Phylogenetic TreesTutorial 5

Agenda

• How to construct a tree using Neighbor Joining algorithm

• Phylogeny.fr tool

• Cool story of the day: Horizontal gene transfer

3

Neighbor Joining Algorithm

• Constructs an unrooted guide tree from a distance matrix• We do not assume constant rate of evolution

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

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?

• 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

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

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

, , ( )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

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

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:

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:

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

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

Phylogeny.fr

One click mode

One click mode

One click mode

Multiple sequence alignment (MSA) is a basic step in phylogenetic tree construction and is the base for the distance matrix

“A la carte” mode

“On-click” default settings

Cool Story of the day

Horizontal gene transfer

Is horizontal gene transfer possible?

Viruses

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”.

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

Bioinformatics/ David W.Mount p. 244

Until the full speciation…