Burkhard MorgensternInstitut für Mikrobiologie und Genetik

Molekulare Evolution und Rekonstruktion von phylogenetischen Bäumen

WS 2006/2007

Goal:

Phylogeny reconstruction based on molecular sequence data (DNA, RNA, protein sequences)

Multiple sequence alignment

Molecular phylogeny reconstruction relies on comparative nucleic acid and protein sequence analysis

Alignment most important tool for sequence comparison

Multiple alignment contains more information than pair-wise alignment

Tools for multiple sequence alignment

Y I M Q E V Q Q E R

Sequence duplicates in history (e.g. speciation event)

Tools for multiple sequence alignment

Y I M Q E V Q Q E R

Tools for multiple sequence alignment

Y I M Q E V Q Q E R

Y I M Q E V Q Q E R

Tools for multiple sequence alignment

Y I M Q E A Q Q E R

Y L M Q E V Q Q E R

Substitutions occur

Tools for multiple sequence alignment

Y I M Q E A Q Q E R

Y L M Q E V Q Q E R

Tools for multiple sequence alignment

YAI M Q E A Q Q E R

Y L M - - V Q Q E R V

Insertions/deletions (indels) occur

Tools for multiple sequence alignment

YAI M Q E A Q Q E R

Y L M - - V Q Q E R V

Tools for multiple sequence alignment

Y A I M Q E A Q Q E R

Y L M V Q Q E R V

because of insertions/deletions: sequence similarity no longer immediately visible!

Tools for multiple sequence alignment

Y A I M Q E A Q Q E R -

Y - L M V - - Q Q E R V

Alignment brings together related parts of the sequences by inserting gaps into sequences

Tools for multiple sequence alignment

Y A I M Q E A Q Q E R -

Y - L M V - - Q Q E R V

Tools for multiple sequence alignment

Y A I M Q E A Q Q E R -

Y - L M V - - Q Q E R V

Mismatches correspond to substitutions Gaps correspond to indels

Tools for multiple sequence alignment

Pairwise alignment: alignment of two sequences

Multiple alignment: alignment of N > 2 sequences

Tools for multiple sequence alignment

s1 R Y I M R E A Q Y E S A Qs2 R C I V M R E A Y Es3 Y I M Q E V Q Q E Rs4 W R Y I A M R E Q Y E

Assumtion: sequence family related by common ancestry; similarity due to common history

Sequence similarity not obvious (insertions and deletions may have happened)

Tools for multiple sequence alignment

s1 - R Y I - M R E A Q Y E S A Qs2 - R C I V M R E A - Y E - - -s3 - - Y I - M Q E V Q Q E R - - s4 W R Y I A M R E - Q Y E - - -

Multiple alignment = arrangement of sequences by introducing gaps

Alignment reveals sequence similarities

Tools for multiple sequence alignment

s1 - R Y I - M R E A Q Y E S A Qs2 - R C I V M R E A - Y E - - -s3 - - Y I - M Q E V Q Q E R - -

s4 W R Y I A M R E - Q Y E - - -

Tools for multiple sequence alignment

s1 - R Y I - M R E A Q Y E S A Qs2 - R C I V M R E A - Y E - - -s3 - - Y I - M Q E V Q Q E R - -

s4 W R Y I A M R E - Q Y E - - -

Tools for multiple sequence alignment

s1 - R Y I - M R E A Q Y E S A Qs2 - R C I V M R E A - Y E - - -s3 - - Y I - M Q E V Q Q E R - - s4 W R Y I A M R E - Q Y E - - -

General information in multiple alignment: Functionally important regions more conserved than

non-functional regions Local sequence conservation indicates functionality!

Tools for multiple sequence alignment

s1 - R Y I - M R E A Q Y E S A Qs2 - R C I V M R E A - Y E - - -s3 - - Y I - M Q E V Q Q E R - -

s4 W R Y I A M R E - Q Y E - - -

Phylogeny reconstruction based on multiple alignment: Estimate pairwise distances between sequences

(distance-based methods for tree reconstruction) Estimate evloutionary events in evolution (parsimony

and maximum likelihood methods)

Tools for multiple sequence alignment

s1 - R Y I - M R E A Q Y E S A Qs2 - R C I V M R E A - Y E - - -s3 - - Y I - M Q E V Q Q E R - -

s4 W R Y I A M R E - Q Y E - - -

Task in bioinformatics: Find best multiple alignment for given sequence set

Tools for multiple sequence alignment

s1 - R Y I - M R E A Q Y E S A Qs2 - R C I V M R E A - Y E - - -s3 - - Y I - M Q E V Q Q E R - -

s4 W R Y I A M R E - Q Y E - - -

Astronomical number of possible alignments!

Tools for multiple sequence alignment

s1 - R Y I - M R E A Q Y E S A Qs2 - R C I V M R E A - - - Y E -s3 Y I - - - M Q E V Q Q E R - -

s4 W R Y I A M R E - Q Y E - - -

Astronomical number of possible alignments!

Tools for multiple sequence alignment

s1 - R Y I - M R E A Q Y E S A Qs2 - R C I V M R E A - - - Y E -s3 Y I - - - M Q E V Q Q E R - -

s4 W R Y I A M R E - Q Y E - - -

Computer has to decide: which one is best??

Tools for multiple sequence alignment

Questions in development of alignment programs:

(1) What is a good alignment? → objective function (`score’)

(2) How to find a good alignment? → optimization algorithm

First question far more important !

Tools for multiple sequence alignment

Before defining an objective function (scoring scheme)

What is a biologically good alignment ??

Tools for multiple sequence alignment

Criteria for alignment quality:

1. 3D-Structure: align residues at corresponding positions in 3D structure of protein!

Tools for multiple sequence alignment

Criteria for alignment quality:

Tools for multiple sequence alignment

Criteria for alignment quality:

1. 3D-Structure: align residues at corresponding positions in 3D structure of protein!

Tools for multiple sequence alignment

Species related by common history

Tools for multiple sequence alignment

Genes / proteins related by common history

Tools for multiple sequence alignment

Criteria for alignment quality:

1. 3D-Structure: align residues at corresponding positions in 3D structure of protein!

2. Evolution: align residues with common ancestors!

Tools for multiple sequence alignment

s1 - R Y I - M R E A Q Y E S A Qs2 - R C I V M R E A - Y E - - -s3 - - Y I - M Q E V Q Q E R - - s4 W R Y I A M R E - Q Y E - - -

Alignment hypothesis about sequence evolution Mismatches correspond to substitutions Gaps correspond to insertions/deletions

Tools for multiple sequence alignment

s1 - R Y I - M R E A Q Y E S A Qs2 - R C I V M R E A - Y E - - -s3 - - Y I - M Q E V Q Q E R - - s4 W R Y I A M R E - Q Y E - - -

Alignment hypothesis about sequence evolution Search for most plausible scenario! Estimate probabilities for individual evolutionary

events: insertions/deletions, substitutions

Tools for multiple sequence alignment

s1 - R Y I - M R E A Q Y E S A Qs2 - R C I V M R E A - Y E - - -s3 - Y - I - M Q E V Q Q E R - - s4 W R Y I A M R E - Q Y E - - -

Alignment hypothesis about sequence evolution Search for most plausible scenario! Estimate probabilities for individual evolutionary

events: insertions/deletions, substitutions

Tools for multiple sequence alignment

Compute score s(a,b) for degree of similarity between amino acids a and b based on probability

pa,b

of substitution a → b (or b → a)

(Extremely simplified!)

Tools for multiple sequence alignment

Tools for multiple sequence alignment

Reason for different substitutin probabilities pa,b :

Different physical and chemical properties of amino acids

Amino acids with similar properties more likely to be substituted against each other

Tools for multiple sequence alignment

Use penalty for gaps introduced into alignment

Simplest approach: linear gap costs: penalty proportional to gap length

Non-linear gap penalties more realistic: long gap caused by single insertion/deletion

Most frequently used: affine linear gap penalties: more realistic, but efficient to calculate!

Traditional Objective functions:

Define Score of alignments as

Sum of individual similarity scores s(a,b) Minus gap penalties

Needleman-Wunsch scoring system for pairwise alignment (1970)

Pair-wise sequence alignment

T Y W I V T - - L V

Example:

Score = s(T,T) + s(I,L) + s (V,V) – 2 g

Assumption: linear gap penalty!

Pair-wise sequence alignment

T Y W I V T - - L V

Dynamic-programming algorithm findsalignment with best score.

(Needleman and Wunsch, 1970)

Pair-wise sequence alignment

T Y W I V T - - L V

Running time proportional to product of sequence length

Time-complexity O(l1 * l2)

Pair-wise sequence alignment Algorithm for pairwise alignment can be

generalized to multiple alignment of N sequences

Time-complexity O(l1 * l2 * … * lN)

Not feasable in reality (too long running time!)

Heuristic necessary, i.e. fast algorithm that does not necessarily produce mathematically best alignment

`Progressive´ Alignment

Most popular approach to (global) multiple sequence alignment:

Progressive Alignment

Since mid-Eighties: Feng/Doolittle, Higgins/Sharp, Taylor, …

`Progressive´ Alignment

WCEAQTKNGQGWVPSNYITPVN

WWRLNDKEGYVPRNLLGLYP

AVVIQDNSDIKVVPKAKIIRD

YAVESEAHPGSFQPVAALERIN

WLNYNETTGERGDFPGTYVEYIGRKKISP

`Progressive´ Alignment

WCEAQTKNGQGWVPSNYITPVN

WWRLNDKEGYVPRNLLGLYP

AVVIQDNSDIKVVPKAKIIRD

YAVESEAHPGSFQPVAALERIN

WLNYNETTGERGDFPGTYVEYIGRKKISP

Guide tree

`Progressive´ Alignment

WCEAQTKNGQGWVPSNYITPVN

WW--RLNDKEGYVPRNLLGLYP- AVVIQDNSDIKVVP--KAKIIRD

YAVESEASFQPVAALERIN

WLNYNEERGDFPGTYVEYIGRKKISP

Profile alignment, “once a gap - always a gap”

`Progressive´ Alignment

WCEAQTKNGQGWVPSNYITPVN

WW--RLNDKEGYVPRNLLGLYP- AVVIQDNSDIKVVP--KAKIIRD

YAVESEASVQ--PVAALERIN------ WLN-YNEERGDFPGTYVEYIGRKKISP

Profile alignment, “once a gap - always a gap”

`Progressive´ Alignment

WCEAQTKNGQGWVPSNYITPVN- WW--RLNDKEGYVPRNLLGLYP- AVVIQDNSDIKVVP--KAKIIRD

YAVESEASVQ--PVAALERIN------ WLN-YNEERGDFPGTYVEYIGRKKISP

Profile alignment, “once a gap - always a gap”

`Progressive´ Alignment

WCEAQTKNGQGWVPSNYITPVN-------- WW--RLNDKEGYVPRNLLGLYP-------- AVVIQDNSDIKVVP--KAKIIRD------- YAVESEA---SVQ--PVAALERIN------ WLN-YNE---ERGDFPGTYVEYIGRKKISP

Profile alignment, “once a gap - always a gap”

`Progressive´ Alignment

WCEAQTKNGQGWVPSNYITPVN-------- WW--RLNDKEGYVPRNLLGLYP-------- AVVIQDNSDIKVVP--KAKIIRD------- YAVESEA---SVQ--PVAALERIN------ WLN-YNE---ERGDFPGTYVEYIGRKKISP

Most important implementation: CLUSTAL W

`Progressive´ Alignment

CLUSTAL W; Thompson et al., 1994 (~17.000 citations)

Pairwise distances as 1 - percentage of identity Calculate un-rooted tree with Neighbor Joining Define root as central position in tree Define sequence weights based on tree Gap penalties calculated based on various

parameters

Tools for multiple sequence alignment

Problems with traditional approach:

Results depend on gap penalty

Heuristic guide tree determines alignment; alignment used for phylogeny reconstruction

Algorithm produces global alignments.

Tools for multiple sequence alignment

Problems with traditional approach:

But:

Many sequence families share only local similarity

E.g. sequences share one conserved motif

The DIALIGN approach

Morgenstern, Dress, Werner (1996),PNAS 93, 12098-12103

Combination of global and local methods

Assemble multiple alignment from gap-free local pair-wise alignments (,,fragments“)

The DIALIGN approach

atctaatagttaaactcccccgtgcttag

cagtgcgtgtattactaacggttcaatcgcg

caaagagtatcacccctgaattgaataa

The DIALIGN approach

atctaatagttaaactcccccgtgcttag

cagtgcgtgtattactaacggttcaatcgcg

caaagagtatcacccctgaattgaataa

The DIALIGN approach

atctaatagttaaactcccccgtgcttag

cagtgcgtgtattactaacggttcaatcgcg

caaagagtatcacccctgaattgaataa

The DIALIGN approach

atctaatagttaaactcccccgtgcttag

cagtgcgtgtattactaacggttcaatcgcg

caaagagtatcacccctgaattgaataa

The DIALIGN approach

atctaatagttaaactcccccgtgcttag

cagtgcgtgtattactaacggttcaatcgcg

caaagagtatcacccctgaattgaataa

The DIALIGN approach

atctaatagttaaactcccccgtgcttag

cagtgcgtgtattactaacggttcaatcgcg

caaagagtatcacccctgaattgaataa

The DIALIGN approach

atc------taatagttaaactcccccgtgcttag

cagtgcgtgtattactaacggttcaatcgcg

caaagagtatcacccctgaattgaataa

The DIALIGN approach

atc------taatagttaaactcccccgtgcttag

cagtgcgtgtattactaacggttcaatcgcg

caaa--gagtatcacccctgaattgaataa

The DIALIGN approach

atc------taatagttaaactcccccgtgcttag

cagtgcgtgtattactaacggttcaatcgcg

caaa--gagtatcacc----------cctgaattgaataa

The DIALIGN approach

atc------taatagttaaactcccccgtgc-ttag

cagtgcgtgtattactaac----------gg-ttcaatcgcg

caaa--gagtatcacc----------cctgaattgaataa

The DIALIGN approach

atc------taatagttaaactcccccgtgc-ttag

cagtgcgtgtattactaac----------gg-ttcaatcgcg

caaa--gagtatcacc----------cctgaattgaataa

Consistency!

The DIALIGN approach

atc------TAATAGTTAaactccccCGTGC-TTag

cagtgcGTGTATTACTAAc----------GG-TTCAATcgcg

caaa--GAGTATCAcc----------CCTGaaTTGAATaa

More methods for multiple alignment:

T-Coffee PIMA Muscle Prrp Mafft ProbCons

Substitution matrices

Similarity score s(a,b) for amino acids a and b based on probability pa,b of substitution a -> b

Idea: it is more reasonable to align amino acids that are often replaced by each other!

Substitution matrices

Assumptions:

pa,b does not depend on sequence position Sequence positions independent of each other pa,b = pb,a (symmetry!)

Substitution matrices

Compute score s(a,b) for degree of similarity between amino acids a and b:

Probability pa,b of substitution

a → b (or b → a), Frequency qa of a

Define s(a,b) = log (pa,b / qa qb)

Substitution matrices

Substitution matrices

To calculate pa,b:

Consider alignments of related proteins and count substitutions

a → b (or b → a)

Substitution matrices

To calculate pa,b:

Consider alignments of related proteins and count substitutions

a → b (or b → a)

ESWTS-RQWERYTIALMSDQRREVLYWIALYERWTSERQWERYTLALMS-QRREALYWIALY

Substitution matrices

To calculate pa,b:

Consider alignments of related proteins and count substitutions

a → b (or b → a)

ESWTS-RQWERYTIALMSDQRREVLYWIALYERWTSERQWERYTLALMS-QRREALYWIALY

Substitution matrices

Problems involved:

1. Probability pa,b depends on time t since sequences separated in evolution: pa,b = pa,b (t)

2. Protein families contain multiple sequences: phylogenetic tree must be known!

3. Alignment of protein families must be known!

4. Multiple mutations at one sequence position

Substitution matrices

M. Dayhoff et al., Atlas of Protein sequence and Structure, 1978

PAM matrices

Substitution matrices

Calculation of pa,b(t) : Consider multiple alignments of closely related

protein families Count occurrence of a and b at corresponding

positions in alignments using phylogenetic tree Estimate pa,b(t) for small times t Calculate conditional probabilities p(a|b,t) for small t Normalize to distance 1 PAM (= percentage of

accepted mutations) Calculate p(a|b,t) for larger evolutionary distances by

matrix multiplication Calculate pa,b(t) for larger evolutionary distances

Substitution matrices

Substitution matrices

Alternative: BLOSUM matrices

S. Henikoff and J.G. Henikoff, PNAS, 1992

Basis: BLOCKS database, gap-free regions of multiple alignments.

Cluster of sequences if percentage of similarity > L Estimate pa,b(t) directly.

Default values: L = 62, L = 50