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    "# Elasticities\n",
    "\n",
    "In some cases we might be interested in testing certain intervention strategies on our models. In general we will be most intested in what is the consequence for the environment, meaning what happens with the exchange reactions in the model. Here, `micom` allows you to respond two kind of questions:\n",
    "\n",
    "1. What impact does changing a bacterial abundance have on the exchanges?\n",
    "2. What impact does changing the exchnage bounds (ergo diet) have on the exchanges?\n",
    "\n",
    "For that we use the concept of *elasticity coefficients* which are a dimensionless normalized measure of how much the parameter $p$ affects the flux $v$: \n",
    "\n",
    "$$\n",
    "\\varepsilon_p^v = \\frac{\\partial v}{\\partial p}\\frac{p}{v} = \\frac{\\partial\\ln v}{\\partial\\ln p}\n",
    "$$\n",
    "\n",
    "`micom` can calculate the elasticities for abundances and diet in one go.\n",
    "\n",
    "This again uses cooperative tradeoff to limit the solution space."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 5/5 [00:02<00:00,  2.39models/s]\n",
      "100%|██████████| 4/4 [00:00<00:00, 16.06optimizations/s]\n",
      "100%|██████████| 5/5 [00:00<00:00,  7.38optimizations/s]\n"
     ]
    },
    {
     "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>reaction</th>\n",
       "      <th>taxon</th>\n",
       "      <th>effector</th>\n",
       "      <th>direction</th>\n",
       "      <th>elasticity</th>\n",
       "      <th>type</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>EX_ac_m</td>\n",
       "      <td>medium</td>\n",
       "      <td>EX_glc__D_m</td>\n",
       "      <td>zero</td>\n",
       "      <td>0.000014</td>\n",
       "      <td>exchanges</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>EX_acald_m</td>\n",
       "      <td>medium</td>\n",
       "      <td>EX_glc__D_m</td>\n",
       "      <td>zero</td>\n",
       "      <td>0.000012</td>\n",
       "      <td>exchanges</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>EX_akg_m</td>\n",
       "      <td>medium</td>\n",
       "      <td>EX_glc__D_m</td>\n",
       "      <td>zero</td>\n",
       "      <td>0.000017</td>\n",
       "      <td>exchanges</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>EX_co2_m</td>\n",
       "      <td>medium</td>\n",
       "      <td>EX_glc__D_m</td>\n",
       "      <td>forward</td>\n",
       "      <td>0.923854</td>\n",
       "      <td>exchanges</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>EX_etoh_m</td>\n",
       "      <td>medium</td>\n",
       "      <td>EX_glc__D_m</td>\n",
       "      <td>zero</td>\n",
       "      <td>0.000009</td>\n",
       "      <td>exchanges</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     reaction   taxon     effector direction  elasticity       type\n",
       "0     EX_ac_m  medium  EX_glc__D_m      zero    0.000014  exchanges\n",
       "1  EX_acald_m  medium  EX_glc__D_m      zero    0.000012  exchanges\n",
       "2    EX_akg_m  medium  EX_glc__D_m      zero    0.000017  exchanges\n",
       "3    EX_co2_m  medium  EX_glc__D_m   forward    0.923854  exchanges\n",
       "4   EX_etoh_m  medium  EX_glc__D_m      zero    0.000009  exchanges"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from micom import Community, data\n",
    "from micom.elasticity import elasticities\n",
    "\n",
    "tax = data.test_taxonomy()\n",
    "com = Community(tax)\n",
    "\n",
    "eps = elasticities(com, fraction=1.0, reactions=com.exchanges)\n",
    "eps.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here reaction refers to the target flux and effector to the changed parameter. The direction indicates the flux direction and the type whether we changed an exchange bound or a taxa abundance. So for instance the 4th row would tell us that raising glucose import by one unit (one unit of additional glucose in the diet) would increase the carbon dioxide production by 0.92 units. The other rows do not impose a significant change, are not sensitive to glucose availability."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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