Metabolic Flux Analysis by MATLAB
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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
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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. - PowerPoint PPT Presentation
Transcript of 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. [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)
Genome-scale metabolic model
Amino acids
Model reconstruction
GC-MS
ProteinHydrolysis
Isotopiclabeling
Software development
Metabolic Flux Analysis
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
Flux Balance Analysis (FBA)
Glucose
G6P R5P
Pyr
AcCoA Acetate
ICIT
AKGSUC
OAA
v1
v2
v3
v4
v5v6
v7
v8
v9
v10
v11
v12
v13
v14
v15
v16
Transport flux
Intracellular flux
Building block flux
16 fluxes, 8 intracellular metabolitesG6P : v1=v2+v3+v16
R5P : v2=v4
Pyr : 2 v3+v4=v5+v11+v15
AcCoA : v5=v6+v7+v14
ICIT : v7=v8
AKG : v8=v9+v12
SUC: v9=v10
OAA : v10+v11=v7+v13
The transport fluxes were measured:
The building block fluxes can be assumed from biomass composition:
v1=11.0 mmol/g DCW/h
v6=6.4 mmol/g DCW/h
v12=1.078
v13=1.786
v14=2.928
v15=2.833
v16=0.205
17 variables 15 equationsFreedom = 2
1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0
0 1 0 1 0 0 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 0 0 1 1 1 0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 1 1 0 0 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 0 0 1 1 0 0 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 0 0 1 0 0 0 0 1.078
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1.786
0 0 0 0 0 0 0 0 0 0
v1
v2
v3 0
v4 0
v5 0
v6 0
v7 0
v8 0
v9
v10
v11
v12
0 0 0 1 0 0 2.928 v13
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 2.833 v14
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0.205 v15
v16
0
0
0
0
0
0
0
S ∙ v = 0
Line
arco
nstr
aint
sVariables (fluxes)
Flux Balance Analysis (FBA)
maximize μ
s.t. S∙v = 0
0 < v < 20 mmol/g DCW/h
T
T
T
obj 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
lb 11.0 0 0 0 0 6.4 0 0 0 0 0 0 0 0 0 0 0
ub 11.0 20 20 20 20 6.4 20 20 20 20 20 20 20 20 20 20 20
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”
Put the objective
vector
S∙v=0
lb and ub
Options to stop the
optimization
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)
Glucose
G6P R5P
Pyr
AcCoA Acetate
ICIT
AKGSUC
OAA
v1
v2
v3
v4
v5v6
v7
v8
v9
v10
v11
v12
v13
v14
v15
v16
Transport flux
Intracellular flux
Building block flux
CO2
A simple case:
0.5 v3 v4Pyr000
v3 v40.5 v3
Pyr001v3 v4
ratio: v3/v4
16 fluxes, 8 intracellular metabolites
G6P : v1=v2+v3+v16
R5P : v2=v4
Pyr : 2 v3+v4=v5+v11+v15
AcCoA : v5=v6+v7+v14
ICIT : v7=v8
AKG : v8=v9+v12
SUC: v9=v10
OAA : v10+v11=v7+v13
The transport fluxes were measured:
v1=11.0 mmol/g DCW/h
v6=6.4 mmol/g DCW/h
The building block fluxes are not necessary to be assumed
1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0
0 1 0 1 0 0 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 0 0 1 1 1 0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 1 1 0 0 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 0 0 1 1 0 0 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 0 0 1 0 0 0 0 1.078
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1.786
0 0 0 0 0 0 0 0 0 0
v1
v2
v3 0
v4 0
v5 0
v6 0
v7 0
v8 0
v9
v10
v11
v12
0 0 0 1 0 0 2.928 v13
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 2.833 v14
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0.205 v15
v16
0
0
0
0
0
0
0
S ∙ v = 0
Line
arco
nstr
aint
sVariables (fluxes)
13C-assisted Metabolic Flux Analysis (13C-MFA)
T
T
lb 11.0 0 0 0 0 6.4 0 0 0 0 0 0 0 0 0 0
ub 11.0 20 20 20 20 6.4 20 20 20 20 20 20 20 20 20 20
minimize (MDVexp-MDVsim)2
s.t. IDV = f(v, IMM, IDV)
MDV = M∙IDV
S∙v = 0
0< v < 20
achieved in .m file
MATLAB Code for 13C-MFA
Input the variables
Input the experimentalobserved MDV
Identify labeling of CO2
Isotopomertransitions
Reach the Isotopic steadystate in TCA cycle
Optimization Toolbox for Flux Analysis
Using “fmincon” solver in Optimization Toolbox for 13C-MFA
S∙v=0
Use “fmincon” for 13C-MFA
Change to “Interior point”
Put the objective function
lb and ub
S∙v=0
Initial guess
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?
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