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

Variables (fluxes) constraints Linear S ∙ v = 0

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

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

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

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

Variables (fluxes) constraints Linear S ∙ v = 0

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 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 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?