1. Genetic modification of flux (GMF) for flux prediction of mutants Kyushu Institute of Technology Quanyu Zhao, Hiroyuki Kurata

2. Topics Background of computational modeling of biological systems Elementary mode analysis based Enzyme Control Flux (ECF) Genetic Modification of Flux (GMF)

3. Our objectives Quantitative modeling of metabolic networks is necessary for computer-aided rational design.

4. Computer model of metabolic systems Metabolic NetworksQuantitative Model Omics data Molecular Biology data Integration of heterogenous data BASE Genomics Transcriptomics Proteomics Metabolomics Fluxomics Physiomics

5. Differential equations Dynamic model ， Many unknown parameters Quantitative Models Linear Algebraic equations Constraint based flux analysis at the steady state

6. S Stoichiometric matrix v flux distribution Constraint Prediction of a flux distribution at the steady state Objective function FLUX BALANCE ANALYSIS: ＦＢＡ

7. For gene deletion mutants, steady state flux is predicted using Boolean Logic MethodOptimization AlgorithmAdditional information rFBA (regulatory FBA) Linear ProgrammingRegulatory network (genomics) SR-FBA (Steady-state Regulatory-FBA) Mixed Integer Linear Programming Regulatory network MOMA (Minimization Of Metabolic Adjustment) Quadratic ProgrammingFlux distribution of wild type (fluxomics) ROOM (Regulatory On/Off Minimization) Mixed Integer Linear Programming Flux distribution of wild type Reactions for knockout gene = 0 Other reactions =1

8. Current problem: In gene deletion mutants, many gene expressions are varied, not digital. How to integrate transcriptome or proteome into metabolic flux analysis. Proposal: Elementary mode analysis is employed for such integration.

9. Elementary Modes (EMAs) AB EM1 EM2 EM1 EM2 Minimum sets of enzyme cascades consisting of irreversible reactions at the steady state

10. Elementary Modes (Ems) Stoichiometric Matrix １ ２ ３ ４ ５ EM Flux distribution Elementary mode matrix Coefficients

11. 1 2 3 4 5 EMC is not uniquely determined. EM Flux Flux ＝ EM Matrix ・ EMC Objective function is required.

12. Objective functions Growth maximization: Linear programming Convenient function: Quadratic programming Maximum Entropy Principle (MEP)

13. Shannon information entropy Constraint Quanyu Zhao, Hiroyuki Kurata, Maximum entropy decomposition of flux distribution at steady state to elementary modes. J Biosci Bioeng, 107: 84-89, 2009

14. ECF integrates enzyme activity profiles into elementary modes. ECF presents the power-law formula describing how changes in an enzyme activity profile between wild-type and a mutant is related to changes in the elementary mode coefficients (EMCs). Enzyme Control Flux (ECF) Kurata H, Zhao Q, Okuda R, Shimizu K. Integration of enzyme activities into metabolic flux distributions by elementary mode analysis. BMC Syst Biol. 2007;1:31.

15. Network model with flux of WT Enzyme activity profile Mutant / WT Estimation of a flux distribution of a mutant Power-Law formula Enzyme Control Flux (ECF)

16. Reference model Power Law Formula Change in enzyme activity profile Prediction of a flux distribution of a target cell MEP ＥＣＦ Algorithm

17. a1a1 a5a5 a2a2 EMi Power Law Formula EMi Enzyme activity profile Optimal  ＝ 1

18. pykF knockout in a metabolic network 74 EMs

19. Effect of the number of the integrated enzymes on model error (ECF) An increase in the number of integrated enzymes enhances model accuracy. Model Error = Difference in the flux distributions between WT and a mutant

20. Prediction accuracy of ECF Gene deletionNumber of enzymes used for prediction Prediction accuracy (control: no enzyme activity profile is used) pykF11+++ ppc8+++ pgi5+ cra6+++ gnd4+ fnr6+++ FruR6+++

21. ECF provides quantitative correlations between enzyme activity profile and flux distribution. Summary of ECF

22. Genetic Modification of Flux Quanyu Zhao, Hiroyuki Kurata, Genetic modification of flux for flux prediction of mutants, Bioinformatics, 25: 1702-1708, 2009

23. Gene expression (enzyme activity) profile Metabolic networks /gene deletion Metabolic flux distribution Metabolic flux distribution for genetic mutants ECF MOMA/rFBA Prediction of Flux distribution for genetic mutants

24. Flow chart of GMF Gene expression (enzyme activity) profile Metabolic networks /genetic modification Metabolic flux distribution Metabolic flux distribution for genetic mutants mCEF ECF

25. Expected advantage of GMF Available to gene knockout, over-expressing or under-expressing mutants MOMA/rFBA are available only for gene deletion, because they use Boolean Logic.

26. Control Effective Flux (CEF) Transcript ratio for the growth on glycerol versus glucose Stelling J, et al, Nature, 2002, 420, 190-193 Transcript ratio of metabolic genes CEFs for different substrates glucose, glycerol and acetate.

27. mCEF is an extension of CEF available for Genetically modification mutants Up-regulation Down-regulation Deletion

28. GMF = mCEF+ECF S (Stoichiometric matrix) P (EMs matrix) mCEF ECF mCEF WT Mutant Experimental data

29. Ishii N, et al. Science 316 : 593-597,2007 mCEF predicts the transcript ratio of a mutant to wild type

30. Comparison of GMF(CEF+ECF) with FBA and MOMA for E. coli gene deletion mutants Characterization of GMF

31. FBA MOMA V k is the flux of gene knockout reaction k

32. Prediction of the flux distribution of an E. coli zwf mutant by GMF, FBA, and MOMA Zhao J, Baba T, Mori H, Shimizu K. Appl Microbiol Biotechnol. 2004;64(1):91-8.

33. Prediction of the flux distribution of an E. coli gnd mutant by CEF+ECF, FBA, and MOMA Zhao J, Baba T, Mori H, Shimizu K. Appl Microbiol Biotechnol. 2004;64(1):91-8.

34. Prediction of the flux distribution of an E. coli ppc mutant by CEF+ECF, FBA, and MOMA Peng LF, Arauzo-Bravo MJ, Shimizu K. FEMS Microbiol Letters, 2004, 235(1): 17-23

35. Prediction of the flux distribution of an E. coli pykF mutant by CEF+ECF, FBA, and MOMA Siddiquee KA, Arauzo-Bravo MJ, Shimizu K. Appl Microbiol Biotechol 2004, 63(4):407-417

36. Prediction of the flux distribution of an E. coli pgi mutant by CEF+ECF, FBA, and MOMA Hua Q, Yang C, Baba T, Mori H, Shimizu K. J Bacteriol 2003, 185(24):7053-7067

37. Prediction errors of FBA, MOMA and GMF for five mutants of E. coli MethodzwfgndpgippcpykF FBA18.3814.7623.6829.9221.10 MOMA18.0614.2729.3819.7925.83 GMF6.439.2118.4718.9520.46 Model Error = Difference in the flux distributions between WT and a mutant

38. Is GMF applicable to over-expressing or less-expressing mutants? (FBA and MOMA are not applicable to these mutants.)

39. Up/down-regulation mutants FBP over-expressing mutant of C. glutamicum G6P dehydrogenase over-expressing mutant of C. glutamicum gnd deficient mutant of C. glutamicum G6P dehydrogenase over-expressing mutant of E. coli

40. Summary of GMF mCEF is combined to ECF for the accurate prediction of flux distribution of mutants. GMF is applied to the mutants where an enzyme is over-expressed, less-expressed. It has an advantage over rFBA and MOMA.

41. Conclusion ECF is available for the quantitative correlation between an enzyme activity profile and its associated flux distribution GMF is a new tool for predicting a flux distribution for genetically modified mutants.

42. Thank you very much