documentation_builder/phenotype_phase_plane.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Production envelopes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Production envelopes (aka phenotype phase planes) will show distinct phases of optimal growth with different use of two different substrates. For more information, see [Edwards et al.](http://dx.doi.org/10.1002/bit.10047)\n",
    "\n",
    "Cobrapy supports calculating these production envelopes and they can easily be plotted using your favorite plotting package. Here, we will make one for the \"textbook\" _E. coli_ core model and demonstrate plotting using [matplotlib](http://matplotlib.org/)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "import cobra.test\n",
    "from cobra.flux_analysis import production_envelope\n",
    "\n",
    "model = cobra.test.create_test_model(\"textbook\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "We want to make a phenotype phase plane to evaluate uptakes of Glucose and Oxygen."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "prod_env = production_envelope(model, [\"EX_glc__D_e\", \"EX_o2_e\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>EX_glc__D_e</th>\n",
       "      <th>EX_o2_e</th>\n",
       "      <th>direction</th>\n",
       "      <th>flux</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-10.0</td>\n",
       "      <td>-60.000000</td>\n",
       "      <td>minimum</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-10.0</td>\n",
       "      <td>-56.842105</td>\n",
       "      <td>minimum</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-10.0</td>\n",
       "      <td>-53.684211</td>\n",
       "      <td>minimum</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-10.0</td>\n",
       "      <td>-50.526316</td>\n",
       "      <td>minimum</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-10.0</td>\n",
       "      <td>-47.368421</td>\n",
       "      <td>minimum</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   EX_glc__D_e    EX_o2_e direction  flux\n",
       "0        -10.0 -60.000000   minimum   0.0\n",
       "1        -10.0 -56.842105   minimum   0.0\n",
       "2        -10.0 -53.684211   minimum   0.0\n",
       "3        -10.0 -50.526316   minimum   0.0\n",
       "4        -10.0 -47.368421   minimum   0.0"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prod_env.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "If we specify the carbon source, we can also get the carbon and mass yield. For example, temporarily setting the objective to produce acetate instead we could get production envelope as follows and pandas to quickly plot the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "prod_env = production_envelope(\n",
    "    model, [\"EX_o2_e\"], objective=\"EX_ac_e\", c_source=\"EX_glc__D_e\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>EX_o2_e</th>\n",
       "      <th>carbon_source</th>\n",
       "      <th>carbon_yield</th>\n",
       "      <th>direction</th>\n",
       "      <th>flux</th>\n",
       "      <th>mass_yield</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-60.000000</td>\n",
       "      <td>EX_glc__D_e</td>\n",
       "      <td>0.0</td>\n",
       "      <td>minimum</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-56.842105</td>\n",
       "      <td>EX_glc__D_e</td>\n",
       "      <td>0.0</td>\n",
       "      <td>minimum</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-53.684211</td>\n",
       "      <td>EX_glc__D_e</td>\n",
       "      <td>0.0</td>\n",
       "      <td>minimum</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-50.526316</td>\n",
       "      <td>EX_glc__D_e</td>\n",
       "      <td>0.0</td>\n",
       "      <td>minimum</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-47.368421</td>\n",
       "      <td>EX_glc__D_e</td>\n",
       "      <td>0.0</td>\n",
       "      <td>minimum</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     EX_o2_e carbon_source  carbon_yield direction  flux  mass_yield\n",
       "0 -60.000000   EX_glc__D_e           0.0   minimum   0.0         0.0\n",
       "1 -56.842105   EX_glc__D_e           0.0   minimum   0.0         0.0\n",
       "2 -53.684211   EX_glc__D_e           0.0   minimum   0.0         0.0\n",
       "3 -50.526316   EX_glc__D_e           0.0   minimum   0.0         0.0\n",
       "4 -47.368421   EX_glc__D_e           0.0   minimum   0.0         0.0"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prod_env.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x10fc37630>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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pQKyIrDDGFP6o1AJjzLsF4/sC04FeDsirHOT0hUwemBfH9pSzTO3XnPs61rc6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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10fc24a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "prod_env[prod_env.direction == 'maximum'].plot(\n",
    "    kind='line', x='EX_o2_e', y='carbon_yield')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Previous versions of cobrapy included more tailored plots for phase planes which have now been dropped in order to improve maintainability and enhance the focus of cobrapy. Plotting for cobra models is intended for another package."
   ]
  }
 ],
 "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": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}