Test_For_Scenario2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "based-experiment",
   "metadata": {},
   "source": [
    "# Tests for Scenario 2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "laden-wrist",
   "metadata": {},
   "source": [
    "imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "fifty-helicopter",
   "metadata": {},
   "outputs": [],
   "source": [
    "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",
    "import matplotlib.pyplot as plt # plot data and results"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "crude-travel",
   "metadata": {},
   "source": [
    "### Get data from excel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "determined-pickup",
   "metadata": {},
   "outputs": [],
   "source": [
    "data = './datasets/Stephan_pH7.xlsx'\n",
    "df = pd.read_excel(data)\n",
    "#print(df)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "transsexual-drive",
   "metadata": {},
   "source": [
    "### Convert dataframe to np-array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "offensive-walnut",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.         0.08333333 0.16666667 0.25       0.33333333 0.41666667\n",
      " 0.5        0.58333333 0.66666667 0.75       0.83333333 0.91666667\n",
      " 1.         1.08333333 1.16666667 1.25       1.33333333 1.41666667\n",
      " 1.5        1.58333333 1.66666667 1.75       1.83333333 1.91666667\n",
      " 2.         2.08333333 2.16666667 2.25       2.33333333 2.41666667\n",
      " 2.5        2.58333333 2.66666667 2.75       2.83333333 2.91666667\n",
      " 3.         3.08333333 3.16666667 3.25       3.33333333 3.41666667\n",
      " 3.5        3.58333333 3.66666667 3.75       3.83333333 3.91666667\n",
      " 4.         4.08333333 4.16666667 4.25       4.33333333 4.41666667\n",
      " 4.5        4.58333333 4.66666667 4.75       4.83333333 4.91666667]\n",
      "[0.9862 0.9734 0.9734 0.9666 0.9403 0.9353 0.9137 0.903  0.8932 0.8748\n",
      " 0.8651 0.8453 0.8308 0.817  0.7955 0.7839 0.7665 0.7448 0.7251 0.7068\n",
      " 0.688  0.665  0.6449 0.6267 0.6079 0.5852 0.5643 0.546  0.5259 0.5044\n",
      " 0.4838 0.4647 0.4419 0.4202 0.3998 0.38   0.358  0.3403 0.3208 0.3027\n",
      " 0.2828 0.264  0.2484 0.2317 0.2155 0.1998 0.1855 0.1715 0.1597 0.1506\n",
      " 0.141  0.1322 0.1263 0.1218 0.1166 0.1133 0.1106 0.11   0.1068 0.1053]\n"
     ]
    }
   ],
   "source": [
    "data_time = df[df.columns[0]].to_numpy(np.float64)\n",
    "print(data_time)\n",
    "data_s = df[df.columns[1]].to_numpy(np.float64)\n",
    "print(data_s)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "mexican-illinois",
   "metadata": {},
   "source": [
    "## Fit data to system of odes"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "tracked-version",
   "metadata": {},
   "source": [
    "### define the ode functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "gentle-williams",
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(w, t, paras):\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",
    "    try:\n",
    "        a = paras['a'].value\n",
    "        vmax = paras['vmax'].value\n",
    "        km = paras['km'].value\n",
    "\n",
    "    except KeyError:\n",
    "        a, vmax, km = paras\n",
    "    \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": 6,
   "id": "severe-yacht",
   "metadata": {},
   "outputs": [],
   "source": [
    "# WITH BIAS\n",
    "def f_b(w, t, paras):\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",
    "    try:\n",
    "        a = paras['a'].value\n",
    "        vmax = paras['vmax'].value\n",
    "        km = paras['km'].value\n",
    "        b = paras['b'].value\n",
    "\n",
    "    except KeyError:\n",
    "        a, vmax, km, b = paras\n",
    "    \n",
    "    \n",
    "    # f(v',s'):\n",
    "    f0 = a*(vmax-v) # v'\n",
    "    f1 = -v*(s+b)/(km+s+b) # s'\n",
    "    return [f0,f1]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "alpine-humidity",
   "metadata": {},
   "source": [
    "### Solve ODE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "approximate-karaoke",
   "metadata": {},
   "outputs": [],
   "source": [
    "def g(t, w0, paras):\n",
    "    '''\n",
    "    Solution to the ODE w'(t)=f(t,w,p) with initial condition w(0)= w0 (= [v0, s0])\n",
    "    '''\n",
    "    w = odeint(f, w0, t, args=(paras,))\n",
    "    return w"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "weird-marina",
   "metadata": {},
   "outputs": [],
   "source": [
    "# WITH BIAS\n",
    "def g_b(t, w0, paras):\n",
    "    '''\n",
    "    Solution to the ODE w'(t)=f(t,w,p) with initial condition w(0)= w0 (= [v0, s0])\n",
    "    '''\n",
    "    w = odeint(f_b, w0, t, args=(paras,))\n",
    "    return w"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "impressed-placement",
   "metadata": {},
   "source": [
    "### compute residual between actual data (s) and fitted data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "surrounded-brain",
   "metadata": {},
   "outputs": [],
   "source": [
    "def residual(paras, t, data_s):\n",
    "    w0 = paras['v0'].value, paras['s0'].value\n",
    "    model = g(t, w0, paras)\n",
    "    # only have data for s not v\n",
    "    s_model = model[:,1]\n",
    "    return (s_model- data_s).ravel()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "wired-aspect",
   "metadata": {},
   "outputs": [],
   "source": [
    "# WITH BIAS\n",
    "def residual_b(paras, t, data_s):\n",
    "    w0 = paras['v0'].value, paras['s0'].value\n",
    "    model = g_b(t, w0, paras)\n",
    "    # only have data for s not v\n",
    "    s_model = model[:,1]\n",
    "    bias = paras['b'].value\n",
    "    s_model_b = s_model + bias\n",
    "    return (s_model_b - data_s).ravel()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "understood-mumbai",
   "metadata": {},
   "outputs": [],
   "source": [
    "# WITH fixed BIAS\n",
    "def residual_bf(paras, t, data_s):\n",
    "    w0 = paras['v0'].value, paras['s0'].value\n",
    "    model = g(t, w0, paras)\n",
    "    # only have data for s not v\n",
    "    s_model = model[:,1]\n",
    "    bias = paras['b'].value\n",
    "    s_model_b = s_model + bias\n",
    "    return (s_model_b - data_s).ravel()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "stupid-johnson",
   "metadata": {},
   "source": [
    "### Bringing all together"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "former-balance",
   "metadata": {},
   "outputs": [],
   "source": [
    "# initial conditions:\n",
    "v0 = 0\n",
    "s0 = data_s[0]\n",
    "w0 = [v0,s0]\n",
    "# 0,970877378\n",
    "\n",
    "\n",
    "# measured data\n",
    "t_measured = data_time\n",
    "s_measured = data_s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "international-economy",
   "metadata": {},
   "outputs": [],
   "source": [
    "# WITH BIAS\n",
    "# initial conditions:\n",
    "v0_b = 0\n",
    "s0_b = 0.861847366499791\n",
    "w0_b = [v0_b,s0_b]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "indoor-principal",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "improved-visibility",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Set parameters including bounds\n",
    "params = Parameters()\n",
    "params.add('v0', value=v0, vary=False)\n",
    "params.add('s0', value=s0, vary=False)\n",
    "params.add('a', value=1., min=0.0001, max=2.)\n",
    "params.add('vmax', value=0.2, min=0.0001, max=1.)\n",
    "params.add('km', value=0.05, min=0.0001, max=1.)\n",
    "#params.add('km', value=0.05, vary=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "reverse-feeling",
   "metadata": {},
   "outputs": [],
   "source": [
    "# WITH BIAS\n",
    "# Set parameters including bounds\n",
    "params_b = Parameters()\n",
    "params_b.add('v0', value=v0_b, vary=False)\n",
    "params_b.add('s0', value=s0_b, vary=False)\n",
    "params_b.add('a', value=1., min=0.0001, max=2.)\n",
    "params_b.add('vmax', value=0.2, min=0.0001, max=1.)\n",
    "params_b.add('km', value=0.05, min=0.0001, max=1.)\n",
    "#params_b.add('km', value=0.05, vary=False)\n",
    "#params_b.add('b', value=0.1, min=0.01, max=0.5)\n",
    "params_b.add('b', value=0.109, vary=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "vocal-butler",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "adjacent-banana",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[Fit Statistics]]\n",
      "    # fitting method   = leastsq\n",
      "    # function evals   = 34\n",
      "    # data points      = 60\n",
      "    # variables        = 3\n",
      "    chi-square         = 0.01045809\n",
      "    reduced chi-square = 1.8348e-04\n",
      "    Akaike info crit   = -513.283455\n",
      "    Bayesian info crit = -507.000422\n",
      "[[Variables]]\n",
      "    v0:    0 (fixed)\n",
      "    s0:    0.9862 (fixed)\n",
      "    a:     1.50226977 +/- 0.16983479 (11.31%) (init = 1)\n",
      "    vmax:  0.39214515 +/- 0.03741561 (9.54%) (init = 0.2)\n",
      "    km:    0.28910462 +/- 0.05745140 (19.87%) (init = 0.05)\n",
      "[[Correlations]] (unreported correlations are < 0.100)\n",
      "    C(vmax, km) =  0.989\n",
      "    C(a, vmax)  = -0.949\n",
      "    C(a, km)    = -0.897\n"
     ]
    },
    {
     "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": [
    "# fit model\n",
    "result = minimize(residual, params, args=(t_measured, s_measured), method='leastsq')  # leastsq nelder\n",
    "# check results of the fit\n",
    "data_fitted = g(t_measured, w0, result.params)\n",
    "\n",
    "# plot fitted data\n",
    "plt.plot(t_measured, data_fitted[:, 1], '-', linewidth=2, color='red', label='fitted data')\n",
    "plt.legend()\n",
    "plt.xlim([0, max(t_measured)])\n",
    "plt.ylim([0, 1.1 * max(data_fitted[:, 1])])\n",
    "# display fitted statistics\n",
    "report_fit(result)\n",
    "\n",
    "plt.scatter(t_measured, s_measured, marker='o', color='b', label='measured substrate')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "equal-religious",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[Fit Statistics]]\n",
      "    # fitting method   = leastsq\n",
      "    # function evals   = 37\n",
      "    # data points      = 60\n",
      "    # variables        = 3\n",
      "    chi-square         = 0.00732127\n",
      "    reduced chi-square = 1.2844e-04\n",
      "    Akaike info crit   = -534.678951\n",
      "    Bayesian info crit = -528.395917\n",
      "[[Variables]]\n",
      "    v0:    0 (fixed)\n",
      "    s0:    0.8618474 (fixed)\n",
      "    a:     1.06527018 +/- 0.12971569 (12.18%) (init = 1)\n",
      "    vmax:  0.48245218 +/- 0.06391023 (13.25%) (init = 0.2)\n",
      "    km:    0.40123596 +/- 0.08668977 (21.61%) (init = 0.05)\n",
      "    b:     0.109 (fixed)\n",
      "[[Correlations]] (unreported correlations are < 0.100)\n",
      "    C(vmax, km) =  0.993\n",
      "    C(a, vmax)  = -0.972\n",
      "    C(a, km)    = -0.940\n"
     ]
    },
    {
     "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": [
    "# fit model\n",
    "result_b = minimize(residual_b, params_b, args=(t_measured, s_measured), method='leastsq')  # leastsq nelder\n",
    "# check results of the fit\n",
    "data_fitted_b = g_b(t_measured, w0_b, result_b.params)\n",
    "\n",
    "# plot fitted data\n",
    "plt.plot(t_measured, data_fitted_b[:, 1]+params_b['b'].value, '-', linewidth=2, color='red', label='fitted data')\n",
    "plt.legend()\n",
    "plt.xlim([0, max(t_measured)])\n",
    "plt.ylim([0, 1.1 * max(data_fitted_b[:, 1]+params_b['b'].value)])\n",
    "# display fitted statistics\n",
    "report_fit(result_b)\n",
    "\n",
    "plt.scatter(t_measured, s_measured, marker='o', color='b', label='measured substrate')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "touched-eligibility",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[Fit Statistics]]\n",
      "    # fitting method   = leastsq\n",
      "    # function evals   = 37\n",
      "    # data points      = 60\n",
      "    # variables        = 3\n",
      "    chi-square         = 0.00732127\n",
      "    reduced chi-square = 1.2844e-04\n",
      "    Akaike info crit   = -534.678951\n",
      "    Bayesian info crit = -528.395917\n",
      "[[Variables]]\n",
      "    v0:    0 (fixed)\n",
      "    s0:    0.8618474 (fixed)\n",
      "    a:     1.06527018 +/- 0.12971569 (12.18%) (init = 1)\n",
      "    vmax:  0.48245218 +/- 0.06391023 (13.25%) (init = 0.2)\n",
      "    km:    0.40123596 +/- 0.08668977 (21.61%) (init = 0.05)\n",
      "    b:     0.109 (fixed)\n",
      "[[Correlations]] (unreported correlations are < 0.100)\n",
      "    C(vmax, km) =  0.993\n",
      "    C(a, vmax)  = -0.972\n",
      "    C(a, km)    = -0.940\n"
     ]
    },
    {
     "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": [
    "# fit model\n",
    "result_bf = minimize(residual_bf, params_b, args=(t_measured, s_measured), method='leastsq')  # leastsq nelder\n",
    "# check results of the fit\n",
    "data_fitted_bf = g(t_measured, w0_b, result_bf.params)\n",
    "\n",
    "# plot fitted data\n",
    "plt.plot(t_measured, data_fitted_bf[:, 1]+params_b['b'].value, '-', linewidth=2, color='red', label='fitted data')\n",
    "plt.legend()\n",
    "plt.xlim([0, max(t_measured)])\n",
    "plt.ylim([0, 1.1 * max(data_fitted_b[:, 1]+params_b['b'].value)])\n",
    "# display fitted statistics\n",
    "report_fit(result_b)\n",
    "\n",
    "plt.scatter(t_measured, s_measured, marker='o', color='b', label='measured substrate')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "signal-genesis",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}