phylogenetic trees tutorial 5. agenda how to construct a tree using neighbor joining algorithm...
TRANSCRIPT
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Phylogenetic TreesTutorial 5
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Agenda
• How to construct a tree using Neighbor Joining algorithm
• Phylogeny.fr tool
• Cool story of the day: Horizontal gene transfer
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3
Neighbor Joining Algorithm
• Constructs an unrooted guide tree from a distance matrix• We do not assume constant rate of evolution
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1. Calculate all pairwise distances.
2. Find 2 nodes i and j, such that the relative distance between i and j is minimal.
3. Remove the rows and columns of i and j
4. Add a new row and column k (the parent of i and j), and compute the distance from k to any other remaining node.
5. Continue until two nodes remain – connect them with an edge.
Neighbor Joining Algorithm2 matrices
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E D C B A
41 39 39 22 0 A
43 41 41 0 22 B
20 18 0 41 39 C
10 0 18 41 39 D
0 10 20 43 41 E
Step 1. Calculate all pairwise distances
• A, B, …, E are tree nodes. Each character represents a sequence.
• How can we measure distance between sequences?
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• Euclidean Distance: Given a multiple sequence alignment, calculate the square root of the sum of the score at every position between two sequences
• The score increases as the dissimilarity between residues increases.
2,1
( , )n
a b i ii
d s a b
Step 1. Calculate all pairwise distances
distance between sequences
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If we assume constant evolution rate we may construct a wrong tree.
Closest leaves aren’t necessarily neighbors:i and j are neighbors, but (dij = 13) > (djk = 12)
Step 2. Two nodes with minimal relative distance
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Step 2. Two nodes with minimal relative distance
• Find a pair of leaves that are close to each other, but far from other leaves.
• This is called “relative distance”.
, , ( )i j i j i jM D r r
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, , ( )i j i j i jM D r r
,
,
2
2
i ki
j kj
Dr
LD
rL
,i jM Relative distance between i and j
,i jD Distance between i and j (from the distance table)
ir Distance between i and all other nodes
L Number of leaves (=sequences) left in the tree
Step 2. Two nodes with minimal relative distance
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1
22 39 39 41 14147
2 5 2 341 41 43 22
493
18 20 41 3939.3
310 39 41 18
363
41 43 20 1038
3
n AiA i
B
C
D
E
Dr
L
r
r
r
r
Step 2. Two nodes with minimal relative distance
E D C B A
41 39 39 22 0 A
43 41 41 0 22 B
20 18 0 41 39 C
10 0 18 41 39 D
0 10 20 43 41 E
Distances matrix:
A B
C
DE
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E D C B A
-44 -44 -47.3 -74 - A
-44 -44 -47.3 - - B
-57.3 -57.3 - - - C
-64 - - - - D
- - - - - E
A,B is the pair with the minimal Mi,j distance.
The Mij Table is used only to choose the closest pairs (lowest value) and not for calculating the distances
, ( ) 22 (47 49) 74
39 (47 39.3) 47.3AB A B A B
AC
M D r r
M
Step 2. Two nodes with minimal relative distance
The relative distance table:
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Steps 3+4. Remove i, j and add k to the matrix
Dkm = (Dim + Djm – Dij)/2
Compress i and j into k, iterate algorithm for rest of tree
the distance from k to any other leaf m can be computed as:
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22 47 4910
2 222 49 47
122 2
AB A BAk
AB B ABk
D r rD
D r rD
E D C k
31 29 29 0 k
20 18 0 29 C
10 0 18 29 D
0 10 20 31 E
Now we’ll calculate the distance from X to all other nodes:
39 41 2229
2 239 41 22
292 2
41 43 2231
2 2
AC BC ABCk
AD BD ABDk
AE BE ABEk
D D DD
D D DD
D D DD
Steps 3+4. Remove i, j and add k to the matrix
A B
C
DE
K
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The final tree:
Steps 5. Continue till 2 nodes remain
AB
C D
E
K
Y
12
10
20
56
4
9
What is missing?
Z
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Phylogeny.fr
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One click mode
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One click mode
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One click mode
Multiple sequence alignment (MSA) is a basic step in phylogenetic tree construction and is the base for the distance matrix
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“A la carte” mode
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“On-click” default settings
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Cool Story of the day
Horizontal gene transfer
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Is horizontal gene transfer possible?
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Viruses
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Horizontal gene transfer is the primary reason for bacterial antibiotic resistance and plays an important role in the evolution of bacteria.
Horizontal gene transfer in Bacteria
http://en.wikipedia.org/wiki/Horizontal_gene_transfer
Horizontal gene transfer is very abundant in bacteria, it is hard to talk about a bacteria’s genome, but more of the genome of a “society of bacteria”.
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Sea slug
The sea slug Elysia chlorotica incorporates chloroplasts from the algae that it eats into its body. Photosynthesis continues for up to 12 months using genes within the chloroplast, which are directed by algal nuclear genes that were transferred to the nuclei of the slug.
http://en.wikipedia.org/wiki/Horizontal_gene_transfer
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Bioinformatics/ David W.Mount p. 244
Until the full speciation…