1. 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, Gif-sur-Yvette, France

2. 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

3. « Quantitative » genetics
Quantitative traits
Most phenotypic traits …
Growth rate, flowering date, fruit pH, behaviour traits,
morphological traits, blood pressure, metabolic flux,
enzyme activity, mRNA/protein concentrations, etc.
… Display a continuous variation within populations :

4. « Recherche sur les hybrides d’autres plantes »
G. J. Mendel, 1865
AaBb
aaBB
AAbb 1 2 3 4 5 6 N
Number of
«Capital letter » alleles
Aabb
aaBb A B a b x  F2
AABb
AaBB
aabb
AABB
Continuous variation can be maintained by independent segregation of multiple factors. George Udny Yule, 1902.

5. The metabolic fluxes as model quantitative traits
E E Ej En
X0 S1 … Sj1 Sj … Xn
Enzymes
The “genotype” : all the genes that determine enzyme activities
(concentrations and kinetic parameters, genetically variable)
The “phenotype” : the flux
Kacser H. and Burns J.A., The molecular basis of dominance. Genetics, 97,

6. Stationary phase : v1 = v2 = … = vj = … = vn = J
Metabolic control theory (1) E1 E2 Ej
Ej+1 En
Sn-1 Sj … S1 S0 Sn
En-1
Michaelis-Menten enzymes
Stationary phase : v1 = v2 = … = vj = … = vn = J
Enzymes far from saturation
Enzyme concentrations are independent
Kacser and Burns, 1973
Heinrich and Rappoport, 1974

7. At stationary phase : v1 = v2 = … = vj = … = vn = J
Metabolic control theory (2) E1 E2 Ej
Ej+1 En
Sn-1 Sj … S1 S0 Sn
En-1
At stationary phase : v1 = v2 = … = vj = … = vn = J
Kacser and Burns, 1973
Heinrich and Rappoport, 1974

8. Metabolic control theory (3) : genetically variable parameters
Enzyme efficiency : Ej
= Aj Qj Aj
Kinetic parameters : Qj
Enzyme cellular concentration

9. Genetic variability of kinetic parameters
- Few in vivo data
- Slightly variable
Wang & Dykhuisen, Pathway of gluconate metabolism in E. coli. Evolution, 55:897.

10. Number of molecules per cell
fba1
IPG
SDS
Genetic variability of enzyme concentrations
- Highly variables
Number of molecules per cell
Fiévet et al, 2004

11. Relationship between enzymes and flux : independent enzymes
Jmax
n enzymes
Flux J
1 enzyme
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

12. 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

13. Experimental validation : in vivo
Kacser and Burns, Genetics 97:639

14. Relationship RubisCO-photosynthesis
A typical example: dependence of carbon assimilation flux on rubisco levels in transgenic tobacco plants.
Laurer et al, Planta (1993).

15. Experimental validation : in vitro
First part of glycolysis
glucose
fructose 1,6 bisP
GAP
DHAP
glycérol 3 P
NADH
NAD+
GPI
FBA
TPI
Créatine-P + ADP
Créatine + ATP
Créatine kinase
ATP
ADP
PFK1 HK
glucose 6 P
fructose 6 P
Temps
Concentration
du NADH
Etat stationnaire
Julie Fievet et Gilles Curien

16. One tube  one «genotype»
Mixing enzymes, substrates, cofactors
Enzymes
HXK+PGI+PFK+
FBA+TPI+G3DH+CK
Substrates
Glucose+
Creatine P+
NADH+
buffer
ATP
One tube  one «genotype»

17. 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

18. Estimation of kinetic parameters : explicit modelling
Complex equations
Many parameters

19. Estimation of kinetic parameters : MCT-based modelling
Ai composite activity parameter
pi dispensability
The maximum value for the flux is estimated from titration curves :
pi=0
Jmax
pi≠0 J0

20. Predicting the flux Fievet et al, submitted
Qref
Jmax J0
Spi
SAi
hxk
0,1
18,24 0 
379,93
pgi
0,15
13,27
520,5
pfk
0,29
17,87
107,02
fba
1,54
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

21. Flux measured in vitro (µM/s)
Testing the predictor for the flux on 122 genotubes
r = 0,94
Flux measured in vitro (µM/s)
Predicted flux (µM/s)
Fievet et al, submitted

22. 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 … S1 S2 S3 S4 S5 S6 S7 S8 E1 E2 E3 E5 E4 E6 E7 E8 E9
E10
… with one stable stationary state

23. 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

24. 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

25. 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.

26. Dominance : Fisher’s model does not work
Population genetics models : mutations are eliminated before they become recessive.
Mutations in Chlamydomonas reinhardtii (Orr, 1991).

27. Dominance : Fisher’s model does not work
Recessive mutations occur in Chlamydomonas as frequently as in drosophila

28. Dominance : S. Wright was rightEi
Flux
A1A1
A1A2
A2A2 Ei
Flux
Weak
dominance
Kacser H. and Burns J.A., The molecular basis of dominance. Genetics, 97,

29. E. Coli - Dykhuisen et al., 1987, Genetics, 115, 25
Généralisation : several variables enzymes
E. Coli - Dykhuisen et al., 1987, Genetics, 115, 25
Flux

30. Generalization : metabolic model for heterosis
Huître P1
Homozygous line
Maïs
F1 hybrid
Increased vigor
F1 > (P1 ,P2 ) P2
i ii iii
hybrid
Levure

31. Metabolic heterosis due to dominance at different lociEj Ei
Line 1 x Line 2 Hybrid F1 J Ej Ei

32. Heterosis in vitro Fievet et al, in prep JP2 JP1 Simulations Flux
Tube1
Tube 2
Tube (1+2)/2
JP1
JP2
Flux
Simulations
Fievet et al, in prep

33. 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

34. 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

35. Evolution of enzyme concentration under selection for increasing the fluxW=
Monte-Carlo simulations
Analytical predictions
Natural selection shapes the sharing out of the control of the flux
Talbot et al, in prep

36. Dominique de Vienne
Bruno Bost
Julie Fiévet
Frédéric Gabriel
Sébastien Lion
Delphine Sicard
Grégoire Talbot
Gilles Curien
Olivier Martin

37. 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 background
Flux
EA2
EB2
EA1
EB1

38. Heterosis and epistasis
Synergistic epistasis in tryptophane metabolic pathway
Tryptophane
flux
Niederberger et al., 1992, Biochem. J. 287, 473.

39. Heterosis and epistasis
Jhyb J J
H =
Heterosis index
Antagonistic
Synergistic
Epistasis index
Additivity
I = 1
Fievet et al, in prep

40. 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

41. Autres axes de recherche
2- Comment agit la sélection pour maximiser/optimiser un flux ? J Ej
Red curve:
No co-regulation
Blue curves:
Co-regulations
- Evolution des flux avec ou sans contraintes sur les concentrations d’enzymes.
- Approche expérimentale : variabilité des paramètres enzymatiques et évolution expérimentale chez la levure (modèle : glycolyse)