The COSTEX model: a cost-benefit model relating gene expression and selection

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 444:171-178

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 expression cost expression level Dekel & Alon, 2005, Nature436:588-592 C(X) cost function X expression level k cost parameter M maximal capacity M

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

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. 1 Low X0 Medium X0 High X0 fitness Expression-dependent fitness Loss of duplication 0.5 1 1.5 0 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 etal., 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 97:639-666

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 = 1,144metabolic 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 %