1. 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

2. 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

3. Duplications in the Paramecium genome
Aury et al., 2006, Nature 444:

4. Three successive rounds of WGD

5. Gene content: 2 x 2 x 2  2

6. Fate of genes after WGD
A brief introduction about Whole-Genome Duplications (WGDs)‏
ohnologon
WGD creates identical copies of all genes (ohnologs)‏

7. Fate of genes after WGD
A brief introduction about Whole-Genome Duplications (WGDs)‏
WGD creates identical copies of all genes (ohnologs)‏
Mutations lead to pseudogenization of some ohnologs

8. Fate of genes after WGD
A brief introduction about Whole-Genome Duplications (WGDs)‏
WGD creates identical copies of all genes (ohnologs)‏
Mutations lead to pseudogenization of some ohnologs

9. Fate of genes after WGD
A brief introduction about Whole-Genome Duplications (WGDs)‏
WGD creates identical copies of all genes (ohnologs)‏
Mutations lead to pseudogenization of some ohnologs
Finally, only a few pairs of genes are retained

10. Fate of genes after WGD
A brief introduction about Whole-Genome Duplications (WGDs)‏
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

11. Relationship between gene retention and gene expression
Frequency of gene retention
Data from Paramecium post-genomics consortium
Jean Cohen & coll.
Expression level (log2)

12. 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)

13. Modelling the cost of expression
Dekel & Alon, 2005, Nature 436:
C(X) cost function
X expression level
k cost parameter
M maximal capacity
expression level
expression cost M

14. Cost-benefit optimization
Cost: C(X)
Benefit : B(X)
expression level
fitness
expression cost Xo Xo
fitness
expression cost

15. The COSTEX model
Express fitness as a function of expression x relatively to optimum level X0

16. The COSTEX model
Approximate fitness around optimum X0 by Taylor expansion:
Therefore selection on expression can be quantified by:

17. Expression-dependent fitness1
fitness
Low X0
Medium X0
High X0
Loss of duplication
0.5 1
1.5
Relative dosage or expression X/Xo

18. Selection against loss of duplicated gene
Fitness loss
Optimal expression X0

19. Selection against pseudogene formation
Pseudogene formation after WGD entails a loss of fitness that can be expressed in the COSTEX model:
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.

20. 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:
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

21. 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

22. 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

23. 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?

24. Metabolic genes are more expressed

25. 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:
Ultimately this would result in half of the flux, which should be strongly counter-selected in general

27. Metabolic fluxes are not proportional to enzyme activities
They typically show a hyperbolic dependency
Most enzymes have low control on flux
Summation theorem
Kacser & Burns 1981, Genetics 97:

28. Therefore little selective pressure is expected on the dosage of individual enzyme genes
This a classical explanation of the recessivity of metabolic defects

29. 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

35. 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 %