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Introduction on metabolism & refresher in enzymology
Daniel KahnLaboratoire de Biométrie & Biologie EvolutiveLyon 1 University & INRA MIA Department
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