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biocham
Commits
93059bd6
Commit
93059bd6
authored
Jan 16, 2019
by
FAGES Francois
Browse files
TD12
parent
796d2e8b
Changes
2
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library/examples/C2-19-Biochemical-Programming/TD1_lotka_volterra.ipynb
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library/examples/C2-19-Biochemical-Programming/TD2_enzyme_kinetics.ipynb
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93059bd6
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# TD2: Enzyme kinetics\n",
"* Michaelis-Menten enzymatic reaction network\n",
" * conservation laws\n",
" * time scales\n",
"* Michaelis-Menten kinetics \n",
" * with quasi-steady state approximation (QSSA)\n",
" * with quasi-equilibrium (QE) approximation\n",
"* Cooperative allosteric enzymatic reaction network\n",
" * Hill kinetics\n",
"\n",
"F. Fages, 18 Jan 2019"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Michaelis-Menten enzymatic reaction CRN\n",
"* CRN of 3 reactions with mass action law kinetics\n",
"* Real parameter values for the hydrolysis of benzoyl-L-arginine ethyl ester by trypsin (protein of 247 amino acids)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"present(E,z). parameter(z=1e-8). \n",
"present(S,s). parameter(s=1e-5). \n",
"absent(C). \n",
"absent(P)."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"parameter(k1=4e6, k2=25, k3=15). "
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"k1*E*S for E+S => C.\n",
"k2*C for C => E+S. \n",
"k3*C for C => E+P."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"list_model."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"draw_influences."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"draw_reactions."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"search_conservations."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"list_ode."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"option(time:500)."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"numerical_simulation. plot."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"numerical_simulation(time:0.1). plot(show:{E,C,P})."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"numerical_simulation(time:1). plot(show:{E,C})."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"plot(show: {E, C}, against: S)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Michaelis-Menten kinetics\n",
"* Michaelis-Menten reduced reaction `Vm*A/(Km+A) for A => B.` obtained by Quasi-Steady State Approximation(QSSA) \n",
"* Vm=k3*z and Km=(k2+k3)/k1"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"present(A,s). \n",
"absent(B)."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"function(Vm=k3*z)."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"function(Km=(k2+k3)/k1)."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"Vm*A/(Km+A) for A => B."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"draw_influences."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"list_model."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"list_ode."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"option(show:{A,B,S,P})."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"numerical_simulation. plot."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"numerical_simulation(time:0.1). plot(show:{E,C,P,B})."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Questions\n",
"\n",
"1) change the values of the kinetic parameters to evaluate the robustness of that approximation on the long time scale (500 units)\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"%slider k1 k2 k3"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Quasi-Equilibrium (QE) approximation\n",
"\n",
"2) Implement the Quasi-Equilibrium reduced reaction `Vm*X/(Kd+X) for X => Y.` with Kd=k2/k1\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"3) compare the results with the QSSA approximation\n",
"\n",
"4) to which kinetic parameters is the quality of the QE reduction sensitive ?\n",
"\n",
"*write your answer here*\n",
"\n",
"*...*"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"%slider k1 k2 k3"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Biocham",
"language": "",
"name": "biocham"
},
"language_info": {
"codemirror_mode": "biocham",
"file_extension": ".bc",
"mimetype": "text/plain",
"name": "biocham",
"pygments_lexer": "prolog"
}
},
"nbformat": 4,
"nbformat_minor": 1
}
%% Cell type:markdown id: tags:
# TD2: Enzyme kinetics
*
Michaelis-Menten enzymatic reaction network
*
conservation laws
*
time scales
*
Michaelis-Menten kinetics
*
with quasi-steady state approximation (QSSA)
*
with quasi-equilibrium (QE) approximation
*
Cooperative allosteric enzymatic reaction network
*
Hill kinetics
F. Fages, 18 Jan 2019
%% Cell type:markdown id: tags:
## Michaelis-Menten enzymatic reaction CRN
*
CRN of 3 reactions with mass action law kinetics
*
Real parameter values for the hydrolysis of benzoyl-L-arginine ethyl ester by trypsin (protein of 247 amino acids)
%% Cell type:code id: tags:
```
present(E,z). parameter(z=1e-8).
present(S,s). parameter(s=1e-5).
absent(C).
absent(P).
```
%% Cell type:code id: tags:
```
parameter(k1=4e6, k2=25, k3=15).
```
%% Cell type:code id: tags:
```
k1*E*S for E+S => C.
k2*C for C => E+S.
k3*C for C => E+P.
```
%% Cell type:code id: tags:
```
list_model.
```
%% Cell type:code id: tags:
```
draw_influences.
```
%% Cell type:code id: tags:
```
draw_reactions.
```
%% Cell type:code id: tags:
```
search_conservations.
```
%% Cell type:code id: tags:
```
list_ode.
```
%% Cell type:code id: tags:
```
option(time:500).
```
%% Cell type:code id: tags:
```
numerical_simulation. plot.
```
%% Cell type:code id: tags:
```
numerical_simulation(time:0.1). plot(show:{E,C,P}).
```
%% Cell type:code id: tags:
```
numerical_simulation(time:1). plot(show:{E,C}).
```
%% Cell type:code id: tags:
```
plot(show: {E, C}, against: S).
```
%% Cell type:markdown id: tags:
## Michaelis-Menten kinetics
*
Michaelis-Menten reduced reaction
`Vm*A/(Km+A) for A => B.`
obtained by Quasi-Steady State Approximation(QSSA)
*
Vm=k3
*
z and Km=(k2+k3)/k1
%% Cell type:code id: tags:
```
present(A,s).
absent(B).
```
%% Cell type:code id: tags:
```
function(Vm=k3*z).
```
%% Cell type:code id: tags:
```
function(Km=(k2+k3)/k1).
```
%% Cell type:code id: tags:
```
Vm*A/(Km+A) for A => B.
```
%% Cell type:code id: tags:
```
draw_influences.
```
%% Cell type:code id: tags:
```
list_model.
```
%% Cell type:code id: tags:
```
list_ode.
```
%% Cell type:code id: tags:
```
option(show:{A,B,S,P}).
```
%% Cell type:code id: tags:
```
numerical_simulation. plot.
```
%% Cell type:code id: tags:
```
numerical_simulation(time:0.1). plot(show:{E,C,P,B}).
```
%% Cell type:markdown id: tags:
# Questions
1) change the values of the kinetic parameters to evaluate the robustness of that approximation on the long time scale (500 units)
%% Cell type:code id: tags:
```
%slider k1 k2 k3
```
%% Cell type:markdown id: tags:
## Quasi-Equilibrium (QE) approximation
2) Implement the Quasi-Equilibrium reduced reaction
`Vm*X/(Kd+X) for X => Y.`
with Kd=k2/k1
%% Cell type:code id: tags:
```
```
%% Cell type:code id: tags:
```
```
%% Cell type:code id: tags:
```
```
%% Cell type:code id: tags:
```
```
%% Cell type:code id: tags:
```
```
%% Cell type:code id: tags:
```
```
%% Cell type:markdown id: tags:
3) compare the results with the QSSA approximation
4) to which kinetic parameters is the quality of the QE reduction sensitive ?
*write your answer here*
*...*
%% Cell type:code id: tags:
```
%slider k1 k2 k3
```
%% Cell type:code id: tags:
```
```
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