{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Growth rates and fluxes\n",
    "\n",
    "One of the major applications of micom is to identify growth rates and fluxes for a given community. We will return to our *E. coli* toy example."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": [
       "\u001b[?25l"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "1e9aca04b03846c494888870dc28f077",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\n",
       "\u001b[?25h"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from micom import Community, data\n",
    "\n",
    "tax = data.test_taxonomy()\n",
    "com = Community(tax)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### FBA\n",
    "\n",
    "If one is only interested in the community growth rate $\\mu_c$ we can use normal FBA to optimize this growth rate. By default micom assigns the community growth rate as the objective for a community model. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0*community_objective\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<strong>community growth:</strong> 0.874<br><strong>status:</strong> optimal<br><strong>taxa:</strong><div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        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>abundance</th>\n",
       "      <th>growth_rate</th>\n",
       "      <th>reactions</th>\n",
       "      <th>metabolites</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>compartments</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Escherichia_coli_1</th>\n",
       "      <td>0.25</td>\n",
       "      <td>1.526449</td>\n",
       "      <td>95</td>\n",
       "      <td>72</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Escherichia_coli_2</th>\n",
       "      <td>0.25</td>\n",
       "      <td>0.653014</td>\n",
       "      <td>95</td>\n",
       "      <td>72</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Escherichia_coli_3</th>\n",
       "      <td>0.25</td>\n",
       "      <td>0.242410</td>\n",
       "      <td>95</td>\n",
       "      <td>72</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Escherichia_coli_4</th>\n",
       "      <td>0.25</td>\n",
       "      <td>1.073813</td>\n",
       "      <td>95</td>\n",
       "      <td>72</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>medium</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>20</td>\n",
       "      <td>20</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "<CommunitySolution 0.874 at 0x7f8bae1e7650>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(com.objective.expression)\n",
    "com.optimize()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`optimize` returns a full-fledged solution object and you can inspect several aspects of it. For instance to get individual growth rates and information for the taxa:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        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>abundance</th>\n",
       "      <th>growth_rate</th>\n",
       "      <th>reactions</th>\n",
       "      <th>metabolites</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>compartments</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Escherichia_coli_1</th>\n",
       "      <td>0.25</td>\n",
       "      <td>1.526449</td>\n",
       "      <td>95</td>\n",
       "      <td>72</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Escherichia_coli_2</th>\n",
       "      <td>0.25</td>\n",
       "      <td>0.653014</td>\n",
       "      <td>95</td>\n",
       "      <td>72</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Escherichia_coli_3</th>\n",
       "      <td>0.25</td>\n",
       "      <td>0.242410</td>\n",
       "      <td>95</td>\n",
       "      <td>72</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Escherichia_coli_4</th>\n",
       "      <td>0.25</td>\n",
       "      <td>1.073813</td>\n",
       "      <td>95</td>\n",
       "      <td>72</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>medium</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>20</td>\n",
       "      <td>20</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    abundance  growth_rate  reactions  metabolites\n",
       "compartments                                                      \n",
       "Escherichia_coli_1       0.25     1.526449         95           72\n",
       "Escherichia_coli_2       0.25     0.653014         95           72\n",
       "Escherichia_coli_3       0.25     0.242410         95           72\n",
       "Escherichia_coli_4       0.25     1.073813         95           72\n",
       "medium                    NaN          NaN         20           20"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sol = com.optimize()\n",
    "sol.members"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By default micom does not return fluxes since that can be slow for realistic large community models. If you want fluxes as well you can do so by passing the `fluxes` argument to `optimize`. You can also specifiy if you would like the fluxes to be obtained by parsimonious FBA."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        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>reaction</th>\n",
       "      <th>ACALD</th>\n",
       "      <th>ACALDt</th>\n",
       "      <th>ACKr</th>\n",
       "      <th>ACONTa</th>\n",
       "      <th>ACONTb</th>\n",
       "      <th>ACt2r</th>\n",
       "      <th>ADK1</th>\n",
       "      <th>AKGDH</th>\n",
       "      <th>AKGt2r</th>\n",
       "      <th>ALCD2x</th>\n",
       "      <th>...</th>\n",
       "      <th>RPI</th>\n",
       "      <th>SUCCt2_2</th>\n",
       "      <th>SUCCt3</th>\n",
       "      <th>SUCDi</th>\n",
       "      <th>SUCOAS</th>\n",
       "      <th>TALA</th>\n",
       "      <th>THD2</th>\n",
       "      <th>TKT1</th>\n",
       "      <th>TKT2</th>\n",
       "      <th>TPI</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>compartment</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Escherichia_coli_1</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>9.657372</td>\n",
       "      <td>9.657372</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>8.010490</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>-4.124228</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>8.010490</td>\n",
       "      <td>-8.010490</td>\n",
       "      <td>2.753937</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.753937</td>\n",
       "      <td>2.202890</td>\n",
       "      <td>12.573226</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Escherichia_coli_2</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>4.771520</td>\n",
       "      <td>4.771520</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>4.066985</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>-1.657659</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>4.066985</td>\n",
       "      <td>-4.066985</td>\n",
       "      <td>1.071449</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.071449</td>\n",
       "      <td>0.835711</td>\n",
       "      <td>5.752211</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Escherichia_coli_3</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>2.474664</td>\n",
       "      <td>2.474664</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.213129</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.498116</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.213129</td>\n",
       "      <td>-2.213129</td>\n",
       "      <td>0.280506</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.280506</td>\n",
       "      <td>0.192996</td>\n",
       "      <td>2.545629</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Escherichia_coli_4</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-0.000327</td>\n",
       "      <td>7.125203</td>\n",
       "      <td>7.125203</td>\n",
       "      <td>-0.000327</td>\n",
       "      <td>0.0</td>\n",
       "      <td>5.966669</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>-2.846022</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>5.966669</td>\n",
       "      <td>-5.966669</td>\n",
       "      <td>1.882062</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.882062</td>\n",
       "      <td>1.494416</td>\n",
       "      <td>9.038452</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>medium</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 115 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "reaction            ACALD  ACALDt      ACKr    ACONTa    ACONTb     ACt2r  \\\n",
       "compartment                                                                 \n",
       "Escherichia_coli_1    0.0     0.0  0.000000  9.657372  9.657372  0.000000   \n",
       "Escherichia_coli_2    0.0     0.0  0.000000  4.771520  4.771520  0.000000   \n",
       "Escherichia_coli_3    0.0     0.0  0.000000  2.474664  2.474664  0.000000   \n",
       "Escherichia_coli_4    0.0     0.0 -0.000327  7.125203  7.125203 -0.000327   \n",
       "medium                NaN     NaN       NaN       NaN       NaN       NaN   \n",
       "\n",
       "reaction            ADK1     AKGDH  AKGt2r  ALCD2x  ...       RPI  SUCCt2_2  \\\n",
       "compartment                                         ...                       \n",
       "Escherichia_coli_1   0.0  8.010490     0.0     0.0  ... -4.124228       0.0   \n",
       "Escherichia_coli_2   0.0  4.066985     0.0     0.0  ... -1.657659       0.0   \n",
       "Escherichia_coli_3   0.0  2.213129     0.0     0.0  ... -0.498116       0.0   \n",
       "Escherichia_coli_4   0.0  5.966669     0.0     0.0  ... -2.846022       0.0   \n",
       "medium               NaN       NaN     NaN     NaN  ...       NaN       NaN   \n",
       "\n",
       "reaction            SUCCt3     SUCDi    SUCOAS      TALA  THD2      TKT1  \\\n",
       "compartment                                                                \n",
       "Escherichia_coli_1     0.0  8.010490 -8.010490  2.753937   0.0  2.753937   \n",
       "Escherichia_coli_2     0.0  4.066985 -4.066985  1.071449   0.0  1.071449   \n",
       "Escherichia_coli_3     0.0  2.213129 -2.213129  0.280506   0.0  0.280506   \n",
       "Escherichia_coli_4     0.0  5.966669 -5.966669  1.882062   0.0  1.882062   \n",
       "medium                 NaN       NaN       NaN       NaN   NaN       NaN   \n",
       "\n",
       "reaction                TKT2        TPI  \n",
       "compartment                              \n",
       "Escherichia_coli_1  2.202890  12.573226  \n",
       "Escherichia_coli_2  0.835711   5.752211  \n",
       "Escherichia_coli_3  0.192996   2.545629  \n",
       "Escherichia_coli_4  1.494416   9.038452  \n",
       "medium                   NaN        NaN  \n",
       "\n",
       "[5 rows x 115 columns]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sol = com.optimize(fluxes=True, pfba=True)\n",
    "sol.fluxes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By defaults fluxes are stratified by taxa and the external medium to aid further analysis. \n",
    "\n",
    "Returning to the growth rates we can see the major problem with regular FBA for community levels. Usually it will maximize growth for only a few taxa in the model yielding unrealistically high growth rates. However, in our setup we have 5 identical *E. coli* strains and we would expect all of the taxa to grow with the same rate (see Methods section)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Cooperative tradeoff\n",
    "\n",
    "Cooperative tradeoff is a two step methods that allows you to get a unique solution for the the individuals growth rates that favors individual growth but still allows for a sup-optimal community growth rate. For that we always have to decide on a fraction of the maximum community growth rate we want to enforce. Our own results based on a data set of 189 gut microbiomes suggest that this tradeoff has tobe substantially lower than the optimal community growth rate to yield realistic growth rates (<=50% optimum). For our *E. coli* model we can start with getting the best solution while still maintaining optimal community growth (100% of maximum).\n",
    "\n",
    "**Cooperative tradeoff requires a QP-capable solver such as cplex or gurobi (both have academic licenses available)!**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<strong>community growth:</strong> 0.874<br><strong>status:</strong> optimal<br><strong>taxa:</strong><div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        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>abundance</th>\n",
       "      <th>growth_rate</th>\n",
       "      <th>reactions</th>\n",
       "      <th>metabolites</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>compartments</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Escherichia_coli_1</th>\n",
       "      <td>0.25</td>\n",
       "      <td>0.873922</td>\n",
       "      <td>95</td>\n",
       "      <td>72</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Escherichia_coli_2</th>\n",
       "      <td>0.25</td>\n",
       "      <td>0.873922</td>\n",
       "      <td>95</td>\n",
       "      <td>72</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Escherichia_coli_3</th>\n",
       "      <td>0.25</td>\n",
       "      <td>0.873922</td>\n",
       "      <td>95</td>\n",
       "      <td>72</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Escherichia_coli_4</th>\n",
       "      <td>0.25</td>\n",
       "      <td>0.873922</td>\n",
       "      <td>95</td>\n",
       "      <td>72</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>medium</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>20</td>\n",
       "      <td>20</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "<CommunitySolution 0.874 at 0x7f8bae2b6cd0>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sol = com.cooperative_tradeoff(fraction=1.0)\n",
    "sol"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we see all taxa now grow at the same rate as would be expected. If we want fluxes as well we can again request those using the `fluxes` and `pfba` arguments."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    }\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>reaction</th>\n",
       "      <th>ACALD</th>\n",
       "      <th>ACALDt</th>\n",
       "      <th>ACKr</th>\n",
       "      <th>ACONTa</th>\n",
       "      <th>ACONTb</th>\n",
       "      <th>ACt2r</th>\n",
       "      <th>ADK1</th>\n",
       "      <th>AKGDH</th>\n",
       "      <th>AKGt2r</th>\n",
       "      <th>ALCD2x</th>\n",
       "      <th>...</th>\n",
       "      <th>RPI</th>\n",
       "      <th>SUCCt2_2</th>\n",
       "      <th>SUCCt3</th>\n",
       "      <th>SUCDi</th>\n",
       "      <th>SUCOAS</th>\n",
       "      <th>TALA</th>\n",
       "      <th>THD2</th>\n",
       "      <th>TKT1</th>\n",
       "      <th>TKT2</th>\n",
       "      <th>TPI</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>compartment</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Escherichia_coli_1</th>\n",
       "      <td>2.558942e-09</td>\n",
       "      <td>1.258398e-09</td>\n",
       "      <td>-1.022332e-07</td>\n",
       "      <td>6.007249</td>\n",
       "      <td>6.007249</td>\n",
       "      <td>-1.022332e-07</td>\n",
       "      <td>2.584638e-09</td>\n",
       "      <td>5.064376</td>\n",
       "      <td>1.595951e-09</td>\n",
       "      <td>1.300544e-09</td>\n",
       "      <td>...</td>\n",
       "      <td>-2.281503</td>\n",
       "      <td>3.842359e-09</td>\n",
       "      <td>2.496730e-09</td>\n",
       "      <td>5.064376</td>\n",
       "      <td>-5.064376</td>\n",
       "      <td>1.496984</td>\n",
       "      <td>2.593182e-09</td>\n",
       "      <td>1.496984</td>\n",
       "      <td>1.181498</td>\n",
       "      <td>7.477382</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Escherichia_coli_2</th>\n",
       "      <td>2.558942e-09</td>\n",
       "      <td>1.258398e-09</td>\n",
       "      <td>-1.022332e-07</td>\n",
       "      <td>6.007249</td>\n",
       "      <td>6.007250</td>\n",
       "      <td>-1.022332e-07</td>\n",
       "      <td>2.584638e-09</td>\n",
       "      <td>5.064376</td>\n",
       "      <td>1.595951e-09</td>\n",
       "      <td>1.300544e-09</td>\n",
       "      <td>...</td>\n",
       "      <td>-2.281503</td>\n",
       "      <td>3.842359e-09</td>\n",
       "      <td>2.496730e-09</td>\n",
       "      <td>5.064376</td>\n",
       "      <td>-5.064376</td>\n",
       "      <td>1.496984</td>\n",
       "      <td>2.593182e-09</td>\n",
       "      <td>1.496984</td>\n",
       "      <td>1.181498</td>\n",
       "      <td>7.477382</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Escherichia_coli_3</th>\n",
       "      <td>2.558942e-09</td>\n",
       "      <td>1.258398e-09</td>\n",
       "      <td>-1.022332e-07</td>\n",
       "      <td>6.007250</td>\n",
       "      <td>6.007249</td>\n",
       "      <td>-1.022332e-07</td>\n",
       "      <td>2.584638e-09</td>\n",
       "      <td>5.064375</td>\n",
       "      <td>1.595951e-09</td>\n",
       "      <td>1.300544e-09</td>\n",
       "      <td>...</td>\n",
       "      <td>-2.281503</td>\n",
       "      <td>3.842359e-09</td>\n",
       "      <td>2.496730e-09</td>\n",
       "      <td>5.064375</td>\n",
       "      <td>-5.064375</td>\n",
       "      <td>1.496984</td>\n",
       "      <td>2.593182e-09</td>\n",
       "      <td>1.496984</td>\n",
       "      <td>1.181498</td>\n",
       "      <td>7.477382</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Escherichia_coli_4</th>\n",
       "      <td>2.558942e-09</td>\n",
       "      <td>1.258398e-09</td>\n",
       "      <td>-1.022332e-07</td>\n",
       "      <td>6.007249</td>\n",
       "      <td>6.007250</td>\n",
       "      <td>-1.022332e-07</td>\n",
       "      <td>2.584638e-09</td>\n",
       "      <td>5.064376</td>\n",
       "      <td>1.595951e-09</td>\n",
       "      <td>1.300544e-09</td>\n",
       "      <td>...</td>\n",
       "      <td>-2.281503</td>\n",
       "      <td>3.842359e-09</td>\n",
       "      <td>2.496730e-09</td>\n",
       "      <td>5.064376</td>\n",
       "      <td>-5.064376</td>\n",
       "      <td>1.496984</td>\n",
       "      <td>2.593182e-09</td>\n",
       "      <td>1.496984</td>\n",
       "      <td>1.181498</td>\n",
       "      <td>7.477382</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>medium</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 115 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "reaction                   ACALD        ACALDt          ACKr    ACONTa  \\\n",
       "compartment                                                              \n",
       "Escherichia_coli_1  2.558942e-09  1.258398e-09 -1.022332e-07  6.007249   \n",
       "Escherichia_coli_2  2.558942e-09  1.258398e-09 -1.022332e-07  6.007249   \n",
       "Escherichia_coli_3  2.558942e-09  1.258398e-09 -1.022332e-07  6.007250   \n",
       "Escherichia_coli_4  2.558942e-09  1.258398e-09 -1.022332e-07  6.007249   \n",
       "medium                       NaN           NaN           NaN       NaN   \n",
       "\n",
       "reaction              ACONTb         ACt2r          ADK1     AKGDH  \\\n",
       "compartment                                                          \n",
       "Escherichia_coli_1  6.007249 -1.022332e-07  2.584638e-09  5.064376   \n",
       "Escherichia_coli_2  6.007250 -1.022332e-07  2.584638e-09  5.064376   \n",
       "Escherichia_coli_3  6.007249 -1.022332e-07  2.584638e-09  5.064375   \n",
       "Escherichia_coli_4  6.007250 -1.022332e-07  2.584638e-09  5.064376   \n",
       "medium                   NaN           NaN           NaN       NaN   \n",
       "\n",
       "reaction                  AKGt2r        ALCD2x  ...       RPI      SUCCt2_2  \\\n",
       "compartment                                     ...                           \n",
       "Escherichia_coli_1  1.595951e-09  1.300544e-09  ... -2.281503  3.842359e-09   \n",
       "Escherichia_coli_2  1.595951e-09  1.300544e-09  ... -2.281503  3.842359e-09   \n",
       "Escherichia_coli_3  1.595951e-09  1.300544e-09  ... -2.281503  3.842359e-09   \n",
       "Escherichia_coli_4  1.595951e-09  1.300544e-09  ... -2.281503  3.842359e-09   \n",
       "medium                       NaN           NaN  ...       NaN           NaN   \n",
       "\n",
       "reaction                  SUCCt3     SUCDi    SUCOAS      TALA          THD2  \\\n",
       "compartment                                                                    \n",
       "Escherichia_coli_1  2.496730e-09  5.064376 -5.064376  1.496984  2.593182e-09   \n",
       "Escherichia_coli_2  2.496730e-09  5.064376 -5.064376  1.496984  2.593182e-09   \n",
       "Escherichia_coli_3  2.496730e-09  5.064375 -5.064375  1.496984  2.593182e-09   \n",
       "Escherichia_coli_4  2.496730e-09  5.064376 -5.064376  1.496984  2.593182e-09   \n",
       "medium                       NaN       NaN       NaN       NaN           NaN   \n",
       "\n",
       "reaction                TKT1      TKT2       TPI  \n",
       "compartment                                       \n",
       "Escherichia_coli_1  1.496984  1.181498  7.477382  \n",
       "Escherichia_coli_2  1.496984  1.181498  7.477382  \n",
       "Escherichia_coli_3  1.496984  1.181498  7.477382  \n",
       "Escherichia_coli_4  1.496984  1.181498  7.477382  \n",
       "medium                   NaN       NaN       NaN  \n",
       "\n",
       "[5 rows x 115 columns]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sol = com.cooperative_tradeoff(fluxes=True, pfba=True)\n",
    "sol.fluxes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Also if you have prior information about the growth rates you can also enforce a minimum individual growth rate for the taxa."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<CommunitySolution 0.874 at 0x7f8bae77c110> <CommunitySolution 0.874 at 0x7f8bae299190>\n"
     ]
    }
   ],
   "source": [
    "sol1 = com.cooperative_tradeoff(min_growth=0.1)  # single value\n",
    "sol2 = com.cooperative_tradeoff(min_growth=[0.1, 0.2, 0.3, 0.4])  # one value for each taxa\n",
    "print(sol1, sol2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, you might want to see the impact of the tradeoff parameter on your solution. For this you can simply pass in an array-like type as the `fraction` parameter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>tradeoff</th>\n",
       "      <th>solution</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.0</td>\n",
       "      <td>&lt;CommunitySolution 0.874 at 0x7f8bae2c3050&gt;</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.9</td>\n",
       "      <td>&lt;CommunitySolution 0.787 at 0x7f8bae568490&gt;</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.8</td>\n",
       "      <td>&lt;CommunitySolution 0.699 at 0x7f8bae742450&gt;</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.7</td>\n",
       "      <td>&lt;CommunitySolution 0.612 at 0x7f8bae4893d0&gt;</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.6</td>\n",
       "      <td>&lt;CommunitySolution 0.524 at 0x7f8bae540950&gt;</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.5</td>\n",
       "      <td>&lt;CommunitySolution 0.437 at 0x7f8bae107650&gt;</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.4</td>\n",
       "      <td>&lt;CommunitySolution 0.350 at 0x7f8bae1104d0&gt;</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.3</td>\n",
       "      <td>&lt;CommunitySolution 0.262 at 0x7f8bae69b0d0&gt;</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.2</td>\n",
       "      <td>&lt;CommunitySolution 0.175 at 0x7f8bae5311d0&gt;</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.1</td>\n",
       "      <td>&lt;CommunitySolution 0.087 at 0x7f8bae437190&gt;</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   tradeoff                                     solution\n",
       "0       1.0  <CommunitySolution 0.874 at 0x7f8bae2c3050>\n",
       "1       0.9  <CommunitySolution 0.787 at 0x7f8bae568490>\n",
       "2       0.8  <CommunitySolution 0.699 at 0x7f8bae742450>\n",
       "3       0.7  <CommunitySolution 0.612 at 0x7f8bae4893d0>\n",
       "4       0.6  <CommunitySolution 0.524 at 0x7f8bae540950>\n",
       "5       0.5  <CommunitySolution 0.437 at 0x7f8bae107650>\n",
       "6       0.4  <CommunitySolution 0.350 at 0x7f8bae1104d0>\n",
       "7       0.3  <CommunitySolution 0.262 at 0x7f8bae69b0d0>\n",
       "8       0.2  <CommunitySolution 0.175 at 0x7f8bae5311d0>\n",
       "9       0.1  <CommunitySolution 0.087 at 0x7f8bae437190>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "sols = com.cooperative_tradeoff(fraction=np.arange(0.1, 1.01, 0.1))\n",
    "sols"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The solutions can than be inspected by the usual pandas methods. See the [pandas documentation](https://pandas.pydata.org/pandas-docs/stable/) for more infos."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "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>compartments</th>\n",
       "      <th>Escherichia_coli_1</th>\n",
       "      <th>Escherichia_coli_2</th>\n",
       "      <th>Escherichia_coli_3</th>\n",
       "      <th>Escherichia_coli_4</th>\n",
       "      <th>medium</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.873922</td>\n",
       "      <td>0.873922</td>\n",
       "      <td>0.873922</td>\n",
       "      <td>0.873922</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.786529</td>\n",
       "      <td>0.786529</td>\n",
       "      <td>0.786529</td>\n",
       "      <td>0.786529</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.699137</td>\n",
       "      <td>0.699137</td>\n",
       "      <td>0.699137</td>\n",
       "      <td>0.699137</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.611745</td>\n",
       "      <td>0.611745</td>\n",
       "      <td>0.611745</td>\n",
       "      <td>0.611745</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.524353</td>\n",
       "      <td>0.524353</td>\n",
       "      <td>0.524353</td>\n",
       "      <td>0.524353</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.436961</td>\n",
       "      <td>0.436961</td>\n",
       "      <td>0.436961</td>\n",
       "      <td>0.436961</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.349569</td>\n",
       "      <td>0.349569</td>\n",
       "      <td>0.349569</td>\n",
       "      <td>0.349569</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.262176</td>\n",
       "      <td>0.262176</td>\n",
       "      <td>0.262176</td>\n",
       "      <td>0.262176</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.174784</td>\n",
       "      <td>0.174784</td>\n",
       "      <td>0.174784</td>\n",
       "      <td>0.174784</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.087392</td>\n",
       "      <td>0.087392</td>\n",
       "      <td>0.087392</td>\n",
       "      <td>0.087392</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "compartments  Escherichia_coli_1  Escherichia_coli_2  Escherichia_coli_3  \\\n",
       "0                       0.873922            0.873922            0.873922   \n",
       "1                       0.786529            0.786529            0.786529   \n",
       "2                       0.699137            0.699137            0.699137   \n",
       "3                       0.611745            0.611745            0.611745   \n",
       "4                       0.524353            0.524353            0.524353   \n",
       "5                       0.436961            0.436961            0.436961   \n",
       "6                       0.349569            0.349569            0.349569   \n",
       "7                       0.262176            0.262176            0.262176   \n",
       "8                       0.174784            0.174784            0.174784   \n",
       "9                       0.087392            0.087392            0.087392   \n",
       "\n",
       "compartments  Escherichia_coli_4  medium  \n",
       "0                       0.873922     NaN  \n",
       "1                       0.786529     NaN  \n",
       "2                       0.699137     NaN  \n",
       "3                       0.611745     NaN  \n",
       "4                       0.524353     NaN  \n",
       "5                       0.436961     NaN  \n",
       "6                       0.349569     NaN  \n",
       "7                       0.262176     NaN  \n",
       "8                       0.174784     NaN  \n",
       "9                       0.087392     NaN  "
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rates = sols.solution.apply(lambda x: x.members.growth_rate)\n",
    "rates"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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