Genetic modification of flux GMF for flux prediction

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

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

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

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

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

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

For gene deletion mutants, steady state flux is predicted using Boolean Logic Method Optimization Algorithm Additional information r. FBA (regulatory FBA) Linear Programming Regulatory network (genomics) SR-FBA (Steady-state Regulatory-FBA) Mixed Integer Linear Programming Regulatory network MOMA (Minimization Of Metabolic Adjustment) Quadratic Programming Flux 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

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.

Elementary Modes (EMAs) Minimum sets of enzyme cascades consisting of irreversible reactions at the steady state EM 1 A EM 2 B EM 2

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

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

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

Maximum Entropy Principle (MEP) 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

Enzyme Control Flux (ECF) 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). 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.

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

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

Power Law Formula Optimal b＝ 1 EMi a 1 a 2 a 5 Enzyme activity profile

pyk. F knockout in a metabolic network 74 EMs

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

Prediction accuracy of ECF Gene deletion Number of enzymes used for prediction Prediction accuracy (control: no enzyme activity profile is used) pyk. F 11 +++ ppc 8 +++ pgi 5 + cra 6 +++ gnd 4 + fnr 6 +++ Fru. R 6 +++

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

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

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

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

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

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

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

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

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

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

• FBA Vk is the flux of gene knockout reaction k • MOMA Vk is the flux of gene knockout reaction k

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.

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.

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

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

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

Prediction errors of FBA, MOMA and GMF for five mutants of E. coli Method zwf gnd pgi ppc pyk. F FBA 18. 38 14. 76 23. 68 29. 92 21. 10 MOMA 18. 06 14. 27 29. 38 19. 79 25. 83 GMF 6. 43 9. 21 18. 47 18. 95 20. 46 Model Error = Difference in the flux distributions between WT and a mutant

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

Up/down-regulation mutants FBP over-expressing mutant of C. glutamicum G 6 P dehydrogenase over-expressing mutant of C. glutamicum gnd deficient mutant of C. glutamicum G 6 P dehydrogenase over-expressing mutant of E. coli

Summary of GMF • m. CEF 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 r. FBA and MOMA.

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.

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