Introduction on metabolism & refresher in enzymology Daniel Kahn Laboratoire de Biométrie & Biologie Evolutive Lyon 1 University & INRA MIA Department Daniel.Kahn@univ-lyon1.fr
General objectives of the course Understand the general behaviour of metabolic systems Ability to model their dynamics Express how kinetic enzyme properties affect metabolite concentrations and fluxes Express how networks respond to changes in environment Examine how experimental data may be used to identify a metabolic model Interpret these behaviours in terms of biological regulation Generalize to signal transduction networks
Course prerequisites Knowledge of enzyme kinetics Linear algebra Matrix rank analysis, diagonalization, etc Familiarity with a mathematical package such as Scilab, Maple, R or Matlab Dynamical systems Jacobian Stability analysis
Course schedule November 2 November 30 Introduction to Metabolic Control Theory Regulation analysis November 23, December 7 & 14 Morning 9am Practical on metabolic model and MCT Afternoon 2pm Theory
Outline 1. Introduction on metabolism 2. Methods to investigate metabolism 3. Refresher of enzyme kinetics 5
1. What is metabolism? Life s chemical factory Typically several hundred reactions involving small molecules Balances Nutrients and outputs Energy Redox Fast turnover Almost always catalyzed by enzymes
Central C metabolism subnetwork Pentose Phosphates Entner-Doudoroff Glycolysis/Gluconeogenesis Methylglyoxal Acetate TCA
Glycolysis / gluconeogenesis
TCA cycle
TCA cycle
Anaplerosis
Regulation
2. Methods to investigate metabolism Metabolomics: metabolite identification and quantitation Fluxomics Analytical tools based on Nuclear Magnetic Resonance (NMR) Mass spectrometry (MS) Liquid chromatography (LC)
Metabolomics Metabolites LC-MS LC-NMR IC-MS NMR Complex mixtures Identification / Structure LC-NMR Targetted Suitable for high throughput MS/MS LC-MS/MS Lipids, sugars, organic acids, aminoacids, coa esters IC-MS/MS Sugar phosphates, nucleotides, organic acids
Flux measurements [U- 13 C]-glucose Metabolic network Ala C2 Biomass Metabolites NMR: position isotopomers 45 40 35 30 25 20 15 10 5 0 45.0 70.0 72.0 69.0 74.0 56.0 51.0 79.0 57.0 60 80 MS: mass isotopomers (GC-MS or LC-MS) Mapping of fluxes
In vivo NMR 13 C (cells, tissues, organs) Benzène C1 glucane HCO - 3 C1 PHB C2 glucane Carbon distribution In vivo dynamics Aimant RMN (physiological conditions) 16,5 h C4 PHB 14,5 h 12,5 h 10,5 h 8,5 h C1 pyruvate C3 alanine 6,5 h C2 pyruvate 4,5 h C1 alanine C2 alanine 2,5 h C6 glucose 0,5 h 220 200 180 160 140 120 100 80 60 40 20 0 (ppm) C1β C1α C2β C2α glc glc glc glc 31 P Energy metabolism ph, compartmentation etc. 15 N Nitrogen metabolism N/C metabolic coupling
3. Enzyme kinetics: Michaelis-Menten E + S ES E + P Mass action kinetics: v = k E. S k ES v 1 1 1 = 2 2 k ES Quasi steady-state: v = v = v 1 2 E+ ES = E 0
Michaelis-Menten E + S ES E + P ks E v = E0 M s S 1+ K K m 1 1 m cat 1 reaction rate (. ) Michaelis constant ( M) cat 1 1 ke = catalytic efficiency ( M. s ) Km k cat = k k + k k 1 is the maximal turnover rate ( ) s
Reversible Michaelis-Menten E + S ES E + P v = E ks kp + 0 S P 1 + + KS KP This is the default expression for kinetic modelling, even when k_ = 0, because it also accounts for competitive product inhibition.
Competitive inhibition E + S ES E + P E.I E.I v = E ks kp + 0 S P I 1 + + + KS KP KIc
Other inhibitions Uncompetitive (more effective at high substrate concentration) v = E 0 ks + kp S P I 1+ + 1 KS K + P K Iu Mixed v = E 0 ks + kp S P I I 1+ + 1+ + K K K K S P Iu Ic
Multiple substrates and products If substrates and products bind independently and in random order: v = E Convenience kinetics 0 i k + i cat cat i KS S P i j 1+ + 1+ 1 K S j K i Pj Liebermeister & Klipp, 2006, Theoret. Biol. Med. Mod. 3:41 S i k j P K j P j
Haldane relationships Equilibrium constraint: K eq = k k + cat cat j i K K P S j i
Cooperativity Hill equation: v = E 0 kcat( S / K0.5) 1 + ( S / K ) 0.5 h h h is the Hill coefficient. Typically : 0.5 < h < 4 This equation is purely empirical (actually it is wrong for S << K 0.5 ) K 0.5 is a phenomenological constant (not a K m )
2-site cooperative binding Adair equation v = 2E k S / K + S / K K 2 1 1 2 0 cat 2 1+ 2 S / K1+ S / K1K2 realistically captures site dependencies
Saturation E + S ES E+ ES = E ES. ES Y 0 1 = = 0 k k 1 K ES S / Kd = = E 1 + S / K d d saturation coefficient
Further reading Understanding the Control of Metabolism, by David Fell Portland Press, London, 1997 Fundamentals of Enzyme Kinetics, by Athel Cornish-Bowden Portland Press, London, 2004
For the practical course The practical course will rely heavily on the theoretical course Familiarize yourself with the COPASI modeling environment http://www.copasi.org COPASI handbook Refresh your course in linear algebra Be prepared to use your favourite mathematical package such as Scilab, Maple, R or Matlab You will be evaluated on the practical course