docs/propkatraj-example.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# $pKa$ estimates from propka using a molecular dynamics trajectory"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import MDAnalysis as mda\n",
    "from MDAnalysisTests.datafiles import PSF, DCD"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For demo purposes we'll use a topology and trajectory used in the [MDAnalysis](http://mdanalysis.org) test suite to make a `Universe`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "u = mda.Universe(PSF, DCD)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Universe with 3341 atoms>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We want to use the function `propkatraj.get_propka`, so we need to import `propkatraj`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import propkatraj"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function get_propka in module propkatraj.propkatraj:\n",
      "\n",
      "get_propka(universe, sel='protein', start=None, stop=None, step=None)\n",
      "    Get and store pKas for titrateable residues near the binding site.\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    universe : :class:`MDAnalysis.Universe`\n",
      "        Universe to obtain pKas for.\n",
      "    sel : str, array_like\n",
      "        Selection string to use for selecting atoms to use from given\n",
      "        ``universe``. Can also be a numpy array or list of atom indices to use.\n",
      "    start : int\n",
      "        Frame of trajectory to start from. `None` means start from beginning.\n",
      "    stop : int\n",
      "        Frame of trajectory to end at. `None` means end at trajectory end.\n",
      "    step : int\n",
      "        Step by which to iterate through trajectory frames. propka is slow,\n",
      "        so set according to how finely you need resulting timeseries.\n",
      "    \n",
      "    Results\n",
      "    -------\n",
      "    pkas : :class:`pandas.DataFrame`\n",
      "        DataFrame giving estimated pKa value for each residue for each\n",
      "        trajectory frame. Residue numbers are given as column labels, times as\n",
      "        row labels.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(propkatraj.get_propka)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Universe with 3341 atoms>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "   98/98 t=      97.000 ps  [100.0%]\n"
     ]
    }
   ],
   "source": [
    "pkas = propkatraj.get_propka(u)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
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       "      <td>14.761506</td>\n",
       "      <td>1.729482</td>\n",
       "      <td>2.799022</td>\n",
       "      <td>12.025731</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14.999999</th>\n",
       "      <td>8.414506</td>\n",
       "      <td>12.784329</td>\n",
       "      <td>8.470610</td>\n",
       "      <td>3.832190</td>\n",
       "      <td>11.725337</td>\n",
       "      <td>11.059030</td>\n",
       "      <td>2.225377</td>\n",
       "      <td>14.306852</td>\n",
       "      <td>10.200622</td>\n",
       "      <td>3.673139</td>\n",
       "      <td>...</td>\n",
       "      <td>11.252247</td>\n",
       "      <td>13.925398</td>\n",
       "      <td>12.159504</td>\n",
       "      <td>2.640144</td>\n",
       "      <td>12.567493</td>\n",
       "      <td>2.863452</td>\n",
       "      <td>15.239711</td>\n",
       "      <td>1.660120</td>\n",
       "      <td>1.870052</td>\n",
       "      <td>12.101239</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15.999999</th>\n",
       "      <td>8.371333</td>\n",
       "      <td>12.848333</td>\n",
       "      <td>10.129915</td>\n",
       "      <td>3.117226</td>\n",
       "      <td>11.007835</td>\n",
       "      <td>11.938541</td>\n",
       "      <td>2.346508</td>\n",
       "      <td>13.945860</td>\n",
       "      <td>10.183767</td>\n",
       "      <td>3.800733</td>\n",
       "      <td>...</td>\n",
       "      <td>11.183520</td>\n",
       "      <td>14.156408</td>\n",
       "      <td>12.055522</td>\n",
       "      <td>2.755561</td>\n",
       "      <td>12.632353</td>\n",
       "      <td>2.848002</td>\n",
       "      <td>15.677537</td>\n",
       "      <td>1.871720</td>\n",
       "      <td>2.284396</td>\n",
       "      <td>12.152405</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16.999999</th>\n",
       "      <td>8.378297</td>\n",
       "      <td>12.828879</td>\n",
       "      <td>10.227821</td>\n",
       "      <td>3.825448</td>\n",
       "      <td>11.721341</td>\n",
       "      <td>11.042335</td>\n",
       "      <td>2.420939</td>\n",
       "      <td>14.055141</td>\n",
       "      <td>10.222493</td>\n",
       "      <td>3.886415</td>\n",
       "      <td>...</td>\n",
       "      <td>11.261430</td>\n",
       "      <td>13.732772</td>\n",
       "      <td>12.292913</td>\n",
       "      <td>2.374433</td>\n",
       "      <td>12.673657</td>\n",
       "      <td>2.839859</td>\n",
       "      <td>15.291801</td>\n",
       "      <td>1.798649</td>\n",
       "      <td>1.983634</td>\n",
       "      <td>12.187030</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17.999998</th>\n",
       "      <td>8.292563</td>\n",
       "      <td>12.869862</td>\n",
       "      <td>10.099728</td>\n",
       "      <td>3.860648</td>\n",
       "      <td>11.564296</td>\n",
       "      <td>11.240792</td>\n",
       "      <td>1.885192</td>\n",
       "      <td>14.340119</td>\n",
       "      <td>10.221502</td>\n",
       "      <td>3.860210</td>\n",
       "      <td>...</td>\n",
       "      <td>11.291725</td>\n",
       "      <td>14.183267</td>\n",
       "      <td>12.221660</td>\n",
       "      <td>2.399617</td>\n",
       "      <td>12.590243</td>\n",
       "      <td>2.879767</td>\n",
       "      <td>15.247374</td>\n",
       "      <td>1.862175</td>\n",
       "      <td>1.978016</td>\n",
       "      <td>12.127560</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18.999998</th>\n",
       "      <td>8.382053</td>\n",
       "      <td>12.786648</td>\n",
       "      <td>10.145979</td>\n",
       "      <td>3.258580</td>\n",
       "      <td>11.670429</td>\n",
       "      <td>11.124776</td>\n",
       "      <td>2.018004</td>\n",
       "      <td>14.369498</td>\n",
       "      <td>10.265462</td>\n",
       "      <td>3.753562</td>\n",
       "      <td>...</td>\n",
       "      <td>11.206447</td>\n",
       "      <td>13.463249</td>\n",
       "      <td>12.233887</td>\n",
       "      <td>2.431544</td>\n",
       "      <td>12.620136</td>\n",
       "      <td>2.889585</td>\n",
       "      <td>15.726940</td>\n",
       "      <td>1.782645</td>\n",
       "      <td>2.033880</td>\n",
       "      <td>12.146693</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19.999998</th>\n",
       "      <td>8.211868</td>\n",
       "      <td>12.742334</td>\n",
       "      <td>10.313352</td>\n",
       "      <td>3.568430</td>\n",
       "      <td>11.098646</td>\n",
       "      <td>11.965724</td>\n",
       "      <td>2.167110</td>\n",
       "      <td>14.304788</td>\n",
       "      <td>10.238550</td>\n",
       "      <td>3.496947</td>\n",
       "      <td>...</td>\n",
       "      <td>11.313595</td>\n",
       "      <td>14.380316</td>\n",
       "      <td>12.215145</td>\n",
       "      <td>2.363613</td>\n",
       "      <td>12.546385</td>\n",
       "      <td>2.969960</td>\n",
       "      <td>15.591372</td>\n",
       "      <td>1.720737</td>\n",
       "      <td>1.897033</td>\n",
       "      <td>12.087506</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20.999998</th>\n",
       "      <td>8.257995</td>\n",
       "      <td>12.757468</td>\n",
       "      <td>10.449350</td>\n",
       "      <td>3.724438</td>\n",
       "      <td>11.463569</td>\n",
       "      <td>11.389872</td>\n",
       "      <td>2.671116</td>\n",
       "      <td>13.535897</td>\n",
       "      <td>10.246585</td>\n",
       "      <td>3.832061</td>\n",
       "      <td>...</td>\n",
       "      <td>11.232083</td>\n",
       "      <td>14.314579</td>\n",
       "      <td>12.014115</td>\n",
       "      <td>1.902365</td>\n",
       "      <td>12.576891</td>\n",
       "      <td>2.851240</td>\n",
       "      <td>15.255943</td>\n",
       "      <td>2.200353</td>\n",
       "      <td>2.018013</td>\n",
       "      <td>12.095198</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21.999998</th>\n",
       "      <td>8.113168</td>\n",
       "      <td>12.761162</td>\n",
       "      <td>10.065824</td>\n",
       "      <td>3.317323</td>\n",
       "      <td>11.667095</td>\n",
       "      <td>11.096297</td>\n",
       "      <td>1.840592</td>\n",
       "      <td>14.437534</td>\n",
       "      <td>10.239143</td>\n",
       "      <td>3.835208</td>\n",
       "      <td>...</td>\n",
       "      <td>11.290388</td>\n",
       "      <td>13.853130</td>\n",
       "      <td>12.261211</td>\n",
       "      <td>2.294885</td>\n",
       "      <td>12.623248</td>\n",
       "      <td>2.856827</td>\n",
       "      <td>15.187722</td>\n",
       "      <td>1.911463</td>\n",
       "      <td>2.479582</td>\n",
       "      <td>12.181959</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22.999998</th>\n",
       "      <td>8.295169</td>\n",
       "      <td>12.764637</td>\n",
       "      <td>9.953557</td>\n",
       "      <td>3.172156</td>\n",
       "      <td>12.218926</td>\n",
       "      <td>10.592353</td>\n",
       "      <td>2.458398</td>\n",
       "      <td>14.377380</td>\n",
       "      <td>10.245402</td>\n",
       "      <td>3.440673</td>\n",
       "      <td>...</td>\n",
       "      <td>11.262670</td>\n",
       "      <td>13.198834</td>\n",
       "      <td>12.099587</td>\n",
       "      <td>2.378581</td>\n",
       "      <td>12.552729</td>\n",
       "      <td>2.859978</td>\n",
       "      <td>15.091411</td>\n",
       "      <td>1.931532</td>\n",
       "      <td>2.825360</td>\n",
       "      <td>12.072635</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23.999998</th>\n",
       "      <td>8.284094</td>\n",
       "      <td>12.806121</td>\n",
       "      <td>10.034232</td>\n",
       "      <td>3.440143</td>\n",
       "      <td>10.985647</td>\n",
       "      <td>11.885309</td>\n",
       "      <td>2.564673</td>\n",
       "      <td>14.025089</td>\n",
       "      <td>10.248480</td>\n",
       "      <td>3.909020</td>\n",
       "      <td>...</td>\n",
       "      <td>11.268737</td>\n",
       "      <td>13.972354</td>\n",
       "      <td>12.155925</td>\n",
       "      <td>2.238125</td>\n",
       "      <td>12.566474</td>\n",
       "      <td>2.857207</td>\n",
       "      <td>14.769518</td>\n",
       "      <td>1.988179</td>\n",
       "      <td>2.708782</td>\n",
       "      <td>12.075159</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24.999998</th>\n",
       "      <td>8.126062</td>\n",
       "      <td>12.709277</td>\n",
       "      <td>9.801690</td>\n",
       "      <td>3.279765</td>\n",
       "      <td>11.725067</td>\n",
       "      <td>11.287446</td>\n",
       "      <td>3.301121</td>\n",
       "      <td>13.968335</td>\n",
       "      <td>10.241705</td>\n",
       "      <td>3.836124</td>\n",
       "      <td>...</td>\n",
       "      <td>11.246447</td>\n",
       "      <td>14.047488</td>\n",
       "      <td>12.199055</td>\n",
       "      <td>2.305825</td>\n",
       "      <td>12.506562</td>\n",
       "      <td>2.988004</td>\n",
       "      <td>14.746881</td>\n",
       "      <td>1.970614</td>\n",
       "      <td>2.961683</td>\n",
       "      <td>12.021080</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25.999998</th>\n",
       "      <td>8.162831</td>\n",
       "      <td>12.633829</td>\n",
       "      <td>9.772473</td>\n",
       "      <td>3.552084</td>\n",
       "      <td>11.108169</td>\n",
       "      <td>11.859889</td>\n",
       "      <td>3.360765</td>\n",
       "      <td>14.290826</td>\n",
       "      <td>10.294848</td>\n",
       "      <td>3.931618</td>\n",
       "      <td>...</td>\n",
       "      <td>11.251597</td>\n",
       "      <td>14.204981</td>\n",
       "      <td>11.849512</td>\n",
       "      <td>2.289983</td>\n",
       "      <td>12.523388</td>\n",
       "      <td>2.955526</td>\n",
       "      <td>14.683662</td>\n",
       "      <td>2.035451</td>\n",
       "      <td>2.650493</td>\n",
       "      <td>12.015273</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26.999998</th>\n",
       "      <td>8.278571</td>\n",
       "      <td>12.622226</td>\n",
       "      <td>9.760007</td>\n",
       "      <td>3.165328</td>\n",
       "      <td>11.457409</td>\n",
       "      <td>11.449697</td>\n",
       "      <td>3.286872</td>\n",
       "      <td>14.233380</td>\n",
       "      <td>10.335272</td>\n",
       "      <td>3.857353</td>\n",
       "      <td>...</td>\n",
       "      <td>11.250853</td>\n",
       "      <td>14.178894</td>\n",
       "      <td>12.178238</td>\n",
       "      <td>2.245625</td>\n",
       "      <td>12.545863</td>\n",
       "      <td>3.061258</td>\n",
       "      <td>14.890460</td>\n",
       "      <td>1.779405</td>\n",
       "      <td>2.942830</td>\n",
       "      <td>12.063742</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27.999998</th>\n",
       "      <td>8.220750</td>\n",
       "      <td>12.486997</td>\n",
       "      <td>9.667534</td>\n",
       "      <td>3.749728</td>\n",
       "      <td>11.044923</td>\n",
       "      <td>11.878662</td>\n",
       "      <td>3.152892</td>\n",
       "      <td>14.712181</td>\n",
       "      <td>10.383807</td>\n",
       "      <td>3.917601</td>\n",
       "      <td>...</td>\n",
       "      <td>11.249229</td>\n",
       "      <td>14.044079</td>\n",
       "      <td>11.828196</td>\n",
       "      <td>1.914703</td>\n",
       "      <td>12.618773</td>\n",
       "      <td>2.847718</td>\n",
       "      <td>14.426377</td>\n",
       "      <td>2.077088</td>\n",
       "      <td>2.887995</td>\n",
       "      <td>12.140975</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28.999997</th>\n",
       "      <td>8.148228</td>\n",
       "      <td>12.877762</td>\n",
       "      <td>9.688051</td>\n",
       "      <td>3.110205</td>\n",
       "      <td>12.262636</td>\n",
       "      <td>10.336828</td>\n",
       "      <td>2.436431</td>\n",
       "      <td>14.702594</td>\n",
       "      <td>10.391474</td>\n",
       "      <td>3.774150</td>\n",
       "      <td>...</td>\n",
       "      <td>11.304092</td>\n",
       "      <td>14.398155</td>\n",
       "      <td>11.850579</td>\n",
       "      <td>2.218279</td>\n",
       "      <td>12.561512</td>\n",
       "      <td>2.832006</td>\n",
       "      <td>14.912857</td>\n",
       "      <td>1.908869</td>\n",
       "      <td>2.897482</td>\n",
       "      <td>12.101310</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>67.999994</th>\n",
       "      <td>8.234069</td>\n",
       "      <td>12.688287</td>\n",
       "      <td>9.485276</td>\n",
       "      <td>3.853542</td>\n",
       "      <td>11.154103</td>\n",
       "      <td>12.797969</td>\n",
       "      <td>2.129729</td>\n",
       "      <td>14.037797</td>\n",
       "      <td>10.415446</td>\n",
       "      <td>3.662374</td>\n",
       "      <td>...</td>\n",
       "      <td>10.311450</td>\n",
       "      <td>13.958548</td>\n",
       "      <td>12.017318</td>\n",
       "      <td>1.393603</td>\n",
       "      <td>12.529074</td>\n",
       "      <td>2.917622</td>\n",
       "      <td>14.235408</td>\n",
       "      <td>2.099357</td>\n",
       "      <td>2.647973</td>\n",
       "      <td>11.966785</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>68.999994</th>\n",
       "      <td>8.217370</td>\n",
       "      <td>12.752877</td>\n",
       "      <td>9.576426</td>\n",
       "      <td>3.293057</td>\n",
       "      <td>11.194304</td>\n",
       "      <td>12.669399</td>\n",
       "      <td>2.161224</td>\n",
       "      <td>14.530920</td>\n",
       "      <td>10.410714</td>\n",
       "      <td>3.909284</td>\n",
       "      <td>...</td>\n",
       "      <td>10.234222</td>\n",
       "      <td>13.785087</td>\n",
       "      <td>12.026379</td>\n",
       "      <td>2.183224</td>\n",
       "      <td>12.558827</td>\n",
       "      <td>2.939777</td>\n",
       "      <td>14.875788</td>\n",
       "      <td>1.861912</td>\n",
       "      <td>2.725743</td>\n",
       "      <td>12.023297</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>69.999994</th>\n",
       "      <td>8.236185</td>\n",
       "      <td>12.821083</td>\n",
       "      <td>9.358998</td>\n",
       "      <td>3.247034</td>\n",
       "      <td>11.128970</td>\n",
       "      <td>13.004205</td>\n",
       "      <td>2.043081</td>\n",
       "      <td>14.455010</td>\n",
       "      <td>10.419782</td>\n",
       "      <td>3.805671</td>\n",
       "      <td>...</td>\n",
       "      <td>10.050680</td>\n",
       "      <td>13.795882</td>\n",
       "      <td>12.066310</td>\n",
       "      <td>1.553042</td>\n",
       "      <td>12.657426</td>\n",
       "      <td>2.893078</td>\n",
       "      <td>14.565254</td>\n",
       "      <td>2.124258</td>\n",
       "      <td>3.035445</td>\n",
       "      <td>12.085516</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>70.999994</th>\n",
       "      <td>8.096684</td>\n",
       "      <td>12.779223</td>\n",
       "      <td>9.532746</td>\n",
       "      <td>4.090790</td>\n",
       "      <td>11.174571</td>\n",
       "      <td>12.857135</td>\n",
       "      <td>2.431482</td>\n",
       "      <td>14.511018</td>\n",
       "      <td>10.415055</td>\n",
       "      <td>3.382305</td>\n",
       "      <td>...</td>\n",
       "      <td>10.211636</td>\n",
       "      <td>14.016347</td>\n",
       "      <td>12.076282</td>\n",
       "      <td>1.757155</td>\n",
       "      <td>12.581834</td>\n",
       "      <td>2.810367</td>\n",
       "      <td>14.041358</td>\n",
       "      <td>2.034538</td>\n",
       "      <td>2.708400</td>\n",
       "      <td>11.945573</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>71.999994</th>\n",
       "      <td>8.063028</td>\n",
       "      <td>12.602990</td>\n",
       "      <td>9.621926</td>\n",
       "      <td>3.330637</td>\n",
       "      <td>11.193111</td>\n",
       "      <td>12.981678</td>\n",
       "      <td>2.215755</td>\n",
       "      <td>14.507810</td>\n",
       "      <td>10.418598</td>\n",
       "      <td>3.578107</td>\n",
       "      <td>...</td>\n",
       "      <td>10.369944</td>\n",
       "      <td>13.928295</td>\n",
       "      <td>11.925509</td>\n",
       "      <td>1.514957</td>\n",
       "      <td>12.600303</td>\n",
       "      <td>2.846444</td>\n",
       "      <td>14.787398</td>\n",
       "      <td>2.053882</td>\n",
       "      <td>2.636972</td>\n",
       "      <td>11.997957</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>72.999994</th>\n",
       "      <td>8.191486</td>\n",
       "      <td>12.978181</td>\n",
       "      <td>9.380550</td>\n",
       "      <td>3.434643</td>\n",
       "      <td>11.238603</td>\n",
       "      <td>12.810054</td>\n",
       "      <td>2.126122</td>\n",
       "      <td>14.476278</td>\n",
       "      <td>10.418777</td>\n",
       "      <td>3.863152</td>\n",
       "      <td>...</td>\n",
       "      <td>10.302589</td>\n",
       "      <td>13.993648</td>\n",
       "      <td>12.012218</td>\n",
       "      <td>1.406113</td>\n",
       "      <td>12.576336</td>\n",
       "      <td>2.893936</td>\n",
       "      <td>14.526091</td>\n",
       "      <td>2.168644</td>\n",
       "      <td>2.901869</td>\n",
       "      <td>11.952610</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>73.999993</th>\n",
       "      <td>8.199479</td>\n",
       "      <td>12.915186</td>\n",
       "      <td>9.524838</td>\n",
       "      <td>3.584678</td>\n",
       "      <td>11.146036</td>\n",
       "      <td>12.966132</td>\n",
       "      <td>2.387495</td>\n",
       "      <td>14.394837</td>\n",
       "      <td>10.413967</td>\n",
       "      <td>3.608844</td>\n",
       "      <td>...</td>\n",
       "      <td>10.291056</td>\n",
       "      <td>13.963564</td>\n",
       "      <td>12.198527</td>\n",
       "      <td>1.585866</td>\n",
       "      <td>12.637036</td>\n",
       "      <td>2.886667</td>\n",
       "      <td>14.205150</td>\n",
       "      <td>2.071123</td>\n",
       "      <td>3.117254</td>\n",
       "      <td>12.064325</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>74.999993</th>\n",
       "      <td>8.182842</td>\n",
       "      <td>12.895985</td>\n",
       "      <td>9.426143</td>\n",
       "      <td>3.221568</td>\n",
       "      <td>11.184200</td>\n",
       "      <td>12.831282</td>\n",
       "      <td>2.111825</td>\n",
       "      <td>14.172176</td>\n",
       "      <td>10.408776</td>\n",
       "      <td>3.982070</td>\n",
       "      <td>...</td>\n",
       "      <td>10.149291</td>\n",
       "      <td>14.172377</td>\n",
       "      <td>12.088119</td>\n",
       "      <td>2.442481</td>\n",
       "      <td>12.621662</td>\n",
       "      <td>2.841235</td>\n",
       "      <td>14.867746</td>\n",
       "      <td>1.918196</td>\n",
       "      <td>2.742337</td>\n",
       "      <td>12.127236</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75.999993</th>\n",
       "      <td>8.358634</td>\n",
       "      <td>12.628319</td>\n",
       "      <td>9.481202</td>\n",
       "      <td>3.765051</td>\n",
       "      <td>11.357670</td>\n",
       "      <td>10.415960</td>\n",
       "      <td>2.375430</td>\n",
       "      <td>14.373560</td>\n",
       "      <td>10.401463</td>\n",
       "      <td>4.010099</td>\n",
       "      <td>...</td>\n",
       "      <td>9.951641</td>\n",
       "      <td>14.152224</td>\n",
       "      <td>12.044310</td>\n",
       "      <td>2.021854</td>\n",
       "      <td>12.579555</td>\n",
       "      <td>2.829770</td>\n",
       "      <td>14.369837</td>\n",
       "      <td>2.188297</td>\n",
       "      <td>2.893287</td>\n",
       "      <td>12.071683</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>76.999993</th>\n",
       "      <td>8.119584</td>\n",
       "      <td>12.751737</td>\n",
       "      <td>9.483233</td>\n",
       "      <td>3.174579</td>\n",
       "      <td>11.161498</td>\n",
       "      <td>10.624141</td>\n",
       "      <td>2.305992</td>\n",
       "      <td>14.380449</td>\n",
       "      <td>10.406850</td>\n",
       "      <td>3.946893</td>\n",
       "      <td>...</td>\n",
       "      <td>9.789693</td>\n",
       "      <td>14.122811</td>\n",
       "      <td>12.032042</td>\n",
       "      <td>2.174867</td>\n",
       "      <td>12.584618</td>\n",
       "      <td>2.895526</td>\n",
       "      <td>15.001334</td>\n",
       "      <td>1.882042</td>\n",
       "      <td>2.640203</td>\n",
       "      <td>11.981535</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>77.999993</th>\n",
       "      <td>8.085736</td>\n",
       "      <td>12.850429</td>\n",
       "      <td>9.696542</td>\n",
       "      <td>4.020946</td>\n",
       "      <td>11.139483</td>\n",
       "      <td>12.881709</td>\n",
       "      <td>2.849733</td>\n",
       "      <td>14.196280</td>\n",
       "      <td>10.370254</td>\n",
       "      <td>3.971105</td>\n",
       "      <td>...</td>\n",
       "      <td>10.069996</td>\n",
       "      <td>14.268926</td>\n",
       "      <td>12.085710</td>\n",
       "      <td>1.610458</td>\n",
       "      <td>12.565278</td>\n",
       "      <td>2.863997</td>\n",
       "      <td>14.072404</td>\n",
       "      <td>1.968966</td>\n",
       "      <td>2.789703</td>\n",
       "      <td>12.077567</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>78.999993</th>\n",
       "      <td>8.213239</td>\n",
       "      <td>12.825219</td>\n",
       "      <td>9.552877</td>\n",
       "      <td>3.942106</td>\n",
       "      <td>11.138348</td>\n",
       "      <td>12.633567</td>\n",
       "      <td>2.669322</td>\n",
       "      <td>13.948247</td>\n",
       "      <td>10.401099</td>\n",
       "      <td>3.944989</td>\n",
       "      <td>...</td>\n",
       "      <td>10.108002</td>\n",
       "      <td>13.868984</td>\n",
       "      <td>12.192199</td>\n",
       "      <td>2.145694</td>\n",
       "      <td>12.542187</td>\n",
       "      <td>2.821602</td>\n",
       "      <td>14.144374</td>\n",
       "      <td>1.888087</td>\n",
       "      <td>2.705698</td>\n",
       "      <td>12.007610</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>79.999993</th>\n",
       "      <td>8.237191</td>\n",
       "      <td>12.760774</td>\n",
       "      <td>9.536422</td>\n",
       "      <td>4.278961</td>\n",
       "      <td>11.357289</td>\n",
       "      <td>10.264614</td>\n",
       "      <td>2.545300</td>\n",
       "      <td>14.012014</td>\n",
       "      <td>10.409996</td>\n",
       "      <td>3.766398</td>\n",
       "      <td>...</td>\n",
       "      <td>9.661010</td>\n",
       "      <td>14.057171</td>\n",
       "      <td>11.847876</td>\n",
       "      <td>2.215782</td>\n",
       "      <td>12.501813</td>\n",
       "      <td>2.779889</td>\n",
       "      <td>13.876635</td>\n",
       "      <td>1.912921</td>\n",
       "      <td>2.775303</td>\n",
       "      <td>12.026346</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>80.999993</th>\n",
       "      <td>8.270470</td>\n",
       "      <td>12.948032</td>\n",
       "      <td>9.313148</td>\n",
       "      <td>3.800876</td>\n",
       "      <td>11.168530</td>\n",
       "      <td>12.896368</td>\n",
       "      <td>2.284218</td>\n",
       "      <td>13.642745</td>\n",
       "      <td>10.419199</td>\n",
       "      <td>3.914046</td>\n",
       "      <td>...</td>\n",
       "      <td>10.093286</td>\n",
       "      <td>14.040334</td>\n",
       "      <td>11.970192</td>\n",
       "      <td>2.251428</td>\n",
       "      <td>12.596084</td>\n",
       "      <td>2.854473</td>\n",
       "      <td>14.338475</td>\n",
       "      <td>1.911809</td>\n",
       "      <td>2.662349</td>\n",
       "      <td>12.081114</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>81.999993</th>\n",
       "      <td>8.242363</td>\n",
       "      <td>12.751857</td>\n",
       "      <td>9.423453</td>\n",
       "      <td>3.280641</td>\n",
       "      <td>11.160552</td>\n",
       "      <td>10.611587</td>\n",
       "      <td>2.037363</td>\n",
       "      <td>13.566716</td>\n",
       "      <td>10.416939</td>\n",
       "      <td>3.873082</td>\n",
       "      <td>...</td>\n",
       "      <td>9.911026</td>\n",
       "      <td>14.063027</td>\n",
       "      <td>11.856137</td>\n",
       "      <td>2.149956</td>\n",
       "      <td>12.553984</td>\n",
       "      <td>2.911541</td>\n",
       "      <td>14.791251</td>\n",
       "      <td>1.840909</td>\n",
       "      <td>2.783413</td>\n",
       "      <td>11.987493</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>82.999993</th>\n",
       "      <td>8.195895</td>\n",
       "      <td>12.668728</td>\n",
       "      <td>9.570311</td>\n",
       "      <td>4.007506</td>\n",
       "      <td>11.206878</td>\n",
       "      <td>12.803643</td>\n",
       "      <td>2.430262</td>\n",
       "      <td>13.477929</td>\n",
       "      <td>10.413229</td>\n",
       "      <td>3.287594</td>\n",
       "      <td>...</td>\n",
       "      <td>10.088110</td>\n",
       "      <td>13.863771</td>\n",
       "      <td>12.086154</td>\n",
       "      <td>2.139944</td>\n",
       "      <td>12.580946</td>\n",
       "      <td>3.270617</td>\n",
       "      <td>13.814350</td>\n",
       "      <td>1.528530</td>\n",
       "      <td>2.974642</td>\n",
       "      <td>12.063377</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>83.999993</th>\n",
       "      <td>8.157127</td>\n",
       "      <td>12.871825</td>\n",
       "      <td>9.407316</td>\n",
       "      <td>3.654933</td>\n",
       "      <td>11.165676</td>\n",
       "      <td>12.791376</td>\n",
       "      <td>2.234646</td>\n",
       "      <td>13.514556</td>\n",
       "      <td>10.408521</td>\n",
       "      <td>3.590304</td>\n",
       "      <td>...</td>\n",
       "      <td>10.166735</td>\n",
       "      <td>14.061047</td>\n",
       "      <td>11.990947</td>\n",
       "      <td>2.079924</td>\n",
       "      <td>12.577767</td>\n",
       "      <td>2.832545</td>\n",
       "      <td>14.469007</td>\n",
       "      <td>1.857598</td>\n",
       "      <td>2.722474</td>\n",
       "      <td>12.127180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>84.999993</th>\n",
       "      <td>8.172470</td>\n",
       "      <td>12.795459</td>\n",
       "      <td>9.502325</td>\n",
       "      <td>3.652660</td>\n",
       "      <td>11.183684</td>\n",
       "      <td>13.069655</td>\n",
       "      <td>2.273025</td>\n",
       "      <td>13.535413</td>\n",
       "      <td>10.412635</td>\n",
       "      <td>3.940653</td>\n",
       "      <td>...</td>\n",
       "      <td>10.100105</td>\n",
       "      <td>13.696244</td>\n",
       "      <td>11.897562</td>\n",
       "      <td>2.110835</td>\n",
       "      <td>12.612457</td>\n",
       "      <td>2.890827</td>\n",
       "      <td>14.318709</td>\n",
       "      <td>1.844699</td>\n",
       "      <td>2.899924</td>\n",
       "      <td>12.058972</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>85.999992</th>\n",
       "      <td>8.324049</td>\n",
       "      <td>12.567936</td>\n",
       "      <td>9.480613</td>\n",
       "      <td>3.622231</td>\n",
       "      <td>11.373683</td>\n",
       "      <td>10.393116</td>\n",
       "      <td>2.353251</td>\n",
       "      <td>13.480614</td>\n",
       "      <td>10.402455</td>\n",
       "      <td>3.303033</td>\n",
       "      <td>...</td>\n",
       "      <td>9.861688</td>\n",
       "      <td>14.164806</td>\n",
       "      <td>11.871102</td>\n",
       "      <td>1.249881</td>\n",
       "      <td>12.576047</td>\n",
       "      <td>2.896164</td>\n",
       "      <td>14.532731</td>\n",
       "      <td>1.943396</td>\n",
       "      <td>2.875820</td>\n",
       "      <td>12.090662</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>86.999992</th>\n",
       "      <td>8.247670</td>\n",
       "      <td>12.714223</td>\n",
       "      <td>9.515493</td>\n",
       "      <td>3.794445</td>\n",
       "      <td>11.158621</td>\n",
       "      <td>10.722389</td>\n",
       "      <td>2.270400</td>\n",
       "      <td>13.462865</td>\n",
       "      <td>10.412977</td>\n",
       "      <td>3.473437</td>\n",
       "      <td>...</td>\n",
       "      <td>9.758040</td>\n",
       "      <td>14.080611</td>\n",
       "      <td>12.032261</td>\n",
       "      <td>2.021434</td>\n",
       "      <td>12.589366</td>\n",
       "      <td>2.871884</td>\n",
       "      <td>14.230057</td>\n",
       "      <td>1.845855</td>\n",
       "      <td>2.867483</td>\n",
       "      <td>12.035030</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>87.999992</th>\n",
       "      <td>8.139357</td>\n",
       "      <td>12.774905</td>\n",
       "      <td>9.516041</td>\n",
       "      <td>3.553928</td>\n",
       "      <td>11.152201</td>\n",
       "      <td>12.780928</td>\n",
       "      <td>2.147438</td>\n",
       "      <td>13.508428</td>\n",
       "      <td>10.417374</td>\n",
       "      <td>3.897503</td>\n",
       "      <td>...</td>\n",
       "      <td>10.092891</td>\n",
       "      <td>14.278969</td>\n",
       "      <td>11.913697</td>\n",
       "      <td>1.353076</td>\n",
       "      <td>12.660511</td>\n",
       "      <td>2.868119</td>\n",
       "      <td>14.519116</td>\n",
       "      <td>1.974390</td>\n",
       "      <td>2.910038</td>\n",
       "      <td>12.043164</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>88.999992</th>\n",
       "      <td>8.123216</td>\n",
       "      <td>12.682819</td>\n",
       "      <td>9.465195</td>\n",
       "      <td>3.337765</td>\n",
       "      <td>11.140135</td>\n",
       "      <td>12.252150</td>\n",
       "      <td>2.097442</td>\n",
       "      <td>13.614001</td>\n",
       "      <td>10.412341</td>\n",
       "      <td>3.483184</td>\n",
       "      <td>...</td>\n",
       "      <td>10.484858</td>\n",
       "      <td>14.084620</td>\n",
       "      <td>11.921196</td>\n",
       "      <td>1.978535</td>\n",
       "      <td>12.562530</td>\n",
       "      <td>2.810249</td>\n",
       "      <td>14.712487</td>\n",
       "      <td>1.853410</td>\n",
       "      <td>2.765294</td>\n",
       "      <td>12.148617</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>89.999992</th>\n",
       "      <td>8.234053</td>\n",
       "      <td>13.070980</td>\n",
       "      <td>9.518752</td>\n",
       "      <td>3.832726</td>\n",
       "      <td>11.142022</td>\n",
       "      <td>12.608172</td>\n",
       "      <td>2.567818</td>\n",
       "      <td>13.236013</td>\n",
       "      <td>10.408648</td>\n",
       "      <td>3.142208</td>\n",
       "      <td>...</td>\n",
       "      <td>10.086789</td>\n",
       "      <td>14.153632</td>\n",
       "      <td>11.780808</td>\n",
       "      <td>2.231474</td>\n",
       "      <td>12.599925</td>\n",
       "      <td>2.850730</td>\n",
       "      <td>14.302761</td>\n",
       "      <td>1.857987</td>\n",
       "      <td>2.738830</td>\n",
       "      <td>12.160411</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>90.999992</th>\n",
       "      <td>8.143206</td>\n",
       "      <td>12.869614</td>\n",
       "      <td>9.715161</td>\n",
       "      <td>3.967450</td>\n",
       "      <td>11.106568</td>\n",
       "      <td>12.603831</td>\n",
       "      <td>1.867534</td>\n",
       "      <td>13.795809</td>\n",
       "      <td>10.409642</td>\n",
       "      <td>3.151011</td>\n",
       "      <td>...</td>\n",
       "      <td>10.139014</td>\n",
       "      <td>14.087207</td>\n",
       "      <td>11.792202</td>\n",
       "      <td>2.046611</td>\n",
       "      <td>12.568710</td>\n",
       "      <td>2.841544</td>\n",
       "      <td>14.150493</td>\n",
       "      <td>1.929554</td>\n",
       "      <td>2.728138</td>\n",
       "      <td>12.092189</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>91.999992</th>\n",
       "      <td>8.131866</td>\n",
       "      <td>12.912778</td>\n",
       "      <td>9.725321</td>\n",
       "      <td>3.532969</td>\n",
       "      <td>11.088002</td>\n",
       "      <td>12.908841</td>\n",
       "      <td>1.746542</td>\n",
       "      <td>13.727827</td>\n",
       "      <td>10.410205</td>\n",
       "      <td>3.211003</td>\n",
       "      <td>...</td>\n",
       "      <td>10.120012</td>\n",
       "      <td>14.165063</td>\n",
       "      <td>12.005584</td>\n",
       "      <td>2.098791</td>\n",
       "      <td>12.584911</td>\n",
       "      <td>2.899087</td>\n",
       "      <td>14.531872</td>\n",
       "      <td>1.802502</td>\n",
       "      <td>2.936365</td>\n",
       "      <td>12.207916</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>92.999992</th>\n",
       "      <td>8.227663</td>\n",
       "      <td>12.859320</td>\n",
       "      <td>9.685207</td>\n",
       "      <td>3.288962</td>\n",
       "      <td>11.160589</td>\n",
       "      <td>10.748242</td>\n",
       "      <td>2.199330</td>\n",
       "      <td>13.464198</td>\n",
       "      <td>10.415339</td>\n",
       "      <td>3.170045</td>\n",
       "      <td>...</td>\n",
       "      <td>9.880471</td>\n",
       "      <td>13.949351</td>\n",
       "      <td>11.992260</td>\n",
       "      <td>2.222933</td>\n",
       "      <td>12.586705</td>\n",
       "      <td>2.850050</td>\n",
       "      <td>14.934541</td>\n",
       "      <td>1.907153</td>\n",
       "      <td>2.651611</td>\n",
       "      <td>12.088406</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>93.999992</th>\n",
       "      <td>8.186176</td>\n",
       "      <td>12.757756</td>\n",
       "      <td>9.513816</td>\n",
       "      <td>3.238071</td>\n",
       "      <td>11.190640</td>\n",
       "      <td>12.769068</td>\n",
       "      <td>2.529363</td>\n",
       "      <td>13.107833</td>\n",
       "      <td>10.406756</td>\n",
       "      <td>2.799962</td>\n",
       "      <td>...</td>\n",
       "      <td>10.121907</td>\n",
       "      <td>14.081723</td>\n",
       "      <td>11.870259</td>\n",
       "      <td>1.986225</td>\n",
       "      <td>12.608072</td>\n",
       "      <td>2.871361</td>\n",
       "      <td>14.891981</td>\n",
       "      <td>1.832945</td>\n",
       "      <td>2.814808</td>\n",
       "      <td>12.156833</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>94.999992</th>\n",
       "      <td>8.238244</td>\n",
       "      <td>12.467099</td>\n",
       "      <td>9.666167</td>\n",
       "      <td>3.109121</td>\n",
       "      <td>11.158498</td>\n",
       "      <td>10.730249</td>\n",
       "      <td>2.559985</td>\n",
       "      <td>13.364670</td>\n",
       "      <td>10.399769</td>\n",
       "      <td>3.161105</td>\n",
       "      <td>...</td>\n",
       "      <td>9.794297</td>\n",
       "      <td>14.102544</td>\n",
       "      <td>11.972831</td>\n",
       "      <td>2.111825</td>\n",
       "      <td>12.587400</td>\n",
       "      <td>2.832126</td>\n",
       "      <td>15.088873</td>\n",
       "      <td>1.840302</td>\n",
       "      <td>2.677849</td>\n",
       "      <td>12.124620</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>95.999992</th>\n",
       "      <td>8.138980</td>\n",
       "      <td>12.766968</td>\n",
       "      <td>9.568431</td>\n",
       "      <td>3.444933</td>\n",
       "      <td>11.150028</td>\n",
       "      <td>12.756027</td>\n",
       "      <td>1.412159</td>\n",
       "      <td>14.025942</td>\n",
       "      <td>10.418870</td>\n",
       "      <td>3.141029</td>\n",
       "      <td>...</td>\n",
       "      <td>10.065119</td>\n",
       "      <td>14.162129</td>\n",
       "      <td>11.981639</td>\n",
       "      <td>2.033930</td>\n",
       "      <td>12.618683</td>\n",
       "      <td>2.878073</td>\n",
       "      <td>14.697977</td>\n",
       "      <td>1.832371</td>\n",
       "      <td>2.831865</td>\n",
       "      <td>12.164143</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>96.999991</th>\n",
       "      <td>8.233431</td>\n",
       "      <td>13.041351</td>\n",
       "      <td>9.442419</td>\n",
       "      <td>3.863899</td>\n",
       "      <td>11.100317</td>\n",
       "      <td>12.028295</td>\n",
       "      <td>2.390857</td>\n",
       "      <td>13.257782</td>\n",
       "      <td>10.402669</td>\n",
       "      <td>2.822537</td>\n",
       "      <td>...</td>\n",
       "      <td>9.727817</td>\n",
       "      <td>14.142641</td>\n",
       "      <td>12.038303</td>\n",
       "      <td>1.731744</td>\n",
       "      <td>12.538244</td>\n",
       "      <td>2.932928</td>\n",
       "      <td>14.210130</td>\n",
       "      <td>1.880199</td>\n",
       "      <td>2.871634</td>\n",
       "      <td>12.139620</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>98 rows × 75 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                1          2          13        22         23         24   \\\n",
       "time                                                                        \n",
       "0.000000   7.463827  12.394323   8.344347  4.089682  11.542252  11.014674   \n",
       "1.000000   7.295912  13.246053   8.292964  3.854538  11.335496  11.264583   \n",
       "2.000000   7.446632  13.206571   7.998785  4.045926  11.002587  11.863192   \n",
       "3.000000   7.364847  12.870917   7.608654  3.205676  11.649248  11.196828   \n",
       "4.000000   8.431659  12.497731   8.108605  3.366243  11.438484  11.422239   \n",
       "5.000000   8.413805  12.758642   7.928219  3.546709  11.525468  11.435645   \n",
       "5.999999   8.424927  12.865650   7.763595  3.572566  11.005743  11.877428   \n",
       "6.999999   8.458619  12.602061   8.214971  3.191635  11.073781  11.930756   \n",
       "7.999999   8.302842  12.761938   7.907986  3.244834  11.477911  11.293736   \n",
       "8.999999   8.351575  13.005559   8.009939  3.481800  11.918353  10.815883   \n",
       "9.999999   8.343245  12.754983   8.281422  3.698913  11.114288  11.980105   \n",
       "10.999999  8.227969  12.894425   7.990719  3.563498  11.604705  11.340859   \n",
       "11.999999  8.217106  12.778370   8.183820  2.985624  11.625326  11.232681   \n",
       "12.999999  8.319235  12.663789   8.119284  3.201226  11.516159  11.469543   \n",
       "13.999999  8.389114  12.750756   8.451446  3.441493  11.847955  11.066462   \n",
       "14.999999  8.414506  12.784329   8.470610  3.832190  11.725337  11.059030   \n",
       "15.999999  8.371333  12.848333  10.129915  3.117226  11.007835  11.938541   \n",
       "16.999999  8.378297  12.828879  10.227821  3.825448  11.721341  11.042335   \n",
       "17.999998  8.292563  12.869862  10.099728  3.860648  11.564296  11.240792   \n",
       "18.999998  8.382053  12.786648  10.145979  3.258580  11.670429  11.124776   \n",
       "19.999998  8.211868  12.742334  10.313352  3.568430  11.098646  11.965724   \n",
       "20.999998  8.257995  12.757468  10.449350  3.724438  11.463569  11.389872   \n",
       "21.999998  8.113168  12.761162  10.065824  3.317323  11.667095  11.096297   \n",
       "22.999998  8.295169  12.764637   9.953557  3.172156  12.218926  10.592353   \n",
       "23.999998  8.284094  12.806121  10.034232  3.440143  10.985647  11.885309   \n",
       "24.999998  8.126062  12.709277   9.801690  3.279765  11.725067  11.287446   \n",
       "25.999998  8.162831  12.633829   9.772473  3.552084  11.108169  11.859889   \n",
       "26.999998  8.278571  12.622226   9.760007  3.165328  11.457409  11.449697   \n",
       "27.999998  8.220750  12.486997   9.667534  3.749728  11.044923  11.878662   \n",
       "28.999997  8.148228  12.877762   9.688051  3.110205  12.262636  10.336828   \n",
       "...             ...        ...        ...       ...        ...        ...   \n",
       "67.999994  8.234069  12.688287   9.485276  3.853542  11.154103  12.797969   \n",
       "68.999994  8.217370  12.752877   9.576426  3.293057  11.194304  12.669399   \n",
       "69.999994  8.236185  12.821083   9.358998  3.247034  11.128970  13.004205   \n",
       "70.999994  8.096684  12.779223   9.532746  4.090790  11.174571  12.857135   \n",
       "71.999994  8.063028  12.602990   9.621926  3.330637  11.193111  12.981678   \n",
       "72.999994  8.191486  12.978181   9.380550  3.434643  11.238603  12.810054   \n",
       "73.999993  8.199479  12.915186   9.524838  3.584678  11.146036  12.966132   \n",
       "74.999993  8.182842  12.895985   9.426143  3.221568  11.184200  12.831282   \n",
       "75.999993  8.358634  12.628319   9.481202  3.765051  11.357670  10.415960   \n",
       "76.999993  8.119584  12.751737   9.483233  3.174579  11.161498  10.624141   \n",
       "77.999993  8.085736  12.850429   9.696542  4.020946  11.139483  12.881709   \n",
       "78.999993  8.213239  12.825219   9.552877  3.942106  11.138348  12.633567   \n",
       "79.999993  8.237191  12.760774   9.536422  4.278961  11.357289  10.264614   \n",
       "80.999993  8.270470  12.948032   9.313148  3.800876  11.168530  12.896368   \n",
       "81.999993  8.242363  12.751857   9.423453  3.280641  11.160552  10.611587   \n",
       "82.999993  8.195895  12.668728   9.570311  4.007506  11.206878  12.803643   \n",
       "83.999993  8.157127  12.871825   9.407316  3.654933  11.165676  12.791376   \n",
       "84.999993  8.172470  12.795459   9.502325  3.652660  11.183684  13.069655   \n",
       "85.999992  8.324049  12.567936   9.480613  3.622231  11.373683  10.393116   \n",
       "86.999992  8.247670  12.714223   9.515493  3.794445  11.158621  10.722389   \n",
       "87.999992  8.139357  12.774905   9.516041  3.553928  11.152201  12.780928   \n",
       "88.999992  8.123216  12.682819   9.465195  3.337765  11.140135  12.252150   \n",
       "89.999992  8.234053  13.070980   9.518752  3.832726  11.142022  12.608172   \n",
       "90.999992  8.143206  12.869614   9.715161  3.967450  11.106568  12.603831   \n",
       "91.999992  8.131866  12.912778   9.725321  3.532969  11.088002  12.908841   \n",
       "92.999992  8.227663  12.859320   9.685207  3.288962  11.160589  10.748242   \n",
       "93.999992  8.186176  12.757756   9.513816  3.238071  11.190640  12.769068   \n",
       "94.999992  8.238244  12.467099   9.666167  3.109121  11.158498  10.730249   \n",
       "95.999992  8.138980  12.766968   9.568431  3.444933  11.150028  12.756027   \n",
       "96.999991  8.233431  13.041351   9.442419  3.863899  11.100317  12.028295   \n",
       "\n",
       "                33         36         40        44     ...            192  \\\n",
       "time                                                   ...                  \n",
       "0.000000   2.364393  14.056423  10.092552  3.505057    ...      11.181185   \n",
       "1.000000   2.638269  13.262729  10.088877  3.794538    ...      11.221025   \n",
       "2.000000   2.235340  13.454440  10.065400  3.569236    ...      11.217360   \n",
       "3.000000   1.891373  13.442788  10.079494  3.280471    ...      11.272248   \n",
       "4.000000   2.458694  13.349054  10.050490  3.805812    ...      11.202101   \n",
       "5.000000   2.373255  14.912229   9.960275  3.702452    ...      11.276864   \n",
       "5.999999   2.545704  13.553502  10.072688  3.628277    ...      11.275164   \n",
       "6.999999   2.676321  13.342114  10.056925  3.948229    ...      11.223411   \n",
       "7.999999   3.170560  13.115886  10.149841  3.727501    ...      11.219728   \n",
       "8.999999   3.299541  13.851676  10.087693  3.731568    ...      11.306882   \n",
       "9.999999   3.211439  12.838007  10.101450  3.951770    ...      11.238651   \n",
       "10.999999  3.010283  13.683737  10.060025  3.978007    ...      11.233255   \n",
       "11.999999  2.308900  14.928786  10.147672  3.845300    ...      11.289601   \n",
       "12.999999  2.247972  13.981869  10.149026  3.918088    ...      11.253381   \n",
       "13.999999  2.960558  13.732937  10.157360  3.824709    ...      11.273781   \n",
       "14.999999  2.225377  14.306852  10.200622  3.673139    ...      11.252247   \n",
       "15.999999  2.346508  13.945860  10.183767  3.800733    ...      11.183520   \n",
       "16.999999  2.420939  14.055141  10.222493  3.886415    ...      11.261430   \n",
       "17.999998  1.885192  14.340119  10.221502  3.860210    ...      11.291725   \n",
       "18.999998  2.018004  14.369498  10.265462  3.753562    ...      11.206447   \n",
       "19.999998  2.167110  14.304788  10.238550  3.496947    ...      11.313595   \n",
       "20.999998  2.671116  13.535897  10.246585  3.832061    ...      11.232083   \n",
       "21.999998  1.840592  14.437534  10.239143  3.835208    ...      11.290388   \n",
       "22.999998  2.458398  14.377380  10.245402  3.440673    ...      11.262670   \n",
       "23.999998  2.564673  14.025089  10.248480  3.909020    ...      11.268737   \n",
       "24.999998  3.301121  13.968335  10.241705  3.836124    ...      11.246447   \n",
       "25.999998  3.360765  14.290826  10.294848  3.931618    ...      11.251597   \n",
       "26.999998  3.286872  14.233380  10.335272  3.857353    ...      11.250853   \n",
       "27.999998  3.152892  14.712181  10.383807  3.917601    ...      11.249229   \n",
       "28.999997  2.436431  14.702594  10.391474  3.774150    ...      11.304092   \n",
       "...             ...        ...        ...       ...    ...            ...   \n",
       "67.999994  2.129729  14.037797  10.415446  3.662374    ...      10.311450   \n",
       "68.999994  2.161224  14.530920  10.410714  3.909284    ...      10.234222   \n",
       "69.999994  2.043081  14.455010  10.419782  3.805671    ...      10.050680   \n",
       "70.999994  2.431482  14.511018  10.415055  3.382305    ...      10.211636   \n",
       "71.999994  2.215755  14.507810  10.418598  3.578107    ...      10.369944   \n",
       "72.999994  2.126122  14.476278  10.418777  3.863152    ...      10.302589   \n",
       "73.999993  2.387495  14.394837  10.413967  3.608844    ...      10.291056   \n",
       "74.999993  2.111825  14.172176  10.408776  3.982070    ...      10.149291   \n",
       "75.999993  2.375430  14.373560  10.401463  4.010099    ...       9.951641   \n",
       "76.999993  2.305992  14.380449  10.406850  3.946893    ...       9.789693   \n",
       "77.999993  2.849733  14.196280  10.370254  3.971105    ...      10.069996   \n",
       "78.999993  2.669322  13.948247  10.401099  3.944989    ...      10.108002   \n",
       "79.999993  2.545300  14.012014  10.409996  3.766398    ...       9.661010   \n",
       "80.999993  2.284218  13.642745  10.419199  3.914046    ...      10.093286   \n",
       "81.999993  2.037363  13.566716  10.416939  3.873082    ...       9.911026   \n",
       "82.999993  2.430262  13.477929  10.413229  3.287594    ...      10.088110   \n",
       "83.999993  2.234646  13.514556  10.408521  3.590304    ...      10.166735   \n",
       "84.999993  2.273025  13.535413  10.412635  3.940653    ...      10.100105   \n",
       "85.999992  2.353251  13.480614  10.402455  3.303033    ...       9.861688   \n",
       "86.999992  2.270400  13.462865  10.412977  3.473437    ...       9.758040   \n",
       "87.999992  2.147438  13.508428  10.417374  3.897503    ...      10.092891   \n",
       "88.999992  2.097442  13.614001  10.412341  3.483184    ...      10.484858   \n",
       "89.999992  2.567818  13.236013  10.408648  3.142208    ...      10.086789   \n",
       "90.999992  1.867534  13.795809  10.409642  3.151011    ...      10.139014   \n",
       "91.999992  1.746542  13.727827  10.410205  3.211003    ...      10.120012   \n",
       "92.999992  2.199330  13.464198  10.415339  3.170045    ...       9.880471   \n",
       "93.999992  2.529363  13.107833  10.406756  2.799962    ...      10.121907   \n",
       "94.999992  2.559985  13.364670  10.399769  3.161105    ...       9.794297   \n",
       "95.999992  1.412159  14.025942  10.418870  3.141029    ...      10.065119   \n",
       "96.999991  2.390857  13.257782  10.402669  2.822537    ...       9.727817   \n",
       "\n",
       "                 193        195       197        200       204        206  \\\n",
       "time                                                                        \n",
       "0.000000   13.954125  12.392177  2.179990  12.578384  3.817193  14.744914   \n",
       "1.000000   13.739182  12.308242  2.276176  12.686712  3.638481  15.098640   \n",
       "2.000000   13.806216  12.258947  2.343485  12.692147  2.838206  14.823071   \n",
       "3.000000   14.030501  12.313860  2.576164  12.626028  3.056464  15.060629   \n",
       "4.000000   13.930253  12.187661  2.475596  12.687261  2.804341  14.958514   \n",
       "5.000000   14.364916  12.283782  2.351434  12.634666  2.875394  14.585283   \n",
       "5.999999   13.754629  12.249282  2.516046  12.620409  2.873569  14.684630   \n",
       "6.999999   13.850106  12.139345  2.540835  12.581422  2.831289  14.934267   \n",
       "7.999999   14.444294  12.046917  2.350866  12.591843  2.767964  14.928158   \n",
       "8.999999   14.170464  12.156431  2.209389  12.676753  2.848183  14.597813   \n",
       "9.999999   14.283578  12.108489  2.428701  12.641191  2.898898  14.477845   \n",
       "10.999999  14.218972  12.067041  1.867755  12.666754  2.854968  14.628168   \n",
       "11.999999  14.426477  11.967290  2.175321  12.573636  2.875844  14.753737   \n",
       "12.999999  14.378054  12.071353  2.010782  12.616561  2.795358  15.082855   \n",
       "13.999999  14.362476  12.199661  2.241914  12.562384  3.137046  14.761506   \n",
       "14.999999  13.925398  12.159504  2.640144  12.567493  2.863452  15.239711   \n",
       "15.999999  14.156408  12.055522  2.755561  12.632353  2.848002  15.677537   \n",
       "16.999999  13.732772  12.292913  2.374433  12.673657  2.839859  15.291801   \n",
       "17.999998  14.183267  12.221660  2.399617  12.590243  2.879767  15.247374   \n",
       "18.999998  13.463249  12.233887  2.431544  12.620136  2.889585  15.726940   \n",
       "19.999998  14.380316  12.215145  2.363613  12.546385  2.969960  15.591372   \n",
       "20.999998  14.314579  12.014115  1.902365  12.576891  2.851240  15.255943   \n",
       "21.999998  13.853130  12.261211  2.294885  12.623248  2.856827  15.187722   \n",
       "22.999998  13.198834  12.099587  2.378581  12.552729  2.859978  15.091411   \n",
       "23.999998  13.972354  12.155925  2.238125  12.566474  2.857207  14.769518   \n",
       "24.999998  14.047488  12.199055  2.305825  12.506562  2.988004  14.746881   \n",
       "25.999998  14.204981  11.849512  2.289983  12.523388  2.955526  14.683662   \n",
       "26.999998  14.178894  12.178238  2.245625  12.545863  3.061258  14.890460   \n",
       "27.999998  14.044079  11.828196  1.914703  12.618773  2.847718  14.426377   \n",
       "28.999997  14.398155  11.850579  2.218279  12.561512  2.832006  14.912857   \n",
       "...              ...        ...       ...        ...       ...        ...   \n",
       "67.999994  13.958548  12.017318  1.393603  12.529074  2.917622  14.235408   \n",
       "68.999994  13.785087  12.026379  2.183224  12.558827  2.939777  14.875788   \n",
       "69.999994  13.795882  12.066310  1.553042  12.657426  2.893078  14.565254   \n",
       "70.999994  14.016347  12.076282  1.757155  12.581834  2.810367  14.041358   \n",
       "71.999994  13.928295  11.925509  1.514957  12.600303  2.846444  14.787398   \n",
       "72.999994  13.993648  12.012218  1.406113  12.576336  2.893936  14.526091   \n",
       "73.999993  13.963564  12.198527  1.585866  12.637036  2.886667  14.205150   \n",
       "74.999993  14.172377  12.088119  2.442481  12.621662  2.841235  14.867746   \n",
       "75.999993  14.152224  12.044310  2.021854  12.579555  2.829770  14.369837   \n",
       "76.999993  14.122811  12.032042  2.174867  12.584618  2.895526  15.001334   \n",
       "77.999993  14.268926  12.085710  1.610458  12.565278  2.863997  14.072404   \n",
       "78.999993  13.868984  12.192199  2.145694  12.542187  2.821602  14.144374   \n",
       "79.999993  14.057171  11.847876  2.215782  12.501813  2.779889  13.876635   \n",
       "80.999993  14.040334  11.970192  2.251428  12.596084  2.854473  14.338475   \n",
       "81.999993  14.063027  11.856137  2.149956  12.553984  2.911541  14.791251   \n",
       "82.999993  13.863771  12.086154  2.139944  12.580946  3.270617  13.814350   \n",
       "83.999993  14.061047  11.990947  2.079924  12.577767  2.832545  14.469007   \n",
       "84.999993  13.696244  11.897562  2.110835  12.612457  2.890827  14.318709   \n",
       "85.999992  14.164806  11.871102  1.249881  12.576047  2.896164  14.532731   \n",
       "86.999992  14.080611  12.032261  2.021434  12.589366  2.871884  14.230057   \n",
       "87.999992  14.278969  11.913697  1.353076  12.660511  2.868119  14.519116   \n",
       "88.999992  14.084620  11.921196  1.978535  12.562530  2.810249  14.712487   \n",
       "89.999992  14.153632  11.780808  2.231474  12.599925  2.850730  14.302761   \n",
       "90.999992  14.087207  11.792202  2.046611  12.568710  2.841544  14.150493   \n",
       "91.999992  14.165063  12.005584  2.098791  12.584911  2.899087  14.531872   \n",
       "92.999992  13.949351  11.992260  2.222933  12.586705  2.850050  14.934541   \n",
       "93.999992  14.081723  11.870259  1.986225  12.608072  2.871361  14.891981   \n",
       "94.999992  14.102544  11.972831  2.111825  12.587400  2.832126  15.088873   \n",
       "95.999992  14.162129  11.981639  2.033930  12.618683  2.878073  14.697977   \n",
       "96.999991  14.142641  12.038303  1.731744  12.538244  2.932928  14.210130   \n",
       "\n",
       "                208       210        211  \n",
       "time                                      \n",
       "0.000000   1.736156  2.083698  11.366898  \n",
       "1.000000   1.747098  2.081976  11.334325  \n",
       "2.000000   1.801874  2.187098  12.052625  \n",
       "3.000000   1.706005  2.709781  12.031399  \n",
       "4.000000   1.825790  2.589898  12.055694  \n",
       "5.000000   1.965401  2.853581  11.972007  \n",
       "5.999999   1.971753  2.685383  12.087627  \n",
       "6.999999   1.966715  2.872946  12.051454  \n",
       "7.999999   1.881919  2.774251  12.144520  \n",
       "8.999999   1.876699  2.807556  12.200815  \n",
       "9.999999   1.922496  2.761199  12.071012  \n",
       "10.999999  2.098414  2.748605  12.115915  \n",
       "11.999999  1.975975  3.189720  12.116735  \n",
       "12.999999  1.847353  2.696677  12.163013  \n",
       "13.999999  1.729482  2.799022  12.025731  \n",
       "14.999999  1.660120  1.870052  12.101239  \n",
       "15.999999  1.871720  2.284396  12.152405  \n",
       "16.999999  1.798649  1.983634  12.187030  \n",
       "17.999998  1.862175  1.978016  12.127560  \n",
       "18.999998  1.782645  2.033880  12.146693  \n",
       "19.999998  1.720737  1.897033  12.087506  \n",
       "20.999998  2.200353  2.018013  12.095198  \n",
       "21.999998  1.911463  2.479582  12.181959  \n",
       "22.999998  1.931532  2.825360  12.072635  \n",
       "23.999998  1.988179  2.708782  12.075159  \n",
       "24.999998  1.970614  2.961683  12.021080  \n",
       "25.999998  2.035451  2.650493  12.015273  \n",
       "26.999998  1.779405  2.942830  12.063742  \n",
       "27.999998  2.077088  2.887995  12.140975  \n",
       "28.999997  1.908869  2.897482  12.101310  \n",
       "...             ...       ...        ...  \n",
       "67.999994  2.099357  2.647973  11.966785  \n",
       "68.999994  1.861912  2.725743  12.023297  \n",
       "69.999994  2.124258  3.035445  12.085516  \n",
       "70.999994  2.034538  2.708400  11.945573  \n",
       "71.999994  2.053882  2.636972  11.997957  \n",
       "72.999994  2.168644  2.901869  11.952610  \n",
       "73.999993  2.071123  3.117254  12.064325  \n",
       "74.999993  1.918196  2.742337  12.127236  \n",
       "75.999993  2.188297  2.893287  12.071683  \n",
       "76.999993  1.882042  2.640203  11.981535  \n",
       "77.999993  1.968966  2.789703  12.077567  \n",
       "78.999993  1.888087  2.705698  12.007610  \n",
       "79.999993  1.912921  2.775303  12.026346  \n",
       "80.999993  1.911809  2.662349  12.081114  \n",
       "81.999993  1.840909  2.783413  11.987493  \n",
       "82.999993  1.528530  2.974642  12.063377  \n",
       "83.999993  1.857598  2.722474  12.127180  \n",
       "84.999993  1.844699  2.899924  12.058972  \n",
       "85.999992  1.943396  2.875820  12.090662  \n",
       "86.999992  1.845855  2.867483  12.035030  \n",
       "87.999992  1.974390  2.910038  12.043164  \n",
       "88.999992  1.853410  2.765294  12.148617  \n",
       "89.999992  1.857987  2.738830  12.160411  \n",
       "90.999992  1.929554  2.728138  12.092189  \n",
       "91.999992  1.802502  2.936365  12.207916  \n",
       "92.999992  1.907153  2.651611  12.088406  \n",
       "93.999992  1.832945  2.814808  12.156833  \n",
       "94.999992  1.840302  2.677849  12.124620  \n",
       "95.999992  1.832371  2.831865  12.164143  \n",
       "96.999991  1.880199  2.871634  12.139620  \n",
       "\n",
       "[98 rows x 75 columns]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pkas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>13</th>\n",
       "      <th>22</th>\n",
       "      <th>23</th>\n",
       "      <th>24</th>\n",
       "      <th>33</th>\n",
       "      <th>36</th>\n",
       "      <th>40</th>\n",
       "      <th>44</th>\n",
       "      <th>...</th>\n",
       "      <th>192</th>\n",
       "      <th>193</th>\n",
       "      <th>195</th>\n",
       "      <th>197</th>\n",
       "      <th>200</th>\n",
       "      <th>204</th>\n",
       "      <th>206</th>\n",
       "      <th>208</th>\n",
       "      <th>210</th>\n",
       "      <th>211</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>98.000000</td>\n",
       "      <td>98.000000</td>\n",
       "      <td>98.000000</td>\n",
       "      <td>98.000000</td>\n",
       "      <td>98.000000</td>\n",
       "      <td>98.000000</td>\n",
       "      <td>98.000000</td>\n",
       "      <td>98.000000</td>\n",
       "      <td>98.000000</td>\n",
       "      <td>98.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>98.000000</td>\n",
       "      <td>98.000000</td>\n",
       "      <td>98.000000</td>\n",
       "      <td>98.000000</td>\n",
       "      <td>98.000000</td>\n",
       "      <td>98.000000</td>\n",
       "      <td>98.000000</td>\n",
       "      <td>98.000000</td>\n",
       "      <td>98.000000</td>\n",
       "      <td>98.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>8.180723</td>\n",
       "      <td>12.760629</td>\n",
       "      <td>9.402281</td>\n",
       "      <td>3.488373</td>\n",
       "      <td>11.418135</td>\n",
       "      <td>11.642697</td>\n",
       "      <td>2.496965</td>\n",
       "      <td>14.049808</td>\n",
       "      <td>10.348338</td>\n",
       "      <td>3.734203</td>\n",
       "      <td>...</td>\n",
       "      <td>10.754325</td>\n",
       "      <td>14.010479</td>\n",
       "      <td>12.066464</td>\n",
       "      <td>2.110729</td>\n",
       "      <td>12.593243</td>\n",
       "      <td>2.899029</td>\n",
       "      <td>14.802091</td>\n",
       "      <td>1.901808</td>\n",
       "      <td>2.643808</td>\n",
       "      <td>12.076064</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.190336</td>\n",
       "      <td>0.159973</td>\n",
       "      <td>0.627494</td>\n",
       "      <td>0.303028</td>\n",
       "      <td>0.355354</td>\n",
       "      <td>0.864402</td>\n",
       "      <td>0.418063</td>\n",
       "      <td>0.506330</td>\n",
       "      <td>0.129717</td>\n",
       "      <td>0.261795</td>\n",
       "      <td>...</td>\n",
       "      <td>0.589032</td>\n",
       "      <td>0.259118</td>\n",
       "      <td>0.142012</td>\n",
       "      <td>0.325367</td>\n",
       "      <td>0.046812</td>\n",
       "      <td>0.147478</td>\n",
       "      <td>0.420380</td>\n",
       "      <td>0.121053</td>\n",
       "      <td>0.331949</td>\n",
       "      <td>0.120737</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>7.295912</td>\n",
       "      <td>12.268418</td>\n",
       "      <td>7.608654</td>\n",
       "      <td>2.946900</td>\n",
       "      <td>10.985647</td>\n",
       "      <td>10.264614</td>\n",
       "      <td>1.412159</td>\n",
       "      <td>12.838007</td>\n",
       "      <td>9.960275</td>\n",
       "      <td>2.799962</td>\n",
       "      <td>...</td>\n",
       "      <td>9.661010</td>\n",
       "      <td>13.174104</td>\n",
       "      <td>11.733061</td>\n",
       "      <td>1.249881</td>\n",
       "      <td>12.442245</td>\n",
       "      <td>2.767964</td>\n",
       "      <td>13.814350</td>\n",
       "      <td>1.528530</td>\n",
       "      <td>1.861152</td>\n",
       "      <td>11.334325</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>8.127513</td>\n",
       "      <td>12.703356</td>\n",
       "      <td>9.423932</td>\n",
       "      <td>3.240714</td>\n",
       "      <td>11.152677</td>\n",
       "      <td>10.915393</td>\n",
       "      <td>2.234819</td>\n",
       "      <td>13.556806</td>\n",
       "      <td>10.252726</td>\n",
       "      <td>3.625440</td>\n",
       "      <td>...</td>\n",
       "      <td>10.111005</td>\n",
       "      <td>13.878456</td>\n",
       "      <td>11.970498</td>\n",
       "      <td>1.980458</td>\n",
       "      <td>12.566704</td>\n",
       "      <td>2.839813</td>\n",
       "      <td>14.535488</td>\n",
       "      <td>1.836325</td>\n",
       "      <td>2.591431</td>\n",
       "      <td>12.055367</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>8.201208</td>\n",
       "      <td>12.762834</td>\n",
       "      <td>9.544703</td>\n",
       "      <td>3.395640</td>\n",
       "      <td>11.221198</td>\n",
       "      <td>11.460753</td>\n",
       "      <td>2.430872</td>\n",
       "      <td>14.136217</td>\n",
       "      <td>10.410696</td>\n",
       "      <td>3.835666</td>\n",
       "      <td>...</td>\n",
       "      <td>11.209223</td>\n",
       "      <td>14.035418</td>\n",
       "      <td>12.066676</td>\n",
       "      <td>2.177655</td>\n",
       "      <td>12.587065</td>\n",
       "      <td>2.861878</td>\n",
       "      <td>14.795910</td>\n",
       "      <td>1.888335</td>\n",
       "      <td>2.754077</td>\n",
       "      <td>12.089534</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>8.273955</td>\n",
       "      <td>12.849905</td>\n",
       "      <td>9.710506</td>\n",
       "      <td>3.718057</td>\n",
       "      <td>11.620171</td>\n",
       "      <td>12.428121</td>\n",
       "      <td>2.682613</td>\n",
       "      <td>14.404762</td>\n",
       "      <td>10.430810</td>\n",
       "      <td>3.918784</td>\n",
       "      <td>...</td>\n",
       "      <td>11.260263</td>\n",
       "      <td>14.164137</td>\n",
       "      <td>12.191065</td>\n",
       "      <td>2.293660</td>\n",
       "      <td>12.621373</td>\n",
       "      <td>2.895128</td>\n",
       "      <td>15.024900</td>\n",
       "      <td>1.968771</td>\n",
       "      <td>2.852710</td>\n",
       "      <td>12.133085</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>8.458619</td>\n",
       "      <td>13.246053</td>\n",
       "      <td>10.449350</td>\n",
       "      <td>4.278961</td>\n",
       "      <td>12.282208</td>\n",
       "      <td>13.113857</td>\n",
       "      <td>3.608263</td>\n",
       "      <td>15.182562</td>\n",
       "      <td>10.460633</td>\n",
       "      <td>4.010099</td>\n",
       "      <td>...</td>\n",
       "      <td>11.331529</td>\n",
       "      <td>14.472733</td>\n",
       "      <td>12.392177</td>\n",
       "      <td>3.000020</td>\n",
       "      <td>12.692147</td>\n",
       "      <td>3.817193</td>\n",
       "      <td>15.909253</td>\n",
       "      <td>2.200353</td>\n",
       "      <td>3.381706</td>\n",
       "      <td>12.207916</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>8 rows × 75 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "             1          2          13         22         23         24   \\\n",
       "count  98.000000  98.000000  98.000000  98.000000  98.000000  98.000000   \n",
       "mean    8.180723  12.760629   9.402281   3.488373  11.418135  11.642697   \n",
       "std     0.190336   0.159973   0.627494   0.303028   0.355354   0.864402   \n",
       "min     7.295912  12.268418   7.608654   2.946900  10.985647  10.264614   \n",
       "25%     8.127513  12.703356   9.423932   3.240714  11.152677  10.915393   \n",
       "50%     8.201208  12.762834   9.544703   3.395640  11.221198  11.460753   \n",
       "75%     8.273955  12.849905   9.710506   3.718057  11.620171  12.428121   \n",
       "max     8.458619  13.246053  10.449350   4.278961  12.282208  13.113857   \n",
       "\n",
       "             33         36         40         44     ...            192  \\\n",
       "count  98.000000  98.000000  98.000000  98.000000    ...      98.000000   \n",
       "mean    2.496965  14.049808  10.348338   3.734203    ...      10.754325   \n",
       "std     0.418063   0.506330   0.129717   0.261795    ...       0.589032   \n",
       "min     1.412159  12.838007   9.960275   2.799962    ...       9.661010   \n",
       "25%     2.234819  13.556806  10.252726   3.625440    ...      10.111005   \n",
       "50%     2.430872  14.136217  10.410696   3.835666    ...      11.209223   \n",
       "75%     2.682613  14.404762  10.430810   3.918784    ...      11.260263   \n",
       "max     3.608263  15.182562  10.460633   4.010099    ...      11.331529   \n",
       "\n",
       "             193        195        197        200        204        206  \\\n",
       "count  98.000000  98.000000  98.000000  98.000000  98.000000  98.000000   \n",
       "mean   14.010479  12.066464   2.110729  12.593243   2.899029  14.802091   \n",
       "std     0.259118   0.142012   0.325367   0.046812   0.147478   0.420380   \n",
       "min    13.174104  11.733061   1.249881  12.442245   2.767964  13.814350   \n",
       "25%    13.878456  11.970498   1.980458  12.566704   2.839813  14.535488   \n",
       "50%    14.035418  12.066676   2.177655  12.587065   2.861878  14.795910   \n",
       "75%    14.164137  12.191065   2.293660  12.621373   2.895128  15.024900   \n",
       "max    14.472733  12.392177   3.000020  12.692147   3.817193  15.909253   \n",
       "\n",
       "             208        210        211  \n",
       "count  98.000000  98.000000  98.000000  \n",
       "mean    1.901808   2.643808  12.076064  \n",
       "std     0.121053   0.331949   0.120737  \n",
       "min     1.528530   1.861152  11.334325  \n",
       "25%     1.836325   2.591431  12.055367  \n",
       "50%     1.888335   2.754077  12.089534  \n",
       "75%     1.968771   2.852710  12.133085  \n",
       "max     2.200353   3.381706  12.207916  \n",
       "\n",
       "[8 rows x 75 columns]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pkas.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's plot it all:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import seaborn as sns\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
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HcvDg8h4o293nyAx72DrvHwBgJ0mqAADbtlkioJkkQCIRkCz/W12YOp/sH2580PDyEpQX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\nfPMPbOl8//fPbj0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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b3d25d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = sns.plt.figure(figsize=(28, 8))\n",
    "ax = fig.add_subplot(1,1,1)\n",
    "sns.boxplot(data=pkas, ax=ax)\n",
    "ax.set_xlabel(\"residue number\")\n",
    "ax.set_ylabel(r\"p$K_a$\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Want only the lysines?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "resids = u.select_atoms('resname LYS').residues.resids"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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fLuZcZeXzdoK//S7gZwTnfHf4vnbgfwP/5O7fyC5PRF7vJOJzZGZ/Ff5encDV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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e8dbd10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.boxplot(data=pkas[resids])\n",
    "ax = sns.plt.gca()\n",
    "ax.set_xlabel(\"residue number\")\n",
    "ax.set_ylabel(r\"p$K_a$\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can use this strategy to look at any residues of interest."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}