8. lecture ws 2003/04bioinformatics iii1 phylogenetic prediction (of single genes) material of this...

8. Lecture WS 2003/04

Bioinformatics III 1

Phylogenetic Prediction (of single genes)

Material of this lecture taken from

- chapter 6, DW Mount „Bioinformatics“

- A. Okas et al., Nature 425, 798 (2003)

Genome-scale approaches to resolving incongruence in molecular phylogenies.

A phylogenetic analysis of a family of related nucleic acid or protein

sequences is a determination of how the family might have been derived

during evolution.

Placing the sequences as outer branches on a tree, the evolutionary

relationships among the sequences are depicted.



3 main approaches in single-gene phylogeny

- maximum parsimony

- distance

- maximum likelihood

Popular programs:

PHYLIP (phylogenetic inference package – J Felsenstein)

PAUP (phylogenetic analysis using parsimony – Sinauer Assoc



Concept of evolutionary trees

An evolutionary tree is a 2-dimensional graph showing evolutionary relationships

among organisms, or in the case of sequences, in certain genes from separate

organisms.

nodes

branches

sequence A

sequence B

sequence C

sequence D

rooted tree

unrooted tree

sequence A

sequence B

sequence C

sequence D

length of branchesreflects number of sequence changes.

Often: assume uniformrate of mutations(molecular clock hypothesis).



Concept of evolutionary trees

Number of substitutions in each branch is generally assumed to vary

according to the Poisson distribution that gives the probability Pn around an

average number x :

!n

xeP

nx

n

The number of possible trees increases very rapidly

with the number of sequences:

#sequences #rooted trees #unrooted trees

3 3 1

4 15 3

5 105 15

-

7 10395 954

A B C D



Methods for Single-Gene Phylogeny

Choose set of

related sequences

Obtain multiple

sequence

alignment

Is there

strong

sequence

similarity?

Maximum

parsimony

methods

Yes

No

Is there clearly recogniza-

ble sequence similarity?

YesDistance

methods

No

Maximum likelihood

methods

Analyze how well

data support

prediction



Maximum Parsimony Method

Method predicts the evolutionary tree that minimizes the number of steps

required to generate the observed variation in the sequences.

Step 0 Input: multiple sequence alignment

Step 1 For each aligned position, identify phylogenetic trees that require the

smallest number of evolutionary changes to produce the observed

sequence changes.

Step 1.5 Continue analysis for every position in the sequence alignment.

Step 2 Sequence variations at each site in the alignment are placed at the tips

of the trees. Identify the tree (trees) that produce the smallest number

of changes overall for all sequence positions.

Because all possible trees are examined, method is best suited for sequences

that are quite similar + for small number of sequences.

It is guaranteed to find the best tree.



Example

Sequence# Sequence position

1 2 3 4 5 6 7 8 9

1 A A G A G T G C A

2 A G C C G T G C G

3 A G A T A T C C A

4 A G A G A T C C G

These are 4 sequences giving 3 possible unrooted trees. E.g. trees for position 5:

G

G

A

A

AG

G G

A

A

A

A

G G

A

A

A

A

Informative sites: (1) must favor one tree over another (site 5 is informative, but sites 1, 6, 8 are not).(2) To be informative, a site must also have the same sequence character in at least two genomes (only sites 5, 7, and 9 are informative according to this rule).

Combining sites 5, 7, and 9, the left tree is the best tree for these 4 sequences.

Seq4Seq3 Seq4 Seq3

Seq2Seq1Seq2Seq1

Seq4Seq2

Seq3Seq1



Where maximum parsimony fails

Parsimony can give misleading information when rates of sequence change vary

in the different branches of a tree that are represented by the sequence data.

G G

AA

Real tree: 2 long branches inwhich G has turned to A independently, possibly withsome intermediate steps.

Seq3Seq2

Seq4Seq1

G

G

A

ASeq3Seq4

Seq2Seq1

In parsimony analysis rates of changealong all branches of the tree areassumed equal.Therefore the tree predicted fromparsimony will not be correct.



Distance methods

The distance method employs the number of changes between each pair in a

group of sequences to produce a phylogenetic tree of the group.

The sequence pairs that have the smallest number of sequence changes

between them are termed „neighbors“. On a tree, these sequences share a

node or common ancestor position and are each joined to that node by branch.

Goal of distance methods: identify tree that correctly positions neighbors and that

also has branch lengths that reproduce the original data as closely as possible.

neighbor-joining algorithm, Fitch-Margoliash algorithm

Finding the closest neighbors among a group of sequences by the distance

method is often the first step in producing a multiple sequence alignment.

E.g. ClustalW uses the neighbor-joining distance method.



Example

sequence A A C G C G T T G G G C G A T G G C A A C

sequence B A C G C G T T G G G C G A C G G T A A T

sequence C A C G C A T T G A A T G A T G A T A A T

sequence D A C A C A T T G A G T G A T A A T A A T

distances beween sequences distance table

nAB 3

nAC 7

nAD 8

nBC 6

nBD 7

nCD 3A

B

C

D

2

1

41

2

A B C D

A - 3 7 8

B - - 6 7

C - - - 3

D - - - -



Maximum likelihood approach

Method uses probability calculations to find a tree that best accounts for the

variation in a set of sequences.

Similar to maximum parsimony method in that analysis is performed on each

column of a multiple sequence alignment. All trees are considered.

Because the rate of appearance of new mutations is very small, the more

mutations are needed to fit a tree to the data, the less likely that tree.

Start with an evolutionary model of sequence change that provides estimates of

rates of substitution of one base for another (transitions and transversions).

Base A C G T

A -u(aC+bG+cT) uaC ubG ucT

C ugA -u(gA+dG+eT) udG ueT

G uhA ujG -u(hA+jG+fT) ufT

T uiA ukG ulT -u(iA+kG+lT)



Maximum likelihood approach

Step1 Align set of sequences

Step2 Examine substitutions in each column for their fit to a set of trees that

describe possible phylogenetic relationships among the sequences.

Each tree has a certain likelihood based on the series of mutations that are

required to give the sequence data.

The probability of each tree is the product of the mutation rates in each branch of

the tree, which itself is the product of the rate of substitution in each branch times

the branch length.

branch(i) oflength ibranchin on substituti of rate

ratemutation

1

1

ibranch

ibranch

ibranch

ibranchtree

n

n

iP

Advantage of maximum likelihood approach:

allows to evaluate trees with variations in mutation rates in different lineages.

Can be used for more diverse sequences.

Disadvantage: computationally intense.



Resolve Incongruences in Phylogeny

Many possible reasons that may make decisions on how to handle conflicts in

larger sets of molecular data difficult.

E.g. two genes with different evolutionary history (e.g. owing to hybridization or

horizontal transfer) will necessarily give incongruent pictures while still depicting

true histories.

Here: compare genome sequence data for 7 Saccharomyces yeast species:

S. cerevisae

S. paradoxus

S. mikatae

S. kudriavzevii

S. bayanus

S. castelli

S. kluyveri

plus one outgroup fungus Candida albicans.

Rokas et al. Nature 425, 798 (2003)




Identify orthologous genes to serve as phylogenetic markers:

106 genes which are distributed throughout the S. cerevisae genome on all 16

chromosomes and comprise a total length of 127026 nt = 42342 amino acids

corresponding to roughly 1% of the genomic sequence and 2% of the predicted

genes.

Criteria to select genes spaced ca. every 40 kb:

(1) genes have homologous sequence in each of the 8 species

(2) genes have at least two homologous flanking syntenic genes

(3) genes can be aligned over most of the protein.

3 types of analysis:

- maximum likelihood (ML) analysis of nucleotide data

- maximum parsimony (MP) analysis of nucleotide data

- MP of the amino acid data





Align individual genes with ClustalW. Edit manually to exclude indels and areas of

uncertain alignment left with 76% of the sequence of each gene on average.

Tree construction with PAUP by branch-and-bound algorithm which guarantees to

find the optimal tree. Estimate tree reliability using non-parametric bootstrap re-

sampling.

Analysis of the 106 genes gave more than 20 alternative ML or MP trees.

Generate 50% majority-rule consensus trees by bootstrapping.

Next slide shows several strongly supported trees.




A method for testing how well a particular data set fits a model.

E.g. the validity of the branch arrangement in a predicted phylogenetic tree can

be tested by resampling columns in a multiple sequence alignment to create

many new alignments.

The appearance of a particular branch in trees generated from these resampled

sequences can then be measured.

Alternatively, a sequence may be left out of an analysis to determine how

much the sequence influences the results of an analysis.

Here: swap individual nucleotide sites or positions of genes (bootstrap replicas).

Bootstrap analysis.



Alternative Tree topologies

Single-gene data sets generate multiple, robustly supported alternative topologies.

Representative alternative trees recovered from analyses of nucleotide data of 106

selected single genes and six commonly used genes are shown. The trees are the

50% majority-rule consensus trees from the genes YBL091C (a), YDL031W (b),

YER005W (c), YGL001C (d), YNL155W (e) and YOL097C (f).

These 6 genes were selected without consideration of their function. Maybe

commonly used, well known genes of important functions provide a better resolution?




Results from the commonly used genes actin (g), hsp70 (h), -tubulin (i), RNA

polymerase II (j) elongation factor 1- (k) and 18S rDNA (l). Numbers above

branches indicate bootstrap values (ML on nucleotides/MP on nucleotides).

Same problem of alternative topologies as before.

Alternative Tree topologies




The alternative phylogenies could have resulted from a number of different

scenarios:

(1) most genes could have weakly supported most phylogenies and strongly

supported only a few alternative trees,

(2) most genes could have strongly supported one phylogeny and a few genes

strongly supported only a small number of alternatives,

(3) there could have been some combinations of these scenarios so that each

branch among alternative phylogenies had either weak or strong support

depending on the gene.

To distinguish between these possibilities, identify all branches recovered during

single-gene analyses, record each bootstrap value with respect to the gene and

method of analysis.

8 branches were shared by all three analyses with multiple instances of

bootstrap values > 50%.

Explanations?




Common Branches

The distribution of bootstrap values for the eight prevalent branches recovered

from 106 single-gene analyses highlights the pervasive conflict among single-

gene analyses. a, Majority-rule consensus tree of the 106 ML trees derived from

single-gene analyses. Across all analyses, there were eight commonly observed

branches; the five branches in the consensus tree (numbers 1–5; a) and the three

branches (numbers 6–8) shown in b.




c, For each of the eight branches, the ranked distribution of per cent bootstrap values recovered from

the three analyses of 106 genes is shown. Results from ML (blue) and MP (red) analyses of

nucleotide data sets, and MP analyses of amino acid data sets (black), are shown. For each branch,

the mean bootstrap value and 95% confidence intervals from the ML analyses and the percentage of

ML trees supporting this branch (in parentheses) are indicated below each graph. Although the

ranked distributions of bootstrap values from the three analyses are remarkably similar for most

branches, on a gene-by-gene basis there is no tight correspondence between bootstrap values from

ML and MP analyses

Bootstrap Values of Common Branches

Only branches 1 and 4are supported by amajority of genes.




How different are the trees?

The degree of conflict among the trees could be relatively minor.

Determine how many taxa (genes) would need to be removed to make two

trees congruent (deckungsgleich).




Reversal distance problem

Extensive incongruence between trees derived from

the 106 individual-gene data sets. Pairwise

comparisons between 50% majority-rule consensus

trees from 106 single-gene ML analyses of

nucleotide data (black bars), MP analyses of

nucleotide data (white bars), and MP analyses of

amino acid data (grey bars) were categorized on the

basis of the minimum number of taxa that need to

be removed for two trees to reach congruence (x

axis).

For each of the analyses, the majority of

pairwise comparisons require the

removal of two or more taxa before

congruence is attained.




What leads to incongruence?

Many factors were checked that could lead to incongruence between single-gene

phylogenies:

- outgroup choice

repeat all analyses without C. albicans

- number of variable sites significantly correlated with

- number of parsimony-informative sites bootstrap values for some

- gene size branches

- rate of evolution

- nucleotide composition

- base compositional bias

- genome location

- gene ontology

no parameters can systematically account for or predict the performance of single

genes!

}




Can incongruence be overcome?

Although we do not know the cause(s) of incongruence between single-gene

phylogenies, the critical question is how this incongruence between single trees

might be overcome to arrive at the actual species tree.

Can single gene trees be concatenated into one large data set?




Concatenation of single genes gives a single tree!

Phylogenetic analyses of the

concatenated data set composed

of 106 genes yield maximum

support for a single tree,

irrespective of method and type of

character evaluated. Numbers

above branches indicate bootstrap

values (ML on nucleotides/MP on

nucleotides/MP on amino acids).

All alternative topologies were rejected.

This level of support for a single tree with 5 internal branches is unprecedented.

This tree can now be referred to as species tree.




How much data is required?

The concatanated data recovered a tree with maximum support on all branches,

despite divergent levels of support for each branch among single-gene analyses.

At what size did the data set arrive at the species tree?




Convergence on single tree

A minimum of 20 genes is required to recover >95% bootstrap values for each

branch of the species tree. a, b, The bootstrap values for branches 3 (a) and 5 (b)

were constructed from the concatenation of randomly re-sampled orthologous

nucleotides (left) or random subsets of genes (right).

The species tree is recovered with robust support (>95% bootstrap values in all

branches at 95% confidence interval) by analyses of a minimum of 20

concatenated genes. All analyses were performed using MP.

branch 3

branch 5




Independent evolution?It has been suggested that nucleotides within a given gene do not evolve

independently.

Re-sample subset of orthologous nucleotides from the total data set.

Only 3000 randomly chosen nucleotide positions (corresponding to less than three

concatenated genes) are sufficient to generate single tree with > 95% confidence.

This indicates that nucleotides in genes have not evolved independently (because

when using complete genes more than 20 genes are necessary to generate single

tree).




Implications for resolution of phylogenies

Unreliability of single-gene data sets stems from the fact that each gene is shaped

by a unique set of functional constraints through evolution.

Phylogenetic algorithms are sensitive to such constraints.

Such problems can be avoided with genome-wide sampling of independently

evolving genes.

In other cases the amount of sequence information needed to resolve specific

relationships will be dependent on the particular phylogenetic history under

examination.

Branches depicting speciation events separated by long time intervals may be

resolved with a smaller amount of data, and those depicting speciation events

separated by shorter invtervals may be much harder to resolve.




SummaryRobust strategies exist for phylogenies built on single-gene comparisons

(maximum parsimony, distance, maximum likelihood).

Problem of incongruence of phylogenies derived from individual genes.

Can be resolved by integrative analysis of multiple (here > 20) genes.

It is desirable to combine results from phylogenies constructed from local

sequence information with trees constructed from genome rearrangement.

The power of genome rearrangement studies is the construction of ancestral

genomes. Then one can derive the speed of evolution at different times, disect

mutation biases at different times from the influence of genomic context ...

and possibly derive the driving forces of biological evolution.

This lecture rounds up the first block of the Bioinformatics III course ongenome structure, rearrangements etc.Next block until Christmas: gene finding, SNPs, functional genomics

8. lecture ws 2003/04bioinformatics iii1 phylogenetic prediction (of single genes) material of this...

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