Transcript Metabolic Flux Analysis by MATLAB

Metabolic Flux Analysis by MATLAB
Xueyang Feng (from Tang Lab)
Dept. of Energy, Environmental & Chemical Engineering
Washington University in St. Louis
[email protected]
314-935-6125
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)
Metabolic Flux Analysis
Model
reconstruction
Genome-scale
metabolic model
Software
development
Protein
Hydrolysis
Isotopic
labeling
Amino acids
GC-MS
Metabolic Flux Analysis
Flux Balance Analysis (FBA)
13C-assisted
• in silico simulation
• Linear programming (LP)
• Genome-scale
• in vivo analysis
• Nonlinear programming (NLP)
• Simplified model
Metabolic Flux Analysis
maximize ∑ci ∙vi
minimize (MDVexp-MDVsim)2
s.t.
s.t.
S∙v = 0
lb < v < ub
S∙v = 0
IDV = f(v, IMM, IDV)
MDV = M∙IDV
lb < v < ub
Metabolic Steady state
Metabolic & isotopic Steady state
Flux Balance Analysis (FBA)
16 fluxes, 8 intracellular metabolites
Glucose
v1
G 6 P : v1= v2+ v3+ v16
R 5P : v2= v4
v16
G6P v2
v3
P yr : 2  v3+ v4= v5+ v11+ v15
R5P
A cC oA : v5= v6+ v7+ v14
v4
IC IT : v7= v8
Pyr
A K G : v8= v9+ v12
v15
v5
v11
v14
S U C : v9= v10
v6
AcCoA
Acetate
O A A : v10+ v11= v7+ v13
The transport fluxes were measured:
v13
v7
OAA
v1= 11.0 m m ol/g D C W /h
ICIT
v6= 6.4 m m ol/g D C W /h
v10
v8
SUC
AKG
v9
v12
Transport flux
Intracellular flux
Building block flux
The building block fluxes can be assumed
from biomass composition:
v12= 1.078  
v13= 1.786  
v14= 2.928  
v15= 2.833  
v16= 0.205  
17 variables
15 equations
Freedom = 2
Linear
constraints
Variables (fluxes)
1

0

 0

 0
 0

 0
 0

 0

 0
 0

 0
 0

 0
1
1
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
2
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1 1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
S∙v=0
 v1 


v2



0 
v3   0 
  
 
0
v
4
 0 
 
0   v5   0 
  
 
0   v6  0 
0   v7  0 
  
 
0   v8   0 


0    v9    0 

 


0  v10
0
  
 
1.078   v11   0 
1.786   v12   0 
  
 
2.928   v13   0 

  
2.833  v14
0

  

0.205   v15   0 


v16


 


Flux Balance Analysis (FBA)
maximize μ
s.t.
S∙v = 0
0 < v < 20 mmol/g DCW/h
obj   0
lb  11.0
ub  11.0
0
0
0
20
0
0
0
0
20
0
0
20
0
0
0
0
0
0
0
0
0
0
1
6.4
0
0
0
0
0
0
0
0
0
0
20
6.4
20
20
20
20
20
20
T
0
20
T
20
20
20
20 
T
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
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
13C-assisted
Metabolic Flux Analysis (13C-MFA)
A simple case:
Glucose
v1
v16 G6P v2
v3
CO2
P yr 000 
P yr 001 
Pyr
v15
0.5  v3
ratio: v3/v4
v3  v 4
16 fluxes, 8 intracellular metabolites
v5
v14
v3  v 4
R5P
v4
v11
0.5  v3  v 4
v6
AcCoA
Acetate
G 6 P : v1= v2+ v3+ v16
R 5P : v2= v4
v13
P yr : 2  v3+ v4= v5+ v11+ v15
v7
OAA
ICIT
A cC oA : v5= v6+ v7+ v14
IC IT : v7= v8
v10
v8
SUC
AKG
v9
v12
A K G : v8= v9+ v12
S U C : v9= v10
O A A : v10+ v11= v7+ v13
The transport fluxes were measured:
Transport flux
v1= 11.0 m m ol/g D C W /h
Intracellular flux
v6= 6.4 m m ol/g D C W /h
Building block flux
The building block fluxes are not
necessary to be assumed
Linear
constraints
Variables (fluxes)
1

0

 0

 0
 0

 0
 0

 0

 0
 0

 0
 0

 0
1
1
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
2
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1 1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
S∙v=0
 v1 


v2



0 
v3   0 
  
 
0
v
4
 0 
 
0   v5   0 
  
 
0   v6  0 
0   v7  0 
  
 
0   v8   0 


0    v9    0 

 


0  v10
0
  
 
1.078   v11   0 
1.786   v12   0 
  
 
2.928   v13   0 

  
2.833  v14
0

  

0.205   v15   0 


v16


 


13C-assisted
Metabolic Flux Analysis (13C-MFA)
minimize (MDVexp-MDVsim)2
s.t.
IDV = f(v, IMM, IDV)
achieved in .m file
MDV = M∙IDV
S∙v = 0
0< v < 20
lb  11.0
ub  11.0
0
20
0
0
20
0
20
6.4
20
0
6.4
0
0
20
0
20
0
0
20
0
20
0
20
0
0
20

20
T
20
20
20

T
MATLAB Code for 13C-MFA
Input the variables
Isotopomer
transitions
Identify labeling of CO2
Input the experimental
observed MDV
Reach the
Isotopic steady
state in TCA
cycle
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
v.s.
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?