Metabolomics

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
Benzoapyrene

• 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

• Benzoapyrene (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) At
• y(2) Bt

9
First-Order Kinetics

• A ? B

Bt At
Conc
Time
10
Second Order Kinetics

• A B ? AB
• Define y as the states of the system
• y(1) At
• y(2) Bt
• y(3) ABt

11
Exercise 1

• What is the result of entering the following
  commands into Matlab?
• t15
• k0.5
• aexp(-kt)
• plot(t,a)
• b1-a
• concab
• 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 dydtfirst_order(t,y)
• dydt-0.05y(1) 0.05y(1)
• Save m-file
• Switch back to Matlab command window
• Enter
• t,yode45(_at_first_order,0100,1 0)
• plot(t,y)

• y is a 101 x 2 matrix
• 101 different time points
• 2 different chemical species

14
Differential Equation Solver in Matlab Second
Order Kinetics

• In Matlab command window, select File, New,
  M-file, and enter
• function dydtsecond_order(t,y)
• dydt-0.05y(1)y(2) -0.05y(1)y(2)
  0.05y(1)y(2)
• Save m-file
• Switch back to Matlab command window
• Enter
• t,yode45(_at_second_order,0100,1.1 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
Benzoapyrene Metabolism Network
k7
Qn
k5
k10
k11
2,3 ox
3-OH
1A1BP
1A1inact
k19
k8
k2
k10
4,5 diol
EH4,5 ox
4,5 ox
k1
BP
k25
k27
k13
1A1
k13
k16
1A19,10 diol
7,8 ox
k10
k14
unk
EH
EH7,8 ox
1A1inact
k3
k4
k18
k17
k6
k10
9,10 ox
k21
1A17,8 diol
k15
k26
k9
EH9,10 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
• So 1.0 ?M 50 ?M Eo 0.03 ?M
• ESo 0 Po 0
• KM 10 ?M vmax 15 nmol/nmol E/min
• Plot vinitial vs. So

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
0
1
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 Ao Bo Co
• t,yode45(_at_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_qualfit_model(rates,data,model)
• model.krates
• t,yode23tb(_at_kinfun,010,1 0 0, ,model)
• fit_qualsum(sum(y-data).2))
• Fit the data using this function
• Opt_ratesfminsearch(_at_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
• So 1.0 ?M Eo 0.03 ?M ESo 0 Po 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
  
• So 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
Benzoapyrene Metabolism Network
k7
Qn
k5
k10
k11
2,3 ox
3-OH
1A1BP
1A1inact
k19
k8
k2
k10
4,5 diol
EH4,5 ox
4,5 ox
k1
BP
k25
k27
k13
1A1
k13
k16
1A19,10 diol
7,8 ox
k10
k14
unk
EH
EH7,8 ox
1A1inact
k3
k4
k18
k17
k6
k10
9,10 ox
k21
1A17,8 diol
k15
k26
k9
EH9,10 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
Reaction of Cytochrome 1A1 w/ BP
k1

• 1A1 BP 1A1?BP
• 1A1?BP 1A1 Qn
• Is really the same as
• E S ES
• ES E P

k2
k11
k1
k2
k3
43
Dynamics for 1A1?BP
44
Differential Equations for BP/1A1 Reactions
species X dX/dt
BP k21A1BP k101A1BP - k1BP1A1
1A1 k41A17,8-diol (k25 k30 k26)1A19,10-diol k91A17,8-diol k111A1BP k21A1BP (k5 k6 k7 k8)1A1BP - k11A1BP - k141A19,10-diol - k101A1 - k31A17,8-diol
1A1inactiv. k10(1A1 1A17,8-diol 1A1BP 1A19,10-diol)
1A1BP k1BP1A1 - (k5 k6 k7 k8 k2 k10 k11)1A1BP
4,5-ox k81A1BP k27EH4,5-ox - k164,5-ox - k13EH4,5-ox
7,8-ox k71A1BP k18EH7,8-ox - k207,8-ox - k13EH7,8-ox
9,10-ox k61A1BP k21EH9,10-ox - k13EH9,10-ox - k179,10-ox - k159,10-ox
3-OH k51A1BP
9-OH k159,10-ox
quinones k111A1BP
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
species X dX/dt
EH (k12 k21)EH9,10-ox (k18 k22)EH7,8-ox (k27 k19)EH4,5-ox k13EH (4,5-ox 7,8-ox 9,10-ox)
EH4,5-ox k134,5-oxEH - (k27 k19)EH4,5-ox
EH7,8-ox k137,8-oxEH - (k18 k22)EH7,8-ox
EH9,10-ox k139,10-oxEH - (k21 k12)EH9,10-ox
4,5-diol k19EH4,5-ox
7,8-diol k22EH7,8-ox k41A17,8-diol k101A17,8-diol - k31A17,8-diol
9,10-diol k12EH9,10-ox k251A19,10-diol k101A19,10-diol - k149,10-diol1A1
1A17,8-diol k31A17,8-diol - (k4 k9 k10)1A17,8-diol
1A19,10-diol k141A19,10-diol - (k25 k10 k26 k30)1A19,10-diol
DE2 k91A17,8-diol - (k23 k24)DE2
DE3 k261A19,10-diol - (k29 k28)DE3
T2-tetrol k24DE2 k28DE3
adducts k179,10-ox k207,8-ox k164,5-ox k23DE2 k29DE3 k301A19,10-diol
Gautier, J. C. Urban, P. Beaune, P. Pompon, D.
Chem. Res. Toxicol. 1996, 9, 418-425.
46
Kinetic Constants for BP Model
Enzyme/substrate complexes Association constants (?M-1min-1) Dissociation constants (min-1) Products Catalytic constants (min-1) Products Nonenzymatic constants (min-1)
1A1BP 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    
1A17,8-diol k3 40 k4 100        
      DE2 k9 85 adducts k23 60
          T2-tetrol k24 30
1A19,10-diol k14 26 k25 100        
      DE3 k26 4.5 adducts k29 40
          T2-tetrol k28 60
      adducts k30 15    
mEH4,5-ox k13 180 k27 100        
      4,5-diol k19 23    
mEH7,8 ox k13 180 k18 100        
      7,8 diol k22 11.5    
mEH9,10 ox k13 180 k21 100        
      9,10 diol k12 7.5    
Gautier, J. C. Urban, P. Beaune, P. Pompon, D.
Chem. Res. Toxicol. 1996, 9, 418-425.
Inactivation constant k10 0.022 min-1
47
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
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
Reaction Profiles for IntermediatesInitial
Concentrations BP 5 ?M 1A1 0.0058 ?M
EH 0.10 ?M k10 0
50
Reaction Profiles for IntermediatesInitial
Concentrations BP 5 ?M 1A1 0.0058 ?M
EH 0.10 ?M k10 0
tetrol
51
Exercise 6

• Start Matlab, and type the following commands
• load bap_model
• t,yode23tb(_at_kinfun,0200,initial_conc,,kine
  tics)
• 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.