metabolic control theory and the genetics and evolution of metabolic fluxes umr de génétique...

Metabolic Control Theory and the genetics and evolution of metabolic

fluxes

UMR de Génétique Végétale, INRA/UPS/CNRS/INA PG

Ferme du Moulon, 91190 Gif-sur-Yvette, France

[email protected]

Christine Dillmann, Julie Fievet, Sébastien Lion, Frédéric Gabriel, Grégoire Talbot, Delphine Sicard, Dominique de Vienne

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 traitsMost phenotypic traits …

Growth rate, flowering date, fruit pH, behaviour traits,

morphological traits, blood pressure, metabolic flux,

enzyme activity, mRNA/protein concentrations, etc.

« Quantitative » genetics

A

0

1

2

3

4

5

6

7

150 160 170 180 190 200Taille (cm)

N

… Display a continuous variation within populations :

Continuous variation can be maintained by independent segregation of multiple factors. George Udny Yule, 1902.

G. J. Mendel, 1865

« Recherche sur les hybrides d’autres plantes »

A

A B

B a

a b

bx

A

a b

B

F2

aabb

Aabb

aaBb

AaBb

aaBB

AAbb

AABb

AaBB

AABB

0123456N

0 1 2 3 4 Number of«Capital letter » alleles

E1 E2 Ej En

X0 S1 … Sj1 Sj … Xn

Enzymes

The “genotype” : all the genes that determine enzyme activities(concentrations and kinetic parameters, genetically variable)

The metabolic fluxes as model quantitative traits

The “phenotype” : the flux

Kacser H. and Burns J.A., 1981. The molecular basis of dominance. Genetics, 97, 639-666.

E1 E2 Ej Ej+1 En

Sn-1Sj…S1S0 Sn…En-1

Stationary phase : v1 = v2 = … = vj = … = vn = J

Kacser and Burns, 1973 Heinrich and Rappoport, 1974

Metabolic control theory (1)

Michaelis-Menten enzymes

Enzymes far from saturation

)/()/(//1

)/()/(1max

11

1max

eqiiimiimiimi

eqiiimii KSSKV

KSKS

KSSKVv

Enzyme concentrations are independent

E1 E2 Ej Ej+1 En

Sn-1Sj…S1S0 Sn…En-1

At stationary phase : v1 = v2 = … = vj = … = vn = J

Kacser and Burns, 1973 Heinrich and Rappoport, 1974

n

jj

n

n

E

KS

S

J

1

,00

1

Metabolic control theory (2)

AjKinetic parameters :1,0 j

M

catK

K

k

j

j

Enzyme efficiency : Ej

Enzyme cellular concentration Qj

1,0

max

jM

KK

V

j

j= Aj Qj

Metabolic control theory (3) : genetically variable parameters

n

jj

n

n

E

KS

S

J

1

,00

1

Genetic variability of kinetic parameters

- Few in vivo data

- Slightly variable

Wang & Dykhuisen, 2001. Pathway of gluconate metabolism in E. coli. Evolution, 55:897.

fba1

IPGS

DS

Num

ber

of

mole

cule

s p

er

cell

Genetic variability of enzyme concentrations

- Highly variables

Fiévet et al, 2004

Flu

x J

Qj or Aj or Ej = Qj x Aj

Jmax

n enzymes

1 enzyme

Relationship between enzymes and flux : independent enzymes

• 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

n

jj

n

n

E

KS

S

J

1

,00

1

Experimental validation : in vivo

Kacser and Burns, 1981. Genetics 97:639

Relationship RubisCO-photosynthesis

A typical example: dependence of carbon assimilation flux on rubisco levels in transgenic tobacco plants.

Laurer et al, Planta 190 332-345 (1993).

Experimental validation : in vitro

glucose fructose 1,6 bisP

GAP

DHAP

glycérol 3 P

NADH

NAD+

GPI FBA

TPI

Créatine-P + ADP Créatine + ATPCréatine kinase

ATP

ADP

PFK1

ATP

ADP

HKglucose 6 P fructose 6 P

First part of glycolysis

Julie Fievet et Gilles Curien

Temps

Concentration

du NADH

Etat stationnaire

Mixing enzymes, substrates, cofactors

EnzymesHXK+PGI+PF

K+FBA+TPI+G3

DH+CK

SubstratesGlucose+Creatine P+NADH+buffer

ATP

One tube one «genotype»

Experimental validation

HXK concentration (µM)

Each enzyme vary at a turn, the other being kept constant

= Titration curves

• 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

Complex equationsComplex equations

Many parametersMany parameters

Estimation of kinetic parameters : explicit modelling

Estimation of kinetic parameters : MCT-based modelling

i iiii iii SpQSApQA

SJ

11

1 Ai composite activity parameterpi dispensability

ppii=0=0ppii≠0≠0

J0

Jmax

0max

max0

ˆii

iii JJ

JJpS

i

j ij

refi

i pS

Jn

J

n

QAS ˆ

1111ˆ

maxmax

The maximum value for the flux is estimated from titration curves :

Qref Jmax J0 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 Activity parameters are estimated “in systemo”. They are different from what can be estimated on isolated enzymesfrom what can be estimated on isolated enzymes

The global equation can be used to predict the flux for other enzyme The global equation can be used to predict the flux for other enzyme concentrations :concentrations :

i iii

prédit

pSQAS

J

ˆˆ1

1

Predicting the flux

Fievet et al, submitted

Predicted flux (µM/s)

Flux m

easu

red in v

itro

(µM

/s)

r = 0,94

Testing the predictor for the flux on 122 genotubesTesting the predictor for the flux on 122 genotubes

Fievet et al, submitted


(1) Based on MCT, we validated a simple model which describes the relationship between flux and enzyme concentrations

i iii pSQAS

J

ˆˆ1

1

(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

Genetical consequences of ~hyperbolic relationships : dominance

- Most deleterious mutations are recessive

- There is ~ additivity between highly deleterious mutations

Three observations

- There is ~ additivity between slightly deleterious mutations

- 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.

Two hypothesis to explain dominance

Dominance : Fisher’s model does not work

Population genetics models : mutations are eliminated before they become recessive.

Mutations in Chlamydomonas reinhardtii (Orr, 1991).

Recessive mutations occur in Chlamydomonas as frequently as in drosophila

Dominance : Fisher’s model does not work

Dominance

Ei

Flux

A1A1 A1A2 A2A2

Kacser H. and Burns J.A., 1981. The molecular basis of dominance. Genetics, 97, 639-666.

Ei

Flux

Weak dominance

Dominance : S. Wright was right

Généralisation : several variables enzymes

E. Coli - Dykhuisen et al., 1987, Genetics, 115, 25

Flu

x

Generalization : metabolic model for heterosis

i ii iii

hybrid

Levure

Huître

P1 Homozygous line

Maïs

F1 hybrid

Increased vigorF1 > (P1 ,P2 )

P2 Homozygous line

J

Ej

Ei

Ej

Ei

Line 1 x Line 2 Hybrid F1

Metabolic heterosis due to dominance at different loci

JP1

JP2

Heterosis in vitro

0%

20%

40%

60%

80%

100%

dis01 01*12 dis12

TPI

FBA

PFK

PGI

HXK

Tube1

Tube 2

Tube (1+2)/2

0,00

1,00

2,00

3,00

4,00

5,00

6,00

7,00

8,00

9,00

dis01 01*12 dis12

Flux

Simulations

Fievet et al, in prep


(4) Dominance and heterosis arise as emergent properties of metabolic systems

(5) Heterosis can be explained by antagonistic epistatic relationships between enzymes

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 VienneDominique de Vienne

Bruno BostBruno Bost

Julie FiévetJulie Fiévet

Frédéric GabrielFrédéric Gabriel

Sébastien LionSébastien Lion

Delphine SicardDelphine Sicard

Grégoire TalbotGrégoire Talbot

Gilles CurienGilles Curien

Olivier MartinOlivier 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 background

EA1 EB1EB2

EA2

Enzyme A Enzyme B

sJ

A1B2

A2B1

A1B1

A2B2

Flux

Heterosis and epistasis

Tryptophane

flux

Synergistic epistasis in tryptophane metabolic pathway

Niederberger et al., 1992, Biochem. J. 287, 473.

-2-1.5

-1-0.5

00.5

11.5

22.5

33.5

4

-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Epistasis index

Antagonistic SynergisticAdditivity

I = 1

Jhyb J

JH =

Enzyme A Enzyme B

sJ

A1B2

A2B1

A1B1

A2B2

Heterosis and epistasisH

ete

rosi

s in

de

x

Fievet et al, in prep

Autres axes de recherche

La concentration d’enzymes allouée à une chaîne est nécessairement finie ( « compétition » corrélations négatives)

Corrélations physiologiques, positives ou négatives

Matrice n x n des Ej/Ei Etotal fixé, ou fonction de coût

1- Les concentrations des enzymes ne sont pas nécessairement indépendantes

Autres axes de recherche

2- Comment agit la sélection pour maximiser/optimiser un flux ?

- Approche expérimentale : variabilité des paramètres enzymatiques et évolution expérimentale chez la levure (modèle : glycolyse)

- Evolution des flux avec ou sans contraintes sur les concentrations d’enzymes.

J

Ej

Red curve: No co-regulation

Blue curves:Co-regulations

metabolic control theory and the genetics and evolution of metabolic fluxes umr de génétique...

Documents

j q j metabolic control

flux j q j

j j max n enzymes

j kacser

e j e n x

s j x n enzymes

independent slide

pathway slide