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Elucidating the Roadmap of Metabolism by Pathway Analysis

Elucidating the Roadmap of Metabolism by Pathway Analysis. Stefan Schuster Friedrich Schiller University Jena Dept. of Bioinformatics. Topics of this talk:. Introduction. Metabolism is bridge between genotype and phenotype

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Elucidating the Roadmap of Metabolism by Pathway Analysis

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  1. Elucidating the Roadmap of Metabolism by Pathway Analysis Stefan Schuster Friedrich Schiller University Jena Dept. of Bioinformatics

  2. Topics of this talk:

  3. Introduction • Metabolism is bridge between genotype and phenotype • Networks of metabolic reactions are complex due to their size and the presence of bimolecular reactions • Many kinetic parameters unknown. Maximal velocities depend on enzyme concentrations

  4. „Roadmap“ as a metaphor Roads form simple graph

  5. Metabolism is hypergraph

  6. Technologically relevant metabolic syntheses: • Antibiotics by fungi • Ethanol by yeast • Amino acids by bacteria • Dyes • Perfumes • etc. etc.

  7. Theoretical Methods • Dynamic Simulation • Stability and bifurcation analyses • Metabolic Control Analysis (MCA) • Metabolic Pathway Analysis • Metabolic Flux Analysis (MFA) • Optimization, Evolutionary Game Theory • and others

  8. Theoretical Methods • Dynamic Simulation • Stability and bifurcation analyses • Metabolic Control Analysis (MCA) • Metabolic Pathway Analysis • Metabolic Flux Analysis (MFA) • Optimization, Evolutionary Game Theory • and others

  9. Metabolic Pathway Analysis (or Metabolic Network Analysis) • Decomposition of the network into the smallest functional entities (metabolic pathways) • Does not require knowledge of kinetic parameters!! • Uses stoichiometric coefficients and reversibility/irreversibility of reactions

  10. History of pathway analysis • „Direct mechanisms“ in chemistry (Milner 1964, Happel & Sellers 1982) • Clarke 1980 „extreme currents“ • Seressiotis & Bailey 1986 „biochemical pathways“ • Leiser & Blum 1987 „fundamental modes“ • Mavrovouniotis et al. 1990 „biochemical pathways“ • Fell (1990) „linearly independent basis vectors“ • Schuster & Hilgetag 1994 „elementary flux modes“ • Liao et al. 1996 „basic reaction modes“ • Schilling, Letscher and Palsson 2000 „extreme pathways“

  11. Mathematical background Steady-state condition NV(S) = 0 If the kinetic parameters were known, this could be solved for S. If not, one can try to solve it for V. The equation system is linear in V. However, usually there is a manifold of solutions. Mathematically: kernel (null-space) of N. Spanned by basis vectors. These are not unique.

  12. P S 4 3 non-elementary flux mode 1 1 P 1 3 S S 1 2 2 2 S 4 P P 1 2 P S 4 3 1 1 P 3 1 S S S S 1 2 1 2 1 1 1 1 S S 4 4 P P P P 1 2 1 2 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

  13. 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

  14. Mathematical background (2) Steady-state condition NV = 0 Sign restriction for irreversible fluxes: Virr 0 This represents a linear equation/inequality system. Solution is a convex region. All edges correspond to elementary modes. In addition, there may be elementary modes in theinterior.

  15. Geometrical interpretation Elementary modes correspond to generating vectors (edges) of a convex polyhedral cone (= pyramid) in flux space (if all modes are irreversible)

  16. Rate 3 Rate 2 generating vectors Rate of enzyme 1

  17. Software for computing elementary modes EMPATH (in SmallTalk) - J. Woods METATOOL (in C++) - Th. Pfeiffer, F. Moldenhauer, A. von Kamp Included in GEPASI - P. Mendes and JARNAC - H. Sauro part of METAFLUX (in MAPLE) -K. Mauch part of FluxAnalyzer (in MATLAB) -S. Klamt part of ScrumPy (in Python) - M. Poolman Alternative algorithm in MATLAB – C. Wagner (Bern) On-line computation: pHpMetatool - H. Höpfner, M. Lange http://pgrc-03.ipk-gatersleben.de/tools/phpMetatool/index.php

  18. Biochemical Applications:1. 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

  19. AcCoA is linked with glucose by a chain of reactions. However, no elementary mode realizes this conversion in the absence of the glyoxylate shunt. Glucose CO2 AcCoA Pyr PEP Cit Oxac CO2 IsoCit Mal CO2 OG Fum SucCoA Succ CO2

  20. Elementary mode representing conversion of AcCoA into glucose. It requires the glyoxylate shunt. Glucose CO2 AcCoA Pyr PEP Cit Oxac CO2 Mas Icl IsoCit Gly Mal CO2 OG Fum CO2 SucCoA Succ

  21. 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 insufficient… S. Schuster, D.A. Fell: Modelling and simulating metabolic networks. In: Bioinformatics: From Genomes to Therapies (T. Lengauer, ed.) Wiley-VCH, Weinheim, in press.

  22. A successful theoretical prediction Glucose Red elementary mode: Usual TCA cycle Green elementary mode: Catabolic pathway predicted in Liao et al. (1996) and Schuster et al. (1999). Experimental hints in Wick et al. (2001). Experimental proof in: CO2 E. Fischer and U. Sauer: A novel metabolic cycle catalyzes glucose oxidation and anaplerosis in hungry Escherichia coli, AcCoA Pyr PEP J. Biol. Chem. 278 (2003) 46446–46451 Cit Oxac CO2 IsoCit Gly Mal CO2 OG Fum Succ CO2 SucCoA

  23. 2. Crassulacean Acid Metabolism (CAM) • Variant of photosynthesis employed by a range of plants (e.g. cacti) as an adaptation to arid conditions • To reduce water loss, stomata are closed during daytime • At nighttime, PEP + CO2 oxaloacetate  malate • At daytime, malate  pyruvate (or PEP) + CO2  carbohydrates

  24. P hexose i starch P 7 i 5 RBP CO 2 9 TP TP 8 12 4 P P i i CO 2 PEP PEP 3 11 P P 6 i oxac i CO P 2 2 i mal pyr pyr 1 10 chloroplast cytosol CAM metabolism during daytime

  25. P P hexose hexose i i starch starch P P i i RBP RBP CO CO 2 2 TP TP TP TP P P P P i i i i CO CO 2 2 PEP PEP PEP PEP P P P P i i oxac oxac i i CO CO P P 2 2 i i mal mal pyr pyr pyr pyr chloroplast chloroplast cytosol cytosol Elementary modes A) B) Starch synthesis via malic enzyme as occurring in Cactaceae and Crassulacea Hexose synthesis via malic enzyme as occurring in Agavaceae and Dracaenaceae Dracaena Ferocactus

  26. P hexose i starch P i RBP CO 2 TP TP P P i i CO 2 PEP PEP P P i oxac i CO P 2 i mal pyr pyr chloroplast cytosol P hexose i starch P i RBP CO 2 TP TP P P i i CO 2 PEP PEP P P i oxac i CO P 2 i mal pyr pyr chloroplast cytosol C) D) Simultaneous starch and hexose synthesis via malic enzyme as occurring in: Hexose synthesis via PEPCK as occurring in Clusia rosea and in: Clusia minor Ananus comosus = pineapple

  27. P P hexose hexose i i starch starch P P i i RBP RBP CO CO 2 2 TP TP TP TP P P P P i i i i CO CO 2 2 PEP PEP PEP PEP P P P P i i oxac oxac i i CO CO P P 2 2 i i mal mal pyr pyr pyr pyr chloroplast chloroplast cytosol cytosol F) E) Starch synthesis via PEPCK as occurring in Asclepadiaceae Simultaneous starch and hexose synthesis via PEPCK as occurring in: Caralluma hexagona Aloe vera

  28. „Pure“ pathways • In a review by Christopher and Holtum (1996), only cases A), B), D), and E) were given as “pure” functionalities. F) was considered as a superposition, and C) was not mentioned. • However, F) is an elementary mode as well, although it produces two products. It does not use the triose phosphate transporter • The systematic overview provided by elementary modes enables one to look for missing examples. Case C) is indeed realized in Clusia minor (Borland et al, 1994). • Interestingly, (almost) pure elementary modes are realized here, although this should reduce robustness S. Schuster, D.A. Fell: Modelling and simulating metabolic networks. In: Bioinformatics: From Genomes to Therapies (T. Lengauer, ed.) Wiley-VCH, Weinheim, in press.

  29. 3. Adenine and adenosine salvage pathways • Human erythrocytes cannot synthesize nucleotide phosphates de novo • They can recycle nucleotides to give nucleotide phosphates • In particular, they can recycle adenine and adenosine, but not hypoxanthine S. Schuster, D. Kenanov: Adenine and adenosine salvage pathways in erythrocytes and the role of S-adenosylhomocysteine hydrolase – A theoretical study using elementary flux modes. FEBS J. 272 (2005) 5278-5290.

  30. membrane 2,3DPG DPGM DPGase GLCim HK PGI PFK ALD GAPDH PGK GLCext GA3P FDP 1,3 DPG GLC G6P F6P 3PG TPI ADP NADH ATP NAD ATP ADP ATP ADP PGM DHAP G6PDH NADP 2GSH 2PG GL6P EN PGLase PEP ADP GSSGR GSHox GO6P PK PYRtrans ATP PYRext PYR GL6PDH GSSG NADH NADPH LDH LACtrans NAD R5PI LACext F6P LAC GA3P CO S7P R5P 2 TKI TA RU5P TKII Xu5PE X5P GA3P E4P R5P PRM + Na leak PRPPsyn + + Na Na ATP R1P PRPP HGPRT ADP HXtrans HYPXext HYPX IMP PRPP NaK ATPase 3'KetoRibose ADPRT NUC AMPDA ATP ADENINE AMP INO PNPase HCY ADA NUC + K + K ADO + K leak ATP AMP SAHH2 HCY ApK AK S-AdoHcy MetAcc ADP ADP AMP MT Acc SAHH1 SAM SAMext

  31. Question • As salvage pathways use enzymes consuming ATP as well as enzymes producing ATP, it is not easy to see whether a net synthesis of ATP is possible. • Invest ATP to gain ATP - Bootstrapping like Baron Münchhausen?

  32. Goal: • Analyse theoretically how many salvage pathways exist • Which enzymes involves each of these and in what flux proportions (i.e. relative fluxes) • Compute the net overall stoichiometry of ATP anabolism • Medical impact of enzyme deficiencies

  33. External metabolites • Adenine or adenosine depending on which salvage is analysed • glucose, lactate, CO2, ATP • hypoxanthine, sodium and potassium outside the cell

  34. Adenine as a source • 153 elementary modes • 4 of these produce ATP • ATP per adenine yield: 1:1 • ATP per glucose yields: 3:10, 2:7, 1:4, 1:6

  35. membrane 2,3DPG DPGM DPGase GLCim HK PGI PFK ALD GAPDH PGK GLCext GA3P FDP 1,3 DPG GLC G6P F6P 3PG TPI ADP NADH ATP NAD ATP ADP ATP ADP PGM DHAP G6PDH NADP 2GSH 2PG GL6P EN PGLase PEP ADP GSSGR GSHox GO6P PK PYRtrans ATP PYRext PYR GL6PDH GSSG NADH NADPH LDH LACtrans NAD R5PI LACext F6P LAC GA3P CO S7P R5P 2 TKI TA RU5P TKII Xu5PE X5P GA3P E4P R5P PRM + Na leak PRPPsyn + + Na Na ATP R1P PRPP HGPRT ADP HXtrans HYPXext HYPX IMP PRPP NaK ATPase 3'KetoRibose ADPRT NUC AMPDA ATP ADENINE AMP INO PNPase HCY ADA NUC + K + K ADO + K leak ATP AMP SAHH2 HCY ApK AK S-AdoHcy MetAcc ADP ADP AMP MT Acc SAHH1 SAM SAMext Elementary mode with highest ATP:glucose yield (3:10)

  36. membrane 2,3DPG DPGM DPGase GLCim HK PGI PFK ALD GAPDH PGK GLCext GA3P FDP 1,3 DPG GLC G6P F6P 3PG TPI ADP NADH ATP NAD ATP ADP ATP ADP PGM DHAP G6PDH NADP 2GSH 2PG GL6P EN PGLase PEP ADP GSSGR GSHox GO6P PK PYRtrans ATP PYRext PYR GL6PDH GSSG NADH NADPH LDH LACtrans NAD R5PI LACext F6P LAC GA3P CO S7P R5P 2 TKI TA RU5P TKII Xu5PE X5P GA3P E4P R5P PRM + Na leak PRPPsyn + + Na Na ATP R1P PRPP HGPRT ADP HXtrans HYPXext HYPX IMP PRPP NaK ATPase 3'KetoRibose ADPRT NUC AMPDA ATP ADENINE AMP INO PNPase HCY ADA NUC + K + K ADO + K leak ATP AMP SAHH2 HCY ApK AK S-AdoHcy MetAcc ADP ADP AMP MT Acc SAHH1 SAM SAMext Elementary mode with lowest ATP:glucose yield (1:6)

  37. Adenosine as a source • 97 elementary modes • 12 of these produce ATP • ATP per adenosine yield: 1:1, 2:3, 5:8, 8:17, 2:5, 5:14, and 1:4. • ATP per glucose yields: 1:1, 5:6, 2:3, 5:9, 1:3, 1:6, and: 1:0!! • When ATP/glucose = 1:0, then all adenosine is used as exclusive energy source

  38. membrane 2,3DPG DPGM DPGase GLCim HK PGI PFK ALD GAPDH PGK GLCext GA3P FDP 1,3 DPG GLC G6P F6P 3PG TPI ADP NADH ATP NAD ATP ADP ATP ADP PGM DHAP G6PDH NADP 2GSH 2PG GL6P EN PGLase PEP ADP GSSGR GSHox GO6P PK PYRtrans ATP PYRext PYR GL6PDH GSSG NADH NADPH LDH LACtrans NAD R5PI LACext F6P LAC GA3P CO S7P R5P 2 TKI TA RU5P TKII Xu5PE X5P GA3P E4P R5P PRM + Na leak PRPPsyn + + Na Na ATP R1P PRPP HGPRT ADP HXtrans HYPXext HYPX IMP PRPP NaK ATPase 3'KetoRibose ADPRT NUC AMPDA ATP ADENINE AMP INO PNPase HCY ADA NUC + K + K ADO + K leak ATP AMP SAHH2 HCY ApK AK S-AdoHcy MetAcc ADP ADP AMP MT Acc SAHH1 SAM SAMext One elementary mode using adenosine as energy and nucleotide source

  39. 2.3-Diphosphoglycerate bypass • Neither for adenine nor adenosine salvage, any elementary mode involves the 2.3DPG bypass • ATP balance would not be positive anymore

  40. moles of ATP consumed moles of ATP produced - moles of ATP consumed In elementary mode 1 of adenine salvage, this ratio is 18:(20-18) = 9:1. S. Schuster, D. Kenanov: FEBS J. 272 (2005) 5278-5290. Molar investment ratio 2 4-2 In glycolysis: =1

  41. Maximization of tryptophan:glucose yield Model of 65 reactions in the central metabolism of E. coli. 26 elementary modes. 2 modes with highest tryptophan: glucose yield: 0.451. S. Schuster, T. Dandekar, D.A. Fell, Trends Biotechnol. 17 (1999) 53 Glc PEP 233 Pyr G6P Anthr 3PG PrpP GAP 105 Trp

  42. Conclusions • Elementary modes are an appropriate concept to describe biochemical pathways • Information about network structure can be used to derive far-reaching conclusions about performance of metabolism • Elementary modes reflect specific characteristics of metabolic networks such as steady-state mass flow, thermodynamic constraints and and the systemic interactions (Systems Biology)

  43. Conclusions (2) • It can be tested whether connected routes can function at steady state • A complete list of potential pathways can be generated. Thereafter, experimental search for realized pathways. • Pathway analysis is well-suited for computing maximal and submaximal molar yields

  44. Cooperations • Steffen Klamt, Jörg Stelling, Ernst Dieter Gilles • (MPI Magdeburg) • Thomas Dandekar (U Würzburg) • David Fell (Brookes U Oxford) • Thomas Pfeiffer, Sebastian Bonhoeffer (ETH Zürich) • Thomas Wilhelm (IMB Jena) • Reinhart Heinrich, Thomas Höfer (HU Berlin) • Marko Marhl (U Maribor, Slovenia) • Hans Westerhoff (VU Amsterdam) • and others • Acknowledgement to DFG and BMBF for financial support

  45. Current group members • Dr. Axel von Kamp • Dr. Ina Weiß • Dimitar Kenanov • Jörn Behre • Beate Knoke • Ralf Bortfeldt • Gunter Neumann

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