Project_Final .ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "a6624bb8-028b-448f-8df2-c0d0d5ec6b32",
   "metadata": {},
   "source": [
    "## Modelling Drug Protein Interactions with Isothermal-Titration Calorimetry (ITC)\n",
    "In an ITC experiment, aliquots of a ligand (drug) in a syringe is periodically injected into a reaction cell containing a macromolecule (protein). The reaction is essentially a complexation reaction where the ligand is injected until the macromolecule reaches saturation. The saturation of the macromolecule indicates the end of the titration.  Titration of Calcium chloride (CaCl2) into EDTA is a well known and characterized experiment used as a standard for ITC experiments. \n",
    "\n",
    "First, we generated a model from scratch using the principles of energy and mass conservation by writing energy and mass balance equations for our system. Then we tested our model with Ca-EDTA experimental data to validate the model and compared it with an elaborate theoritical model developed by (Dumas, 2019), here in referred to as the Dumas model. Fitting of our model to experimental data showed a step change between the saturated (lower section) and unsaturated region(upper section) of the binding isotherm. The fit returned a negative R squared value. This could be due to over approximation in our model. The Dumas Model yielded a better fit and an R squared value of 0.94. \n",
    "We employed this model model to fit out Drug-Protein reaction. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5feb964c-fb8d-4d37-9387-ccb7e5fc514b",
   "metadata": {},
   "source": [
    "## Section 1   : Validating our model with Ca-EDTA experimental data\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "8b09515e-a3b1-4dc7-a7c3-41bd8a15dd42",
   "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>Region</th>\n",
       "      <th>Q (µJ)</th>\n",
       "      <th>Corrected Q (µJ)</th>\n",
       "      <th>inj volume (µL)</th>\n",
       "      <th>moles titrant (moles)</th>\n",
       "      <th>moles titrate (moles)</th>\n",
       "      <th>moles titrant / moles titrate</th>\n",
       "      <th>total volume (µL)</th>\n",
       "      <th>inj interval (s)</th>\n",
       "      <th>i</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>-26.366210</td>\n",
       "      <td>-13.104910</td>\n",
       "      <td>9.975</td>\n",
       "      <td>9.975000e-09</td>\n",
       "      <td>1.200000e-07</td>\n",
       "      <td>0.083125</td>\n",
       "      <td>809.975</td>\n",
       "      <td>300</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>-185.315424</td>\n",
       "      <td>-172.054124</td>\n",
       "      <td>9.975</td>\n",
       "      <td>1.995000e-08</td>\n",
       "      <td>1.200000e-07</td>\n",
       "      <td>0.166250</td>\n",
       "      <td>819.950</td>\n",
       "      <td>300</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>-179.939055</td>\n",
       "      <td>-166.677755</td>\n",
       "      <td>9.975</td>\n",
       "      <td>2.992500e-08</td>\n",
       "      <td>1.200000e-07</td>\n",
       "      <td>0.249375</td>\n",
       "      <td>829.925</td>\n",
       "      <td>300</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>-183.457728</td>\n",
       "      <td>-170.196428</td>\n",
       "      <td>9.975</td>\n",
       "      <td>3.990000e-08</td>\n",
       "      <td>1.200000e-07</td>\n",
       "      <td>0.332500</td>\n",
       "      <td>839.900</td>\n",
       "      <td>300</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>-191.176430</td>\n",
       "      <td>-177.915130</td>\n",
       "      <td>9.975</td>\n",
       "      <td>4.987500e-08</td>\n",
       "      <td>1.200000e-07</td>\n",
       "      <td>0.415625</td>\n",
       "      <td>849.875</td>\n",
       "      <td>300</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Region      Q (µJ)  Corrected Q (µJ)  inj volume (µL)  \\\n",
       "0       1  -26.366210        -13.104910            9.975   \n",
       "1       2 -185.315424       -172.054124            9.975   \n",
       "2       3 -179.939055       -166.677755            9.975   \n",
       "3       4 -183.457728       -170.196428            9.975   \n",
       "4       5 -191.176430       -177.915130            9.975   \n",
       "\n",
       "   moles titrant (moles)  moles titrate (moles)  \\\n",
       "0           9.975000e-09           1.200000e-07   \n",
       "1           1.995000e-08           1.200000e-07   \n",
       "2           2.992500e-08           1.200000e-07   \n",
       "3           3.990000e-08           1.200000e-07   \n",
       "4           4.987500e-08           1.200000e-07   \n",
       "\n",
       "   moles titrant / moles titrate  total volume (µL)  inj interval (s)  i  \n",
       "0                       0.083125            809.975               300  1  \n",
       "1                       0.166250            819.950               300  2  \n",
       "2                       0.249375            829.925               300  3  \n",
       "3                       0.332500            839.900               300  4  \n",
       "4                       0.415625            849.875               300  5  "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "%matplotlib inline\n",
    "import pandas as pd\n",
    "from numpy import sqrt \n",
    "from scipy.optimize import curve_fit\n",
    "from sklearn.metrics import r2_score \n",
    "x = pd.read_excel(r'/Users/mac/Downloads/modelling meeting/Ca-EDTA Data only.xlsx')\n",
    "x.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "81d4a93c-78a3-4626-a5df-9098cefa4664",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Experiment parameters\n",
    "\n",
    "Vo=800 #Initial volume of EDTA in the cell, uL\n",
    "v= 9.975 #Volume of CaCl2 per injection, uL\n",
    "Lo= 1 # Concentration of CaCl2 in the syringe, mM\n",
    "Mo=0.150 #Concentration of EDTA in the cell , mM\n",
    "\n",
    "#Parameters to calculate\n",
    "#Mt,#Lt, #ML,#ML[i-1] = ML2,#Lt[i-1]=L2t,#Mt[i-1]=M2t,#n"
   ]
  },
  {
   "cell_type": "raw",
   "id": "03b16019-b03c-46e9-b885-1269caa3912e",
   "metadata": {},
   "source": [
    "Mt= Mo*(1-v/Vo)**i                        #Mt is the total macromolecule concetration in the cell(mM)\n",
    "Lt= Lo(1-(1-v/Vo)**i)                     #Lt is the total ligand concentration in the cell(mM)\n",
    "A= 1+Ka(Mt+Lt)                            #Ka is the association constant(1/M)\n",
    "B= sqrt((A**2)-(4*Ka**2*Mt*Lt))           #H is the change in enthalpy kJ/mol\n",
    "ML=(A-B)/(2*Ka)                           #ML is the concentration of bound ligand or macromolecule or complex.\n",
    "Qpi=((Vo*H)/(v*Lo))*(MLi-MLi-1(1-v/Vo))   #Qpi is the predicted heat rate using from the model\n",
    "N= ML/Mt                                  #N is fractional saturation of the macromolecule\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "829f6231-41b6-46e6-afec-59b059679df5",
   "metadata": {},
   "outputs": [],
   "source": [
    "#MLi vector and list generation for i,Mt and Lt \n",
    "Region = np.array(list(range(0,25)))  \n",
    "Mt = []\n",
    "Lt = []\n",
    "Mt_below = []\n",
    "Lt_below = []\n",
    "for idx, i in enumerate(Region):\n",
    "    try: \n",
    "        Mt_= Mo*(1-v/Vo)**(i)\n",
    "        Lt_= Lo*(1-(1-v/Vo)**((i)))\n",
    "        Mt.append(Mt_)\n",
    "        Lt.append(Lt_)\n",
    "\n",
    "        Mt_below_= Mo*(1-v/Vo)**(Region[idx+1])\n",
    "        Lt_below_= Lo*(1-(1-v/Vo)**(Region[idx+1]))\n",
    "        Mt_below.append(Mt_below_)\n",
    "        Lt_below.append(Lt_below_)\n",
    "    except: \n",
    "        pass\n",
    "\n",
    "Mt_below.append(0)\n",
    "Lt_below.append(0)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "f87f79f8-31f2-4c24-b87b-b132d194e39d",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Making Lt and Mt arrays\n",
    "Mt = np.array(Mt)\n",
    "Lt = np.array(Lt)\n",
    "Mt_below = np.array(Mt_below)\n",
    "Lt_below = np.array(Lt_below)\n",
    "N = np.array(Lt/Mt)\n",
    "\n",
    "matrix = np.row_stack((Region, Mt, Lt, Mt_below, Lt_below))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "a6a295f1-297f-4e7d-89c0-9fd5944d6080",
   "metadata": {},
   "outputs": [
    {
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TDeEt0dqGcCvM+zKPuhXwwHkw+yboMQAOuwp2aFmniZZq7glw0IR78vaZEvDKpYcUbTul6FhSDA2TGaRVR23wSqBY2ktDuFl1e24q3Dse3n0L9v0ufO5s2LRbWUNoybf5lrTdtWQ7Lb2/odRXANV453VLlXp/tbU2DbPqtHIJ3HES/P7r0H0bOG0GHHRR2RMGtOzmtpa03bVkO829Wa1cbS3VeOd1S5RjfzlpmLXWm8/BL/aGBQ/AFy+A0/4KvUdULJyWnABb0kjbku00NzmV4+5uqM47r1uiHPvL1VNmrTX3VvjoffjOzKroR9/SbuLNbaRtyXaa27GkXFcA48cOydumUck7r1uiHPvLScOsNSLghXtg0P5VkTCgfCfAlm6nOcmpVPdJ5YsJittLshLKsb+cNMxaY9mLyf0X+zY6kk3ZlesEWI7tlPMKoD10hy3H/nLSaAcefPBBrrjiCu6++26mTp3Kc889x4QJ+UeNX7FiBbfddhvf+c53mrWN888/n+7du/P973+/GCG3H7X3Jj93+lJl42igXCfAUm+nvVwBlEs59peTRhVbu3YtnTp1anrGHIcffvj6sazyWbFiBddcc02zk4Y1ovY+2H4P2NInsVJpD1cA5VTq/eXeUxXy6quvsvPOO3PyySczbNgwjj32WN577z0GDhzIBRdcwJgxY/jDH/7A9OnTGTVqFHvuuSfHHXccq1evBuD+++9n5513ZsyYMUyaNGn9em+66SbOPDOpKnnzzTc56qij2GOPPdhjjz147LHHmDBhAgsXLmT48OGMHz8egMsvv5zPfOYzDBs2jPPOO2/9ui6++GKGDBnCgQceSG1tcXurtAvvLoPXnoQhX650JGZl4yuN+ybAG88Wd53bDYUvXdrkbLW1tfz6179m9OjRfPOb3+Saa64BoEuXLvztb39j2bJlHH300TzwwAN069aNyy67jCuvvJIf/OAHnHbaacyYMYMdd9yR448/Pu/6zzrrLD772c8yefJk1q5dy+rVq7n00kuZN28ec+fOBWD69Om89NJLPPnkk0QEhx9+OA8//DDdunXjjjvuYM6cOeuHbx85cmTRdlG78OI0IGBIdVVNmZWSk0YF9evXj9GjRwPwta99jauvvhpgfRKYOXMmzz333Pp5PvzwQ0aNGsULL7zAoEGDGDx48PplJ06c+LH1z5gxg1tuuQWATp06seWWW/LOO+9sNM/06dOZPn06I0Yk9xWsXr2al156iVWrVuUdvt1y1N4LW/SB7YZVOhKzsnHSyHBFUCoNh0ev/9ytW3IXcUTwxS9+kdtvv32j+ebOnZt3aPWWiAjOPvtsvvWtb21UftVVVxVtG+3Smvdh4YxkIELvJ+tA3KZRQf/4xz94/PHHAbj99tsZM2bjRz7us88+PProoyxYsACA9957jxdffJGdd96ZV155hYULF65fNp8vfOELXHvttUDSqL5y5cqPDbM+duxYbrjhhvVtJYsXL+att95qdPh2S73yMKx5z+0Z1uE4aVTQLrvsws0338ywYcN4++23+fa3v73R9F69enHTTTdx4oknMmzYMPbZZx9eeOEFunTpwsSJEznkkEMYM2YMAwYMyLv+n/3sZ/z1r39l6NChjBw5kvnz59OzZ09Gjx7N7rvvzvjx4znooIP46le/yqhRoxg6dCjHHnssq1at2mj49mOOOWb98O2Wqr0XNu0Og7xfrGPx0OgV8uqrr3LooYcyb968isbRWtWwL8suAq7cBfp+Bo7/TaWjMSuJxoZG95WGWXO9PhdWve6qKeuQnDQqZODAgW3+KqPDqr0P9AkYfFClIzEru6pLGpIul/SCpGckTZbUIy0fKKlO0tz09cvWbKe9V8uVQ4fdh7X3Qr99qvbRrWalVHVJA/gzsHtEDANeBM7OmbYwIoanr9NbuoEuXbqwfPnyjnvSK4KIYPny5XTp0qXSoZTXiteSm0GHHFzpSMwqouru04iI6TkfZwLHFnsbffv2ZdGiRSxdurTYq+5QunTpQt++fSsdRnm9eH/y0+0Z1kFVXdJo4JvA73I+D5I0B1gJnBsRj+RbSNI4YBxA//79Pza9c+fODBo0qPjRWvtXey/03BG2HlzWzZbjOdlmWVQkaUh6ANguz6RzIuJP6TznAB8Bt6bTXgf6R8RySSOBKZJ2i4iVDVcSEROBiZB0uS3F72Ad0Psr4ZVHYJ8W14y2SP1zn+ufkVD/3GfAicPKriJJIyIOLDRd0snAocAXIm14iIgPgA/S97MlLQR2AmY1uiKzYlo4A9atKXvVVKHnPjtpWLlVXUO4pIOB/wQOj4j3csp7SeqUvv80MBh4uTJRWodUex903Qr67lXWzZbrOdlmWVRd0gD+F9gc+HODrrX7A89Iehr4I3B6RLxdqSCtg1n7Ebw0DXYaC53Ke4He2POdi/2cbLMsqq4hPCJ2bKT8TuDOModjlnjtCah7B3Yqf1fbcj4n26wpVZc0zKpS7b3QaVPY8Qtl37Sfk23VxEnDrCkRSdIYuB98cvOKhODnZFu1qMY2DbPqsuwlePtlP9bVDCcNs6bV3pv8dNIwc9Iwa9KL9yfPAd+ygw2ZYpaHk4ZZIe8uS3pOeawpM6BAQ7ikVUDuEBxKPwuIiNiixLGZVd5L0yHWeVRbs1SjSSMiKtNNxKya1N4Lm28P2w+vdCRmVSFTl1tJewD7pR8fjohnSheSWZVY8z4smAF7HA9SpaMxqwpNtmlI+jeSkWa3SV+3SvpuqQMzq7hXH4E177o9wyxHliuNfwH2joh3ASRdBjwO/LyUgZlVXO290LlbclOfmQHZek8JyB2XeW1aZtZ+RUDt/bDjAdC5gz3S1qyALFcaNwJPSJqcfj4S+HXJIjKrBq8/DauWwJAfVToSs6rSZNKIiCslPQiMIbnCODUi5pQ6MLOKqr0PEAw+qNKRmFWVrAMWvkLy6NVNAEnaMyKeKl1YZhVWey/02xu6bV3pSMyqSpNJQ9KFwCnAQjbc7BfAAaULy6yC/rkI3ngGDvxJpSMxqzpZrjS+AuwQER+WOhizqlB7X/LTXW3NPiZL76l5QI8Sx7GepPMlLU4f9TpX0pdzpp0taYGkWkljyxWTdSAfvgvP3wVb7QBbD650NGZVJ8uVxiXAHEnzgA/qCyPi8JJFBf8TEVfkFkjaFTgB2A3oDTwgaaeIWJtvBWbrffQhvPsWrH4TVi9Nf9Z/fhPezSn7cHWyzL7f9V3gZnlkSRo3A5cBzwLrShtOQUcAd0TEB8ArkhYAe5HcaFh8txwBy18uyarLL5qe5WOLtGCZxrbT6LoizzxZyiIZRHD9e5LPRP7paxupWe36Kei2DXTfBnrvCd23he69oPt2sLOrpszyyZI0lkXE1SWPZGNnSvoGMAv4XkS8A/QBZubMsygt+xhJ44BxAP37929ZBL33hM17t2zZatSib80tWKbRRRqZsFFcylamTyTlUp73fLy8c7ckMaxPCttCt16wySeb+cuZWZakMVvSJcBUNq6eanGXW0kPANvlmXQOcC1wIcn3xwuB/wa+Sf6zTt6vsBExEZgIUFNT05KvzHDgeS1azMysPcuSNEakP/fJKWtVl9uIODDLfJKuA+5OPy4C+uVM7gssaWkMZmbWfIUewjQKmBkRny9jPEjaPiJeTz8eRdJ7C5IrndskXUnSED4YeLKcsZmZdXSFrjROBn4h6UXgfuD+iHijDDH9VNJwkquZV4FvAUTEfEm/B54juTv9DPecMjMrL0UTvWQk7Qx8CRgLbAn8lSSJPNoWTto1NTUxa9asSodhZtamSJodETUNy5u8uS8iXoiI/4mIg0naMf4GHAc8UfwwzcysmhVq09iqkUkzgYfqH8pkZmYdR6E2jdkk7Qr5urpuoqTf/ISIuLUUgZmZWfVpNGlExKDGpqVXIZ2Ah0ieH25mZh1Ao20akq5vpLwv8HBELAX+s1SBmZlZ9SnUEN5Z0m8lrZ8nHTTwEeAKgIi4q8TxmZlZFSmUNE4B3gN+J6mTpH2BacCZEXFTGWIzM7Mq02jSiMQ4kqE6HgTuAI6LiHvKFJuZmVWZQl1uf86G3lO7Ak8BX5X0VYCIOKssEZqZWdUo1OV2ViPvzcysgyrU5fbmcgZiZmbVL8szws3MzAAnDTMzawYnDTMzy6zgk/skdQEOBfYjefBRHclDke6JiPmlD8/MzKpJoS635wOHkdyj8QTwFtAF2Am4NE0o34uIZ0ofppmZVYNCVxr/FxHnNzLtSknbAP2LHZCk3wFD0o89gBURMVzSQOB5oDadNjMiTi/29s3MrHGFutxudOe3pG65z9CIiLdIrj6KKiKOz9nmfwP/zJm8MCKGF3ubZmaWTZMN4ZL2lfQcybd8JO0h6ZpSB6bkgR1fAW4v9bbMzCybgg3hqf8heT74VICIeFrS/iWNKrEf8GZEvJRTNkjSHGAlcG5EPJJvQUnjgHEA/fsXvQbNrFWmzFnM5dNqWbKijt49ujJ+7BCOHNGn0mGZZZIlaRARr6VP6qu3tjUblfQAsF2eSedExJ/S9yey8VXG60D/iFguaSQwRdJuEbEyT7wTgYkANTU10ZpYzYppypzFnD3pWerWJP9Ci1fUcfakZwGcOKxNyJI0XkuHRQ9JmwJnkVZVtVREHFhouqRNgKOBkTnLfAB8kL6fLWkhSU8uj4tlbcbl02rXJ4x6dWvWcvm0WicNaxOy3Nx3OnAG0AdYBAxPP5fSgcALEbGovkBSL0md0vefBgYDL5c4DrOiWrKirlnlZtWmySuNiFgGnFSGWHKdwMcbwPcHLpD0EUn12OkR8XaZ4zJrld49urI4T4Lo3aNrBaIxa74sz9PIq5TP04iIU/KU3QncWaptmpXD+LFDNmrTAOjauRPjxw4psJRZ9cj6PA0zK4L6dgv3nrK2KvPzNCRtnhTH6pJHZdaOHTmij5OEtVlZbu7bPb03Yh7wnKTZknYrfWhmZlZtsvSemgj8R0QMiIj+wPeA60oblpmZVaMsSaNbRPy1/kNEPAh0K1lEZmZWtbLc3PeypB8Bv0k/fw14pXQhmZlZtcpypfFNoBcwCZicvj+1lEGZmVl1ynJz3zskQ4eYmVkH12TSkFQD/BAYmDt/RAwrXVhmZlaNsrRp3AqMB54F1pU2HDMzq2ZZksbSiJha8kjMzKzqZUka50m6HvgL6dDkABExqWRRmZlZVcqSNE4FdgY6s6F6Kkh6U5mZWQeSJWnsERFDSx6JmZlVvSz3acyUtGvJIzEzs6qX5UpjDHCypFdI2jREMtqtu9yamXUwWZLGwSWPwszM2oQmq6ci4u/5Xq3ZqKTjJM2XtC69eTB32tmSFkiqlTQ2p3ykpGfTaVdLUmtiMDOz5svSplEK84CjgYdzC9O2kxOA3UiucK6R1CmdfC0wDhicvnwFZGZWZhVJGhHxfETU5pl0BHBHRHwQEa8AC4C9JG0PbBERj0dEALcAR5YvYjMzgyaShqROkh4oVzBAH+C1nM+L0rI+6fuG5XlJGidplqRZS5cuLUmgZmYdUcGkERFrgfckbdncFUt6QNK8PK8jCi2WL4wC5XlFxMSIqImIml69ejU3dDMza0SW3lPvA89K+jPwbn1hRBQcLj0iDmxBPIuAfjmf+wJL0vK+ecrNzKyMsiSNe9JXOUwFbpN0JdCbpMH7yYhYK2mVpH2AJ4BvAD8vU0xmZpbK8hCmmyV1Bfo30njdbJKOIjnp9wLukTQ3IsZGxHxJvweeAz4CzkiryAC+DdwEdAXuS19mZlZGSjojFZhBOgy4Atg0IgZJGg5cEBGHlyG+VqupqYlZs2ZVOgwzszZF0uyIqGlYnqXL7fnAXsAKgIiYCwwqYmxmZtZGZEkaH0XEPxuUFb48MTOzdilLQ/g8SV8FOkkaDJwFPFbasMzMrBpludL4LsmwHh8AtwMrgX8vYUxmZlalsvSeeg84R9JlycdYVfqwzMysGjV5pSHpM5KeBZ4hucnvaUkjSx+amZlVmyxtGr8GvhMRjwBIGgPcCPghTGZmHUyWNo1V9QkDICL+BriKysysA8pypfGkpF+RNIIHcDzwoKQ9ASLiqRLGZ2ZmVSRL0hie/jyvQfm+JEnkgGIGZGZm1StL76nPlyMQMzOrfpV63KuZmbVBThpmZpZZlvs0PpmlzMzM2r8sVxqPZywzM7N2rtGGcEnbAX2ArpJGsOE53VsAm5UhNjMzqzKFek+NBU4heR73lTnlq4AfljAmMzOrUo0mjYi4GbhZ0jERcWcxNyrpOJKHO+0C7BURs9LyLwKXApsCHwLjI2JGOu1BYHugLl3NQRHxVjHjMjOzwrLcp3GnpENIhkfvklN+QSu2Ow84GvhVg/JlwGERsUTS7sA0kiqyeifVJxgzMyu/JpOGpF+StGF8HrgeOBZ4sjUbjYjn03U3LJ+T83E+0EXSJyPig9Zsz8zMiiNL76l9I+IbwDsR8RNgFNCvtGEBcAwwp0HCuFHSXEk/UsOMk0PSOEmzJM1aunRp6SM1M+sgsiSN+jaE9yT1BtYAg5paSNIDkubleR2RYdndgMuAb+UUnxQRQ4H90tfXG1s+IiZGRE1E1PTq1aupzZmZWUZZBiy8W1IP4HLgKZJBCq9vaqGIOLAlAUnqC0wGvhERC3PWtzj9uUrSbcBewC0t2YZZsUyZs5jLp9WyZEUdvXt0ZfzYIRw5ok/TC5q1UVkawi9M394p6W6gS0T8sxTBpMnpHuDsiHg0p3wToEdELJPUGTgUeKAUMZhlNWXOYs6e9Cx1a9YCsHhFHWdPehbAicParSzDiGyWtiFcl7YvbCPp0NZsVNJRkhaRtI/cI2laOulMYEfgR2nbxVxJ2wCfBKZJegaYCywGrmtNDGatdfm02vUJo17dmrVcPq22QhGZlV6W6qkbgdkkJ3iARcAfgLtbutGImExSBdWw/CLgokYW83PJraosWVHXrHKz9iBLQ/gOEfFTkgZwIqKODUOKmHVYvXt0bVa5WXuQJWl8KKkrSQM4knYAfN+EdXjjxw6ha+dOG5V17dyJ8WOHVCgis9LLUj11HnA/0E/SrcBokjGpzDq0+sZu956yjkQR0fRMUk9gH5JqqZkRsazUgRVLTU1NzJrlkUfMzJpD0uyIqGlYXmho9D0bFL2e/uwvqX9EPFXMAM3MrPoVqp7675z3I4FZbGgAD+CAUgVlVgy+8c6s+AoNjf75+veS5kSEk4S1Gb7xzqw0svSegrTnlFlb4RvvzEoja9Iwa1N8451ZaRRqCP85G64w+kq6Ond6RJxVysDMWqN3j64szpMgfOOdWesUagjP7ac6u9SBmBXT+LFDNmrTAN94Z1YMTT0j3KxN8o13ZqVRqHpqInB1RMzLM60bcDzwQUTcWsL4zFrsyBF9nCTMiqxQ9dQ1wI8lDQXmAUuBLsBgYAvgBsAJw8ysAylUPTUX+Iqk7kANsD3Jo1+fjwj3WzQz64CyDFi4Dng7fdWmD2IyM7MOqNH7NCR1lnQVyUOXbgRuBl6WNCGdPqKlG5V0nKT5ktZJqskpHyipLuepfb/MmTZS0rOSFki6WpKf6WFmVmaFbu77b6A7MCAiRkbECGAX4NOSrgUmtWK784CjgYfzTFsYEcPT1+k55dcC40jaVAYDB7di+2Zm1gKFqqe+DAyOnLHTI2KlpG8Dy4AvtXSjEfE8QNaLBUnbA1tExOPp51uAI4H7WhqDmZk1X6GksS7yPGwjItZKWhoRM0sU0yBJc4CVwLkR8QjQh6SarN6itCwvSeNIrkro379/icK0cvKItWbVoVDSeE7SNyLiltxCSV8Dnm9qxZIeALbLM+mciPhTI4u9DvSPiOWSRgJTJO1G/meSNzqIYkRMBCZC8hCmpmK16uYRa82qR6GkcQYwSdI3SYYRCeAzQFfgqKZWHBEHNjeYtGfWB+n72ZIWAjuRXFn0zZm1L7Ckueu3tqnQiLXFThq+ojErrNB9GouBvSUdANR/278vIv5SqmAk9QLeTqvAPk3S4P1yRLwtaZWkfYAngG8APy9VHFZdyjVira9ozJrW5NDoETEjIn4eEVcXK2FIOkrSImAUcI+kaemk/YFnJD0N/BE4PSLeTqd9G7geWAAsxI3gHUZjI9MWe8RaP4PDrGlZbu4ruoiYDEzOU34ncGcjy8wCdi9xaFaFyjVirZ/BYdY0P4TJqt6RI/pwydFD6dOjKwL69OjKJUcPLXqVUbmuaMzasopcaZg1VzlGrPUzOMya5qRhlvIzOMya5qRhFVGtXVv9DA6zwpw0rOzctdWs7XJDuJWdu7aatV1OGlZ27tpq1nY5aVjZuWurWdvlpFEhU+YsZvSlMxg04R5GXzqDKXMWVzqkshk/dghdO3faqMxdW83aBjeEV0BHbwh211aztstJowLKOWprtXLXVrO2yUmjAqq5Ibha758ws+rgpFEBvXt0ZXGeBNFUQ3CpT+gdvdrMzJrmhvAKaElDcP0JffGKOoINJ/RiNqD7/gkza4qvNIqkOVcBLWkILkc7SDVXm5lZdXDSKIKWVOs0tyG4HCf0llabmVnH4eqpIihHtU45bojz/RNm1pSKJA1Jx0maL2mdpJqc8pMkzc15rZM0PJ32oKTanGnbVCL2fMpxFVCOE3q5HnZkZm1Xpaqn5gFHA7/KLYyIW4FbASQNBf4UEXNzZjkpfexrVSlHtU65bojz/RNmVkilnhH+PICkQrOdCNxeloBaqVxPfPMJ3cwqrZobwo8HjmhQdqOktcCdwEUREfkWlDQOGAfQv3//kgYJ1T0shm/WM7NiUiPn3davWHoA2C7PpHMi4k/pPA8C329Y5SRpb+D6iBiaU9YnIhZL2pwkafw2Im5pKo6ampqYNavqarTKomGvLkiugNxOYWZNkTQ7ImoalpfsSiMiDmzF4ifQoGoqIhanP1dJug3YC2gyaXRkHuPKzIqt6rrcSvoEcBxwR07ZJpK2Tt93Bg4laUy3AnyznpkVW6W63B4laREwCrhH0rScyfsDiyLi5ZyyTwLTJD0DzAUWA9eVK962yg87MrNiq1TvqcnA5EamPQjs06DsXWBk6SNrX8rVq8vMOo5q7j1lrVTNvbrMrG1y0mjnfG+HmRVT1TWEm5lZ9XLSMDOzzJw0zMwsMycNMzPLzA3h1moe38qs43DSsFZpyVMLzaztcvWUtUo5nlpoZtXDScNaxeNbmXUsThrWKh7fyqxjcdKwVinHs8vNrHq4IdxaxeNbmXUsThrWah7fyqzjcPWUmZll5qRhZmaZOWmYmVlmThpmZpaZk4aZmWWmiKh0DCUlaSnwd2BrYFmFw8mnWuOC6o3NcTWP42oex5UYEBG9Gha2+6RRT9KsiKipdBwNVWtcUL2xOa7mcVzN47gKc/WUmZll5qRhZmaZdaSkMbHSATSiWuOC6o3NcTWP42oex1VAh2nTMDOz1utIVxpmZtZKThpmZpZZu0gakg6WVCtpgaQJeaZL0tXp9Gck7Zl12RLHdVIazzOSHpO0R860VyU9K2mupFlljutzkv6ZbnuupB9nXbbEcY3PiWmepLWStkqnlXJ/3SDpLUnzGpleqeOrqbgqdXw1FVeljq+m4qrU8dVP0l8lPS9pvqR/yzNPRY6xvCKiTb+ATsBC4NPApsDTwK4N5vkycB8gYB/giazLljiufYFPpe+/VB9X+vlVYOsK7a/PAXe3ZNlSxtVg/sOAGaXeX+m69wf2BOY1Mr3sx1fGuMp+fGWMq+zHV5a4Knh8bQ/smb7fHHixGs5hjb3aw5XGXsCCiHg5Ij4E7gCOaDDPEcAtkZgJ9JC0fcZlSxZXRDwWEe+kH2cCfYu07VbFVaJli73uE4Hbi7TtgiLiYeDtArNU4vhqMq4KHV9Z9ldjKrq/Gijn8fV6RDyVvl8FPA80fEBNRY6xfNpD0ugDvJbzeREf3+GNzZNl2VLGletfSL5J1AtguqTZksYVKabmxDVK0tOS7pO0WzOXLWVcSNoMOBi4M6e4VPsri0ocX81VruMrq3IfX5lV8viSNBAYATzRYFLVHGPt4cl9ylPWsB9xY/NkWbalMq9b0udJ/qnH5BSPjoglkrYB/izphfSbUjnieopk3JnVkr4MTAEGZ1y2lHHVOwx4NCJyvzWWan9lUYnjK7MyH19ZVOL4ao6KHF+SupMkqn+PiJUNJ+dZpCLHWHu40lgE9Mv53BdYknGeLMuWMi4kDQOuB46IiOX15RGxJP35FjCZ5DK0LHFFxMqIWJ2+vxfoLGnrLMuWMq4cJ9Cg6qCE+yuLShxfmVTg+GpShY6v5ij78SWpM0nCuDUiJuWZpXqOsVI2mJTjRXK19DIwiA0NQbs1mOcQNm5EejLrsiWOqz+wANi3QXk3YPOc948BB5cxru3YcOPnXsA/0n1X0f2VzrclSb10t3Lsr5xtDKTxht2yH18Z4yr78ZUxrrIfX1niqtTxlf7utwBXFZinYsdYw1ebr56KiI8knQlMI+lJcENEzJd0ejr9l8C9JL0PFgDvAacWWraMcf0Y6AlcIwngo0hGsdwWmJyWbQLcFhH3lzGuY4FvS/oIqANOiOQIrfT+AjgKmB4R7+YsXrL9BSDpdpIeP1tLWgScB3TOiavsx1fGuMp+fGWMq+zHV8a4oALHFzAa+DrwrKS5adkPSZJ+RY+xfDyMiJmZZdYe2jTMzKxMnDTMzCwzJw0zM8vMScPMzDJz0jAzs8ycNMwaISkk/Sbn8yaSlkq6u4nlTpH0vyWIp4ek7+R87i3pj8XejlkhThpmjXsX2F1S1/TzF4HFpdygpEL3TvUA1ieNiFgSEceWMh6zhpw0zAq7j+RuXGgw8qmkrSRNSZ9vMDMdsmMjknpJulPS/6Wv0XnmOUXSHyTdRTIoXndJf5H0VPoMh/pRSy8Fdkif6XC5pIFKnw0hqYukG9P556TjTZkVXZu/I9ysxO4AfpxWSQ0DbgD2S6f9BJgTEUdKOoBkKIjhDZb/GfA/EfE3Sf1J7tzdJc92RgHDIuLt9GrjqIhYmY7JNFPSVGACsHtEDIf1I6LWOwMgIoZK2pkk+ewUEe+38vc324iThlkBEfFMenI+kWQoh1xjgGPS+WZI6ilpywbzHAjsmg5BAbCFpM0jeW5Crj/HhlFVBfyXpP2BdSRDXW/bRKhjgJ+nsbwg6e/ATsAzGX5Ns8ycNMyaNhW4gmTcop455VmGpf4EMCoi6prYRu5YRycBvYCREbFG0qtAlyaWzxeLWdG5TcOsaTcAF0TEsw3KHyY5wSPpc8Cy+PhzEKYDZ9Z/kDQ8w/a2BN5KE8bngQFp+SqSx4HmkxvLTiSD3dVm2JZZszhpmDUhIhZFxM/yTDofqJH0DEkj9cl55jmrfh5JzwGnZ9jkrekys0gSwQtpHMuBRyXNk3R5g2WuATpJehb4HXBKRHyQYVtmzeJRbs3MLDNfaZiZWWZOGmZmlpmThpmZZeakYWZmmTlpmJlZZk4aZmaWmZOGmZll9v8ByWvgnlxG4mgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "#### Qpi predicts heat values according to our model. \n",
    "def Qpi(matrix,H,Ka,N):\n",
    "    '''\n",
    "    Function that returns predicted heat value. \n",
    "    '''\n",
    "    i,Mt, Lt, Mt_below, Lt_below = matrix \n",
    "    A= 1+Ka*(Mt+Lt)\n",
    "    A_below = 1+Ka*(Mt_below+Lt_below)\n",
    "    B= sqrt((A**2)-(4*Ka**2*Mt*Lt))\n",
    "    B_below = sqrt((A_below**2)-(4*Ka**2*Mt_below*Lt_below))\n",
    "    ML=((A-B)/(2*Ka))\n",
    "    ML_below = ((A_below-B_below)/(2*Ka))\n",
    "    Qpi=((Vo*10*H)/(v*Lo))*(ML_below-ML*(1-v/Vo))*N\n",
    "\n",
    "\n",
    "    return Qpi\n",
    "                                                  \n",
    "                                      \n",
    "H, Ka,N = [-10, 170000,0.5]        #guess parameters                             \n",
    "results = Qpi(matrix,H,Ka,N)\n",
    "\n",
    "results\n",
    "plt.plot(x['moles titrant / moles titrate'].values[1:],x['Corrected Q (µJ)'][1:], 'o', label=\"data\")\n",
    "plt.plot(x['moles titrant / moles titrate'].values[:-1],results[:-1],label=\"predicted\")\n",
    "plt.xlabel('Mole ratio')\n",
    "plt.ylabel('Q(Heat per mole) KJ/mol')\n",
    "plt.title('Ca-EDTA binding isotherm - Prediction')\n",
    "plt.legend(loc=\"best\")\n",
    "plt.savefig('Ca-EDTA binding isotherm - Prediction.png',dpi=300)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "65e59a07-48ac-4700-bd20-7938bee86938",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-1.7e+01  2.5e+05  1.0e+00] [1.69369892e+09 2.24336852e+07 9.96293482e+07]\n"
     ]
    }
   ],
   "source": [
    "#Fitting experimental data to the model equation with scipy.curve_fit \n",
    "\n",
    "\n",
    "\n",
    "\n",
    "optimal_parameters,covariance = curve_fit(Qpi,matrix,x['Corrected Q (µJ)'].values,bounds=[[-20,250000,1.0],[-17,300000,1.2]])\n",
    "parameter_errors = np.sqrt(np.diag(covariance))\n",
    "print(optimal_parameters,parameter_errors)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "26c085e8-990b-4ca0-9bd2-0efa5d798ad9",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import r2_score "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "4cad5135-54ef-4e05-af69-6b856ce7e701",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-14.445596594460694\n"
     ]
    }
   ],
   "source": [
    "R_square = r2_score(x['Corrected Q (µJ)'].values,Qpi(matrix,*optimal_parameters))\n",
    "print(R_square)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "c36e22dc-6946-4b6f-b341-d0399b6b6c72",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x['moles titrant / moles titrate'].values[1:],x['Corrected Q (µJ)'][1:], 'o', label=\"data\")\n",
    "plt.plot(x['moles titrant / moles titrate'].values[:-1],Qpi(matrix,*optimal_parameters)[:-1],label=\"fitted\")\n",
    "plt.xlabel('Mole ratio')\n",
    "plt.ylabel('Q(Heat per mole) kJ/mol')\n",
    "plt.title('Ca-EDTA binding isotherm Data and Fit')\n",
    "plt.legend(loc=\"best\")\n",
    "plt.savefig('Ca-EDTA binding isotherm - Data and Fit.png',dpi=300)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5c2ce58d-27aa-4a65-9261-e2d6901ecc6d",
   "metadata": {},
   "source": [
    "## Section 2 :  Drug - Protein Data Analysis with our generated model. The drug is Carvedilol and the protein is Mucin. \n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "69dd5088-a84d-46d4-b069-a8084d665558",
   "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>Region</th>\n",
       "      <th>Q (µJ)</th>\n",
       "      <th>Corrected Q (µJ)</th>\n",
       "      <th>inj volume (µL)</th>\n",
       "      <th>moles titrant (moles)</th>\n",
       "      <th>moles titrate (moles)</th>\n",
       "      <th>moles titrant / moles titrate</th>\n",
       "      <th>total volume (µL)</th>\n",
       "      <th>inj interval (s)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>-12.623274</td>\n",
       "      <td>-18.730724</td>\n",
       "      <td>9.975</td>\n",
       "      <td>1.915200e-09</td>\n",
       "      <td>6.184000e-09</td>\n",
       "      <td>0.309702</td>\n",
       "      <td>809.975</td>\n",
       "      <td>300</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>-50.921046</td>\n",
       "      <td>-57.028496</td>\n",
       "      <td>9.975</td>\n",
       "      <td>3.830400e-09</td>\n",
       "      <td>6.184000e-09</td>\n",
       "      <td>0.619405</td>\n",
       "      <td>819.950</td>\n",
       "      <td>300</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>-39.431629</td>\n",
       "      <td>-45.539079</td>\n",
       "      <td>9.975</td>\n",
       "      <td>5.745600e-09</td>\n",
       "      <td>6.184000e-09</td>\n",
       "      <td>0.929107</td>\n",
       "      <td>829.925</td>\n",
       "      <td>300</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>-21.759127</td>\n",
       "      <td>-27.866577</td>\n",
       "      <td>9.975</td>\n",
       "      <td>7.660800e-09</td>\n",
       "      <td>6.184000e-09</td>\n",
       "      <td>1.238810</td>\n",
       "      <td>839.900</td>\n",
       "      <td>300</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>-21.499471</td>\n",
       "      <td>-27.606921</td>\n",
       "      <td>9.975</td>\n",
       "      <td>9.576000e-09</td>\n",
       "      <td>6.184000e-09</td>\n",
       "      <td>1.548512</td>\n",
       "      <td>849.875</td>\n",
       "      <td>300</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Region     Q (µJ)  Corrected Q (µJ)  inj volume (µL)  \\\n",
       "0       1 -12.623274        -18.730724            9.975   \n",
       "1       2 -50.921046        -57.028496            9.975   \n",
       "2       3 -39.431629        -45.539079            9.975   \n",
       "3       4 -21.759127        -27.866577            9.975   \n",
       "4       5 -21.499471        -27.606921            9.975   \n",
       "\n",
       "   moles titrant (moles)  moles titrate (moles)  \\\n",
       "0           1.915200e-09           6.184000e-09   \n",
       "1           3.830400e-09           6.184000e-09   \n",
       "2           5.745600e-09           6.184000e-09   \n",
       "3           7.660800e-09           6.184000e-09   \n",
       "4           9.576000e-09           6.184000e-09   \n",
       "\n",
       "   moles titrant / moles titrate  total volume (µL)  inj interval (s)  \n",
       "0                       0.309702            809.975               300  \n",
       "1                       0.619405            819.950               300  \n",
       "2                       0.929107            829.925               300  \n",
       "3                       1.238810            839.900               300  \n",
       "4                       1.548512            849.875               300  "
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = pd.read_excel(r'/Users/mac/Downloads/modelling meeting/Mucin Carvedilol Data (1) (1).xlsx')\n",
    "y.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "a3421b96-bca6-4866-b468-f8008db7cc68",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Experiment parameters\n",
    "\n",
    "Vo_=800 #Initial volume of EDTA in the cell, uL\n",
    "v_= 9.975 #Volume of CaCl2 per injection, uL\n",
    "Lo_= 0.192 # Concentration of CaCl2 in the syringe, mM\n",
    "Mo_=0.0077 #Concentration of EDTA in the cell , mM\n",
    "\n",
    "#Parameters to calculate\n",
    "#Mt,#Lt, #ML,#ML[i-1] = ML2,#Lt[i-1]=L2t,#Mt[i-1]=M2t,#n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "7b168320-39e1-4186-92c0-7959087ac52c",
   "metadata": {},
   "outputs": [],
   "source": [
    "#MLi vector and list generation for i,Mt and Lt \n",
    "Region_ = np.array(list(range(0,25)))  \n",
    "Mt_ = []\n",
    "Lt_ = []\n",
    "Mt_below_ = []\n",
    "Lt_below_ = []\n",
    "for idx, i in enumerate(Region_):\n",
    "    try: \n",
    "        Mt__= Mo_*(1-v_/Vo_)**(i)\n",
    "        Lt__= Lo_*(1-(1-v_/Vo_)**((i)))\n",
    "        Mt_.append(Mt__)\n",
    "        Lt_.append(Lt__)\n",
    "\n",
    "        Mt_below__= Mo_*(1-v_/Vo_)**(Region_[idx+1])\n",
    "        Lt_below__= Lo_*(1-(1-v_/Vo_)**(Region_[idx+1]))\n",
    "        Mt_below_.append(Mt_below__)\n",
    "        Lt_below_.append(Lt_below__)\n",
    "    except: \n",
    "        pass\n",
    "\n",
    "Mt_below_.append(0)\n",
    "Lt_below_.append(0)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "81ff90dd-fc51-447b-b892-b5803c699eb9",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Making Lt and Mt arrays\n",
    "Mt_ = np.array(Mt_)\n",
    "Lt_ = np.array(Lt_)\n",
    "Mt_below_ = np.array(Mt_below_)\n",
    "Lt_below_ = np.array(Lt_below_)\n",
    "N_ = np.array(Lt_/Mt_)\n",
    "\n",
    "matrix_ = np.row_stack((Region_, Mt_, Lt_, Mt_below_, Lt_below_))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "a4d29335-dbbc-4126-9481-083e70abdc53",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "#### Qpi_ predicts heat values according to our model. \n",
    "def Qpi_(matrix_,H_,Ka_,N_):\n",
    "    '''\n",
    "    Function that returns predicted heat value. \n",
    "    '''\n",
    "    i,Mt_, Lt_, Mt_below_, Lt_below_ = matrix_ \n",
    "    A_= 1+Ka_*(Mt_+Lt_)\n",
    "    A_below_ = 1+Ka_*(Mt_below_+Lt_below_)\n",
    "    B_= sqrt((A_**2)-(4*Ka_**2*Mt_*Lt_))\n",
    "    B_below_ = sqrt((A_below_**2)-(4*Ka_**2*Mt_below_*Lt_below_))\n",
    "    ML_=((A_-B_)/(2*Ka_))\n",
    "    ML_below_ = ((A_below_-B_below_)/(2*Ka_))\n",
    "    Qpi_=((Vo_*10*H_)/(v_*Lo_))*(ML_below_-ML_*(1-v_/Vo_))*N_\n",
    "\n",
    "\n",
    "    return Qpi_\n",
    "                                                  \n",
    "                                      \n",
    "H_, Ka_,N_ = [-120, 500000,0.1]        #guess parameters                             \n",
    "results_ = Qpi_(matrix_,H_,Ka_,N_)\n",
    "\n",
    "results_\n",
    "plt.plot(y['moles titrant / moles titrate'].values[1:],y['Corrected Q (µJ)'][1:], 'o', label=\"data\")\n",
    "plt.plot(y['moles titrant / moles titrate'].values[:-1],results_[:-1],label=\"predicted\")\n",
    "plt.xlabel('Mole ratio')\n",
    "plt.ylabel('Q(Heat per mole) KJ/mol')\n",
    "plt.title('Carvedilol-Mucin binding isotherm - Prediction')\n",
    "plt.legend(loc=\"best\")\n",
    "plt.savefig('Carvedilol-Mucin binding isotherm - Prediction.png',dpi=300)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "b5b093b6-8e04-45ce-8d76-40dca5aa2434",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-5.17890225e+00  6.00000000e+04  2.51664711e-01] [2.97935393e+08 1.35922930e+06 1.44779378e+07]\n"
     ]
    }
   ],
   "source": [
    "#Fitting experimental data to the model equation with scipy.curve_fit \n",
    "\n",
    "\n",
    "\n",
    "\n",
    "optimal_parameters,covariance = curve_fit(Qpi_,matrix_,y['Corrected Q (µJ)'].values,bounds=[[-30,30000,0.1],[10,60000,0.5]])\n",
    "parameter_errors = np.sqrt(np.diag(covariance))\n",
    "print(optimal_parameters,parameter_errors)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "9b0bc28f-dbff-4efa-9acb-914b691c99e9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.500500143021819\n"
     ]
    }
   ],
   "source": [
    "R_square = r2_score(y['Corrected Q (µJ)'].values,Qpi_(matrix_,*optimal_parameters))\n",
    "print(R_square)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "7dc9e426-5db3-408a-98fe-32b6b0048c39",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(y['moles titrant / moles titrate'].values[1:],y['Corrected Q (µJ)'][1:], 'o', label=\"data\")\n",
    "plt.plot(y['moles titrant / moles titrate'].values[:-1],Qpi_(matrix_,*optimal_parameters)[:-1],label=\"fitted\")\n",
    "plt.xlabel('Mole ratio')\n",
    "plt.ylabel('Q(Heat per mole) kJ/mol')\n",
    "plt.title('Carvedilol-Mucin binding isotherm Data and Fit')\n",
    "plt.legend(loc=\"best\")\n",
    "plt.savefig('Carvedilol-Mucin binding isotherm - Data and Fit.png',dpi=300)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e7d696b0-251e-4291-8ed7-995dafde8d8e",
   "metadata": {},
   "source": [
    "## Section 3  : Validation of Dumas Model with Ca-EDTA Experimental Data.\n",
    "\n",
    "  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "ab583007-a611-4260-9bb5-c4d825afd85c",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>s(exp)</th>\n",
       "      <th>Qexp</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.166250</td>\n",
       "      <td>-41.121923</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.249375</td>\n",
       "      <td>-39.836940</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.332500</td>\n",
       "      <td>-40.677923</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.415625</td>\n",
       "      <td>-42.522737</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.498750</td>\n",
       "      <td>-40.376389</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.581875</td>\n",
       "      <td>-45.317552</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.665000</td>\n",
       "      <td>-38.654584</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.748125</td>\n",
       "      <td>-36.510428</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.831250</td>\n",
       "      <td>-33.319762</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0.914375</td>\n",
       "      <td>-36.836833</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>0.997500</td>\n",
       "      <td>-31.158612</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>1.080625</td>\n",
       "      <td>-18.459198</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>1.163750</td>\n",
       "      <td>-6.679864</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>1.246875</td>\n",
       "      <td>-1.787778</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>1.330000</td>\n",
       "      <td>-0.981214</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>1.413125</td>\n",
       "      <td>-1.615076</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>1.496250</td>\n",
       "      <td>-1.162432</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>1.579375</td>\n",
       "      <td>-1.849468</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>1.662500</td>\n",
       "      <td>0.353390</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>1.745625</td>\n",
       "      <td>-1.465771</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>1.828750</td>\n",
       "      <td>0.731496</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>1.911875</td>\n",
       "      <td>0.101702</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>1.995000</td>\n",
       "      <td>0.794889</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>2.078125</td>\n",
       "      <td>-1.938414</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      s(exp)       Qexp\n",
       "0   0.000000        NaN\n",
       "1   0.166250 -41.121923\n",
       "2   0.249375 -39.836940\n",
       "3   0.332500 -40.677923\n",
       "4   0.415625 -42.522737\n",
       "5   0.498750 -40.376389\n",
       "6   0.581875 -45.317552\n",
       "7   0.665000 -38.654584\n",
       "8   0.748125 -36.510428\n",
       "9   0.831250 -33.319762\n",
       "10  0.914375 -36.836833\n",
       "11  0.997500 -31.158612\n",
       "12  1.080625 -18.459198\n",
       "13  1.163750  -6.679864\n",
       "14  1.246875  -1.787778\n",
       "15  1.330000  -0.981214\n",
       "16  1.413125  -1.615076\n",
       "17  1.496250  -1.162432\n",
       "18  1.579375  -1.849468\n",
       "19  1.662500   0.353390\n",
       "20  1.745625  -1.465771\n",
       "21  1.828750   0.731496\n",
       "22  1.911875   0.101702\n",
       "23  1.995000   0.794889\n",
       "24  2.078125  -1.938414"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "z = pd.read_excel(r'/Users/mac/Downloads/modelling meeting/Ca-EDTA Data_ Model_Validation  .xlsx')\n",
    "z.head(25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "5adb04e6-e5f8-43e8-83cd-6d889f27c7a4",
   "metadata": {},
   "outputs": [],
   "source": [
    "s1 = np.array([0,\n",
    "0.1663,\n",
    "0.2494,\n",
    "0.3325,\n",
    "0.4156,\n",
    "0.4988,\n",
    "0.5819,\n",
    "0.6650,\n",
    "0.7481,\n",
    "0.8313,\n",
    "0.9144,\n",
    "0.9975,\n",
    "1.0806,\n",
    "1.1638,\n",
    "1.2469,\n",
    "1.3300,\n",
    "1.4131,\n",
    "1.4963,\n",
    "1.5794,\n",
    "1.6625,\n",
    "1.7456,\n",
    "1.8288,\n",
    "1.9119,\n",
    "1.9950,\n",
    "2.0781,\n",
    "])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "5675629d-0aaa-4694-8544-4cc9e4e1f70c",
   "metadata": {},
   "outputs": [],
   "source": [
    "Qexp = np.array([-41.1219,\n",
    "-39.8369,\n",
    "-40.6779,\n",
    "-42.5227,\n",
    "-40.3764,\n",
    "-45.3176,\n",
    "-38.6546,\n",
    "-36.5104,\n",
    "-33.3198,\n",
    "-36.8368,\n",
    "-31.1586,\n",
    "-18.4592,\n",
    "-6.6799,\n",
    "-1.7878,\n",
    "-0.9812,\n",
    "-1.6151,\n",
    "-1.1624,\n",
    "-1.8495,\n",
    "0.3534,\n",
    "-1.4658,\n",
    "0.7315,\n",
    "0.1017,\n",
    "0.7949,\n",
    "-1.9384\n",
    "])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "4f0f184c-4a15-4f95-b0fd-c2d9c8416645",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Guess parameters\n",
    "ActiveFraction =0.8\n",
    "H = -10 #(kcal/mol)\n",
    "Kd =0.5 #uM\n",
    "Shift = 0.275038395603541"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "9d9dfe11-7b97-4cfb-9c82-e1edc7c9213f",
   "metadata": {},
   "outputs": [],
   "source": [
    "A0=150 #in uM - cell concentration\n",
    "B0= 1000 # in uM - syringe concentration\n",
    "\n",
    "def Qp(s1,H,ActiveFraction,Kd,Shift):\n",
    "    s2 = s1/ActiveFraction\n",
    "    r = B0/(ActiveFraction*A0) \n",
    "    gamma = B0/Kd #gamma = rc\n",
    "    c = A0/Kd #Wiseman parameter\n",
    "    \n",
    "    Z = []\n",
    "    for i in range(0,len(s1)):\n",
    "        z = np.sqrt(((r+gamma)**2)+ 2*s2[i]*(r+gamma+(r-gamma)*gamma) + (s2[i]**2)*((1+gamma)**2))\n",
    "        Z = np.append(Z,z)\n",
    "    # print(Z)\n",
    "    \n",
    "    Q = []\n",
    "    for i in range(0,len(s1)-1):\n",
    "        q = Shift+((1+gamma-((Z[i+1]-Z[i])/(s2[i+1]-s2[i])))/(2*gamma))*10*H\n",
    "        Q = np.append(Q,q)\n",
    "    \n",
    "    return Q"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "50200965-99f1-434d-ba4a-7fcd3187f143",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fa4aa465af0>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
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    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(s1[1:],Qexp, 'o',label=\"data\")\n",
    "plt.plot(s1[1:],Qp(s1,H,ActiveFraction,Kd,Shift),label=\"Predicted_Q\")\n",
    "plt.xlabel('Mole ratio')\n",
    "plt.ylabel('Q(Heat per mole) Kcal/mol')\n",
    "plt.title('Ca-EDTA binding isotherm - Prediction')\n",
    "plt.legend(loc=\"best\")\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "411278a7-8e49-4360-9997-3b6aa466e10d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-4.10817503  1.02914844  0.5         0.275     ] [0.11598672 0.0109113  0.16709777 0.72195791]\n"
     ]
    }
   ],
   "source": [
    "optimal_parameters,covariance = curve_fit(Qp,s1,Qexp,bounds=[[-50,0.5,0.5,0.275],[50,1.1,1.2,0.6]])\n",
    "parameter_errors = np.sqrt(np.diag(covariance))\n",
    "print(optimal_parameters,parameter_errors)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "0a8c40fe-3eb3-4ac7-a4e3-773edbafb38e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9897054489317347\n"
     ]
    }
   ],
   "source": [
    "R_square = r2_score(Qexp,Qp(s1,*optimal_parameters))\n",
    "print(R_square)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "6807aa4c-6d02-4237-b85e-60bec833c970",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fa4aa4876a0>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(s1[1:],Qexp, 'o',label=\"data\")\n",
    "plt.plot(s1[1:],Qp(s1,*optimal_parameters),label=\"fitted\")\n",
    "plt.xlabel('Mole ratio')\n",
    "plt.ylabel('Q(Heat per mole) Kcal/mol')\n",
    "plt.title('Ca-EDTA binding isotherm - Data and Fit')\n",
    "plt.legend(loc=\"best\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fb6358b1-269e-4e47-b3c2-b5eca4e2fc1b",
   "metadata": {},
   "source": [
    "## Section 4 :Data Analysis of Carvedilol-Mucin Experiment with Dumas Model.  \n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "03a5e866-d020-4f08-9a68-8f3680d37595",
   "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>Region</th>\n",
       "      <th>s(exp)</th>\n",
       "      <th>Q(exp) uJ</th>\n",
       "      <th>Q(exp) ucal</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>0.619405</td>\n",
       "      <td>-57.028496</td>\n",
       "      <td>-13.630138</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>0.929107</td>\n",
       "      <td>-45.539079</td>\n",
       "      <td>-10.884101</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>1.238810</td>\n",
       "      <td>-27.866577</td>\n",
       "      <td>-6.660272</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>1.548512</td>\n",
       "      <td>-27.606921</td>\n",
       "      <td>-6.598212</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>6</td>\n",
       "      <td>1.858215</td>\n",
       "      <td>-20.835550</td>\n",
       "      <td>-4.979816</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>7</td>\n",
       "      <td>2.167917</td>\n",
       "      <td>-14.283615</td>\n",
       "      <td>-3.413866</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>8</td>\n",
       "      <td>2.477620</td>\n",
       "      <td>-19.454248</td>\n",
       "      <td>-4.649677</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>9</td>\n",
       "      <td>2.787322</td>\n",
       "      <td>-13.662097</td>\n",
       "      <td>-3.265320</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>10</td>\n",
       "      <td>3.097025</td>\n",
       "      <td>-15.089138</td>\n",
       "      <td>-3.606390</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>11</td>\n",
       "      <td>3.406727</td>\n",
       "      <td>-0.667147</td>\n",
       "      <td>-0.159452</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>12</td>\n",
       "      <td>3.716429</td>\n",
       "      <td>-13.404391</td>\n",
       "      <td>-3.203726</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>13</td>\n",
       "      <td>4.335834</td>\n",
       "      <td>-7.878150</td>\n",
       "      <td>-1.882923</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>14</td>\n",
       "      <td>4.645537</td>\n",
       "      <td>-7.159553</td>\n",
       "      <td>-1.711174</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>15</td>\n",
       "      <td>4.955239</td>\n",
       "      <td>-5.072788</td>\n",
       "      <td>-1.212425</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>16</td>\n",
       "      <td>5.264942</td>\n",
       "      <td>-6.201407</td>\n",
       "      <td>-1.482172</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>17</td>\n",
       "      <td>5.574644</td>\n",
       "      <td>-6.039917</td>\n",
       "      <td>-1.443575</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>18</td>\n",
       "      <td>5.884347</td>\n",
       "      <td>-1.546794</td>\n",
       "      <td>-0.369693</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>19</td>\n",
       "      <td>6.194049</td>\n",
       "      <td>-2.024240</td>\n",
       "      <td>-0.483805</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>20</td>\n",
       "      <td>6.503752</td>\n",
       "      <td>-0.775666</td>\n",
       "      <td>-0.185389</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>21</td>\n",
       "      <td>6.813454</td>\n",
       "      <td>-1.759159</td>\n",
       "      <td>-0.420449</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>22</td>\n",
       "      <td>7.123157</td>\n",
       "      <td>1.630077</td>\n",
       "      <td>0.389598</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>23</td>\n",
       "      <td>7.432859</td>\n",
       "      <td>0.166757</td>\n",
       "      <td>0.039856</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>24</td>\n",
       "      <td>7.742561</td>\n",
       "      <td>1.249543</td>\n",
       "      <td>0.298648</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>25</td>\n",
       "      <td>8.052264</td>\n",
       "      <td>-5.915514</td>\n",
       "      <td>-1.413842</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Region    s(exp)  Q(exp) uJ  Q(exp) ucal\n",
       "0        1  0.000000   0.000000     0.000000\n",
       "1        2  0.619405 -57.028496   -13.630138\n",
       "2        3  0.929107 -45.539079   -10.884101\n",
       "3        4  1.238810 -27.866577    -6.660272\n",
       "4        5  1.548512 -27.606921    -6.598212\n",
       "5        6  1.858215 -20.835550    -4.979816\n",
       "6        7  2.167917 -14.283615    -3.413866\n",
       "7        8  2.477620 -19.454248    -4.649677\n",
       "8        9  2.787322 -13.662097    -3.265320\n",
       "9       10  3.097025 -15.089138    -3.606390\n",
       "10      11  3.406727  -0.667147    -0.159452\n",
       "11      12  3.716429 -13.404391    -3.203726\n",
       "12      13  4.335834  -7.878150    -1.882923\n",
       "13      14  4.645537  -7.159553    -1.711174\n",
       "14      15  4.955239  -5.072788    -1.212425\n",
       "15      16  5.264942  -6.201407    -1.482172\n",
       "16      17  5.574644  -6.039917    -1.443575\n",
       "17      18  5.884347  -1.546794    -0.369693\n",
       "18      19  6.194049  -2.024240    -0.483805\n",
       "19      20  6.503752  -0.775666    -0.185389\n",
       "20      21  6.813454  -1.759159    -0.420449\n",
       "21      22  7.123157   1.630077     0.389598\n",
       "22      23  7.432859   0.166757     0.039856\n",
       "23      24  7.742561   1.249543     0.298648\n",
       "24      25  8.052264  -5.915514    -1.413842"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = pd.read_excel(r'/Users/mac/Downloads/modelling meeting/Mucin Carvedilol Data xlsx.xlsx')\n",
    "a.head(25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "438aa97a-fc66-43ae-90b2-1409501ad6cf",
   "metadata": {},
   "outputs": [],
   "source": [
    "s1_ = np.array([0,\n",
    "0.619404916,\n",
    "0.929107374,\n",
    "1.238809832,\n",
    "1.54851229,\n",
    "1.858214748,\n",
    "2.167917206,\n",
    "2.477619664,\n",
    "2.787322122,\n",
    "3.09702458,\n",
    "3.406727038,\n",
    "3.716429495,\n",
    "4.335834411,\n",
    "4.645536869,\n",
    "4.955239327,\n",
    "5.264941785,\n",
    "5.574644243,\n",
    "5.884346701,\n",
    "6.194049159,\n",
    "6.503751617,\n",
    "6.813454075,\n",
    "7.123156533,\n",
    "7.432858991,\n",
    "7.742561449,\n",
    "8.052263907\n",
    "])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "165688ac-bf3b-48b2-badc-0d13301c3aa3",
   "metadata": {},
   "outputs": [],
   "source": [
    "Qexp_ = np.array([-13.63013762,\n",
    "-10.88410121,\n",
    "-6.66027175,\n",
    "-6.598212448,\n",
    "-4.979815979,\n",
    "-3.413866032,\n",
    "-4.649676897,\n",
    "-3.265319529,\n",
    "-3.6063905,\n",
    "-0.15945191,\n",
    "-3.203726338,\n",
    "-1.882923062,\n",
    "-1.711174233,\n",
    "-1.212425424,\n",
    "-1.482171953,\n",
    "-1.443574799,\n",
    "-0.369692559,\n",
    "-0.483804904,\n",
    "-0.185388512,\n",
    "-0.420449152,\n",
    "0.389597806,\n",
    "0.039855827,\n",
    "0.298648043,\n",
    "-1.413841831\n",
    "])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "b68ccc3f-dfb2-4f51-9df9-020bce0a2ac9",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Guess parameters\n",
    "ActiveFraction_ =0.15\n",
    "H_ = -18 #(kcal/mol)\n",
    "Kd_ =15 #uM\n",
    "Shift_ = 0.6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "608cb92a-985a-46af-951b-f18363f6f366",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Lets make the parameters arrays\n",
    "#s1_corrected = s1/ActiveFraction\n",
    "#s2 = s1_corrected\n",
    "#print(s1_corrected)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "d0d5d25b-1c0f-4d7d-a7b3-d203fd98fa23",
   "metadata": {},
   "outputs": [],
   "source": [
    "A0_=7.73 #in uM - cell concentration\n",
    "B0_= 192 # in uM - syringe concentration\n",
    "\n",
    "def Qp_(s1_,H_,ActiveFraction_,Kd_,Shift_):\n",
    "    s2_ = s1_/ActiveFraction_\n",
    "    r_ = B0_/(ActiveFraction_*A0_) \n",
    "    gamma_ = B0_/Kd_ #gamma = rc\n",
    "    c_ = A0_/Kd_ #Wiseman parameter\n",
    "    \n",
    "    Z_ = []\n",
    "    for i in range(0,len(s1)):\n",
    "        z_ = np.sqrt(((r_+gamma_)**2)+ 2*s2_[i]*(r_+gamma_+(r_-gamma_)*gamma_) + (s2_[i]**2)*((1+gamma_)**2))\n",
    "        Z_ = np.append(Z_,z_)\n",
    "    # print(Z)\n",
    "    \n",
    "    Q_ = []\n",
    "    for i in range(0,len(s1_)-1):\n",
    "        q_ = Shift_+((1+gamma_-((Z_[i+1]-Z_[i])/(s2_[i+1]-s2_[i])))/(2*gamma_))*10*H_\n",
    "        Q_ = np.append(Q_,q_)\n",
    "    \n",
    "    return Q_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "22279865-13b8-4cbb-877c-a88c2ef224c3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fa4aa835f40>"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(s1_[1:],Qexp_, 'o',label=\"data\")\n",
    "plt.plot(s1_[1:],Qp_(s1_,H_,ActiveFraction_,Kd_,Shift_),label=\"Predicted_Q\")\n",
    "plt.xlabel('Mole ratio')\n",
    "plt.ylabel('Q(Heat per mole) Kcal/mol')\n",
    "plt.title('Carvedilol-Mucin binding isotherm - Prediction')\n",
    "plt.legend(loc=\"best\")\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "90c1553e-4b97-49a9-978f-39b1ab7a7613",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-24.31523774   0.2         19.17231764   1.        ] [253.37616928   1.97806685  23.39956765   1.09053767]\n"
     ]
    }
   ],
   "source": [
    "optimal_parameters,covariance = curve_fit(Qp_,s1_,Qexp_,bounds=[[-50,0.2,10,1],[50,0.5,20,3]])\n",
    "parameter_errors = np.sqrt(np.diag(covariance))\n",
    "print(optimal_parameters,parameter_errors)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "2fd15446-be60-4d3c-9726-8306f10a7394",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9450819595624241\n"
     ]
    }
   ],
   "source": [
    "R_square = r2_score(Qexp_,Qp_(s1_,*optimal_parameters))\n",
    "print(R_square)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "47651b91-1eac-4a93-b5e7-d161110e799b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fa4aa6e49d0>"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(s1_[1:],Qexp_, 'o',label=\"data\")\n",
    "plt.plot(s1_[1:],Qp_(s1_,*optimal_parameters),label=\"fitted\")\n",
    "plt.xlabel('Mole ratio')\n",
    "plt.ylabel('Q(Heat per mole) Kcal/mol')\n",
    "plt.title('Carvedilol-Mucin binding isotherm Data and Fit')\n",
    "plt.legend(loc=\"best\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "181d3848-2553-4a08-82d9-24f3918058b9",
   "metadata": {},
   "outputs": [],
   "source": [
    "# sensitivity \n",
    "\n",
    "from SALib.sample import morris as ms\n",
    "from SALib.analyze import morris as ma\n",
    "from SALib.plotting import morris as mp "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "a19df2be-8099-48b8-9a29-83b420bd55eb",
   "metadata": {},
   "outputs": [],
   "source": [
    "morris_problem = {\n",
    "    'num_vars' : 4, \n",
    "    'names' : ['H_','ActiveFraction_','Kd_','Shift_'], \n",
    "    'bounds' : [[-50, 50], \n",
    "                [0.5, 1.1], \n",
    "                [0.5, 1.2], \n",
    "                [0.275038395603541,0.6]\n",
    "               ],\n",
    "    'groups' : None\n",
    "    }\n",
    "       "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "e93fc420-ca24-460b-9f90-7e28e8882e29",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(50, 4)\n"
     ]
    }
   ],
   "source": [
    "number_of_trajectories = int(1e1)\n",
    "sample = ms.sample(morris_problem, number_of_trajectories, num_levels=4)\n",
    "print(sample.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "7288b290-c63b-4514-980e-cc731d65c621",
   "metadata": {
    "scrolled": true,
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-164.97842711141828\n",
      "-164.76178604182064\n",
      "496.685358125462\n",
      "496.685358125462\n",
      "494.2340488008919\n",
      "497.8142141013291\n",
      "497.8142141013291\n",
      "495.34757109590237\n",
      "-164.4602844116992\n",
      "-164.67692548129685\n",
      "-494.58085323509766\n",
      "165.22700227250382\n",
      "165.22700227250382\n",
      "165.44364334210147\n",
      "166.26585767724373\n",
      "-164.16132400322826\n",
      "494.01740773129427\n",
      "494.2340488008919\n",
      "496.685358125462\n",
      "496.685358125462\n",
      "165.14468293363055\n",
      "165.96178604182055\n",
      "165.7451449722229\n",
      "165.7451449722229\n",
      "-495.7019991950596\n",
      "165.63682443742408\n",
      "165.85346550702172\n",
      "165.03636239883173\n",
      "165.03636239883173\n",
      "-493.1423693356907\n",
      "-164.26964453802708\n",
      "-164.05300346842944\n",
      "494.12572826609306\n",
      "496.57703759066317\n",
      "496.57703759066317\n",
      "495.2392505611036\n",
      "495.2392505611036\n",
      "497.70589356653034\n",
      "-165.39081928164026\n",
      "-165.17417821204262\n",
      "494.01740773129427\n",
      "496.4687170558644\n",
      "-164.97842711141828\n",
      "-164.76178604182064\n",
      "-164.76178604182064\n",
      "-495.81031972985846\n",
      "-493.35901040528836\n",
      "164.81972132923408\n",
      "165.03636239883173\n",
      "165.03636239883173\n"
     ]
    }
   ],
   "source": [
    "output= []\n",
    "for i in sample: \n",
    "    H,Active_fraction,Kd,Shift = i \n",
    "    Qp_ = Qp(s1,H,ActiveFraction,Kd,Shift)\n",
    "    print(Qp_[0])\n",
    "    output.append(Qp_[15])\n",
    "    \n",
    "output_ = np.array(output)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "53186492-56eb-479e-a29d-b4868a797d41",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(50, 4)"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "d33b20b0-a020-49c0-b651-7cc4a4eacbc1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(50,)"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "output_.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "1d02b106-2821-450b-bc79-9d73dfeebc15",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Store the results for plotting of the analysis\n",
    "Si = ma.analyze(morris_problem, \n",
    "                sample, \n",
    "                output_, \n",
    "                print_to_console=False, \n",
    "                num_levels=4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "f02b1972-ca98-4304-b575-8e83484f40af",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Name                      mu mu_star   sigma\n",
      "H_                     15.92   15.92    4.04\n",
      "ActiveFraction_         0.00    0.00    0.00\n",
      "Kd_                     3.32    4.41    3.54\n",
      "Shift_                  0.32    0.32    0.00\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Sensitivity_Analysis')"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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TfPPNN9xyyy1+rzsnJ4dly5Yxa9YsmjSxr9BAsnffh0RkJjATIPzswFwnMKYh2rp1KxCYKaTOPvtsNm3aRIsWLfxetzmdJbCaneUeelzqXOA9T05U1XnAPIBmHXoEbVeMOd35U572WlmrbEVmnwj0IpZ9+/YNSL3mdDYKsWZ55WYmSACCfnodYxo6x3GIioqiS5cufq13z549TJ48mdTUVL/WaypnCcwYE3IcxyE+Pp6wMP9+hS1cuJDFixfbqstBwhKYMSakqGpAFrFUVV5//XUuu+wyYmNj/Vq3qZwlMGNMSNm3bx/Z2dl+T2CbNm1i586ddu9XELFBHDUofw+Y+/l8YH5AgjHGBGwAR2JiIhEREdx0001+rddUzVpgxpiQUprA+vevOJWjb3Xo0IFf/vKXnHPOOX6t11TNWmB1JCJzgIp/iv1LVb03W6gx5gyO4xAbG0urVq38Wu/vfvc7v9ZnamYJrI7cicqSlTF+FogBHCkpKfTp08dm3ggy1oVojAkZ+fn57Nq1y68J7OTJkwwbNozZs2f7rU7jGUtgxpiQsX37dkpKSvyawJYuXcrJkye58cYb/Van8YwlMGNMyAjECMTExERiYmL4yU9+4rc6jWcsgRljQobjOERGRhIXF+eX+jIzM/noo4+YMmWK32f9MDWz/xFjTMhwHIf+/fsTHh7ul/reeecdiouL7eblIGUJzBgTElSVLVu2+LX78L//+79Zs2YN/fr181udxnOWwIxpBEQkUkTWicgWEdkmIo9VcoyIyAsisltEHBEZFIhYq5KZmcmhQ4f8msDCw8MZNmyY3+oztWMJzJjG4RRwhaoOBBKAq0Xk4grHjAZ6uH9mAn/za4Q18PcAjueee47f/e53qNpSfsHK7srzk/hOrVhvixuaAFHXt/AJ99Om7p+K38zXA6+5j/1KRFqLSAdVPejHUKtUmsDi4+N9Xpeq8sILL9C9e3dExOf1mbqxFpgxjYSIhLtXF/8BWKmqaysc0gnYV+55hntbUHAch44dO9K2bVuf1/Xll1/y3Xff2eCNIGcJzJhGQlWL3auKRwNDRaTibLiVNTUq7T8TkZkisl5E1mdlZXk50sr5cwqpxMREzjrrLG644Qa/1GfqxhKYMY2Mqh4DVgFXV9iVAXQu9zwaOFBFGfNUdbCqDm7Xrp0vwjxNYWEh27dv90sCKygo4I033mDs2LFERUX5vD5Td5bAjGkERKSdiLR2Pz4L+Cmws8Jh7wE/d49GvBjIDpbrX7t27aKwsNAvCSwnJ4drrrmGW2+91ed1mfqxQRzGNA4dgAUiEo7rD9c3VfUDEfkVgKrOBZYDY4DdQC4QNN/g/hyB2LZtWxYsWODzekz9WQIzphFQVQe4oJLtc8s9VmCWP+PylOM4NG3alF69evm0nuPHj/Ptt98ycOBAn9ZjvMO6EI0xQc9xHPr06UNERIRP6/nXv/5FQkICmzZt8mk9xjssgRljgp6/RiAmJiYSFxdHQkKCz+sy9WddiH6Ssj+b2PuXBToMAPbYDdUmhBw+fJj9+/f7PIFlZGSwatUqHnnkEbt5OURYC8wYE9RSUlIA3w/gWLRoEarK1KlTfVqP8R5LYMaYoOavEYhvv/02F198sd/WGjP1Z12Ixpig5jgObdu25fzzz/dpPStXruTAgUrv2zZBylpgxpigVjqAw9fXpVq2bEnPnj19WofxLktgxpigVVxczNatW33afVhSUsLo0aN59913fVaH8Q1LYMaYoPXNN9+Ql5fn0wT273//m+TkZAoKCnxWh/ENS2DGmKDljwEciYmJREVFce211/qsDuMblsCMMUHLcRzCwsLo27evT8rPy8vjrbfe4sYbb+Sss87ySR3GdyyBGWOCVkpKCj179vRZcvnggw/IycmxhStDlCUwY0zQ8vUUUm3btmXSpEmMGDHCZ3UY37EEZowJSqUzw/sygY0cOZJFixYRHh7uszqM71gCM8YEpa1btwK+G8CxZcsWDh4MivU6TR3ZTBzGmKDk6xGId9xxBydPnmTz5s0+Kd/4nrXA3ETkRLnHY0QkTURiqjvOGOM7juNw9tlnExNzxq9hvX377besWbOGyZMne71s4z+WwCoQkf8C/gJcrap7Ax2PMd4gIp1F5DMR2SEi20TkzkqOGSEi2SKy2f3zcCBiLeXLKaSSkpIAmDJlitfLNv5jXYjliMhlwCvAGFX9xr2tK7AQ13uVHMDwPPb9wvur3T/iq2eq3b9q1SovRmOCRBEwW1U3ikgUsEFEVqrq9grHfaGq1wQgvtOoKo7j+GR4u6qSmJjIiBEj6Ny5s9fLN/5jLbAfNQOWAmNVdWe57c8Df1PVIcD3tSlQRGaKyHoRWV+cm+3FUI2pHVU9qKob3Y+PAzuAToGNqmp79+4lJyfHJ9e/du3aRVpamt371QBYC+xHhcAa4BdA+e6VS4Eb3Y9fB/7gaYGqOg+YB9CsQw/1Tpg1O3/K09XuX2UrMjdqIhILXACsrWT3MBHZAhwA7lHVbf6MrZQvB3D07t2bvXv30rp1a6+XbfzLWmA/KgEmAENE5MEK+/yWfIzxJRFpCSwB7lLVnAq7NwJdVHUgruvA71ZTTlnvQlZWltfjLE1g/fv393rZANHR0bRs2dInZRv/sQRWjqrmAtcAU0XkF+7Nq4FJ7se21rgJWSLSFFfySlLVtyvuV9UcVT3hfrwcaCoibSsrS1XnqepgVR3crl07r8fqOA7dunUjKirKq+V++OGHjB49mv3793u1XBMYlsAqUNUjwNXA/4rI9bi6E2eJyNdAq4AGZ0wdiWso3z+AHar65yqOOd99HCIyFNf3w2H/RfkjX00h9dprr7Fu3Tp8kXSN/9k1MDdVbVnu8T6ga7ndw8o9rv4CkzHB6VJgGpAiIpvd2x4EYgBUdS4wHrhdRIqAPGCSqvq9+zwvL4/U1FQmTJjg1XKPHz/OO++8wy233EJERIRXyzaBYQnMmEZAVf8DVHtDlaq+CLzon4iqtn37dkpKSrzeAnv33XfJy8uz0YcNiCWwOhCReFwjEss7paoXBSIeYxoSX41ATExMJDY2lksuucSr5ZrAsQRWB6qaAiQEOg5jGiLHcWjevDndunXzWpmqyqhRoxg7dqxPZvYwgWEJzBgTVBzHoX///l5d4kREuOeee7xWngkONgrRGBM0VJUtW7Z4vftw2bJl5ObmerVME3iWwIwxQeP777/n8OHDXk1g27dv55prruGVV17xWpkmOFgCM8YEDV8M4EhKSiI8PJxJkybVfLAJKZbAjDFBozSBxcfHe6W8kpISkpKSGDVqFOedd55XyjTBwxKYMSZoOI5DdHQ05557rlfKW716Nenp6UydarPANUSWwIwxQcPbU0h99NFHNG/enLFjx3qtTBM8LIEZY4JCQUEBO3bs8GoCe/zxx9mxY4fNPN9A2X1gfhLfqRXrbR0uY6q0a9cuCgsLvZrARISYmBivlWeCi7XAjDFBwdsjEGfMmMF9993nlbJMcLIEZkyIeeyxxwIdgk84jkNERAQ9e/asd1lHjx4lKSmJU6dOeSEyE6ysC9GYEPPYY4+Rm5vLkSNHGDRoUIO5v8lxHPr27UvTpk3rXdZbb71FQUGBzTzfwFkLzJgQIyJERkZy1VVXsW/fvtLZ1c8KdFz15c0RiImJifTu3ZsLL7zQK+WZ4GQtMGNCTO/evcu6EcePH8/06dPp1atX5wCHVS+HDh3iwIEDXklg6enpfP755zz55JM283wDZy0wY0JM27Zt2bBhQ9lz9zWjav8YFZHOIvKZiOwQkW0icmclx4iIvCAiu0XEEZFBXg++CikpKYB3BnCEh4fzm9/8hilTptS7LBPcrAVmTIh54YUXmDRpEhdeeCHx8fGlo/cKajitCJitqhtFJArYICIrVXV7uWNGAz3cPxcBf3P/63PeHIEYHR3N888/X+9yTPCzFpgxIWbgwIFs3ryZyZMnAzBy5EiAb6s7R1UPqupG9+PjwA6gU4XDrgdeU5evgNYi0sHb8VfGcRzat29f7/kKv/32W/79739TUlLipchMMLME5icp+7OJvX8ZsfcvC3QopgFo1qwZP/vZz7jvvvv45S9/CeDxN7aIxAIXAGsr7OoE7Cv3PIMzk5xPeGsAx0svvcSoUaM4evSoF6Iywc4SmDGNiIi0BJYAd6lqTsXdlZyiVZQzU0TWi8j6rKysesVUXFzM1q1b653AiouLWbhwIWPGjKFNmzb1KsuEBktgxjQSItIUV/JKUtW3KzkkAyg/mjEaOFBZWao6T1UHq+rgdu3a1Suu3bt3k5+fX+8E9umnn/L999/bvV+NiCUwYxoBcY0n/wewQ1X/XMVh7wE/d49GvBjIVtWDvo7NWwM4kpKSOPvss7nmmmu8EZYJATYK0ZjG4VJgGpAiIpvd2x4EYgBUdS6wHBgD7AZygVv9EZjjOISHh9OnT586l1FSUsLnn3/OTTfdRGRkpBejM8HMEpgxjYCq/ofKr3GVP0aBWf6J6EeO49CrV696JZ6wsDB27drF8ePHvRiZCXbWhWiMCShvjEBUVZo2beq1lZxNaLAEZowJmOzsbPbs2VOvBPbDDz/Qs2dPPvzwQy9GZkKBJTBjTMBs3boVqN8AjjfffJPdu3fTqZNfblkzQcQSmDEmYLwxAjExMZGBAwfSv39/b4VlQoQlMGNMwDiOQ+vWrYmOjq7T+Wlpaaxdu9bu/WqkLIEZYwKmdABHXZc9SUpKQkTK5oU0jYslMGNMQJSUlJCSklKv7sPLL7+cxx57zK5/NVJ2H5gxJiDS09M5fvx4vRLYyJEjS2fjN42QtcCMMQFR3wEcy5YtIzU11ZshmRDTKBKYiMxxr0LriMhmEblIRPaISNtKjr1ORO53P24nImtFZJOIXCYid/g/emMaJsdxEBH69etX63MLCwu55ZZbePjhh30QmQkVDT6Bicgw4BpgkKoOAH7K6WsenUZV31PVp91P/wvYqaoXuM+xBGaMlziOQ/fu3WnZsmWtz/3www85fPiwjT5s5BrDNbAOwCFVPQWgqoeA0lFP/yMi1wJNgZtUdaeITAcGA38H/h9wlnvy011Ad/fjlar6u5oqFpGZwEyA8LPrt+SEMQ1NfaaQSkxMpE2bNlx11VVejsoEg8OHDxMZGUmLFi2qPa7Bt8CAj4DOIpIqIn8VkcvL7TukqoOAvwH3lD9JVTcDDwNvqGoCcB/wjaomeJK83GWUrZkU3ryVN16LMQ1Cbm4uaWlpdUpgOTk5LF26lEmTJtG0aVMfRGcCKSsrix49evDMM8/UeGyDT2CqegK4EFdLKAt4w93KAihd1G8DEOv34IxppLZt24aq1imBrV+/npKSEus+bEBUlQ0bNgDQrl077rvvPm688cYaz2sMXYioajGwClglIinALe5dp9z/FtNI3gtjgkF9RiBeccUVZGZm0qqV9Wo0BF9++SWzZ89m7dq1bN++nV69enHfffd5dG6Db4GJSC8R6VFuUwKQXoeijgNRXgnKmEbOcRxatGhB165da3Wea8kyaN26dZ1n7zDB4ZtvvmHChAlccskl7Nmzh1deeYW4uLhaldHgExjQElggIttFxAH6Ao/WthBVPQysFpGtIlJz56wxQUZEXhWRH0RkaxX7R4hItvtWk80i4rMx6o7jEB8fT1hY7b6C/vSnPzFs2DByc3N9FJnxtSNHjnD33XfTp08fli1bxqOPPkpaWhozZswgPDy8VmU1+G4zVd0AXFLJrthyx6wHRrgfzwfmV3zsfj7FR2Ea4w/zgReB16o55gtVvcaXQagqjuMwfvz4Wp+bmJhIZGQkzZs390FkxpcKCgp46aWXeOKJJzh27BgzZszg8ccfp2PHjnUuszG0wIwxgKp+DhwJdBwHDhzgyJEjtb7+lZKSwpYtW2zwRoh66KGHuPvuuxk8eDCbN2/m73//e72SFzSCFpgviEg88HqFzadU9aJAxGOMFw0TkS3AAeAeVd3m7QrqOoAjKSmJ8PBwJk6c6O2QjI+sXbuW5s2bEx8fz5133snIkSO56qqrvHb90hJYHahqCq7BIMY0JBuBLqp6QkTGAO8CPSo7sPxN+jExMbWqpDSBxcfHe3xOSUkJSUlJXH311bRrZ5MChIL8/Hyuv/56Lr30UpYsWULHjh3r3eKqyLoQjTEAqGqO+75JVHU50LSy+ULd+8tu0q9tQnEch5iYGFq3bu3xOUVFRfzv//4vv/3tb2tVl/GvY8eO8Yc//IGioiIiIyN5//33mT9/vs/qsxaYMQYAETkfyFRVFZGhuP7APezteuoyhVRERAS33Xabt0MxXlJYWMjcuXN57LHHOHLkCEOGDOGKK65gyJAhPq3XWmDGNBIisgj4EuglIhki8gsR+ZWI/Mp9yHhgq/sa2AvAJC298cpLTp06xc6dO2uVwPLz85k7dy5HjgR8/ImpQFV599136devH7/5zW9ISEhg48aNXHHFFX6p31pgxjQSqjq5hv0v4hpm7zM7d+6kqKioVgnsgw8+4PbbbycuLo6f/vSnPozO1MbXX3/NPffcw+eff152T9fo0aP9eoO5tcCMMX5TlxGIiYmJdOjQwVZeDhLp6elMnTqVoUOHsnPnTubOnYvjOIwZM8bvs6NYAjPG+I3jODRr1owePSod3HiGw4cPs3z5cqZMmVLrWRqMb/znP//h7bffZs6cOaSlpXHbbbfRpElgOvOsC9EY4zeO49CvXz+Pv/D+9a9/UVhYaDcvB5Cq8te//pUmTZpw2223MXnyZEaOHOn1IfF1YS0wY4zf1HYEYkpKCv369WPgwIE+jMpUR0RYtmwZycnJAISFhQVF8gJrgflNfKdWrH/6Z4EOw5iA+eGHH/j+++9rlcBeeuklTp48aTPP+9mGDRt44IEHmDt3Lt26dePNN9+scXXkQLAWmDHGL1JSUgDPB3AUFxcDBOUXZ0O1b98+pk2bxuDBg9m0aRO7d+8GoGXLlkH5R4QlMGOMX9RmBKKqMmjQIB555BFfh2WAnJwcHnzwQXr27Mm//vUvHnjgAXbv3s2VV14Z6NCqZV2Ixhi/cByH888/36O5DDds2IDjOPzP//yPHyKrncLCQjIyMsjPzw90KPWmqpw4cYJjx44xfPhwRo8eTevWrWnSpAkHDhzgwIEDfoslMjKS6OhomjZt6vE5lsCMMX5RmwEciYmJRERE1GnNMF/LyMggKiqK2NjYoOxW89TJkyf57rvvCAsLIyYmhs6dOwesu1ZVOXz4MBkZGbVapdu6EI0xPldUVMS2bds8SmBFRUUsWrSIa6+9tlYT/vpLfn4+bdq0CdnkVTo7WJMmTRAR4uLi6NWrV0CvNYoIbdq0qXWr1lpgxhifS0tL49SpUx4lsI8//pgffvghqO/9CtXktXfvXk6dOkWPHj1o1qwZffv2DZrXUpc4LIEZY3yuNmuA9e3bl8cff5zRo0f7OqxGobi4mLCwMESEZs2aERYWhqoiIkGTvOrKEpgxxuccxyE8PJw+ffrUeGxMTAwPPfSQH6Jq2FSVQ4cOceDAAaKjo2nTpg3nnXdeoMPyKrsGZozxOcdx6N27N82aNav2uM8//5ylS5eW3QNmak9VufXWW0lMTCQ9PZ1mzZoRGRlZ6bEZGRn1qmvGjBm0b9+e/v37V3tccnIyvXr1Ii4ujqeffrpedZZnCcwY43MpKSkeXf/6v//7P+68886Q79oKlNzcXNLS0li9ejXx8fF079690gEaqsozzzzDtGnT6jVUfvr06WVTTFWluLiYWbNmsWLFCrZv386iRYvYvn17nesszxKYMcansrOzSU9PrzGBff/996xcuZKpU6cSFmZfTTXZsmULw4cPp2/fvmXXuO688062bt1K7969GTBgAOPGjSM1NRVwzexf2lIqHX04atSoes1rOHz4cM4999xqj1m3bh1xcXF069aNiIgIJk2axNKlS+tcZ3l2DcwY41OeTiG1ePFiSkpKmDp1qj/CCmn5+flMnDiR1157jX79+nHnnXdSUFDAQw89xBtvvMHYsWMJCwtj9+7dZUvXOI5z2iCacePGMW7cuErLv+yyyzh+/PgZ2//4xz/WelHR/fv307lz57Ln0dHRrF27tlZlVMUSmDGNhIi8ClwD/KCqZ1y0EFe/3fPAGCAXmK6qG+tbr6dTSCUmJjJo0CD69u1b3yr95q677mLz5s1eLTMhIYHnnnuu2mNWrlzJwIEDGTp0KKrKhRdeyNq1a4mJieHjjz/mn//8J+np6XTq1KmsNVubG8m/+OKL+r6MMqX3nZXnrS5ia6cb03jMB66uZv9ooIf7ZybwN29U6jgO55xzDp06darymGPHjnHkyBGmTZvmjSobvP/85z+0b9+e4uJiRIS9e/cyZMgQcnNzOXbsGB07dmTz5s2nJawNGzZ4nMAuu+wyEhISzvj5+OOPax1rdHQ0+/btK3uekZHhteVYrAVmTCOhqp+LSGw1h1wPvKauP5m/EpHWItJBVQ/Wp97Sv/yr+6u7devWfPPNNxQWFtanKr+rqaXkTXl5eYSHhxMREUFMTAyffvopYWFhpKam8vbbb7NmzRo+++wzRo4cCbiukZXObJGWlsbSpUt58sknParLmy2wIUOGkJaWxnfffUenTp1YvHgxCxcu9ErZ1gIzxpTqBOwr9zzDva3OSkpKahyBqKoUFBQgIkRERNSnugapoKCAPXv2sG3bNg4edP0tccstt1BQUEB8fDwzZ85k0aJFtGnThhUrVnD11a5G9ubNmykpKWHgwIE8/vjj9OnThwULFng1tsmTJzNs2DB27dpFdHQ0//jHPwAYM2ZM2ejGJk2a8OKLL3LVVVfRp08fJkyYQL9+/bxSv7XAjDGlKmsinXkBAxCRmbi6GYmJiamywD179nDixIlqE9jq1asZO3Ysy5Yt46KLLqpdxA1YcXExmZmZfP/996gq5513Hh06dABc63O9//77Z5yzZs0ann32WcDV8t20aRNRUVE+i3HRokWVbl++fPlpz8eMGcOYMWO8Xr8lMGNMqQygc7nn0UClNwmp6jxgHsDgwYMrTXLg2QCOxMRE8vLyvPZXeagrnZl9//79FBYWll0/rOpm5PI2bnSNuTl+/DhhYWE+TV7BwBKYMabUe8CvRWQxcBGQ7Y3rXyJSZXIqKCjgzTffZOzYsbRs2bI+VTUIOTk57Nu3j7y8PFq0aEH37t3r9L5ERUWV3f/VkFkCM6aREJFFwAigrYhkAI8ATQFUdS6wHNcQ+t24htHfWt86HcchLi6uyqU6VqxYwdGjR4N65nl/OXXqFKmpqURERNCtWzfOOeccm5GkBpbAjGkkVHVyDfsVmOXNOmu69ygxMZF27doxatQob1YbMgoLCzl27Bjt2rWjWbNm9OjRg6ioKJuJxEP2LhljfOLkyZPs3r272gR211138Ze//IUmTRrn39JZWVlla3QBtGrVypJXLXj0TonIOBFREeldw3F3iUjzcs+Xi0jrugQmIsUisrncT2xdyilXXoKIjCn3/DoRub8+ZRpjqrZt2zZUtdoEdumllzJx4kQ/RhVYpUucZGdnA3DeeefRr1+/GmfpN5XzNNVPBv4DTKrhuLuAsgSmqmNU9VidIoM8VU0o97OndIe41PbPlARc/fulsb2nqt6b198Yc5qaRiA+//zzXp+GKZjl5OSwY8cO9uzZw+HDhwEIDw/3aHShqVyNSUBEWgKXAr/AncBEJFxE/igiKSLiiMj/iMhvgI7AZyLymfu4PSLSVkT+ICJ3lCvzURGZ7X78OxH52l3OY9XEESsiO0Tkr8BGoLOI/E1E1ovItvLnisgQEVkjIltEZJ2ItAIeBya6W3MTRWS6iLzoPr6LiHzijuETEYlxb58vIi+4y/pWRMbX8v01ptFyHIeWLVsSGxt7xr69e/dy11138cEHH/g/MD/Ly8sjLS2N1NRUioqK6Nq1K127dg10WA2CJx3PY4FkVU0VkSMiMgjXENuuwAWqWiQi56rqERG5GxipqocqlLEYeA74q/v5BOBqEbkS17xrQ3HdRPmeiAxX1c+Bs0Rks/v474DfAr2AW1X1DgARmeOuNxz4REQGADuBN4CJqvq1iJyNa0TVw8BgVf21+9zp5eJ7EdcUOgtEZAbwgvt1A3QAfgL0xjXM+C0P3jPcdXh0s6cxDVHp7OeVXdMpvQF2ypQp/g7LbwoLCzlw4ABZWVmEh4cTHR1N+/bt7RqXF3mSwCbjSj7gSkSTgW7AXFUtAlDVI9UVoKqbRKS9iHQE2gFHVXWvu9V2JbDJfWhLXAntc9xdiKVluK+BpavqV+WKnuBOEk1wJZq+uGYOOKiqX7vrznGfX12Iw4Ab3I9fB/5fuX3vqmoJsF1EarUet6c3exrT0KgqjuMwYcKESve9/vrrXHLJJXTr1i0A0flWSUkJmZmZHDx4kJKSEtq3b0+HDh1o2rRpoENrcKr9U0BE2gBXAH8XkT3A74CJ7vNq+4X8FjDeff7i0iqA35e7zhWnqv+opoyT5WLrCtwD/JeqDgCWAZHuMuubLMqff6rcY7spwxgP7N+/n6NHj1Z6/ctxHLZt29ag7/06dOgQZ599Nv379ycmJsbvyeu2225j9erVNR6XkZFRr3qSk5Pp1asXcXFxPP101UMKYmNjiY+PJyEhgcGDB9erzvJqasuOx9W11kVVY1W1M67uvI3Ar0SkCYCIlC7JeRyoau6SxbiuoY3nx264D4EZ7utsiEgnEWnvYexn40po2e6W0Wj39p1ARxEZ4i4zyh1ndbGt4ccBKlNxDVgxxtRRdQM4UlNTadu2baWts1BVestAcXExYWFh9OnTh7i4uIAN0Fi7di0XX3xxlftVlWeeeYZp06aVTbpbW8XFxcyaNYsVK1awfft2Fi1axPbt26s8/rPPPmPz5s2sX7++TvVVpqYENhl4p8K2JbgGa+wFHBHZApR2ZM8DVpQO4ihPVbfhSiD7S6enUdWPgIXAlyKSgiuxeTR5l6puwdX1uA14FVjt3l6Aq5X3F3dsK3G1zD4D+pYO4qhQ3G+AW0XEAaYBd3oSgzGmcqUJrPwKwKVuuukmDh48SJs2bfwdlteVLtZYUlJCbm5u2f1c/rivbcuWLQwfPpy+ffsSFhaGiPDII4+wY8cOevbsSXh4OCNGjGDXrl0AHD58mP79XeuYighxcXGMGjWqzmtzrVu3jri4OLp160ZERASTJk1i6dKlXnt9nqj2XVbVEZVse6Hc07sr7PsL8Jdyz2Mr7D/j06yqz+NaBbbi9pYVnu8B+lfYNr2KuL8GKvvzY0iF5/PLlX1FJeVMr/DcJmszxgOO49ClSxdatWp12vbc3FzOOuuskL9xubCwkIMHDyIidO7cmaioKPr37++3ARr5+flMnDiR1157jaFDh/LQQw+Rn5/Po48+yrPPPlu2pMru3bvp0aMH8OOgmlLjxo1j3LhxlZZ/2WWXcfz48TO2//GPf+SnP/0p4Oom7tz5x7mfo6OjWbt2baXliQhXXnklIsJtt93GzJkz6/bCKwjtT5ExJihVNYXUrFmz2LFjB19++WVIzvOXn59PdnY2W7dupbi4mPbt26OqiIhfRxd+/PHHDBo0iKFDhwKurtrk5GREhA8//JB//vOfpKen06lTp7K4aprWqzxPFrQsbX2WV9X/6erVq+nYsSM//PADo0aNonfv3gwfPtyjWKpjCayWRCQe10jF8k6pqi1kZAyuSWl37tzJ2LFjT9uem5vLkiVLuOmmm0IueZWUlLB48WIeeOABXn75Zbp37050dDRnnXUWI0aMOOP4CRMmcMcdd5Cbm1vpOljTp09n+vTpHDp0iPHjT7+9dNWqVTXGs3Xr1tNaUxs3bmTQoEHk5uZy7NgxOnbsyNKlS09LWBs2bPB41hNPWmDR0dHs2/fj+qcZGRlVdkeWbm/fvj3jxo1j3bp1lsACQVVTcM3qYYypxI4dOyguLj7jr/3333+f48ePh9zowy+++ILZs2fz9ddfc8EFF3DeeeeVdcsFSps2bfj0008B16CYt99+mzVr1vDZZ58xcuRIwHWNLD8/H4C0tDSWLl3Kk08+6VH5nrTAhgwZQlpaGt999x2dOnVi8eLFLFy48IzjTp48SUlJCVFRUZw8eZKPPvqIhx9+2NOXWi1LYMYYr6pqBGJiYiLR0dFcfvnlgQir1oqKipg0aRJLliyhU6dOLFiwgJtvvrlsUESp6lpMzZs3r3Z/27ZtPWpxVTR58mTee+89+vfvT9u2bVm0aBFt2rRhxYoVZS26zZs3c9ZZZzFw4EAGDBhAnz59WLBgAQ899FCt66tMkyZNePHFF7nqqqsoLi5mxowZZeu+jRkzhr///e907NiRzMzMsmttRUVFTJkypewaXb1j8Eopxhjj5jgOkZGRxMXFlW3LysoiOTmZu+++O+hnosjNzaV58+Y0adKE9u3b88QTT3D33XfTvHnzmk/2k5YtW/L++++fsX3NmjU8++yzgOv/YdOmTT5dlXnMmDGVdpEuX7687HG3bt3YsmWLT+q3BGaM8SrHcejXr99pIw2joqJITExk0KBBAYysZv/+97+54YYb+OSTT0hISOCvf/1rzScFkY0bNwJw/PhxwsLCfJq8gkFw/ylkjPEaEblaRHaJyO7KlhISkREikl1uCaM6XaiobLRbZGQkEydODPi1o8qoKpmZmQAMHDiQUaNGBVVrqy6ioqJITU0NdBg+ZwnMmEbAPeH1S7hmrOkLTBaRvpUc+kW5qd0er209mZmZZGZmnpbAvv32W37/+9+XLSESTFavXs2wYcO48sorKS4upnXr1ixevJiePXsGOjTjAUtgxjQOQ4Hdqvqte7aaxcD13q4kJSUFOH0Ax+uvv86cOXPIy8vzdnV19s033zB+/Hh+8pOfsHfvXu680ybfCUWWwIxpHDoB+8o9z3Bvq2iYex29FSLSr7aVVJxCSlVJTExk5MiRREdH1z5qLzty5Ai//e1v6dOnD8nJyTz22GOkpaUxY8YMwsPDAx2eqSUbxGFM41DZncMVp1LYCHRR1RMiMgZ4F9fyRmcWVsVad47j0KFDB9q1awe45svbvXs3Dz74YL1fQH2cOnWKl156iSeeeIKcnBxmzJjB448/TocOHQIal6kfa4EZ0zhkAJ3LPY8GTpuGXFVzVPWE+/FyoKmItK2sMFWdp6qDVXVwabKCMwdwJCYmEhkZyQ033FBZMX5z5ZVXMnv2bC666CI2b97MK6+8YsmrAbAEZkzj8DXQQ0S6ikgEruWD3it/gIicL+45nkRkKK7vB49HXhQVFbFt27bTElhOTg433HDDGZP6+sO6desoKCgAYPbs2SQnJ5OcnFzpDPkmNFkXojGNgKoWicivca3BFw68qqrbRORX7v1zca3Vd7uIFAF5wCStbMbWKqSmplJQUHBaAluwYAElJSXefCke2bRpExdddBEvvfQSd9xxB9ddd53fYzC+ZwnMmEbC3S24vMK2ueUevwi8WNfyK04hlZ2dTatWrfw288bRo0f56quvGD16NAkJCbz66qvcdNNNfqnbBIZ1IRpjvMJxHJo0aULv3r05fvw4nTp1KpvWyJcKCgp4/vnniYuLY/z48Rw7dgwR4dZbb6VlS1vCryGzBGaM8QrHcejTpw8RERG88847nDx5stpl7etLVXn77bfp168fd911F4MGDWLNmjW0bt3aZ3WGittuu43Vq1fXeFxGRka96klOTqZXr17ExcXx9NNPV3ncjBkzaN++fdmK0N5iCcwY4xXlRyAmJibSrVs3nyWw0vWkbrzxRiIiIli+fDkfffQRAwcO9El9oWbt2rXVvveqyjPPPMO0adM4cOBAlcdVp7i4mFmzZrFixQq2b9/OokWL2L59e6XHTp8+neTk5DrVUx1LYMaYejt69Cj79u1jwIABHDhwgE8++YSbb77Z6wtX7tmzh8mTJ3PRRReRmprKyy+/zJYtWxg9enTILZJZX1u2bGH48OH07duXsLAwRIRHHnmEHTt20LNnT8LDwxkxYkTZ8i+HDx8uawGJCHFxcYwaNarKRShrsm7dOuLi4ujWrRsRERFMmjSJpUuXVnrs8OHDOffcc+v2QqthgziMMfVWfgqpRYsWUVJSwtSpU71ez7333sv777/PnDlzuO+++xr8bOtVyc/PZ+LEibz22msMHTqUhx56iPz8fB599FGeffbZsvW2du/eXTaBsuM4p91CMG7cuLJ1uiryZEXm/fv307nzj7cWRkdHs3btWq+9Rk9YAjPG1Fv5EYgJCQm0b9/eKxPiFhYW8vLLLzNq1Ch69erFH//4R/785z8HxbRUpUaMGFHjMddccw333HNP2fHTp09n+vTpHDp0qGwBylKeLHD58ccfM2jQIIYOHQq43vfk5GREhA8//JB//vOfpKen06lTp7JRoJWtElAVT1ZkruwOC3+3gi2BGWPqzXEc2rRpQ4cOHRARpk2b5pVyjx49yoMPPkhWVhaPPfbYadNWNWZbt249rTW1ceNGBg0aRG5uLseOHaNjx44sXbr0tIS1YcMGJk6c6FH5nrTAoqOj2bfvx+k1MzIy6twdWVeWwIwx9Vb61/38+fNp2rQpN998c53LWr9+PQsWLOCFF16gffv2bNmyhdjYWO8F62WetJiqOr5t27a1Ph+gTZs2fPrpp4DrBvK3336bNWvW8NlnnzFy5EjAdY0sPz8fgLS0NJYuXcqTTz7pUfmetMCGDBlCWloa3333HZ06dWLx4sUsXLiw1q+lPmwQhzGm3lJSUoiPj+eRRx6p85fY3r17ufnmmxkyZAhvvPEG3333HQBdu3ZtdAM0ajJ58mROnDhB//79mTlzJosWLaJNmzasWLGi7PrX5s2bKSkpYeDAgTz++OP06dOHBQsWeC2GJk2a8OKLL3LVVVfRp08fJkyYQL9+rgUMxowZc9roxsmTJzNs2DB27dpFdHQ0//jHP7wThKrajx9+LrzwQjXGV4D1GqDPdv/+/RXQe++9VwFNSkqqVezZ2dl6//33a7NmzTQyMlIffPBBzc7OrvN74Wvbt28PdAhVuuCCC7SgoEBVVbt37645OTkBjqh2Kntvq/tsWxeiMaZeSheq3LVrFy1atOD66z1bJ7OwsJBXXnmFRx99lKysLKZNm8aTTz5p17nqYePGjQAcP36csLCwBj9K07oQjTH1kpubi4iwatUqbrzxRlq0aFHjOR9++CEDBgxg1qxZ9O3bl/Xr1/Paa69Z8vKSqKgoUlNTAx2Gz1kLzBhTL3l5ecTGxtKqVSuPB2+kpqaiqixdupRrr73WrnGZOrEWmDGmXvLy8hg8eDCbNm0qG2Jd0cmTJ7nlllt49dVXAbj99ttJSUnhuuuus+Rl6sxaYMaYejl16hS9evUCzryRtaSkhLCwMJo3b05GRgaHDh0CXCPYjKkva4EZY+rtmWeeIT09vex5UVERc+fOpWfPnmRmZiIirFy5knvvvTeAUXqPa3Cc8aa6vKeWwIxpJETkahHZJSK7ReT+SvaLiLzg3u+IyCBPy+7cuTMxMTGoKsuWLWPAgAHcfvvtdOzYkZycHAC/LWzpa5GRkRw+fNiSmBepKocPHyYyMrJW51k73phGQETCgZeAUUAG8LWIvKeq5de/GA30cP9cBPzN/W+N9u/fzznnnEN2djYA559/Pu+88w7XX399g7vGFR0dTUZGBllZWYEOpUGJjIys9RyXlsCMaRyGArtV9VsAEVkMXA+UT2DXA6+5bx79SkRai0gHVT1YU+F5eXll94MBZGdnc/LkyQaXvACaNm1K165dAx2GwboQjWksOgH7yj3PcG+r7TEeycvLY86cOXU51RiPWQvMmMahsqZQxYs4nhzjOlBkJjCzugr37t3rWWTG1JElMGMahwygc7nn0UDFteQ9OQYAVZ0HzAMQkUqTnM2qYXxNbCSNf4jIcWBXoOOoRlvgUKCDqEIwxwbBEV8XVW1X1U4RaQKkAv8F7Ae+Bqao6rZyx/wM+DUwBtfgjRdUdWhNFVeRwEqAdOBIbV6EHwXD/1ldhGLc9Y25ys+2tcD8Z5eqDg50EFURkfXBGl8wxwbBHx+AqhaJyK+BD4Fw4FVV3SYiv3Lvnwssx5W8dgO5wK0eFr8h2F9/RaHwf1aZUIzblzFbAjOmkVDV5biSVPltc8s9VmCWv+Mypq5sFKIxxpiQZAnMf+YFOoAaBHN8wRwbBH98vhaKrz8UY4bQjNtnMdsgDmOMMSHJWmDGGGNCkiUwY4wxIckSmB/UNAt4IInIHhFJEZHNIrI+COJ5VUR+EJGt5badKyIrRSTN/e85QRTboyKy3/3+bRaRMYGILRCC+XNdnWD7zFclmH8XquLv3xFLYD5Wbhbw0UBfYLKI9A1sVGcYqaoJQXJ/yXzg6grb7gc+UdUewCfu54EwnzNjA3jW/f4luIeqN3gh8rmuTjB95qsyn+D9XajKfPz4O2IJzPfKZgFX1QKgdBZwUwlV/ZwzZ2+4HljgfrwAGOvPmEpVEVtjZZ9rHwvm34Wq+Pt3xBKY73lthm8fUeAjEdngnqA1GJ1XuqSH+9/2AY6nol+7F4B8Ndi6dHwo2D/X1QmFz3xVgv13oSo++R2xBOZ7Hs/wHSCXquogXF1Bs0RkeKADCjF/A7oDCcBB4E8BjcZ/gv1zXR37zPuXz35HLIH5nsczfAeCqh5w//sD8A6urqFgkykiHQDc//4Q4HjKqGqmqharagnwCsH5/vlCUH+uqxMin/mqBO3vQlV8+TtiCcz3vgZ6iEhXEYkAJgHvBTgmAESkhYhElT4GrgS2Vn9WQLwH3OJ+fAuwNICxnKb0y8RtHMH5/vlC0H6uqxNCn/mqBO3vQlV8+Ttik/n6WFWzgAc4rFLnAe+4l31vAixU1eRABiQii4ARQFsRyQAeAZ4G3hSRXwB7gZuCKLYRIpKAq/tsD3BbIGLztyD/XFcn6D7zVQnm34Wq+Pt3xKaSMsYYE5KsC9EYY0xIsgRmjDEmJFkCM8YYE5IsgRljjAlJlsCMMcaEJEtgxhhjQpIlMBMSRCQ60DEY4232ua4fS2AmqInL74DXRaRjoOMxxhvsc+0dlsBMwInIKhHp5X7cpvxieOq60343sLJ0DjtjQoF9rn3PppIywSAOSHM/HgCklN+pqu/gmnTVmFBin2sfsxaYCSgR6QLsd89UDa5fdCeAIRlTb/a59g9LYCbQEjj9F/tC7BfdhL4E7HPtc5bATKANBCIBRKQHriXTU6o9w5jgZ59rP7AEZgItAQgTkS3Aw8AOflzvyJhQlYB9rn3OllMxASUiu4ELVPV4oGMxxlvsc+0f1gIzAeNeGbfEfslNQ2Kfa/+xFpgxxpiQZC0wY4wxIckSmDHGmJBkCcwYY0xIsgRmjDEmJFkCM8YYE5IsgRljjAlJlsCMMcaEJEtgxhhjQpIlMGOMMSHp/wNaWVOO2amfuQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(\"{:20s} {:>7s} {:>7s} {:>7s}\".format(\"Name\", \"mu\", \"mu_star\", \"sigma\"))\n",
    "for name, s1, st, mean in zip(morris_problem['names'], Si['mu'], Si['mu_star'], Si['sigma']):\n",
    "    print(\"{:20s} {:=7.2f} {:=7.2f} {:=7.2f}\".format(name, s1, st, mean))\n",
    "    \n",
    "fig, (ax1, ax2) = plt.subplots(1,2)\n",
    "mp.horizontal_bar_plot(ax1, Si) #  param_dict={}\n",
    "mp.covariance_plot(ax2, Si, {})\n",
    "plt.title('Sensitivity_Analysis')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "5f66dfb7-5a7f-4646-bb94-8c38aec97343",
   "metadata": {},
   "outputs": [],
   "source": [
    "fig.savefig('Sensitivity_Analysis.png',dpi=300)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5e49e202-2372-40df-a03c-ab398bdbf6a6",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7e5951d3-d0c9-438b-a083-3ff03808eac5",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fdeabd3d-795c-4aa1-800a-0931d9ed73dd",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a2b85cc3-4e3c-4f16-8f72-ee015ffc3b99",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f22cd318-e164-4740-9a6a-e995bd5ba5b5",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}