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 in vivo search Nonlinear programming (NLP) Simplified model maximize ∑c i ∙v i s.t. S∙v = 0 lb < v < ub minimize (MDV exp -MDV sim ) 2 s.t. S∙v = 0 IDV = f(v, IMM, IDV) MDV = M∙IDV lb < v < ub Metabolic Steady stateMetabolic & isotopic Steady state

Flux Balance Analysis (FBA) Glucose G6PR5P Pyr AcCoAAcetate ICIT AKGSUC OAA v1 v2 v3 v4 v5 v6 v7 v8 v9 v10 v11 v12 v13 v14 v15 v16 Transport flux Intracellular flux Building block flux 16 fluxes, 7 intracellular metabolites The transport fluxes were measured: The building block fluxes can be assumed from biomass composition: 17 variables 15 equations Freedom = 2

S ∙ v = 0 Linear constraints Variables (fluxes)

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 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” 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

13 C-assisted Metabolic Flux Analysis ( 13 C-MFA) Glucose G6PR5P Pyr AcCoAAcetate ICIT AKGSUC 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, 7 intracellular metabolites The transport fluxes were measured: The building block fluxes are not necessary to be assumed

S ∙ v = 0 Linear constraints Variables (fluxes)

13 C-assisted Metabolic Flux Analysis ( 13 C-MFA) minimize (MDV exp -MDV sim ) 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 Input the variables Input the experimental observed MDV Identify labeling of CO2 Isotopomer transitions Reach the Isotopic steady state in TCA cycle

Optimization Toolbox for Flux Analysis Using “fmincon” solver in Optimization Toolbox for 13 C-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 13 C-MFA are different. Choose wisely ! More assumptions in FBA than 13 C-MFA Scale of FBA is commonly much larger than 13 C-MFA Both FBA and 13 C-MFA are at metabolic steady state Question: how to calculate dynamic flux distribution?