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Metabolomics

Metabolomics. Sarah C. Rutan Ernst Bezemer Department of Chemistry Virginia Commonwealth University July 29 – 31, 2003. What is Metabolomics?. Small molecule/metabolite complement of individual cells or tissues Network model of cells

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Metabolomics

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  1. Metabolomics Sarah C. Rutan Ernst Bezemer Department of Chemistry Virginia Commonwealth University July 29 – 31, 2003

  2. What is Metabolomics? • Small molecule/metabolite complement of individual cells or tissues • Network model of cells • S. cerevisiae – 45 reactions (16 reversible; 29 irreversible); 42 internal metabolites; 7 external metabolites • Time-dependent small molecule/ metabolite profiles in biological tissue (serum, urine) --- metabonomics

  3. Why do Metabolomics?

  4. How to do Metabolomics? • In-vivo • Studies in the species of interest • Fermentation broths – microbes • Animals – blood and urine • Plants • In-vitro • Test tube experiments • Incubations under physiological conditions • In-silico • Computer simulations

  5. Benzo[a]pyrene • Product of incomplete combustion of organic matter • Flame-broiled/smoked food • Cigarette smoke • Coal-tar • Activated by enzymes such as cytochrome P450 and epoxide hydrolase to form diols and tetrols • BP diols and tetrols form adducts with DNA • Mutagenic • Teratogenic • Carcinogenic

  6. BP Metabolites • Benzo[a]pyrene (BP) • Quinones (Qn) • 7,8,9,10-tetrahydrotetrol (tetrol) • 7,8-dihydroxy-9,10-epoxy-7,8,9,10 tetrahydro BP (DE2) • 7,8-oxide-9,10 dihydrodiol BP (DE3) • BP-2,3 oxide (n.d.) • BP-4,5 oxide (4,5-ox) • BP-4,5 diol (4,5-diol) • BP-7,8 oxide (7,8-ox) • BP-7,8 diol (7,8-diol) • BP-9,10 oxide (9,10-ox) • BP-9,10 diol (9,10-diol) • BP-7,8 oxide-9,10 dihydrodiol • 3-Hydroxy BP (3-OH) • 9-Hydroxy BP (9-OH) • Cytochrome P450 1A1 (1A1) • Epoxide Hydrolase (EH)

  7. Elementary Reaction Steps • Steps that occur as written • A + B  AB • A collides with B to form a product AB • Reaction rates

  8. First-Order Kinetics • A  B • Define y as the ‘states’ of the system • y(1) = [A]t • y(2) = [B]t

  9. First-Order Kinetics A  B [B]t [A]t Conc Time

  10. Second Order Kinetics • A + B  AB • Define y as the ‘states’ of the system • y(1) = [A]t • y(2) = [B]t • y(3) = [AB]t

  11. Exercise 1 What is the result of entering the following commands into Matlab? • t=[1:5] • k=0.5 • a=exp(-k*t) • plot(t,a) • b=1-a • conc=[a;b] • plot(t,conc)

  12. Ordinary Differential Equations • Analytical solutions • via standard mathematical integration methods • Numerical solutions • computer based integration • required for systems for no analytical solution • Runge-Kutta algorithm is commonly used • Stiff equations • Have both fast and slow reaction components • Non-stiff equations • All reactions occur over ~ the same time scale

  13. [B]t [A]t Differential Equation Solver in Matlab – First Order Kinetics • In Matlab command window, select File, New, M-file, and enter: function [dydt]=first_order(t,y) dydt=[-0.05*y(1); 0.05*y(1)]; • Save m-file • Switch back to Matlab command window • Enter: [t,y]=ode45(@first_order,[0:100],[1 0]) plot(t,y) • y is a 101 x 2 matrix • 101 different time points • 2 different chemical species

  14. [AB]t [A]t [B]t Differential Equation Solver in Matlab – Second Order Kinetics • In Matlab command window, select File, New, M-file, and enter: function [dydt]=second_order(t,y) dydt=[-0.05*y(1)*y(2); -0.05*y(1)*y(2); 0.05*y(1)*y(2)]; • Save m-file • Switch back to Matlab command window • Enter: [t,y]=ode45(@second_order,[0:100],[1.1 1 0]) plot(t,y) • y is a 101 x 3 matrix • 101 different time points • 3 different chemical species

  15. Michaelis-Menten Kinetics • Enzyme kinetics • A + B AB • AB A + C • More commonly represented as: • E + S ES • ES E + P • Assumptions for Michaelis-Menten derivation • ES reaches a steady state concentration • Rate of E + P  ES is neglible • ES  E + P is the rate limiting step k1 k2 k3 k1 k2 k3

  16. Steady State Assumption k1 E + S ES ES E + P k3 k2

  17. Session 2 • Creating chemical kinetic models • Enzyme kinetics • Model fitting

  18. Benzo[a]pyrene Metabolism Network k7 Qn k5 k10 k11 2,3 ox 3-OH 1A1·BP 1A1inact k19 k8 k2 k10 EH·4,5 ox 4,5 diol 4,5 ox k1 BP k25 k27 k13 1A1 k16 k13 1A1·9,10 diol 7,8 ox k10 k14 unk EH EH·7,8 ox 1A1inact k4 k18 k3 k17 k6 k10 9,10 ox k21 1A1·7,8 diol k15 k26 k9 EH·9,10 ox diol-ox2 diol-ox3 9-OH k22 k12 k28 k24 9,10 diol tetrol 7,8 diol k23 k29 unk Gautier, J. C.; Urban, P.; Beaune, P.; Pompon, D. Chem. Res. Toxicol. 1996, 9, 418-425. k30

  19. Improving the model • Fit model to data • Optimize rate constants

  20. Steady State Assumption k1 E + S ES ES E + P k3 k2

  21. Exercise 2 Determine the initial rate for the following conditions using the Michaelis-Menten formula: [S]o= 1.0 M – 50 M ; [E]o = 0.03 M; [ES]o = 0; [P]o = 0 KM = 10 M; vmax = 15 nmol/nmol E/min Plot vinitial vs. [S]o

  22. Implementing a Kinetic Model

  23. Implementing a Kinetic Model

  24. Implementing a Kinetic Model

  25. Implementing a Kinetic Model

  26. Implementing a Kinetic Model

  27. Implementing a Kinetic Model Oni 1 0 0 O = 0 1 0 - 1 0 Rmj 1 -1 R = 1 0 E. Bezemer, S. C. Rutan, Chemom. Intell. Lab. Systems, 59, 19-31, 2001

  28. Exercise 3 • Combine all kinetic model related variables into a structure: kinetics.order = O kinetics.states = R kinetics.k = [k1 k2] initial_conc = [ [A]o [B]o [Co] ] [t,y]=ode45(@kinfun,times,initial_conc,[],kinetics); plot(t,y)

  29. Simulated Kinetic Profiles k1 = k2 = 0.5 1 C 0.8 A 0.6 Relative Concentration 0.4 B 0.2 0 2 4 6 8 10 Reaction Time

  30. Optimizing the Kinetic Model 1. Set initial rate constants 2. Simulate kinetic model 3. Calculate difference between simulated model and ALS resolved kinetic profile 4. Change rate constants 5. Go to step 2 unless fit is good enough

  31. Simplex optimization 1 2 3 Parameter 2 Parameter 1

  32. Simplex optimization 1 2 3 Parameter 2 4 Parameter 1

  33. Simplex optimization 1 2 3 Parameter 2 4 5 Parameter 1

  34. Simplex optimization 1 2 3 Parameter 2 4 5 6 Parameter 1

  35. Simplex optimization 1 2 3 Parameter 2 4 7 5 6 Parameter 1

  36. Optimizing the Kinetic Model 1. Set initial rate constants 2. Simulate kinetic model 3. Calculate difference between simulated model and ALS resolved kinetic profile 4. Change rate constants

  37. Exercise 4 • Create a function that determines the fit quality of the model Function fit_qual=fit_model(rates,data,model) model.k=rates; [t,y]=ode23tb(@kinfun,[0:10],[1 0 0],[],model); fit_qual=sum(sum(y-data).^2)); • Fit the data using this function Opt_rates=fminsearch(@fit_model,[.1 1],[1 0 0],[],y,kinetics)

  38. Improving the model • Fit model to data • Optimize rate constants

  39. Exercise 5 • Set up the states and orders matrices for Michaelis-Menten kinetics. • Calculate the time-dependent profiles for the species E, S, P, ES for the following conditions: • [S]o= 1.0 M; [E]o = 0.03 M; [ES]o = 0; [P]o = 0 • k1 = 0.6 M-1min-1; k2 = 5 min-1; k3 = 0.3 min-1 • Plot a Michaelis-Menten plot for vinitial vs. [S] • [S]o = 1 – 50 M

  40. Metabolism and the Liver • Liver – key organ for processing xenobiotic compounds • Environmental toxins • Pharmaceuticals • Contains many different types of enzymes • Cytochrome P450 • Several genetic variants • Responsible for oxidation of numerous types of function groups • Epoxide hydrolase • Converts epoxides to diols

  41. Benzo[a]pyrene Metabolism Network k7 Qn k5 k10 k11 2,3 ox 3-OH 1A1·BP 1A1inact k19 k8 k2 k10 EH·4,5 ox 4,5 diol 4,5 ox k1 BP k25 k27 k13 1A1 k16 k13 1A1·9,10 diol 7,8 ox k10 k14 unk EH EH·7,8 ox 1A1inact k4 k18 k3 k17 k6 k10 9,10 ox k21 1A1·7,8 diol k15 k26 k9 EH·9,10 ox diol-ox2 diol-ox3 9-OH k22 k12 k28 k24 9,10 diol tetrol 7,8 diol k23 k29 unk Gautier, J. C.; Urban, P.; Beaune, P.; Pompon, D. Chem. Res. Toxicol. 1996, 9, 418-425. k30

  42. Qn k11 1A1·BP k2 k1 BP 1A1 Reaction of Cytochrome 1A1 w/ BP • 1A1 + BP 1A1BP • 1A1BP 1A1 + Qn Is really the same as… • E + S ES • ES E + P k1 k2 k11 k1 k2 k3

  43. k5 2,3 ox k6 9,10 ox k7 7,8 ox k8 Qn 4,5 ox k10 k11 1A1·BP 1A1inact k2 k1 BP 1A1 Dynamics for 1A1BP

  44. Differential Equations for BP/1A1 Reactions Gautier, J. C.; Urban, P.; Beaune, P.; Pompon, D. Chem. Res. Toxicol. 1996, 9, 418-425.

  45. Additional Differential Equations for BP/1A1/EH Reactions Gautier, J. C.; Urban, P.; Beaune, P.; Pompon, D. Chem. Res. Toxicol. 1996, 9, 418-425.

  46. Kinetic Constants for BP Model Gautier, J. C.; Urban, P.; Beaune, P.; Pompon, D. Chem. Res. Toxicol. 1996, 9, 418-425. Inactivation constant k10 = 0.022 min-1

  47. BP 3OH 9OH quinones tetrol adducts Reaction Profiles for Major ProductsInitial Concentrations: [BP] = 5 M; [1A1] = 0.0058 M; [EH] = 0.10 M 5 4.5 4 3.5 3 Concentration (M) 2.5 2 1.5 1 0.5 0 0 20 40 60 80 100 120 140 160 180 200 Time (min)

  48. BP 3OH 9OH quinones tetrol adducts Reaction Profiles for Major ProductsInitial Concentrations: [BP] = 5 M; [1A1] = 0.0058 M; [EH] = 0.10 M; k10 = 0 5 4.5 4 3.5 3 2.5 Concentration (M) 2 1.5 1 0.5 0 0 20 40 60 80 100 120 140 160 180 200 Time (min)

  49. 3 DE2 DE3 x 10-4 2.5 2 Concentration (M) 1.5 1 0.5 0 0 20 40 60 80 100 120 140 160 180 200 Time (min) Reaction Profiles for IntermediatesInitial Concentrations: [BP] = 5 M; [1A1] = 0.0058 M; [EH] = 0.10 M; k10 = 0

  50. 0.7 7,8 diol 9,10 diol 0.6 0.5 0.4 Concentration (M) 0.3 0.2 0.1 0 0 20 40 60 80 100 120 140 160 180 200 Time (min) Reaction Profiles for IntermediatesInitial Concentrations: [BP] = 5 M; [1A1] = 0.0058 M; [EH] = 0.10 M; k10 = 0 tetrol

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