Pseudogenes contd Evolution and motif finding

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Pseudogenes (contd) Evolution and motif finding

• Lecture 11/9

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Quiz Answers
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Pseudogenes Coin Durbin

• Novel methods for separating pseudogenes from
  functional genes
• Unprocessed genes result of gene duplication,
  and loss of function of one copy
• Processed pseudogenes due to reverse
  transcription of processed mRNA
• lack introns

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Pseudogene loss

• Pseudogene dies very quickly, therefore expect
  few pseudogenes in genome
• Prokaryotes have few pseudogenes
• Eukaryotes have many pseudogenes
• 20,000 human pseudogenes

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Pseudogene detection

• Detect truncations in genes
• Ratio of synonymous to non-synonymous
  substitution rate
• Approach in this paper
• Pattern of substitution in conserved protein
  domains
• Profile HMMs to model protein domains

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Program PSILC

• Given an alignment A, an unrooted tree T, profile
  HMM D representing a protein domain aligned to A
• Output for each leaf-node n, a score
  representing our belief that the node is a
  pseudogene
• Assume that the rest of the tree evolves as the
  protein domain would

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Two scores

• Final branch to node n evolved as neutral
  (non-coding) OR as a protein domain
• Final branch to node n evolved as protein-coding
  OR as a protein domain
• Log odds ratio
• If a node is a pseudogene, it does not have the
  protein domain constraint, so both scores should
  be higher than usual

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Terminology

• A alignment
• T Tree
• Xn Row n, i.e., sequence at node n
• Xi, Column i, i.e., ith position of all
• Fig 4 (whiteboard)

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Terminology

• Probability that evolution on branch b in the
  tree is due to
• neutral DNA Pnuc(b)
• protein-coding Pprot(b)
• protein domain encoding Pdom(b)

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Terminology

• Cnuc Pnuc(bn), Pdom(T\bn) neutral Dna on
  bn, otherwise domain encoding
• Cprot Pprot(bn), Pdom(T\bn) protein-coding
  on bn, otherwise domain encoding
• Cdom Pdom(T) Pdom(bn), Pdom(T\bn) domain
  encoding on all T

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Scores

• PSILCnuc/dom(n)
• PSILCprot/dom(n)
• Each computed in a manner similar to
  Felsensteins algorithm

• Fig 5 (whiteboard)

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Likelihood calculation

• Compute prob. distr. at parent node pn given the
  entire tree T, except node n (assume
  domain-encoding evolution)
• Compute probability of parent pn mutating to leaf
  n, given whatever evolutionary constraint Ck

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First step Rest of the tree

• Reroot the tree at parent pn and remove branch to
  node n. New tree is T\bn.
• Fig 6 (whiteboard)
• Product of two terms
• Probability of leaves of tree T\bn given root
• Felsensteins algorithm
• Prior probability of root of T\bn
• Use equilibrium distribution

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Second step (and part of first)The branch
mutation model

• P(xchild,ixparent,i,bchild,Pk(bchild))
• Phylogenetic models available
• neutral Dna evolution (Pnuc) HKY model
• protein-coding evolution (Pprot) WAG model
• domain-encoding evolution (Pdom) profile HMM
  match state emission probabilities
• These give us the rate matrix Q
• Pk(t) exp(Qrt)
• Free rate parameter r

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Tests

• On human, mouse, rat data
• Pprot/dom outperforms all others, including
  Pnuc/dom

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PhyloGibbs

• Motif finding combined with model of evolution
• Neutral evolution selection operating on
  binding sites
• Gibbs sampling approach

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Basics placing motif windows
ttttCGTGAT-GCGTCGtttttttttt gagaCGTGATcGCGTCGagaat
atata cccc-------------CCAAGATCAGAccc aaata-------
-----CCAACATCAGAaaa
Multiple alignment from DIALIGN Vertically
aligned caps are evolutionarily related bases.
3 legal windows, 1 illegal window All possible
legal windows identified in preprocessing.
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Motif windows

• A legal window does not have gaps
• A legal window can span one species or multiple
  species
• If spanning multiple species, the sites in the
  window are assumed to be evolutionarily related
  binding sites

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Sampling probability

• For a single-species motif window, sampling
  probability is
• For a window spanning multiple species, sampling
  probability is

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Evolutionary model

• is given by evolutionary model

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Evolutionary model

• Evolving binding site must bind the same protein
• Pr (s1,s2 W) ?a Pr(a W) ?i Pr (si a, W, t)
• Can be generalized to more than two species
  (recursively)

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Configurations

• Given a set of sequences, a configuration is a
  set of (legally placed) motif window
• AND a color assigned to each window
• Could have multiple windows assigned with the
  same color
• Different colors represent different
  transcription factors
• Goal is to find multiple types of motifs
  together, by using different colors
• Color 0 is background (random) sequence

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Sampling

• The algorithm samples configurations from their
  posterior probability distribution
• P(SC) is the probability that all windows of
  color C were sampled from the same PWM, though
  that PWM is unknown
• Integration of all PWMs

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Sampling

• We have to sample configuration C from the
  posterior distribution P(CS)
• Monte Carlo Markov Chain (MCMC)
• Take the current configuration C and move
  probabilistically to a new configuration C such
  that detailed balance holds
• P(CS)P(C --gt C) P(CS)P(C --gt C)

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Move set

• What kinds of moves are allowed ?
• The move set needs to be ergodic, i.e., every
  possible configuration C must be reachable by
  repeated moves
• Moves are shift one or more colored windows,
  or add or remove a colored window, or recolor a
  randomly chosen window from current configuration
• Window shift move resample the position of a
  window,

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Anneal and track

• After many moves, each configuration will be
  sampled as per P(CS)
• What to report ?
• Simulated annealing to find maximum likelihood
  configuration C
• sample from P(CS)?
• slowly increase ? over time

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Tracking

• Fix the reference configuration C
• Continue sampling from P(CS), and for each
  window w in C, track the probability p(w,c) that
  window w belongs to the same motif (color) as the
  windows in color c of reference configuration C
• Whiteboard explanation