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

Duplications in the Paramecium genome Aury et al., 2006, Nature 444:171-178

Three successive rounds of WGD

Gene content: 2 x 2 x 2  2

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

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

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

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

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

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

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)

Modelling the cost of expression Dekel & Alon, 2005, Nature 436:588-592 C(X) cost function X expression level k cost parameter M maximal capacity expression level expression cost M

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

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

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

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

Selection against loss of duplicated gene Fitness loss Optimal expression X0

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.

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

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

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

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?

Metabolic genes are more expressed

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

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

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

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

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 %