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

CO2

ICT

Protein

GOX

CO2

OGT

CO2

MAL

SUC

AcCoA

CITOAA

Glucose-6-P

Lipid

CO2Pyruvate

Carbohydrates

CO2

Isocitrate

Citratev6 v17

v14

v16v4

v3

v2

v1

v10

v18

v8

v15v9

v13

v12

v7

v5

v11

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

CO2

ICT

Protein

GOX

CO2

OGT

CO2

MAL

SUC

AcCoA

CITOAA

Glucose-6-P

Lipid

CO2Pyruvate

Carbohydrates

CO2

Isocitrate

Citratev6 v17

v14

v16v4

v3

v2

v1

v10

v18

v8

v15v9

v13

v12

v7

v5

v11

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

CO2

ICT

Protein

GOX

CO2

OGT

CO2

MAL

SUC

AcCoA

CITOAA

Glucose-6-P

Lipid

CO2Pyruvate

Carbohydrates

CO2

Isocitrate

Citratev6 v17

v14

v16v4

v3

v2

v1

v10

v18

v8

v15v9

v13

v12

v7

v5

v11

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

CO2

ICT

Protein

GOX

CO2

OGT

CO2

MAL

SUC

AcCoA

CITOAA

Glucose-6-P

Lipid

CO2Pyruvate

Carbohydrates

CO2

Isocitrate

Citratev6 v17

v14

v16v4

v3

v2

v1

v10

v18

v8

v15v9

v13

v12

v7

v5

v11

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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0   0

0 1 0 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0   0

0 0 0 1 0 -1 0 0 0 0 0 0 -1 -1 0 0 0 0   0

0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 -1 0   0

0 0 0 0 0 0 1 -1 0 0 0 -1 0 0 0 0 0 -1   0

0 0 0 0 0 0 0 1 -1 0 0 0 0 0 -1 0 0 0 v = 0

0 0 0 0 0 0 0 0 1 -1 0 1 0 0 0 0 0 0   0

0 0 0 0 0 0 0 0 0 1 -1 0 1 0 0 0 0 0   0

0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0   0

0 0 0 0 1 -1 0 0 0 0 1 0 0 0 0 0 0 0   0

0 0 0 1 -1 0 0 1 1 0 0 0 0 0 0 -1 0 0   0

Matrix Solution for Intracellular Fluxes

                           -1

               

V2   

-0.5 0 0 0 0 0 0 0 0 0 0 

1 -1 0 0 0 0 0 

V4   

1 -1 -1 0 0 0 0 0 0 0 0 

0 0 0 0 0 0 0 

V5   

0 1 0 -1 0 0 0 0 0 -1 -1 

0 0 0 0 0 0 0 rglc

V6   

0 0 0 1 1 0 0 0 0 0 0 

0 0 0 0 0 -1 0 rcar

V7   

0 0 0 0 1 1 0 0 0 0 0 

0 0 -1 0 0 0 -1 0

V8 = - 0 0 0 0 0 1 -1 0 0 0 0 X 0 0 0 -1 0 0 0 rprot

V9   

0 0 0 0 0 0 1 -1 0 0 0 

0 0 1 0 0 0 0 rc

V10   

0 0 0 0 0 0 0 1 1 1 0 

0 0 0 0 0 0 0 rcit

V11   

0 0 0 0 0 0 0 0 0 1 0 

0 0 1 0 0 0 0 rict

V13   

0 0 1 -1 0 0 0 0 1 0 0 

0 0 0 0 0 0 0 

V14   

0 1 -1 0 0 1 1 0 0 0 0 

0 0 0 0 -1 0 0 

Simplified Intracellular Flux Matrix

V2  2 -2 0 0 0 0 0  

V4  2 -2 1 -1 0 -1 -1  

V5  0 0 -1 1 0 1 1 rglc

V6  -1 1 0 1.5 0.5 2 2 rcar

V7  -1 1 0 1.5 0.5 1 2 0

V8 = -1 1 -1 1.5 0.5 1 1 rprot

V9  -1 1 -1 0.5 0.5 1 1 rc

V10  -1 1 0 0.5 0.5 1 1 rcit

V11  -1 1 1 0.5 0.5 1 1 rict

V13  0 0 1 0 0 0 0  

V14  3 -3 0 -2.5 -0.5 -3 -3  

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.