Integration of enzyme activities into metabolic flux distributions by elementary mode analysis Kyushu Institute of Technology Hiroyuki Kurata, Quanyu Zhao, Ryuichi Okuda, Kazuyuki Shimizu

Background A computational model for large-scale biochemical networks is required for the integration of postgenomic data and molecular biology data and should be readily updated with new experimental data. Network pathway-based models are promising models e.g., flux balance analysis, elementary mode analysis, extreme pathways.

Network pathway analysis facilitates understanding or designing metabolic systems and enables prediction of metabolic flux distributions. Network-based flux analysis requires considering not only pathway architectures but also the proteome or transcriptome to predict flux distributions, because recombinant microbes significantly change the distribution of gene expressions. The current problem is how to integrate such heterogeneous data to build a network-based model.

S: Stoichiometric matrix v: Flux distribution vector F(v): Objective function A problem of Flux Balance Analysis Q: How do you integrate transcriptome or proteome data into flux balance analysis? A: Few answers. A new method for integrating these data into metabolic flux analysis is required.

Elementary Mode Analysis (EMA) AB EM1 EM2 The elementary mode is the minimal set of enzymes that can operate at steady-state, with all the irreversible reactions operating properly EM1 EM2

Example of EM decomposition Stoichiometric Matrix EM1 EM2 EM3 EM4 EM5 EM

EM flux EMC EM matrix A flux distribution is decomposed onto EMs. In general, EMCs are not determined uniquely.

To link enzyme activity data to flux distributions of metabolic networks, we have proposed Enzyme Control Flux (ECF), a novel model that integrates enzyme activity into elementary mode analysis (EMA). ECF presents the power-law formula describing how changes in enzyme activities between wild-type and a mutant are related to changes in the elementary mode coefficients (EMCs). Enzyme Control Flux (ECF)

A flux distribution of wild type Enzyme activity data for wild type and mutants ECF Strategy ECF Prediction of a flux distribution for a mutant

For wild type mt: mutant For a mutant P: n x m EM matrix (n: reaction number, m: number of EMs ECF correlation:

ECF model based on the power law formula :the i-th EMC for a mutant :the i-th EMC for wild type :relative enzyme activity of a mutant to wild type :coefficient for normalized substrate uptake :power coefficient (adjustment parameter) a1a1 anan a2a2 i-th EM

To validate the feasibility of ECF, we integrated enzyme activity data into the EMCs of Escherichia coli and Bacillus subtilis wild-type. The ECF model effectively uses an enzyme activity profile to estimate the flux distribution of the mutants and the increase in the number of incorporated enzyme activities decreases the model error of ECF. Validation of ECF

pykF knockout mutant 1. The EM matrix is obtained by FluxAnayzer (Klamt et al). 2. The EMCs for wild type are calculated by using a flux distribution of wild type. 3. Relative enzyme activities of a mutant to wild type are integrated into the EMCs for wild type by the ECF model to obtain the EMCs for a mutant 4. A flux distribution of a mutant is predicted.

Metabolic model for a pyk knockout mutant 74 EMs

The ECF model predicts the flux distribution of a mutant Flux spectra for a mutant is predicted by ECF The mean values are used. EMCs for wild type are calculated.

Effect of the number of the integrated enzymes on model error (ECF) Model Error = |experimental flux value - predicted flux value| An increase in the number of integrated enzymes enhances model accuracy. Model Error spectrum max min mean + s.d. mean mean - s.d.

 =0.5  =1  =2  =4 A unique adjustment parameter of  is determined. A  of 1 is a best choice for accurate prediction or correlation. Best

Successful application of ECF to other mutants KnockoutNumber of enzymes Model error pykF 11Very small ppc 8Very small pgi 5 not clear cra 6Very small gnd 4 not clear fnr 6Very small FruR 6Very small

Conclusion The ECF model is a non-mechanistic and static model to link an enzyme activity profile to a metabolic flux distribution by introducing the power- law formula into EMA, suggesting that the change in an enzyme profile rather reflects the change in the flux distribution. The ECF model is highly applicable to the central metabolism in knockout mutants of E. coli and B. subtilis.