Metabolic Control Theory and the genetics and evolution
Metabolic Control Theory and the genetics and evolution of metabolic fluxes Christine Dillmann, Julie Fievet, Sébastien Lion, Frédéric Gabriel, Grégoire Talbot, Delphine Sicard, Dominique de Vienne UMR de Génétique Végétale, INRA/UPS/CNRS/INA PG Ferme du Moulon, 91190 Gif-sur-Yvette, France dillmann@moulon. inra. fr
Metabolic Control Theory and the genetics and evolution of metabolic fluxes - Metabolic fluxes as model quantitative traits and the relationship between genotype and phenotype - Experimental validation of the Metabolic Control Theory - The metabolic bases of dominance and heterosis - Evolution of enzyme concentrations in natural populations
« Quantitative » genetics Quantitative traits Most phenotypic traits … Growth rate, flowering date, fruit p. H, behaviour traits, morphological traits, blood pressure, metabolic flux, enzyme activity, m. RNA/protein concentrations, etc. … Display a continuous variation within populations :
G. J. Mendel, 1865 « Recherche sur les hybrides d’autres plantes » Aa. Bb aa. BB AAbb A A B B a a x A a B b b b N 6 5 4 3 2 1 0 Aabb AABb aa. Bb Aa. BB AABB aabb 0 1 2 3 4 Number of «Capital letter » alleles F 2 Continuous variation can be maintained by independent segregation of multiple factors. George Udny Yule, 1902.
The metabolic fluxes as model quantitative traits The “genotype” : all the genes that determine enzyme activities (concentrations and kinetic parameters, genetically variable) Enzymes E 1 E 2 X 0 S 1 … Ej Sj 1 Sj En … Xn The “phenotype” : the flux Kacser H. and Burns J. A. , 1981. The molecular basis of dominance. Genetics, 97, 639 -666.
Metabolic control theory (1) E 1 S 0 E 2 S 1 … Ej Ej+1 Sj … En-1 Sn-1 En Sn Michaelis-Menten enzymes Stationary phase : v 1 = v 2 = … = vj = … = vn = J Enzymes far from saturation Enzyme concentrations are independent Kacser and Burns, 1973 Heinrich and Rappoport, 1974
Metabolic control theory (2) E 1 S 0 E 2 S 1 … Ej Ej+1 Sj … En-1 Sn-1 En Sn At stationary phase : v 1 = v 2 = … = vj = … = vn = J Kacser and Burns, 1973 Heinrich and Rappoport, 1974
Metabolic control theory (3) : genetically variable parameters Enzyme efficiency : Kinetic parameters : Ej Aj Enzyme cellular concentration Qj = Aj Qj
Genetic variability of kinetic parameters - Few in vivo data - Slightly variable Wang & Dykhuisen, 2001. Pathway of gluconate metabolism in E. coli. Evolution, 55: 897.
IPG SDS Genetic variability of enzyme concentrations - Highly variables Number of molecules per cell fba 1 Fiévet et al, 2004
Relationship between enzymes and flux : independent enzymes Jmax m nzy es Flux J n e e 1 e m zy n Qj or Aj or Ej = Qj x Aj • non linear relationship between the flux and the concentration of on enzyme of the pathway • the flux tends asymptotically towards a maximum which depends on the concentrations of all the enzymes of the pathway
Metabolic Control Theory and the genetics and evolution of metabolic fluxes - Metabolic fluxes as model quantitative traits and the relationship between genotype and phenotype - Experimental validation of the Metabolic Control Theory - The metabolic bases of dominance and heterosis - Evolution of enzyme concentrations in natural populations
Experimental validation : in vivo Kacser and Burns, 1981. Genetics 97: 639
Relationship Rubis. CO-photosynthesis A typical example: dependence of carbon assimilation flux on rubisco levels in transgenic tobacco plants. Laurer et al, Planta 190 332345 (1993).
Experimental validation : in vitro First part of glycolysis GAP glucose HK glucose 6 P GPI fructose 6 P fructose 1, 6 bis. P FBA PFK 1 DHAP ATP TPI NADH ADP NAD+ glycérol 3 P Créatine-P + ADP Créatine kinase Créatine + ATP Julie Fievet et Gilles Curien Concentration du NADH Etat stationnaire Temps
Mixing enzymes, substrates, cofactors Enzymes HXK+PGI+PFK + FBA+TPI+G 3 D H+CK Substrates Glucose+ Creatine P+ NADH+ buffer ATP One tube one «genotype»
Experimental validation Each enzyme vary at a turn, the other being kept constant = Titration curves HXK concentration (µM) • non linear relationship between the flux and the concentration of on enzyme of the pathway • the flux tends asymptotically towards a maximum which depends ont the concentrations of all the enzymes of the pathway
Estimation of kinetic parameters : explicit modelling Complex equations Many parameters
Estimation of kinetic parameters : MCT-based modelling Ai composite activity parameter pi dispensability The maximum value for the flux is estimated from titration curves : Jmax pi=0 pi≠ 0 J 0
Predicting the flux Qref Jmax J 0 Spi SAi hxk 0, 1 18, 24 0 0 379, 93 pgi 0, 15 13, 27 0 0 520, 5 pfk 0, 29 17, 87 0 0 107, 02 fba 1, 54 18, 54 0 0 18, 54 tpi 0, 84 12, 61 10, 46 61, 35 59, 79 Activity parameters are estimated “in systemo”. They are different from what can be estimated on isolated enzymes The global equation can be used to predict the flux for other enzyme concentrations : Fievet et al, submitted
Flux measured in vitro (µM/s) Testing the predictor for the flux on 122 genotubes r = 0, 94 Predicted flux (µM/s) Fievet et al, submitted
Metabolic Control Theory and the genetics and evolution of metabolic fluxes (1) Based on MCT, we validated a simple model which describes the relationship between flux and enzyme concentrations (2) Composite kinetic parameters can be estimated « in vivo » from titration curves (3) It should also work for more complex networks like … S 1 E 2 E 5 S 3 S 2 E 4 E 3 S 4 S 6 E 8 E 7 E 6 S 5 S 7 E 9 E 10 S 8 … with one stable stationary state
Metabolic Control Theory and the genetics and evolution of metabolic fluxes - Metabolic fluxes as model quantitative traits and the relationship between genotype and phenotype - Experimental validation of the Metabolic Control Theory - The metabolic bases of dominance and heterosis - Evolution of enzyme concentrations in natural populations
Genetical consequences of ~hyperbolic relationships : dominance Three observations - Most deleterious mutations are recessive - There is ~ additivity between highly deleterious mutations - There is ~ additivity between slightly deleterious mutations
Two hypothesis to explain dominance - R. A. Fisher (1928, 1931, 1958) : «modifiers» of dominance relationship between alleles arise due to natural selection - S. Wright (1934) : dominance can be explained by the non linear genotype-phenotype relationship.
Dominance : Fisher’s model does not work Population genetics models : mutations are eliminated before they become recessive. Mutations in Chlamydomonas reinhardtii (Orr, 1991).
Dominance : Fisher’s model does not work Recessive mutations occur in Chlamydomonas as frequently as in drosophila
Dominance : S. Wright was right Flux Dominance Weak dominance A 1 A 1 A 2 A 2 Ei Kacser H. and Burns J. A. , 1981. The molecular basis of dominance. Genetics, 97, 639 -666. Ei
Flux Généralisation : several variables enzymes E. Coli - Dykhuisen et al. , 1987, Genetics, 115, 25
Generalization : metabolic model for heterosis Huître Maïs Levur e P 1 Homozygous line F 1 hybrid Increased vigor F 1 > (P 1 , P 2 ) hybrid P 2 Homozygous line i iii
Metabolic heterosis due to dominance at different loci Line 1 x Line 2 Hybrid F 1 Ej Ej J Ei Ei
Heterosis in vitro JP 2 Tube 1 Tube (1+2)/2 Tube 2 Flux JP 1 Simulations Fievet et al, in prep
Metabolic Control Theory and the genetics and evolution of metabolic fluxes (4) Dominance and heterosis arise as emergent properties of metabolic systems (5) Heterosis can be explained by antagonistic epistatic relationships between enzymes
Metabolic Control Theory and the genetics and evolution of metabolic fluxes - Metabolic fluxes as model quantitative traits and the relationship between genotype and phenotype - Experimental validation of the Metabolic Control Theory - The metabolic bases of dominance and heterosis - Evolution of enzyme concentrations in natural populations
Evolution of enzyme concentration under selection for increasing the flux W= Monte-Carlo simulations Analytical predictions Natural selection shapes the sharing out of the control of the flux Talbot et al, in prep
Dominique de Vienne Bruno Bost Julie Fiévet Frédéric Gabriel Sébastien Lion Delphine Sicard Grégoire Talbot Gilles Curien Olivier Martin
Heterosis and epistasis -A substitution at one locus changes the effects of a substitution at another locus -The effect of a substituion depends on the genetic Flux background EA 2 EA 1 EB 2
Heterosis and epistasis Synergistic epistasis in tryptophane metabolic pathway Tryptophane flux Niederberger et al. , 1992, Biochem. J. 287, 473.
Heterosis and epistasis J Heterosis index H= Jhyb J Antagonistic Additivity Fievet et al, in prep I = 1 Synergistic Epistasis index
Autres axes de recherche 1 - Les concentrations des enzymes ne sont pas nécessairement indépendantes Corrélations physiologiques, positives ou négatives La concentration d’enzymes allouée à une chaîne est nécessairement finie ( « compétition » corrélations négatives) Matrice n x n des Ej/ Ei Etotal fixé, ou fonction de coût
Autres axes de recherche 2 - Comment agit la sélection pour maximiser/optimiser un flux ? J Red curve: No coregulation - Evolution des flux avec ou sans contraintes sur les concentrations d’enzymes. Blue curves: Coregulations Ej - Approche expérimentale : variabilité des paramètres enzymatiques et évolution expérimentale chez la levure (modèle : glycolyse)
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