Phylogenetic Analysis

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Phylogenetic Analysis
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General comments on phylogenetics

• Phylogenetics is the branch of biology that deals
  with evolutionary relatedness
• Uses some measure of evolutionary relatedness
  e.g., morphological features

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• Phylogenetics on sequence data is an attempt to
  reconstruct the evolutionary history of those
  sequences
• Relationships between individual sequences are
  not necessarily the same as those between the
  organisms they are found in

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• The ultimate goal is to be able to use sequence
  data from many sequences to give information
  about phylogenetic history of organisms
• Phylogenetic relationships usually depicted as
  trees, with branches representing ancestors of
  children the bottom of the tree (individual
  organisms) are leaves. Individual branch points
  are nodes.

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Phylogenetic trees
C
A
D
time
B
A
B
C
D
An unrooted tree
A rooted tree
time?
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• We will only consider binary trees edges split
  only into two branches (daughter edges)
• rooted trees have an explicit ancestor the
  direction of time is explicit in these trees
• unrooted trees do not have an explicit ancestor
  the direction of time is undetermined in such
  trees

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Types of phylogenetic analysis methods

• Phenetic trees are constructed based on
  observed characteristics, not on evolutionary
  history
• Cladistic trees are constructed based on fitting
  observed characteristics to some model of
  evolutionary history

Distance methods
Parsimony and Maximum Likelihood methods
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Similarity and Homology

• The evolutionary relationship between sequences
  is inferred from the similarity of the sequences
• Similarity is a measurable quantity (e.g.,
  identity, alignment score, etc.)
• Homology is the inference from sequence
  similarity data that sequences are evolutionarily
  related

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Sequence alignments

• Aligning sequences gives information about
• Similarity
• Areas of sequences that are conserved through
  evolution

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The real problem

• How do we compare sequences?
• Seq 1 CTGCACTA
• Seq 2 CACTA
• or C---ACTA

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The real problem

• How do we compare sequences?
• Seq 1 CTGCACTA
• Seq 2 CACTA
• or C---ACTA
• Scoring tries to approximate evolution scores
  for substitutions and for gaps (insertions/deletio
  ns)
• Scores sum of terms for substitutions and for
  gaps (sequence as character string)

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Sequence alignment I

• Simplest scoring 1 for match, 0 for no match
• CTGCACTA
• CACTA
• CTGCACTA
• C---ACTA

Score 5
Score 5
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Sequence alignment II

• Slightly more advanced scoring 1 for match, 0
  for no match, -1 for gap

• CTGCACTA
• CACTA
• CTGCACTA
• C---ACTA

Score 5
Score 2
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• G C A T
• G 1 0 0 0
• C 0 1 0 0
• A 0 0 1 0
• T 0 0 0 1
• G C A T
• G 1 -1 -1 -1
• C -1 1 -1 -1
• A -1 -1 1 -1
• T -1 -1 -1 1
• Identity scoring matrices top, simple form
  below, with mismatch penalty

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In-class exercise II

• Using the advanced scoring method calculate the
  scores for the following pairs of nucleotide
  sequences

CCTGGGCTATGC CAGGGTT-TGC
CCTGGGCTATGC CA-GGG-TTTGC
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What about proteins?

• Chemistry of amino acids means that some
  substitutions in the sequence are better than
  others
• Substitution matrix empirically derived scores
  for frequency of substitution of each amino acid
  for all 19 others.

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BLOSUM 62 Substitution matrix
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In-class exercise III

• Using the BLOSUM62 substitution matrix and a gap
  penalty of -2, score the following pairs of
  protein sequences (do not penalize end gaps)

YIHMNVFLSFML RVGAANFPNPRL YIHMNVFLSFML FIHMNLFVSFML
YIHMNVFLSFML IHMNLFV--SFML YIHMNVFLSFML IVLSMMFFLNHY
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Dynamic programming strategy

• Break alignment problem into small pieces
• Optimize first piece
• Then extend into second piece since first piece
  is optimized already, program only needs to
  optimize extension
• Continue until end of comparison

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H E E
0 -6 -12 -18
H -6 10 4 -2
E -12 4 16 10
A -18 -2 10 15
E -24 -8 4 16
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H E E
0 -6 -12 -18
H -6 10 4 -2
E -12 4 16 10
A -18 -2 10 15
E -24 -8 4 16
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H E E
0 -6 -12 -18
H -6 10 4 -2
E -12 4 16 10
A -18 -2 10 15
E -24 -8 4 16
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Why multiple alignments?

• Alignment of more than two sequences
• Usually gives better information about conserved
  regions and function (more data)
• Better estimate of significance when using a
  sequence of unknown function
• Must use multiple alignments when establishing
  phylogenetic relationships

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Dynamic programming extended to many dimensions?

• No uses up too much computer time and space
• E.g. 200 amino acids in a pairwise alignment
  must evaluate 4 x 104 matrix elements
• If 3 sequences, 8 x 106 matrix elements
• If 6 sequences, 6.4 x 1013 matrix elements

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• Need to find more efficient method
• Sacrifice certainty of optimum alignment for
  certainty of good alignment but faster

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Feng-doolittle algorithm

• Does all pairwise alignments and scores them
• Converts pairwise scores to distances
• D -logSeff -log (Sobs Srand)/(Smax Srand)
• Sobs pairwise alignment score
• Srand expected score for random alignment
• Smax average of self-alignments of the two
  sequences

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• As Smax approaches Srand (increasing evolutionary
  distance), Seff goes down to make the distance
  measure positive, use the -log

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• Once the distances have been calculated,
  construct a guide tree (more in the phylogeny
  class) tells what order to group the sequences
• Sequences can be aligned with sequences or
  groups groups can be aligned with groups

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• Sequence-sequence alignments dynamic programming
• Sequence-group alignments all possible pairwise
  alignments between sequence and group are tried,
  highest scoring pair is how it gets aligned to
  group
• Group-group alignments all possible pairwise
  alignments of sequences between groups are tried
  highest scoring pair is how groups get aligned

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Example
Seq5
Seq3
Seq4
Seq1
Seq2
Alignment 2
Alignment 1
Alignment 3
Final alignment
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• Notice that this method does not guarantee the
  optimum alignment just a good one.
• Gaps are preserved from alignment to alignment
  once a gap, always a gap

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Distance methods

• Measuring distance -- just like when we talked
  about multiple alignment, distance represents all
  the differences at the various positions these
  differences can be treated as equal or weighted
  according to empirical knowledge of substitution
  rates

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• Another way to say this is that there are a set
  of distances dij between each pair of sequences
  i,j in the dataset. dij can be the fraction f of
  sites u where residues xi and xj differ or dij
  can be such a fraction but weighted in some way
  (e.g. Jukes-Cantor distance)

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Clustering algorithms

• UPGMA -- this is the distance clustering method
  that is used in pileup to make the guide tree
• dij is the average distance between pairs of
  sequences found in two clusters, Ci and Cj.
• Texts notation Ci number of sequences in Ci

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• The algorithm in the text means just what we said
  before find the closest distance between two
  sequences, cluster those then find the next
  closest distance, cluster those as sequences are
  added to existing clusters find the average
  distance between existing clusters
• Work through the notation!
• UPGMA assumes a molecular clock mechanism of
  evolution

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• Neighbor-joining corrects for UPGMAs assumption
  of the same rate of evolution for each branch by
  modifying the distance matrix to reflect
  different rates of change.
• The net difference between sequence i and all
  other sequences is
• ri Sdik

k
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• The rate-corrected distance matrix is then
• Mij dij - (ri rj)/(n - 2)
• Join the two sequences whose Mij is minimal then
  calculate the distance from this new node to all
  other sequences using
• dkm (dim djm - dij)/2
• Again correct for rates and join nodes.

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In-class exercise I

• Retrieve the file named phylo2 from bioinfI.list
  in my directory
• Open it in the editor, select all the sequencs
• Select Functions ? Evolution ? PAUPSearch in
  Tree Optimality Criterion choose distance in
  Method for Obtaining Best Tree choose heuristic.
  Leave everything else as default (make sure
  bootstrap option is not selected)
• Select Run. Inspect output

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Parsimony methods

• Parsimony methods are based on the idea that the
  most probable evolutionary pathway is the one
  that requires the smallest number of changes from
  some ancestral state
• For sequences, this implies treating each
  position separately and finding the minimal
  number of substitutions at each position

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Example of parsimonious tree building

• Tree on left requires only one change, tree on
  left requires two left tree is most parsimonious

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• Parsimony methods assign a cost to each tree
  available to the dataset, then screen trees
  available to the dataset and select the most
  parsimonious
• Screening all the trees available to even a
  smallish dataset would take too much time branch
  and bound method builds trees with increasing
  numbers of leaves but abandons the topology
  whenever the current tree has a bigger cost than
  any complete tree

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In-class exercise II

• Use same data set and program as in exercise I,
  but choose maximum parsimony. Use heuristic for
  the tree building method.
• Inspect your tree. Compare it to the distance
  generated tree.

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Maximum likelihood methods

• Maximum likelihood reconstructs a tree according
  to an explicit model of evolution. For the given
  model, no other method will work as well
• But, such models must be simple, because the
  method is computationally intensive

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• Actually, all the other methods discussed
  implicitly use a simple model of evolution
  similar to the typical model made explicit in
  maximum likelihood
• All sites selectively neutral
• All mutate independently, forward and reverse
  rates equal, given by m

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• Also assume discrete generations and sites change
  independently
• Given this model, can calculate probability that
  a site with initial nucleotide I will change to
  nucleotide j within time t
• Ptij dije-mt (1 - e-mt)gj, where dij 1 if i
  j and dij 0 otherwise, and where gj is the
  equilibrium frequency of nucleotide j

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• The likelihood that some site is in state i at
  the kth node of a tree is Li(k)
• The likelihoods for all states for each site for
  each node are calculated separately the product
  of the likelihoods for each site gives the
  overall likelihood for the observed data
• Different tree topologies are searched to find
  the highest overall likelihood

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• Maximum likelihood is maybe the gold standard
  for phylogenetic analysis but because of its
  computational intensity it can only be used for
  select data and only after much initial fine
  tuning of many parameters of sequence alignments
• Often used to distinguish between several already
  generated trees

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Assessing trees

• The bootstrap randomly sample all positions
  (columns in an alignment) with replacement --
  meaning some columns can be repeated -- but
  conserving the number of positions build a large
  dataset of these randomized samples

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Bootstrap alignment process
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• Then use your method (distance, parsimony,
  likelihood) to generate another tree
• Do this a thousand or so times
• Note that if the assumptions the method is based
  on hold, you should always get the same tree from
  the bootstrapped alignments as you did originally
• The frequency of some feature of your phylogeny
  in the bootstrapped set gives some measure of the
  confidence you can have for this feature

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In-class exercise III

• Use the same dataset, select distance again.
  This time, select the bootstrap box.
• In options, make sure to select the box labelled
  Save a file containing PAUP screen output. Take
  defaults for everything else. Run.
• Inspect your output. In particular, look at the
  paup.log file and compare it to the
  paupdisplay.figure file.

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• Repeat for the maximum parsimony method.
• Were the original trees (not bootstrapped)
  meaningful?