Klaudia Walter, Wally Gilks, Lorenz Wernisch

12th December 2006

HUMAN

Modelling the Boundary of Highly Conserved Non-Coding DNA

Overview

• Background

– What are CNEs?

– A+T nucleotide frequency in and around CNEs

• Phylogenetic Model

– What is a phylogenetic tree model?

– Likelihood of a tree model

– Likelihood of the scaling of a tree

– Likelihood of CNE boundary

– Variable CNE boundaries for each species

Motivation

• DNA sequences that are conserved between organisms are likely to have special functions.

• The Fugu genome represents a good model to find conserved non-coding sequences (CNEs) in the human genome.

• Are conserved regions different from their neighbouring sequences in the genome?

• Is it possible to define CNE boundaries better than with pairwise sequence alignment of Fugu and human?

What are CNEs?

Multiple Alignment of Mouse, Rat, Human and Fugu

Fugu Genome

• Fugu genome contains only 400Mb.

• Only an eighth of human genome.

• Gene repertoire is similar to human.

• Human and Fugu shared last common ancestor 450 million years ago.

(Brenner et al, 1993; Aparicio et al, 2002)

Conserved Non-coding Elements (CNE)

• 1373 CNEs identified in human and Fugu

• 93 - 740 bp long; 68 - 98% identical

• Situated around developmental genes

• Can act over 1 Mb distance, eg. Shh expression (Lettice et al, 2003; Nobrega et al, 2003;

Kleinjan & van Heyningen, 2004)

• Likely to be fundamental to vertebrate life

(Dermitzakis et al, 2002, 2003; Margulies et al, 2003; Bejerano et al 2004a; Woolfe et al, 2005)

Are vertebrate CNEs enhancers?

Coding Exon

Conserved Non-coding Sequence

SOX21 gene

Fugu / Mouse

Fugu / Human Fugu / Rat

element 1element 1

element 19element 19

element 4element 4 element 5element 5

element 8-10element 8-10

sox21 gene element 19

central nervous system

forebrain

eye

Element 19

(Woolfe et al, 2005; McEwen et al, 2006)

CNE Target

Model of duplication of cis-element and target gene

(Vavouri et al, 2006; McEwen et al, 2006)

A+T base frequency in CNEs

Position Specific Base Composition

Upstream flanking region Conserved non-coding

ACTAGCCTCATCGTAGCGCAATTCTAGATGATAACATACCGAGTTCGGTAGGAGCTTAGTATGAGCATAACGCGTGTGCTAGGTCACGGCGCAACATACTTATAGACTACGCCCTTGCACGATCCGGATATCATAGTCTTACAA

A = 0.00C = 0.25G = 0.50T = 0.25

A = 0.50C = 0.00G = 0.25T = 0.25

A+T relative frequency across CNE boundaries in Fugu and human

(Walter et al, 2005)

A+T relative frequency across 2000 genes in human chromosome 1

Genes were aligned at the start and the end.

Distribution of Position Weight Matrix (PWM) Scores for CNEs and Random Sequences

A position weight matrix (PWM) is constructed by dividing the nucleotide probabilities by expected background probabilities.

p(b,i) = probability of base b in position i p(b) = background probability of base b

n

i bp

ibpS

12 )(

),(log

Scoresfor FuguCNEs

Scoresfor HumanCNEs

The sequence logo for the 100 top scoring CNEs.

What do CNEs do?

• Some CNEs enhance GFP (green fluorescent protein) expression in zebrafish embryos.

• The function of CNEs is still unknown.

• Necessary to do more lab experiments.

• Are CNEs defined well enough for experiments?

Conservation pattern across CNE boundaries

1373 Fugu-human CNE pairs plus 100bp flanking regions aligned using Needleman-Wunsch’s algorithm.

A+T frequency in Fugu, Human, Worm and Fly

(Glazov et al, 2005; Vavouri et al, 2006 (submitted))

Are CNE ends well defined?

• Different parameter settings produce different alignments.

• Even just different mismatch penalties change – the alignments– the A+T bias at the CNE boundaries

A+T frequency for Fugu CNEs using pairwise alignments with Human

Phylogenetic Model

5’ flanking conservedHuman ACAGTAT ATCGTAATMouse ACCGTAT ATCGTAATChicken AACGTAT ATCGTAATXenopus CCACTAT ATCGTAATFugu CGACTTA ATCGTAAT

boundary

Multiple sequence alignment

300 bp 100 bp

Phylogenetic tree model

• Substitution rate matrix– Continuous-time Markov process

• Tree topology• Branch lengths• Scaling of tree

AA AC AG AT

CA CC CG CT

GA GC GG GT

TA TC TG TT

q q q q

q q q qQ

q q q q

q q q q

H

M

C

F

Matrix P(t) of substitution probabilities for branch length t

1

( )( ) exp( )

!

i

i

QtP t Qt

i

Q should be diagonalizable. If Q is not symmetric, we need to find the eigensystem of a symmetric matrix S related to Q and to convert results to the eigensystem of Q.

Example:

C G T

A G T

A C T

A C G

a b c

a d eQ

b d f

c e fA, C, G, T

Estimating A+T frequency around Fugu CNE boundary

relative A+Tfrequency

Mouse

Fugu

Xenopus

Chicken

Human

Conserved

scaling C

Mouse

Flanking

scaling F

Fugu

Xenopus

Chicken

Human

Phylogenetic tree with conserved and flanking scalings

flanking scaling F

conserved scaling C

boundary position

sca

le

What is the optimal scaling?

5’ flanking conserved

ACA G TATATCGTAATACC G TATATCGTAATAAC G TATATCGTAATCCA C TATATCGTAATCGA C TTAATCGTAAT

Compute likelihood of scaling

Felsenstein’s algorithm: P(s | T, )

HumanMouseChickenXenopusFugu

Felsenstein’s algorithm

“Pruning” algorithm by Felsenstein (1973, 1981)

uses dynamic programming to calculate likelihood

of a tree model P(S |

Recursion:• If u is a leaf

If xu = a, then

Otherwise,

• Otherwise

( | ) = ( | , ) ( | ) ( | , ) ( | )u v v w wb c

P L a P b a t P L b P c a t P L c

( | ) = 1uP L a

( | ) = 0uP L ab

c

aw

u

v

Likelihood of scaling

• Calculate likelihood P(S | T, ) of scaling vector by

summing over boundary b.

• Assume evolutionary independence of each position i

in the multiple alignment S.

• P(S | T, ) is calculated by Felsenstein’s algorithm.

1

( | , ) ( | , ) ( )N

b bb

P S T P S T P

Model with common scaling and individual boundaries

1 11

( | ,..., ) ( ,..., | ) ( ) ( | ) ( )n

n n ii

P S S P S S P P S P

Probability of scaling given sequences S1, …, Sn

Likelihood of scaling over CNEs

Hierarchical model for

),|,(),|(),|(

),|(),|,...,,(

,

FCFC

Sn

PSPSP

SPSSSP

FC

21

S1 S2 S3 ..... Sn

CF)1 CF)2 CF)3 CF)n

F

C C

Multivariate log normal distribution for (C, F)

Likelihood of boundary b

• The likelihood of the boundary is computed by summing over scalings

• b and are independent.

• Prior on .

)(),|()|( PbSPbSP

Likelihood of boundary b

Boundary shifts for phylogenetic model

Boundary shift 0 bp ≤ 20bp ≤ 50bp ≤ 100bp

Cumulative frequency 12% 40% 61% 80%

density

position

Relative conservation by position

Model for variable boundary

000000 0 11111111000011 1 11111111000011 1 11111111000000 0 00111111000000 0 00111111000000 0 00111111000000 1 11111111000000 1 11111111 0 1

1

0

0

1 1

0

H M C X F

Branches

Positions

Transitions

1. 0000 0001 0010 0011 ......... 1111

2. 0000 0001 0010 0011 ......... 1111

3. 0000 0001 0010 0011 ......... 1111

...... ...... ...... ...... ......

Variable boundary for CNE1031

Human AGTAGTTTCC ATGCCTGTCAMouse AGGAGCCTCT ATGCCTGTCAChicken AGTAGTTTCC ATGCCTGTCAXenopus -GTTATATAC ACGCCTGTCAFugu AATAGTTCCC ATGCCTGTCA

10 bp 10 bp

Boundary shift = 154 bp

Variable boundary for CNE1043

Human TGATGTTGAA TCATTTAAAAMouse TGATGTGTAG TCATTTAAAAChicken TGACGTTCAG TCAGTTAAAAXenopus TGACACTCAA TCATTTAAATFugu TGACGCGCAG TCAGTTAAAT

10 bp 10 bp

Boundary shift = 0 bp

Variable boundary for CNE1037

Human TA-GGCCATT CTGATTTGTAMouse TA-GGCCATT CTGATTTGTAChicken TA-GGCCATT CTGATTTGTAXenopus AA-GACCATA CTGATTTTTTFugu TGTGGTAGGT CTGATTTGTA

10 bp 10 bp

Boundary shift = 65 bp

Conservation structure of CNEs

Summary

• Statistical models for CNE boundaries that incorporates phylogenetic information.

• Aim is to define location of CNE boundaries more reliably than pairwise or multiple sequence alignments.

Acknowledgments

Greg Elgar (Queen Mary College, University of London)

Irina AbnizovaGayle McEwen (MRC Biostatistics Unit, Cambridge)Krys KellyBrian Tom

Tanya Vavouri (QMUL & Sanger Institute, Hinxton)

Adam Woolfe (NHGRI, National Institutes of Health, US)

Yvonne Edwards (University College, University of London)

Martin Goodson

References

• Woolfe A, Goodson M, Goode DK, Snell P, McEwen GK, Vavouri T, Smith SF, North P, Callaway H, Kelly K, Walter K, Abnizova I, Gilks W, Edwards YJ, Cooke JE, Elgar G.

Highly conserved non-coding sequences are associated with vertebrate development. PLoS Biol. 2005, 3(1).

• Walter K, Abnizova I, Elgar G, Gilks WR. Striking nucleotide frequency pattern at the borders of highly conserved vertebrate

non-coding sequences. Trends Genet. 2005, 21(8):436-40.

• Vavouri T, McEwen GK, Woolfe A, Gilks WR, Elgar G. Defining a genomic radius for long-range enhancer action: duplicated conserved

non-coding elements hold the key. Trends Genet. 2006, 22(1):5-10.

• McEwen GK, Woolfe A, Goode D, Vavouri T, Callaway H, Elgar G. Ancient duplicated conserved noncoding elements in vertebrates: a genomic and

functional analysis. Genome Res. 2006,16(4):451-65.

• Vavouri T, Walter K, Gilks WR, Lehner B, Elgar G. Parallel evolution of conserved noncoding elements that target a common set of

developmental regulatory genes from worms to humans. Submitted 2006.

Human CNE boundary

MegaBLAST Phylogenetic

A+Tfrequency

position position

Chicken CNE boundary

MegaBLAST Phylogenetic

A+Tfrequency

position position

Fugu CNE boundary

MegaBLAST Phylogenetic

A+Tfrequency

position position

From rate matrix Q to probability matrix P

' , , ,

AA AC AG AT

CA CC CG CTA C G T

GA GC GG GT

TA TC TG TT

q q q q

q q q qp p Q p p p p

q q q q

q q q q

'

( )A A AA C CA G GA T TA

A AC AG AT C CA G GA T TA

p p q p q p q p q

p q q q p q p q p q

P(t) of substitution probabilities (2)

1/ 2 1/ 2diag( ) diag( )

( , , , )A C G T

S Q

1/ 2 1/ 2

exp( ) diag(exp( )) ( )

exp( ) diag( )exp( ) diag( )

( ) exp( )

TSt V t V

Qt St

P t Qt

is symmetric with

S and Q have the same eigenvalues