curve_fitting_Bradford_assay_values.ipynb

{
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  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook uses curve_fit and initial estimated values to calculate the Y0, plateau and rate constant values to find a model to explain data generated from a protein standard curve using the Bradford assay.  Using SciPy's curve_fit makes GraphPad plotting unnecessary."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from scipy.optimize import curve_fit\n",
    "import numpy as np\n",
    "from scipy import stats"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Import raw data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "xdata = [2000, 1500, 1000, 750, 500, 250, 125, 25]\n",
    "ydata = [0.99815, 0.8708,0.73975,0.6597,0.4659,0.25495,0.15,0.0292]\n",
    "\n",
    "#ydata = [1.07685, 0.9741, 0.8432, 0.74875, 0.4937, 0.2928, 0.1696, 0.02865]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The initial guesses are important. Without them, curve_fit can't coalesce around explanatory values. I wonder how to generate values without human input. Y0 can be zero. The plateau could be Max + a few units. K, the rate, is difficult to estimate. When too high, incomputable values are generated (0's). Initial guesses could be more accurate by taking into account constraints e.g. p != Y0 and k !=0. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "R2 = 0.986118497937112\n"
    },
    {
     "output_type": "display_data",
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "# an array for initial guesses\n",
    "# g = [y0, P, k]\n",
    "\n",
    "# when k < 0.002 then no errors\n",
    "# when k > 0.002 then log(0) = errors\n",
    "\n",
    "g = [0, 1.176, 0.001]\n",
    "\n",
    "def eqn(y, y0, P, k):\n",
    "    '=(LN(($D$76-$D$75)/($D$76-G76))+0)/$D$77'\n",
    "    return (np.log((P-y0)/(P-y)))/k\n",
    "\n",
    "conc_pred = np.empty(len(ydata))\n",
    "for i in range(len(ydata)):\n",
    "    conc_pred[i]=eqn(ydata[i], g[0], g[1], g[2])\n",
    "    \n",
    "plt.plot(xdata, ydata, 'bo', label='data')\n",
    "plt.plot(conc_pred, ydata, 'r.', label='predicted')\n",
    "from sklearn.metrics import r2_score\n",
    "print (\"R2 =\", r2_score(conc_pred, xdata))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When predicted line (red) is below observed (blue) line, then no error in curve_fit. When above observed line, then errors about \"...invalid value encountered in log.\" i.d. log(0)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([1.92230958e-02, 1.14603080e+00, 1.00365075e-03])"
     },
     "metadata": {},
     "execution_count": 15
    }
   ],
   "source": [
    "c,cov = curve_fit(eqn, ydata, xdata, g)\n",
    "c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "Text(1500, 0.5, '0.9946720988406386')"
     },
     "metadata": {},
     "execution_count": 16
    },
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "conc = np.empty(len(ydata))\n",
    "\n",
    "for i in range(len(ydata)):\n",
    "    conc[i]=eqn(ydata[i], c[0], c[1], c[2])\n",
    "    \n",
    "plt.plot(xdata, ydata, 'bo', label='data')\n",
    "plt.plot(conc, ydata, 'r.', label='predicted')\n",
    "plt.xlabel('conc (mg/ml)')\n",
    "plt.ylabel('abs')\n",
    "plt.legend()\n",
    "r_squared = r2_score(conc, xdata)\n",
    "plt.text(1500, 0.5, r_squared) #'R-squared = %' % r_squared)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "1331.31\n1199.33\n642.42\n100.46\n"
    }
   ],
   "source": [
    "# calculate unknowns \n",
    "unk_data = [0.84985,0.8079,0.5547,0.1273]\n",
    "# make new array as long as unknowns\n",
    "unk_calcs = np.empty(len(unk_data))\n",
    "\n",
    "for each in range(len(unk_data)):\n",
    "    #print (type(each))\n",
    "    unk_calcs[each] =eqn(unk_data[each], c[0], c[1], c[2])\n",
    "    \n",
    "for value in unk_calcs:\n",
    "    print (value.round(2))\n"
   ]
  }
 ],
 "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": "3.8.3-final"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}