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Metabolic Pathway Analysis as Part of Systems Biology

Metabolic Pathway Analysis as Part of Systems Biology. Stefan Schuster Dept. of Bioinformatics Friedrich Schiller University Jena, Germany. Famous people at Jena University:. Friedrich Schiller (1759-1805). Ernst Haeckel ( 1834-1919, Biogenetic rule). From: ExPASy. Introduction.

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Metabolic Pathway Analysis as Part of Systems Biology

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  1. Metabolic Pathway Analysis as Part of Systems Biology Stefan Schuster Dept. of Bioinformatics Friedrich Schiller University Jena, Germany

  2. Famous people at Jena University: Friedrich Schiller (1759-1805) Ernst Haeckel (1834-1919, Biogenetic rule)

  3. From: ExPASy

  4. Introduction • Analysis of metabolic systems requires theoretical methods due to high complexity • Systems theoretical approaches used in this field for a long time, for example: • 1960‘s Dynamic simulation of biochemical systems • by David Garfinkel • Metabolic Control Analysis (1973 H. Kacser/J. Burns, • R. Heinrich/T.A. Rapoport, 1980‘s Hans Westerhoff) • „Biochemical Systems Theory“ (1970‘s Michael • Savageau)

  5. Since end 1990‘s: New quality due to high throughput experiments and on-line databases (e.g. KEGG, ExPASy, BRENDA) „Metabolomics“ is a growing field besides „genomics“, „proteomics“... Major challenge: clarify relationship between structure and function in complex intracellular networks

  6. Motivation for the modelling of metabolism • Functional genomics – assignment of gene functions can be improved by consideration of interplay between gene products • Study of robustness to enzyme deficiencies and knock-out mutations is of high medical and biotechnological relevance • Increase of rate and yield of bioprocesses important in biotechnology

  7. The evolutionary aspect • Metabolic pathways result from biological evolution • Evolution is actually co-evolution because various species interact • Each species tends to optimize its properties; the outcome depends also on the properties of the other species

  8. Features often studied in Systems Biology: • Robustness • Flexibility • Fragility • Optimality • Modularity

  9. Theoretical Methods • Dynamic Simulation • Stability and bifurcation analyses • Metabolic Control Analysis (MCA) • Metabolic Pathway Analysis • Metabolic Flux Analysis (MFA) • Optimization • and others

  10. Theoretical Methods • Dynamic Simulation • Stability and bifurcation analyses • Metabolic Control Analysis (MCA) • Metabolic Pathway Analysis • Metabolic Flux Analysis (MFA) • Optimization • and others

  11. 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

  12. 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“

  13. 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 und C. Hilgetag: J. Biol. Syst. 2 (1994) 165-182

  14. 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

  15. Mathematical background 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.

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

  17. flux3 flux2 generating vectors flux1

  18. Pyr ATP X5P S7P E4P ADP Ru5P CO2 PEP NADPH GAP F6P R5P NADP 6PG 2PG 3PG GO6P ATP NADPH ADP NADP G6P F6P FP GAP 1.3BPG 2 NADH NAD DHAP ATP ADP Part of monosaccharide metabolism Red: external metabolites

  19. Pyr ATP 2 ADP PEP 2 2PG 2 3PG ATP 2 ADP G6P F6P FP GAP 1.3BPG 2 2 NADH NAD DHAP ATP ADP 1st elementary mode: glycolysis

  20. F6P FP 2 ATP ADP 2nd elementary mode: fructose-bisphosphate cycle

  21. Pyr ATP X5P 2 S7P E4P 2 2 2 4 ADP Ru5P CO2 PEP NADPH GAP F6P 2 R5P 6 3 2 NADP 2 6PG 2PG 3 2 6 3PG GO6P ATP NADPH 2 6 3 ADP 5 NADP F6P FP GAP 1.3BPG G6P 2 2 2 NADH NAD DHAP ATP ADP 4 out of 7 elementary modes in glycolysis- pentose-phosphate system S. Schuster, D.A. Fell, T. Dandekar: Nature Biotechnol. 18 (2000) 326-332

  22. Software for computing elementary modes ELMO (in Turbo-Pascal) - C. Hilgetag EMPATH (in SmallTalk) - J. Woods METATOOL (in C) - Th. Pfeiffer, F. Moldenhauer, A. von Kamp, M. Pachkov 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 On-line computation: pHpMetatool - H. Höpfner, M. Lange http://pgrc-03.ipk-gatersleben.de/tools/phpMetatool/index.php

  23. Optimization: Maximizing molar yields Pyr ATP X5P 2 S7P E4P 2 ADP Ru5P CO2 PEP NADPH GAP F6P R5P 3 2 NADP 6PG 2PG 3 2 3PG GO6P ATP NADPH 2 3 ADP NADP F6P FP GAP 1.3BPG G6P 2 2 2 NADH NAD DHAP ATP ADP ATP:G6P yield = 3ATP:G6P yield = 2

  24. 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

  25. Optimality of metabolism Example of theoretical prediction: Maximization of pathway flux subject to constant total enzyme concentration (Waley, 1964; Heinrich, Schuster and Holzhütter, 1987) (q: equilibrium constant) Optimal enzyme concn. 1 2 3 4 Position in the chain

  26. However, there are more objective functions besides maximization of pathway flux Maximum stability and other criteria have been suggested (Savageau, Heinrich, Schuster, …) Optimality criterion for a particular species need not coincide with optimality criterion for a community of species Optimization theory needs to be extended to cope with this problem  Game theory

  27. Example: Fermentation has a low yield (2 moles ATP per mole of glucose) but high ATP production rate (cf. striated muscle); respiration has a high yield (>30 moles ATP per mole of glucose) but low ATP production rate Maximum flux vs. maximum molar yield

  28. Two possible strategies Fermentation Glucose Ethanol (Pyruvate, Lactate) Respiration + 2 ATP H2O + CO2 + 32 ATP cell A cell B respiration or fermentation? respiration or fermentation?

  29. Fermentation CO2 Gluc EtOH Pyr Ac.ald. G6P F6P 2 2 ATP ADP ATP ADP ATP ADP ADP ATP

  30. Game-theoreticalproblem The two cells (strains, species) have two strategies. The outcome for each of them depends on their own strategy as well as on that of the competitor. Respiration can be considered as a cooperative strategy because it uses the resource more efficiently. By contrast, fermentation is a competitive strategy. Switch between high yield and high rate has been shown for bacterium Holophaga foetida growing on methoxylated aromatic compounds (Kappler et al., 1997).

  31. How to define the payoff? We propose taking the steady-state population density as the payoff. Particular meaningful in spatially distributed systems because spreading of strain depends on population density. Dependence of the payoff on the strategy of the other species via the steady-state substrate level. This may also be used as a source of information about the strategy of the other species.

  32. Population payoffs and resource level T. Frick, S. Schuster: An example of the prisoner's dilemma in biochemistry. Naturwissenschaften 90 (2003) 327-331.

  33. Payoff matrix of the „game“of two species feeding on the same resource We take the steady-state population density as the payoff. Values calculated with parameter values from model in Pfeiffer et al. (2001). Cooperative strategy Competitive strategy Cooperative 3.2 0.0 strategy larger than in Nash equilibr. Competitive 5.5 2.7 strategy This is equivalent to the „Prisoner‘s dilemma“ Nash equilibrium

  34. Prisoner‘s dilemma • If prisoner A reveals the plan of escape to the jail director, while prisoner B does not, A is set free and gets a reward of 1000 ₤. B is kept in prison for 10 years. • The same vice versa. • If none of them betrays, both can escape. • If both betray, they are kept in prison for 5 years. • They are allowed to know what the other one does.

  35. Payoff matrixfor the Prisoner‘s Dilemma B Cooperate Defect A Pareto optimum 10 years prison/ Escape + Reward Cooperate Escape/Escape 5 years prison/ 5 years prison Escape + Reward/ 10 years prison Defect Nash equilibrium

  36. System equations Substrate level: Population densities: v, constant substrate input rate; JS, resource uptake rates; JATP, ATP production rates; d, death rate. T. Pfeiffer, S. Schuster, S. Bonhoeffer: Cooperation and Competition in the Evolution of ATP Producing Pathways. Science 292 (2001) 504-507.

  37. Michaelis-Menten rate laws (yi = ATP:glucose yield of pathway i)

  38. Do we need anthropomorphic concepts? • …such as „strategy“, „cooperation“, „altruism“ • NO!! They are auxiliary means to understand co-evolution more easily • The game-theoretical problem can alternatively be described by differential equation systems. Nash equilibrium is asymptotically stable steady state

  39. A paradoxical situation: • Both species tend to maximize their population densities. • However, the resultant effect of these two tendencies is that their population densities decrease. The whole can be worse then the sum of its parts!

  40. n-Player games „Tragedy of the commons“ - Generalization of the prisoner‘s dilemma to n players Commons: common possession such as the pasture of a village or fish stock in the ocean. Each of n users of the commons may think s/he could over-use it without damaging the others too much. However, when all of them think so…

  41. Biological examples • S. cerevisiae and Lactobacilli use fermentation even under aerobiosis, if sufficient glucose is available. They behave „egotistically“. • Other micro-organisms, such as Kluyverymyces, use respiration.

  42. Multicellular organisms • For multicellular organisms, it would be disadvantageous if their cells competed against each other. • In fact, most cell types in multicellular organisms use respiration. • Exception: cancer cells. Perhaps, their „egotistic“ behaviour is one of the causes of their pathological effects.

  43. „Healthy“ exceptions: • Cells using fermentation in multicellular organisms Striated muscle during heavy exercise - diffusion of oxygen not fast enough. Erythrocytes - small volume prevents mitochondria. Astrocytes – division of labour with neurons, which degrade lactate to carbon dioxide and water.

  44. How did cooperation evolve? • Deterministic system equations: fermenters always win. • However, they can only sustain low population densities. Susceptible to stochastic extinction. • Further effects in spatially distributed systems. Cooperating cells can form aggregates.

  45. Possible way out of the dilemma: Evolution in a 2D (or 3D) habitat with stochastic effects Blue: respirators Red: fermenters Yellow: both Black: empty sites At low cell diffusion rates and low substrate input, respirators can win in the long run. Aggregates of cooperating cells can be seen as an important step towards multicellularity. T. Pfeiffer, S. Schuster, S. Bonhoeffer: Cooperation and Competition in the Evolution of ATP Producing Pathways. Science 292 (2001) 504-507.

  46. Biotechnological relevance • Communities of different bacteria species • Competition for the same substrate or division of labour so that the product of one bacterium is used as a substrate by another one (crossfeeding, like in astrocytes and neurons) • Pathways operating in microbial communities = „consortium pathways“

  47. Example: Degradation of 4-chlorosalicylate From: O. Pelz et al., Environm. Microb. 1 (1999), 167–174

  48. Another example: E. coli • E. coli in continuous culture (chemostat) evolves, over many generations, so as to show stable polymorphism (Helling et al., 1987) • One resulting strain degrades glucose to acetate, another degrades acetate to CO2 and water • Example of intra-species crossfeeding

  49. Conclusions • „Analysis“ (Greek) means decomposition • Scientists tend to analyse: „function of a gene“, „role of an calcium oscillations“, „impact of an enzyme“

  50. However: The ability of a steel ship to be afloatcannot be explained bydecomposition

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