Metabolomics final

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					     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
  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
   Why do Metabolomics?

             Proteomics




           Systems Biology/
            Bioinformatics


Genomics                      Metabolomics
       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
             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
                      BP Metabolites
•   Benzo[a]pyrene (BP)                               OH
•   Quinones (Qn)                            HO
•   7,8,9,10-tetrahydrotetrol (tetrol)
•   7,8-dihydroxy-9,10-epoxy-7,8,9,10    HO
    tetrahydro BP (DE2)                               OH         O

•   7,8-oxide-9,10 dihydrodiol BP (DE3)
•   BP-2,3 oxide (n.d.)                                     HO
•   BP-4,5 oxide (4,5-ox)                                             OH
•   BP-4,5 diol (4,5-diol)
•   BP-7,8 oxide (7,8-ox)                         O
•   BP-7,8 diol (7,8-diol)                                 HO
•   BP-9,10 oxide (9,10-ox)            O                         OH
•   BP-9,10 diol (9,10-diol)
•   BP-7,8 oxide-9,10 dihydrodiol
•   3-Hydroxy BP (3-OH)
•   9-Hydroxy BP (9-OH)                                                    OH
•   Cytochrome P450 1A1 (1A1)
•   Epoxide Hydrolase (EH)
                                                                 HO
      Elementary Reaction Steps
• Steps that occur as written
  A + B  AB
  A collides with B to form a product AB
• Reaction rates
   d[ A ]
          k[ A ][B]
     dt
    d[B]
   dt  k[ A][B]

   d[ AB]
   dt  k[ A ][B]
             First-Order Kinetics
• AB
• d[ A ]
         k[ A ]
   dt
• d[B]
        k[ A ]
   dt
• Define y as the ‘states’ of the system
   y(1) = [A]t
   y(2) = [B]t
               First-Order Kinetics
AB                                   [ A ] t  0  [ A ]o
d[ A ]                                [B]t 0  0
        k[ A ]
 dt                                   [ A ]o  [ A ]t  [B]t
  [ A ]t                   t
            d[ A ]                    [ A ]o  [ A ]o e kt  [B]t
     [ A ] [ A ]  t0kt
[ A ] o                              [B]t  [ A ]o (1  e kt )
   [ A ]t
ln         kt                                              [B]t
   [ A ]o
                                                             [A]t
                     kt       Conc
[ A ] t  [ A ]o e

                                                  Time
           Second Order Kinetics
• A + B  AB
     d[ A ]
             k[ A ][B]
     dt
     d[B]
            k[ A ][B]
      dt
    d[ AB]
   dt  k[A][B]
• Define y as the ‘states’ of the system
  y(1) = [A]t
  y(2) = [B]t
  y(3) = [AB]t
                         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)
   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
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)];
   d[ A ]                              d[B]
           k[ A ]                          k[ A ]
    dt                                  dt

• Save m-file
• Switch back to Matlab command
  window
• Enter:
   [t,y]=ode45(@first_order,[0:100],[1 0])             [B]t
                                                       [A]t
   plot(t,y)  y is a 101 x 2 matrix
                      • 101 different time points
                      • 2 different chemical species
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)];
d[ A ]                           d[B]                 d[ AB]
        k[ A ][B]                    k[ A ][B]            k[ A ][B]
 dt                               dt                    dt
• Save m-file
• Switch back to Matlab command window
• Enter:
    [t,y]=ode45(@second_order,[0:100],[1.1 1 0])
    plot(t,y)
                                                                           [AB]t
                  y is a 101 x 3 matrix                                    [A]t
                                                                           [B]t
                  • 101 different time points
                  • 3 different chemical species
      Michaelis-Menten Kinetics
• Enzyme kinetics
            k1
  A + B    k2
              AB
       k3
  AB        A+C
• More commonly represented as:
          k  1
  E + S k2 ES
        k3
  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
               Steady State Assumption
                     k1
E + S               k2      ES                             ES          k3      E+P
d [ES ]                                                                 [E]o  [E]  [ES]
         k1[E ][S ]  k 2 [ES ]  k 3 [ES ]  0
   dt                                                                   [E]  [E]o  [ES]
k1[E ][S ]  (k 2  k 3 )[ES ]                                                   [E][S]
                                                                        [ES] 
             k1                                                                   KM
[ES ]            [E ][S ]
          k2  k3                                                       K M [ES]  [E]o [S]  [ES][S]
[E ][S ] k 2  k 3                                                      [ES](K M  [S])  [E]o [S]
                   KM         d[P]
                                      k 3 [ES]
 [ES ]      k1                   dt                                              [E]o [S]
                                                                        [ES] 
                                d[P] k 3 [E]o [S]
                                                                                K M  [S]
                                 dt     K M  [S ]
                                d[P]
                                      v initial ;   k 3 [E]o  v max
                                 dt

                                            v max [S]
                             v initial    
                                            K M  [S ]
             Session 2

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




• Fit model to data
• Optimize rate constants
               Steady State Assumption
                     k1
E + S               k2      ES                             ES          k3      E+P
d [ES ]                                                                 [E]o  [E]  [ES]
         k1[E ][S ]  k 2 [ES ]  k 3 [ES ]  0
   dt                                                                   [E]  [E]o  [ES]
k1[E ][S ]  (k 2  k 3 )[ES ]                                                   [E][S]
                                                                        [ES] 
             k1                                                                   KM
[ES ]            [E ][S ]
          k2  k3                                                       K M [ES]  [E]o [S]  [ES][S]
[E ][S ] k 2  k 3                                                      [ES](K M  [S])  [E]o [S]
                   KM         d[P]
                                      k 3 [ES]
 [ES ]      k1                   dt                                              [E]o [S]
                                                                        [ES] 
                                d[P] k 3 [E]o [S]
                                                                                K M  [S]
                                 dt     K M  [S ]
                                d[P]
                                      v initial ;   k 3 [E]o  v max
                                 dt

                                            v max [S]
                             v initial    
                                            K M  [S ]
                       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


                               v max [S]
                 v initial   
                               K M  [S ]
    Implementing a Kinetic Model
      k1                 k2
A           B       B              C
          Implementing a Kinetic Model
             k1                                             k2
   A                          B                 B                           C
d A
      =   - k1 [A]         = - 1  k1 [A]1[B]0[C]0 + 0  k2 [A]0[B]0[C]1
 dt
d B
      =    k1 [A] - k2 [B] = + 1  k1 [A]1[B]0[C]0 - 1  k2 [A]0[B]1[C]0
 dt
d C
      =              k2 [B] = + 0  k1 [A]1[B]0[C]0 + 1  k2 [A]0[B]1[C]0
 dt
          Implementing a Kinetic Model
             k1                                            k2
   A                          B                  B              C
d A
      =    - k1 [A]        = - 1  k1 [A] + 0  k2 [B]
 dt
d B
      =     k1 [A] - k2 [B] = + 1  k1 [A] - 1  k2 [B]
 dt
d C
      =               k2 [B] = + 0  k1 [A] + 1  k2 [B]
 dt
           Implementing a Kinetic Model
             k1                                          k2
   A                         B                B                         C
d A 
       =    - k1 [A]        = - 1  k1 [A]1[B]0[C]0 + 0  k2 [A]0[B]1[C]0
 dt
d B
       =     k1 [A] - k2 [B] = + 1  k1 [A]1[B]0[C]0 - 1  k2 [A]0[B]1[C]0
 dt
d C
       =               k2 [B] = + 0  k1 [A]1[B]0[C]0 + 1  k2 [A]0[B]1[C]0
 dt
           Implementing a Kinetic Model
             k1                                          k2
   A                         B                B                         C
d A 
       =    - k1 [A]        = - 1  k1 [A]1[B]0[C]0 + 0  k2 [A]0[B]1[C]0
 dt
d B
       =     k1 [A] - k2 [B] = + 1  k1 [A]1[B]0[C]0 - 1  k2 [A]0[B]1[C]0
 dt
d C
       =               k2 [B] = + 0  k1 [A]1[B]0[C]0 + 1  k2 [A]0[B]1[C]0
 dt
         Implementing a Kinetic Model


     O=
              1
              0
                       0
                       1
                                0
                                0
                                        pn  kn  Xi 
                                                       m

                                                       i1
                                                                   Oni
                                                                          
                                     dXm 
                  -1       0

                                                    pj 
                                                       n
                   1       -1
                                                   Rm
       R=
                  0        1           dt     j 1
                                                    j




E. Bezemer, S. C. Rutan, Chemom. Intell. Lab. Systems, 59, 19-31, 2001
                  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)
                               Simulated Kinetic Profiles
                                       k1                       k2
                               A              B       B                  C
                                            k1 = k2 = 0.5
                          1
Relative Concentration




                                                            C
                         0.8
                                   A
                         0.6

                         0.4
                                                  B
                         0.2

                          0
                                   2         4        6              8       10
                                            Reaction Time
   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
              Simplex optimization
               1

                    2



               3
Parameter 2




                        Parameter 1
              Simplex optimization
               1

                    2



               3
Parameter 2




                        4




                            Parameter 1
              Simplex optimization
               1

                    2



               3
Parameter 2




                        4



               5




                            Parameter 1
              Simplex optimization
               1

                    2



               3
Parameter 2




                        4



               5

                        6




                            Parameter 1
              Simplex optimization
               1

                    2



               3
Parameter 2




                        4

                                  7
               5

                        6




                            Parameter 1
   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
                      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)
      Improving the model




• Fit model to data
• Optimize rate constants
                   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
       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
                Benzo[a]pyrene Metabolism Network
  Qn                                                                     k7
       k11                      k10                           k5
                1A1·BP                  1A1inact                                2,3 ox                3-OH
                                                        k8                                   k19
                     k2                         k10            4,5 ox          EH·4,5 ox            4,5 diol
       k1
BP                             k25                                                  k27     k13
                 1A1                  1A1·9,10 diol          k16         k13                         7,8 ox
    k10                         k14
                                                                   unk            EH               EH·7,8 ox
1A1inact        k4        k3                                                                k18
                                                       k6         k17
    k10                                                       9,10 ox
             1A1·7,8 diol                                                           k21
                                          k26                     k15
                k9                                                             EH·9,10 ox
diol-ox2                   diol-ox3                            9-OH                                     k22
                                                                                     k12
       k24                     k28                                              9,10 diol
                 tetrol
                                                                                                    7,8 diol
          k23                  k29
                 unk                               Gautier, J. C.; Urban, P.; Beaune, P.; Pompon, D.
                               k30                 Chem. Res. Toxicol. 1996, 9, 418-425.
Reaction of Cytochrome 1A1 w/ BP
                   k1    Qn
• 1A1 + BP k 1A1BP 2         k11
                                    1A1·BP
• 1A1BP k 1A1 + Qn
              11

                                       k2
Is really the same as…   BP   k1
            k
• E + S k ES
          1
                                     1A1
          2

• ES k E + P
      3
             Dynamics for 1A1BP
                                           k5
                                                       2,3 ox
                                           k6
                                                       9,10 ox
                                           k7
                                                       7,8 ox
                  Qn                       k8
                                                       4,5 ox
                     k11             k10
                            1A1·BP          1A1inact

                       k1     k2
                BP
                            1A1


d[1A1 BP]
            k1[BP][1A1] - (k5  k6  k7  k8  k2  k10  k11)[1A1·BP]
    dt
         Differential Equations for BP/1A1
                      Reactions
species X     d[X]/dt
BP            k2[1A1·BP] + k10[1A1·BP] - k1[BP][1A1]
              k4[1A1·7,8-diol] + (k25 + k30 + k26)[1A1·9,10-diol] + k9[1A1·7,8-diol] +
1A1           k11[1A1·BP]+ k2[1A1·BP]+ (k5 + k6 + k7 + k8)[1A1·BP] - k1[1A1][BP] -
              k14[1A1][9,10-diol] - k10[1A1] - k3[1A1][7,8-diol]
1A1inactiv.   k10([1A1] + [1A1·7,8-diol] + [1A1·BP] + [1A1·9,10-diol])
1A1·BP        k1[BP][1A1] - (k5 + k6 + k7 + k8 + k2 + k10 + k11)[1A1·BP]
4,5-ox        k8[1A1·BP] + k27[EH·4,5-ox] - k16[4,5-ox] - k13[EH][4,5-ox]
7,8-ox        k7[1A1·BP] + k18[EH·7,8-ox] - k20[7,8-ox] - k13[EH][7,8-ox]
9,10-ox       k6[1A1·BP] + k21[EH·9,10-ox] - k13[EH][9,10-ox] - k17[9,10-ox] - k15[9,10-ox]
3-OH          k5[1A1·BP]
9-OH          k15[9,10-ox]
quinones      k11[1A1·BP]


Gautier, J. C.; Urban, P.; Beaune, P.; Pompon, D. Chem. Res. Toxicol. 1996, 9, 418-425.
            Additional Differential Equations for
                   BP/1A1/EH Reactions
species X        d[X]/dt
                 (k12 + k21)[EH·9,10-ox] + (k18 + k22)[EH·7,8-ox] + (k27+ k19)[EH·4,5-ox] –
EH
                 k13[EH] ([4,5-ox] + [7,8-ox] + [9,10-ox])
EH·4,5-ox        k13[4,5-ox][EH] - (k27 + k19)[EH·4,5-ox]
EH·7,8-ox        k13[7,8-ox][EH] - (k18 + k22)[EH·7,8-ox]
EH·9,10-ox       k13[9,10-ox][EH] - (k21 + k12)[EH·9,10-ox]
4,5-diol         k19[EH·4,5-ox]
7,8-diol         k22[EH·7,8-ox] + k4[1A1·7,8-diol] + k10[1A1·7,8-diol] - k3[1A1][7,8-diol]
9,10-diol        k12[EH·9,10-ox] + k25[1A1·9,10-diol] + k10[1A1·9,10-diol] - k14[9,10-diol][1A1]
1A1·7,8-diol     k3[1A1][7,8-diol] - (k4 + k9 + k10)[1A1·7,8-diol]
1A1·9,10-diol    k14[1A1][9,10-diol] - (k25 + k10 + k26 + k30)[1A1·9,10-diol]
DE2              k9[1A1·7,8-diol] - (k23 + k24)[DE2]
DE3              k26[1A1·9,10-diol] - (k29 + k28)[DE3]
T2-tetrol        k24[DE2] + k28[DE3]
adducts          k17[9,10-ox] + k20[7,8-ox] + k16[4,5-ox] + k23[DE2] + k29[DE3] + k30[1A1·9,10-diol]
     Gautier, J. C.; Urban, P.; Beaune, P.; Pompon, D. Chem. Res. Toxicol. 1996, 9, 418-425.
                Kinetic Constants for BP Model
                                                                                 Catalytic                     Nonenzymatic
Enzyme/substrate      Association constants   Dissociation
                                                                  Products       constants (min-   Products    constants (min-
complexes             (M-1·min-1)            constants (min-1)                  1)                            1)


1A1·BP                k1 = 30                 k2 = 100
                                                                  2,3-ox         k5 = 14
                                                                  4,5-ox         k8 = 0.7          adducts     k16 = 0.004
                                                                  7,8-ox         k7 = 10           adducts     k20 = 0.018
                                                                  9,10-ox        k6 = 10           adducts     k17 =0.1
                                                                                                   9-OH        k15 = 0.3
                                                                  quinones       k11= 5.2
1A1·7,8-diol          k3 = 40                 k4 = 100
                                                                  DE2            k9 = 85           adducts     k23 = 60
                                                                                                   T2-tetrol   k24 = 30
1A1·9,10-diol         k14 = 26                k25 = 100
                                                                  DE3            k26 = 4.5         adducts     k29 = 40
                                                                                                   T2-tetrol   k28 = 60
                                                                  adducts        k30 = 15
mEH·4,5-ox            k13 = 180               k27 = 100
                                                                  4,5-diol       k19 = 23
mEH·7,8 ox            k13 = 180               k18 = 100
                                                                  7,8 diol       k22 = 11.5
mEH·9,10 ox           k13 = 180               k21 = 100
                                                                  9,10 diol      k12 = 7.5
Inactivation constant k10 = 0.022 min-1 Gautier, J. C.; Urban, P.; Beaune, P.; Pompon, D. Chem. Res. Toxicol. 1996, 9, 418-425.
           Reaction Profiles for Major Products
                     Initial Concentrations: [BP] = 5 M; [1A1] = 0.0058 M; [EH] = 0.10 M
                         5
                                                                             BP
                       4.5                                                   3OH
                                                                             9OH
                         4                                                   quinones
                                                                             tetrol
Concentration (M)




                       3.5                                                   adducts

                       3

                      2.5

                       2

                      1.5

                       1

                      0.5

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




                      3

                      2.5

                       2

                      1.5

                      1

                      0.5

                       0 0   20   40   60     80 100     120 140   160 180   200
                                            Time (min)
                 Reaction Profiles for Intermediates
Initial Concentrations: [BP] = 5 M; [1A1] = 0.0058 M; [EH] = 0.10 M; k10 = 0

                                3
                                                                                DE2
                                                                                DE3
   Concentration (M) x 10-4




                               2.5

                                                                       O
                                2
                                                                  HO
                                                                           OH
                               1.5
                                                                           OH
                                                                  HO

                                1
                                                                       O


                               0.5


                                0 0   20   40   60   80      100 120 140 160 180 200
                                                          Time (min)
                      Reaction Profiles for Intermediates
Initial Concentrations: [BP] = 5 M; [1A1] = 0.0058 M; [EH] = 0.10 M; k10 = 0
                      0.7
                                                                   7,8 diol
                                                                   9,10 diol
                      0.6                                          tetrol

                      0.5
 Concentration (M)




                      0.4

                      0.3

                      0.2

                      0.1


                       00   20   40   60   80      100 120 140   160 180       200
                                                Time (min)
                    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.

				
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