crispr_model.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "59042a7b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10001\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "from numpy.random import randn\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "from pandas import Series, DataFrame,date_range\n",
    "from matplotlib import cm\n",
    "import seaborn as sns\n",
    "import scipy as sp\n",
    "import math\n",
    "import warnings\n",
    "from scipy.stats import poisson\n",
    "\n",
    "warnings.filterwarnings('ignore')\n",
    "import sys\n",
    "sys.setrecursionlimit(10001)\n",
    "print(sys.getrecursionlimit())\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "e5ba9fe3",
   "metadata": {},
   "outputs": [],
   "source": [
    "### single run\n",
    "# start\n",
    "# single colony, death happens right away\n",
    "# complex model regenerate at diff time and infect at diff time, time_step = 0.1\n",
    "# fixed parameter\n",
    "Max_cell_density = 1e10\n",
    "Pim = 0 #Proportion of cells already immune\n",
    "\n",
    "def currentPim(initialPhagePerCell,Pns,K1,K2,initialCellsPerMl,uninfectedCellsPerMl,immuneCellsPerMl=0,numPhagesPerMl = 0, y = 0):\n",
    "    if y == 0:\n",
    "        numPhagesPerMl = initialCellsPerMl*initialPhagePerCell\n",
    "    # infection \n",
    "    expectedNumCellInfected = K1*numPhagesPerMl*uninfectedCellsPerMl\n",
    "    numCellInfected = min(expectedNumCellInfected,uninfectedCellsPerMl,numPhagesPerMl)\n",
    "    immuneCellsPerMl += Pns*numCellInfected \n",
    "    # then regenerate\n",
    "    numPhagesPerMl += max(K2*numCellInfected,0)\n",
    "    uninfectedCellsPerMl += -numCellInfected \n",
    "    uninfectedCellsPerMl += celldoubling_per_time_step*uninfectedCellsPerMl\n",
    "    immuneCellsPerMl += celldoubling_per_time_step*immuneCellsPerMl\n",
    "    total_cell = (uninfectedCellsPerMl + immuneCellsPerMl)\n",
    "    if total_cell > Max_cell_density:\n",
    "        # reach max cell density\n",
    "        dilution_fold = total_cell/Max_cell_density\n",
    "        immuneCellsPerMl = immuneCellsPerMl/dilution_fold\n",
    "        uninfectedCellsPerMl = uninfectedCellsPerMl/dilution_fold\n",
    "    y += time_step\n",
    "    # eat, dilution\n",
    "    if int(y/eating_time) != int((y - time_step)/eating_time):\n",
    "        dilution_fold = (immuneCellsPerMl+uninfectedCellsPerMl)/initialCellsPerMl\n",
    "        #print('eat',y)\n",
    "        if dilution_fold > 1:\n",
    "            immuneCellsPerMl = immuneCellsPerMl/dilution_fold\n",
    "            uninfectedCellsPerMl = uninfectedCellsPerMl/dilution_fold\n",
    "            numPhagesPerMl = numPhagesPerMl/dilution_fold\n",
    "    Pim = immuneCellsPerMl/(immuneCellsPerMl + uninfectedCellsPerMl)\n",
    "    if uninfectedCellsPerMl == 0:\n",
    "        return y\n",
    "    elif Pim >= detection_limit:\n",
    "        return y\n",
    "    elif y>=y_max:\n",
    "        return y\n",
    "    else:\n",
    "        try:\n",
    "            return currentPim(initialPhagePerCell,Pns,K1,K2,initialCellsPerMl,uninfectedCellsPerMl,immuneCellsPerMl,numPhagesPerMl, y)\n",
    "        except RecursionError:\n",
    "            return y_max\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "17fedb6a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "allchangingparameters = {\n",
    "    'Pnsset':[1e-2,1e-4,1e-6,1e-8,1e-10],\n",
    "    'detection_limitset':[0.1,0.2,0.5,0.9],\n",
    "    'time_stepset':[0.01,0.1,0.2,0.5,1],\n",
    "    'generation_timeset':[0.1,1,2,5,10],\n",
    "    'K1set' : [np.power(0.1,x) for x in range(1,25)],\n",
    "    'K2set' : [0.01,0.1,0.5,1,5,10,100,1000],\n",
    "    'initialCellsPerMlset' :[1e2,1e3,1e4,1e5,1e6,1e7,1e8,1e9,1e10],\n",
    "    'eating_timeset':[5,4,3,2,1,0.5,0.33,0.25,0.1],# * generation_time\n",
    "    'phagePerCellset' : [x/20000000 for x in range(1,3)]+[x/2000000 for x in range(1,3)]+[x/200000 for x in range(1,3)]+[x/20000 for x in range(1,3)]+[x/2000 for x in range(1,3)]+[x/200 for x in range(1,3)]+[x/20 for x in range(1,3)]+[x/2 for x in range(1,3)]\n",
    "}\n",
    "\n",
    "# parameters\n",
    "phagePerCell = 1e-3\n",
    "Pns = 1e-8*(1 + 1e-1 + 1e-2 + 1e-3 + 1e-4 + 1e-5) # Exploitation of the Cooperative Behaviors of Anti-CRISPR Phages, cfu per ml = 1e8, read frequency of additional spacers decrease by 1/10\n",
    "detection_limit = 0.1\n",
    "time_step = 0.1\n",
    "generation_time = 1 # 1 day\n",
    "K1 = 1e-9 # absorption rate, 1e-10 to 1e−9 phage−1 cell−1 ml−1 min−1 for 24h\n",
    "K2 = 1 #effective phage burst size, [https://www.frontiersin.org/articles/10.3389/fcimb.2021.643214/full CrAssphage 2.5] usually 10-100\n",
    "initialCellsPerMl = 1e8 # cells per ml of the species of interest\n",
    "eating_time = 1001# no eat\n",
    "celldoubling_per_time_step = np.power(2,time_step) - 1\n",
    "\n",
    "# others\n",
    "y_max = 1000*generation_time\n",
    "df = pd.DataFrame(columns=allchangingparameters['phagePerCellset'],index = allchangingparameters['initialCellsPerMlset'])\n",
    "for initialCellsPerMl in df.index:\n",
    "    for phagePerCell in df.columns:\n",
    "        eating_time = eating_time*generation_time\n",
    "        df.loc[initialCellsPerMl,phagePerCell] = currentPim(phagePerCell,Pns,K1,K2,initialCellsPerMl,initialCellsPerMl)\n",
    "\n",
    "df.columns = ['%.1e'%i for i in df.columns]\n",
    "df.index = ['%.1e'%i for i in df.index]\n",
    "df = df.astype(float)\n",
    "sns.heatmap(data=df)\n",
    "plt.xlabel('Initial phage/cell')  \n",
    "plt.ylabel('Initial bacterial cell density') \n",
    "plt.savefig('data/model/Nodilution_phagedensityVSbacterialdensity.pdf', bbox_inches='tight')\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "348e9f36",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "allchangingparameters = {\n",
    "    'Pnsset':[1e-2,1e-4,1e-6,1e-8,1e-10],\n",
    "    'detection_limitset':[0.1,0.2,0.5,0.9],\n",
    "    'time_stepset':[0.01,0.1,0.2,0.5,1],\n",
    "    'generation_timeset':[0.1,1,2,5,10],\n",
    "    'K1set' : [np.power(0.1,x) for x in range(1,25)],\n",
    "    'K2set' : [0.01,0.1,0.5,1,5,10,100,1000],\n",
    "    'initialCellsPerMlset' :[1e2,1e3,1e4,1e5,1e6,1e7,1e8,1e9,1e10],\n",
    "    'eating_timeset':[5,4,3,2,1,0.5,0.33,0.25,0.1],# * generation_time\n",
    "    'phagePerCellset' : [x/20000000 for x in range(1,3)]+[x/2000000 for x in range(1,3)]+[x/200000 for x in range(1,3)]+[x/20000 for x in range(1,3)]+[x/2000 for x in range(1,3)]+[x/200 for x in range(1,3)]+[x/20 for x in range(1,3)]+[x/2 for x in range(1,3)]\n",
    "}\n",
    "\n",
    "# parameters\n",
    "phagePerCell = 1e-3\n",
    "Pns = 1e-8*(1 + 1e-1 + 1e-2 + 1e-3 + 1e-4 + 1e-5) # Exploitation of the Cooperative Behaviors of Anti-CRISPR Phages, cfu per ml = 1e8, read frequency of additional spacers decrease by 1/10\n",
    "detection_limit = 0.1\n",
    "time_step = 0.1\n",
    "generation_time = 1 # 1 day\n",
    "K1 = 1e-9 # absorption rate, 1e-10 to 1e−9 phage−1 cell−1 ml−1 min−1 for 24h\n",
    "K2 = 1 #effective phage burst size, [https://www.frontiersin.org/articles/10.3389/fcimb.2021.643214/full CrAssphage 2.5] usually 10-100\n",
    "initialCellsPerMl = 1e8 # cells per ml of the species of interest\n",
    "eating_time = 1# 1 per generation\n",
    "celldoubling_per_time_step = np.power(2,time_step) - 1\n",
    "\n",
    "# others\n",
    "y_max = 1000*generation_time\n",
    "df = pd.DataFrame(columns=allchangingparameters['phagePerCellset'],index = allchangingparameters['initialCellsPerMlset'])\n",
    "for initialCellsPerMl in df.index:\n",
    "    for phagePerCell in df.columns:\n",
    "        eating_time = eating_time*generation_time\n",
    "        df.loc[initialCellsPerMl,phagePerCell] = currentPim(phagePerCell,Pns,K1,K2,initialCellsPerMl,initialCellsPerMl)\n",
    "\n",
    "df.columns = ['%.1e'%i for i in df.columns]\n",
    "df.index = ['%.1e'%i for i in df.index]\n",
    "df = df.astype(float)\n",
    "sns.heatmap(data=df)\n",
    "plt.xlabel('Initial phage/cell')  \n",
    "plt.ylabel('Initial bacterial cell density') \n",
    "plt.savefig('data/model/Dilution_phagedensityVSbacterialdensity.pdf', bbox_inches='tight')\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "4b6f35ab",
   "metadata": {},
   "outputs": [],
   "source": [
    "allchangingparameters = {\n",
    "    'Pnsset':[1e-2,1e-4,1e-6,1e-8,1e-10],\n",
    "    'detection_limitset':[0.1,0.2,0.5,0.9],\n",
    "    'time_stepset':[0.01,0.1,0.2,0.5,1],\n",
    "    'generation_timeset':[0.1,1,2,5,10],\n",
    "    'K1set' : [np.power(0.1,x) for x in range(1,25)],\n",
    "    'K2set' : [0.01,0.1,0.5,1,5,10,100,1000],\n",
    "    'initialCellsPerMlset' :[1e10,1e9,1e8,1e7,1e6,1e5,1e4,1e3,1e2],\n",
    "    'eating_timeset':[1000,100,50,30,25,20,15,10,5,4,1,0.1,0.01],# * generation_time\n",
    "    'phagePerCellset' : [x/20000000 for x in range(1,3)]+[x/2000000 for x in range(1,3)]+[x/200000 for x in range(1,3)]+[x/20000 for x in range(1,3)]+[x/2000 for x in range(1,3)]+[x/200 for x in range(1,3)]+[x/20 for x in range(1,3)]+[x/2 for x in range(1,3)]\n",
    "}\n",
    "\n",
    "# parameters\n",
    "phagePerCell = 1e-3\n",
    "Pns = 1e-8*(1 + 1e-1 + 1e-2 + 1e-3 + 1e-4 + 1e-5) # Exploitation of the Cooperative Behaviors of Anti-CRISPR Phages, cfu per ml = 1e8, read frequency of additional spacers decrease by 1/10\n",
    "detection_limit = 0.1\n",
    "time_step = 0.1\n",
    "generation_time = 1 # 1 day\n",
    "K1 = 1e-9 # absorption rate, 1e-10 to 1e−9 phage−1 cell−1 ml−1 min−1 for 24h\n",
    "K2 = 1 #effective phage burst size, [https://www.frontiersin.org/articles/10.3389/fcimb.2021.643214/full CrAssphage 2.5] usually 10-100\n",
    "initialCellsPerMl = 1e8 # cells per ml of the species of interest\n",
    "eating_time = 1000# no eat\n",
    "celldoubling_per_time_step = np.power(2,time_step) - 1\n",
    "\n",
    "# others\n",
    "y_max = 1000*generation_time\n",
    "df = pd.DataFrame(columns=allchangingparameters['eating_timeset'],\n",
    "                  index = allchangingparameters['initialCellsPerMlset'],data= 0,dtype = float)\n",
    "for initialCellsPerMl in df.index:\n",
    "    for eating_time in df.columns:\n",
    "        eating_time = eating_time*generation_time\n",
    "        sweeping_time = currentPim(phagePerCell,Pns,K1,K2,initialCellsPerMl,initialCellsPerMl)\n",
    "        df.loc[initialCellsPerMl,eating_time] = sweeping_time\n",
    "\n",
    "df.columns = ['%.1e'%i for i in df.columns]\n",
    "df.index = ['%.1e'%i for i in df.index]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "d969cce0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.heatmap(data=df,cmap='rocket')\n",
    "plt.xlabel('No. generations per dilution')  \n",
    "plt.ylabel('Initial bacterial cell density') \n",
    "plt.savefig('data/model/DilutionVSbacterialdensity.pdf', bbox_inches='tight')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "d4f50531",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>1.0e+03</th>\n",
       "      <th>1.0e+02</th>\n",
       "      <th>5.0e+01</th>\n",
       "      <th>3.0e+01</th>\n",
       "      <th>2.5e+01</th>\n",
       "      <th>2.0e+01</th>\n",
       "      <th>1.5e+01</th>\n",
       "      <th>1.0e+01</th>\n",
       "      <th>5.0e+00</th>\n",
       "      <th>4.0e+00</th>\n",
       "      <th>1.0e+00</th>\n",
       "      <th>1.0e-01</th>\n",
       "      <th>1.0e-02</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1.0e+10</th>\n",
       "      <td>1.1</td>\n",
       "      <td>1.1</td>\n",
       "      <td>1.1</td>\n",
       "      <td>1.1</td>\n",
       "      <td>1.1</td>\n",
       "      <td>1.1</td>\n",
       "      <td>1.1</td>\n",
       "      <td>1.1</td>\n",
       "      <td>1.1</td>\n",
       "      <td>1.1</td>\n",
       "      <td>1.1</td>\n",
       "      <td>1.1</td>\n",
       "      <td>1.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.0e+09</th>\n",
       "      <td>1.1</td>\n",
       "      <td>1.1</td>\n",
       "      <td>1.1</td>\n",
       "      <td>1.1</td>\n",
       "      <td>1.1</td>\n",
       "      <td>1.1</td>\n",
       "      <td>1.1</td>\n",
       "      <td>1.1</td>\n",
       "      <td>1.1</td>\n",
       "      <td>1.1</td>\n",
       "      <td>1.1</td>\n",
       "      <td>1.2</td>\n",
       "      <td>1.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.0e+08</th>\n",
       "      <td>4.3</td>\n",
       "      <td>4.3</td>\n",
       "      <td>4.3</td>\n",
       "      <td>4.3</td>\n",
       "      <td>4.3</td>\n",
       "      <td>4.3</td>\n",
       "      <td>4.3</td>\n",
       "      <td>4.3</td>\n",
       "      <td>4.3</td>\n",
       "      <td>4.3</td>\n",
       "      <td>15.7</td>\n",
       "      <td>26.2</td>\n",
       "      <td>26.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.0e+07</th>\n",
       "      <td>7.5</td>\n",
       "      <td>7.5</td>\n",
       "      <td>7.5</td>\n",
       "      <td>7.5</td>\n",
       "      <td>7.5</td>\n",
       "      <td>7.5</td>\n",
       "      <td>7.5</td>\n",
       "      <td>7.5</td>\n",
       "      <td>116.1</td>\n",
       "      <td>1000.0</td>\n",
       "      <td>1000.0</td>\n",
       "      <td>1000.0</td>\n",
       "      <td>1000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.0e+06</th>\n",
       "      <td>10.6</td>\n",
       "      <td>10.6</td>\n",
       "      <td>10.6</td>\n",
       "      <td>10.6</td>\n",
       "      <td>10.6</td>\n",
       "      <td>10.6</td>\n",
       "      <td>10.6</td>\n",
       "      <td>57.6</td>\n",
       "      <td>1000.0</td>\n",
       "      <td>1000.0</td>\n",
       "      <td>1000.0</td>\n",
       "      <td>1000.0</td>\n",
       "      <td>1000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.0e+05</th>\n",
       "      <td>14.1</td>\n",
       "      <td>14.1</td>\n",
       "      <td>14.1</td>\n",
       "      <td>14.1</td>\n",
       "      <td>14.1</td>\n",
       "      <td>14.1</td>\n",
       "      <td>14.1</td>\n",
       "      <td>1000.0</td>\n",
       "      <td>1000.0</td>\n",
       "      <td>1000.0</td>\n",
       "      <td>1000.0</td>\n",
       "      <td>1000.0</td>\n",
       "      <td>1000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.0e+04</th>\n",
       "      <td>17.8</td>\n",
       "      <td>17.8</td>\n",
       "      <td>17.8</td>\n",
       "      <td>17.8</td>\n",
       "      <td>17.8</td>\n",
       "      <td>17.8</td>\n",
       "      <td>1000.0</td>\n",
       "      <td>1000.0</td>\n",
       "      <td>1000.0</td>\n",
       "      <td>1000.0</td>\n",
       "      <td>1000.0</td>\n",
       "      <td>1000.0</td>\n",
       "      <td>1000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.0e+03</th>\n",
       "      <td>21.4</td>\n",
       "      <td>21.4</td>\n",
       "      <td>21.4</td>\n",
       "      <td>21.4</td>\n",
       "      <td>21.4</td>\n",
       "      <td>1000.0</td>\n",
       "      <td>1000.0</td>\n",
       "      <td>1000.0</td>\n",
       "      <td>1000.0</td>\n",
       "      <td>1000.0</td>\n",
       "      <td>1000.0</td>\n",
       "      <td>1000.0</td>\n",
       "      <td>1000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.0e+02</th>\n",
       "      <td>25.1</td>\n",
       "      <td>25.1</td>\n",
       "      <td>25.1</td>\n",
       "      <td>25.1</td>\n",
       "      <td>49.0</td>\n",
       "      <td>1000.0</td>\n",
       "      <td>1000.0</td>\n",
       "      <td>1000.0</td>\n",
       "      <td>1000.0</td>\n",
       "      <td>1000.0</td>\n",
       "      <td>1000.0</td>\n",
       "      <td>1000.0</td>\n",
       "      <td>1000.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         1.0e+03  1.0e+02  5.0e+01  3.0e+01  2.5e+01  2.0e+01  1.5e+01  \\\n",
       "1.0e+10      1.1      1.1      1.1      1.1      1.1      1.1      1.1   \n",
       "1.0e+09      1.1      1.1      1.1      1.1      1.1      1.1      1.1   \n",
       "1.0e+08      4.3      4.3      4.3      4.3      4.3      4.3      4.3   \n",
       "1.0e+07      7.5      7.5      7.5      7.5      7.5      7.5      7.5   \n",
       "1.0e+06     10.6     10.6     10.6     10.6     10.6     10.6     10.6   \n",
       "1.0e+05     14.1     14.1     14.1     14.1     14.1     14.1     14.1   \n",
       "1.0e+04     17.8     17.8     17.8     17.8     17.8     17.8   1000.0   \n",
       "1.0e+03     21.4     21.4     21.4     21.4     21.4   1000.0   1000.0   \n",
       "1.0e+02     25.1     25.1     25.1     25.1     49.0   1000.0   1000.0   \n",
       "\n",
       "         1.0e+01  5.0e+00  4.0e+00  1.0e+00  1.0e-01  1.0e-02  \n",
       "1.0e+10      1.1      1.1      1.1      1.1      1.1      1.1  \n",
       "1.0e+09      1.1      1.1      1.1      1.1      1.2      1.2  \n",
       "1.0e+08      4.3      4.3      4.3     15.7     26.2     26.2  \n",
       "1.0e+07      7.5    116.1   1000.0   1000.0   1000.0   1000.0  \n",
       "1.0e+06     57.6   1000.0   1000.0   1000.0   1000.0   1000.0  \n",
       "1.0e+05   1000.0   1000.0   1000.0   1000.0   1000.0   1000.0  \n",
       "1.0e+04   1000.0   1000.0   1000.0   1000.0   1000.0   1000.0  \n",
       "1.0e+03   1000.0   1000.0   1000.0   1000.0   1000.0   1000.0  \n",
       "1.0e+02   1000.0   1000.0   1000.0   1000.0   1000.0   1000.0  "
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "d7310605",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df[df>=50]=50\n",
    "sns.heatmap(data=df,cmap='rocket')\n",
    "plt.xlabel('No. generations per dilution')  \n",
    "plt.ylabel('Initial bacterial cell density') \n",
    "plt.savefig('data/model/DilutionVSbacterialdensity2.pdf', bbox_inches='tight')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "083d04ca",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "allchangingparameters = {\n",
    "    'Pnsset':[1e-2,1e-4,1e-6,1e-8,1e-10],\n",
    "    'detection_limitset':[0.1,0.2,0.5,0.9],\n",
    "    'time_stepset':[0.01,0.1,0.2,0.5,1],\n",
    "    'generation_timeset':[0.1,1,2,5,10],\n",
    "    'K1set' : [np.power(0.1,x) for x in range(1,25)],\n",
    "    'K2set' : [0.01,0.1,0.5,1,5,10,100,1000],\n",
    "    'initialCellsPerMlset' :[1e2,1e3,1e4,1e5,1e6,1e7,1e8,1e9,1e10],\n",
    "    'eating_timeset':[5,4,3,2,1,0.5,0.33,0.25,0.1],# * generation_time\n",
    "    'phagePerCellset' : [x/20000000 for x in range(1,3)]+[x/2000000 for x in range(1,3)]+[x/200000 for x in range(1,3)]+[x/20000 for x in range(1,3)]+[x/2000 for x in range(1,3)]+[x/200 for x in range(1,3)]+[x/20 for x in range(1,3)]+[x/2 for x in range(1,3)]\n",
    "}\n",
    "\n",
    "# parameters\n",
    "phagePerCell = 1e-3\n",
    "Pns = 1e-8*(1 + 1e-1 + 1e-2 + 1e-3 + 1e-4 + 1e-5) # Exploitation of the Cooperative Behaviors of Anti-CRISPR Phages, cfu per ml = 1e8, read frequency of additional spacers decrease by 1/10\n",
    "detection_limit = 0.1\n",
    "time_step = 0.1\n",
    "generation_time = 1 # 1 day\n",
    "K1 = 1e-9 # absorption rate, 1e-10 to 1e−9 phage−1 cell−1 ml−1 min−1 for 24h\n",
    "K2 = 1 #effective phage burst size, [https://www.frontiersin.org/articles/10.3389/fcimb.2021.643214/full CrAssphage 2.5] usually 10-100\n",
    "initialCellsPerMl = 1e8 # cells per ml of the species of interest\n",
    "eating_time = 1# eating\n",
    "celldoubling_per_time_step = np.power(2,time_step) - 1\n",
    "\n",
    "# others\n",
    "y_max = 1000*generation_time\n",
    "df = pd.DataFrame(columns=allchangingparameters['eating_timeset'],\n",
    "                  index = allchangingparameters['phagePerCellset'],data= 0,dtype = float)\n",
    "for phagePerCell in df.index:\n",
    "    for eating_time in df.columns:\n",
    "        eating_time = eating_time*generation_time\n",
    "        sweeping_time = currentPim(phagePerCell,Pns,K1,K2,initialCellsPerMl,initialCellsPerMl)\n",
    "        df.loc[phagePerCell,eating_time] = sweeping_time\n",
    "\n",
    "df.columns = ['%.1e'%i for i in df.columns]\n",
    "df.index = ['%.1e'%i for i in df.index]\n",
    "sns.heatmap(data=df)\n",
    "plt.xlabel('No. generations per dilution')  \n",
    "plt.ylabel('Initial phage/cell') \n",
    "plt.savefig('data/model/DilutionVSbacterialdensity.pdf', bbox_inches='tight')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "id": "2cbacb7b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "allchangingparameters = {\n",
    "    'Pnsset':[1e-2,1e-4,1e-6,1e-8,1e-10],\n",
    "    'detection_limitset':[0.1,0.2,0.5,0.9],\n",
    "    'time_stepset':[0.01,0.1,0.2,0.5,1],\n",
    "    'generation_timeset':[0.1,1,2,5,10],\n",
    "    'K1set' : [np.power(0.1,x) for x in range(1,25)],\n",
    "    'K2set' : [0.01,0.1,0.5,1,5,10,100,1000],\n",
    "    'initialCellsPerMlset' :[1e2,1e3,1e4,1e5,1e6,1e7,1e8,1e9,1e10],\n",
    "    'eating_timeset':[5,4,3,2,1,0.5,0.33,0.25,0.1],# * generation_time\n",
    "    'phagePerCellset' : [x/20000000 for x in range(1,3)]+[x/2000000 for x in range(1,3)]+[x/200000 for x in range(1,3)]+[x/20000 for x in range(1,3)]+[x/2000 for x in range(1,3)]+[x/200 for x in range(1,3)]+[x/20 for x in range(1,3)]+[x/2 for x in range(1,3)]\n",
    "}\n",
    "\n",
    "# parameters\n",
    "phagePerCell = 1e-3\n",
    "Pns = 1e-8*(1 + 1e-1 + 1e-2 + 1e-3 + 1e-4 + 1e-5) # Exploitation of the Cooperative Behaviors of Anti-CRISPR Phages, cfu per ml = 1e8, read frequency of additional spacers decrease by 1/10\n",
    "detection_limit = 0.1\n",
    "time_step = 0.1\n",
    "generation_time = 1 # 1 day\n",
    "K1 = 1e-9 # absorption rate, 1e-10 to 1e−9 phage−1 cell−1 ml−1 min−1 for 24h\n",
    "K2 = 1 #effective phage burst size, [https://www.frontiersin.org/articles/10.3389/fcimb.2021.643214/full CrAssphage 2.5] usually 10-100\n",
    "initialCellsPerMl = 1e8 # cells per ml of the species of interest\n",
    "eating_time = 1000# no eat\n",
    "celldoubling_per_time_step = np.power(2,time_step) - 1\n",
    "\n",
    "# others\n",
    "y_max = 1000*generation_time\n",
    "df = pd.DataFrame(columns=allchangingparameters['K1set'],\n",
    "                  index = allchangingparameters['initialCellsPerMlset'],data= 0,dtype = float)\n",
    "for initialCellsPerMl in df.index:\n",
    "    for K1 in df.columns:\n",
    "        eating_time = eating_time*generation_time\n",
    "        sweeping_time = currentPim(phagePerCell,Pns,K1,K2,initialCellsPerMl,initialCellsPerMl)\n",
    "        df.loc[initialCellsPerMl,K1] = sweeping_time\n",
    "\n",
    "df.columns = ['%.1e'%i for i in df.columns]\n",
    "df.index = ['%.1e'%i for i in df.index]\n",
    "sns.heatmap(data=df)\n",
    "plt.xlabel('K1')  \n",
    "plt.ylabel('Initial bacterial cell density') \n",
    "plt.savefig('data/model/NodilutionK1VSbacterialdensity.pdf', bbox_inches='tight')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "id": "c730575c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "allchangingparameters = {\n",
    "    'Pnsset':[1e-2,1e-4,1e-6,1e-8,1e-10],\n",
    "    'detection_limitset':[0.1,0.2,0.5,0.9],\n",
    "    'time_stepset':[0.01,0.1,0.2,0.5,1],\n",
    "    'generation_timeset':[0.1,1,2,5,10],\n",
    "    'K1set' : [np.power(0.1,x) for x in range(1,25)],\n",
    "    'K2set' : [0.01,0.1,0.5,1,5,10,100,1000],\n",
    "    'initialCellsPerMlset' :[1e2,1e3,1e4,1e5,1e6,1e7,1e8,1e9,1e10],\n",
    "    'eating_timeset':[5,4,3,2,1,0.5,0.33,0.25,0.1],# * generation_time\n",
    "    'phagePerCellset' : [x/20000000 for x in range(1,3)]+[x/2000000 for x in range(1,3)]+[x/200000 for x in range(1,3)]+[x/20000 for x in range(1,3)]+[x/2000 for x in range(1,3)]+[x/200 for x in range(1,3)]+[x/20 for x in range(1,3)]+[x/2 for x in range(1,3)]\n",
    "}\n",
    "\n",
    "# parameters\n",
    "phagePerCell = 1e-3\n",
    "Pns = 1e-8*(1 + 1e-1 + 1e-2 + 1e-3 + 1e-4 + 1e-5) # Exploitation of the Cooperative Behaviors of Anti-CRISPR Phages, cfu per ml = 1e8, read frequency of additional spacers decrease by 1/10\n",
    "detection_limit = 0.1\n",
    "time_step = 0.1\n",
    "generation_time = 1 # 1 day\n",
    "K1 = 1e-9 # absorption rate, 1e-10 to 1e−9 phage−1 cell−1 ml−1 min−1 for 24h\n",
    "K2 = 1 #effective phage burst size, [https://www.frontiersin.org/articles/10.3389/fcimb.2021.643214/full CrAssphage 2.5] usually 10-100\n",
    "initialCellsPerMl = 1e8 # cells per ml of the species of interest\n",
    "eating_time = 1# eat\n",
    "celldoubling_per_time_step = np.power(2,time_step) - 1\n",
    "\n",
    "# others\n",
    "y_max = 1000*generation_time\n",
    "df = pd.DataFrame(columns=allchangingparameters['K1set'],\n",
    "                  index = allchangingparameters['initialCellsPerMlset'],data= 0,dtype = float)\n",
    "for initialCellsPerMl in df.index:\n",
    "    for K1 in df.columns:\n",
    "        eating_time = eating_time*generation_time\n",
    "        sweeping_time = currentPim(phagePerCell,Pns,K1,K2,initialCellsPerMl,initialCellsPerMl)\n",
    "        df.loc[initialCellsPerMl,K1] = sweeping_time\n",
    "\n",
    "df.columns = ['%.1e'%i for i in df.columns]\n",
    "df.index = ['%.1e'%i for i in df.index]\n",
    "sns.heatmap(data=df)\n",
    "plt.xlabel('K1')  \n",
    "plt.ylabel('Initial bacterial cell density') \n",
    "plt.savefig('data/model/DilutionK1VSbacterialdensity.pdf', bbox_inches='tight')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "id": "85253a28",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "allchangingparameters = {\n",
    "    'Pnsset':[1e-2,1e-4,1e-6,1e-8,1e-10],\n",
    "    'detection_limitset':[0.1,0.2,0.5,0.9],\n",
    "    'time_stepset':[0.01,0.1,0.2,0.5,1],\n",
    "    'generation_timeset':[0.1,1,2,5,10],\n",
    "    'K1set' : [np.power(0.1,x) for x in range(1,25)],\n",
    "    'K2set' : [0.01,0.1,0.5,1,5,10,100,1000],\n",
    "    'initialCellsPerMlset' :[1e2,1e3,1e4,1e5,1e6,1e7,1e8,1e9,1e10],\n",
    "    'eating_timeset':[5,4,3,2,1,0.5,0.33,0.25,0.1],# * generation_time\n",
    "    'phagePerCellset' : [x/20000000 for x in range(1,3)]+[x/2000000 for x in range(1,3)]+[x/200000 for x in range(1,3)]+[x/20000 for x in range(1,3)]+[x/2000 for x in range(1,3)]+[x/200 for x in range(1,3)]+[x/20 for x in range(1,3)]+[x/2 for x in range(1,3)]\n",
    "}\n",
    "\n",
    "# parameters\n",
    "phagePerCell = 1e-3\n",
    "Pns = 1e-8*(1 + 1e-1 + 1e-2 + 1e-3 + 1e-4 + 1e-5) # Exploitation of the Cooperative Behaviors of Anti-CRISPR Phages, cfu per ml = 1e8, read frequency of additional spacers decrease by 1/10\n",
    "detection_limit = 0.1\n",
    "time_step = 0.1\n",
    "generation_time = 1 # 1 day\n",
    "K1 = 1e-9 # absorption rate, 1e-10 to 1e−9 phage−1 cell−1 ml−1 min−1 for 24h\n",
    "K2 = 1 #effective phage burst size, [https://www.frontiersin.org/articles/10.3389/fcimb.2021.643214/full CrAssphage 2.5] usually 10-100\n",
    "initialCellsPerMl = 1e8 # cells per ml of the species of interest\n",
    "eating_time = 1000# no eat\n",
    "celldoubling_per_time_step = np.power(2,time_step) - 1\n",
    "\n",
    "# others\n",
    "y_max = 1000*generation_time\n",
    "df = pd.DataFrame(columns=allchangingparameters['K2set'],\n",
    "                  index = allchangingparameters['initialCellsPerMlset'],data= 0,dtype = float)\n",
    "for initialCellsPerMl in df.index:\n",
    "    for K2 in df.columns:\n",
    "        eating_time = eating_time*generation_time\n",
    "        sweeping_time = currentPim(phagePerCell,Pns,K1,K2,initialCellsPerMl,initialCellsPerMl)\n",
    "        df.loc[initialCellsPerMl,K2] = sweeping_time\n",
    "\n",
    "df.columns = ['%.1e'%i for i in df.columns]\n",
    "df.index = ['%.1e'%i for i in df.index]\n",
    "sns.heatmap(data=df)\n",
    "plt.xlabel('K2')  \n",
    "plt.ylabel('Initial bacterial cell density') \n",
    "plt.savefig('data/model/NoDilutionK2VSbacterialdensity.pdf', bbox_inches='tight')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "id": "05e85e0b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "allchangingparameters = {\n",
    "    'Pnsset':[1e-2,1e-4,1e-6,1e-8,1e-10],\n",
    "    'detection_limitset':[0.1,0.2,0.5,0.9],\n",
    "    'time_stepset':[0.01,0.1,0.2,0.5,1],\n",
    "    'generation_timeset':[0.1,1,2,5,10],\n",
    "    'K1set' : [np.power(0.1,x) for x in range(1,25)],\n",
    "    'K2set' : [0.01,0.1,0.5,1,5,10,100,1000],\n",
    "    'initialCellsPerMlset' :[1e2,1e3,1e4,1e5,1e6,1e7,1e8,1e9,1e10],\n",
    "    'eating_timeset':[5,4,3,2,1,0.5,0.33,0.25,0.1],# * generation_time\n",
    "    'phagePerCellset' : [x/20000000 for x in range(1,3)]+[x/2000000 for x in range(1,3)]+[x/200000 for x in range(1,3)]+[x/20000 for x in range(1,3)]+[x/2000 for x in range(1,3)]+[x/200 for x in range(1,3)]+[x/20 for x in range(1,3)]+[x/2 for x in range(1,3)]\n",
    "}\n",
    "\n",
    "# parameters\n",
    "phagePerCell = 1e-3\n",
    "Pns = 1e-8*(1 + 1e-1 + 1e-2 + 1e-3 + 1e-4 + 1e-5) # Exploitation of the Cooperative Behaviors of Anti-CRISPR Phages, cfu per ml = 1e8, read frequency of additional spacers decrease by 1/10\n",
    "detection_limit = 0.1\n",
    "time_step = 0.1\n",
    "generation_time = 1 # 1 day\n",
    "K1 = 1e-9 # absorption rate, 1e-10 to 1e−9 phage−1 cell−1 ml−1 min−1 for 24h\n",
    "K2 = 1 #effective phage burst size, [https://www.frontiersin.org/articles/10.3389/fcimb.2021.643214/full CrAssphage 2.5] usually 10-100\n",
    "initialCellsPerMl = 1e8 # cells per ml of the species of interest\n",
    "eating_time = 1#  eat\n",
    "celldoubling_per_time_step = np.power(2,time_step) - 1\n",
    "\n",
    "# others\n",
    "y_max = 1000*generation_time\n",
    "df = pd.DataFrame(columns=allchangingparameters['K2set'],\n",
    "                  index = allchangingparameters['initialCellsPerMlset'],data= 0,dtype = float)\n",
    "for initialCellsPerMl in df.index:\n",
    "    for K2 in df.columns:\n",
    "        eating_time = eating_time*generation_time\n",
    "        sweeping_time = currentPim(phagePerCell,Pns,K1,K2,initialCellsPerMl,initialCellsPerMl)\n",
    "        df.loc[initialCellsPerMl,K2] = sweeping_time\n",
    "\n",
    "df.columns = ['%.1e'%i for i in df.columns]\n",
    "df.index = ['%.1e'%i for i in df.index]\n",
    "sns.heatmap(data=df)\n",
    "plt.xlabel('K2')  \n",
    "plt.ylabel('Initial bacterial cell density') \n",
    "plt.savefig('data/model/DilutionK2VSbacterialdensity.pdf', bbox_inches='tight')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "id": "4c16e19e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "allchangingparameters = {\n",
    "    'Pnsset':[1e-2,1e-4,1e-6,1e-8,1e-10,1e-12,1e-14,1e-16,1e-18,1e-20],\n",
    "    'detection_limitset':[0.1,0.2,0.5,0.9],\n",
    "    'time_stepset':[0.01,0.1,0.2,0.5,1],\n",
    "    'generation_timeset':[0.1,1,2,5,10],\n",
    "    'K1set' : [np.power(0.1,x) for x in range(1,25)],\n",
    "    'K2set' : [0.01,0.1,0.5,1,5,10,100,1000],\n",
    "    'initialCellsPerMlset' :[1e2,1e3,1e4,1e5,1e6,1e7,1e8,1e9,1e10],\n",
    "    'eating_timeset':[5,4,3,2,1,0.5,0.33,0.25,0.1],# * generation_time\n",
    "    'phagePerCellset' : [x/20000000 for x in range(1,3)]+[x/2000000 for x in range(1,3)]+[x/200000 for x in range(1,3)]+[x/20000 for x in range(1,3)]+[x/2000 for x in range(1,3)]+[x/200 for x in range(1,3)]+[x/20 for x in range(1,3)]+[x/2 for x in range(1,3)]\n",
    "}\n",
    "\n",
    "# parameters\n",
    "phagePerCell = 1e-3\n",
    "Pns = 1e-8*(1 + 1e-1 + 1e-2 + 1e-3 + 1e-4 + 1e-5) # Exploitation of the Cooperative Behaviors of Anti-CRISPR Phages, cfu per ml = 1e8, read frequency of additional spacers decrease by 1/10\n",
    "detection_limit = 0.1\n",
    "time_step = 0.1\n",
    "generation_time = 1 # 1 day\n",
    "K1 = 1e-9 # absorption rate, 1e-10 to 1e−9 phage−1 cell−1 ml−1 min−1 for 24h\n",
    "K2 = 1 #effective phage burst size, [https://www.frontiersin.org/articles/10.3389/fcimb.2021.643214/full CrAssphage 2.5] usually 10-100\n",
    "initialCellsPerMl = 1e8 # cells per ml of the species of interest\n",
    "eating_time = 1000# no eat\n",
    "celldoubling_per_time_step = np.power(2,time_step) - 1\n",
    "\n",
    "# others\n",
    "y_max = 1000*generation_time\n",
    "df = pd.DataFrame(columns=allchangingparameters['Pnsset'],\n",
    "                  index = allchangingparameters['initialCellsPerMlset'],data= 0,dtype = float)\n",
    "for initialCellsPerMl in df.index:\n",
    "    for Pns in df.columns:\n",
    "        eating_time = eating_time*generation_time\n",
    "        sweeping_time = currentPim(phagePerCell,Pns,K1,K2,initialCellsPerMl,initialCellsPerMl)\n",
    "        df.loc[initialCellsPerMl,Pns] = sweeping_time\n",
    "\n",
    "df.columns = ['%.1e'%i for i in df.columns]\n",
    "df.index = ['%.1e'%i for i in df.index]\n",
    "sns.heatmap(data=df)\n",
    "plt.xlabel('Pns')  \n",
    "plt.ylabel('Initial bacterial cell density') \n",
    "plt.savefig('data/model/NodilutionPnsVSbacterialdensity.pdf', bbox_inches='tight')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "id": "027bde71",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "allchangingparameters = {\n",
    "    'Pnsset':[1e-2,1e-4,1e-6,1e-8,1e-10,1e-12,1e-14,1e-16,1e-18,1e-20],\n",
    "    'detection_limitset':[0.1,0.2,0.5,0.9],\n",
    "    'time_stepset':[0.01,0.1,0.2,0.5,1],\n",
    "    'generation_timeset':[0.1,1,2,5,10],\n",
    "    'K1set' : [np.power(0.1,x) for x in range(1,25)],\n",
    "    'K2set' : [0.01,0.1,0.5,1,5,10,100,1000],\n",
    "    'initialCellsPerMlset' :[1e2,1e3,1e4,1e5,1e6,1e7,1e8,1e9,1e10],\n",
    "    'eating_timeset':[5,4,3,2,1,0.5,0.33,0.25,0.1],# * generation_time\n",
    "    'phagePerCellset' : [x/20000000 for x in range(1,3)]+[x/2000000 for x in range(1,3)]+[x/200000 for x in range(1,3)]+[x/20000 for x in range(1,3)]+[x/2000 for x in range(1,3)]+[x/200 for x in range(1,3)]+[x/20 for x in range(1,3)]+[x/2 for x in range(1,3)]\n",
    "}\n",
    "\n",
    "# parameters\n",
    "phagePerCell = 1e-3\n",
    "Pns = 1e-8*(1 + 1e-1 + 1e-2 + 1e-3 + 1e-4 + 1e-5) # Exploitation of the Cooperative Behaviors of Anti-CRISPR Phages, cfu per ml = 1e8, read frequency of additional spacers decrease by 1/10\n",
    "detection_limit = 0.1\n",
    "time_step = 0.1\n",
    "generation_time = 1 # 1 day\n",
    "K1 = 1e-9 # absorption rate, 1e-10 to 1e−9 phage−1 cell−1 ml−1 min−1 for 24h\n",
    "K2 = 1 #effective phage burst size, [https://www.frontiersin.org/articles/10.3389/fcimb.2021.643214/full CrAssphage 2.5] usually 10-100\n",
    "initialCellsPerMl = 1e8 # cells per ml of the species of interest\n",
    "eating_time = 1# no eat\n",
    "celldoubling_per_time_step = np.power(2,time_step) - 1\n",
    "\n",
    "# others\n",
    "y_max = 1000*generation_time\n",
    "df = pd.DataFrame(columns=allchangingparameters['Pnsset'],\n",
    "                  index = allchangingparameters['initialCellsPerMlset'],data= 0,dtype = float)\n",
    "for initialCellsPerMl in df.index:\n",
    "    for Pns in df.columns:\n",
    "        eating_time = eating_time*generation_time\n",
    "        sweeping_time = currentPim(phagePerCell,Pns,K1,K2,initialCellsPerMl,initialCellsPerMl)\n",
    "        df.loc[initialCellsPerMl,Pns] = sweeping_time\n",
    "\n",
    "df.columns = ['%.1e'%i for i in df.columns]\n",
    "df.index = ['%.1e'%i for i in df.index]\n",
    "sns.heatmap(data=df)\n",
    "plt.xlabel('Pns')  \n",
    "plt.ylabel('Initial bacterial cell density') \n",
    "plt.savefig('data/model/DilutionPnsVSbacterialdensity.pdf', bbox_inches='tight')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "8d35168e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "allchangingparameters = {\n",
    "    'Pnsset':[1e-2,1e-4,1e-6,1e-8,1e-10,1e-12,1e-14,1e-16,1e-18,1e-20],\n",
    "    'detection_limitset':[0.1,0.2,0.5,0.9],\n",
    "    'time_stepset':[0.01,0.02,0.05,0.1,0.2,0.5,1],\n",
    "    'generation_timeset':[0.1,1,2,5,10],\n",
    "    'K1set' : [np.power(0.1,x) for x in range(1,25)],\n",
    "    'K2set' : [0.01,0.1,0.5,1,5,10,100,1000],\n",
    "    'initialCellsPerMlset' :[1e2,1e3,1e4,1e5,1e6,1e7,1e8,1e9,1e10],\n",
    "    'eating_timeset':[5,4,3,2,1,0.5,0.33,0.25,0.1],# * generation_time\n",
    "    'phagePerCellset' : [x/20000000 for x in range(1,3)]+[x/2000000 for x in range(1,3)]+[x/200000 for x in range(1,3)]+[x/20000 for x in range(1,3)]+[x/2000 for x in range(1,3)]+[x/200 for x in range(1,3)]+[x/20 for x in range(1,3)]+[x/2 for x in range(1,3)]\n",
    "}\n",
    "\n",
    "# parameters\n",
    "phagePerCell = 1e-3\n",
    "Pns = 1e-8*(1 + 1e-1 + 1e-2 + 1e-3 + 1e-4 + 1e-5) # Exploitation of the Cooperative Behaviors of Anti-CRISPR Phages, cfu per ml = 1e8, read frequency of additional spacers decrease by 1/10\n",
    "detection_limit = 0.1\n",
    "time_step = 0.1\n",
    "generation_time = 1 # 1 day\n",
    "K1 = 1e-9 # absorption rate, 1e-10 to 1e−9 phage−1 cell−1 ml−1 min−1 for 24h\n",
    "K2 = 1 #effective phage burst size, [https://www.frontiersin.org/articles/10.3389/fcimb.2021.643214/full CrAssphage 2.5] usually 10-100\n",
    "initialCellsPerMl = 1e8 # cells per ml of the species of interest\n",
    "eating_time = 1000# no eat\n",
    "\n",
    "# others\n",
    "y_max = 1000*generation_time\n",
    "df = pd.DataFrame(columns=allchangingparameters['time_stepset'],\n",
    "                  index = allchangingparameters['initialCellsPerMlset'],data= 0,dtype = float)\n",
    "for initialCellsPerMl in df.index:\n",
    "    for time_step in df.columns:\n",
    "        celldoubling_per_time_step = np.power(2,time_step) - 1\n",
    "        eating_time = eating_time*generation_time\n",
    "        sweeping_time = currentPim(phagePerCell,Pns,K1,K2,initialCellsPerMl,initialCellsPerMl)\n",
    "        df.loc[initialCellsPerMl,time_step] = sweeping_time\n",
    "\n",
    "df.columns = ['%.1e'%i for i in df.columns]\n",
    "df.index = ['%.1e'%i for i in df.index]\n",
    "sns.heatmap(data=df)\n",
    "plt.xlabel('Time step')  \n",
    "plt.ylabel('Initial bacterial cell density') \n",
    "plt.savefig('data/model/Nodilutiontime_stepVSbacterialdensity.pdf', bbox_inches='tight')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "e7c955bc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "allchangingparameters = {\n",
    "    'Pnsset':[1e-2,1e-4,1e-6,1e-8,1e-10,1e-12,1e-14,1e-16,1e-18,1e-20],\n",
    "    'detection_limitset':[0.1,0.2,0.5,0.9],\n",
    "    'time_stepset':[0.01,0.02,0.05,0.1,0.2,0.5,1],\n",
    "    'generation_timeset':[0.1,1,2,5,10],\n",
    "    'K1set' : [np.power(0.1,x) for x in range(1,25)],\n",
    "    'K2set' : [0.01,0.1,0.5,1,5,10,100,1000],\n",
    "    'initialCellsPerMlset' :[1e2,1e3,1e4,1e5,1e6,1e7,1e8,1e9,1e10],\n",
    "    'eating_timeset':[5,4,3,2,1,0.5,0.33,0.25,0.1],# * generation_time\n",
    "    'phagePerCellset' : [x/20000000 for x in range(1,3)]+[x/2000000 for x in range(1,3)]+[x/200000 for x in range(1,3)]+[x/20000 for x in range(1,3)]+[x/2000 for x in range(1,3)]+[x/200 for x in range(1,3)]+[x/20 for x in range(1,3)]+[x/2 for x in range(1,3)]\n",
    "}\n",
    "\n",
    "# parameters\n",
    "phagePerCell = 1e-3\n",
    "Pns = 1e-8*(1 + 1e-1 + 1e-2 + 1e-3 + 1e-4 + 1e-5) # Exploitation of the Cooperative Behaviors of Anti-CRISPR Phages, cfu per ml = 1e8, read frequency of additional spacers decrease by 1/10\n",
    "detection_limit = 0.1\n",
    "time_step = 0.1\n",
    "generation_time = 1 # 1 day\n",
    "K1 = 1e-9 # absorption rate, 1e-10 to 1e−9 phage−1 cell−1 ml−1 min−1 for 24h\n",
    "K2 = 1 #effective phage burst size, [https://www.frontiersin.org/articles/10.3389/fcimb.2021.643214/full CrAssphage 2.5] usually 10-100\n",
    "initialCellsPerMl = 1e8 # cells per ml of the species of interest\n",
    "eating_time = 1# Eat\n",
    "\n",
    "# others\n",
    "y_max = 1000*generation_time\n",
    "df = pd.DataFrame(columns=allchangingparameters['time_stepset'],\n",
    "                  index = allchangingparameters['initialCellsPerMlset'],data= 0,dtype = float)\n",
    "for initialCellsPerMl in df.index:\n",
    "    for time_step in df.columns:\n",
    "        celldoubling_per_time_step = np.power(2,time_step) - 1\n",
    "        eating_time = eating_time*generation_time\n",
    "        sweeping_time = currentPim(phagePerCell,Pns,K1,K2,initialCellsPerMl,initialCellsPerMl)\n",
    "        df.loc[initialCellsPerMl,time_step] = sweeping_time\n",
    "\n",
    "df.columns = ['%.1e'%i for i in df.columns]\n",
    "df.index = ['%.1e'%i for i in df.index]\n",
    "sns.heatmap(data=df)\n",
    "plt.xlabel('time_step')  \n",
    "plt.ylabel('Initial bacterial cell density') \n",
    "plt.savefig('data/model/Dilutiontime_stepVSbacterialdensity.pdf', bbox_inches='tight')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8c912a28",
   "metadata": {},
   "outputs": [],
   "source": [
    "allchangingparameters = {\n",
    "    'Pnsset':[1e-2,1e-4,1e-6,1e-8,1e-10,1e-12,1e-14,1e-16,1e-18,1e-20],\n",
    "    'detection_limitset':[0.1,0.2,0.5,0.9],\n",
    "    'time_stepset':[0.01,0.02,0.05,0.1,0.2,0.5,1],\n",
    "    'generation_timeset':[0.1,1,2,5,10],\n",
    "    'K1set' : [np.power(0.1,x) for x in range(1,25)],\n",
    "    'K2set' : [0.01,0.1,0.5,1,5,10,100,1000],\n",
    "    'initialCellsPerMlset' :[1e2,1e3,1e4,1e5,1e6,1e7,1e8,1e9,1e10],\n",
    "    'eating_timeset':[5,4,3,2,1,0.5,0.33,0.25,0.1],# * generation_time\n",
    "    'phagePerCellset' : [x/20000000 for x in range(1,3)]+[x/2000000 for x in range(1,3)]+[x/200000 for x in range(1,3)]+[x/20000 for x in range(1,3)]+[x/2000 for x in range(1,3)]+[x/200 for x in range(1,3)]+[x/20 for x in range(1,3)]+[x/2 for x in range(1,3)]\n",
    "}\n",
    "\n",
    "# parameters\n",
    "phagePerCell = 1e-3\n",
    "Pns = 1e-8*(1 + 1e-1 + 1e-2 + 1e-3 + 1e-4 + 1e-5) # Exploitation of the Cooperative Behaviors of Anti-CRISPR Phages, cfu per ml = 1e8, read frequency of additional spacers decrease by 1/10\n",
    "detection_limit = 0.1\n",
    "time_step = 0.1\n",
    "generation_time = 1 # 1 day\n",
    "K1 = 1e-9 # absorption rate, 1e-10 to 1e−9 phage−1 cell−1 ml−1 min−1 for 24h\n",
    "K2 = 1 #effective phage burst size, [https://www.frontiersin.org/articles/10.3389/fcimb.2021.643214/full CrAssphage 2.5] usually 10-100\n",
    "initialCellsPerMl = 1e8 # cells per ml of the species of interest\n",
    "eating_time = 1# Eat\n",
    "\n",
    "# others\n",
    "y_max = 1000*generation_time\n",
    "df = pd.DataFrame(columns=allchangingparameters['time_stepset'],\n",
    "                  index = allchangingparameters['initialCellsPerMlset'],data= 0,dtype = float)\n",
    "for initialCellsPerMl in df.index:\n",
    "    for time_step in df.columns:\n",
    "        celldoubling_per_time_step = np.power(2,time_step) - 1\n",
    "        eating_time = eating_time*generation_time\n",
    "        sweeping_time = currentPim(phagePerCell,Pns,K1,K2,initialCellsPerMl,initialCellsPerMl)\n",
    "        df.loc[initialCellsPerMl,time_step] = sweeping_time\n",
    "\n",
    "df.columns = ['%.1e'%i for i in df.columns]\n",
    "df.index = ['%.1e'%i for i in df.index]\n",
    "sns.heatmap(data=df)\n",
    "plt.xlabel('time_step')  \n",
    "plt.ylabel('Initial bacterial cell density') \n",
    "plt.savefig('data/model/Dilutiontime_stepVSbacterialdensity.pdf', bbox_inches='tight')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "d3df460d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "allchangingparameters = {\n",
    "    'Pnsset':[1e-2,1e-4,1e-6,1e-8,1e-10,1e-12,1e-14,1e-16,1e-18,1e-20],\n",
    "    'detection_limitset':[0.1,0.2,0.5,0.9],\n",
    "    'time_stepset':[0.01,0.02,0.05,0.1,0.2,0.5,1],\n",
    "    'generation_timeset':[0.1,1,2,5,10],\n",
    "    'K1set' : [np.power(0.1,x) for x in range(1,25)],\n",
    "    'K2set' : [0.01,0.1,0.5,1,5,10,100,1000],\n",
    "    'initialCellsPerMlset' :[1e2,1e3,1e4,1e5,1e6,1e7,1e8,1e9,1e10],\n",
    "    'eating_timeset':[5,4,3,2,1,0.5,0.33,0.25,0.1],# * generation_time\n",
    "    'phagePerCellset' : [x/20000000 for x in range(1,3)]+[x/2000000 for x in range(1,3)]+[x/200000 for x in range(1,3)]+[x/20000 for x in range(1,3)]+[x/2000 for x in range(1,3)]+[x/200 for x in range(1,3)]+[x/20 for x in range(1,3)]+[x/2 for x in range(1,3)]\n",
    "}\n",
    "\n",
    "# parameters\n",
    "phagePerCell = 1e-3\n",
    "Pns = 1e-8*(1 + 1e-1 + 1e-2 + 1e-3 + 1e-4 + 1e-5) # Exploitation of the Cooperative Behaviors of Anti-CRISPR Phages, cfu per ml = 1e8, read frequency of additional spacers decrease by 1/10\n",
    "detection_limit = 0.1\n",
    "time_step = 0.1\n",
    "generation_time = 1 # 1 day\n",
    "K1 = 1e-9 # absorption rate, 1e-10 to 1e−9 phage−1 cell−1 ml−1 min−1 for 24h\n",
    "K2 = 1 #effective phage burst size, [https://www.frontiersin.org/articles/10.3389/fcimb.2021.643214/full CrAssphage 2.5] usually 10-100\n",
    "initialCellsPerMl = 1e8 # cells per ml of the species of interest\n",
    "eating_time = 1000# Eat\n",
    "\n",
    "# others\n",
    "y_max = 1000*generation_time\n",
    "df = pd.DataFrame(columns=allchangingparameters['time_stepset'],\n",
    "                  index = allchangingparameters['initialCellsPerMlset'],data= 0,dtype = float)\n",
    "for initialCellsPerMl in df.index:\n",
    "    for detection_limit in df.columns:\n",
    "        celldoubling_per_time_step = np.power(2,time_step) - 1\n",
    "        eating_time = eating_time*generation_time\n",
    "        sweeping_time = currentPim(phagePerCell,Pns,K1,K2,initialCellsPerMl,initialCellsPerMl)\n",
    "        df.loc[initialCellsPerMl,detection_limit] = sweeping_time\n",
    "\n",
    "df.columns = ['%.1e'%i for i in df.columns]\n",
    "df.index = ['%.1e'%i for i in df.index]\n",
    "sns.heatmap(data=df)\n",
    "plt.xlabel('detection_limit')  \n",
    "plt.ylabel('Initial bacterial cell density') \n",
    "plt.savefig('data/model/Nodilutiondetection_limitVSbacterialdensity.pdf', bbox_inches='tight')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "803dffa9",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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