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
• fengx_at_seas.wustl.edu
• 314-935-6125

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Metabolic Flux Analysis
The in vivo enzymatic reaction rates (i.e. flux)
cannot be directly measured.
How ?
At steady state, dc/dt Sv 0, lb lt v lt ub

Additional information 1) objective function
(FBA) 2) 13C-experiments (13C-MFA)
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Metabolic Flux Analysis
Model reconstruction
Genome-scale metabolic model
Software development
Protein Hydrolysis
Isotopic labeling
Amino acids
GC-MS
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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. Sv 0 lb lt
v lt ub
minimize (MDVexp-MDVsim)2 s.t. Sv 0
IDV f(v, IMM, IDV) MDV MIDV
lb lt v lt ub
Metabolic Steady state
Metabolic isotopic Steady state
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Flux Balance Analysis (FBA)
16 fluxes, 8 intracellular metabolites
The transport fluxes were measured
The building block fluxes can be assumed from
biomass composition
17 variables 15 equations Freedom 2
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Variables (fluxes)
Linear constraints
S v 0
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Flux Balance Analysis (FBA)
maximize µ s.t. Sv 0 0 lt v lt 20
mmol/g DCW/h
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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
Sv0
lb and ub
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Click Start to run the optimization
Optimized objective function value
Optimized flux results
Experimental observed µ0.82 h-1 FBA simulated
µ1.54 h-1
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13C-assisted Metabolic Flux Analysis (13C-MFA)
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
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Variables (fluxes)
Linear constraints
S v 0
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13C-assisted Metabolic Flux Analysis (13C-MFA)
minimize (MDVexp-MDVsim)2 s.t. IDV f(v,
IMM, IDV) MDV MIDV Sv 0
0lt v lt 20
achieved in .m file
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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
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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
Sv0
Put the objective function
Sv0
lb and ub
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v.s.
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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?