Genome-scale Metabolic Network Reconstruction

Genome-scale Metabolic Network Reconstruction Elementary flux modes: system boundaries / external metabolites to be defined Exchange flux A B C E System Boundary D Internal flux Flux – The production or consumption of mass per unit area per unit time. Elementary (flux) modes Schuster & Hilgetag (1994) An elementary mode is a minimal set of enzymes that can operate at steady state with all irreversible reactions used in the appropriate direction All flux distributions in the living cell are non-negative linear combinations of elementary modes Related concept: Extreme pathway (C.H. Schilling, D. Letscher and B.O. Palsson, J. theor. Biol. 203 (2000) 229) - distinction between internal and exchange reactions, all internal reversible reactions are split up into forward and reverse steps The Stoichiometric Matrix: An Example b2 b1 A v1 B v2 v3 C v6 v5 v7 E b4 v4 D b3 Spanning the Null Space A set of basis vectors spanning the null space may be found. This set is not unique. Each vector represents a pathway in the metabolic network by specifying the set of fluxes in the system. Are these pathways biologically feasible ? b2 b1 A v1 B v2 v3 v4 D b3 C v6 v5 v7 E b4 Spanning the Convex Cone Basis vectors must be constrained by flux directionality: vi , bi  0 These constraints define a convex flux cone emanating from the origin, which defines the complete range of biochemically feasible flux distributions. Any vector can be represented as a non-negative combination of the generating vectors of the cone, fk:   n F   v  R | v    k f k ,  k  0 k   Extreme Pathways The generating vectors of the flux cone are a biochemically feasible basis to the distribution of b2 pathways in the network. b1 A v1 B v2 C v6 v5 E v7 b4 v3 v4 D b3 b2 b1 A v1 B v2 v3 C v6 v5 D b3 v7 E b4 v4 Extreme Pathways b2 b2 E b1 A v1 B v2 v3 v4 C v6 v5 D b3 b2 b4 b1 A v1 B v2 v3 C v6 v5 D E v7 b4 v7 v4 b3 b2 E v7 b4 b1 A v1 B v2 v3 v4 D b3 C v6 v5 E v7 b4 b1 A v1 B v2 v3 v4 C v6 v5 D b3 b2 b1 A v1 B v2 v3 v4 D b3 C v6 E v7 b4 b1 A v1 B v2 v3 v4 b2 C v6 E v7 b4 v5 v5 D b3 Elementary Flux Modes When the network includes reversible reactions, the extreme pathway set may not include all elementary pathways: b2 b1 A v1 B v2 v3 v4 C v6 v5 D b3 E v7 b4 b2 b1 A v1 B v2 C v6 E b4 b2 b1 A v1 B v2 v3 v4 D b3 v3 E v7 v4 v5 D b3 v7 C v6 v5 b4 Elementary flux modes are the set of irreducible pathways spanning the solution space. Elementary Flux Modes vs Extreme Pathways PYR PEP OAA PYR PYR PEP OAA PEP OAA Extreme pathways Elementary flux modes Properties of Elementary Flux Modes & Extreme Pathways If e is a EFM or EP then it maintains the following: 1. Pseudo steady state (metabolite balancing equations) 2. Feasibility: flux directionality constraints are satisfied 3. Non-decomposability: There is no vector v satisfying 1+2 s.t. p(v) is a proper subset of p(e). In addition: 1. The set of EFMs and set of EPs are uniquely defined 2. The set of EPs is a subset of the set of EFMs 3. The set of EPs are systematically independent. non-elementary flux mode elementary flux modes S. Schuster et al.: J. Biol. Syst. 2 (1994) 165-182; Trends Biotechnol. 17 (1999) 53-60; Nature Biotechnol. 18 (2000) 326-332 Biochemical Applications: Can sugars be produced from lipids? • Known in biochemistry for a long time that many bacteria and plants can produce sugars from lipids (via C2 units) while animals cannot Glucose CO2 PEP Pyr Oxac AcCoA Cit IsoCit CO2 CO 2 Mal Fum AcCoA is linked with glucose by a chain of reactions. However, no elementary mode realizes this conversion in the absence of the glyoxylate shunt. OG Succ SucCoA CO2 Elementary mode representing conversion of AcCoA into glucose. It requires the glyoxylate shunt. Glucose CO2 PEP Pyr AcCoA Cit Gly Icl IsoCit Oxac CO2 Mal Fum Mas OG Succ SucCoA CO2 CO2 The glyoxylate shunt is present in green plants and many bacteria (e.g. E. coli). This example shows that a description by usual graphs in the sense of graph theory is insufficien. Biological Network Example Reaction scheme representing part of monosaccharide metabolism Elementary Flux Modes of Monosaccharide Metabolism Basic glycolitic pathway Degradation of G6P to pyruvate and CO2 producing ATP, NADPH and NADH Elementary Flux Modes of Monosaccharide Metabolism Conversion of G6P to ribose5-phosphate and CO2 Conversion of 5 hexoses to 6 pentoses (when need for R5P is high) “pentose phosphate cycle” – carbons are cycled several times before ending in CO2. Produces NADPH but not NADH and ATP EFM theoretical predictions Glucose Red elementary mode: Usual TCA cycle CO2 Green elementary mode: Catabolic pathway predicted in Liao et al. (1996) and Schuster et al. (1999). Experimental hints in Wick et al. (2001). PEP Pyr AcCoA Oxac CO2 Mal Gly Cit IsoCit Fum Succ SucCoA OG CO2 CO2 „Hungry“ : […] between optimal growth and starvation, can be studied in glucose-limited continuous (chemostat) cultures with very low glucose concentrations at a rate of growth that is controlled by the experimenter. Catabolite repression is absent […] Physiological relevance: Production of NADH instead of NADPH Basis of 13C metabolic flux analysis: determination of intracellular fluxes Cell Intracellular fluxes Carbon Source 13C1-C2-C3-C4-C5-C6 Glycolysis v3 v2 (labeled) v1 PP Pathway Measurable extracellular fluxes TCA Cycle Amino Acids Measurable carbon labeling pattern of isotopomers Determine the isotopomer distribution in key metabolites NADPH CO2 Isotopic labeling of proteinogenic amino acids is reflective of their precursors in central metabolism. Biomass (Carbohydrate) G6P 6PG C5P Biomass (RNA,DNA, His) Biomass (Phe, Tyr, Trp) Gluconeogenesis Biomass (Ser, Gly, Cys) Serine F6P E4P S7P T3P PGA PP pathway Glycine CO2 PEP C1 pool Pyr + Biomass (Val, Ala, Leu, Ile) NADH2 Pyruvate Lactate 100 [0.77] CO2+NADH/NADPH Biomass (Lipid, Leu) ATP Acetyl-CoA Acetate Biomass (Asp, Asn, Thr, Lys, Met) MAL 0.8 OAA CIT ICT Glyoxylate OXO FUM SUC TCA pathway Biomass (Glu, Gln, Pro, Arg) Example labeling with pyruvate Succinylase pathway Dehydrogenase pathway Ion fragments of derivatized glutamate from cells incubated with [1, 2 13C2]-glucose C1 C2 152 80000 75000 70000 65000 60000 55000 50000 45000 40000 35000 30000 25000 20000 15000 10000 5000 0 198 Abundance C3 C4 C5 P3 M+1 + P1 C1 C2 C3 C4 C5 P3 M+1 M+2 P2 P2 M+2 or P1 145 150 155 160 165 170 175 180 185 190 195 200 205 210 M/Z Journal publications on 13C flux analysis 18 Number of Papers 180 12 Number of papers 120 6 60 0 1996 1998 2000 2002 Year 2004 2006 0 1996 1998 2000 2002 2004 2006 Year “13C metabolic flux analysis” Key words Total Papers “metabolic flux analysis” Review Earliest publication 13C Metabolic flux analysis: Metabolic flux analysis: DNA microarray: 164 1664 23474 14 155 2718 ~1983 1960s 1995 Pubmed query Challenge 1: Achieving steady state Continuous fermentation: best for flux analysis, but very expensive. Shaking flask: approximate approach; growth condition is not stable. 1 C labeling Isotopomer distribution curves in amino acids (shaking flask culture): Shewanella 0.9 a) Ala, Ser, Gly 0.8 (■: gly; ● Ser; ♦: Ala) E.coli growth (□: gly; ○: Ser; ◊: Ala) Fraction of 13 0.7 0.6 16 20 24 Time (hours) 28 Mini-bioreactor: high throughput; low cost for labeled medium (~10mL); controlled growth conditions. Challenge 2: Minimal medium limits the 13C flux analysis Addition of nutrients (amino acids) complicates the isotopomer analysis!!! 1 GC-MS data (culture with amino acids) 0.8 Only Ala, Asp, and Glu ( ♦) Labeling was not affected by addition of amino acids 0.6 0.4 This makes flux analysis for mammalian cells difficult ! 0.2 0 0 0.2 0.4 0.6 0.8 1 GC-MS data (control) Effect of addition of 17 non-labeled amino acid mix (25 μM each) on labeling pattern in Shewanella proteinogenic amino acids Challenge 3: measurement of metabolites Measure metabolites’ Concentrations Measure isotopomer distribution NMR • Lower sensitivity: mM – mM GC/MS • Need to derivatize compounds • Provide “total mass” and α-carbon labeling information CE-MS(MS) /LC-MS(MS) Carbon balance for yeast metabolism CE-FT-ICR