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Metabolic Flux Analysis by MATLAB

Metabolic Flux Analysis by MATLAB. Le You 03-27-1014. Carbon metabolism is highly related to biofuel production. Ethanol. Hydrogen. Fatty acids/ biodiesel. Methanol/ Butanol. Carbon flow. Carbon substrates (i.e. Glucose). Carbon lost as CO 2. G6P. ED pathway. PP pathway.

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Metabolic Flux Analysis by MATLAB

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  1. Metabolic Flux Analysis by MATLAB Le You 03-27-1014

  2. Carbon metabolism is highly related to biofuel production Ethanol Hydrogen Fatty acids/ biodiesel Methanol/ Butanol

  3. Carbon flow Carbon substrates (i.e. Glucose) Carbon lost as CO2 G6P ED pathway PP pathway Glycolysis NADPH Biomass building blocks Pyruvate Amino acids Energy TCA cycle mitochondria Cytosol

  4. Rational metabolic engineering requires the quantification of metabolic pathways Pentose Phosphate Pathway Glucose ED Pathway Glycolysis Branched Chain FA 3-Methyl-1-butanol TCA cycle GAP 2-keto-4-methyl-pentanoate Leucine Valine 2-ketoisovalerate PYR Lactate Production of biofuels via keto-acid pathway Fatty acid Acetyl-CoA Isobutanol Glutamate Nature 2008, 451, 87

  5. The direct measurement of in vivo enzymatic reaction rates is difficult Glucose CO2 v1 Ru5P 6PG v18 v17 G6P R5P v19 v2 F6P X5P v20 v3 GAP S7P v4 GBP E4P v21 v5 3PG v5 PEP CO2 v6 v7 AcCoA PYR v8 v13 OAA CIT v9 v12 ICIT v10 v11 v17 GLX MAL v14 AKG v15 v16 SUC FUM

  6. Metabolic flux analysis can quantify carbon metabolism vin v4 A B A B C D E v2 v5 C v3 v6 D Genome-scale metabolic model Objective function Boundary constraints Sampling stoichiometric matrix Input/output flux Cell culture

  7. Example 11 intracellular fluxes, 8 intracellular metabolites Glucose G6P:V1=V2+V3 R5P:V2=V4 PYR:V2=V4 AceCOA:V5=V6+V7+V14 ICIT:V7=V8 AKG:V8=V9 SUC:V9=V10 OAA:V10+V11=V7 v1 v2 G6P R5P v3 v4 Pyr v5 v11 v6 AcCoA Acetate v7 The input/output fluxes were measured: OAA ICIT V1=11.0 mmol/g DCW/h V6=6.4 mmol/g DCW/h v10 v8 SUC AKG Biomass=1.078*AKG + 1.786*OAA + 2.928*AceCoA + 2.833*Pyr + 0.205*G6P v9 Input/output flux Intracellular flux Building block flux

  8. Stoichiometric matrix S ∙ v = 0 8 intracellular metabolites =

  9. Additional constraints • 0 < v < 20 mmol/g DCW/h lb=[11 0 0 0 0 6.4 0 0 0 0 0 0] T ub=[11 20 20 20 20 6.4 20 20 20 20 20 20] T • Objective function: maximize μ obj=[0 0 0 0 0 0 0 0 0 0 0 1] T

  10. Optimization Toolbox for Flux Analysis To lanch optimization toolbox in MATLAB: • 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

  11. linprog

  12. EXERCISES Aeq= beq=[0 0 0 0 0 0 0 0] T lb=[11 0 0 0 0 6.4 0 0 0 0 0 0] T ub=[11 20 20 20 20 6.4 20 20 20 20 20 20] T obj=[0 0 0 0 0 0 0 0 0 0 0 1] T

  13. start

  14. Results

  15. Optimization Toolbox for Flux Analysis Using “fmincon” solver in Optimization Toolbox for 13C-MFA Use “fmincon” Change to “Interior point” Initial guess S∙v=0 Put the objective function lb and ub v0=Lb+rand.*(Ub-Lb)

  16. EXERCISES Aeq= beq=[0 0 0 0 0 0 0 0] T lb=[11 0 0 0 0 6.4 0 0 0 0 0 0] T ub=[11 20 20 20 20 6.4 20 20 20 20 20 20] T obj=[0 0 0 0 0 0 0 0 0 0 0 1] T

  17. Results

  18. How to extract Stoichiometric matrix equationsToMatrix [A,b] = equationsToMatrix(eqns,vars) X+Y-2*Z=0 X+Y+Z=1 2*Y-Z+5=0 X + Y - 2*Z == 0 X + Y + Z == 1 2*Y – Z + 5 == 0 syms x y z; [A, b] = equationsToMatrix([x + y - 2*z == 0, x + y + z == 1, 2*y - z + 5 == 0], [x y z]) A = [ 1, 1, -2] [ 1, 1, 1] [ 0, 2, -1] b = 0 1 -5

  19. How to extract Stoichiometric matrix syms Glucose G6P R5P Pyr AceCoA ICIT OAA AKG SUC biomass CO2 Acetate X2 [A,b]=equationsToMatrix([Glucose == G6P, G6P == R5P + CO2, G6P == 2*Pyr, R5P == Pyr + X2, Pyr == AceCoA + CO2, AceCoA == Acetate, AceCoA + OAA == ICIT, ICIT == AKG + CO2, AKG == SUC + CO2, SUC == OAA,Pyr + CO2 == OAA, 1.078*AKG + 1.786*OAA + 2.928*AceCoA + 2.833*Pyr + 0.205* G6P == biomass], [G6P R5P Pyr AceCoA ICIT AKG SUC OAA]) Glucose == G6P G6P == R5P + CO2 G6P == 2*Pyr R5P == Pyr + X2 Pyr == AceCoA + CO2 AceCoA == Acetate AceCoA + OAA == ICIT ICIT == AKG + CO2 AKG == SUC + CO2 SUC == OAA Pyr + CO2 == OAA 1.078*AKG + 1.786*OAA + 2.928*AcCoA + 2.833*Pyr + 0.205* G6P == biomass

  20. b = -Glucose CO2 0 X2 CO2 Acetate 0 CO2 CO2 0 -CO2 biomass A = [ -1, 0, 0, 0, 0, 0, 0, 0] [ 1, -1, 0, 0, 0, 0, 0, 0] [ 1, 0, -2, 0, 0, 0, 0, 0] [ 0, 1, -1, 0, 0, 0, 0, 0] [ 0, 0, 1, -1, 0, 0, 0, 0] [ 0, 0, 0, 1, 0, 0, 0, 0] [ 0, 0, 0, 1, -1, 0, 0, 1] [ 0, 0, 0, 0, 1, -1, 0, 0] [ 0, 0, 0, 0, 0, 1, -1, 0] [ 0, 0, 0, 0, 0, 0, 1, -1] [ 0, 0, 1, 0, 0, 0, 0, -1] [ 41/200, 0, 2833/1000, 366/125, 0, 539/500, 0, 893/500] S=A’

  21. Exercises Glucose == G6P G6P == R5P + CO2 G6P == 2*Pyr R5P == Pyr + X2 Pyr == AceCoA + CO2 AceCoA == Acetate AceCoA + OAA == ICIT ICIT == AKG + CO2 AKG == SUC + CO2 SUC == OAA Pyr + CO2 == OAA 1.078*AKG + 1.786*OAA + 2.928*AcCoA + 2.833*Pyr + 0.205* G6P == biomass EXERCISES

  22. Optimization for Flux Analysis Initial guess (random) fmincon Syntax x = fmincon(fun,x0,A,b,Aeq,beq,lb,ub,nonlcon,options) Glucose v1 v2 G6P R5P v3 v4 Pyr Objective function: maximize μ v5 • A,b: Matrix for linear inequality constraints • e.g. v3>v2 v11 v6 AcCoA Acetate • Aeq,beq: Matrix for linear equality constraints • Mass balance v7 OAA ICIT • lb,ub v10 v8 lb=[ 11 0 0 0 0 6.4 0 0 0 0 0 0]T SUC AKG v9 ub=[ 11 20 20 20 20 6.4 20 20 20 20 20 20]T • options Input/output flux Algorithm: 'interior-point' (default) or 'sqp' Intracellular flux Building block flux

  23. MATLAB code using fmincon Glucose v1 v2 G6P R5P v0=Lb+rand.*(Ub-Lb); fun=@(v)(-v(12)); [xbest,min,exit]=fmincon(fun,v0,[],[],Aeq,beq,Lb,Ub,[]); disp(xbest); v3 v4 Pyr v5 v11 v6 AcCoA Acetate v7 OAA ICIT v10 v8 SUC AKG v9 Input/output flux Intracellular flux Building block flux

  24. Exercise 1 Matrix extraction Glucose == G6P G6P == R5P + CO2 G6P == 2*Pyr R5P == Pyr + X2 Pyr == AceCoA + CO2 AceCoA == Acetate AceCoA + OAA == ICIT ICIT == AKG + CO2 AKG == SUC + CO2 SUC == OAA PYR + CO2 == OAA 1.078*AKG + 1.786*OAA + 2.928*AcCoA + 2.833*Pyr + 0.205* G6P == biomass

  25. Exercise 2 Flux calculation Glucose v1 v2 G6P R5P v3 v4 Pyr v5 v11 v6 AcCoA Acetate v7 OAA ICIT v10 v8 SUC AKG v9 Input/output flux Intracellular flux Building block flux

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