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Welcome to
Integrated Bioinformatics
Friday, 18 November 2011
Scenario 5
Metabolic Modeling
The one and only concern I and
most of my classmets have is the
date of most modules needs to be
updated
in this
website
plus
they
This is best
viewed
as a slide
show.
Click
to
start
To view it, click need
Slide Show
on
the
top tool bar, then View show.
current informations.
Friday, 16 November 2012
• What I learned from the questionnaires
• The biological problem
• Overview of glycolysis
• Modeling a spontaneous reaction (ADP-As.pl)
• Vmax and Km
• Problem Set 5, #3 and maybe #11
How things work
At the beginning of each module
the general principle is
discussed… After this, time is
spent more on programming and
how to biologically use it.
Takes up majority of the
time writing/modifying
perl programs. Not much
time analyzing the output
or finding answers to
biological questions.
How things work
Lately we have been devoting the first
hour to notes and defining a problem.
The second hour is spent with Paul
and Adam circulating to answer
questions as the class works
more or less independently.
Usually, the first hour is
devoted to lecture or going
over the concepts of the
module, and the next hour is
spent working with Perl.
About an hour of lecture,
followed by an hour of coding.
What things work
Lectures so far have been a big part of it.
The lectures help me greatly
with understanding more of
the complex concepts.
Sitting and trying to figure out
how to solve a problem helps
me learn about it more.
I learn best by doing,
not seeing nor hearing.
What things work
I have no formal training in differential
equations, but I've been able to work my
through some biological scenarios that used
them. I didn't understand the math,...
I am very weak when it comes to math.
I learn best by doing,
not seeing nor hearing.
Trypanosoma brucei
Causative agent of sleeping sickness
Life Cycle
Central Nervous System
Death
Trypanosoma brucei
How to stop it?
Standard antibiotic targets
Cell wall
e.g. penicillins
Bacterial ribosomes
e.g. neomycin
Bacterial RNA polymerase
e.g. rifampicin
Bacterial DNA gyrase
e.g. nalidixic acid
Trypanosomes have eukaryotic machinery, like us
Trypanosoma brucei
How to stop it?
Them
ATP
Glucose
Us
Glycolysis
Glycolysis
Pyruvate
Pyruvate
Citric Acid
Cycle
ATP
ATP
Trypanosoma brucei
How to stop it?
Glucose
Them
ATP
Us
Glycolysis
Glycolysis
Pyruvate
Pyruvate
Citric Acid
Cycle
ATP
ATP
Alternative to exhaustive lab testing
Symbolically
Glucose Hexokinase Glucose-6-P
+ ATP
+ ADP
Mathematically
dG6P/dt = kf [Glc][ATP]
Computationally
$dG6P_dt = $kf*$glc*$atp
… exhaustive
computational modeling
inhibitor1
Glycolysis
dGlc/dt = +kf1 [Glcx] -kr2[Glc]
-kf2[Glc][ATP]
dG6P/dt = +kf2 [Glc][ATP]
-kf3[G6P]
This is a very detailed
dF6P/dt = +kf3 [G6P]-kr3[F6P]
modeling of glycolysis.
-kf4[F6P][AT]
It seems not feasible to
dFDP/dt = +kf4 [F6P][ATP]-kf5[FDP]
model the enzyme kinetics
dDHAP/dt = +k [FDP]+k [G3P]
-k [DHAP]
when
dealing large system of
dG3P/dt = +k [FDP]+k [DHAP] -k [G3P]
metabolic model.
f5
f5
r6
f6
f6
r6
-kf7[G3P][NAD]+kry[13PGA][NADH]
d13PGA/dt = kf7[G3P][NAD]-kry[13PGA][NADH]
-kf8[13PGA][ADP]+kr8[3PGA][ATP]
...
Modeling Glycolysis
I have studied it in a number of classes
I learned about the glycolytic pathway in the past
Need a little review, but comfortable with the basics.
I understand the concept
but I am definitely not an expert at it.
Glucose->->->Pyruvate ===free energy
Modeling Glycolysis
What is glycolysis
glucose
HO
OH
OH
OH
blood
cell
O
OH
Oxidation state
<
O
O
OH
<
<
OH
electronegativity
O>C>H
2 ATP + 2
OO
OH
pyruvate
What is glycolysis
glucose
HO
OH
OH
O
permease
OH
OH
blood
cell
2
OO
OH
pyruvate
What is glycolysis
glucose
HO
permease
OH
OH
OH
blood
cell
2
OO
OH
pyruvate
O
OH
What is glycolysis
glucose
HO
OH
OH
O
permease
OH
OH
ATP
blood
cell
O O O
O-P-O
O-P-O
O-P-O -Adenosine
O O O
Anhydride (acid + acid)
2
OO
OH
pyruvate
What is glycolysis
glucose
HO
permease
OH
OH
OH
O
OH
ATP
blood
cell
O O O
O-P-O
O-P-O
O-P-O -Adenosine
O O O
Anhydride (acid + acid)
2
OO
OH
pyruvate
What is glycolysis
O
glucose
O-P-O
O
permease
OH
OH
OH
O
OH
ADP
blood
cell
O O
O-P-O
O-P-O -Adenosine
O O
Anhydride (acid + acid)
2
OO
OH
pyruvate
What is glycolysis
glucose
O
permease
OH
OH
OH
O
OH
ADP
blood
cell
O O
O-P-O
O-P-O -Adenosine
O O
Anhydride (acid + acid)
2
OO
OH
pyruvate
What is glycolysis
ATP ADP
glucose
HO
OH
OH
OH
O
glucose-6P
OH
O
OH
O
OH
OH
OH
Hexokinase
Ketone or aldehyde
O
???
O
2 ATP + 2
OO
OH
pyruvate
Enol
What is glycolysis
ATP ADP
glucose
HO
OH
OH
OH
O
glucose-6P
OH
O
OH
O
OH
OH
???
O
OH
???
2 ATP + 2
OH
pyruvate
OHO
OH
Hexokinase
OO
OH
OH
What is glycolysis
ATP ADP
glucose
HO
OH
OH
OH
O
glucose-6P
OH
O
OH
O
OH
OH
O
OH
OH
Hexose-P
isomerase
Hexokinase
OO
2 ATP + 2
fructose-6P
OH
pyruvate
OHO
OH
O
OH
OH
OHO
OH
OH
What is glycolysis
ATP ADP
glucose
HO
OH
OH
OH
O
ATP ADP
glucose-6P
OH
O
OH
O
OH
OH
O
OH
OH
Hexose-P
isomerase
Hexokinase
OO
2 ATP + 2
fructose-6P
OH
pyruvate
OHO
OH
fructose-1,6 diP
O
OH
Phospho
fructokinase
OH
OHO
OH
O
What is glycolysis
ATP ADP
glucose
HO
OH
OH
OH
O
ATP ADP
glucose-6P
OH
O
OH
O
OH
OH
fructose-6P
O
OH
OH
Hexose-P
isomerase
Hexokinase
OHO
OH
fructose-1,6 diP
O
OH
OHO
OH
OH
O
Phospho
fructokinase
Aldolase
O
OH
O
glyceraldehyde
3-P (Gla3P)
2 ATP + 2
OO
OH
pyruvate
OHO
O
Dihydroxy
acetone P
(DHAP)
What is glycolysis
ATP ADP
glucose
HO
OH
OH
OH
O
ATP ADP
glucose-6P
OH
O
OH
O
OH
OH
fructose-6P
O
OH
OH
Hexose-P
isomerase
Hexokinase
OHO
OH
fructose-1,6 diP
O
OH
OHO
OH
OH
O
Phospho
fructokinase
Aldolase
Triose P
isomerase
2 ATP + 2
OO
OH
pyruvate
O
OH
O
Gla3P
OHO
O
DHAP
What is glycolysis
ATP ADP
glucose
HO
OH
OH
OH
O
ATP ADP
glucose-6P
OH
O
OH
O
OH
OH
fructose-6P
O
OH
Hexose-P
isomerase
fructose-1,6 diP
O
OH
OH
OH
Hexokinase
OHO
OHO
OH
O
OH
Phospho
fructokinase
Aldolase
Triose P
isomerase
O
OHO
OH
O
O
Gla3P
DHAP
NAD+
O
2 ATP + 2
OO
OH
pyruvate
NADH
Gla 3-P
dehydrogenase
O
OH
O
O
O
ADP
ATP
OH
O
O
3-P-glycerate (3PG)
What is glycolysis
ATP ADP
glucose
HO
OH
OH
OH
ATP ADP
glucose-6P
O
O
OH
OH
OH
OH
OH
fructose-6P
O
OH
OHO
Ketone or aldehyde
OH
OHO
Hexose-P
isomerase
Hexokinase
pyruvate
2 ATP + 2
O
OO
OH
fructose-1,6 diP
O
OHO
OH
OH
O
Phospho
fructokinase
O
Triose P
isomerase
Aldolase
O
OH
OHO
Enol
O
O
Gla3P
DHAP
NAD+
O
OH
O
O
NADH
ADP
O
Gla 3-P
ATP
dehydrogenase O OH
OH O
O
O
O
O
P-Gla mutase
3-P-glycerate (3PG)
2-P-glycerate (3PG)
What is glycolysis
ATP ADP
glucose
HO
OH
OH
OH
ATP ADP
glucose-6P
O
OH
O
OH
OH
OH
O
OH
pyruvate
OO
OH
ATP
Pyr Kinase
ADP
O
OH
OHO
Ketone or aldehyde
OH
OHO
Hexose-P
isomerase
Hexokinase
2 ATP + 2
fructose-6P
fructose-1,6 diP
O
OH
O
Phospho
fructokinase
O
Triose P
isomerase
Aldolase
O
OH
OHO
Enol
O
O
Gla3P
DHAP
NAD+
O
O
OHO
OH
O
OH
O
O
NADH
ADP
O
Enolase
Gla 3-P
H2O
ATP
dehydrogenase O OH
OH O
O
O
H
O
O
P-Gla mutase
3-P-glycerate (3PG)
2-P-glycerate (3PG)
O
Why is glycolysis
ATP ADP
glucose
HO
OH
OH
OH
ATP ADP
glucose-6P
O
OH
O
OH
OH
OH
O
fructose-6P
O
OH
fructose-1,6 diP
O
OH
OH
OH
Hexose-P
isomerase
Hexokinase
OHO
OH
2 ATP + 2
OH
ATP
Pyr Kinase
ADP
Aldolase
Triose P
isomerase
O
OH
OHO
O
O
Gla3P
DHAP
NAD+
O
O
O
Phospho
fructokinase
pyruvate
OO
OHO
OH
O
OH
O
O
NADH
ADP
O
Enolase
Gla 3-P
H2O
ATP
dehydrogenase O OH
OH O
O
O
H
O
O
P-Gla mutase
3-P-glycerate (3PG)
2-P-glycerate (3PG)
O
Why is glycolysis
ATP ADP
glucose
HO
OH
OH
OH
ATP ADP
glucose-6P
O
OH
O
OH
OH
OH
O
fructose-6P
O
OH
fructose-1,6 diP
O
OH
OH
OH
Hexose-P
isomerase
Hexokinase
OHO
OH
2 ATP + 2
OH
ATP
Pyr Kinase
ADP
Aldolase
Triose P
isomerase
O
OH
OHO
O
O
Gla3P
DHAP
NAD+
O
O
O
Phospho
fructokinase
pyruvate
OO
OHO
OH
O
OH
O
O
NADH
ADP
O
Enolase
Gla 3-P
H2O
ATP
dehydrogenase O OH
OH O
O
O
H
O
O
P-Gla mutase
3-P-glycerate (3PG)
2-P-glycerate (3PG)
O
Trypanosoma brucei
How to exploit dependence on glycolysis?
blood
cell
Treatment
Arsenate
(AsO4 = Asi)
Competitive
with Pi
Trypanosoma brucei
How arsenate poisons glycolysis?
Normal glycolysis
Glyceraldehyde-3-P
NAD+
O
OH O
O-P-O-CH2—CH—C
H
O
NADH
ADP
O
OH O O
O-P-O-CH2—CH—C- O-P-O
O
O
ATP
3-P-Glycerate
O
OH O
O-P-O-CH2—CH—C-O
O
O
O-P-O
O
Trypanosoma brucei
How arsenate poisons glycolysis?
Poisoned glycolysis
Glyceraldehyde-3-P
NAD+
O
O-As-O
O
O
OH O
O-P-O-CH2—CH—C
H
O
H2O
O
OH O
O
O-P-O-CH2—CH—C- O-As-O
O
O
NADH
ADP
ATP
3-P-Glycerate
O
OH O
O-P-O-CH2—CH—C-O
O
+
O
O-As-O
O
How to model this reaction?
1
[S]
0.8
0.6
0.4
0.2
0
0
1
2
3
t (sec)
4
5
How to model this reaction?
1
[S]
0.8
0.6
0.4
0.2
0
0
1
2
3
t (sec)
4
5
Characteristics of enzymes
Chemical reactions
AMP-P-As
[AMP-P-As]
concentration
AMP-P +Asi
k = d[AMP-P ] / dt
rate
constant
rate of change
= d[Asi] / dt
rate of change
= =– d[AMP-P-Asi] / dt
rate of change
Characteristics of enzymes
Chemical reactions
AMP-P-As
[AMP-P-As]
concentration
A differential equation
AMP-P +Asi
k = =– d[AMP-P-Asi] / dt
rate
constant
rate of change
[S] k = =– d[S] / dt
Characteristics of enzymes
Chemical reactions
AMP-P-As
AMP-P +Asi
[AMP-P-As]
concentration
A differential equation
Its solution?
k = =– d[AMP-P-Asi] / dt
rate
constant
rate of change
= d[S] / dt = –k[S]
[S] =
Characteristics of enzymes
Chemical reactions
AMP-P-As
AMP-P +Asi
[AMP-P-As]
concentration
A differential equation
Its solution?
Check:
k = =– d[AMP-P-Asi] / dt
rate
constant
rate of change
= d[S] / dt = –k[S]
[S] = S0 e -k(t-to)
= d[S] / dt = S0 (–k) e -k(t-to)
= -k S0 e -k(t-to)
= -k [S]
Characteristics of enzymes
Chemical reactions
Write an equation for the rate of increase
of a rabbit population over time.
(ignore all environmental effects)
[R] = R0 2t/D
A differential equation
Its solution?
Check:
= d[S] / dt = –k[S]
[S] = S0 e -k(t-to)
= d[S] / dt = S0 (–k) e -k(t-to)
= -k S0 e -k(t-to)
= -k [S]
Characteristics of enzymes
Chemical reactions
AMP-P-As
AMP-P +Asi
[AMP-P-As]
concentration
A differential equation
Its solution?
Check:
k = =– d[AMP-P-Asi] / dt
rate
constant
rate of change
= d[S] / dt = –k[S]
[S] = S0 e -k(t-to)
= d[S] / dt = S0 (–k) e -k(t-to)
= -k S0 e -k(t-to)
= -k [S]
Characteristics of enzymes
Chemical reactions
1
[S]
0.8
[S] = S0 e -k(t-to)
0.6
0.4
= d[S] / dt = –k[S]
0.2
0
0
1
2
3
t (sec)
4
5
Characteristics of enzymes
Chemical reactions
1
[S]
0.8
0.6
0.4
0.2
0
0
1
2
3
t (sec)
4
5
Characteristics of enzymes
Chemical reactions
1
[S] =
[S]
0.8
[S] = S0 e -k(t-to)
0.6
S0
0.4
0.2
Δt
0
0
1
2
3
t (sec)
4
5
Characteristics of enzymes
Chemical reactions
1
[S] = S0 + Δt d[S] / dt
[S]
0.8
0.6
S0
0.4
0.2
= d[S] / dt = –k[S]
Δt
0
0
1
2
3
t (sec)
4
5
Characteristics of enzymes
Chemical reactions
SQ1. Let’s try it.
Link to ADP-As.pl
Upload and plot results in Excel.
For comparison, calculate on the same
graph the analytical solution, using
constants provided in ADP-As.pl
Characteristics of enzymes
[S]S
Chemical reactions
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
[S] = S0 e -k(t-to)
= d[S] / dt = –k[S]
0
1
2
3
t
t (sec)
4
5
Characteristics of enzymes
Chemical reactions
1
[S]
0.8
0.6
S0
0.4
0.2
Δt
0
0
1
2
3
t (sec)
4
5
Characteristics of enzymes
Chemical reactions
= d[S] / dt = –k[S]
[S] = S0 + Δt d[S] / dt
1
[S]
0.8
Slope0 = -k[S0]
[S1] = S0 + Δt d[S] / dt
Slope1 = -k[S1]
0.6
S0
0.4
Use average of Slope0 and Slope1
0.2
Δt
0
0
1
2
3
t (sec)
4
5
Characteristics of enzymes
Chemical reactions
= d[S] / dt = –k[S]
[S] = S0 + Δt d[S] / dt
1
[S]
0.8
Slope0 = -k[S0]
[S1] = S0 + Δt d[S] / dt
Slope1 = -k[S1]
0.6
S0
0.4
Use average of Slope0 and Slope1
Runge-Kutta method
0.2
Δt
0
0
1
2
3
t (sec)
4
5
Characteristics of enzymes
Enzymatic reactions
inhibitor1
Characteristics of enzymes
Enzymatic reactions
What is the rate equation?
Glucose-6-phosphate
[G6P]
concentration
Fructose-6-phosphate
k = = d[F6P] / dt
rate
constant
???
k~0
rate of change
Characteristics of enzymes
Enzymatic reactions
Characteristics of enzymes
Enzymatic reactions
G6P + E
G6P·E
F6P·E
E-complex
v (velocity) =
d[product] / dt =
[S] VMax
[S] + Km
[product] = S0 + Δt d[S] / dt
F6P + E
Characteristics of enzymes
Enzymatic reactions
velocity
[S]
v (velocity) =
d[product] / dt =
[S] VMax
[S] + Km
Modeling systems of metabolic reactions
Spontaneous vs Enzyme-catalyzed
Spontaneous reaction
v = k [AMP~P~As]
product
[S]