Models of Protein Evolution

1
Models of Protein Evolution

• Amino acid sequences (20 amino acids)
• Protein-coding DNA sequences

2
Models for Amino Acid Sequences

• DNA (4 x 4 rate matrix) vs amino acid (20 x 20)
  resulting in many more parameters and thus,
  computation time
• Consequently, amino acid models have
  concentrated on empirical approaches
• EMPIRICAL (several implemented in MrBayes model
  fixed )
• NON-EMPIRICAL (model variable in MrBayes)

3
Models for Amino Acid Sequences

• EMPIRICAL (several implemented in MrBayes model
  fixed ) 20 x 20 matrices
• Dayhoff et al. (1978) matrix based on the
  observation of 1572 accepted mutations between 34
  superfamilies of closely related sequences
• JTT matrix (Jones et al. 1992 Gonnett et al.
  1992) same methodology as Dayhoff, but with
  modern databases (other later modifications for
  transmembrane Jones et al. 1994)
• mtREV (Adachi and Hasegawa 1995, 1996) matrix
  derived from maximum likelihood-inferred
  replacements in mitochondrial proteins of 20
  vertebrate species
• WAG (Whelan and Goldman 2001) matrix derived from
  maximum likelihood improvement of JTT
• Poisson assumes equal stationary state
  frequencies and equal substitution rates
  (equivalent to JC model for DNA). Not really
  empirical, but it is fixed

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Dayhoff Evolutionary Mutation Matrix
5
Models for Amino Acid Sequences

• 2. NON-EMPIRICAL ( variable in MrBayes)
• Equalin in MrBayes substitution rates equal,
  but adjusted for amino acid equilibrium
  frequencies in dataset (equivalent to F81 for
  DNA)
• Cao et al. (2004) and Goldman and Wheelan (2002)
  Empirical matrices adjusted for the equilibrium
  frequencies of amino acids in dataset (similar to
  base frequencies in GTR matrix 19 rate
  parameters)
• GTR allows all stationary state frequencies and
  substitution rates to vary (MANY parameters 19
  free stationary state frequency parameters and
  189 free substitution rate parameters)

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Equalin instantaneous rate matrix
7
GTR instantaneous rate matrix
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Phylogeny inference software for Amino Acid
Sequences

• Parsimony PAUP and others
• Maximum Likelihood
• Molphy (only UNIX)
• TreePuzzle uses quartet puzzling a different
  search strategy
• PhyML (web based or downloadable binary) uses a
  different search algorithm
• RaxML
• ProtML (really old probably slow searches)
• Bayesian MrBayes
• Distance (MEGA)
• www.megasoftware.net
• implements empirical (Dayhoff and JTT, as well as
  Poisson model for inferring pairwise distances)

9
Models of Protein Evolution

• Amino acid sequences (20 amino acids)
• Protein-coding DNA sequences
• Codon-position models (4 nucleotides)
• Codon-based models (64 codons)

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1. Codon-position models (4 nucleotides)

• 1st, 2nd, and 3rd codon positions are treated
  differently
• Equivalent to establishing different partitions
  such as different partitions for different genes
  (covered in Data Partition lecture)
• Uses NO information from the Genetic Code
• Each codon position can have
• A different rate (partition by codon position in
  PAUP and in MrBayes), but all codon positions
  the same base freq and substitution matrix
• A different substitution matrix (MrBayes but not
  PAUP)
• A different base frequencies (MrBayes but not
  PAUP)
• A different gamma distribution (MrBayes but not
  PAUP)
• Or a combination of the above (MrBayes but not
  PAUP)
• see Shapiro et al. 2006

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2. Codon-based models (64 codons)
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2. Codon-based models

• consider a codon triplet as the unit of evolution
  
• A codon can change to another only through steps
  of one nucleotide change at a time
• distinguish between synonymous (silent) and
  nonsynonymous (replacement) substitutions
• Uses a 64 X 64 (or 61 X 61 excluding stop codons
  3721) matrix of probabilities of change among
  codons
• The two most commonly used models employ an
  extension of the HKY DNA model (ts/tv ratio and
  base or codon frequencies) and an additional
  parameter
• nonsynonymous/synonymous rate ratio (?)
• Models
• Goldman and Yang 1994 Yang et al. 1998
• Muse and Gaut 1994
• Widely used for testing hypotheses about natural
  selection (see PAML manual), but not for
  phylogenetic inference because of the
  computational expense
• However, may still be used to select among a
  reduced number of possible trees
• see Ren et al. 2005

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2. Codon-based models

• Goldman and Yang 1994 Yang et al. 1998
• Equilibrium frequencies of each codon are
  estimated from the codon frequency (?j)
• Parameters
• qij transition probability of codon i to codon
  j
• ?j frequency of codon j
• ? transition/transversion ratio
• ? nonsynonymous/synonymous rate ratio

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2. Codon-based models

• Muse and Gaut 1994
• Transition probability of codons in proportional
  to the equilibrium frequencies the target
  nucleotide rather than of the target codon
• Equilibrium frequencies of target nucleotides can
  be treated the same for all three codon positions
  together or separately for each codon position
  (parameter k below)
• Parameters
• qij transition probability of codon i to codon
  j
• ?j frequency of nucleotide j at codon position
  k (k 3)
• ? transition/transversion ratio
• ? nonsynonymous/synonymous rate ratio

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2. Codon-based models

• Inagaki Y, Roger AJ (2006) present a problem of
  codon-based models when codon usage varies among
  lineages
• Similar to a long branch attraction effect when
  two distantly related lineages have similar codon
  biases
• None of the models implemented to date
  incorporates codon usage heterogeneity among
  lineages

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2. Codon-based models Software

• PAML
• implements the two models described (i.e.,
  extension of the HKY)
• Not good for searching trees
• In practice, used to compare hypotheses of models
  or parameters on one or a few trees especially
  tests of positive selection
• Parameters
• ?j frequency of codon j or frequency of
  nucleotide j at codon position k (k 3)
• ? transition/transversion ratio
• ? nonsynonymous/synonymous rate ratio
• Fixed or variable among lineages (branch models)
• Fixed or variable among sites (sites models)
• Fixed or variable among sites and lineages
  (branch-site models)

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2. Codon-based models Software

• MrBayes
• does allow you to search for the tree topology
  (i.e., the topology does not have to be fixed)
• the substitution matrix has 3600 instead of 16
  cells
• Runs 200 times slower
• Require 16 times more memory than nucleotide
  models
• Parameters
• GTR (F81 or JC) rather than HKY
• substitution probabilities and equilibrium
  frequencies of nucleotides? or codons?)
• ? nonsynonymous/synonymous rate ratio
• Fixed among lineages
• May vary among sites
• values 0 lt ?1 lt 1, ?2 1, and ?3 gt 1 (Ny98)
• ?1 lt ?2 lt ?3 (M3)

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References

• Anisimova, M., and C. Kosiol. 2009. Investigating
  Protein-Coding Sequence Evolution with
  Probabilistic Codon Substitution Models.
  Molecular Biology and Evolution 26255-271.
  (deals more with hypothesis testing than
  phylogenetic inference).
• Huelsenbeck, J. P., P. Joyce, C. Lakner, and F.
  Ronquist. 2008. Bayesian analysis of amino acid
  substitution models. Philosophical Transactions
  of the Royal Society B Biological Sciences
  3633941-3953.
• Le, S. Q., N. Lartillot, and O. Gascuel. 2008.
  Phylogenetic mixture models for proteins.
  Philosophical Transactions of the Royal Society
  B Biological Sciences 3633965-3976. (see
  http//www.atgc-montpellier.fr/models/index.php?mo
  delmixture)
• Inagaki Y, Roger AJ (2006) Phylogenetic
  estimation under codon models can be biased by
  codon usage heterogeneity. Mol. Phylogenet. Evol.
  40, 428-434.
• Kosiol C, Holmes I, Goldman N (2007) An empirical
  codon model for protein sequence evolution.
  Molecular Biology and Evolution 24, 1464-1479.
• Shapiro B, Rambaut A, Drummond AJ (2006) Choosing
  appropriate substitution models for the
  phylogenetic analysis of protein-coding
  sequences. Mol. Biol. Evol. 23, 7-9.
• Ren FR, Tanaka H, Yang ZH (2005) An empirical
  examination of the utility of codon-substitution
  models in phylogeny reconstruction. Systematic
  Biology 54, 808-818.

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References

• Chapter 14 Felsensteins textbook Models of
  protein evolution.
• MrBayes manual sections 4.1.34.2.3.
• PAML manual.
• Goldman N, Yang Z (1994) A codon-based model of
  nucleotide substitution for protein-coding DNA
  sequences. Mol. Biol. Evol. 11, 725-736
• Muse SV, Gaut BS (1994) A likelihood approach for
  comparing synonymous and nonsynonymous
  substitution rates, with application to the
  chloroplast genome. Mol. Biol. Evol. 11, 715-724.
• Yang Z, Nielsen R, Hasegawa M (1998) Models of
  amino acid substitution and applications to
  mitochondrial protein evolution. Mol. Biol. Evol.
  15, 1600-1611.