Metabolic Flux Analysis by MATLAB

1. 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

2. 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)

3. Metabolic Flux Analysis Model reconstruction Genome-scale metabolic model Software development Protein Hydrolysis Isotopic labeling Amino acids GC-MS

4. 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

5. Flux Balance Analysis (FBA) 16 fluxes, 8 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

6. Variables (fluxes) Linear constraints S ∙ v = 0

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

8. 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

9. 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

10. 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, 8 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

11. Variables (fluxes) Linear constraints S ∙ v = 0

12. 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

13. 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

14. 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

15. v.s.

16. 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?