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

2. Friedrich Schiller (1759-1805) Famous people at Jena University: 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. S. Schuster und C. Hilgetag: J. Biol. Syst. 2 (1994) 165-182 non-elementary flux mode elementary flux modes

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 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 All flux distributions in the living cell are non-negative linear combinations of elementary modes

15. Mathematical background Steady-state condition NV = 0 Sign restriction for irreversible fluxes: V irr 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 the interior.

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. flux1 flux2 flux3 generating vectors

18. NADP NADPH NADP NADPH NADH NAD ADP ATP ADP ATP CO 2 ATPADP G6P X5P Ru5P R5P S7P GAP 6PG GO6P F6PFP 2 F6P DHAP 1.3BPG 3PG 2PG PEP E4P Part of monosaccharide metabolism Red: external metabolites Pyr

19. NADH NAD ADP ATP ADP ATP ADP G6PGAPF6PFP 2 DHAP 1.3BPG 3PG 2PG PEP 1 st elementary mode: glycolysis Pyr

20. 2 nd elementary mode: fructose-bisphosphate cycle ATPADP F6PFP 2

21. 4 out of 7 elementary modes in glycolysis- pentose-phosphate system NADP NADPH NADP NADPH NADH NAD ADP ATP ADP ATP CO 2 ATPADP G6P X5P Ru5P R5P S7P GAP 6PG GO6P F6PFP 2 F6P DHAP 1.3BPG 3PG 2PG PEP E4P S. Schuster, D.A. Fell, T. Dandekar: Nature Biotechnol. 18 (2000) 326-332 Pyr

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. NADP NADPH NADP NADPH NADH NAD ADP ATP ADP ATP CO 2 ATPADP G6P X5P Ru5P R5P S7P GAP 6PG GO6P F6PFP 2 F6P DHAP 1.3BPG 3PG 2PG PEP E4P Optimization: Maximizing molar yields ATP:G6P yield = 3 ATP:G6P yield = 2 Pyr

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. Glc G6P 233 Anthr Trp 105 PEP Pyr 3PG GAP PrpP S. Schuster, T. Dandekar, D.A. Fell, Trends Biotechnol. 17 (1999) 53

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) Position in the chain Optimal enzyme concn. 1234 (q: equilibrium constant)

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. Maximum flux vs. maximum molar yield 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

28. Two possible strategies

29. ADPATP ADPATP ADP G6PF6P Pyr ATPADP Gluc Ac.ald. CO 2 EtOH Fermentation

30. 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). Game-theoretical problem

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 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“ We take the steady-state population density as the payoff. Values calculated with parameter values from model in Pfeiffer et al. (2001). 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 matrix for the Prisoner‘s Dilemma Cooperate Defect Nash equilibrium Cooperate Defect Escape/Escape A B 10 years prison/ Escape + Reward Escape + Reward/ 10 years prison 5 years prison/ 5 years prison Pareto optimum

36. Substrate level: Population densities: v, constant substrate input rate; J S, resource uptake rates; J ATP, ATP production rates; d, death rate. System equations 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 (y i = 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 Erythrocytes - small volume prevents mitochondria. Striated muscle during heavy exercise - diffusion of oxygen not fast enough. 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 At low cell diffusion rates and low substrate input, respirators can win in the long run. Blue: respirators Red: fermenters Black: empty sites Yellow: both 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. From: O. Pelz et al., Environm. Microb. 1 (1999), 167–174 Example: Degradation of 4-chlorosalicylate

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 CO 2 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. The ability of a steel ship to be afloat cannot be explained by decomposition However:

51. Analytical vs. holistic approaches §Decomposition should not be overdone §Example elementary flux modes: smallest functional units, rather than decomposition into enzymes §It depends on the question at which level the description should be made §Systems biology motivated by reasoning that the whole is more than the sum of ist parts (sometimes worse than…) §Game theory is one possible holistic approach

52. Steffen Klamt, Jörg Stelling, Ernst Dieter Gilles (MPI Magdeburg) Thomas Dandekar (U Würzburg) David Fell (Brookes U Oxford) Thomas Pfeiffer, Sebastian Bonhoeffer (ETH Zürich) Peer Bork (EMBL Heidelberg) Reinhart Heinrich, Thomas Höfer (HU Berlin) I. Zevedei-Oancea (formerly my group, now HU Berlin) Hans Westerhoff (VU Amsterdam) and others Acknowledgement to DFG for financial support Cooperations