{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Production envelopes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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": {},
   "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": {},
   "source": [
    "We want to make a phenotype phase plane to evaluate uptakes of Glucose and Oxygen."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "prod_env = production_envelope(model, [\"EX_glc__D_e\", \"EX_o2_e\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>carbon_source</th>\n",
       "      <th>carbon_yield_maximum</th>\n",
       "      <th>carbon_yield_minimum</th>\n",
       "      <th>flux_maximum</th>\n",
       "      <th>flux_minimum</th>\n",
       "      <th>mass_yield_maximum</th>\n",
       "      <th>mass_yield_minimum</th>\n",
       "      <th>EX_glc__D_e</th>\n",
       "      <th>EX_o2_e</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>EX_glc__D_e</td>\n",
       "      <td>1.442300e-13</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-10.0</td>\n",
       "      <td>-60.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>EX_glc__D_e</td>\n",
       "      <td>1.310050e+00</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.072244</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-10.0</td>\n",
       "      <td>-56.842105</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>EX_glc__D_e</td>\n",
       "      <td>2.620100e+00</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.144488</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-10.0</td>\n",
       "      <td>-53.684211</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>EX_glc__D_e</td>\n",
       "      <td>3.930150e+00</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.216732</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-10.0</td>\n",
       "      <td>-50.526316</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>EX_glc__D_e</td>\n",
       "      <td>5.240200e+00</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.288975</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-10.0</td>\n",
       "      <td>-47.368421</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  carbon_source  carbon_yield_maximum  carbon_yield_minimum  flux_maximum  \\\n",
       "0   EX_glc__D_e          1.442300e-13                   0.0      0.000000   \n",
       "1   EX_glc__D_e          1.310050e+00                   0.0      0.072244   \n",
       "2   EX_glc__D_e          2.620100e+00                   0.0      0.144488   \n",
       "3   EX_glc__D_e          3.930150e+00                   0.0      0.216732   \n",
       "4   EX_glc__D_e          5.240200e+00                   0.0      0.288975   \n",
       "\n",
       "   flux_minimum  mass_yield_maximum  mass_yield_minimum  EX_glc__D_e  \\\n",
       "0           0.0                 NaN                 NaN        -10.0   \n",
       "1           0.0                 NaN                 NaN        -10.0   \n",
       "2           0.0                 NaN                 NaN        -10.0   \n",
       "3           0.0                 NaN                 NaN        -10.0   \n",
       "4           0.0                 NaN                 NaN        -10.0   \n",
       "\n",
       "     EX_o2_e  \n",
       "0 -60.000000  \n",
       "1 -56.842105  \n",
       "2 -53.684211  \n",
       "3 -50.526316  \n",
       "4 -47.368421  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prod_env.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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": {},
   "outputs": [],
   "source": [
    "prod_env = production_envelope(\n",
    "    model, [\"EX_o2_e\"], objective=\"EX_ac_e\", carbon_sources=\"EX_glc__D_e\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>carbon_source</th>\n",
       "      <th>carbon_yield_maximum</th>\n",
       "      <th>carbon_yield_minimum</th>\n",
       "      <th>flux_maximum</th>\n",
       "      <th>flux_minimum</th>\n",
       "      <th>mass_yield_maximum</th>\n",
       "      <th>mass_yield_minimum</th>\n",
       "      <th>EX_o2_e</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>EX_glc__D_e</td>\n",
       "      <td>2.385536e-15</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.345496e-15</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-60.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>EX_glc__D_e</td>\n",
       "      <td>5.263158e-02</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.578947</td>\n",
       "      <td>0.0</td>\n",
       "      <td>5.174819e-02</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-56.842105</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>EX_glc__D_e</td>\n",
       "      <td>1.052632e-01</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3.157895</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.034964e-01</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-53.684211</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>EX_glc__D_e</td>\n",
       "      <td>1.578947e-01</td>\n",
       "      <td>0.0</td>\n",
       "      <td>4.736842</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.552446e-01</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-50.526316</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>EX_glc__D_e</td>\n",
       "      <td>2.105263e-01</td>\n",
       "      <td>0.0</td>\n",
       "      <td>6.315789</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.069927e-01</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-47.368421</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  carbon_source  carbon_yield_maximum  carbon_yield_minimum  flux_maximum  \\\n",
       "0   EX_glc__D_e          2.385536e-15                   0.0      0.000000   \n",
       "1   EX_glc__D_e          5.263158e-02                   0.0      1.578947   \n",
       "2   EX_glc__D_e          1.052632e-01                   0.0      3.157895   \n",
       "3   EX_glc__D_e          1.578947e-01                   0.0      4.736842   \n",
       "4   EX_glc__D_e          2.105263e-01                   0.0      6.315789   \n",
       "\n",
       "   flux_minimum  mass_yield_maximum  mass_yield_minimum    EX_o2_e  \n",
       "0           0.0        2.345496e-15                 0.0 -60.000000  \n",
       "1           0.0        5.174819e-02                 0.0 -56.842105  \n",
       "2           0.0        1.034964e-01                 0.0 -53.684211  \n",
       "3           0.0        1.552446e-01                 0.0 -50.526316  \n",
       "4           0.0        2.069927e-01                 0.0 -47.368421  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prod_env.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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t3AgR4d+r95bZPrXcld3k5hpe/mw7M9ceYPhdwbzWuwVuWuxKUce3Eo9FBvHJ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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1db7b6c048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "prod_env.plot(\n",
    "    kind='line', x='EX_o2_e', y='carbon_yield_maximum');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}