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 Conc Time [B] t [A] t

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. 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 [B] t [A] t

14. 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 [AB] t [A] t [B] t

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 k1k1 k2k2 k3k3 k1k1 k2k2 k3k3

16. Steady State Assumption  E + S ES  ES E + P k1k1 k2k2 k3k3

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

18. 1A1 BP 1A1·BP 1A1 inact 1A1·7,8 diol EH unk k 10 k 11 k1k1 k2k2 1A1·9,10 diol k 25 k3k3 k4k4 k 10 7,8 diol 9,10 diol k 14 k 24 k 23 k 28 k 26 k9k9 unk 7,8 ox k7k7 2,3 ox3-OH k5k5 4,5 diol k 30 k 10 EH·4,5 ox k 19 k 27 k 29 4,5 ox k 13 9,10 ox EH·9,10 ox k 21 k 15 k 17 k8k8 k6k6 k 12 EH·7,8 ox k 13 k 18 k 22 k 16 9-OH tetrol diol-ox2 diol-ox3 Qn Benzo[a]pyrene Metabolism Network Gautier, J. C.; Urban, P.; Beaune, P.; Pompon, D. Chem. Res. Toxicol. 1996, 9, 418-425.

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

20. Steady State Assumption  E + S ES  ES E + P k1k1 k2k2 k3k3

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 K M = 10  M; v max = 15 nmol/nmol E/min Plot v initial vs. [S] o

22. Implementing a Kinetic Model

27. R = - 10 1 0 100 010 O = E. Bezemer, S. C. Rutan, Chemom. Intell. Lab. Systems, 59, 19-31, 2001 RmjRmj O ni 1

28. Exercise 3 Combine all kinetic model related variables into a structure: kinetics.order = O kinetics.states = R kinetics.k = [k 1 k 2 ] initial_conc = [ [A] o [B] o [C o ] ] [t,y]=ode45(@kinfun,times,initial_conc,[ ],kinetics); plot(t,y)

29. 246810 0 0.2 0.4 0.6 0.8 1 Reaction Time A C B Simulated Kinetic Profiles k 1 = k 2 = 0.5 Relative Concentration

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 Parameter 1 Parameter 2 1 2 3

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

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

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

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

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  k 1 = 0.6  M -1 min -1 ; k 2 = 5 min -1 ; k 3 = 0.3 min -1 Plot a Michaelis-Menten plot for v initial 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. 1A1 BP 1A1·BP 1A1 inact 1A1·7,8 diol EH unk k 10 k 11 k1k1 k2k2 1A1·9,10 diol k 25 k3k3 k4k4 k 10 7,8 diol 9,10 diol k 14 k 24 k 23 k 28 k 26 k9k9 unk 7,8 ox k7k7 2,3 ox3-OH k5k5 4,5 diol k 30 k 10 EH·4,5 ox k 19 k 27 k 29 4,5 ox k 13 9,10 ox EH·9,10 ox k 21 k 15 k 17 k8k8 k6k6 k 12 EH·7,8 ox k 13 k 18 k 22 k 16 9-OH tetrol diol-ox2 diol-ox3 Qn Benzo[a]pyrene Metabolism Network Gautier, J. C.; Urban, P.; Beaune, P.; Pompon, D. Chem. Res. Toxicol. 1996, 9, 418-425.

42. 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 k1k1 k2k2 k 11 k1k1 k2k2 k3k3 1A1 BP 1A1·BP k 11 k1k1 k2k2 Qn

43. Dynamics for 1A1  BP 1A1 1A1·BP k1k1 7,8 ox Qn 1A1 inact k 10 k 11 k2k2 k5k5 BP 2,3 ox 4,5 ox 9,10 ox k6k6 k8k8 k7k7

44. Differential Equations for BP/1A1 Reactions species Xd[X]/dt BPk 2 [1A1·BP] + k 10 [1A1·BP] - k 1 [BP][1A1] 1A1 k 4 [1A1·7,8-diol] + (k 25 + k 30 + k 26 )[1A1·9,10-diol] + k 9 [1A1·7,8-diol] + k 11 [1A1·BP]+ k 2 [1A1·BP]+ (k 5 + k 6 + k 7 + k 8 )[1A1·BP] - k 1 [1A1][BP] - k 14 [1A1][9,10-diol] - k 10 [1A1] - k 3 [1A1][7,8-diol] 1A1 inactiv. k 10 ([1A1] + [1A1·7,8-diol] + [1A1·BP] + [1A1·9,10-diol]) 1A1·BPk 1 [BP][1A1] - (k 5 + k 6 + k 7 + k 8 + k 2 + k 10 + k 11 )[1A1·BP] 4,5-oxk 8 [1A1·BP] + k 27 [EH·4,5-ox] - k 16 [4,5-ox] - k 13 [EH][4,5-ox] 7,8-oxk 7 [1A1·BP] + k 18 [EH·7,8-ox] - k 20 [7,8-ox] - k 13 [EH][7,8-ox] 9,10-oxk 6 [1A1·BP] + k 21 [EH·9,10-ox] - k 13 [EH][9,10-ox] - k 17 [9,10-ox] - k 15 [9,10-ox] 3-OHk 5 [1A1·BP] 9-OHk 15 [9,10-ox] quinonesk 11 [1A1·BP] 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. species Xd[X]/dt EH (k 12 + k 21 )[EH·9,10-ox] + (k 18 + k 22 )[EH·7,8-ox] + (k 27 + k 19 )[EH·4,5-ox] – k 13 [EH] ([4,5-ox] + [7,8-ox] + [9,10-ox]) EH·4,5-oxk 13 [4,5-ox][EH] - (k 27 + k 19 )[EH·4,5-ox] EH·7,8-oxk 13 [7,8-ox][EH] - (k 18 + k 22 )[EH·7,8-ox] EH·9,10-oxk 13 [9,10-ox][EH] - (k 21 + k 12 )[EH·9,10-ox] 4,5-diolk 19 [EH·4,5-ox] 7,8-diolk 22 [EH·7,8-ox] + k 4 [1A1·7,8-diol] + k 10 [1A1·7,8-diol] - k 3 [1A1][7,8-diol] 9,10-diolk 12 [EH·9,10-ox] + k 25 [1A1·9,10-diol] + k 10 [1A1·9,10-diol] - k 14 [9,10-diol][1A1] 1A1·7,8-diolk 3 [1A1][7,8-diol] - (k 4 + k 9 + k 10 )[1A1·7,8-diol] 1A1·9,10-diolk 14 [1A1][9,10-diol] - (k 25 + k 10 + k 26 + k 30 )[1A1·9,10-diol] DE2k 9 [1A1·7,8-diol] - (k 23 + k 24 )[DE2] DE3k 26 [1A1·9,10-diol] - (k 29 + k 28 )[DE3] T2-tetrolk 24 [DE2] + k 28 [DE3] adductsk 17 [9,10-ox] + k 20 [7,8-ox] + k 16 [4,5-ox] + k 23 [DE2] + k 29 [DE3] + k 30 [1A1·9,10-diol]

46. Kinetic Constants for BP Model Enzyme/substrate complexes Association constants (  M -1 ·min -1 ) Dissociation constants (min -1 ) Products Catalytic constants (min - 1 ) Products Nonenzymatic constants (min - 1 ) 1A1·BPk 1 = 30k 2 = 100 2,3-oxk 5 = 14 4,5-oxk 8 = 0.7adductsk 16 = 0.004 7,8-oxk 7 = 10adductsk 20 = 0.018 9,10-oxk 6 = 10adductsk 17 =0.1 9-OHk 15 = 0.3 quinonesk 11 = 5.2 1A1·7,8-diolk 3 = 40k 4 = 100 DE2k 9 = 85adductsk 23 = 60 T2-tetrolk 24 = 30 1A1·9,10-diolk 14 = 26k 25 = 100 DE3k 26 = 4.5adductsk 29 = 40 T2-tetrolk 28 = 60 adductsk 30 = 15 mEH·4,5-oxk 13 = 180k 27 = 100 4,5-diolk 19 = 23 mEH·7,8 oxk 13 = 180k 18 = 100 7,8 diolk 22 = 11.5 mEH·9,10 oxk 13 = 180k 21 = 100 9,10 diolk 12 = 7.5 Inactivation constant k 10 = 0.022 min -1 Gautier, J. C.; Urban, P.; Beaune, P.; Pompon, D. Chem. Res. Toxicol. 1996, 9, 418-425.

47. Reaction Profiles for Major Products Initial Concentrations: [BP] = 5  M; [1A1] = 0.0058  M; [EH] = 0.10  M 020406080100120140160180200 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Time (min) Concentration (  M) BP 3OH 9OH quinones tetrol adducts

48. Reaction Profiles for Major Products Initial Concentrations: [BP] = 5  M; [1A1] = 0.0058  M; [EH] = 0.10  M; k 10 = 0 020406080100120140160180200 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Time (min) Concentration (  M) BP 3OH 9OH quinones tetrol adducts

49. Reaction Profiles for Intermediates Initial Concentrations: [BP] = 5  M; [1A1] = 0.0058  M; [EH] = 0.10  M; k 10 = 0 020406080100120140160180200 0 0.5 1 1.5 2 2.5 3 x 10 -4 Time (min) Concentration (  M) DE2 DE3

50. Reaction Profiles for Intermediates Initial Concentrations: [BP] = 5  M; [1A1] = 0.0058  M; [EH] = 0.10  M; k 10 = 0 7,8 diol 9,10 diol 020406080100120140160180200 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Time (min) Concentration (  M) tetrol

51. Exercise 6 Start Matlab, and type the following commands  load bap_model  [t,y]=ode23tb(@kinfun,[0:200],initial_conc,[],kinetics); Choose one of the reactions in the BP metabolism, and vary the rate constant by +50 %, +10 %, -10 % and -50 % and determine which species profiles are most affect by these changes. Use the excel spreadsheet bap_model.xls to determine the position of the different species and terms in the matrices.