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Metabolic Flux Analysis by MATLAB. Xueyang Feng Dept. of Energy, Environmental & Chemical Engineering Washington University in St. Louis. Metabolic Flux Analysis. Flux Balance Analysis (FBA) in silico simulation Linear programming (LP) Genome-scale . 13 C-assisted Metabolic Flux Analysis

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Metabolic Flux Analysis by MATLAB

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Metabolic flux analysis by matlab l.jpg

Metabolic Flux Analysis by MATLAB

XueyangFeng

Dept. of Energy, Environmental & Chemical Engineering

Washington University in St. Louis


Metabolic flux analysis l.jpg

Metabolic Flux Analysis

Flux Balance Analysis (FBA)

  • in silico simulation

  • Linear programming (LP)

  • Genome-scale

13C-assisted Metabolic Flux Analysis

  • in vivo search

  • 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 l.jpg

Flux Balance Analysis (FBA)

16 fluxes, 7 intracellular metabolites

Glucose

v1

v2

G6P

R5P

v16

v3

v4

Pyr

v15

v5

v11

v14

v6

AcCoA

Acetate

The transport fluxes were measured:

v13

v7

OAA

ICIT

v10

v8

The building block fluxes can be assumed

from biomass composition:

SUC

AKG

v9

v12

17 variables

15 equations

Freedom = 2

Transport flux

Intracellular flux

Building block flux


Slide4 l.jpg

Variables (fluxes)

Linear

constraints

S ∙ v = 0


Flux balance analysis fba5 l.jpg

Flux Balance Analysis (FBA)

maximize μ

s.t. S∙v = 0

0 < v < 20 mmol/g DCW/h


Optimization toolbox for flux analysis l.jpg

Optimization Toolbox for Flux Analysis

Two ways to launch 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


Slide7 l.jpg

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


13 c assisted metabolic flux analysis 13 c mfa l.jpg

13C-assisted Metabolic Flux Analysis (13C-MFA)

A simple case:

Glucose

CO2

v1

v2

v16

G6P

R5P

ratio: v3/v4

v3

v4

Pyr

16 fluxes, 7 intracellular metabolites

v15

v5

v11

v14

v6

AcCoA

Acetate

v13

v7

OAA

ICIT

v10

v8

SUC

AKG

v9

v12

The transport fluxes were measured:

Transport flux

Intracellular flux

The building block fluxes are not

necessary to be assumed

Building block flux


Slide9 l.jpg

Variables (fluxes)

Linear

constraints

S ∙ v = 0


13 c assisted metabolic flux analysis 13 c mfa10 l.jpg

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


Matlab code for 13 c mfa l.jpg

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


Optimization toolbox for flux analysis12 l.jpg

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


Slide13 l.jpg

v.s.


Summary l.jpg

Summary

  • The goals of FBA and 13C-MFA are different. Choose wisely !

  • More assumptions in FBA than 13C-MFA

  • Scale of FBA is commonly much larger than 13C-MFA

  • Both FBA and 13C-MFA are at metabolic steady state

    Question:how to calculate dynamic flux distribution?


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