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HUMAN
Modelling the Boundary of
Highly Conserved Non-Coding DNA
Klaudia Walter, Wally Gilks, Lorenz Wernisch
12th December 2006
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?
element 1
element 4
Fugu / Mouse
Fugu / Rat
Fugu / Human
element 8-10
Coding Exon
Conserved
Non-coding
Sequence
SOX21 gene
element 19
element 5
Element 19
sox21 gene
element 19
central nervous system
eye
forebrain
(Woolfe et al, 2005; McEwen et al, 2006)
Model of duplication of cis-element and
target gene
CNE Target
(Vavouri et al, 2006; McEwen et al, 2006)
A+T base frequency in CNEs
Position Specific Base Composition
Upstream flanking region
Conserved non-coding
ACTAGCCTCATCGTAGCGCAATTCTAGATGATAACA
TACCGAGTTCGGTAGGAGCTTAGTATGAGCATAACG
CGTGTGCTAGGTCACGGCGCAACATACTTATAGACT
ACGCCCTTGCACGATCCGGATATCATAGTCTTACAA
A = 0.00
C = 0.25
G = 0.50
T = 0.25
A = 0.50
C = 0.00
G = 0.25
T = 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.
n
p (b, i )
S   log 2
p(b)
i 1
p(b,i) = probability of base b
in position i
p(b) = background probability
of base b
Scores
for
Fugu
CNEs
Scores
for
Human
CNEs
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
Multiple sequence alignment
Human
Mouse
Chicken
Xenopus
Fugu
5’ flanking
conserved
ACAGTAT
ACCGTAT
AACGTAT
CCACTAT
CGACTTA
ATCGTAAT
ATCGTAAT
ATCGTAAT
ATCGTAAT
ATCGTAAT
300 bp
100 bp
boundary
Phylogenetic tree model
 qAA

qCA

• Substitution rate matrix Q 
 qGA
– Continuous-time

Markov process
 qTA
• Tree topology
• Branch lengths
• Scaling of tree
qAC
qAG
qCC
qGC
qTC
qCG
qGG
qTG
C
H
F
M
qAT 

qCT 
qGT 

qTT 
Matrix P(t) of substitution probabilities
for branch length t

(Qt )i
P(t )  exp(Qt )  
i!
i 1
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:
A, C, G, T
aC bG
 

a A 
d G

Q
 bA d C 

 c A eC f G
c T 

eT 
f T 

 
Estimating A+T frequency around
Fugu CNE boundary
relative A+T
frequency
Phylogenetic tree with conserved and flanking scalings g
Mouse
Fugu
Conserved
scaling gC
Xenopus
Chicken
Human
Mouse
Fugu
Flanking
scaling gF
Xenopus
Chicken
Human
scale
What is the optimal scaling?
flanking scaling gF
conserved scaling gC
boundary
position
Compute likelihood of scaling g
5’ flanking
Human
Mouse
Chicken
Xenopus
Fugu
ACA
ACC
AAC
CCA
CGA
G
G
G
C
C
conserved
TATATCGTAAT
TATATCGTAAT
TATATCGTAAT
TATATCGTAAT
TTAATCGTAAT
Felsenstein’s algorithm: P(s | T, g)
Felsenstein’s algorithm
“Pruning” algorithm by Felsenstein (1973, 1981)
uses dynamic programming to calculate likelihood
of a tree model P(S | T ).
u
Recursion:
• If u is a leaf
If xu = a, then P (Lu | a) = 1
Otherwise, P (Lu | a) = 0
a
w
v
b
c
• Otherwise
P (Lu | a) =
 P(b | a,t
b
v
) P (Lv | b)  P (c | a, tw ) P (Lw | c )
c
Likelihood of scaling g
• Calculate likelihood P(S | T, g) of scaling vector g by
summing over boundary b.
• Assume evolutionary independence of each position i
in the multiple alignment S.
• P(S | T, g) is calculated by Felsenstein’s algorithm.
N
P (S | T, g )   P (S | T , g b ) P (g b )
b 1
Model with common scaling and
individual boundaries
Probability of scaling g given sequences S1, …, Sn
n
P ( g | S1,..., Sn )  P (S1,..., Sn | g ) P ( g )   P (Si | g ) P ( g )
i 1
Likelihood of scaling g over CNEs
Hierarchical model for g
(, )
(gC, gF)1
(gC, gF)2
(gC, gF)3
.....
(gC, gF)n
S1
S2
S3
.....
Sn
P (S1,S2 ,..., Sn | , )   P (S | , )
P (S | , ) 
 P(S | g
g C ,g F
S
C
,g F ) P ( gC , g F | , )
Multivariate log normal distribution
for (gC, gF)
gF
gC
gC
Likelihood of boundary b
• The likelihood of the boundary is computed
by summing over scalings g.
• b and g are independent.
• Prior on g.
P (S | b )   P (S | b, g ) P ( g )
g
Likelihood of boundary b
Boundary shifts for phylogenetic model
density
position
Boundary shift
0 bp
≤ 20bp
≤ 50bp
≤ 100bp
Cumulative frequency
12%
40%
61%
80%
Relative conservation by position
Model for variable boundary
Branches
000000 0 11111111
000011 1 11111111
000011 1 11111111
000000 0 00111111
000000 0 00111111
000000 0 00111111
000000 1 11111111
000000 1 11111111
0
1
0
0
0
H
Positions
1
1
M
C
1
X F
Transitions
1.
0000
0001
0010
0011
.........
1111
2.
0000
0001
0010
0011
.........
1111
3.
0000
0001
0010
0011
.........
1111
......
......
......
......
......
Variable boundary for CNE1031
Human
Mouse
Chicken
Xenopus
Fugu
AGTAGTTTCC
AGGAGCCTCT
AGTAGTTTCC
-GTTATATAC
AATAGTTCCC
ATGCCTGTCA
ATGCCTGTCA
ATGCCTGTCA
ACGCCTGTCA
ATGCCTGTCA
10 bp
10 bp
Boundary shift = 154 bp
Variable boundary for CNE1043
Human
Mouse
Chicken
Xenopus
Fugu
TGATGTTGAA
TGATGTGTAG
TGACGTTCAG
TGACACTCAA
TGACGCGCAG
TCATTTAAAA
TCATTTAAAA
TCAGTTAAAA
TCATTTAAAT
TCAGTTAAAT
10 bp
10 bp
Boundary shift = 0 bp
Variable boundary for CNE1037
Human
Mouse
Chicken
Xenopus
Fugu
TA-GGCCATT
TA-GGCCATT
TA-GGCCATT
AA-GACCATA
TGTGGTAGGT
CTGATTTGTA
CTGATTTGTA
CTGATTTGTA
CTGATTTTTT
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 Abnizova
Gayle McEwen
Krys Kelly
Brian Tom
(MRC Biostatistics Unit, Cambridge)
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
position
position
A+T
frequency
Chicken CNE boundary
MegaBLAST
Phylogenetic
position
position
A+T
frequency
Fugu CNE boundary
MegaBLAST
Phylogenetic
position
position
A+T
frequency
From rate matrix Q to probability matrix P
 qAA

qCA
'

p  p  Q  ( pA , pC , pG , pT ) 
 qGA

 qTA
qAC
qAG
qCC
qGC
qTC
qCG
qGG
qTG
qAT 

qCT 
qGT 

qTT 
pA'  pAqAA  pC qCA  pGqGA  pT qTA
 pA (qAC  qAG  qAT )  pC qCA  pGqGA  pT qTA
P(t) of substitution probabilities (2)
S  diag( ) Q diag(
  (A , C , G , T )
1/ 2
1/ 2
) is symmetric with
S and Q have the same eigenvalues
(1, 2, 3, 4).
exp(St )  V diag(exp( t )) (V )T
exp(Qt )  diag( 1/ 2 )exp(St ) diag( 1/ 2 )
P (t )  exp(Qt )