ODE - Inducible Gene Expression - Custom function.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.optimize import least_squares"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def ODE(total_time, timesteps, species, system_of_equations):\n",
    "    steps_taken = 0\n",
    "    current_time = 0\n",
    "    dt = total_time / timesteps\n",
    "    \n",
    "    # Create a list to store all the timepoints used. \n",
    "    timepoints = np.empty(timesteps+1) # fencepost magic +1...\n",
    "    \n",
    "    # Create a list to store each species at each timepoint\n",
    "    results = np.empty((len(species), (timesteps+1))) # fencepost magic +1..\n",
    "\n",
    "    ########################\n",
    "    #### Start ODE loop ####\n",
    "    \n",
    "    while current_time<total_time:\n",
    "        # Log the amount of each species\n",
    "        for i in range(0, len(species)):\n",
    "            results[i][steps_taken] = species[i]\n",
    "        \n",
    "        # Calculate the change in each species and apply it to the current\n",
    "        change_in_species = simulation_set_of_equations(species, dt)\n",
    "        species = np.add(species, change_in_species)\n",
    "\n",
    "        # store current timpoint and then increment time\n",
    "        timepoints[steps_taken] = current_time\n",
    "        current_time += dt\n",
    "        steps_taken += 1\n",
    "\n",
    "    #### End ODE loop ####    \n",
    "    ######################\n",
    "    \n",
    "    return timepoints, results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def simulation_set_of_equations(current_species_concentration, dt):\n",
    "    protein_loss = 0.01 # A summation of dilution and degredation\n",
    "    \n",
    "    # Unpack your current amount of each species\n",
    "    LuxR, GFP, AHL = current_species_concentration\n",
    "    \n",
    "    # Determine the change in each species\n",
    "    dLuxR = dt * (pCon1() - protein_loss*LuxR)\n",
    "    dGFP = dt * (pLux1(LuxR, AHL) - protein_loss*GFP)\n",
    "    dAHL = dt * 0 # for now we're assuming AHL was added exogenously and never degrades\n",
    "    \n",
    "    # Return the change in each species; make sure same order as your init values\n",
    "    return [dLuxR, dGFP, dAHL]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def pCon1():\n",
    "    # This is the module for a specific insubstatiation of a constituitive promoter\n",
    "    # the input is nothing\n",
    "    # the output is a protein production amount per time unit\n",
    "    pCon1_production_rate = 10\n",
    "    \n",
    "    return pCon1_production_rate # MEFL minute**-1\n",
    "    \n",
    "def pLux1(LuxR, AHL):\n",
    "    # This is the module for a specific insubstatiation of a lux promoter\n",
    "    # the input is a LuxR amount and an AHL amount\n",
    "    # the output is a protein production amount per time unit\n",
    "    \n",
    "    # For every promoter there is some function that determines what the promoter's\n",
    "    #     maximal and basal expression are based on the amount of transcriptional factor\n",
    "    #     is floating around in the cell. These numbers are empircally determined, and\n",
    "    #     for demonstration purposes are fictionally and arbitrarily filled in here. \n",
    "    #     These functions take the form of hill functions.\n",
    "    \n",
    "    basal_n = 2\n",
    "    basal_basal = 2\n",
    "    basal_max = 4\n",
    "    basal_kd = 2\n",
    "    basal_expression_rate = basal_basal + (basal_max * (LuxR**basal_n / (LuxR**basal_n + basal_kd))) # MEFL minute**-1\n",
    "    \n",
    "    max_n = 2\n",
    "    max_max = 600\n",
    "    max_kd = 10\n",
    "    maximal_expression_rate = max_max * (LuxR**max_n / (LuxR**max_n + max_kd)) # MEFL minute**-1\n",
    "    \n",
    "    \n",
    "    pLux1_n = 2\n",
    "    pLux1_kd = 10\n",
    "     \n",
    "    pLux1_production_rate = basal_expression_rate + (maximal_expression_rate * (AHL**pLux1_n / (pLux1_kd + AHL**pLux1_n))) \n",
    "    \n",
    "    return pLux1_production_rate # MEFL minute**-1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "#%%timeit\n",
    "initial_conditions = [10, 10, 100] # LuxR, GFP, AHL\n",
    "minutes = 400\n",
    "timesteps = 10000\n",
    "x, y = ODE(minutes, timesteps, initial_conditions, simulation_set_of_equations)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
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558f18MYYk1Bei5iuAE5Q1QMAInIP8BnwkF+B+SlYSR2vJwhVuOsuuO02J0G8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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x27703f9c3c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y[0], c='b', label = 'LuxR')\n",
    "plt.plot(x, y[1], c='g', label = 'GFP')\n",
    "plt.xlabel('Time (minutes)')\n",
    "plt.ylabel('Protein Amount (GeoMean MEFL)')\n",
    "plt.legend(loc = 'best')\n",
    "plt.grid()\n",
    "plt.yscale('log')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}