Metabolic Flux Analysis Metabolic Flux Analysis of Citric Acid Fermentation by Candida lipolytica Presentation by: Miles Beamguard and Wade Mack September 19, 2001

Case Study Aiba, S. & Matsuoka, M. (1979). Identification of metabolic model: Citrate production from glucose by Candida lipolytica. Biotechnology and Bioengineering. 21, 1373-1386. Considered the first application of metabolite balancing to fermentation data

Objectives of Presentation Outline Objectives of Case Study Analyze their reaction equations using matrix algebra calculations Discuss the relevance of the matrix analysis approach to metabolite modeling

Objectives of Presentation Outline Objectives of Case Study Analyze their reaction equations using matrix algebra calculations Discuss the relevance of the matrix analysis approach to metabolite modeling

Objectives of Case Study Analyze the metabolic network Form reaction equations Determine some variables through experimental data Reduce unknowns by a selected model

Metabolic Network Glucose Glucose-6-P Carbohydrates Pyruvate CO2 CO2 Lipid AcCoA v5 v6 v17 OAA CIT Citrate v7 v11 v13 v12 v18 ICT Isocitrate MAL GOX v10 CO2 v8 SUC OGT v15 v9 Protein CO2

Reaction Rate Equations G6P : v1 - v2/2 – v3 = 0 Pyr : v2 – v4 – v5 = 0 AcCoA : v4 – v6 – v13 – v14 = 0 CIT : v6 – v7 – v17 = 0 ICT : v7 – v8 – v12 – v18 = 0 OGT : v8 – v9 – v15 = 0 SUC : v9 – v10 + v12 = 0 MAL : v10 – v11 + v13 = 0 GOX : v12 - v13 = 0 OOA : v5 + v11 – v6 = 0 CO2 : v4 + v8 + v9 – v16 = 0

Determining Known Variables Elimination of v13 due to glyoxylate reaction equal to v12 18 reaction rates but only 11 balance equations resulting in 7 degrees of freedom Measurement within network led to empirical solving for 6 reaction rates.

6 Measured Reaction Rates Glucose Uptake Rate (rglc) = v1 Carbon Dioxide Production Rate (rc) = v16 Citric Acid Production Rate (rcit) = v17 Isocitrate Production Rate(rict) = v18 Protein Synthesis Rate (rprot) = v15 Carbohydrate Synthesis Rate (rcar) = v3

Select A Model With 12 unknown reaction rates and 11 balance equations we have 1 degree of freedom, so a model must be assumed. Model 1 – The glyoxylate shunt is inactive, v12 = 0

Metabolic Network Glucose Glucose-6-P Carbohydrates Pyruvate CO2 CO2 Lipid AcCoA v5 v6 v17 OAA CIT Citrate v7 v11 v13 v12 v18 ICT Isocitrate MAL GOX v10 CO2 v8 SUC OGT v15 v9 Protein CO2

Select A Model With 12 unknown reaction rates and 11 balance equations we have 1 degree of freedom, so a model must be assumed. Model 1 – The glyoxylate shunt is inactive, v12 = 0 Model 2 – Pyruvate carboxylation is inactive, v5 = 0

Metabolic Network Glucose Glucose-6-P Carbohydrates Pyruvate CO2 CO2 Lipid AcCoA v5 v6 v17 OAA CIT Citrate v7 v11 v13 v12 v18 ICT Isocitrate MAL GOX v10 CO2 v8 SUC OGT v15 v9 Protein CO2

Select A Model With 12 unknown reaction rates and 11 balance equations we have 1 degree of freedom, so a model must be assumed. Model 1 – The glyoxylate shunt is inactive, v12 = 0 Model 2 – Pyruvate carboxylation is inactive, v5 = 0 Model 3 – The Tricarboxylic Acid cycle was nullified, v9 = 0

Metabolic Network Glucose Glucose-6-P Carbohydrates Pyruvate CO2 CO2 Lipid AcCoA v5 v6 v17 OAA CIT Citrate v7 v11 v13 v12 v18 ICT Isocitrate MAL GOX v10 CO2 v8 SUC OGT v15 v9 Protein CO2

Which Model????? Verification of Carbon Fluxes Examination of the free-energy change at the biochemical standard state After review, both models 2 and 3 resulted in a negative carbon flux and free energy change and thus were discarded.

Objectives of Presentation Outline Objectives of Case Study Analyze their reaction equations using matrix algebra calculations Discuss the relevance of the matrix analysis approach to metabolite modeling

Reaction Rate Equations G6P : v1 - v2/2 – v3 = 0 Pyr : v2 – v4 – v5 = 0 AcCoA : v4 – v6 – v13 – v14 = 0 CIT : v6 – v7 – v17 = 0 ICT : v7 – v8 – v12 – v18 = 0 OGT : v8 – v9 – v15 = 0 SUC : v9 – v10 + v12 = 0 MAL : v10 – v11 + v13 = 0 GOX : v12 - v13 = 0 OOA : v5 + v11 – v6 = 0 CO2 : v4 + v8 + v9 – v16 = 0

Reaction Rates in Matrix Form 1 -0.5 -1   v =

Matrix Solution for Intracellular Fluxes   -1 V2 -0.5 1 V4 V5 rglc V6 rcar V7 V8 = - X rprot V9 rc V10 rcit V11 rict V13 V14

Simplified Intracellular Flux Matrix V2   2 -2 V4 1 -1 V5 rglc V6 1.5 0.5 rcar V7 V8 = rprot V9 rc V10 rcit V11 rict V13 V14 3 -3 -2.5 -0.5

Objectives of Presentation Outline Objectives of Case Study Analyze their reaction equations using matrix algebra calculations Discuss the relevance of the matrix analysis approach to metabolite modeling

Relevance of Matrix Approach Allows a simplified analysis of a complex metabolic network Succinctly demonstrates 11 different reaction equations in relation to one another

References Aiba, S. & Matsuoka, M. (1979). Identification of metabolic model: Citrate production from glucose by Candida lipolytica. Biotechnology and Bioengineering. 21, 1373-1386. Mathews, C. & Van Holde, K. E. (1996). Biochemistry, 2nd edition. Benjamin/Cummings Inc., Menlo Park, CA. 415-516. Stephanopoulus, G., Aristidou, A., Nielson, J. (1998). Metabolic Engineering. Academic Press, San Diego, CA. 320-326.