TD12

library/examples/C2-19-Biochemical-Programming/TD2_enzyme_kinetics.ipynb

+{
+ "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
+}