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Justin Fay Center for Genome Sciences
Department of Genetics 4515 McKinley Ave. Rm 4305
Molecular evolution is the study of the cause and effects of
evolutionary changes in molecules
Phylogenetics Divergence times Comparative Genomics (mutation and selection)
Species 1 GGCAGTGACATTTTCTAACGCGAAGGTACTT Species 2 GGCAGCGCCATTTTCTAATGCGAGGGTACTT Species 3 GGCAGCGCCATTGTCTAATGCGAGGGTACTT
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Archea Human-chimp-neanderthal Ultraconserved sequences ENCODE, FOXP2
Origins of Molecular Evolution Insulin was the first protein sequenced in 1955 for which Fred Sanger received the Nobel prize. Cytochrome C protein sequence (Margoliash et al. 1961).
The sequencing of the same proteins from different species established a number of key principles of molecular evolution:
1. Most proteins are highly conserved and changes that do occur are not found within functionally important sites. For example human diabetics were treated with insulin purified from pigs and cows.
2. The rate of amino acid substitution is constant across phylogenetic lineages.
Molecular clock - the rate of amino acid or nucleotide substitution is constant per year across phylogenetic lineages (Zuckerkandl and Pauling 1962). Controversial but revolutionized phylogenetics and set the stage for the neutral theory.
Neutral theory or neutral mutation random drift hypothesis - the vast majority of mutations that become polymorphic in a population and fixed between species are not driven by Darwinian selection but are neutral or nearly neutral with respect to fitness (Kimura 1968; King and Jukes 1969). The neutral theory is dead; long live the neutral theory.
Not all amino acid changes are equal
Grantham's Distance – carbon-composition, polarity, volume, weight
Amino Acid Substitution Models PAM (Point Accepted Mutation, 1966) matrix was developed by Margaret Dayhoff. PAM1 matrix estimates what rate of substitution would be expected if 1% of the amino acids had changed. (Global alignments)
BLOSUM (BLOck SUbstitution Matrix, 1992) was developed by Henikoff and Henikoff. PAM didn't do well at modeling sequence changes over long evolutionary time scales since these are not well approximated by compounding small changes that occur over short time scales. The probabilities used in the matrix calculation are computed by looking at "blocks" of conserved sequences found in multiple protein alignments. Sequence with percent identity above a certain threshold are downweighted, e.g. BLOSUM62 which is used for BLASTP. (Local alignments)
Nucleotide Substitution Models
Nucleotide substitution models correct for multiple hits
Jukes and Cantor (JC69) Model (1969)
Assumptions of JC model. 1) Equal base frequencies 2) Equal mutation rates between the bases 3) Constant mutation rate 4) No selection
Jukes Cantor Model
p = 3/31 = 0.097 K = 0.104 substitutions per site
Other nucleotide substitution models
Model Assumption Free Parameters
JC69 A=G=C=T ts=tv
1 Jukes & Cantor 1969
K80 A=G=C=T 2 Kimura 1980
F81 ts=tv 4 Felsenstein 1980
HKY85 5 Hasegawa, Kishino & Yano
GTR unequal rates 9 Tavare 1986
Difference between mutation rate and substitution rate.
Mutation rate the chance of a mutation occurring in each generation or cell division (does NOT depend on selection)
Substitution rate the frequency at which mutations become fixed within a population (depends on selection)
Substitution rate = mutation rate * fixation probability * time Fixation probability depends on selection
Substitution Rates with Selection
No selection: The substitution rate between two species is K = 2t.
1−e −4Ne s
Substitution rate = mutation rate * fixation probability * time
The substitution rate for neutral mutations = 2Nµ * 1/2N * t = µt The substitution rate for adaptive mutations = 2Nµ * 2s * t = 4Nsµt for 4Ns > 1
Rapidly Evolving Genes (dN/dS)
Detecting selection using the nucleotide substitution rate Synonymous change - mutation that does not change the amino
acid sequence of a protein. Nonsynonymous change - mutation that changes the amino acid
sequence of a protein.
Table 1. The genetic code. Codon AA Codon AA Codon AA Codon AA TTT Phe TCT Ser TAT Tyr TGT Cys TTC Phe TCC Ser TAC Tyr TGC Cys TTA Leu TCA Ser TAA Stop TGA Stop TTG Leu TCG Ser TAG Stop TGG Trp
CTT Leu CCT Pro CAT His CGT Arg CTC Leu CCC Pro CAC His CGC Arg CTA Leu CCA Pro CAA Gln CGA Arg CTG Leu CCG Pro CAG Gln CGG Arg
ATT Ile ACT Thr AAT Asn AGT Ser ATC Ile ACC Thr AAC Asn AGC Ser ATA Ile ACA Thr AAA Lys AGA Arg ATG Met ACG Thr AAG Lys AGG Arg
GTT Val GCT Ala GAT Asp GGT Gly GTC Val GCC Ala GAC Asp GGC Gly GTA Val GCA Ala GAA Glu GGA Gly GTG Val GCG Ala GAG Glu GGG Gly
dN or Ka = the nonsynonymous substitution rate = # nonsynonymous changes / # nonsynonymous sites. dS or Ks = the synonymous substitution rate = # synonymous changes / # synonymous sites.
Interpretation of dN/dS ratios (assuming synonymous sites are neutral):
dN/dS = 1No constraint on protein sequence, i.e. nonsynonymous changes are neutral.
dN/dS < 1Functional constraint on the protein sequence, i.e. nonsynonymous mutations are deleterious.
dN/dS > 1Change in the function of the protein sequence, i.e. nonsynonymous mutations are adaptive.
Rapidly Evolving Genes
Nayak et al. 2005
dN increased by positive selection dN decreased by negative selection Problem: dN may be influenced by both and still be less than dS
BRCA1 sliding window Ka/Ks analysis
Branch Model (dN/dS) (rate heterogeneity)
15 copies in human Vary in copy in other primates
Johnson et al. 2001
Site Model (dN/dS) ● Positive selection on the egg receptor
(VERL) for abalone sperm lysin. ● VERL – lysin are a lock and key for
fertilization. ● Co-evolution by sexual selection, conflict or
Gilando et al. 2003
Sites – methods Maximum Parsimony (Suzuki) Maximum Likelihood (PAML, HyPhy)
αs = synonymous rate
βs = nonsynonymous rate
R = tv/ts
πny = frequency of target nucleotide n in codon y
Models for the Evolution of Transcription Factor Binding Sites
● Sequence ~ binding affinity (Schneider et al. 1986, Berg and von Hippel 1987) ● Binding affinity ~ fitness (Gerland and Hwa 2002, Sengupta et al. 2002) ● Fitness ~ substitution rate (Moses et al. 2004)
Moses et al. 2004
Molecular Evolution (Comparative Genomics)
Annotation of genes, regulatory sequences and other functional elements
Functional sequences will remain conserved across distantly related species whereas non-functional sequences will accumulate changes
Evolution of genes, regulatory sequences and other functional elements
Species-specific functional sequences
Functional sequences with new or modified functions
Species Conserved* Conserved Noncoding (non-repetitive aligned)
Humans 3-8% 21% Waterston et al. (2002)
Worms 18-37% 18% Shabalina & Kondrashov (1999)
Flies 37-53% 40-70% Andolfatto (2005)
Yeast 47-68% 30-40% Chin et al. (2005), Doniger et al. (2005)
*Siepel et al. (2005)
Deletion and expression assays of conserved noncoding sequences
Pennacchio et al. 2006 Yun et al. 2012
Scan for positively selected genes using the branch-site model
Koisol et al. (2014)
Models of molecular evolution
➔Tree is correct ➔Alignments are correct ➔Sites are independent ➔Stationarity and time reversibility ➔Mutational & selection parameters
2 1 1 3 3 1 4 15 3 5 954 105
10 34,459,425 2,027,025
Table 1. Number of possible rooted and unrooted trees.
Number of sequences
Number of rooted trees
Number of unrooted trees
Taxonomists have long debated phylogenetic methods.
There are many types of methods:
Character state methods (also called cladistic methods), like parsimony.
Distance or similarity based methods (also called phenetic methods), like UPGMA.
Maximum likelihood and Bayesian Methods.
Parsimony (non-parametric) and Maximum likelihood (parametric) are both used when phylogeny is critical.
PAUP PHYLIP MEGA MrBayes
Table 2. Distance matrix. Sequence A B C A B d(AB) C d(AC) d(BC) D d(AD) d(BD) d(CD) Each d is the dist