Commit 93059bd6 authored by FAGES Francois's avatar FAGES Francois
Browse files

TD12

parent 796d2e8b
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"# 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": []
}
],
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