1. Comparison of networks in cell biology Jörn Behre, Dept. of Bioinformatics, Friedrich-Schiller-University Jena 4th SFB-Workshop "Gene regulatory networks", 07.12.2006

2. 2 Structure of the talk Metabolic pathway analysis properties of metabolic networks properties of metabolic networks concept of elementary modes concept of elementary modes Regulatory networks properties of regulatory networks properties of regulatory networks differences to metabolic networks differences to metabolic networks Boolean networks some basic properties of Boolean networks some basic properties of Boolean networks modelling regulatory networks with Boolean networks modelling regulatory networks with Boolean networks Application of elementary modes Structural robustness of metabolic networks Structural robustness of metabolic networks

3. 3 Metabolic networks Properties of metabolic networks: mass flow mass flow steady state steady state Enzymes have only catalyzing effect, they are not necessarily modified. Enzymes have only catalyzing effect, they are not necessarily modified.

4. 4 Metabolic pathway analysis Decomposition of a network in smallest functional entities (metabolic pathways) Knowledge about kinetic parameters is not necessary! Just stoichiometric coefficients and reversibilities / irreversibilities of reactions must be known. Two possible approaches: Elementary modes Elementary modes Petri nets → minimal T-invariants Petri nets → minimal T-invariants

5. 5 Elementary modes An elementary flux mode (EM) is a minimal set of enzymes that can operate at steady state with all irreversible reactions used in the appropriate direction The enzymes are weighted by the relative flux they carry. The elementary modes are unique up to scaling. All flux distributions in the living cell are non-negative linear combinations of elementary modes Elementarity entails that no elementary mode is a subset of any other flux mode. Elementary modes are usually starting and ending at external metabolites.

6. 6 Elementary modes Examples: Q1Q1 S1S1 P1P1 1 3 Q2Q2 4 S3S3 P2P2 5 2  4 elementary modes: {E 1, E 2 }, {E 1, E 3, E 5 }, {E 4, E 3, E 2 } and {E 4, E 5 }  NO elementary modes: {E 1, E 3 }, {E 1, E 3, E 4 } Q1Q1 S1S1 P1P1 1 3 Q2Q2 4 S3S3 P2P2 5 2

7. 7 Elementary modes S. Schuster et al.: J. Biol. Syst. 2 (1994) 165-182; Trends Biotechnol. 17 (1999) 53-60; Nature Biotechnol. 18 (2000) 326-332 non-elementary flux mode elementary flux modes

8. 8 Software for calculating elementary modes EMPATH - J. Woods METATOOL - Th. Pfeiffer, F. Moldenhauer, A. von Kamp GEPASI - P. Mendes COPASI - P. Mendes, U. Kummer JARNAC - H. Sauro In-Silico-Discovery TM - K. Mauch CellNetAnalyzer (in MATLAB) - S. Klamt ScrumPy - M. Poolman Alternative algorithm in MATLAB – C. Wagner PySCeS – B. Olivier et al. On-line computation: pHpMetatool - H. Höpfner, M. Lange http://pgrc-03.ipk-gatersleben.de/tools/phpMetatool/index.php

9. 9 Structural Analysis of regulatory networks Regulatory networks are field of current interest. Knowledge about kinetic parameters is even more limited than for metabolic systems Superpositions of activations and inhibitions can occur.

10. 10 Structural Analysis of regulatory networks Example from KEGG: Insulin signalling pathway

11. 11 E1E1 E1*E1* E2E2 E2*E2* E3E3 E3*E3* Target Signal Network motif: enzyme cascades Calculation of elementary modes gives trivial result: Every cycle is a separate mode. Flow of information is not reflected. Properties of regulatory networks

12. 12 E1E1 E1*E1* E2E2 E2*E2* E3E3 E3*E3* Target Signal Network motiv: enzyme cascades Calculation of elementary modes gives trivial result: Every cycle is its own mode. Flow of information is not reflected. Properties of regulatory networks

13. 13 Properties of regulatory networks Dashed lines do not correspond to mass flow. Enzymes or proteins (yellow) can also be modified.

14. 14 2 nd motiv: binding reactions: Protein 1Protein 2 Protein complex 1.2 Protein 3 Protein complex 1.2.3 Here mass flow is relevant! Properties of regulatory networks

15. 15 In addition to mass flow we have flow of information. Just to analyze mass flow is not sufficient. Regulatory networks do not usually have a steady state (in terms of constant concentrations). Temporal dynamics like pulses or oscillations are important (e.g. calcium oscillations). Participating "players" have low concentrations. Thus discrete events and stochastic effects may become important. Enzymes do not only have catalytic functions. They can also be modified themselves. Differences between metabolic and regulatory networks

16. 16 Nevertheless elementary modes (or Extreme pathways or minimal T-invariants in Petri-Nets) are also calculated for regulatory systems (if those systems can be described by „pseudo-mass flow“). Xiong et al., Bioinformatics, 2004 Xiong et al., Bioinformatics, 2004 Papin, Palsson, Journal of Theoretical Biology, 2004 Papin, Palsson, Journal of Theoretical Biology, 2004 Heiner, Koch et al., Biosystems, 2004 Heiner, Koch et al., Biosystems, 2004 Results are of biological interest. EMs for regulatory systems ?

17. 17 Reasons for using that concept: If averaged over a longer time period also regulatory systems must be in a stationary state, because after a signalling process the system must be "recharged" for the next event. It is useful to search for elementary routes through regulatory networks. These routes don't need to be mass balanced. But one condition must be fulfilled: Every node of the network must have at least one input and one output Zevedei-Oancea, Schuster: A theoretical framework for detecting signal transfer routes in signalling networks, Comput. Chem. Eng. 29 (2005) 597-617. EMs for regulatory systems ?

18. 18 Here only the activated components of the enzyme cascade are displayed: Signal E1*E1* E2*E2* E4*E4* Target 2 Target 1 E3*E3* EMs for regulatory systems ?

19. 19 Signal E1*E1* E2*E2* E4*E4* Target 2 Target 1 E3*E3* EMs for regulatory systems ? This system has 2 elementary routes.

20. 20 Boolean networks based on Boolean algebra just 2 states are defined: 0 (off) and 1 (on) Example: genes can have approximately 2 states: inactive(0) active(1) In Boolean networks usually discrete time steps are considered. Logical steady states can be defined.

21. 21 Boolean networks Example 1: Rule table: tt+1 Gene 1 Gene 2 Gene 1 Gene 2 0000 0101 1010 1100 0,00,1 1,0 1,1 The system has 3 logical steady states, (0,0), (0,1) and (1,0).

22. 22 Boolean networks Example 2: Rule table: tt+1 Gene 1 Gene 2 Gene 1 Gene 2 0000 0110 1001 1111 The system has 2 logical steady states, (0,0) and (1,1). Starting at (0,1) or (1,0) → oscillation. 0,00,1 1,0 1,1

23. 23 Boolean networks S. Klamt et al.: BMC Bioinformatics (2006) Small example network from CellNetAnalyzer:

24. 24 Boolean networks Signaling paths linking input layer and output layer (1) S. Klamt et al.: BMC Bioinformatics (2006)

25. 25 Boolean networks Signaling paths linking input layer and output layer (2) S. Klamt et al.: BMC Bioinformatics (2006)

26. 26 Boolean networks S. Klamt et al.: BMC Bioinformatics (2006) Shortcomings of interaction graphs: AND connections are not possible! → hypergraphical representation necessary

27. 27 Boolean networks S. Klamt et al.: BMC Bioinformatics (2006) The network as logical interaction hypergraph:

28. 28 Application of elementary modes Structural robustness of metabolic networks How can structural robustness be measured? Just taking the number of elementary modes in the network as a measure of robustness. Just taking the number of elementary modes in the network as a measure of robustness. The network fragility coefficient, based on the concept of minimal cut sets (MCS (Steffen Klamt, 2004), calculated with CellNetAnalyzer) can be correlated with the robustness of the network. The network fragility coefficient, based on the concept of minimal cut sets (MCS (Steffen Klamt, 2004), calculated with CellNetAnalyzer) can be correlated with the robustness of the network. Calculating the average percentage of remaining elementary modes after a knockout of enzyme (Wilhelm et al., 2004). Calculating the average percentage of remaining elementary modes after a knockout of enzyme (Wilhelm et al., 2004).

29. 29 Structural robustness of metabolic networks Both networks have 2 elementary modes. A knockout of enzyme 1 deletes both elementary modes in network A but only one in network B.  Network A is less robust than network B. A) Q1Q1 S1S1 P1P1 1 2 P2P2 3 B) Q1Q1 P2P2 3 S2S2 4 1 2 S P1P1 S1S1

30. 30 A few mathematical details normalised sum of all ratios between the number of remaining EMs after knockout and the number of EMs in the unperturbed network r:Total number of reactions in the system z:Number of elementary flux modes in unperturbed network z (i) :Number of elementary modes remaining after knockout Wilhelm, T., Behre, J., Schuster, S. Analysis of structural robustness of metabolic networks. IEE Proceedings Systems Biology, 2004, 1, 114-120.

31. 31 Simple example Small example network for explaining the calculation: The network contains 4 EMs: {E 1, E 2, E 4 }, {E 3, E 4 }, {E 5, E 6 } and {E 5, E 7 } The network contains 4 EMs: {E 1, E 2, E 4 }, {E 3, E 4 }, {E 5, E 6 } and {E 5, E 7 } The average robustness R 1 is calculated to 0.679 as shown below: The average robustness R 1 is calculated to 0.679 as shown below: S1S1 Q1Q1 Q2Q2 S3S3 P1P1 P2P2 1 2 34 5 6 P3P3 7 S2S2

32. 32 Metabolic network Number of elementary flux modes R1R1R1R1 Human erythrocyte ATP, hypoxanthine, NADPH, 2,3DPG 6670.383 E. coli Ala, Arg, Asn, His 6670.508 Arg, Asn, His, Ile 6560.521 Arg, Asn, Ile, Leu 5670.548 Arg, Asn, Leu, Pro 5400.536 His, Ile, Leu, Lys 8020.511 Ile, Leu, Pro, Val 5970.549 Application to central metabolisms of human erythrocyte and E. coli Wilhelm et al., IEE Proceedings Systems Biology, 2004

33. 33 Outlook We are currently generalizing the analysis to multiple knockouts Calculation can also be based on double knockouts, triple knockouts … Calculation can also be based on double knockouts, triple knockouts … Application to new metabolic pathways Application to new metabolic pathways Comparison of animo acid synthesis in E. coli and human is currently processed. Applying our concept for structural robustness to regulatory networks is possible. Instead of "classical" EMs from metabolic pathways also the pathways through regulatory networks can be used for calculating the structural robustness. Instead of "classical" EMs from metabolic pathways also the pathways through regulatory networks can be used for calculating the structural robustness. Application to the insulin signalling pathway is planned. Application to the insulin signalling pathway is planned.

34. 34 Summary Metabolic pathway analysis structural analysis of networks without knowledge of kinetics structural analysis of networks without knowledge of kinetics Regulatory networks contain also interactions without mass flow contain also interactions without mass flow "Classical" EMs (or T-invariants in Petri-Nets) can not always be computed. "Classical" EMs (or T-invariants in Petri-Nets) can not always be computed. Boolean networks Structural modelling of regulatory networks with Boolean networks is possible. Structural modelling of regulatory networks with Boolean networks is possible. Elementary routes through a network can be computed. Elementary routes through a network can be computed. Structural robustness of networks Structural robustness of metabolic networks can be calculated on the basis of elementary modes. Structural robustness of metabolic networks can be calculated on the basis of elementary modes. This concept can also be applied to regulatory networks. This concept can also be applied to regulatory networks.

35. 35 Acknowledgements Thank you for your attention... and to Prof. Dr. Stefan Schuster (FSU, Jena) Dr. Thomas Wilhelm (FLI, Jena) Dr. Steffen Klamt (MPI, Magdeburg)