BCB 444/544

1BCB 444/544 F07 ISU Terribilini #30- Phylogenetics - Distance-Based Methods 11/02/07

BCB 444/544

Lecture 30

Phylogenetics – Distance-Based Methods

#30_Nov02


Wed Oct 30 - Lecture 29

Phylogenetics Basics

• Chp 10 - pp 127 - 141

Thurs Oct 31 - Lab 9

Gene & Regulatory Element Prediction

Fri Oct 30 - Lecture 30

Phylogenetic – Distance-Based Methods

• Chp 11 - pp 142 – 169

Mon Nov 5 - Lecture 31

Phylogenetics – Parsimony and ML

• Chp 11 - pp 142 - 169

Required Reading (before lecture)


Assignments & Announcements

Mon Oct 29 - HW#5

HW#5 = Hands-on exercises with phylogenetics and tree-building software

Due: Mon Nov 5 (not Fri Nov 1 as previously posted)


BCB 544 "Team" Projects

Last week of classes will be devoted to Projects

• Written reports due: • Mon Dec 3 (no class that day)

• Oral presentations (20-30') will be: • Wed-Fri Dec 5,6,7

• 1 or 2 teams will present during each class period

See Guidelines for Projects posted online


BCB 544 Only: New Homework Assignment

544 Extra#2

Due: √PART 1 - ASAP

PART 2 - meeting prior to 5 PM Fri Nov 2

Part 1 - Brief outline of Project, email to Drena & Michael

after response/approval, then:

Part 2 - More detailed outline of project

Read a few papers and summarize status of problem

Schedule meeting with Drena & Michael to discuss

ideas


Seminars this Week

BCB List of URLs for Seminars related to Bioinformatics:http://www.bcb.iastate.edu/seminars/index.html

• Nov 2 Fri - BCB Faculty Seminar 2:10 in 102 ScI

• Bob Jernigan BBMB, ISU

•Control of Protein Motions by Structure


Chp 10 - Phylogenetics

SECTION IV MOLECULAR PHYLOGENETICS

Xiong: Chp 10 Phylogenetics Basics

• Evolution and Phylogenetics• Terminology• Gene Phylogeny vs. Species Phylogeny• Forms of Tree Representation• Why Finding a True Tree is Dificult• Procedure of Building a Phylogenetic Tree


Tree Building Procedure

• Choose molecular markers• Perform MSA• Choose a model of evolution•Determine tree building method• Assess tree reliability


Choice of Molecular Markers

• Very closely related organisms - nucleic acid sequence will show more differences• For individuals within a species - faster

mutation rate is in noncoding regions of mtDNA• More distantly related species - slowly

evolving nucleic acid sequences like ribosomal RNA or protein sequences• Very distantly related species - use highly

conserved protein sequences


Multiple Sequence Alignment

• Most critical step in tree building - cannot build correct tree without correct alignment• Should build alignments with multiple

programs, then inspect and compare to identify the most reasonable one• Most alignments need manual editing• Make sure important functional residues

align• Align secondary structure elements• Use full alignment or just parts


Automatic Editing of Alignments

• Rascal and NorMD – correct alignment errors, remove potentially unrelated or highly divergent sequences• Gblocks – detect and eliminate poorly

aligned positions and divergent regions


How do we measure divergence between sequences?

• Simple measure – just count the number of substitutions observed between the sequences in the MSA• Problem – number of substitutions may not represent the number of evolutionary events that actually occurred


Multiple Substitutions

C

A

A

G

T

Just because we only see one difference, does not mean that there was only one evolutionary event


Multiple Substitutions

A

A

A

G

T

Just because we only see no difference, does not mean that there were no evolutionary events


Choosing Substitution Models

• Statistical models of evolution are used to correct for the multiple substitution problem• Focus on DNA models


Jukes-Cantor Model

• Jukes-Cantor model assumes all nucleotides are substituted with equal probability• Can be used to

correct for multiple substitutions


Many Other Models


Evolutionary Models for Protein Sequences

• PAM and JTT substitution matrices already take into account multiple substitutions• There are also models similar to Jukes-Cantor for protein sequences


What about differences in mutation rates between positions within a sequence?

• One of our assumptions was that all positions in a sequence are evolving at the same rate• Bad assumption• Third position in a codon changes with higher frequency• In proteins, some amino acids can change and others

cannot

• This variation is called among-site rate heterogeneity• Many tree building programs have parameters

meant to deal with this problem – adds to complexity of getting the correct tree


Chp 11 – Phylogenetic Tree Construction Methods and Programs

SECTION IV MOLECULAR PHYLOGENETICS

Xiong: Chp 11 Phylogenetic Tree Construction Methods and Programs

• Distance-Based Methods• Character-Based Methods• Phylogenetic Tree Evaluation• Phylogenetic Programs


Tree Construction

• Two main categories of tree building methods• Distance-based• Overall similarity between sequences

• Character-based• Consider the entire MSA


Distance-Based Methods

•Given a MSA and an evolutionary model, calculate the distance between all pairs of sequences• Construct distance matrix• Construct phylogenetic tree based on the distance matrix


Distance Matrices

a 0

b 6 0

c 7 3 0

d 14 10 9 0

a b c d

a

b

c

d

1 2 3 4 50 6 7 8


Distance-Based Methods

• Two ways to construct a tree based on a distance matrix• Clustering• Optimality


Clustering-Based Methods

• E.g., UPGMA and Neighbor-Joining• A cluster is a set of taxa• Interspecies distances translate into

intercluster distances• Clusters are repeatedly merged• “Closest” clusters merged first• Distances are recomputed after merging


UPGMA

• UPGMA – Unweighted Pair Group Method Using Arithmetic Average• Uses molecular clock assumption – all

taxa evolve at a constant rate and are equally distant from the root (ultrametric tree)• This assumption is usually wrong• So why use UPGMA?• Very fast


UPGMA Example


UPGMA Example


UPGMA Example


UPGMA Example


Neighbor Joining

• Idea: Find a pair of taxa that are close to each other but far from other taxa• Implicitly finds a pair of neighboring taxa

•No molecular clock assumption


Neighbor Joining

•NJ corrects for unequal evolutionary rates between sequences by using a conversion step• The conversion step requires calculation of “r-values” and “transformed r-values”


Neighbor Joining

iji dr

The r-value for a sequence is:

The sum of the distances between sequence i and all other sequences


Neighbor Joining

2'

n

rr ii

The transformed r-value for a sequence is:

Where n is the number of taxaTransformed r-values are used to determine the distance of a taxon to the nearest node


Neighbor Joining

jiijij rrdd 2

1'

The converted distance between two sequences is:

These converted distances are used in building the tree


Neighbor Joining

2

'' jiijiu

rrdd

The final equation we need is for computing the distance from a new cluster to each taxa. Assume taxa i and j were merged into a cluster u. The distance from taxa i to cluster u is:


Neighbor Joining Example

A B C

B 0.40

C 0.35 0.45

D 0.60 0.70 0.55



• Initialize tree into a star shape with all taxa connected to the center• Step 1: Compute r-values and transformed r-values for all taxa

675.02

35.1

24'

35.16.035.04.0

AA

ADACABA

rr

dddr



• Step 2: Compute converted distances

05.1

55.135.12

14.0

2

1'

BAABAB rrdd



A B C

B -1.05

C -1 -1

D -1 -1 -1.05

• Step 3: Fill out converted distance matrix



• Step 4: Create a node by merging closest taxa• In this example, the distance between A and B

is the same as the distance between C and D• We can pick either pair to start with• Let’s pick A and B and create a node called U

U

?

?B

A

DC

BA



• Step 5: Compute branch lengths• Use the equation for computing the distance

from a taxa to a node

15.02

775.0675.04.02

''

BAAB

AU

rrdd

U

0.15

0.25B

A



• Step 6: Construct reduced distance matrix by computing converted distances from each taxa to the new node U• In UPGMA, we simply calculated the average

2.0

2

25.045.015.035.02

UBBCUAAC

CU

ddddd



U C

C 0.20

D 0.45 0.55

Our reduced distance matrix:



• From here, we go back to step 1• Continue until all taxa have been decomposed

from the star tree•


Optimality-Based Methods

• Clustering methods produce a single tree with no ability to judge how good it is compared to alternative tree topologies• Optimality-based methods compare all possible

tree topologies and select a tree that best fits the distance matrix• Two algorithms:• Fitch-Margoliash• Minimum evolution


Fitch-Margoliash

• Selects best tree among all possible trees based on minimum deviation between distances calculated in the tree and distances in the distance matrix• Basically, a least squares method• Dij = distance between i and j in matrix• dij = distance between i and j in tree• Objective: Find tree that minimizes

nji1

2ijij )dD(


Minimum Evolution

• Similar to Fitch-Margoliash, but uses a different optimality criterion• Searches for a tree with the minimum

total branch length• This is an indirect way of achieving the

best fit of the branch lengths with the original data


Summary of Distance-Based Methods

• Clustering-based methods:• Computationally very fast and can handle large

datasets that other methods cannot• Not guaranteed to find the best tree

• Optimality-based methods:• Better overall accuracies• Computationally slow

• All distance-based methods lose all sequence information and cannot infer the most likely state at an internal node

Documents

BCB 444/544