Model_MM_and_Hill.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "frank-korea",
   "metadata": {},
   "source": [
    "# kinetic Modeling with ODE Solver"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "scheduled-german",
   "metadata": {},
   "source": [
    "Description"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "comic-master",
   "metadata": {},
   "source": [
    "### Imports\n",
    "Import packages and set global varibales used in this notebook"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "advanced-forward",
   "metadata": {},
   "outputs": [],
   "source": [
    "import os # operating system to work with directories and files\n",
    "import matplotlib.pyplot as plt # plot data and results\n",
    "import seaborn as sns # prettier visualization\n",
    "import pandas as pd # convert excel to dataframe\n",
    "import numpy as np # convert dataframe to nparray for solver\n",
    "from scipy.integrate import odeint # solve ode\n",
    "from lmfit import minimize, Parameters, Parameter, report_fit # fitting\n",
    "from pyenzyme.enzymeml.tools import EnzymeMLReader # EnzymeML document functionalities"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "gorgeous-press",
   "metadata": {},
   "source": [
    "## Select EnzymeML document\n",
    "Select the EnzymeML document created with BioCatHub, by changing the path vriable accodingly. <br>\n",
    "The whole EnzymeML document is stored in the enzmldoc varible. <br>\n",
    "Prints a short overview."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "environmental-string",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      ">>> Units\n",
      "\tID: u0 \t Name: ml\n",
      "\tID: u1 \t Name: K\n",
      "\tID: u2 \t Name: mmole / l\n",
      "\tID: u3 \t Name: ug\n",
      "\tID: u4 \t Name: sec\n",
      ">>> Reactants\n",
      "\tID: s0 \t Name: ADP\n",
      "\tID: s1 \t Name: ATP\n",
      "\tID: s2 \t Name: AMP\n",
      ">>> Proteins\n",
      "\tID: p0 \t Name: thermostable adenylate kinase\n",
      ">>> Reactions\n",
      "\tID: r0 \t Name: ATP formation\n"
     ]
    }
   ],
   "source": [
    "path = 'datasets/Hathaway/Experiment Hathaway.omex'\n",
    "\n",
    "# check for correct file path and file extension:\n",
    "if os.path.isfile(path) and os.path.basename(path).lower().endswith('.omex'):\n",
    "    enzmldoc = EnzymeMLReader().readFromFile(path)\n",
    "    print(enzmldoc)\n",
    "else:\n",
    "    print('Incorrect file path.')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "further-lounge",
   "metadata": {},
   "source": [
    "## Visualization of timecourse data\n",
    "A short visualisation to get a first impression of the data. <br>\n",
    "First select the reaction to visualize by changing the reaction_id accordingly, see overview above for selction options."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "chubby-workshop",
   "metadata": {},
   "outputs": [],
   "source": [
    "#basic/general settings\n",
    "sns.set_theme(style=\"whitegrid\", palette ='bright',color_codes=True, context = 'notebook')\n",
    "\n",
    "# set reaction id to 'r0' or 'r1'\n",
    "reaction_id = 'r0'\n",
    "reaction = enzmldoc.getReaction(reaction_id)\n",
    "reaction_name = reaction.getName()\n",
    "educts = reaction.getEducts() # list of tuples: (Reactant ID, stoichiometry, Constant, Replicate, Initial-Concentration)\n",
    "products = reaction.getProducts()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "automated-setup",
   "metadata": {},
   "source": [
    "Visualize educts, if the EnzymeML document contains time course data for educts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "wound-trance",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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P06ZNw/bt23H8+HGzBEtERFRfiouL4enpyQKiFjY2Nmjbti3s7Ozw3XffITs7u2YbXZ0sWLAAo0ePhkKhQGBgIJYvX26WYImIiOoTCwjdbGxsIAgCbGxsVAtlVqXz44zS0lL06dMH69atQ5cuXeq8LgUREVFTsHbtWhw8eBB2dnZ466234O/vX2v7iIgI/POf/8SiRYtU+3x9ffHoo48CuPfzuH///pg1axYEQcDAgQPRtm1b2NjYQBRFuLq6YuXKlXBxcTF5LoIgoLy8vMZ+nWWYg4MDDh8+DKVSid9//13rzRVERER0z6lTp/Drr79ix44deP/997F48eJa28tkMnTv3h2//PKL2iSPLVu2REJCAhISErB9+3bcunULX331ler4pk2bkJCQgK+++gqdOnXCrl27zJaTJjqLiKVLl2LXrl0oKCjApk2b8Pbbb9dDWERERI1DVlYWxo8fj0mTJiEyMhLXr1+HTCZD//79IQgC2rVrh4qKCuTn5yM1NRVJSUk1+tixYweGDh2KwYMHIzk5WeM4giDgueeew549e2ocE0URd+/erXWFbXPQ+nFGWVkZAMDNzQ3vvvtuvQVERETUmKSnp8Pf3x8xMTHIyMjA3bt3UVhYCFdXV1UbZ2dn3L17t8aaUgBQWFgImUyGZcuWoVu3bnj11VcxadIkjWO1bt0aBQUFqu1p06ap7lvw9/fHyJEjTZ1erbQWEcOGDYMgCBBFEYIgAIDq9f79++stQCIiooZszJgx2LhxI6ZPn47mzZsjOjoaLi4uKCoqUrUpKipC8+bNNZ6/e/duKJVKvPjiiwCAvLw8HDlyBH369KnRNjs7G23atFFtb9q0yaL3KmotIg4cOKC2fevWLbi6usLW1tbsQRERETUW+/fvR0BAAKKiovDdd9/hs88+w8SJE7F69Wo8//zzuHHjBpRKJdzc3DSev3PnTqxfv141D8Pu3buRmJhYo4hQKpXYtGkTwsLCzJ6TvnQ+nXH06FHMnz8fLi4uuHPnDpYuXYp+/frVR2xEREQNnq+vL+bOnYt169ZBqVTizTffRK9evRAYGIhx48ZBqVRi4cKFAIDU1FQUFxdj3LhxAO7dgCmKotpETkOHDsWKFStw/fp13L59G5MnT1Y9HdG3b1+MGTPGInlqorOI+OCDD5CYmAhPT0/k5OQgKiqKRQQREdF9HTt2xLZt22rsnzlzJmbOnKm2r/o9Eb169cK3336rts/BwQFHjhwBAJw8eVLruNU/MbAEnU9n2NrawtPTEwDg6enJeSKIiIgIgB5XIlxcXJCQkIB//etf+O2339CyZcv6iIuIiIgaOJ1XIlavXo1r164hPj4e169fxzvvvFMfcREREVEDp/NKhJOTEyIiIiCXyyEIAi5fvqxz6k4iIiKyfjqLiBdeeAFlZWVo2bKlap6ItWvX1kdsRERE1IDpLCLkcrnaPN1EREREgB73RAQGBuLw4cO4du2a6g8RERFZhj7TLOTn52Po0KGQy+U621ZUVGDWrFn46aefDI5F55WIW7du4Z133kGLFi0A3FsA5OuvvzZ4ICIiIjK/w4cP47333kNeXp7OtleuXMGcOXOQk5Nj1CRWOouIixcv4ocffjC4YyIiosZgSxqw2cQ/5qYOB6TDam+za9cufPPNN1AqlZg8eTK+/PJL2NjYICAgAP/3f/+HNWvW4OLFi7h16xbu3LmD2NhYBAYG6hzbxsYGX3zxBUaPHq2zbXFxMZYvX46NGzfqm5oanUVEjx498Pvvv6Nnz56qffb29kYNRkRERA+0aNECK1asQGRkJL755hs4OjoiJiYG//3vfwEAzZo1w5YtW3D+/Hm88cYb2L17t84+DZlV2sfHx+jYAT2KiN9++w0HDx5Ubeu7imdqairWrVsHhUKBqVOnYuLEiWrHT58+jdjYWBQWFiIwMBCLFy+GnZ0dcnNzERsbi9zcXDRr1gxxcXFo37694ZkRERHpQTpM91UDc+ncuTOuXLmC/Px8vPDCCwDurfh55coVAEBQUBAAwNvbGzdv3rRMkLXQeWNlamoqDhw4oPqjTwGRk5OD+Ph4bN26FSkpKUhKSsKFCxfU2sTExGDBggX48ccfIYoitm/fDgCYM2cOBgwYgOTkZERERCAuLs7I1IiIiBo2GxsbtG/fHm3btsWmTZuQkJCASZMmoXfv3gDuLdAFAOfOnVMtQdGQ6LwS8fXXXyMpKUntDs89e/bUek56ejqCgoLg6uoK4N6KZGlpaYiKigJwbz300tJS1Zs0atQofPTRRxg2bBjOnDmDL774AgAwevRojeupExERWQs3NzdMnToVkydPRkVFBby8vDB8+HAA967aT5kyBSUlJVi6dKmFI61JZxGxZcsWbNiwwaA1M3Jzc+Hu7q7a9vDwQGZmptbj7u7uyMnJwdWrV9GuXTu88847OHr0KNq1a4cFCxboPS4REVFjMWrUKNXriIgIRERE1GgTGhqKCRMmqO2rvF9CF0NW+Vy5cqXebavS68bKtm3bwtbWVu9ORVGssU8QBJ3Hy8vL8ccff2DmzJmYP38+duzYgXnz5iEhIUHvsWtbNtUQMpnMJP00FszX+jW1nJmvdWtq+VaXlJSE7777rsb+119/HY8++qjavszMTKxevbpG2+HDhyMyMrJOcegsIoKCghASEoIOHTqopr3esmVLred4enoiIyNDtZ2bmwsPDw+141VvEMnLy4OHhwfc3d3h7OyMAQMGAABGjBiBZcuWGZSQr69vnZcrl8lkCAgIqFMfjQnztX5NLWfma90MyVcul5vsl8v6NnPmTK3Hxo0bh3HjxunVj7+/v0G/jBtCZxGRlJSEDz74AM2bN9e70759+2LNmjXIz8+Ho6Mj9u7dq/ZZjpeXFxwcHFTfCMnJyQgODkbHjh3h6emJQ4cO4cknn8R//vMf9OrVy7jMiIiIyKx0FhGenp7w8/ODjY3OBznUzomOjoZUKoVCocCYMWPg7++PGTNmYNasWfDz80NcXBxiY2NRVFSEnj17QiqVAgDWrl2LRYsWYfXq1XBxcTH6cxoiIiIyL51FRFlZGSIiIuDt7a26r+G9997T2XF4eDjCw8PV9lWdEcvHxwc7d+6scV6XLl3MdtmFiIiITEdnEfHiiy/WRxxERETUyGj9jOL5558HADz22GM1/lQ9TkRERPVH17TWmzdvxtixYzF27FisXbtWZ39mWcXz6NGj6N+/v9YTb9++bfBgREREZD5Xr17F7t27sWPHDtjY2GDChAkICQnRukaG2VbxbKyPxBARERnkf1uAY5tM2+c/pwGPSmttYo5VPNu0aYPPPvtMNbdTeXl5rdMemH0VTyIiIjIPU6/iKZFI4ObmBlEUsWrVKvTs2ROdO3fW2t7sq3gSERFZtUelOq8amIs5VvGUy+V466234OzsjEWLFpkn8Pv0n/yBiIiITMrUq3iKoohXXnkFPXr0wJIlSwxassIYOq9EJCcn49NPP0VZWZlq2mt9lgMnIiIi3Uy5iue+ffvw66+/oqysDIcPHwageT0NU9FZRGzcuBHr169H27ZtzRIAERFRU2SOVTwHDx6MEydOGByL2Vbx7NChAzp16mRU50RERGR6jWYVz2bNmmH69Ol45JFHVNNev/7663UalIiIiGpnFat4Pvnkk2YZmIiIiBo3nU9nhIeHo7i4GJmZmbhz5w7CwsLqIy4iIiJq4HQWEQsXLsTVq1fRr18/ZGdnIzY2tj7iIiIiogZO58cZly9fRmJiIgAgJCQE48ePN3tQRERE1PDpvBIhl8tRUlICACgtLUVFRYXZgyIiIiLNdK3imZiYiNGjR2PMmDHYs2ePzv7MsopnJalUioiICHh7e+PChQu13i1KRERElpOfn49t27bh22+/hVwuR1hYGIYPH656urI6s63iWenpp59GcHAwrl69ivbt26NVq1YGD0JERNRQ7bi5B0l5NedcqItx7iMwtnVorW3MsYqnm5sbkpOTYWdnh+zsbDg4OGgtIAAzruL5ySef4JVXXsHrr79eI4D33nvPqMGIiIjoAVOv4gkAdnZ2+Oqrr7BmzRpMnjy51rZmW8Vz4MCBAMAbKYmIyKqNbR2q86qBuZhjFU8AmDRpEp599lnMmDEDv/zyi6ofU9N6Y6W3tzfKysqwZcsWPProo+jduzf8/f2xdu1aswRCRETU1Jh6Fc+LFy8iKioKoihCIpHA3t4eNjbmW7Bb65WIb775BuvXr8fNmzcxbNgwiKIIW1tbBAQEmC0YIiKipsaUq3h26dIFPj4+GDduHARBwBNPPIHHHnvMbLFrLSKeffZZPPvss9i5c6dRd2wSERGRduZYxRMAoqKiEBUVZVAsZlvF81//+hc+/fRTKBQKAEBubi6WLFli1GBERERUd41mFc833ngDgwcPxrFjx+Dh4YHi4uI6DUhERES6NYZVPHXebeHk5IQXX3wRnp6eWLlypUF3hxIREZH10llECIKAvLw8FBUVobi4WO8rEampqQgNDcXgwYNVa29Udfr0aYwePRpDhw7F/PnzUV5ernb8jz/+gK+vr55pEBERUX3TWURERUVh3759iIiIQEhICPr06aOz05ycHMTHx2Pr1q1ISUlBUlISLly4oNYmJiYGCxYswI8//ghRFLF9+3bVsZKSEixZskR1HwYRERE1PDqLiMzMTEyYMAGDBg1Ceno65s6dq7PT9PR0BAUFwdXVFU5OThg6dCjS0tJUx7Ozs1FaWqp6DnbUqFFqx1euXImpU6cang0RERHVG51FxKFDhwxeuTM3Nxfu7u6qbQ8PD+Tk5Gg97u7urjq+f/9+lJaWYtiwYQaNSURE1BToWsUTAJRKJaZPn45t27bpbGvWVTwLCgrwxBNPoH379hAEAYIg4Ouvv671HFEUa+yruv6GtuN5eXlYt24dNm/erEfomp08edLoc6uSyWQm6aexYL7Wr6nlzHytW1PL11AffPAB7ty5o7Od2VfxXLNmDSQSiWr79u3bOjv19PRERkaGajs3NxceHh5qx6s+5ZGXlwcPDw8cPHgQf//9NyZOnKg6FhERgcTERLi4uOjOBoCvry8cHBz0aquNTCZrUjNzMl/r19RyZr7WzZB85XK5zl8uS7ZsRcmmLaYITcVxmhSO0trnYDDHKp4AkJaWppqtUpe6ruKp9eOMvLw8ZGVlYc6cOVAoFCgrK0NpaSkWLlyos9O+ffviyJEjyM/PR0lJCfbu3Yvg4GDVcS8vLzg4OKgqyeTkZAQHB2Ps2LHYt28fUlJSkJKSAgBISUnRu4AgIiJqTFq0aIF169Zh7dq12Lx5M7Zt24acnJwaq3iuXr1ar4kez507h++++w6vvfaaXuP7+Piga9euRsev9UrE8ePH8eWXXyIrKwsLFiwAcG+hkP79++vs1NPTE9HR0ZBKpVAoFBgzZgz8/f0xY8YMzJo1C35+foiLi0NsbCyKiorQs2dPSKVSo5MgIiIylqM0UudVA3Mx9SqeycnJyMnJwZQpU5CdnQ2JRAIvLy+1X+RNSWsRERISgpCQEBw6dAhPPvmkwR2Hh4cjPDxcbV/VyyU+Pj7YuXNnrX2cPXvW4HGJiIgai+qreEokEuzatQuPPPII9u3bh1OnTiEiIkLvVTznzJmjer1mzRq0bt3abAUEoMc9ER4eHnj77bchl8tV+1asWGG2gIiIiJoSU67iWd90FhHz5s3DpEmT0KZNm/qIh4iIqEkw1yqelWpbe6M6s63i2bp1a4wdO9aozomIiMj0Gs0qnl5eXtiwYQMeeeQR1VwP+txcSURERMZrDKt46iwiFAoFsrKykJWVpdrHIoKIiIh0FhErVqxAVlYWrly5gh49eqhNGkVERERNl84i4quvvsK///1v3L59G8888wwuX76s14RTREREZN10LsD1/fff44svvkDz5s0xZcoUHD9+vD7iIiIiogZOZxEhiqJq4S0AsLe3N3tQREREpJmuVTyXLVuGUaNGYfLkyZg8eTLu3r1ba/uSkhKMHz8ef/75p8Gx6Pw4Y8SIEZg4cSKuXbuGGTNmICQkxOBBiIiIqH6cOnUKn332Gdzc3HS2PXHiBBYtWoScnByjxtJZREyaNAlBQUE4f/48unTpgh49ehg1EBERUUN0KqUIJ74tMmmffs84o1eEc61tzLGKp1KpVN27ePPmTYwZM6bWJb7Lysrw8ccfq02XbQidRcT27duRlZWFuXPnYtq0aXj66acxcuRIowYjIiKiB1q0aIEVK1YgMjIS33zzDRwdHRETE1NjFc/z58/jjTfewO7du2vtr7i4GJMmTcJzzz2HiooKSKVS+Pr6wsfHR2P7ui4hr7OI2LZtG3bs2AEA+PTTTzFp0iQWEUREZDV6Rei+amAupl7F09HREVKpFI6Ojqrzz5w5o7WIqCudN1ba2NjAzu5erSGRSFQ3WBIREVHdVF/FMyEhAZMmTULv3r0B3Lu/AYDeq3heunQJEyZMQEVFBRQKBY4dO4ZevXqZLX6dVyIGDRqEyMhI+Pv749SpUxg4cKDZgiEiImpqTLmKZ9euXREREYFnn30WEokEERER8Pb2NlvsOouIV155BQMGDEBWVhZGjhxptksiRERETYm5VvGcPn06pk+fblAsxq6tobOIuH79On7++WfI5XJcvHgR+/btQ1RUlFGDERERUd0Zsorn/v37sXnz5hptpVIpBg8eXKc4dBYRr732Gvr06YO2bdvWaSAiIiLSn6lW8Rw0aBAGDRpkqrDU6CwinJ2dER0dbZbBiYiIqPHSWUR4e3vj+++/xyOPPKJ6MqNz585mD4yIiIgaNp1FxOnTp3H69GnVtiAI2LJli1mDsqiyIjTPPQr8WWDpSKqp8mit2mO2Wh651dZGwyO6LjfPApeK69C/qeI0cz/3Of59Brhuq8dYtfejd3sTx19rey1j2Rf9BeS71r1/s7Q3/ftvV3oTuHtD7/YN430wtP2D1zaKQkBe+/oIdR3DdLkZEI+NHWCjcyYCsiCdRURCQgIKCgpw9epVtG/fXq+5uBu1A4vQPf09IN3SgdSfHgDws6WjqD89AeCghYOoZ34A8G9LR1F//gEAaZaOov48CgDfWzoKM/AeBkh/sHQUVAudRcQPP/yADz74AF27dsX58+cRFRWl8TEUqzFoGc7YPAKfhrRGiChW3dCyH3q00dz+3Lmz6O7d3bj+TRVnXfoxsP8LFy6gW9eu+vevV5xa2uvx/tfHuFlZWTU/hjTHuIa2N9P7c/nKZXTq2Env9ob2b/H21dpcvXoVHTq013KeCcYwWQ5aA9K82+tfBvbTNPTr16/WxzwPHTqEjz/+GKIoolevXli0aFGtE0VWVFQgOjoaY8aMQXBwsEGx6CwiNm/ejF27dsHZ2RmFhYWYMmWKdRcRkmYoeqg30Klu84k3JncLWgJdm06+t4tlQM+mky8A5FfI0Ll308n5pq0Mneq4JkBjkiuToUMType0KywsxOrVq7Flyxa4ublh48aNKCgo0PopwpUrVzBnzhzk5OTUulCXNjqLCEEQ4Ox8b05xFxcXODg4GDwIERFRQ3Vh3xac37vJpH16D5mGbiHSWtuYYxXP//3vf+jevTveffddXL16FWPHjq31NoTi4mIsX74cGzduNCpPnUVEhw4dsHLlSgQGBiIjIwMdO3Y0aiAiIiJSZ+pVPAsKCnD06FEkJyfDyckJEydORO/evbU+VVnXWah1FhErVqxAUlIS0tPT0bVrV7zxxht6dZyamop169ZBoVBg6tSpmDhxotrx06dPIzY2FoWFhQgMDMTixYthZ2cHmUyGd955B+Xl5XB1dcU777wDLy8v47IjIiLSoVuIVOdVA3Mx9Sqerq6u8PPzg7u7OwAgMDAQp0+fNtvUDDqfnTl16hQqKiqwcOFCHDt2DOfPn9fZaU5ODuLj47F161akpKQgKSkJFy5cUGsTExODBQsW4Mcff4Qoiti+fbtq//Lly5GSkoLw8HAsW7bMyNSIiIgaNlOv4tmrVy+cO3cO+fn5KC8vx/Hjx9GtWzfzxa+rwZIlS/DUU08BAGbPno3ly5fr7DQ9PR1BQUFwdXWFk5MThg4dirS0B89bZWdno7S0VPUmjRo1CmlpaSgrK8Nrr72murzSo0cPXL9+3Yi0iIiIGoeqq3iOHTsWP/30Ex5++GEAD1bxjI2N1WsVz4ceeghvvPEGpk+fjmeffRaDBw9G9+7ddZ5nLJ0fZ0gkEtV9EB06dICNHhN/5Obmqi6lAICHhwcyMzO1Hnd3d0dOTg7s7e1VT34olUqsXbsWISEh+mdDRETUSJhrFc+wsDCEhYUZFMvKlSsNal9JZxHRrl07vP/+++jduzcyMzPh4eGhs1NRwzPCVZ9R1XW8rKwM8+bNQ3l5OV588UWd41V18uRJg9prI5PJTNJPY8F8rV9Ty5n5Wremlm91hqzimZmZidWrV9doO3z4cERGRtYpDr1urNy2bRsOHTqErl274pVXXtHZqaenJzIyMlTbubm5asWHp6en2g0ieXl5quNFRUV4+eWX4erqinXr1kEikRiUkK+vb50fQ5XJZAhoQs9cM1/r19RyZr7WzZB85XK5yX65rG+mWsXT398fCQkJpgpLjc4iwsHBAVOnTjWo0759+2LNmjXIz8+Ho6Mj9u7dq/ZZjpeXFxwcHFTfCMnJyapZsmJiYtCpUycsWbKk1hm2iIiIyLJ0FhHG8PT0RHR0NKRSKRQKBcaMGQN/f3/MmDEDs2bNgp+fH+Li4hAbG4uioiL07NkTUqkUf/zxB/bv349u3bph5MiRAO7dT2HsJBhERETaKJVKve7za8qUSmWtx81SRABAeHg4wsPD1fZVLQZ8fHywc+dOteM9e/bE2bNnzRUSERERAMDJyQk3btxAmzZtWEhooVQqcePGDSgUCoiiqPF9MlsRQURE1FB17doVp0+fxrVr1/jReS0UCgWysrJQUVGBVq1a1TjOIoKIiJoce3t7+Pn54eeff8axY8dYSNRCFEU8/vjj6NKlS41jLCKIiKhJsrGxQXBwMPr06QOFQmHpcBosiUSi9UlJFhFERNSk1fZDkmrHu0mIiIjIKCwiiIiIyCgsIoiIiMgovCeimrsVRfhNPImCv0stHYpeBNT9juIL4gX8/bfcBNGYJh7jxtXfefEC7vxdZrZYAMu9D9pcEC+g8Ha5pcPQyVTv2znxHIpuV5ikr8bgvHgexbdrnxSovpniaYeuzTqirb3u9ZrIclhEVPNB9iasV24Fzlk6knrGfK1fU5vHjfk2ev5OPvjB9wtLh0G1YBFRzdz2L8E71ws+Pj6WDkUnETVXQzXGmTNnTJKvaaIxZlzDRjZVvtpoWqXWkkSIOHv2LHr06GHpUHQw3ft25uxZ+NQx34b1VazdmbNnGtTX11T/D3Rp1tEk/ZD5sIioxt5GAm+hE3q79LR0KPVGKZTiUZdelg6j/ghyBLj4WjqKemUjKBDQ3N/SYdQbG6EcAc3/Yekw6o2tUI6A5r0tHQY1QbyxkoiIiIzCIoKIiIiMwiKCiIiIjMIigoiIiIzCIoKIiIiMwiKCiIiIjMIigoiIiIzCeSKqqfgrG87fpqL4WKalQ9GPgVPLapqK1unSZZT8ftIk/dcysHnbG9CP06VLKDl5pt7HtWQ/jpcuoeTMhXof11Szfxs6hbLjxSyUnr+oqSNTBWSafkzUv+PFiyi9eNkkfWllgX7s/HrBzrubacYls2ARUU3Jhk1otTwOdy0dSD1yA3DH0kHUo6aWLwA8hKaV80MAbls6iHpkrfnaPRaIh44etHQYVAsWEdU4L47F+T7/gr9/I5jdz9CpZbW0P5F5An7+fnXv38BxTdbewH5OnDgJP7+aM1aabLrqBtjPqZOn0MtXz1lJG2D8hjp16hR69aqWb0PLy4T9nzr1B3r10jDLroliNd3/G4Y1t+3Y3jTjktmwiKhGEAQoPdxh69XO0qHUm4rcHNh2aDr/s1bk34Jt54ctHUa9Kr9zu0ldFi4vKoSdT8NZS8LcyktLYKepiCAyM95YSUREREZhEUFERERG4ccZ1fx5sAS/r3PFxRa59TKe6q5z4d4f1abN/dfCvTaCAOD+PtV+G0GtfeX5giDcP67eXtM5ggDk5Lrg7oG/H5xvUxnbvfZVYxMEDeMI0Nym6lhV4ocACFCPUT0HQeN4qvNsqu2vFqvq5m8t5+dfkOByWalqfFV8OsZWfb2qH6tyvloftcSA6vsE7XHUloum/Zr6UZYDFQqx2rEqbYiIjMAiopoKhYgKuQBFsZlvnkLlPUai6mYjUXn/Bia17Xt/A/eOicr7p1TuFx/c9FTZHsr7XYiAqBTvta3cL1YOKd4/DlRUNEOOUPjgWOU4UB/HerTCceRZOoh65oFD+Kv2JhqKGqBmQaIqVLSdo6HA0VxUCVXaV2lXvXBCtbYajlePv7TUDSccb1SLv0rsNc4TavShignVzxVUr7X2Dy3tNRWemvpHzf013+MHrwsKWuC6262a/VfGoWmcKp1ofG8Etb+q9SPUbF9LTqrvCUD7OBpq2bZ+9vAOcap5gBoMFhHVeA9qhlvCH/Dz0/C0gpU6ceIE/PR4GqWywKksNu7tw4NCRqy6ff+4skrBcr+QUTsXDwodVXu1/kX1Pquco96P8KBYqlJYQXzwp/LYhYsX0bVzF/W4NP1dJT+oxVQtZ1TfX2XM6mMAVU6oWjQKD96DGnHUfN9rff9RPQbgxo0baOPZRmvOVd8rURVozf7EKm1V7aq8B9VjEERBvTCGhn40vDc1vsdQ7XX1r3G1vm7f+Rstm7tW+dqI+vWt6T2oNsa9P+pfL0051nhd7WtVY9xq8ai30Rx/pdJSORTXC6vEJFY5t9r7UzWPGjFWe0+rxCJW/rSvHq/qlFreYy3d1hi3mof7tmUR0cCZrYhITU3FunXroFAoMHXqVEycOFHt+OnTpxEbG4vCwkIEBgZi8eLFsLOzw7Vr1xATE4Nbt26hc+fOiIuLg7Ozs7nCrOF/CQtx9uvlOFtvIzYMTS3f65YOwAL+tHQA9ez2TUtHYDqClteVnCRQ/wmt64RGwsEhGMAhS4dBtTBLEZGTk4P4+Hjs2rUL9vb2GD9+PB5//HF06/bgEbOYmBgsW7YMvXv3xltvvYXt27cjMjISixcvRmRkJMLCwvDxxx/jk08+QUxMjDnC1Mgn/FXcktvi4YcfrrcxLe3SpSw83OlhS4dhNNHAz1ouX7qETg3p62vueQcAXL58GZ06dTL7OGrqIS9tzJmvyeZMMKErVy6jY0dzfn0tk7Nb10ctMi7pzyxFRHp6OoKCguDq6goAGDp0KNLS0hAVFQUAyM7ORmlpKXr37g0AGDVqFD766COMHTsWv/32Gz7++GPV/kmTJtVrEeHk1hZuAU/DOyCg3sa0tDsyWZPK965Mhu5NKF+g6eXc1PItlMnQownlSw2HWYqI3NxcuLu7q7Y9PDyQmZmp9bi7uztycnJQUFAAFxcX2NnZqe03xMmTWtaAMJBMJjNJP40F87V+TS1n5mvdmlq+DZVZighNl/uq3nGs7biu8/Th6+sLBwcHg86pTiaTIaAJVfXM1/o1tZyZr3UzJF+5XG6yXy6pJrNMNuXp6YmbNx/c1ZSbmwsPDw+tx/Py8uDh4QE3NzcUFhaioqJCbT8RERE1PGYpIvr27YsjR44gPz8fJSUl2Lt3L4KDg1XHvby84ODgoLoclZycjODgYEgkEgQGBmLPnj1q+4mIiKjhMduViOjoaEilUowcORIjRoyAv78/ZsyYgRMnTgAA4uLisGLFCgwfPhwlJSWQSqUAgEWLFmH79u0IDQ1FRkYGZs+ebY4QiYiIqI7MNk9EeHg4wsPD1fZt3LhR9drHxwc7d+6scZ6XlxcSEhIMHq/yfoqysjKDz9VELpebpJ/Ggvlav6aWM/O1bvrmW/kzoSE+mmsNBNFK3tm7d+/i3Llzlg6DiIgaoO7du6N58+aWDsPqWE0RoVQqUVRUBIlEwgWFiIgIwL0rEAqFAs7OzrCx4cLVpmY1RQQRERHVL5ZlREREZBQWEURERGQUFhFERERkFBYRREREZBQWEURERGQUFhFERERkFBYRREREZBQWEdWkpqYiNDQUgwcPRmJioqXDMYvCwkKMGDECf/31FwAgPT0d4eHhGDJkCOLj4y0cnemtXbsWYWFhCAsLw6pVqwBYd84ffvghQkNDERYWhi+++AKAdedb6d1338W8efMAAKdPn8bo0aMxdOhQzJ8/H+Xl5RaOznSkUinCwsIQERGBiIgIHD9+3Kr/3Tpw4ABGjRqFYcOGYdmyZQCaxvdzoyGSyo0bN8QBAwaIBQUFYlFRkRgeHi6eP3/e0mGZ1O+//y6OGDFC7NWrl3j16lWxpKREfPLJJ8UrV66ICoVCnDZtmnjw4EFLh2ky//3vf8Vx48aJcrlcLCsrE6VSqZiammq1OR89elQcP368qFAoxJKSEnHAgAHi6dOnrTbfSunp6eLjjz8uzp07VxRFUQwLCxP/97//iaIoim+++aaYmJhowehMR6lUiv369RMVCoVqnzX/u3XlyhWxf//+4vXr18WysjJxwoQJ4sGDB63++7kx4ZWIKtLT0xEUFARXV1c4OTlh6NChSEtLs3RYJrV9+3YsWrQIHh4eAIDMzEx06tQJHTp0gJ2dHcLDw60qZ3d3d8ybNw/29vaQSCTo2rUrLl26ZLU5P/bYY9iyZQvs7Oxw69YtVFRU4M6dO1abLwD8/fffiI+Px0svvQQAyM7ORmlpKXr37g0AGDVqlNXke/HiRQiCgBkzZuDpp5/GV199ZdX/bv373/9GaGgo2rRpA4lEgvj4eDg6Olr193NjwyKiitzcXLi7u6u2PTw8kJOTY8GITG/58uUIDAxUbVt7zt7e3qofJpcuXcKePXsgCIJV5yyRSPDRRx8hLCwMffr0sfqv8cKFCxEdHY0WLVoAqPk97e7ubjX53rlzB3369MHHH3+MzZs34+uvv8a1a9es9ut7+fJlVFRU4Pnnn8fTTz+NrVu3Wv33c2PDIqIKUcMyIta+mFdTyfn8+fOYNm0a5s6di44dO9Y4bm05z5o1C0eOHMH169dx6dKlGsetJd8dO3agbdu26NOnj2qfNX9PP/roo1i1ahWcnJzg5uaGMWPG4KOPPqrRzlryraiowJEjR7B69Wps374dJ06cUN3LVZW15NsY2Vk6gIbE09MTGRkZqu3c3FzVZX9r5enpiZs3b6q2rTFnmUyGWbNm4a233kJYWBh+/fVXq835zz//RFlZGR555BE4OjpiyJAhSEtLg62traqNNeW7Z88e5OXlISIiArdv30ZxcTEEQVD7+ubl5VlNvhkZGVAoFKqiSRRFeHl5We33c+vWrdGnTx+4ubkBAAYNGmTV38+NEa9EVNG3b18cOXIE+fn5KCkpwd69exEcHGzpsMzqH//4B7KyslSXDb/77juryvn69et49dVXERcXh7CwMADWnfNff/2F2NhYlJWVoaysDPv378f48eOtNt8vvvgC3333HVJSUjBr1iwMHDgQK1asgIODA2QyGQAgOTnZavK9e/cuVq1aBblcjsLCQnz77bdYvXq11f67NWDAAPz888+4c+cOKioqcPjwYQwbNsxqv58bI16JqMLT0xPR0dGQSqVQKBQYM2YM/P39LR2WWTk4OGDlypWYOXMm5HI5nnzySQwbNszSYZnM559/DrlcjpUrV6r2jR8/3mpzfvLJJ3H8+HGMHDkStra2GDJkCMLCwuDm5maV+WoTFxeH2NhYFBUVoWfPnpBKpZYOySQGDBig+voqlUpERkYiICDAav/d+sc//oHp06cjMjISCoUC/fr1w4QJE9ClS5cm9f3ckAmipg8QiYiIiHTgxxlERERkFBYRREREZBQWEURERGQUFhFERERkFBYRREREZBQWEUQWJpfLsWPHDgDArl27sH//fpP0O2/ePISHh+PIkSN16ic+Ph79+vXDTz/9ZJK4iMh6cJ4IIgvLy8vDjh07MHbsWIwaNcqkfcfExKhNCW2M6Ohork1ARBqxiCCysPXr1+PChQtYu3YtRFFE69at0aVLF2zYsAESiQQ3btzA+PHj8csvv+DMmTOQSqWIjIzEr7/+ivj4eNja2qJDhw5YsmQJJBKJxjHi4+Nx9OhRlJeXY8iQIXjhhRdw9uxZLFu2DADg6uqKd955By4uLli6dCkyMzOhUCgwc+ZMhISE1OfbQUSNCD/OILKwl156Cd26dUNUVJTa/hs3bmDNmjV4++23sW7dOqxatQobN25EUlISRFHEggULsHbtWnz11Vfw9PTEt99+q3WM1NRUxMXFYevWrarVLhcsWIBFixYhISEBwcHB+Oyzz7Bv3z4UFBRg586d2LJlC06ePGnW3ImoceOVCKIGytvbGxKJBM2bN0fHjh1hb2+Pli1bQi6XIz8/H7m5uZg9ezYAoLS0FH379tXa1+rVq/Hee+/h5s2beOKJJwDcW6xr8eLFAACFQoGHH34Yzs7OqqXTW7ZsqeqfiEgTFhFEFmZjYwOlUlljf23LG7dq1Qpt2rTBJ598gubNm2P//v1wcnLS2LasrAxpaWl4//33AQChoaEICwtD586d8e6776Jdu3aQyWTIy8uDnZ0d0tLSANxb7Gn27Nn4/PPPTZAlEVkjFhFEFvbQQw9BoVBg9erVaNasmV7n2NjYYP78+XjhhRcgiiKcnZ2xatUqjW0rr2A8++yzaNasGfr164d27drh7bffxty5c1FeXg5BELB8+XI8/PDDOHLkCCZMmICKigq8+uqrpkyViKwMF+AislLz5s1DaGioSZZJNmVfRGQ9eGMlkRVbvXq1SeaJOHz4sIkiIiJrwisRREREZBReiSAiIiKjsIggIiIio7CIICIiIqOwiCAiIiKjsIggIiIio7CIICIiIqP8P93TxEL7TpMUAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 504x252 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Educts:\n",
    "for reactant_id, stoich, _, replicates, init_conc in educts:\n",
    "        \n",
    "    if len(replicates) > 0:\n",
    "            \n",
    "        df = reaction.exportReplicates(reactant_id)\n",
    "        time_val = df.index.tolist()\n",
    "        time = df.index.name.split('/')[0]\n",
    "        time_unit_name = df.index.name.split('/')[1]\n",
    "        time_unit = enzmldoc.getUnitDict()[time_unit_name].getName()\n",
    "            \n",
    "        f, ax = plt.subplots(figsize=(7,3.5))\n",
    "            \n",
    "        # Visualization\n",
    "        for col in df.columns:\n",
    "                \n",
    "            name = col.split('/')[1]+': '+enzmldoc.getReactant(col.split('/')[1]).getName()\n",
    "            unit_name = enzmldoc.getReactant(col.split('/')[1]).getSubstanceUnits()\n",
    "            unit = enzmldoc.getUnitDict()[unit_name].getName()\n",
    "                \n",
    "            sns.lineplot( x=time_val, y=df[col], label = col.split('/')[0] )\n",
    "            \n",
    "        #set graph title, legend, axes \n",
    "        ax.set_title(reaction_name, fontsize = 12)\n",
    "\n",
    "        ax.legend(fontsize = 10, \\\n",
    "                    bbox_to_anchor= (1, 0.75), \\\n",
    "                    title= name, \\\n",
    "                    title_fontsize = 10, \\\n",
    "                    shadow = True, \\\n",
    "                    facecolor = 'white');\n",
    "\n",
    "        xlabel = f\"{time} [{time_unit}]\"\n",
    "        ylabel = f\"{'concentration'} [{unit}]\"\n",
    "\n",
    "        ax.set_xlabel(xlabel , fontsize=10)\n",
    "        ax.set_ylabel(ylabel, fontsize=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "neural-jesus",
   "metadata": {},
   "source": [
    "Visualize products, if the EnzymeML document contains time course data for products <br>\n",
    "The example data does not contain measurments of products."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "greek-twist",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x252 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for reactant_id, stoich, _, replicates, init_conc in products:\n",
    "        \n",
    "    if len(replicates) > 0:\n",
    "            \n",
    "        df = reaction.exportReplicates(reactant_id)\n",
    "        time_val = df.index.tolist()\n",
    "        time = df.index.name.split('/')[0]\n",
    "        time_unit_name = df.index.name.split('/')[1]\n",
    "        time_unit = enzmldoc.getUnitDict()[time_unit_name].getName()\n",
    "            \n",
    "        f, ax = plt.subplots(figsize=(7,3.5))\n",
    "            \n",
    "        # Visualization\n",
    "        for col in df.columns:\n",
    "                \n",
    "            name = enzmldoc.getReactant(col.split('/')[1]).getName()\n",
    "            unit_name = enzmldoc.getReactant(col.split('/')[1]).getSubstanceUnits()\n",
    "            unit = enzmldoc.getUnitDict()[unit_name].getName()\n",
    "                \n",
    "            sns.lineplot( x=time_val, y=df[col], label = col.split('/')[0] )\n",
    "            \n",
    "        #set graph title, legend, axes \n",
    "        ax.set_title(reaction_name, fontsize = 12)\n",
    "\n",
    "        ax.legend(fontsize = 10, \\\n",
    "                    bbox_to_anchor= (1, 0.75), \\\n",
    "                    title= name, \\\n",
    "                    title_fontsize = 10, \\\n",
    "                    shadow = True, \\\n",
    "                    facecolor = 'white');\n",
    "\n",
    "        xlabel = f\"{time} [{time_unit}]\"\n",
    "        ylabel = f\"{'concentration'} [{unit}]\"\n",
    "\n",
    "        ax.set_xlabel(xlabel , fontsize=10)\n",
    "        ax.set_ylabel(ylabel, fontsize=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ready-murder",
   "metadata": {},
   "source": [
    "## Parameter Estimation and Modeling\n",
    "#### Data preparation\n",
    "Convert pandas dataframe from EnzymeML data to numpy arrays. <br>\n",
    "First select the reactant to model by changing the reactant_id accordingly, see overview above for selction options.<br>\n",
    "In this example substrate 's0' will be modeled.<br>\n",
    "##### Choose against which timecourse you want to fit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "every-calvin",
   "metadata": {},
   "outputs": [],
   "source": [
    "reactant_id = 's0'\n",
    "is_product = False\n",
    "lag = 5\n",
    "replicates = reaction.exportReplicates(reactant_id)\n",
    "# time:\n",
    "data_time = replicates.index.values # numpy array shape (9,)\n",
    "data_time = data_time[lag:]\n",
    "# substrate data (absorption):\n",
    "data_s = np.transpose(replicates.iloc[lag:,:].to_numpy(np.float64)) # shape: (4, 9)\n",
    "#data_s = np.transpose(replicates.iloc[:,:-1].to_numpy(np.float64)) # shape: (3, 9)\n",
    "#data_s = np.transpose(replicates.iloc[:,:-2].to_numpy(np.float64)) # shape: (2, 9)\n",
    "#data_s = np.transpose(replicates.iloc[lag:,0].to_numpy(np.float64)) # shape: (1, 9)\n",
    "#print(data_s.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "juvenile-divide",
   "metadata": {},
   "outputs": [],
   "source": [
    "# if product \"cheating\"\n",
    "if is_product:\n",
    "    for i in range(data_s.shape[0]):\n",
    "        grr = np.transpose(replicates.iloc[lag:,:].to_numpy(np.float64))\n",
    "        init = np.max(grr[i])\n",
    "        temp = np.full(data_s[i].shape,init)\n",
    "        data_s[i]= temp-data_s[i]\n",
    "#print(data_s)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "every-document",
   "metadata": {},
   "source": [
    "### Fit data to a system of ODEs\n",
    "#### Define the ODE functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "distributed-marriage",
   "metadata": {},
   "outputs": [],
   "source": [
    "# not used\n",
    "def michaelis_menten_with_lag(w, t, params):\n",
    "    '''\n",
    "    System of differential equations\n",
    "    Arguments:\n",
    "        w: vector of state variables: w = [v,S]\n",
    "        t: time\n",
    "        params: parameters\n",
    "    '''\n",
    "    v, s = w\n",
    "    \n",
    "    a = params['a'].value\n",
    "    vmax = params['vmax'].value\n",
    "    km = params['Km'].value\n",
    "    \n",
    "    # f(v',s'):\n",
    "    f0 = a*(vmax-v) # v'\n",
    "    f1 = -v*s/(km+s) # S'\n",
    "    return [f0,f1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "emotional-major",
   "metadata": {},
   "outputs": [],
   "source": [
    "def michaelis_menten(w, t, params):\n",
    "    '''\n",
    "    Differential equations\n",
    "    Arguments:\n",
    "        w: vector of state variables, here only one: w = [S]\n",
    "        t: time\n",
    "        params: parameters\n",
    "    '''\n",
    "    s = w\n",
    "    \n",
    "    vmax = params['vmax'].value\n",
    "    km = params['Km'].value\n",
    "    \n",
    "    # f(s'):\n",
    "    f1 = -vmax*s/(km+s) # S'\n",
    "    return f1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "rising-invalid",
   "metadata": {},
   "outputs": [],
   "source": [
    "def hill_equation(w, t, params):\n",
    "    '''\n",
    "    Differential equations\n",
    "    Arguments:\n",
    "        w: vector of state variables, here only one: w = [S]\n",
    "        t: time\n",
    "        params: parameters\n",
    "    '''\n",
    "    s = w\n",
    "    \n",
    "    vmax = params['vmax'].value\n",
    "    km = params['Km'].value\n",
    "    n = params['n'].value\n",
    "    \n",
    "    # f(s'):\n",
    "    f1 = -vmax*(s**n)/(km+(s**n)) # S'\n",
    "    return f1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "satellite-conspiracy",
   "metadata": {},
   "source": [
    "#### Solve ODE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "short-april",
   "metadata": {},
   "outputs": [],
   "source": [
    "# not used\n",
    "def solve_MM_with_lag(t, w0, params):\n",
    "    '''\n",
    "    Solution to the ODE w'(t)=f(t,w,p) with initial condition w(0)= w0 (= [S0])\n",
    "    '''\n",
    "    w = odeint(michaelis_menten_with_lag, w0, t, args=(params,))\n",
    "    return w"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "german-still",
   "metadata": {},
   "outputs": [],
   "source": [
    "def solve_MM(t, w0, params):\n",
    "    '''\n",
    "    Solution to the ODE w'(t)=f(t,w,p) with initial condition w(0)= w0 (= [S0])\n",
    "    '''\n",
    "    w = odeint(michaelis_menten, w0, t, args=(params,))\n",
    "    return w"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "cutting-cartridge",
   "metadata": {},
   "outputs": [],
   "source": [
    "def solve_Hill(t, w0, params):\n",
    "    '''\n",
    "    Solution to the ODE w'(t)=f(t,w,p) with initial condition w(0)= w0 (= [S0])\n",
    "    '''\n",
    "    w = odeint(hill_equation, w0, t, args=(params,))\n",
    "    return w"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "hungry-vietnamese",
   "metadata": {},
   "source": [
    "#### Compute residual between actual data (S) and fitted data\n",
    "In this model we assume that the data contains a bias on the y-axis. <br>\n",
    "Therfore we compute the distance between the modeled substrate + bias and the actual mesuared substrate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "leading-grocery",
   "metadata": {},
   "outputs": [],
   "source": [
    "# not used\n",
    "def residual_with_lag_and_bias(params, t, data_s):\n",
    "    ndata, nt = data_s.shape # get dimensions of data (here we fit against 3 measurments => ndata = 3)\n",
    "    resid = 0.0*data_s[:] # initialize the residual vector\n",
    "    # compute residual per data set\n",
    "    for i in range(ndata):\n",
    "        w0 = params['v0'].value, params['S0'].value\n",
    "        model = solve_MM_with_lag(t, w0, params) # solve the ODE with the given parameters\n",
    "        # get modeled substrate\n",
    "        s_model = model[:,1]\n",
    "        s_model_b = s_model + params['b'].value # adding bias\n",
    "        resid[i,:]=data_s[i,:]-s_model_b # compute distance to measured data\n",
    "    return resid.flatten()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "underlying-nepal",
   "metadata": {},
   "outputs": [],
   "source": [
    "def residual_MM(params, t, data_s):\n",
    "    ndata, nt = data_s.shape # get dimensions of data (here we fit against 4 measurments => ndata = 4)\n",
    "    resid = 0.0*data_s[:] # initialize the residual vector\n",
    "    # compute residual per data set\n",
    "    for i in range(ndata):\n",
    "        w0 = data_s[i,0]\n",
    "        model = solve_MM(t, w0, params) # solve the ODE with the given parameters\n",
    "        # get modeled substrate\n",
    "        s_model = model[:,0]\n",
    "        resid[i,:]=data_s[i,:]-s_model # compute distance to measured data\n",
    "    return resid.flatten()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "laughing-transcription",
   "metadata": {},
   "outputs": [],
   "source": [
    "def residual_MM_single(params, t, data_s):\n",
    "    w0 = data_s[0]\n",
    "    model = solve_MM(t, w0, params)\n",
    "    # only have data for s not v\n",
    "    s_model = model[:,0]\n",
    "    return (s_model - data_s).ravel()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "median-liechtenstein",
   "metadata": {},
   "outputs": [],
   "source": [
    "def residual_Hill(params, t, data_s):\n",
    "    ndata, nt = data_s.shape # get dimensions of data (here we fit against 4 measurments => ndata = 4)\n",
    "    resid = 0.0*data_s[:] # initialize the residual vector\n",
    "    # compute residual per data set\n",
    "    for i in range(ndata):\n",
    "        w0 = data_s[i,0]\n",
    "        model = solve_Hill(t, w0, params) # solve the ODE with the given parameters\n",
    "        # get modeled substrate\n",
    "        s_model = model[:,0]\n",
    "        resid[i,:]=data_s[i,:]-s_model # compute distance to measured data\n",
    "    return resid.flatten()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "reduced-evanescence",
   "metadata": {},
   "outputs": [],
   "source": [
    "def residual_Hill_single(params, t, data_s):\n",
    "    w0 = data_s[0]\n",
    "    model = solve_Hill(t, w0, params)\n",
    "    # only have data for s not v\n",
    "    s_model = model[:,0]\n",
    "    return (s_model - data_s).ravel()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "weighted-pepper",
   "metadata": {},
   "source": [
    "#### Functions to compute initial value for vmax and Km\n",
    "To get a good guess for vmax, v is computed for each time step. <br>\n",
    "For Km the mean of s values at aproximatly vmax/2 is taken."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "coordinated-numbers",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_v(time, data_s):\n",
    "    v_all = 0.0*data_s[:] # initialize velocity vector\n",
    "    if len(data_s.shape)>1:\n",
    "        for i in range(data_s.shape[0]):\n",
    "            prev_value = data_s[i,0]\n",
    "            prev_time = 0.0\n",
    "            for j in range(data_s.shape[1]):\n",
    "                if time[j] == 0:\n",
    "                    delta = prev_value - data_s[i,j]\n",
    "                else:\n",
    "                    delta = abs( (prev_value - data_s[i,j])/(time[j]-prev_time))\n",
    "                v_all[i,j] = delta\n",
    "                prev_value = data_s[i,j]\n",
    "                prev_time = time[j]\n",
    "        v = np.max(v_all, axis=0)\n",
    "    else:\n",
    "        prev_value = data_s[0]\n",
    "        prev_time = 0.0\n",
    "        for j in range(data_s.shape[0]):\n",
    "            if time[j] == 0:\n",
    "                delta = prev_value - data_s[j]\n",
    "            else:\n",
    "                delta = abs( (prev_value - data_s[j])/(time[j]-prev_time))\n",
    "            v_all[j] = delta\n",
    "            prev_value = data_s[j]\n",
    "            prev_time = time[j]\n",
    "        v = v_all\n",
    "    return v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "boring-scholarship",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_initial_vmax(time, data_s):\n",
    "    v = get_v(time,data_s)\n",
    "    return np.max(v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "formal-scottish",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_initial_Km(time, data_s):\n",
    "    v = get_v(time,data_s)\n",
    "    idx_max = np.where(v == np.max(v))[0][0]\n",
    "    idx_Km = (np.abs(v[idx_max:]-np.max(v)/2)).argmin()\n",
    "    if len(data_s.shape)>1:\n",
    "        km = np.mean(data_s,axis=0)[idx_max+idx_Km]\n",
    "    else:\n",
    "        km = data_s[idx_max+idx_Km]\n",
    "    return km"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "leading-concert",
   "metadata": {},
   "source": [
    "#### Bringing everything together\n",
    "Initialize parameters:\n",
    "- $v_0$ is fixed on 0.\n",
    "- bias is estimated by taking the mean of the last data point for all measured data.\n",
    "- for $S_0$ the mean of first data point for all measured data is taken and substracted by the estimated bias.\n",
    "- functions to get initial values for $v_{max}$ and $K_m$ are called.\n",
    "- initial value for a is set to 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "parental-prisoner",
   "metadata": {},
   "outputs": [],
   "source": [
    "# time\n",
    "t_measured = data_time[:]\n",
    "\n",
    "# initial conditions:\n",
    "#v0 = 0\n",
    "if len(data_s.shape)>1:\n",
    "    s0 = np.max(data_s,axis=0)[0]\n",
    "else:\n",
    "    s0 = data_s[0]\n",
    "\n",
    "# Set parameters including bounds\n",
    "#bias = np.min(data_s,axis=0)[-1]\n",
    "vmax = get_initial_vmax(t_measured, data_s)\n",
    "km = get_initial_Km(t_measured, data_s)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "heated-kingston",
   "metadata": {},
   "source": [
    "Parameters for different Models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "permanent-occasion",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 'standard' Michaelis Menten\n",
    "params_MM = Parameters()\n",
    "params_MM.add('vmax', value=vmax, min=0.0)\n",
    "params_MM.add('Km', value=km, min=0.0001)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "opposed-theory",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Hill equation\n",
    "n = 2\n",
    "\n",
    "params_Hill = Parameters()\n",
    "params_Hill.add('vmax', value=vmax, min=0.0)\n",
    "params_Hill.add('Km', value=km, min=0.0001)\n",
    "params_Hill.add('n', value=n, min=0.99, max=3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "acoustic-pakistan",
   "metadata": {},
   "source": [
    "#### Fit model and visualize results\n",
    "Statistics for the Fit and the parameters a printed. <br>\n",
    "In the graph the red line shows the result of the model. <br>\n",
    "The dotted curves are the measured data sets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "editorial-trader",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[Fit Statistics]]\n",
      "    # fitting method   = leastsq\n",
      "    # function evals   = 28\n",
      "    # data points      = 330\n",
      "    # variables        = 2\n",
      "    chi-square         = 1.0160e-05\n",
      "    reduced chi-square = 3.0976e-08\n",
      "    Akaike info crit   = -5703.72817\n",
      "    Bayesian info crit = -5696.12999\n",
      "[[Variables]]\n",
      "    vmax:  8.1636e-05 +/- 9.2252e-05 (113.00%) (init = 2.003577e-05)\n",
      "    Km:    0.48794348 +/- 0.65280338 (133.79%) (init = 0.02451704)\n",
      "[[Correlations]] (unreported correlations are < 0.100)\n",
      "    C(vmax, Km) =  0.999\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 'standard' Michaelis Menten\n",
    "if len(data_s.shape)>1:\n",
    "    result = minimize(residual_MM , params_MM, args=(t_measured, data_s), method='leastsq')\n",
    "    report_fit(result) # access values of fitted parameters: result.params['Km'].value\n",
    "    # plot the data sets and fits\n",
    "    plt.figure()\n",
    "    for i in range(data_s.shape[0]):\n",
    "        plt.plot(t_measured, data_s[i, :], 'o')\n",
    "        #w0 = params['v0'].value, data_s[i,0]\n",
    "        w0 = data_s[i,0]\n",
    "        data_fitted = solve_MM(t_measured, w0, result.params)\n",
    "        plt.plot(t_measured, data_fitted[:, 0], '-', linewidth=2, label='fitted data')\n",
    "    plt.show()\n",
    "else:\n",
    "    result = minimize(residual_MM_single , params_MM, args=(t_measured, data_s), method='leastsq')\n",
    "    report_fit(result) # access values of fitted parameters: result.params['Km'].value\n",
    "    # plot the data sets and fits\n",
    "    plt.figure()\n",
    "    plt.plot(t_measured, data_s[:], 'o')\n",
    "    w0 = data_s[0]\n",
    "    data_fitted = solve_MM(t_measured, w0, result.params)\n",
    "    plt.plot(t_measured, data_fitted[:, 0], '-', linewidth=2, label='fitted data')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "second-pasta",
   "metadata": {},
   "source": [
    "$v_{max} = k_{cat} * E_0$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "marked-vulnerability",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[Fit Statistics]]\n",
      "    # fitting method   = leastsq\n",
      "    # function evals   = 742\n",
      "    # data points      = 330\n",
      "    # variables        = 3\n",
      "    chi-square         = 1.0149e-05\n",
      "    reduced chi-square = 3.1038e-08\n",
      "    Akaike info crit   = -5702.06941\n",
      "    Bayesian info crit = -5690.67213\n",
      "[[Variables]]\n",
      "    vmax:  8.1374e-05 +/- 4.2033e-04 (516.55%) (init = 2.003577e-05)\n",
      "    Km:    0.49810090 +/- 3.64513165 (731.81%) (init = 0.02451704)\n",
      "    n:     0.99000000 +/- 0.43113138 (43.55%) (init = 2)\n",
      "[[Correlations]] (unreported correlations are < 0.100)\n",
      "    C(vmax, Km) =  0.999\n",
      "    C(Km, n)    =  0.983\n",
      "    C(vmax, n)  =  0.976\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Hill equation\n",
    "if len(data_s.shape)>1:\n",
    "    result = minimize(residual_Hill , params_Hill, args=(t_measured, data_s), method='leastsq')\n",
    "    report_fit(result) # access values of fitted parameters: result.params['Km'].value\n",
    "    # plot the data sets and fits\n",
    "    plt.figure()\n",
    "    for i in range(data_s.shape[0]):\n",
    "        plt.plot(t_measured, data_s[i, :], 'o')\n",
    "        #w0 = params['v0'].value, data_s[i,0]\n",
    "        w0 = data_s[i,0]\n",
    "        data_fitted = solve_Hill(t_measured, w0, result.params)\n",
    "        plt.plot(t_measured, data_fitted[:, 0], '-', linewidth=2, label='fitted data')\n",
    "    plt.show()\n",
    "else:\n",
    "    result = minimize(residual_Hill_single , params_Hill, args=(t_measured, data_s), method='leastsq')\n",
    "    report_fit(result) # access values of fitted parameters: result.params['Km'].value\n",
    "    # plot the data sets and fits\n",
    "    plt.figure()\n",
    "    plt.plot(t_measured, data_s[:], 'o')\n",
    "    w0 = data_s[0]\n",
    "    data_fitted = solve_Hill(t_measured, w0, result.params)\n",
    "    plt.plot(t_measured, data_fitted[:, 0], '-', linewidth=2, label='fitted data')\n",
    "    plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}