1. Metabolic Flux Analysis by MATLAB
Xueyang Feng (from Tang Lab)
Dept. of Energy, Environmental & Chemical Engineering
Washington University in St. Louis

2. Metabolic Flux Analysis
The in vivo enzymatic reaction rates (i.e. flux) cannot be directly measured.
How ?
At steady state,
dc/dt = S∙v = 0, lb <= v <= ub +
Additional information:
1) objective function (FBA)
2) 13C-experiments (13C-MFA)

3. Metabolic Flux Analysis
Model
reconstruction
Genome-scale
metabolic model
Software
development
Protein
Hydrolysis
Isotopic
labeling
Amino acids
GC-MS

4. Metabolic Flux Analysis
Flux Balance Analysis (FBA)
in silico simulation
Linear programming (LP)
Genome-scale
13C-assisted Metabolic Flux Analysis
in vivo analysis
Nonlinear programming (NLP)
Simplified model
maximize ∑ci ∙vi
s.t. S∙v = 0
lb < v < ub
minimize (MDVexp-MDVsim)2
s.t. S∙v = 0
IDV = f(v, IMM, IDV)
MDV = M∙IDV
lb < v < ub
Metabolic Steady state
Metabolic & isotopic Steady state

5. Flux Balance Analysis (FBA)
16 fluxes, 8 intracellular metabolites
Glucose
G6P
R5P
Pyr
AcCoA
Acetate
ICIT
AKG
SUC
OAA v1 v2 v3 v4 v5 v6 v7 v8 v9
v10
v11
v12
v13
v14
v15
v16
Transport flux
Intracellular flux
Building block flux
The transport fluxes were measured:
The building block fluxes can be assumed
from biomass composition:
17 variables
15 equations
Freedom = 2

6. Variables (fluxes)
constraints
Linear
S ∙ v = 0

7. Flux Balance Analysis (FBA)
maximize μ
s.t. S∙v = 0
0 < v < 20 mmol/g DCW/h

8. Optimization Toolbox for Flux Analysis
Two ways to lanch optimization toolbox in MATLAB:
“Start”  “Toolboxes”  “Optimization”
 “Optimization Tool (optimtool)”
In the command window, enter “optimtool”
Use “linprog” for FBA
Change to “Medium scale-simplex”
Options to stop the optimization
Put the objective vector
S∙v=0
lb and ub

9. Experimental observed: μ=0.82 h-1 FBA simulated : μ=1.54 h-1
Click “Start” to run the optimization
Optimized objective function value
Optimized flux results
Experimental observed:
μ=0.82 h-1
FBA simulated :
μ=1.54 h-1

10. 13C-assisted Metabolic Flux Analysis (13C-MFA)
Glucose
G6P
R5P
Pyr
AcCoA
Acetate
ICIT
AKG
SUC
OAA v1 v2 v3 v4 v5 v6 v7 v8 v9
v10
v11
v12
v13
v14
v15
v16
Transport flux
Intracellular flux
Building block flux
CO2
A simple case:
ratio: v3/v4
16 fluxes, 8 intracellular metabolites
The transport fluxes were measured:
The building block fluxes are not
necessary to be assumed

11. Variables (fluxes)
constraints
Linear
S ∙ v = 0

12. 13C-assisted Metabolic Flux Analysis (13C-MFA)
minimize (MDVexp-MDVsim)2
s.t. IDV = f(v, IMM, IDV)
MDV = M∙IDV
S∙v = 0
0< v < 20
achieved in .m file

13. MATLAB Code for 13C-MFA Input the variables Isotopomer transitions
Identify labeling of CO2
Reach the
Isotopic steady
state in TCA cycle
Input the experimental
observed MDV

14. Optimization Toolbox for Flux Analysis
Using “fmincon” solver in Optimization Toolbox for 13C-MFA
Use “fmincon” for 13C-MFA
Change to “Interior point”
Initial guess
S∙v=0
Put the objective function
S∙v=0
lb and ub

15. v.s.

16. Summary The goals of FBA and 13C-MFA are different. Choose wisely !
Scale of FBA is commonly much larger than 13C-MFA
Both FBA and 13C-MFA assume metabolic steady state
Question: how to calculate dynamic flux distribution?