Transcript Metabolomics - Virginia Commonwealth University

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
Benzo[a]pyrene Metabolism Network
k7
Qn
k11
BP
k10
1A1·BP
1A1inact
k2
k1
k10
k25
1A1
k10
k5
k8
k14
k13
unk
1A1inact
k4
k3
k6
k10
1A1·7,8 diol
diol-ox2
k9
diol-ox3
k26
k17
9,10 ox
k15
9-OH
k27
EH
k23
tetrol
unk
k28
k19
k13
k18
4,5 diol
7,8 ox
EH·7,8 ox
k21
EH·9,10 ox
k12
k24
3-OH
EH·4,5 ox
4,5 ox
k16
1A1·9,10 diol
2,3 ox
k22
9,10 diol
7,8 diol
k29
k30
Gautier, J. C.; Urban, P.; Beaune, P.; Pompon, D.
Chem. Res. Toxicol. 1996, 9, 418-425.
BP Metabolites
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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)
O
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)
OH
HO
HO
O
OH
HO
OH
O
HO
OH
OH
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 ]
 k[ A ]
dt
[B]t 0  0
[ A ]t
[ A ]o  [ A ]t  [B]t
t
d[ A ]
   kt

[A]
[ A ] [ A ] o
t 0
[ A ]o  [ A ]o e kt  [B]t
kt
[B]t  [ A ]o (1  e )
[ A ]t
ln
 kt
[ A ]o
[ A ]t  [ A ]o e kt
[B]t
[A]t
Conc
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
• Non-stiff equations
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 ]
 k[ A ]
dt
d[B]
 k[ A ]
dt
• 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
Differential Equation Solver in Matlab –
Second Order Kinetics
• In Matlab command window, select File, New, Mfile, 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 ]
 k[ A ][B]
dt
d[B]
 k[ A ][B]
dt
d[ AB]
 k[ A ][B]
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)
y is a 101 x 3 matrix
• 101 different time points
• 3 different chemical species
[AB]t
[A]t
[B]t
Michaelis-Menten Kinetics
• Enzyme kinetics
A + B
k3
AB
k1
AB
A+C
k2
• 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
E + S
k1
k2
ES
ES
[E]  [E]o  [ES ]
[ES ] 
k1
[E][S]
k2  k3
[ES ]
k1

 KM
[E][S] k 2  k 3
E+P
[E]o  [E]  [ES ]
d[ES ]
 k1[E][S]  k 2 [ES ]  k 3 [ES ]  0
dt
k1[E][S]  (k 2  k 3 )[ES ]
[ES ] 
k3
[E][S]
KM
K M [ES ]  [E]o [S]  [ES ][S]
[ES ](K M  [S])  [E]o [S]
d[P]
 k 3 [ES ]
dt
d[P] k 3 [E]o [S]

dt
K M  [S ]
d[P]
 v initial ;
dt
v initial
[ES ] 
k 3 [E]o  v max
v max [S]

K M  [S]
[E]o [S]
K M  [S ]
Exercise 2
Determine the initial rate for the following
conditions using the Michaelis-Menten
formula:
[S]o= 1.0 M; [E]o = 0.03 M; [ES]o = 0; [P]o = 0
KM = 10 M; vmax = 15 nmol/nmol E/min
Implementing a Kinetic Model
A
k1
B
B
k2
C
Implementing a Kinetic Model
A
d A 
=
dt
d B
=
dt
d C
=
dt
k1
- k1 [A]
B
B
k2
= - 1  k1 [A]1[B]0[C]0 + 0  k2 [A]0[B]0[C]1
k1 [A] - k2 [B] = + 1  k1 [A]1[B]0[C]0 - 1  k2 [A]0[B]1[C]0
k2 [B] = + 0  k1 [A]1[B]0[C]0 + 1  k2 [A]0[B]1[C]0
C
Implementing a Kinetic Model
A
d A 
=
dt
d B
=
dt
d C
=
dt
k1
- k1 [A]
B
B
k2
C
= - 1  k1 [A]1[B]0[C]0 + 0  k2 [A]0[B]1[C]0
k1 [A] - k2 [B] = + 1  k1 [A]1[B]0[C]0 - 1  k2 [A]0[B]1[C]0
k2 [B] = + 0  k1 [A]1[B]0[C]0 + 1  k2 [A]0[B]1[C]0
Implementing a Kinetic Model
A
d A 
=
dt
d B
=
dt
d C
=
dt
k1
- k1 [A]
B
B
k2
C
= - 1  k1 [A]1[B]0[C]0 + 0  k2 [A]0[B]1[C]0
k1 [A] - k2 [B] = + 1  k1 [A]1[B]0[C]0 - 1  k2 [A]0[B]1[C]0
k2 [B] = + 0  k1 [A]1[B]0[C]0 + 1  k2 [A]0[B]1[C]0
Implementing a Kinetic Model

i1
m
O=
R=
1
0
0
1
0
0
-1
0
1
-1
0
1
pn  k n  Xi 
Oni

dXm 
Rm
   j  pj 
dt
j1
n
E. Bezemer, S. C. Rutan, Chemom. Intell. Lab. Systems, 59, 19-31, 2001
Simulated Kinetic Profiles
k1
A
Relative Concentration
B
B
C
k1 = k2 = 0.5
1
0.8
k2
C
A
0.6
0.4
B
0.2
0
2
4
6
Reaction Time
8
10
Exercise 3
• 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
Differential Equations for BP/1A1
Reactions
species X
d[X]/dt
BP
k2[1A1·BP] + k10[1A1·BP] - k1[BP][1A1]
1A1
k4[1A1·7,8-diol] + (k25 + k30 + k26)[1A1·9,10-diol] + k9[1A1·7,8-diol] +
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·BPb
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
EH
(k12 + k21)[EH·9,10-ox] + (k18 + k22)[EH·7,8-ox] + (k27+ k19)[EH·4,5-ox] –
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
Enzyme/substrate
complexes
Association constants
(M-1·min-1)
Dissociation
constants (min-1)
1A1·BP
k1 = 30
k2 = 100
1A1·7,8-diol
1A1·9,10-diol
k3 = 40
k14 = 26
Products
Catalytic
constants (min1)
Products
Nonenzymatic
constants (min1)
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
adducts
k23 = 60
T2-tetrol
k24 = 30
adducts
k29 = 40
T2-tetrol
k28 = 60
quinones
k11= 5.2
DE2
k9 = 85
k4 = 100
k25 = 100
DE3
mEH·4,5-ox
mEH·7,8 ox
mEH·9,10 ox
k13 = 180
k13 = 180
k13 = 180
k26 = 4.5
adducts
k30 = 15
4,5-diol
k19 = 23
7,8 diol
k22 = 11.5
9,10 diol
k12 = 7.5
k27 = 100
k18 = 100
k21 = 100
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
3OH
9OH
quinones
tetrol
adducts
4.5
Concentration (M)
4
3.5
3
2.5
2
1.5
1
0.5
0 0
20
40
60
80 100
Time (min)
120 140
160 180
200
Reaction Profiles for Intermediates
Initial Concentrations: [BP] = 5 M; [1A1] = 0.0058 M; [EH] = 0.10 M
Concentration (M) x 10-4
3
DE2
DE3
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
0.7
7,8 diol
9,10 diol
tetrol
Concentration (M)
0.6
0.5
0.4
0.3
0.2
0.1
00
20
40
60
80
100 120 140
Time (min)
160 180
200
Exercise 4
• 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.