecular clock hypothesis often involves disagreement on dates of species divergence. To avoid this problem, several test have been developed.

Margoliash, Sarich and Wilson’ s testSuppose that we want to compare the rates in lineage A and B. Then, we use a third species, C, as an outgroup reference.



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The number of substitutions between species A and B, KAB, is equal to the sum of substitutions that have occurred frin point O to the point A (KOA) and from point O to the point B (KOB). That is,

KAB = KOA + KOB

Similarly,KAC = KOA + KOC

andKBC = KOB + KOC

O

A B C



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Since KAB, KAC, and KBC can be direct estimated from the nucleotide sequences, we can easily solve the three equations to find the values of KOA, KOB, and KOC

KOA = (KAC + KAB – KBC)/2

KOB = (KAB + KBC – KAC)/2

KOA = (KAC + KBC – KAB)/2

O

A B C



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The time has passed since species A and B last shared a common ancestor is by definition equal for both lineage. Thus, according to the molecular clock hypothesis, KOA and KOB should be equal, i.e., KOA – KOB = 0.

KOA – KOB = (KAC + KAB – KBC)/2 – (KAB + KBC – KAC)/2

= KAC – KBC = d

where d is the difference in branch length between the two lineages leading from O to species A and B.

O

A B CSource: Dan Graur and Wen-Hsiung Li2000. Fundamentals of Molecular Evolution., p. 143. Sinauer Associates, Inc. Sunderland, MA, USA.


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Nearly equal rates in mouse and ratsUsing relative rate test, KAC–KBC values for both synonymous and nonsynonymous are not significantly different from 0. Therefore, the null hypothesis of equal substitution rates in mice and rats cannot be rejected. The results are also consistent with the neutral mutation hypothesis.



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Tajima’s 1D (one-degree of freedom) method

We start with three aligned nucleotide sequences, 1, 2, and 3. Let nijk be the obsevered number of sites where sequences 1, 2, and 3 have nucleotide i, j, and k, respectively, where i, j, and k can be nucleotides A,G, C, or T. If sequence 3 is the out group, then the expectation of nijk should be equal to that of njik, i.e.,

E(nijk) = E(njik)Source: Dan Graur and Wen-Hsiung Li2000. Fundamentals of Molecular Evolution., p. 144. Sinauer Associates, Inc. Sunderland, MA, USA.

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This equality holds regardless of the substitution model or the pattern of variation in substitution rates among sites.We define m1 as follows:

m1 = nijj = nAGG + nACC + nATT + nGAA + nGCC + nGTT + nCAA + nCGG + nCTT + nTAA + nTGG + nTCC

Similarly, we define m2 as

m2 = njij = nAGA + nACA + nATA + nGAG + nGCG + nGTG + nCAC + nCGC + nCTC + nTAT + nTGT + nTCT

Note that only sites in which exactly two types of nucleotides exist in the three sequences are used in this analysis.



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When sequence 3 is outgroup, the expectation of m1 is equal to that of m2 under molecular clock:

E(m1) = E(m2)

The equality can be tested by using 2 with one degree of freedom, namely,

2= (m1– m2)2/( m1+ m2)Source: Dan Graur and Wen-Hsiung Li2000. Fundamentals of Molecular Evolution., p. 145. Sinauer Associates, Inc. Sunderland, MA, USA.

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“The rate of nucleotide substitution, r, is defined as he number of substitutions per site per year. … K, between two homologous sequences by 2T, where T is the time of divergence between the two sequences. That is “

“ Dan Graur and Wen-Hsiung Li2000. Fundamentals of Molecular Evolution., p. 100. Sinauer Associates, Inc. Sunderland, MA, USA.It is used subject to the fair use doctrine of:•Taiwan Copyright Act Articles 52 & 65•The "Code of Best Practices in Fair Use for OpenCourseWare 2009 (http://www.centerforsocialmedia.org/sites/default/files/10-305-OCW-Oct29.pdf)" by A Committee of Practitioners of OpenCourseWare in the U.S. The contents are based on Section 107 of the 1976 U.S. Copyright Act

P2

“The rate of nonsynonymous … human and fly and which differs among animal, plant, and fungi by only 2 or 3 out of 76 amino acid residues.”

Dan Graur and Wen-Hsiung Li2000. Fundamentals of Molecular Evolution., p. 101. Sinauer Associates, Inc. Sunderland, MA, USA.It is used subject to the fair use doctrine of:•Taiwan Copyright Act Articles 52 & 65•The "Code of Best Practices in Fair Use for OpenCourseWare 2009 (http://www.centerforsocialmedia.org/sites/default/files/10-305-OCW-Oct29.pdf)" by A Committee of Practitioners of OpenCourseWare in the U.S. The contents are based on Section 107 of the 1976 U.S. Copyright Act

P3

“In the vast majority of genes, the synonymous substitution rate greatly exceeds the nonsynonymous substitution rate.”


P3

“At fourfold degenerate sites it is possible to compare the rate of transitional substitution …, since both types of substitution are synonymous.”


P4

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P4


P5, P8

“A pseudogene is a nongenic DNA segment that exhibits a high degree of similarity to a functional gene but which contains defects, such as nonsense and frameshift mutations, that prevent it from being expressed properly.”


P6

“In almost all genes, the substitution rates in the 5’ and 3’ UTR are lower than those at … The rate in pseudogenes is slightly higher than that in the other regions.”


P7


P7

34















“The rate of substitution is determined by two factors:(1)

the rate of mutations(2) the probability of fixation of a mutation (Ch. 2)“


P9

“Functional constraints or selective constraints defines … nearly neutral mutations and K is the substitution rate”


P10

“Whenever a particularly conservative sequence is found, researchers start looking for a specific function in this region “


P10

“The pattern of nucleotide substitution is defined as the relative frequency with which a certain nucleotide changes into another during evolution. “


P11

35














“Where nij is the number of substitutions from i to j, and ni is the number of i nucleotides in the ancestral sequence “


P11


P11


P12


P13


P14

36















“Physicochemical distance are based on such properties of the amino acid as polarity, molecular weight, and chemical composition. “


P15, P17

Grantham’s distance (1974, Table 4.7)conserved replacementLeuIle d=5Radical … Idiosyncratic amino acid

cysteine, tryptophan, tyrosine, glycine


P15, P17

Wikipedia Dancojocjrihttp://en.wikipedia.org/wiki/File:Amino_Acids.svg2012/07/25 visited

P16


P18


P19

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http://en.wikipedia.org/wiki/File:Amino_Acids.svg









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“In their comparative studies of hemoglobin and cytochrome … is approximately constant over time in all lineage or, in other words, that there exists a molecular clock.”


P20

Wiki brian0918™http://en.wikipedia.org/wiki/File:ADN_animation.gif2012/02/21 visited

P20

Open Clip Art Library fzaphttp://openclipart.org/detail/16605/clock-sportstudio-design-by-fzap2012/02/21 visited

P20


P21

“If a proteins evolve at a constant rates, they can be used to determine dates of species divergence and to reconstruct phylogeny relationships among organisms.”


P22

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http://openclipart.org/detail/16605/clock-sportstudio-design-by-fzap








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“Let us assume that the rate of nonsynonymous substitution for the chain of hemoglobin is … estimated to be approximately 0.93/(2 x 0.56 x 10-9)= 80 million years ago.”


P22

“For each protein, the rate of evolution in terms of amino acid substitution is approximately constant per year per site for various lineage, as long as the function is and tertiary structure of the molecule remain essentially unaltered”

Motoo Kimura1983. The Neutral Theory of Molecular Evolution., p. 98. Cambridge University Press, Cambridge, USA.http://books.google.com.tw/books?id=olIoSumPevYC&printsec=frontcover&dq#v=onepage&q&f=falseIt is used subject to the fair use doctrine of:•Taiwan Copyright Act Articles 52 & 65•The "Code of Best Practices in Fair Use for OpenCourseWare 2009 (http://www.centerforsocialmedia.org/sites/default/files/10-305-OCW-Oct29.pdf)" by A Committee of Practitioners of OpenCourseWare in the U.S. The contents are based on Section 107 of the 1976 U.S. Copyright Act

P22

“Classical evolutionists argued against it because the suggestion of rate constancy did not sit well with … adaptive radiation than during periods in which no speciation occurred”


P23

“The controversy over molecular clock hypothesis often involves disagreement on dates of species divergence. To avoid this problem, several test have been developed.”


P24

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http://books.google.com.tw/books?id=olIoSumPevYC&printsec=frontcover&dq

http://books.google.com.tw/books?id=olIoSumPevYC&printsec=frontcover&dq











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“Margoliash, Sarich and Wilson’ s testSuppose that we want to compare the rates in lineage A and B. Then, we use a third species, C, as an outgroup reference.”


P24

“The number of substitutions between species A and B, KAB, is equal to the sum of substitutions that have occurred frin point O to the point A (KOA) and from point O to the point B (KOB). That is, ”


P25


P25, P26, P27

“Since KAB, KAC, and KBC can be direct estimated from the nucleotide sequences, we can easily solve the three equations to find the values of KOA, KOB, and KOC”


P26













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“The time has passed since species A and B last shared a common ancestor is by definition equal for both lineage … between the two lineages leading from O to species A and B.”


P27

“Using relative rate test, KAC–KBC values for both synonymous and … rates in mice and rats cannot be rejected. The results are also consistent with the neutral mutation hypothesis.”


P28


P28

“We start with three aligned nucleotide sequences, 1, 2, and 3. Let nijk be the obsevered number of sites where sequences … expectation of nijk should be equal to that of njik, i.e.,”


P29













42


“This equality holds regardless of the substitution model or the pattern of variation in substitution rates among sites. … ”


P30

“Note that only sites in which exactly two types of nucleotides exist in the three sequences are used in this analysis.”


P30

“When sequence 3 is outgroup, the expectation of m1 is equal to that of m2 under molecular clock: …”


P31


P32



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Chapter 5 Rate and Patterns of Nucleotide Substitution 1 Chau-Ti Ting [email protected] Unless...

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