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CMSC 838T – Lecture 5
CMSC 838T – Lecture 5
X Phylogenetics
0 Study of evolutionary relationships (sequences / species) 0 Infer evolutionary relationship from shared features 0 May improve multiple sequence alignment (MSA)
Phylogenetics
X Phylogeny
0 Relationship between organisms with common ancestor
X Phylogenetic tree
0 Graph representing evolutionary history of sequence / species
X Premise
0 Members sharing common evolutionary history (i.e., common ancestor) are more related to each other 0 Can infer evolutionary relationship from shared features
X Long history of phylogenetics (from field of genetics)
0 Historically → based on analysis of observable features (e.g., morphology, behavior, geographical distribution) 0 Now → mostly analysis of DNA / RNA / amino acid sequences
CMSC 838T – Lecture 5
Phylogenetics – Motivation & Alignment
X Goal of phylogenetics
0 Understand relationship of sequence to similar sequences 0 Construct phylogenetic tree representing evolutionary history
X Motivation / application
0 Identify closely related families O Use phylogenetic relationships to predict gene function 0 Follow changes in rapidly evolving species (e.g., viruses) O Analysis can reveal which genes are under selection O Provide epidemiology for tracking infections & vectors 0 Few direct applications
X Relationship to multiple sequence alignment (MSA)
0 Alignment of sequences should take evolution into account 0 More precise phylogenetic relationships ↔ improved MSA
Plylogenetics Overview
X Phylogenetic trees
X Tree construction algorithms
0 Distance methods O UPGMA O Neighbor-joining 0 Maximum parsimony 0 Maximum likelihood
X Assessing phylogenetic trees
CMSC 838T – Lecture 5
Phylogenetic Trees
X Leaves / taxa
0 Original sequences
X Branches
0 Represent change 0 Length represents evolutionary distance
X Cluster / clade
0 All sequences in subtree with common ancestor (treated as single node)
X Join / node
0 Point of joining two leaves / clusters
distance
Phylogenetic Trees
X Use binary trees (evolution is bifurcating process)
0 Can approximate all tree shapes (w/ arbitrarily short edges) 0 Simplifies tree generation & analysis
X Trees can be represented in rectangular form
0 Alternative form of representation 0 Distance determined only by “height” of branch
D B C A
normal form
D B C A
rectangular form
CMSC 838T – Lecture 5
Phylogenetic Trees
X Can label branches of tree with change to sequence
N Y L S
Phylogenetic Trees – Distance
X (Evolutionary) Distance
0 Many possible measures O Fraction of sites that differ between two sequences O # of changes needed to convert one sequence to another O Pairwise alignment scores, normalized by average score for random alignment [Feng & Doolittle 1996] Score = (S.actual – S.random) / (S.identical – S.random) Where s.identical = score for aligning identical sequence
X Distance matrix
0 Matrix of pairwise distances between all sequences 0 Used to generate tree
X Tree shape
0 Varies with construction method, distance metric
Seq. A B C D A — 8 7 12 B — 9 14 C — 11 D —
CMSC 838T – Lecture 5
Tree Construction – UPGMA
X UPGMA (Unweighted Pair Group Method using
Arithmetic Averages) [Sokal & Michener 1958]
X Algorithm
- Find pair of sequences A, B with smallest distance D (^) AB
- Insert join for A, B at tree height = ½ D (^) AB
- Update distance to new cluster as the average distance betweens pairs of sequences in each cluster
- Repeat until all sequences / clusters joined
- Produces rooted tree
X Assumptions
0 Distances for tree are ultrametric O Branch lengths for 2 leaves same after join 0 Distances for tree are additive
A
B
A
B
C
½ D AB
½ D C(AB)
Tree Construction Example
Distance matrix
Sequences A B C D
A — 8 7 12
B — 9 14
C — 11
D —
Original tree
Note that tree distances are additive (i.e., distance between X, Y = sum of lengths of edges connecting X, Y)
CMSC 838T – Lecture 5
Tree Construction Example – UPGMA
A B C D
A — 8 7 12
B — 9 14
C — 11
D —
A-C B D
A-C — 8.5 11.
B — 14
D —
D —
A-C-B — 12.
A-C-B D D B C A
Distance matrices UPGMA tree
A-C
A-C-B
UPGMA keeps all leaves in clusters and uses them in calculations
A, C
closest
A-C, B
closest
Height = ½ distance
X Goal
0 Join closest neighbors (nodes w / same parent) in tree 0 Avoids problem with UPGMA when rates of change differ
X Example
0 Closest leaves not neighbors in correct tree, but joined first by UPGMA
X Assumptions
0 Rate of change can differ O Branch lengths may differ after join 0 Branch lengths for tree are additive
Tree Construction – Neighbor-Joining
A D A D B C
B C
CMSC 838T – Lecture 5
X Exploit principle for neighbor-joining algorithm
X Replace distance to C
0 Used normalized divergence r (^) A r (^) B (~ avg. distance to nodes) 0 We can calculate O a = ½ (d (^) A,B + d (^) A,C – dB,C ) → ½ (d (^) A,B + r (^) A– r (^) B) O b = ½ (d (^) A,B + dB,C – d (^) A,C ) → ½ (d (^) A,B + r (^) B– r (^) A) O c = ½ (dB,C + d (^) A,C – d (^) A,B ) → ½ (dB,C + d (^) A,C – d (^) A,B )
Neighbor-Joining – Basic Principle
A
C
B
A B C
A — d (^) A,B d (^) A,C B — dB,C C —
a
b
c
K
r (^) B
r (^) A
Simply treat all other nodes as C, and treat distance to C as r
r (^) A
r (^) B
Tree Construction – Neighbor-Joining
X Approach
0 To find closest pair of neighbors O Reduce branch length for a node by (approximately) the average distance of the node from all other nodes O Find smallest distance between nodes (after reduction)
X Definitions
For all pairs of nodes A & B in set of all nodes L, let d (^) A,B = distance between A,B R (^) X = Σ dX,N where N ∈ L (total distance from X to all N) r (^) X = R (^) X / (L– 2), whereL= # of nodes (normalized divergence from X to all other nodes) D (^) A,B = d (^) A,B – (r (^) A + r (^) B) (rate-corrected distance)
X Key property − 2 nodes w/ mininum D are always neighbors!
CMSC 838T – Lecture 5
Tree Construction – Neighbor-Joining
X Algorithm [Saitou & Nei 1987, Studier & Keppler 1988]
- Begin with star tree & all sequences as nodes in L
- Find pair of nodes A & B ∈ L with minimum D (^) A,B
- Create & insert new join (node K) w/ branch lengths 0 d (^) A,K = ½ (d (^) A,B + r (^) A – r (^) B) 0 dB,K = ½ (d (^) A,B + r (^) B – r (^) A)
- For remaining nodes C ∈ L, update distance to K as 0 dK,C = ½ (d (^) A,C + dB,C – d (^) A,B)
- Insert K and remove A, B from L
- Repeat steps 2−5 until only two nodes left
A
B
K
Tree Construction Example – Neighbor Joining
(Rate-corrected) distance matrix
D -20 -20 -21 — 18.
C -20 -20 — 11 13.
B -21 — 9 14 15.
A — 8 7 12 13.
A B C D R A
B C
D
Rate-corrected distances
D (^) A,B = d (^) A,B – (r (^) A + r (^) B) = 8 – (13.5 + 15.5) = -
D (^) A,C = d (^) A,C – (r (^) A + r (^) C) = 7 – (13.5 + 13.5) = -
D (^) A,D = d (^) A,D – (r (^) A + r (^) D) = 12 – (13.5 + 18.5) = -
D (^) B,C = dB,C – (rB + rC) = 9 – (15.5 + 13.5) = -
D (^) B,D = dB,D – (rB + rD) = 14 – (15.5 + 18.5) = -
D (^) C,D = dC,D – (rC + rD) = 11 – (13.5 + 18.5) = -
normalized divergence =
Σ d / (L– 2)
= Σ d / 2
CMSC 838T – Lecture 5
Tree Construction Example – Neighbor Joining
K 1 -24 -24 — 13
D -24 — 9 20
C — 11 4 15
C D K 1 r
(Rate-corrected) distance matrix
averaged distance =
Σ d / (L– 2)
= Σ d / 1
Edge lengths for C,D
dC,K2 = ½ (dC,D + r (^) C – r (^) D) = ½ (11 + 15 – 20) = 3
dD,K2 = ½ (dC,D + r (^) D – r (^) C) = ½ (11 + 20 – 15) = 8
Distances to K (^2)
dK2,K1 = ½ (dK1,C + dK1,D – dC,D) = ½ (4 + 9 – 11) = 1
A
B C
D
K 1 K 2
A
B
C
D
K 1 K 2
Tree Construction Example – Neighbor Joining
K 1 -24 -24 — 13
D -24 — 9 20
C — 11 4 15
C D K 1 r
(Rate-corrected) distance matrix
averaged distance =
Σ d / (L– 2)
= Σ d / 1
Edge lengths for C, K (^1)
dC,K2 = ½ (dC,K1 + r (^) C – r (^) K1) = ½ (4 + 15 – 13) = 3
dK1,K2 = ½ (dC,K1 + r (^) K1 – rC) = ½ (4 + 13 – 15) = 1
Distances to K (^2)
dK2,D = ½ (dD,C + dD,K1 – dC,K1 ) = ½ (11 + 9 – 4) = 8
A
B C
D
K 1 K 2
A
B
C
D
K 1 K 2
CMSC 838T – Lecture 5
Tree Construction Example – Neighbor Joining
K 1 -24 -24 — 13
D -24 — 9 20
C — 11 4 15
C D K 1 r
(Rate-corrected) distance matrix
averaged distance =
Σ d / (L– 2)
= Σ d / 1
Edge lengths for D, K (^1)
dD,K2 = ½ (dD,K1 + r (^) D – r (^) K1) = ½ (9 + 20 – 13) = 8
dK1,K2 = ½ (dD,K1 + r (^) K1 – rD) = ½ (9 + 13 – 20) = 1
Distances to K (^2)
dK2,C = ½ (dC,D + dC,K1 – dD,K1 ) = ½ (11 + 4 – 9) = 3
A
B C
D
K 1 K 2
A
B
C
D
K 1 K 2
Tree Construction Example – Neighbor Joining
A
B
C
D
K 1 K 2
Original tree Neighbor-joining tree
Except for missing root,
finds same tree topology
CMSC 838T – Lecture 5
Tree Construction – Maximum Parsimony
X Maximum parsimony [Fitch 1971]
0 Minimize number of sequence changes in tree 0 Assume fewest changes (mutations) = most likely (evolution)
X Informative site
0 Position with useful change information (for parsimony) 0 I.e., # of changes in position dependent on tree chosen
0 Must have ≥ 2 different bases / residues, such that
each base / residue appears in ≥ 2 sequences
Seq1 A A G A G T G C A
Seq2 A G C C G T G C G
Seq3 A G A T A T C C A
Seq4 A G A G A T C C G
Informative Sites
Tree Construction – Maximum Parsimony
X Most parsimonious tree
0 Tree with fewest total # of changes at informative sites
G G A
G G G
A C A
A C G
ACA
ACA
Tree 1 ACG
Tree 3
Tree 2
GGA
GGA
GGG
GGA
GGA
ACA
GGG
GGG
ACG
GGG
GGA
ACA
GGA
GGA
ACG
Sites Changed Tree 1 = 4 Tree 2 = 6 Tree 3 = 5
Informative Sites
CMSC 838T – Lecture 5
Tree Construction – Maximum Parsimony
X Algorithm
0 Generate all possible tree topologies 0 Count number of changes required 0 Select tree with minimum # changes 0 Use branch-and-bound to reduce search O Search trees with increasing # of leaves
O Abandon subtree when # changes ≥ best completed tree
X Characteristics
0 Computationally expensive 0 Analyze only informative sites 0 Misleading if rates of changes vary among branches 0 Evolution is not always parsimonious
Tree Construction – Maximum Likelihood
X Goal
0 Given the probability P(x|y,t) for a sequence y to evolve (mutate) to sequence x along an edge of length t (time) 0 Find tree that has highest probability of taking place
X Mutation probabilities
0 Bases: Jukes-Cantor model [Jukes-Cantor 1969, Kimura 1980] 0 Amino acids: PAM [Dayhoff+ 1978]
X Algorithm
0 Seach over all tree topologies & sequence assignments 0 For each topology & assignment, search all branch lengths
X Characteristics
0 Very computationally expensive
CMSC 838T – Lecture 5
Plylogenetics Summary
X Phylogenetic prediction
0 Infer evolutionary relationships from shared features 0 May have application to sequence alignment, epidemiology
X Phylogenetic trees
0 May be ultrametric and / or additive
X Tree construction
0 Inexpensive distance-based (UPGMA, neighbor-joining) 0 Expensive (exhaustive) tree searches (parsimony, likelihood)
X Assessing phylogenetic trees
0 Algorithms always produce some tree (of varying accuracy) 0 Expert biology knowledge to assess correctness / significance
Where Are We Now?
X Bioinformatics topics covered
0 Molecular biology background 0 Pairwise sequence alignment 0 Multiple sequence alignment 0 Phylogenetics
X Remaining bioinformatics topics
0 Protein structure prediction 0 Gene assembly and prediction 0 Microarrays & expressed sequence tag (EST) analysis 0 Sequence / structure database search & organization
X High performance computing…
CMSC 838T – Lecture 5
More Bioinformatics Terms
X Functional genomics
0 Identify function of genes in organism
X Comparative genomics
0 Identify genes O Related to other genes in organism O Related to genes in other species 0 Create evolutionary history of related genes 0 Locate insertions, deletions, substitutions occurring in evolution
X Proteomics
0 Identify & characterize all gene products (proteins) in organism
X Structural proteomics
0 Identify or predict 3D structure of all proteins in organism
More Bioinformatics Terms
X Pharmacogenomics
0 Application of genomic approaches to identify drug targets O Searching genomes for potential drug receptors O Examining characteristic gene expression in pathogens & hosts during infection for diagnostics or therapy targets 0 Cataloguing & processing info on pharmacology & genetics
X Pharmacogenetics
0 Identifying genetic causes for individualized drug responses O Identify genetic variation (e.g., SNPs) characteristic of particular patient response profiles O Use to improve administration & development of therapies O Identify receptive patient subsets, optimize drug dosages
X Lots of data mining…
