Introduction on metabolism & refresher in enzymology

Transcription

1 Introduction on metabolism & refresher in enzymology Daniel Kahn Laboratoire de Biométrie & Biologie Evolutive Lyon 1 University & INRA MIA Department Daniel.Kahn@univ-lyon1.fr

2 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

3 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

4 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

5 Outline 1. Introduction on metabolism 2. Methods to investigate metabolism 3. Refresher of enzyme kinetics 5

6 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

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8 Central C metabolism subnetwork Pentose Phosphates Entner-Doudoroff Glycolysis/Gluconeogenesis Methylglyoxal Acetate TCA

9 Glycolysis / gluconeogenesis

10 TCA cycle

11 TCA cycle

12 Anaplerosis

13 Regulation

14 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)

15 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

16 Flux measurements [U- 13 C]-glucose Metabolic network Ala C2 Biomass Metabolites NMR: position isotopomers MS: mass isotopomers (GC-MS or LC-MS) Mapping of fluxes

17 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 (ppm) C1β C1α C2β C2α glc glc glc glc 31 P Energy metabolism ph, compartmentation etc. 15 N Nitrogen metabolism N/C metabolic coupling

18 3. Enzyme kinetics: Michaelis-Menten E + S ES E + P Mass action kinetics: v = k E. S k ES v = 2 2 k ES Quasi steady-state: v = v = v 1 2 E+ ES = E 0

19 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

20 Reversible Michaelis-Menten E + S ES E + P v = E ks kp + 0 S P KS KP This is the default expression for kinetic modelling, even when k_ = 0, because it also accounts for competitive product inhibition.

21 Competitive inhibition E + S ES E + P E.I E.I v = E ks kp + 0 S P I KS KP KIc

22 Other inhibitions Uncompetitive (more effective at high substrate concentration) v = E 0 ks + kp S P I KS K + P K Iu Mixed v = E 0 ks + kp S P I I K K K K S P Iu Ic

23 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 K S j K i Pj Liebermeister & Klipp, 2006, Theoret. Biol. Med. Mod. 3:41 S i k j P K j P j

24 Haldane relationships Equilibrium constraint: K eq = k k + cat cat j i K K P S j i

25 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 )

26 2-site cooperative binding Adair equation v = 2E k S / K + S / K K cat S / K1+ S / K1K2 realistically captures site dependencies

27 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

28 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

29 For the practical course The practical course will rely heavily on the theoretical course Familiarize yourself with the COPASI modeling environment 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

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