Phylogenetic Trees

1
Phylogenetic Trees

• What?
• How?
• Why?
• Methods

2
What is a phylogenetic tree?

• A phylogenetic tree is a data structure that
  stores information regarding the relationship of
  several sequences
• Given an appropriate scoring function, a given
  sequence can always be found to be more related
  to one sequence than to another, non-identical
  sequence. In other words, these relationships
  can be approximated by a binary tree.

3
What relationships are stored in the tree
structure?

• The relationship represented in a phylogenetic
  tree is a measure of homology.
• The actual definition of homology is biological
  in nature (the precise definition of which is
  also a matter of some debate), but
  computationally it is usually thought of in terms
  of an identity or similarity score di, j between
  two entities (taxa, sequences, etc.).

4
How is this homology represented in a tree?

• As seen before, sequence identity/similarity is
  calculated by aligning two or more sequences in a
  multiple sequence alignment.
• Thus, a phylogenetic tree is simply an
  arrangement of the data inherent within a
  multiple sequence alignment into a tree.

5
Why use phylogenetic trees?

• This arrangement is useful to biologists because
  it organizes the sequences into their projected
  evolutionary history.
• Due to the construction method of a phylogenetic
  tree, each node represents a common ancestor.
• The distance from the leaves to this common
  ancestor is a measure of the evolutionary
  distance between the leaves.

6
Example Phylogenetic trees
?
?
?
?
Problem given several sequences, determine how
to arrange them according to evolutionary
distance.
7
Example Phylogenetic trees
x1
x2
sequence 1
sequence 1
sequence 2
sequence 2
y1
y2
sequence 3
sequence 3
z2
z1
sequence 4
sequence 4
The first arrangement differs from the second
only in that sequence 4 is more closely related
to the others (z1 lt z2). The evolutionary
distance between sequences 1, 2, and 3 remain the
same as evidenced by the horizontal distance from
each leaf to the respective node connecting them
(x1 x2 and y1y2).
8
Why use phylogenetic trees?

• Thus, the tree structure provides a context for
  the evolutionary information inherent in a
  sequence alignment.
• This context represents the divergent
  relationship of the sequences.
• Furthermore, this contextual information is
  weighted according to evolutionary distance.

9
Why use phylogenetic trees? Summary

• The tree structure shows that two sequences are
  related, how they are related in the context of
  other sequences, and how distantly they are
  related.

10
How is a phylogenetic tree constructed?

• While the weighted score di, j is known from the
  multiple sequence alignment, the rate of
  evolutionary change is not known.
• The rate of change depends on mutation rates,
  which are not constant.

11
How is a phylogenetic tree constructed?

• Mutations can occur in several ways
• forward mutations in one sequence from the
  original sequence
• backward mutations in one sequence towards the
  original sequence
• parallel mutations in two or more sequences
• insertions in one or more sequences
• deletions in one or more sequences

12
How is a phylogenetic tree constructed?

• To re-iterate from the sequence alignment
  discussions not all mutations are alike.
• Mutation rates vary between organisms.
• Mutation rates vary with amino acid type.
• Mutation rates vary with the environment the
  amino acids are in (mutations in the core of the
  protein are less likely than those at the
  surface).

13
How is a phylogenetic tree constructed?

• Mutation rates vary with mutation type
  (substitutions more likely than
  insertions/deletions).
• Mutations that conserve properties of the
  original amino acid (such as charge, size, etc.)
  are more likely than those that modify or invert
  those properties (such as changing a
  positively-charged amino acid to a neutral or
  negatively-charged one).

14
Methods to calculate rate of evolutionary change

• Poisson process model
• Define Unit Evolutionary Time (average time to
  produce one substitution per 100 amino acids) Tu
  1/100?, solve for ?.
• Find probability of a substitution and
  approximate rate of change from theoretical
  considerations
• Not used because this model assumes that rate is
  independent of residue position and amino acid
  type

15
Methods to calculate rate of evolutionary change

• Amino acid substitution matrix
• Use empirically-determined matrix obtained by
  comparing many protein sequences to estimate
  probability pi, j that during one evolutionary
  time unit Tu, amino acid i will be substituted by
  residue j.
• The substitution matrix obtained M (pi, j) is
  called PAM1 matrix (one point-accepted mutation
  per 100 residues).

16
Methods to calculate rate of evolutionary change

• Since the matrix was calculated using proteins
  with small evolutionary distances (close
  homologs), the matrix is then scaled to
  approximate the probabilities for proteins with
  larger evolutionary distances (more remote
  homologs).
• PAM250 is one commonly-used matrix (corresponding
  to M250, the 250-th power of the PAM1 matrix)
• (One problem with this is that zero to the 250-th
  power is still zero)

17
Methods to calculate rate of evolutionary change

• Using this model, the probability p that a
  substitution at a given site (at either position
  i in sequence X or position j in sequence Y) has
  occurred during t time units is
• 20
• p 1 - S (pi, j)(2t) pi
• i1
• where p is a column vector (p1,, p20)T
  representing the amino acid composition frequency
  of a given polypeptide

18
Methods to calculate rate of evolutionary change

• Currently, NCBIs BLAST search tool offers PAM30
  70 and BLOSUM60, 70, 45. The default choice
  (and thus the most commonly-used substitution
  matrix) is BLOSUM60.
• BLOSUM was created in a manner similar to that of
  the PAM matrix, but using a more diverse set of
  sequences.
• Thus it is (arguably) more accurate when
  comparing more diverse proteins with less
  sequence homology.
• Since the function of BLAST is to identify
  (possibly remote) homologs, it is ideal for BLAST
  searches.

19
Nucleotide Sequences

• Nucleotide sequences are handled differently due
  to their unique properties
• there is redundancy in the genetic code (multiple
  nucleotide codons specify a given amino acid)
• nucleotide substitutions dont always translate
  to amino acid substitutions
• many third positions in the codon
• introns and other non-coding regions

20
Nucleotide Sequences

• some substitutions alter the protein sequence at
  more than a single position
• creation of stop codon
• frameshift mutation
• altered promoter/operator/splice site, etc.
• may totally destroy protein functionality
• may instead alter only amount of expression
• other sites (such as poly-A binding) may allow
  normal protein to be expressed, but mRNA is
  rapidly degraded, or not exported from the
  nucleus, or secluded in some cellular organelle

21
Nucleotide Sequences

• computer simulations have found that the genetic
  code is optimized such that many nucleotide
  substitutions change an amino acid to a related
  type, thus preserving properties such as
  hydrophobicity or charge.

22
Nucleotide Sequences

• Other features are shared
• substitution rate is species-dependent
• forward/backward/parallel mutations
• insertions/deletions - although they must occur
  in multiples of 3 nucleotides to avoid a
  frameshift mutation

23
Nucleotide Sequences

• The PAM matrices assumed a discrete Markov chain
  where
• the 1 PAM matrix is the transition matrix of the
  markov chain
• the parameters are estimated from close homologs
  using local sequence alignment
• it is assumed that the two sequences being
  compared are generated using one application of
  the transition matrix gt and thus, that multiple
  substitutions did not occur

24
Nucleotide Sequences

• it is also assumed that the evolutionary distance
  of more distantly related sequences can be
  modeled by n-times iteration of the Markov chain
  gt although this allows only evolutionary
  distances that are multiples of the evolutionary
  distance used for setting up the PAM matrix
• again, the only multiple of zero is zero...

25
Nucleotide Sequences

• Can use continuous Markov process instead of
  discrete Markov chain to avoid the assumptions of
  no multiple substitutions and discrete
  evolutionary time
• omit long formal definition, but basically
  analogous to Markov chain except the transition
  matrix is substituted by a matrix of transition
  probability functions that depend on time
  parameter t