introduction on metabolism & refresher in enzymology -...

Introduction on metabolism & refresher in enzymology

Daniel KahnLaboratoire de Biométrie & Biologie EvolutiveLyon 1 University & INRA MIA Department

Daniel.Kahn@univ-lyon1.fr

D. Kahn, Introduction on metabolism & refresher in enzymology

General objectives of the courseUnderstand the general behaviour of metabolic systemsAbility to model their dynamicsExpress how kinetic enzyme properties affect metaboliteconcentrations and fluxes Express how networks respond to changes in environmentExamine how experimental data may be used to identify a metabolic model Interpret these behaviours in terms of biological regulationGeneralize to signal transduction networks

D. Kahn, Introduction on metabolism & refresher in enzymology

Course prerequisitesKnowledge of enzyme kineticsLinear algebra

Matrix rank analysis, diagonalization, etc…

Familiarity with a mathematical package such as Scilab, Maple, R or Matlab

Dynamical systemsJacobian

Stability analysis

D. Kahn, Introduction on metabolism & refresher in enzymology

Course scheduleNovember 2 Introduction to Metabolic Control TheoryNovember 30 Regulation analysisNovember 23, December 7 & 14Morning 9am Practical on metabolic model and MCTAfternoon 2pm Theory

D. Kahn, Introduction on metabolism & refresher in enzymology 5

Outline

1. Introduction on metabolism2. Methods to investigate metabolism 3. Refresher of enzyme kinetics

D. Kahn, Introduction on metabolism & refresher in enzymology

1. What is metabolism?Life’s chemical factory

Typically several hundred reactions involving small molecules

BalancesNutrients and outputs

Energy

Redox…

Fast turnoverAlmost always catalyzed by enzymes

D. Kahn, Introduction on metabolism & refresher in enzymology

TCA

Pentose Phosphates

Methylglyoxal

Acetate

Entner-Doudoroff

Glycolysis/Gluconeogenesis

Central C metabolism subnetwork

D. Kahn, Introduction on metabolism & refresher in enzymology

Glycolysis / gluconeogenesis

D. Kahn, Introduction on metabolism & refresher in enzymology

TCA cycle

D. Kahn, Introduction on metabolism & refresher in enzymology

TCA cycle

D. Kahn, Introduction on metabolism & refresher in enzymology

Anaplerosis

D. Kahn, Introduction on metabolism & refresher in enzymology

Regulation

D. Kahn, Introduction on metabolism & refresher in enzymology

2. Methods to investigate metabolismMetabolomics: metabolite identification and quantitationFluxomicsAnalytical tools based on

Nuclear Magnetic Resonance (NMR)

Mass spectrometry (MS)

Liquid chromatography (LC)

D. Kahn, Introduction on metabolism & refresher in enzymology

Metabolites

NMR• Complex mixtures• Identification / Structure

LC-NMR

LC-NMR• Targetted• Suitable for high throughput

IC-MSIC-MS/MSSugar phosphates, nucleotides, organic acids…

LC-MS MS/MS

LC-MS/MSLipids, sugars, organic acids, aminoacids, coA esters…

Metabolomics

D. Kahn, Introduction on metabolism & refresher in enzymology

60 8005

1015202530354045

72 .0

70.045 .0

69 .0 74.056.0

51.0 79 .057.0

MS: mass isotopomers(GC-MS or LC-MS)

Ala C2

NMR: position isotopomersBiomassMetabolites

[U-13C]-glucoseMetabolic network

Mapping of fluxes

Flux measurements

D. Kahn, Introduction on metabolism & refresher in enzymology

31P

13C

15N

Energy metabolismpH, compartmentationetc.

Carbon distributionIn vivo dynamics

Nitrogen metabolismN/C metabolic coupling

Aimant RMN(ppm)

020406080100120140160180200220

0,5 h

2,5 h

4,5 h

6,5 h

8,5 h

10,5 h

12,5 h

14,5 h

16,5 h

C1 PHB

HCO3-

Benzène

C1 glucane

C4 PHB

C2 alanineC1 alanine

C2 pyruvate

C1 pyruvate

C2 glucane

C3 alanine

C6 glucose

C1βglc

C1αglc

C2βglc

C2αglc

(ppm)020406080100120140160180200220 020406080100120140160180200220

0,5 h

2,5 h

4,5 h

6,5 h

8,5 h

10,5 h

12,5 h

14,5 h

16,5 h

C1 PHB

HCO3-

Benzène

C1 glucane

C4 PHB

C2 alanineC1 alanine

C2 pyruvate

C1 pyruvate

C2 glucane

C3 alanine

C6 glucose

C1βglc

C1αglc

C2βglc

C2αglc

(physiological conditions)

(cells, tissues, organs)

In vivo NMR

D. Kahn, Introduction on metabolism & refresher in enzymology

3. Enzyme kinetics: Michaelis-MentenE + S ES E + P

1 1 1

2 2

1 2

0

Mass action kinetics:.

Quasi steady-state:

v k E S k ESv k ES

v v vE ES E

−= −=

= =+ =

D. Kahn, Introduction on metabolism & refresher in enzymology

Michaelis-MentenE + S ES E + P

10

1

1

1 1

1

reaction rate ( . )1

Michaelis constant ( )

catalytic efficiency ( . )

is the maximal turnover rate ( )

E

m

catm

catE

m

cat

k Sv E M sSK

k kK Mk

kk M sK

k s

−

−

− −

−

=+

+=

=

D. Kahn, Introduction on metabolism & refresher in enzymology

Reversible Michaelis-MentenE + S ES E + P

This is the default expression for kinetic modelling, even when k_ = 0, because it also accounts for competitive product inhibition.

0

1S P

k S k Pv E S PK K

+ −−=

+ +

D. Kahn, Introduction on metabolism & refresher in enzymology

Competitive inhibitionE + S ES E + P

E.I E.I

0

1S P Ic

k S k Pv E S P IK K K

+ −−=

+ + +

D. Kahn, Introduction on metabolism & refresher in enzymology

Other inhibitionsUncompetitive (more effective at high substrate concentration)

Mixed

0

1 1S P Iu

k S k Pv ES P I

K K K

+ −−=

⎛ ⎞⎛ ⎞+ + +⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

0

1 1S P Iu Ic

k S k Pv ES P I I

K K K K

+ −−=

⎛ ⎞⎛ ⎞+ + + +⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

D. Kahn, Introduction on metabolism & refresher in enzymology

Multiple substrates and productsIf substrates and products bind independently and in random order:

‘Convenience kinetics’ Liebermeister & Klipp, 2006, Theoret. Biol. Med. Mod. 3:41

0

1 1 1

i j

i j

jicat cat

i jS P

ji

i jS P

PSk kK K

v EPS

K K

+ −−

=⎛ ⎞⎛ ⎞

+ + + −⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

∏ ∏

∏ ∏

D. Kahn, Introduction on metabolism & refresher in enzymology

Haldane relationshipsEquilibrium constraint:

j

i

Pjcat

eqcat S

i

KkKk K

+

−=∏∏

D. Kahn, Introduction on metabolism & refresher in enzymology

CooperativityHill equation:

h is the Hill coefficient. Typically : 0.5 < h < 4This equation is purely empirical (actually it is wrong for S << K0.5 )K0.5 is a phenomenological constant (not a Km )

0.50

0.5

( / )1 ( / )

hcat

h

k S Kv ES K

=+

D. Kahn, Introduction on metabolism & refresher in enzymology

2-site cooperative bindingAdair equation

realistically captures site dependencies

21 1 2

0 21 1 2

/ /21 2 / /cat

S K S K Kv E kS K S K K

+=

+ +

D. Kahn, Introduction on metabolism & refresher in enzymology

SaturationE + S ES

0

1

1

0

.

/ saturation coefficient1 /

d

d

d

E ES EE S k KES k

ES S KYE S K

−

+ =

= =

= =+

D. Kahn, Introduction on metabolism & refresher in enzymology

Further readingUnderstanding the Control of Metabolism, by David Fell Portland Press, London, 1997Fundamentals of Enzyme Kinetics, by Athel Cornish-BowdenPortland Press, London, 2004

D. Kahn, Introduction on metabolism & refresher in enzymology

For the practical courseThe practical course will rely heavily on the theoretical courseFamiliarize yourself with the COPASI modeling environmenthttp://www.copasi.org

COPASI handbook

Refresh your course in linear algebraBe prepared to use your favourite mathematical package such as Scilab, Maple, R or MatlabYou will be evaluated on the practical course