The COSTEX model: a cost-benefit model
relating gene expression and selection
Daniel Kahn, Jean-François Gout & Laurent Duret
Laboratoire de Biométrie & Biologie Evolutive
Lyon 1 University, INRIA BAMBOO team
& INRA MIA Department
Whole genome duplications as a tool to
investigate dosage selection
Following whole-genome duplication (WGD)
 Relative gene dosage is initially unchanged
 Duplicated genes are gradually lost with probability inversely related to
selective pressure
 This may be exploited to analyze selective pressure on gene dosage
D. Kahn, COSTEX model
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Duplications in the Paramecium genome
Aury et al., 2006, Nature 444:171-178
D. Kahn, COSTEX model
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Three successive rounds of WGD
Gene content: 2 x 2 x 2  2
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Fate
A brief introduction about Whole-Genome Duplications
(WGDs)
of genes after WGD
ohnologon
• WGD creates identical copies of all genes (ohnologs)
D. Kahn, COSTEX model
Fate
A brief introduction about Whole-Genome Duplications
(WGDs)
of genes after WGD
• WGD creates identical copies of all genes (ohnologs)
• Mutations lead to pseudogenization of some ohnologs
D. Kahn, COSTEX model
Fate
A brief introduction about Whole-Genome Duplications
(WGDs)
of genes after WGD
• WGD creates identical copies of all genes (ohnologs)
• Mutations lead to pseudogenization of some ohnologs
D. Kahn, COSTEX model
Fate
A brief introduction about Whole-Genome Duplications
(WGDs)
of genes after WGD
• WGD creates identical copies of all genes (ohnologs)
• Mutations lead to pseudogenization of some ohnologs
• Finally, only a few pairs of genes are retained
D. Kahn, COSTEX model
Fate
A brief introduction about Whole-Genome Duplications
(WGDs)
of genes after WGD
Ohnologon that lost one copy
Retained ohnologon
• WGD creates identical copies of all genes (ohnologs)
• Mutations lead to pseudogenization of some ohnologs
• Finally, only a few pairs of genes are retained
D. Kahn, COSTEX model
Relationship between gene retention
and gene expression
Frequency
of gene
retention
Data from Paramecium
post-genomics
consortium
Jean Cohen & coll.
D. Kahn, COSTEX model
Expression level (log2)
11
Model for expression-dependent selection
 Protein expression has a cost
=>Trade-off between cost and benefit
 The model assumes that expression was optimal before WGD
 In vitro evolution experiments have shown that an optimum can indeed
be reached in only a few hundred generations (e.g. Dekel & Alon, 2005)
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Modelling the cost of expression
Dekel & Alon, 2005, Nature 436:588-592
kX
C( X ) 
MX
expression cost
C(X)
X
k
M
expression level
D. Kahn, COSTEX model
cost function
expression level
cost parameter
maximal capacity
M
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Cost-benefit optimization
Benefit : B(X)
fitness
fitness
expression cost
cost
expression
Cost: C(X)
levelX
Xexpression
o
o
The COSTEX model
Express fitness as a function of expression x relatively to
optimum level X0
X
x
X0
kX 0 x
w( x )  B ( x ) 
M  X0x
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The COSTEX model
Approximate fitness around optimum X0 by Taylor expansion:
1 2w
2
w( x ) 1 
(1)(
x

1)
2 x 2
Therefore selection on expression can be quantified by:
2w
d 2B
2kMX 02
(1)  2 (1) 
0
2
3
x
dx
(M  X 0 )
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Expression-dependent fitness
1
fitness
Low X0
Medium X0
High X0
Loss of duplication
0
0.5
1
1.5
Relative dosage or expression X/Xo
Fitness loss
Selection against loss of duplicated gene
kMX 0 2
1 d 2B
s 

(1)
3
2
4( M  X 0 ) 8 dx
Optimal expression X0
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Selection against pseudogene formation
Pseudogene formation after WGD entails a loss of fitness that
can be expressed in the COSTEX model:
1
1 dB
kMX 0
s  B( )  B(1)  
(1) 
2
2 dx
2( M  X 0 ) 2
Therefore the pseudogenization path to gene loss is also under
expression-dependent selection: the higher the gene is
expressed, the less likely is the fixation of disabling mutations.
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Expression constrains evolutionary rates
More generally, mutations that decrease the benefit function by
a fraction a are counter-selected in an expression-dependent
manner in the COSTEX model:
s(a )  a B(1)  a (1 
kX 0
)
M  X0
Mutations with an equivalent effect on protein function are more
deleterious for highly expressed genes because of higher
expression cost, a price the organism had to ‘pay’ for their
function.
This relationship also applies for potentially suboptimal
expression X  X0
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Expression constrains evolutionary rates
Expression is the best predictor of evolutionary rates in coding
sequences (Duret & Mouchiroud, 2000, Drummond et al., 2006)
Drummond et al, 2005
PNAS,102:14338
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Expression-dependent selection
 The COSTEX model can explain the relationship between
retention rate and gene expression
 The model is also supported by gene knockout experiments in
yeast (measure of fitness in heterozygotes wt/KO)
 The model predicts that the level of expression is all the more
conserved in evolution as expression is high
 It also explains the observation that highly expressed genes
have low rates of sequence evolution
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Retention of metabolic genes
 Unexpected observation that metabolic genes are more
retained than other genes following WGD
 However little selective pressure is expected on the dosage of
individual enzyme genes (Kacser & Burns, 1981)
 Is this a paradox?
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Metabolic genes are more expressed
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High retention of metabolic genes: why?
 Retention of metabolic genes is best explained
by selection for gene expression
 Although the loss of individual enzyme genes should generally
be neutral, each successive loss will be more and more
counter-selected. For instance in a linear pathway:
J

J0
1
p
1   CiJ0
i 1
 Ultimately this would result in half of the flux, which should be
strongly counter-selected in general
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 Metabolic fluxes are not proportional to enzyme activities
 They typically show a hyperbolic dependency
 Most enzymes have low control on flux
 Summation theorem
n
C
i 1
J0
i
1
Kacser & Burns 1981, Genetics 97:639-666
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 Therefore little selective pressure is expected on the dosage of
individual enzyme genes
 This a classical explanation of the recessivity of metabolic defects
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Ongoing dynamics of gene inactivation
 49% loss of duplicated genes following the recent WGD
 Contrary to initial expectation, metabolic genes are more
retained than other genes: 42% gene loss
( n = 1,144 metabolic genes, P-value < 10-3 )
 Why?
Gout, Duret & Kahn 2009, Mol. Biol. Evol., in press
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50%
45%
40%
Gene frequency
35%
30%
25%
20%
15%
10%
5%
0%
1
2
3
4
5
6
7
8
Number of genes within ohnologon
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b. Intermediary WGD
a. Recent WGD
100%
100%
Gene loss frequency
88% *
80%
80%
60%
60%
40%
54% **
40%
44%
42%
20%
0%
0%
D. Kahn, COSTEX model
2 genes or more
63% **
40%
20%
1 gene before WGD
78%
76%
1 gene before WGD
2 genes or more
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1.2
Relative fitness
1.0
0.8
0.6
0.4
0.2
0.0
0
0.2
0.4
0.6
0.8
1
1.2
Relative dosage or expression
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P. tetraurelia : the best model organism for studying
WGDs

P. tetraurelia : 3 successive WGDs with different loss rates
(Aury et al, 2006)
92 %
76 %
49 %
D. Kahn, COSTEX model