Phylogenetics Marek Kimmel Statistics, Rice kimmelrice'edu 713 348 5255

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PhylogeneticsMarek Kimmel (Statistics,
Rice)kimmel_at_rice.edu713 348 5255
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Molecular phylogenetics

• Study of evolutionary relationships among
  organisms, genes or proteins, by a combination of
  molecular biology and statistical techniques
• Molecular data are more powerful DNA and protein
  sequences generally evolve in a more regular
  manner than morphological and physiological
  characters. Also, they are more amenable to
  quantitative treatment.

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Trees

• Phylogenetic relationships are usually
  represented in the form of trees.
• Observations available only at the bottom of the
  tree. Find tree structure (topology) and branch
  lengths.

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Vocabulary of trees

• Phylogenetic tree A graph composed of nodes and
  branches, in which only one branch connects any
  two adjacent nodes.
• Nodes Taxonomic units. Usually represented by
  sequences (DNA or AA).
• Branches Relationships among units in terms of
  descent/ancestry.
• Topology Branching pattern of a tree. Number of
  topologies is generally enormous,
• N(n)(2n-3)!/2n-2(n-2)!.
• Branch length changes in the branch.
• Terminal (external) nodes Extant TUs OTUs
  (operational taxonomic units).
• Internal nodes Ancestral TUs.
• Root A node from which unique path leads to any
  other node, in the direction of evolutionary
  time. The root is the common ancestor of all
  OTUs under study.
• Rooted/unrooted tree Specifies (does not
  specify) the evolutionary path.

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Phylogenetic Tree
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Tree building methodologies

• Distance methods construct tree by joining
  sequences with small distance between them.
• Maximum parsimony finds tree which explains
  observed data using smallest of substitution.
• Maximum likelihood maximizes the likelihood of
  all possible trees. Probabilistic model of
  evolution is assumed

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Overview

• Principles of maximum likelihood trees
• Variation in substitution rates
  Felsenstein-Churchill algorithm
• Finding functionally important sites in proteins
  Comparison with Evolutionary Trace

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Phylogenetic tree
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Maximum likelihood (Felsensteins) trees

• Want to find a tree with the highest probability
  (i.e., likelihood) of reproducing data on OTUs
• Assume independence of evolution at different
  sites.
• Compute probability of given tree site by site.
• Take product of all sites at end
• If all sequences know, likelihood is product of
  probabilities of change in each segment times
  prior probability of initial state.

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Model of evolution

• Start with a rate matrix (Q) one which states
  the rates of change from one amino acid to
  another
• Obtain a prob. matrix via P(t)eQt or by
  iterating PAM1 or BLOSUM1 substitution matrices

A K R N K T T H H N V P P A D
substitution
time
A K R N K T N H H N V P P A D
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Likelihood

• If all ancestors are known, likelihood is simple
  to compute
• L product of probability of change in each leaf
  of tree times prior prob. of given ancestor,
  calculated site by site along sequence
• Pij(t) probability of a lineage initially
  having amino acid i will have amino acid j after
  t time units

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Phylogenetic tree and its likelihood
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Likelihood calculations with internal nodes
unknown

• Problem amino acids at interior nodes are not
  generally known
• Solution
• generalize the likelihood
• sum over all possible assignments of amino acids
  to the splits of the trees

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Phylogenetic tree and its likelihood
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Likelihood calculation

• Restate in terms of conditional likelihoods
• Ls(k) likelihood based on data at or above
  point k on tree, given point k is known to have
  amino acid s for the specific site under
  consideration
• Work up tree from tips to root

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Pulley principle

• Any segment of an unrooted tree can contain the
  root
• Related to reversibility of the evolutionary
  model
• Allows us to alter the length of branches in an
  optimal fashion
• Can construct an algorithm to alter branches one
  at a time to find tree with highest likelihood

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Are likelihood trees significant?Non-Parametric
(Felsenteins) Bootstrap
Species 1 A T K Species 2 A R K
Species 3 K T F
MSA
Sampling columns with replacement
Bootstrapping allows investigating the influence
of misalignments
Bootstrapped MSA Species 1 T K T Species
2 R K R Species 3 T F T
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Non-parametric (Felsenteins) bootstrap

• For each resampled MSA a new bootstrap tree is
  computed.
• Bootstrapping allows investigating the influence
  of misalignments on tree structure and branch
  length.
• Various statistics can be collected, e.g.,
  fraction of trees including given branch
  (bootstrap support for the branch).

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Hidden Markov Model
Simultaneous estimation of phylogeny and site
specific substitution rates

• Felsenstein, J. and Churchill, G. (1996) A Hidden
  Markov Model Approach to Variation Among Sites in
  Rate of Evolution. Molecular Biology and
  Evolution, 13(1) 93-104
• Allows for unequal unknown evolutionary rates
  at different sites
• Allows for correlations between rates at
  neighboring sites
• Uses Markov process to assign rates to sites

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HMM graphical depiction
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PAML method

• Yang, Z. (2000) Phylogenetic Analysis by Maximum
  Likelihood (PAML) 3.0, University College
  London, London, England.
• Uses Felsensteins algorithm to reconstruct
  phylogeny.
• Allows for each site to evolve at a different
  rate.
• Returns rates of evolution for each site.

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Evolutionary Trace

• Lichtarge, O., Bourne, H.R., and Cohen, F.E.
  (1996) An Evolutionary Trace Method Defines
  Binding Surfaces Common to Protein Families.
  Journal of Molecular Biology, 257 342-358.
• Identifies active sites
• Looks for conserved residues in branches
• Maps functionally important residues (FIR) onto
  surface

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Trace Integral(ET reduced to a parameter)
integral is area under the graph
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Substitution rates and ET ranks along the
aminoacid sequence
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Comparison of functional sites by ET vs. HMM
Epitope (true active region)
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Remarks

• ML is a powerful technique to investigate
  phylogeny.
• Computational difficulties are serious and
  require much machine power.
• Insights can be gained into various aspects of
  evolution.

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Maximum Parsimony

• No model of protein evolution
• Selects tree which minimizes of transformations
  from one state to another at all sites

A K R N K T T H H N V P P A D
substitution
time
A K R N K T N H H N V P P A D