classification of elementary flux modes in mitochondrial energetic metabolism (« physiopathologie...

CLASSIFICATION OF ELEMENTARY FLUX MODES IN MITOCHONDRIAL ENERGETIC METABOLISM

(« Physiopathologie Mitochondriale », (« Physiopathologie Mitochondriale », INSERM U688 & Université de BORDEAUX 2)INSERM U688 & Université de BORDEAUX 2)

Marie BEURTON-AIMAR Marie BEURTON-AIMAR

Charles LALÈS (Dcrt)Charles LALÈS (Dcrt)

Jean-Pierre MAZAT Jean-Pierre MAZAT [email protected]

Nicolas PARISEY (Dcrt)Nicolas PARISEY (Dcrt) Sabine PÉRÈS (Dcrte)Sabine PÉRÈS (Dcrte)

- Bernard KORZENIEWSKI - Bernard KORZENIEWSKI (Université de Krakow)(Université de Krakow)

- Christine NAZARET- Christine NAZARET(ESTBB et MAB- Bordeaux 1)(ESTBB et MAB- Bordeaux 1)

- Christine REDER - Christine REDER (MAB- Bordeaux 1)(MAB- Bordeaux 1)

- Pascal BALLET & Abdallah ZEMIRLINE - Pascal BALLET & Abdallah ZEMIRLINE (Université de Brest)(Université de Brest)

- Frank MOLINA & Pierre MAZIÈRE- Frank MOLINA & Pierre MAZIÈRE (CNRS Montpellier)(CNRS Montpellier)

MITOSCOPEMITOSCOPE

MITOCHONDRIA

J.-P. Mazat Jena March 2005

SYMBIOTIC ORIGIN OF MITOCHONDRIASYMBIOTIC ORIGIN OF MITOCHONDRIA

Mitochondria are ancient bacteria. They host

their own genome, their own ribosomes and

a metabolism of procaryotic origin.

AAncncient cellient cell

Bacteria ancestryBacteria ancestryof mitochondriaof mitochondria

DNDNAA

NucleusNucleus

mtDNmtDNAA

mitochondrimitochondriaa


Different types of mitochondria

Epithélium Spermatozoo

Butterfly’sAdiposetissue

Rat heart

Mouse Heart

Cortico-surrénales


Mitochondrial networkFragmentation


Oxidative Phosphorylation and mitochondrial genetics

Complexe I

Succinate

Respiratory chain and ATP synthase Functions of mitochondria

ATP synthesis.

NADH reoxidation

Metabolism

Ca2+ accumulation

Heat production

Free radicals production

Apoptosis

ADN mt ADN nucl.

Complexe I 7 >30

Complexe II 0 4

Complexe III 1 10

Complexe IV 3 10

Complexe V (ATPase) 2 9

Double genetic origin

Sous-unités codées par


DECOMPOSITION OF THE MITOCHONDRIAL ENERGETIC

METABOLISM IN ELEMENTARY MODES


Succinate

Fumarate

H

H

H

+

+

+

+

H

n

n‘

n

n‘

S

(André CASSAIGNE, Rachid OUHABI & Stéphane LUDINARD)

FAMN FeS

UQb565, b566 FeS ; C1

Cu1 ; Cu2 a ; a3

F0 F1

C I

C II

C III

C IV

DHODH

FAD

Q

G3-PDH

NADH

NAD

Dihydrorotate

Orotate

FADH2

3GP

DHAP

2e2e

2e

2e

2e

Cyt c

2e

O + 2H1/2 2+

H O2

H

H

H

H

H H

n

n

n‘

n‘

S

++

+

+

+

+

ATPATP

ADP ADP 3-3-

4- 4-

Pi Pi

HH+ +

28

2930

31

32

33

34

35

TP

Mitochondrial Metabolism

Citrate

Isocitrate

α-CÉtoglutarate

Succinyl-CoASuccinate

Fumarate

Malate

OxaloacÉtate

Pyruvate

Pyruvate

AcÉtyl-CoA

ADP + Pi

2

NAD

NADH + CO2

H O2

NAD

NADH + CO2

NAD

NADH + CO

GDP + Pi

GTPH O

2

FAD

FADH2

NAD

NADH2

H O2

CitrateMalate

GDP + Pi

GTP

Acyl-CoA (Cn)

Trans enoyl CoA

β-OH-acyl-CoA

β-cÉtoacyl-CoA

Acyl-CoA (n-2C)

AcÉtyl-CoAPropionyl-CoA

MÉthylmalonyl-CoA

En fin d’hÉlice,si nC est impair

ATP + CO2

AMP + PPi

Hs-CoA

Acyl-CoA (>12C) Acyl-CoA (<12C)

Carnitine

Carnitine

Hs-CoA

AcÉtyl-CoA

Carnitine

AcÉtyl-CoA

AcÉtoacÉtyl-CoA

HO mÉthylGlutaryl CoA

AcÉtoacÉtate

HO Butyrate

Hs-CoA

AcÉtyl-CoA

α-CÉtoglutarate Glutamate

NAD NADH

NH3

Carbamyl-P

Citrulline

Citrulline Ornithine

Ornithine

2 ATP + CO2

2 ADP + Pi

Argininosuccinate Arginine UrÉe

Aspartate + ATP

AMP + PPi

Malate

H O2

Pi

18

19

20

21

22

23

Fumarate

SuccinatePi

2-

α-CÉtoglutarateH +

+H

α-CÉtoglutarate

Malate

MalatePi

2-

SuccinateMalate

GlutamateAspartate

Ca

Ca2+

2+

+

Cplx TIM22

CplxOXA1

ATP

8

8

8

1313

13

9

1010

1010

109

9

9

9

9

12

22

54

17

17

2323

44

44

70

70

E

40567

J.-P. Mazat Montpellier Fev 2005

WHY A DECOMPOSITION OF THIS NETWORK

IN ELEMENTARY FLUX MODES ?

-To compare mitochondrial metabolism in different tissues or organisms. How is it possible to obtain different types of mitochondria with the same metabolism ?


-To point out specific prevailing pathways, which could be strongly represented in particular tissues and give them their specificity.

- To unveil those mutations, which can be tolerated,those, which cannot and to understand why.

R6i : Pyr + CO2 + ATP = OAA + Pi + ADP .R7i : Pyr + NAD + CoA = ACoA + NADH2 + CO2 .R8i : OAA + ACoA + H2O = Cit + CoA .R9 : Cit = Isocit .R10i : Isocit + NAD = Akg + NADH2 + CO2 .R11i : Akg + NAD + CoA = SucCoA + NADH2 + CO2 . R12 : SucCoA + Pi + ADP = Succ + CoA + ATP .R13 : Succ + FAD = Fum + FADH2 .R14 : Fum + H2O = Mal .R15 : Mal + NAD = OAA + NADH2 . R16 : Akg + NADH2 = Glu + NAD .R17 : Ala + NAD + H2O = Pyr + NH3 + NADH2 .R18 : OAA + Glu = Asp + Akg .R20i : 2 ATP + NH3 + CO2 + H2O = 2 ADP + Pi + CarbamoylP .R21 : CarbamoylP + Ornit = Pi + Citrulline .R25i : 2 ACoA = CoA + AcetoACoA .R26 : ACoA + H2O + AcetoACoA = HmethylGlutCoA + CoA .R27 : HmethylGlutCoA = ACoA + Acetoacetate .R28 : Acetoacetate + NADH2 = Hbutanoate + NAD .R1i : NADH2 + 10 H = NAD + 10 H_ext .R2i : FADH2 + 6 H = FAD + 6 H .R3 : ADP + Pi + 3 H_ext = ATP + 3 H .R4i : H_ext = H .R30 : Acylcarnitine + CoA = Carnitine + AcylCoA .R31i : AcylCoA + 7 FAD + 7 NAD + 7 CoA + 7 H2O = 7 NADH2 + 7 FADH2 + 8 ACoA .T1 : Cit + H + Mal_ext = Mal + Cit_ext + H_ext .T2 : AKG_ext + Mal = Mal_ext + Akg .T3 : AcylC_ext + Carnitine = Carnitine_ext + Acylcarnitine .T4 : ADP_ext + ATP + H_ext = ADP + ATP_ext + H .T5 : Pi_ext + H_ext = Pi + H .T6 : Pyr_ext + H_ext = Pyr + H .T7 : Mal + Pi_ext = Pi + Mal_ext .T8 : Citrulline + Ornit_ext = Citru_ext + Ornit .T9 : Mal + Asp_ext = Mal_ext + Asp .T10 : Hbutanoate = HB_ext .T11 : AA_ext = Acetoacetate .T12 : Asp + Glu_ext + H_ext = Asp_ext + Glu + H .T13 : Mal + Succ_ext = Mal_ext + Succ .T14 : Asp + Succ_ext = Asp_ext + Succ .T15 : Asp + AKG_ext = Asp_ext + Akg .T16 : Asp + Pi_ext = Asp_ext + Pi .T17 : Succ + AKG_ext = Succ_ext + Akg .T18 : Succ + Pi_ext = Succ_ext + Pi .T19 : Akg + Pi_ext = AKG_ext + Pi .T20 : Glu_ext + H_ext = Glu + H .

BIOCHEMICAL REACTIONS INBIOCHEMICAL REACTIONS INENERGETIC ENERGETIC MITOCHONDRIAL MITOCHONDRIAL

MMEETABOLISMTABOLISM


45 reactions including 20 transporters

31 metabolites

ENERGETIC MITOCHONDRIAL METABOLIC NETWORK


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STOICHIOMETRY MATRIX OF THE ENERGETIC MITOCHONDRIAL METABOLIC

NETWORK

matrix dimension r31 x c45

The following line indicates reversible (0) and irreversible reactions (1)

1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

rows and columns are sorted as declared in the inputfile

N =


ELEMENTARY FLUX MODES

435 324 elementary flux modes ! *

How to make things clear ?

Interest ?

* With the help of Stefan KlamtJ.-P. Mazat Jena March 2005

Why such a huge number ?

- many exchangers

- several non-equivalent way to maintain the steady-state of « currency metabolites ».

EXAMPLE OF ELEMENTARY FLUX MODE (1)

T17 – T18 – T19


EXEMPLE OF ELEMENTARY FLUX MODE (2)8R8-8R10-8R11-4R20-16R25-5R31-8R9-8R12-(-35)R13-(-35)R14-8R15-(-43)R17-4R21-16-R26-16-R27-16R28-5R30-5T3-(-43)T5-4T8-(-43)T9-16T10-(-43)T12-43T18-43T20

4343

16

16

16

16

16

43

43

43

43

H+

5

5

543

43

8

88

8

88

35

35

43

4343

43

444

J.-P. Mazat Jena March 2005 H

+

TOP 10 OF REACTIONS

R6

T20

R8

T3

R31

R30

T6

R14

R13

T4

Pyruvate carboxylase

Glutamate carrier

Citrate synthase

Acylcarnitine translocase

-oxydation of fatty acids

Acylcarnitine transferase II

Pyruvate carrier

Fumarase

Succinate deshydrogenase

ATP/ADP Translocator

333 737

300 052

290 389

278 232

278 232

278 232

274 024

246 041

246 041

245 698

STEP NAME NUMBER of Elem. Modes


CLUSTERING ACCORDING TO « CURRENCY METABOLITE » (1)

FAD/FADH2 : R13 – R2 + 7 R31 = 0

NAD/NADH2 : R7 + R10 + R11 + R15 – R16 + R17 – R28 – R1 + 7 R31 = 0

ADP/ATP : -R6 + R12 – 2 R20 + R3 – T4 = 0

CoA : R7 – R8 + R11 – R12 – R25 – R26 + R30 + 7 R31 = 0

Pi : -R6 + R12 6 R20 – R21 + R3 – T5 – T7 – T16 – T18 – T19 = 0

H+ : 10 R1 + 6 R2 – 3 R3 – R4 + T1 – T5 – T6 – T12 – T20 = 0


CLUSTERING ACCORDING TO « CURRENCY METABOLITE » (2)

FAD/FADH2 :

NAD/NADH2 :

ATP/ADP :

CoA :

Pi :

H :

542

7 052

4 165

927

51 281

9 236

Motifs« Currency metabolite »


CONCLUSIONCONCLUSION

Analysis of a network in terms of elementary flux modes modes :- Combinatory explosion of the number of elementary modes.- Usefulness ?-Thermodynamic considerations could decrease the number of elementary

modes (metabolite concentrations outside mitochondria will give gradients)

- Kinetic considerations could considerably decrease the number

of elementary modes actually used in a given type of mitochondria.

Metabolism organisation :-are in vivo only some elementary used depending on the cell type ?- or would the metabolism a functioning actually be this mess,

whose the huge number of elementary flux modes give an idea ? J.-P. Mazat Jena March 2005

Important occurrence of some enzymes or exchangers :

pyruvate carboxylase; glu and pyr carriers,…

Implication for mitochondrial diseases

There are less molecule in the cellThere are less molecule in the cell

than elementary modes …..than elementary modes …..

Is it possible that one metabolite participate to all elementary modes in a mito ?

- 500 000 elementary modes = 500 000 true molecules

A mitochondrion is a cube of 1 µm, which gives a volume of 1µm3 = 1 dm3 . (10-5)3 = 10-15 l.

500 000 true molecules = 500 000/6. 10-23 moles 100 000.10-23 = 10-18 moles.

Thus the concentration of this metabolite should have to be :

10-18 moles / 10-15 l = 1 mM

- Kacser, H., Burns, J.A., The control of flux, Symp. Soc. Exp. Biol. 32 (1973) 65-104.

- Heinrich, R., Rapoport, T.A., A linear steady-state treatment of enzymatic chains. General properties, control and effector strength, Eur. J. Biochem. 42 (1974), 89-95.

Kacser, H. and Burns, J.A. 1980. The molecular basis of dominance. Genetics 97: 639-666. A seminal paper answering the long-standing riddle concerning the equivalence of heterozygote with the normal homozygote.

- Reder, C., Metabolic control theory: a structural approach, J. Theor. Biol. 135 (1988) 175-201.

- Groen AK, Wanders RJA, Westerhoff HV, Van der Meer R and Tager JM, Quantification of the contribution of various steps to the control of mitochondrial respiration, J. Biol. Chem. 257 : 2754-2757.

-Tager JM, Wanders RJA, Groen AK, Kunz W, Bohnensack R, Kuster U, Letko , Bohme G, Duszynski J, Wojtczak L : Control of mitochondrial respiration FEBS Lett 151 1-9, 1983.

- David Fell : Understanding the control of metabolism Protland Press 1997, London and Miami.

-Reinhart Heinrich and Stefan Schuster (1996) : The regulation of cellular systems Chapman & Hall.

-Schuster S, Hilgetag C, Woods JH, Fell DA. Reaction routes in biochemical reaction systems: algebraic properties, validated calculation procedure and example from nucleotide metabolism. J Math Biol. 2002;45:153-81

-Papin JA, Stelling J, Price ND, Klamt S, Schuster S, Palsson BO. Comparison of network-based pathway analysis methods. Trends Biotechnol. 2004;22:400-5.

BIBLIOGRAPHIEBIBLIOGRAPHIE

mtDNAtRNA

mRNA

} Subunits of Respiratory Chain

complexesVO2 VATP

MODEL OF mtDNA EXPRESSIONMODEL OF mtDNA EXPRESSION

Respiratory Complex

VO2

WTmtDNA (WTmRNA)

WTmRNA (Complex)

WTmtDNA

VO2

Seuil tARN mt

+ +

100806040200

0

20

40

60

80

100

WTmtDNA (WTmRNA)

WTmRNA (Complex)

MODEL OF mtDNA and of mt-mRNA MODEL OF mtDNA and of mt-mRNA EXPRESSIONEXPRESSION

WTmRNA = 2 * WTmtDNA

KmtDNA + WTmtDNA

(KmtDNA = 100)

Complex = 2 * WTmRNA

KmRNA + WTmRNA

(KmRNA = 100)

THRESHOLD in tRNATHRESHOLD in tRNA

WT-tRNA = 2 * WTmtDNA

KmtDNA + WTmtDNA (KmtDNA = 100)


KmRNA + WTmRNA

(KmRNA = 100)

If tRNA >= tRNA0


KmRNA + WTmRNA

(KmRNA = 100)

If tRNA < tRNA0

2 * WT-tRNA

Km-tRNA + WT-tRNA

(Km-tRNA = 100)

10080604 02000

20

40

60

80

100

Respiratory Complex

Cplxth

VO2th

VO2

Slope = Control Coefficient

MODEL OF COMPLEX EXPRESSION IN FLUXMODEL OF COMPLEX EXPRESSION IN FLUX

1008060402000

20

40

60

80

100

WTmtDNA

VO2

MODEL OF COMPLEX EXPRESSION IN FLUXMODEL OF COMPLEX EXPRESSION IN FLUX

2ème Solution2ème Solution

Traiter la synthèse des protéines et les régulations par des systèmes discrets multivalués :

MetaReg par Ron Shamir & Gat-Viks (Tel-Aviv) :

-Considèrent différents niveaux successifs en remontant de la voiemétabolique (voie de biosynthèse de la lysine chez S. cerevisiae) :

Ac. Am. Ext. / Ac. Am. Perméases / Ac. Am. Int. / Trpt. Comp. N / Trad. Prot. / Cont. Transcription / Enz. / Voie Métabolique

-Les espèces à ces différents niveaux constituent les nœuds du réseau qui sont reliés par des interactions qui sont exprimées selondes tableaux comme ci-dessous :

1

2

3

12

3

00

0

10

1

11

2Etc.

3 - MULTI-AGENTS MODELS (FERBER)

- Agents are entities, objects for which distinctive properties are described :Ex: enzymes, metabolites,…...

- Roles : function representation. Ex : interactions between enzymes andmetabolites, probability of reaction, etc…..

- A group is defined by a set of roles between agents, a graph of interactions and a language or a protocol of interactions.

Collaboration Pascal Ballet et Abdalla Zermiline Université de Brest.

Example : Michaelis - Henri equation:

S + E ES E + P

- E, ES, S and P are agents.

Roles : agent movingcollision and reaction probabilities

System free to evolve.S + E ES E + P

3ème Solution : Réseaux de Petri hybrides3ème Solution : Réseaux de Petri hybridesHFPN (Hybrid Functional Petri Net)HFPN (Hybrid Functional Petri Net)

H. Matsuno et al. : Biopathways Representation and Simulation on Hybrid Functional Petri Net. (http://www.GenomiObjet.Net)

m1

3

Deux sortes de réseaux :

Discontinus : Continus :

m2

m3

21

T

t =1.0If m1 2 and m2 3

P1

P2

P3

m1

m2

m3

T

v = m1 - m2 / 10

P1

P2

P3

Permet une modélisation mixte continu-discontinu avec le même type de représentationPermet la modélisation en même temps (de manière intégrée)des voies métaboliques (glycolyse) et des réseaux génétiques (opéron lactose).

PROJET : MITOCHONDRIE VIRTUELLEMarie Beurton-Aimar, Jean-Pierre Mazat, Christine Nazaret, Nicolas Parisey

et Sabine Pérès

1 - Analyse des modèles existant des ox-phos : .Article et mise sur le web juin 2002 avec aide à l’utilisation des différents modèles. . Application aux courbes de seuil expériemntales (coll. TL)

2 - Modélisation du métabolisme mitochondrial global :Ox-phos, cycle de Krebs, oxydation des acides gras, cycle de l ’urée,….

3 – Construction d’une base de donnée mitochondrieà l’aide du langage d’annotation des processus biologiques Bio. (Collaboration Frank Molina et Pierre Mazières, Montpellier)

4 – Exploration de différentes méthodes de modélisation . Modes élémentaires. . Réseaux hybrides ?

MATRICE DE STOECHIOMÉTRIE - - EXEMPLE 2

X1

V1

V3

V2

N = [ 1 -1 -1 ]V1

V2

V3

= V1 – V2 – V3

dX1

dt

etdX

dt= N . V avec :

dX

dt=

dX1

dtV = =

II

LE CONTRÔLE DES OXYDATIONS PHOSPHORYLANTES

Complexe IComplexe I

CoQCoQ

FAD + 2 FeS centersFAD + 2 FeS centers

Cyt bCyt b FeSFeS Cyt cCyt c 11(Rieske(Rieske))

Complexe IIIComplexe III

Complex IIComplex II

Cyt cCyt c Cyt aCyt a Cyt aCyt a33

Complexe IVComplexe IV( Cytochrome c Oxidase)( Cytochrome c Oxidase)

RotenoneRotenone

AntimycineAntimycineKCNKCN

CHAÎNE RESPIRATOIRECHAÎNE RESPIRATOIRE

NADHNADH

FMN + 5 FeS centersFMN + 5 FeS centers

PyruvatePyruvateGlutamateGlutamate

Succinate, Fatty AcidsSuccinate, Fatty Acids

OO22 HH22OO

NADNAD


KCN µMKCN µM4030201000

Inhibition par le KCN de la Cytochrome-Inhibition par le KCN de la Cytochrome-c-Oxidase et de la vitesse de respirationc-Oxidase et de la vitesse de respiration

0

20

40

60

80

100 A

Letellier et al. (1994) The kinetic basis of threshold effects observed in mitochondrial diseasesLetellier et al. (1994) The kinetic basis of threshold effects observed in mitochondrial diseasesBiochem. J. Biochem. J. 302302 171-174. 171-174.

% C

OX

Act

ivit

y o

r V

O%

CO

X A

ctiv

ity

or

VO

22

% inhibition de la cytochrome c oxidase

0

20

40

60

80

100 B

1008060402000

% R

esp

irat

ory

rat

e (V

O ) 2


COEFFICIENTS DE CONTRÔLE DES OXYDATIVE PHOSPHORYLTION

DANS LES MITOCHONDRIES DE MUSCLE

Pyruvate transport 0.1 0.09

Complex I 0.1 0.15

Complex III 0.26 0.19

Complex IV 0.08 0.10

ATP Synthase 0.11 0.08

Translocase 0.16 0.14

Phosphate Carrier 0.10 0.12

Somme : 0.91 0.87

VATP VO2

COEFFICIENTS DE CONTRÔLE


EFFET DE SEUIL MÉTABOLIQUEdans le cadre de la théorie du contrôle du métabolisme

Le contrôle est partagéLe contrôle est partagé

CCii = 1 = 1

La plupart des coefficients La plupart des coefficients de contrôle sont faiblesde contrôle sont faibles..

Effet de seuilEffet de seuil..

FluxFlux

Étape Étape

InhibiteurInhibiteur

Faible coefficient de contrôleFaible coefficient de contrôle

CCii = = F/F/vvii i


GÉNÉTIQUE MITOCHONDRIALE

hérédité maternelle.

Hétéroplasmie de l’ADN mitochondrial

La proportion (heteroplasmie) de l’ADNmt mutépeut varier de 0 à 100 %


Activité COX

(50 biopsies)

0

2

4

6

0 5 10 15 20 25 30

Vite

sse

de

re

spira

tion

MISE EN ÉVIDENCE D’UN SEUILDANS LES PATHOLOGIES MITOCHONDRIALES


COURBES D’EFFET DE SEUIL MÉTABOLIQUECOURBES D’EFFET DE SEUIL MÉTABOLIQUEComplexe I and IIIComplexe I and III

ROSSIGNOL, R., MALGAT, M., MAZAT, J.-P and .LETELLIER, T., : . (1999) J. Biol. Chem. , 274: 33426-33432.


COURBES D’EFFET DE SEUIL MÉTABOLIQUECOURBES D’EFFET DE SEUIL MÉTABOLIQUEComplexe IV , ATP synt., Pi carrier, Pyr. Carrier, Complexe IV , ATP synt., Pi carrier, Pyr. Carrier,

ANTANT

ROSSIGNOL, R., LETELLIER, T., MALGAT, M., ROCHER, C. AND MAZAT, J.-P. (2000) : Biochem. J. 347 : ROSSIGNOL, R., LETELLIER, T., MALGAT, M., ROCHER, C. AND MAZAT, J.-P. (2000) : Biochem. J. 347 :

45-5345-53..J.-P. Mazat Montpellier Fev 2005

0,50,40,30,20,10,00

10

20

30

40

50

60

70

80

90

100

Complexe IComplexe III

Complexe IV

ATPase

ANT

Transport du Phosphate

Coefficients de Contrôle

Th

resh

old

val

ue

(% in

hib

itio

n o

f is

olat

ed s

tep

act

ivit

y)

y = 90,811 - 153,42x R^2 = 0,805

RELATION ENTRE LES COEFFICIENTS DE CONTRÔLE ET LES VLEURS DE SEUIL


classification of elementary flux modes in mitochondrial energetic metabolism (« physiopathologie...

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