cobrapy-04-simulating-and-analyzing-metabolic-models.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Simulating models"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Preparation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from cobra.io import read_sbml_model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "model = read_sbml_model('data/iJO1366.xml.gz')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "model.solver = \"cplex\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Parsimonious flux balance analysis (pFBA) (5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from cobra.flux_analysis import pfba"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "pFBA is the same as regular FBA except that our objective instead of maximizing the growth rate, is to minimize the total sum of absolute flux values. Since this on its own would lead to the trivial solution of all fluxes equal to zero (death), we also have the constraint that the original objective must be some fraction of its FBA solution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "fba_solution = model.optimize()\n",
    "pfba_solution = pfba(model, fraction_of_optimum=0.95)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.982371812727\n",
      "763.156674113\n"
     ]
    }
   ],
   "source": [
    "print(fba_solution.fluxes.BIOMASS_Ec_iJO1366_core_53p95M)\n",
    "print(fba_solution.fluxes.abs().sum())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.933253222091\n",
      "663.848000167\n"
     ]
    }
   ],
   "source": [
    "print(pfba_solution.fluxes.BIOMASS_Ec_iJO1366_core_53p95M)\n",
    "print(pfba_solution.fluxes.abs().sum())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Flux variability analysis (10 + 10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Preparation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from cobra.flux_analysis import flux_variability_analysis\n",
    "import escher"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "core_model = read_sbml_model('data/e_coli_core.xml.gz')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "core_model.solver = \"cplex\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Flux variability analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate all possible maximum and minimum fluxes for all reactions using FVA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "result = flux_variability_analysis(core_model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Inspect the result."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>maximum</th>\n",
       "      <th>minimum</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>ACALD</th>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.0000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ACALDt</th>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.0000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ACKr</th>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.0000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ACONTa</th>\n",
       "      <td>6.0072</td>\n",
       "      <td>6.0072</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ACONTb</th>\n",
       "      <td>6.0072</td>\n",
       "      <td>6.0072</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
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       "      <th>TALA</th>\n",
       "      <td>1.4970</td>\n",
       "      <td>1.4970</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>THD2</th>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.0000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TKT1</th>\n",
       "      <td>1.4970</td>\n",
       "      <td>1.4970</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TKT2</th>\n",
       "      <td>1.1815</td>\n",
       "      <td>1.1815</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TPI</th>\n",
       "      <td>7.4774</td>\n",
       "      <td>7.4774</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>95 rows × 2 columns</p>\n",
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      ],
      "text/plain": [
       "        maximum  minimum\n",
       "ACALD    0.0000   0.0000\n",
       "ACALDt   0.0000   0.0000\n",
       "ACKr     0.0000   0.0000\n",
       "ACONTa   6.0072   6.0072\n",
       "ACONTb   6.0072   6.0072\n",
       "...         ...      ...\n",
       "TALA     1.4970   1.4970\n",
       "THD2     0.0000   0.0000\n",
       "TKT1     1.4970   1.4970\n",
       "TKT2     1.1815   1.1815\n",
       "TPI      7.4774   7.4774\n",
       "\n",
       "[95 rows x 2 columns]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Get an overview of a few key statistics of the resulting flux ranges."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>maximum</th>\n",
       "      <th>minimum</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>95.0000</td>\n",
       "      <td>95.0000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>23.5738</td>\n",
       "      <td>2.6278</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>143.9744</td>\n",
       "      <td>10.6981</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>-29.1758</td>\n",
       "      <td>-29.1758</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.0000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.0000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>5.0122</td>\n",
       "      <td>4.9600</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1000.0000</td>\n",
       "      <td>45.5140</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      "text/plain": [
       "         maximum  minimum\n",
       "count    95.0000  95.0000\n",
       "mean     23.5738   2.6278\n",
       "std     143.9744  10.6981\n",
       "min     -29.1758 -29.1758\n",
       "25%       0.0000   0.0000\n",
       "50%       0.0000   0.0000\n",
       "75%       5.0122   4.9600\n",
       "max    1000.0000  45.5140"
      ]
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     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Visualize the flux ranges on a pathway map of _E. coli's_ central carbon metabolism."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
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5894.515691375733}, \"text_labels\": {}}]'),\n",
       "               model_data: JSON.parse('null'),\n",
       "               static_site_index: JSON.parse('null'),\n",
       "           };\n",
       "       }\n",
       "   })();\n",
       "  </script>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "abs_flux_ranges = abs(result.maximum - result.minimum).to_dict()\n",
    "escher.Builder('e_coli_core.Core metabolism', reaction_data=abs_flux_ranges).display_in_notebook()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Those reactions showing up in red are futile cyles."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>maximum</th>\n",
       "      <th>minimum</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>FRD7</th>\n",
       "      <td>994.9356</td>\n",
       "      <td>0.0000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SUCDi</th>\n",
       "      <td>1000.0000</td>\n",
       "      <td>5.0644</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         maximum  minimum\n",
       "FRD7    994.9356   0.0000\n",
       "SUCDi  1000.0000   5.0644"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result[result.maximum > 500]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Loopless FVA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We add constraints to get rid of the loops using [cycle free flux](https://academic.oup.com/bioinformatics/article-lookup/doi/10.1093/bioinformatics/btv096)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "loopless_result = flux_variability_analysis(core_model, loopless=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "\n",
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       "\n",
       "  \n",
       "  \n",
       "\n",
       "  \n",
       "  \n",
       "    <link rel=\"stylesheet\" href=\"//unpkg.com/escher-vis@1.6.0/css/dist/builder.min.css\"/>\n",
       "  \n",
       "\n",
       "\n",
       "\n",
       "  <div style=\"height: 500px; width: 100%;\" id=\"kiyeshkzpl\"></div>\n",
       "\n",
       "  <script>\n",
       "   /* Closure to make sure data only applies to this map. */\n",
       "   (function() {\n",
       "       /* data from python */\n",
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       "\n",
       "       function load_lib(url, callback) {\n",
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       "           s.src = url;\n",
       "           s.async = true;\n",
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       "\n",
       "       function check_global_and_load(name, url, callback) {\n",
       "           /** Look for the name in the global scope. If it isn't present, then\n",
       "              load the library at url. Returns the object. */\n",
       "           if (window[name] !== undefined) {\n",
       "               callback(window[name]);\n",
       "           } else {\n",
       "               load_lib(url, function() {\n",
       "                   callback(window[name]);\n",
       "               });\n",
       "           }\n",
       "       }\n",
       "\n",
       "       function draw_escher(escher) {\n",
       "           /** Get data and draw */\n",
       "           var load = function(t_map_data, t_model_data, t_options) {\n",
       "               escher.Builder(t_map_data, t_model_data, data.builder_embed_css,\n",
       "                              escher.libs.d3_select('#' + data.id), t_options);\n",
       "           }\n",
       "\n",
       "           // for the static site, use the url attributes for the map and model\n",
       "           // information\n",
       "           if (data.static_site_index !== null) {\n",
       "               escher.static.load_map_model_from_url(data.map_download_url, data.model_download_url,\n",
       "                                                     data.static_site_index, data.options, load);\n",
       "           } else {\n",
       "               load(data.map_data, data.model_data, data.options);\n",
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       "       }\n",
       "\n",
       "       // Load dependencies and draw\n",
       "       if (typeof define === 'function' && define.amd) {\n",
       "           // require.js is available: use it to load escher\n",
       "           require.config({\n",
       "             paths: {\n",
       "               escher: '//unpkg.com/escher-vis@1.6.0/js/dist/escher.min',\n",
       "             },\n",
       "             // Override urlArgs that adds ?v= to the end of the escher URL and\n",
       "             // messes up unpkg links. Honestly, I'm not sure if this will lead\n",
       "             // to downstream bugs in the notebook, but they really shouldn't be\n",
       "             // doing this cache-busting anyway.\n",
       "             urlArgs: null,\n",
       "           })\n",
       "           require([ 'escher' ], function(escher) {\n",
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       "           // require.js not available: dynamically load escher\n",
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       "           return {\n",
       "               id: JSON.parse('\"kiyeshkzpl\"'),\n",
       "               map_download_url: JSON.parse('\"//escher.github.io/1-0-0/5/maps/\"'),\n",
       "               model_download_url: JSON.parse('\"//escher.github.io/1-0-0/5/models/\"'),\n",
       "               options: JSON.parse('{\"ignore_bootstrap\": true, \"never_ask_before_quit\": true, \"gene_data\": null, \"enable_editing\": false, \"reaction_data\": {\"SUCCt3\": 0.0, \"EX_h_e\": 1.4210854715202004e-14, \"ATPS4r\": 2.842170943040401e-14, \"EX_pi_e\": 1.2434497875801753e-14, \"EX_for_e\": 0.0, \"EX_mal__L_e\": 0.0, \"PPC\": 5.728750807065808e-14, \"NH4t\": 0.0, \"FORt2\": 0.0, \"FRD7\": 0.0, \"CO2t\": 3.552713678800501e-15, \"PGK\": 7.105427357601002e-15, \"BIOMASS_Ecoli_core_w_GAM\": 5.551115123125783e-16, \"NADTRHD\": 0.0, \"EX_pyr_e\": 0.0, \"PYRt2\": 0.0, \"PFK\": 4.3520742565306136e-14, \"EX_succ_e\": 0.0, \"H2Ot\": 0.0, \"PGL\": 1.4210854715202004e-14, \"GLCpts\": 0.0, \"EX_akg_e\": 0.0, \"ETOHt2r\": 0.0, \"FUMt2_2\": 0.0, \"EX_nh4_e\": 0.0, \"EX_fum_e\": 0.0, \"ACONTb\": 1.7763568394002505e-14, \"EX_glc__D_e\": 0.0, \"SUCCt2_2\": 0.0, \"G6PDH2r\": 4.796163466380676e-14, \"ICL\": 0.0, \"AKGDH\": 3.6415315207705135e-14, \"TKT2\": 1.5987211554602254e-14, \"THD2\": 0.0, \"PDH\": 2.1316282072803006e-14, \"FBA\": 1.5987211554602254e-14, \"PPCK\": 0.0, \"ME1\": 0.0, \"GND\": 4.796163466380676e-14, \"ATPM\": 1.4210854715202004e-14, \"SUCDi\": 6.039613253960852e-14, \"AKGt2r\": 0.0, \"ACALDt\": 0.0, \"PTAr\": 0.0, \"EX_lac__D_e\": 0.0, \"FORti\": 0.0, \"EX_fru_e\": 0.0, \"GLNS\": 0.0, \"ME2\": 0.0, \"GLUSy\": 0.0, \"EX_gln__L_e\": 0.0, \"EX_ac_e\": 0.0, \"ALCD2x\": 0.0, \"PYK\": 3.352873534367973e-14, \"EX_glu__L_e\": 0.0, \"EX_h2o_e\": 0.0, \"TALA\": 4.440892098500626e-15, \"PIt2r\": 1.7763568394002505e-15, \"EX_co2_e\": 3.552713678800501e-15, \"GLNabc\": 0.0, \"ICDHyr\": 4.796163466380676e-14, \"D_LACt2\": 0.0, \"GLUDy\": 0.0, \"CYTBD\": 1.4210854715202004e-14, \"TPI\": 1.5987211554602254e-14, \"RPE\": 3.0548896745585807e-12, \"ACONTa\": 1.7763568394002505e-14, \"ACKr\": 0.0, \"EX_o2_e\": 0.0, \"ACALD\": 0.0, \"GAPD\": 7.105427357601002e-15, \"EX_etoh_e\": 0.0, \"ADK1\": 0.0, \"MALS\": 0.0, \"RPI\": 1.5987211554602254e-14, \"GLUN\": 0.0, \"FBP\": 0.0, \"MALt2_2\": 0.0, \"GLUt2r\": 0.0, \"O2t\": 7.105427357601002e-15, \"ENO\": 3.979039320256561e-13, \"PGM\": 1.7763568394002505e-14, \"LDH_D\": 0.0, \"CS\": 5.329070518200751e-15, \"FRUpts2\": 0.0, \"PPS\": 0.0, \"TKT1\": 1.5987211554602254e-14, \"NADH16\": 9.947598300641403e-14, \"EX_acald_e\": 0.0, \"PFL\": 0.0, \"ACt2r\": 0.0, \"FUM\": 6.217248937900877e-15, \"MDH\": 6.750155989720952e-13, \"SUCOAS\": 9.414691248821327e-14, \"PGI\": 4.796163466380676e-14}, \"enable_keys\": false, \"menu\": \"zoom\", \"scroll_behavior\": \"none\", \"metabolite_data\": null, \"fill_screen\": false}'),\n",
       "               builder_embed_css: JSON.parse('null'),\n",
       "               map_data: JSON.parse('[{\"map_name\": \"e_coli_core.Core metabolism\", \"map_id\": \"0df3827fde8464e80f455a773a52c274\", \"map_description\": \"E. coli core metabolic network\\\\nLast Modified Fri Dec 05 2014 16:39:44 GMT-0800 (PST)\", \"homepage\": \"https://escher.github.io\", \"schema\": \"https://escher.github.io/escher/jsonschema/1-0-0#\"}, {\"reactions\": {\"1577514\": {\"name\": \"Formate transport in via proton symport\", \"bigg_id\": \"FORt2\", \"segments\": {\"11\": {\"to_node_id\": \"1577044\", \"from_node_id\": \"1576666\", \"b2\": {\"y\": 4749.209372712298, \"x\": 1360.0}, \"b1\": {\"y\": 4827.353507999329, \"x\": 1360.0}}, \"10\": {\"to_node_id\": \"1577046\", \"from_node_id\": \"1577045\", \"b2\": null, \"b1\": null}, \"13\": {\"to_node_id\": \"1576590\", \"from_node_id\": \"1577046\", \"b2\": {\"y\": 4275.94781629675, \"x\": 1360.0}, \"b1\": {\"y\": 4411.784344889025, \"x\": 1360.0}}, \"12\": {\"to_node_id\": \"1577044\", \"from_node_id\": 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phosphate\", \"label_x\": 3957.985595703125, \"node_type\": \"metabolite\", \"y\": 3759.0, \"x\": 4043.0, \"bigg_id\": \"nadp_c\", \"label_y\": 3736.215576171875}, \"1576659\": {\"node_is_primary\": false, \"name\": \"H+\", \"label_x\": 2954.28076171875, \"node_type\": \"metabolite\", \"y\": 1010.0, \"x\": 2940.0, \"bigg_id\": \"h_c\", \"label_y\": 1038.4132080078125}, \"1576658\": {\"node_is_primary\": false, \"name\": \"H+\", \"label_x\": 2962.214599609375, \"node_type\": \"metabolite\", \"y\": 700.0, \"x\": 2940.0, \"bigg_id\": \"h_e\", \"label_y\": 718.4132080078125}, \"1576912\": {\"y\": 3995.0, \"x\": 1255.0, \"node_type\": \"multimarker\"}, \"1576913\": {\"y\": 3995.0, \"x\": 1415.0, \"node_type\": \"multimarker\"}, \"1576910\": {\"y\": 3330.0, \"x\": 3776.0, \"node_type\": \"multimarker\"}, \"1576911\": {\"y\": 3995.0, \"x\": 1335.0, \"node_type\": \"midmarker\"}, \"1576916\": {\"y\": 3526.0, \"x\": 1404.0, \"node_type\": \"midmarker\"}, \"1576917\": {\"y\": 3554.0, \"x\": 1485.0, \"node_type\": \"multimarker\"}, \"1576914\": {\"y\": 1660.0, \"x\": 4970.0, \"node_type\": \"midmarker\"}, \"1576918\": {\"y\": 3503.0, \"x\": 1335.0, \"node_type\": \"multimarker\"}, \"1576919\": {\"y\": 4520.0, \"x\": 2880.0, \"node_type\": \"multimarker\"}, \"1577028\": {\"y\": 3360.0, \"x\": 2310.0, \"node_type\": \"multimarker\"}, \"1577021\": {\"y\": 3918.0, \"x\": 2840.0, \"node_type\": \"multimarker\"}, \"1577020\": {\"y\": 3837.0, \"x\": 2744.0, \"node_type\": \"multimarker\"}, \"1577023\": {\"y\": 3945.0, \"x\": 375.0, \"node_type\": \"multimarker\"}, \"1577022\": {\"y\": 3886.0, \"x\": 2798.0, \"node_type\": \"midmarker\"}, \"1577025\": {\"y\": 3945.0, \"x\": 505.0, \"node_type\": \"midmarker\"}, \"1577024\": {\"y\": 3945.0, \"x\": 645.0, \"node_type\": \"multimarker\"}, \"1577027\": {\"y\": 3410.0, \"x\": 2220.0, \"node_type\": \"multimarker\"}, \"1577026\": {\"y\": 3390.0, \"x\": 2260.0, \"node_type\": \"midmarker\"}, \"1576967\": {\"y\": 4604.0, \"x\": 3621.0, \"node_type\": \"midmarker\"}, \"1576966\": {\"y\": 1735.0, \"x\": 2175.0, \"node_type\": \"multimarker\"}, \"1576965\": {\"y\": 1695.0, \"x\": 2175.0, \"node_type\": \"midmarker\"}, \"1576964\": {\"y\": 1645.0, \"x\": 2175.0, \"node_type\": \"multimarker\"}, \"1576962\": {\"y\": 4924.0, \"x\": 3257.0, \"node_type\": \"midmarker\"}, \"1576961\": {\"y\": 4614.0, \"x\": 3257.0, \"node_type\": \"midmarker\"}, \"1576960\": {\"y\": 3341.0, \"x\": 2582.0, \"node_type\": \"multimarker\"}, \"1576969\": {\"y\": 3228.0, \"x\": 5032.0, \"node_type\": \"midmarker\"}, \"1576499\": {\"node_is_primary\": false, \"name\": \"H+\", \"label_x\": 3522.892333984375, \"node_type\": \"metabolite\", \"y\": 1080.287841796875, \"x\": 3510.0, \"bigg_id\": \"h_c\", \"label_y\": 1099.0072021484375}, \"1576999\": {\"y\": 1041.710205078125, \"x\": 1056.5867919921875, \"node_type\": \"multimarker\"}}, \"canvas\": {\"y\": 314.36893920898433, \"x\": 7.857062530517567, \"height\": 4860.457037353515, \"width\": 5894.515691375733}, \"text_labels\": {}}]'),\n",
       "               model_data: JSON.parse('null'),\n",
       "               static_site_index: JSON.parse('null'),\n",
       "           };\n",
       "       }\n",
       "   })();\n",
       "  </script>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "abs_flux_ranges = abs(loopless_result.maximum - loopless_result.minimum).to_dict()\n",
    "escher.Builder('e_coli_core.Core metabolism', reaction_data=abs_flux_ranges).display_in_notebook()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Further constraints to the FVA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "FVA examines how extreme the fluxes for each reaction can be. This includes solutions with very low growth rate, or with very high total flux, that means solutions that are quite unlikely for an actual organism. We can add additional constraints to the FVA to make it a bit more realistic using the parameters `fraction_of_optimium` which sets growth rate to not go below a given ratio of the max (e.g. 0.9 which implies growth rate should not be less than 90% of the previous optimum), or `pfba_factor` which says we are not interested in solutions that have very high total absolute flux (e.g. 1.1 which implies no more than 10% over the minimum total flux)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>maximum</th>\n",
       "      <th>minimum</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>ACALD</th>\n",
       "      <td>0.0000</td>\n",
       "      <td>-2.5424</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ACALDt</th>\n",
       "      <td>0.0000</td>\n",
       "      <td>-2.5424</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ACKr</th>\n",
       "      <td>0.0000</td>\n",
       "      <td>-3.8136</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ACONTa</th>\n",
       "      <td>8.7538</td>\n",
       "      <td>3.3709</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ACONTb</th>\n",
       "      <td>8.7538</td>\n",
       "      <td>3.3709</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TALA</th>\n",
       "      <td>3.1389</td>\n",
       "      <td>0.0000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>THD2</th>\n",
       "      <td>0.8068</td>\n",
       "      <td>0.8068</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TKT1</th>\n",
       "      <td>3.1389</td>\n",
       "      <td>0.0000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TKT2</th>\n",
       "      <td>2.8549</td>\n",
       "      <td>-0.3118</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TPI</th>\n",
       "      <td>9.0769</td>\n",
       "      <td>5.9381</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>95 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "        maximum  minimum\n",
       "ACALD    0.0000  -2.5424\n",
       "ACALDt   0.0000  -2.5424\n",
       "ACKr     0.0000  -3.8136\n",
       "ACONTa   8.7538   3.3709\n",
       "ACONTb   8.7538   3.3709\n",
       "...         ...      ...\n",
       "TALA     3.1389   0.0000\n",
       "THD2     0.8068   0.8068\n",
       "TKT1     3.1389   0.0000\n",
       "TKT2     2.8549  -0.3118\n",
       "TPI      9.0769   5.9381\n",
       "\n",
       "[95 rows x 2 columns]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "flux_variability_analysis(core_model, fraction_of_optimum=0.9, loopless=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>maximum</th>\n",
       "      <th>minimum</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>ACALD</th>\n",
       "      <td>0.0000</td>\n",
       "      <td>-2.5424</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ACALDt</th>\n",
       "      <td>0.0000</td>\n",
       "      <td>-2.5424</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ACKr</th>\n",
       "      <td>0.0000</td>\n",
       "      <td>-3.8136</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ACONTa</th>\n",
       "      <td>8.1200</td>\n",
       "      <td>2.9175</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ACONTb</th>\n",
       "      <td>8.1200</td>\n",
       "      <td>2.9175</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TALA</th>\n",
       "      <td>3.1389</td>\n",
       "      <td>0.0000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>THD2</th>\n",
       "      <td>3.0627</td>\n",
       "      <td>0.0000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TKT1</th>\n",
       "      <td>3.1389</td>\n",
       "      <td>0.0000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TKT2</th>\n",
       "      <td>2.8549</td>\n",
       "      <td>-0.2968</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TPI</th>\n",
       "      <td>9.0769</td>\n",
       "      <td>5.4747</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>95 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "        maximum  minimum\n",
       "ACALD    0.0000  -2.5424\n",
       "ACALDt   0.0000  -2.5424\n",
       "ACKr     0.0000  -3.8136\n",
       "ACONTa   8.1200   2.9175\n",
       "ACONTb   8.1200   2.9175\n",
       "...         ...      ...\n",
       "TALA     3.1389   0.0000\n",
       "THD2     3.0627   0.0000\n",
       "TKT1     3.1389   0.0000\n",
       "TKT2     2.8549  -0.2968\n",
       "TPI      9.0769   5.4747\n",
       "\n",
       "[95 rows x 2 columns]"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "flux_variability_analysis(core_model, fraction_of_optimum=0.9, pfba_factor=1.1, loopless=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Modify the code to explore flux ranges for $\\mu \\gt 0.7 \\ h^{-1}$ "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using FVA, determine all blocked reactions ($ v = 0 $) in the model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Production envelopes (5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Production envelopes are useful to illustrate how max and min fluxes for a given reaction varies when you fix flux of another reaction to a given value. E.g, \"how much can product can I get given different growth rates?\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from cobra.flux_analysis import production_envelope"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "prod_env = production_envelope(model, reactions=model.reactions.BIOMASS_Ec_iJO1366_core_53p95M, \n",
    "                               objective=model.reactions.EX_ac_e)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>BIOMASS_Ec_iJO1366_core_53p95M</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>0.0000</td>\n",
       "      <td>EX_glc__D_e</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>minimum</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.0000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.0517</td>\n",
       "      <td>EX_glc__D_e</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>minimum</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.0000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.1034</td>\n",
       "      <td>EX_glc__D_e</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>minimum</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.0000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.1551</td>\n",
       "      <td>EX_glc__D_e</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>minimum</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.0000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.2068</td>\n",
       "      <td>EX_glc__D_e</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>minimum</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.0000</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",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>0.7756</td>\n",
       "      <td>EX_glc__D_e</td>\n",
       "      <td>0.2498</td>\n",
       "      <td>maximum</td>\n",
       "      <td>7.4940</td>\n",
       "      <td>0.2456</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>0.8273</td>\n",
       "      <td>EX_glc__D_e</td>\n",
       "      <td>0.1918</td>\n",
       "      <td>maximum</td>\n",
       "      <td>5.7534</td>\n",
       "      <td>0.1886</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>0.8790</td>\n",
       "      <td>EX_glc__D_e</td>\n",
       "      <td>0.1279</td>\n",
       "      <td>maximum</td>\n",
       "      <td>3.8356</td>\n",
       "      <td>0.1257</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>0.9307</td>\n",
       "      <td>EX_glc__D_e</td>\n",
       "      <td>0.0639</td>\n",
       "      <td>maximum</td>\n",
       "      <td>1.9178</td>\n",
       "      <td>0.0629</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>0.9824</td>\n",
       "      <td>EX_glc__D_e</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>maximum</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>-0.0000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>40 rows × 6 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    BIOMASS_Ec_iJO1366_core_53p95M carbon_source  carbon_yield direction  \\\n",
       "0                           0.0000   EX_glc__D_e        0.0000   minimum   \n",
       "1                           0.0517   EX_glc__D_e        0.0000   minimum   \n",
       "2                           0.1034   EX_glc__D_e        0.0000   minimum   \n",
       "3                           0.1551   EX_glc__D_e        0.0000   minimum   \n",
       "4                           0.2068   EX_glc__D_e        0.0000   minimum   \n",
       "..                             ...           ...           ...       ...   \n",
       "35                          0.7756   EX_glc__D_e        0.2498   maximum   \n",
       "36                          0.8273   EX_glc__D_e        0.1918   maximum   \n",
       "37                          0.8790   EX_glc__D_e        0.1279   maximum   \n",
       "38                          0.9307   EX_glc__D_e        0.0639   maximum   \n",
       "39                          0.9824   EX_glc__D_e        0.0000   maximum   \n",
       "\n",
       "      flux  mass_yield  \n",
       "0   0.0000      0.0000  \n",
       "1   0.0000      0.0000  \n",
       "2   0.0000      0.0000  \n",
       "3   0.0000      0.0000  \n",
       "4   0.0000      0.0000  \n",
       "..     ...         ...  \n",
       "35  7.4940      0.2456  \n",
       "36  5.7534      0.1886  \n",
       "37  3.8356      0.1257  \n",
       "38  1.9178      0.0629  \n",
       "39  0.0000     -0.0000  \n",
       "\n",
       "[40 rows x 6 columns]"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prod_env"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fca1a82d7f0>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Q+f0aEZjHjz5fb6Lft5s5fSnO6dI8koa7UipDVSuRn/n9GzG0VUV+2XmSlmPC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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fca1a8c5e48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "prod_env[prod_env.direction == 'maximum'].plot(kind='line', x='BIOMASS_Ec_iJO1366_core_53p95M', y='carbon_yield')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gene and reaction essentiality (5 + 5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Which genes and reactions can knock-out and which are essential?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from cobra.flux_analysis import single_gene_deletion, single_reaction_deletion"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>flux</th>\n",
       "      <th>status</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>b0002</th>\n",
       "      <td>0.9824</td>\n",
       "      <td>optimal</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>b0003</th>\n",
       "      <td>0.0000</td>\n",
       "      <td>optimal</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>b0004</th>\n",
       "      <td>0.0000</td>\n",
       "      <td>optimal</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>b0007</th>\n",
       "      <td>0.9824</td>\n",
       "      <td>optimal</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>b0008</th>\n",
       "      <td>0.9824</td>\n",
       "      <td>optimal</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>b4481</th>\n",
       "      <td>0.9824</td>\n",
       "      <td>optimal</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>b4485</th>\n",
       "      <td>0.9824</td>\n",
       "      <td>optimal</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>b4513</th>\n",
       "      <td>0.9824</td>\n",
       "      <td>optimal</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>b4544</th>\n",
       "      <td>0.9824</td>\n",
       "      <td>optimal</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>s0001</th>\n",
       "      <td>0.0000</td>\n",
       "      <td>optimal</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1367 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "         flux   status\n",
       "b0002  0.9824  optimal\n",
       "b0003  0.0000  optimal\n",
       "b0004  0.0000  optimal\n",
       "b0007  0.9824  optimal\n",
       "b0008  0.9824  optimal\n",
       "...       ...      ...\n",
       "b4481  0.9824  optimal\n",
       "b4485  0.9824  optimal\n",
       "b4513  0.9824  optimal\n",
       "b4544  0.9824  optimal\n",
       "s0001  0.0000  optimal\n",
       "\n",
       "[1367 rows x 2 columns]"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gene_deletions = single_gene_deletion(model)\n",
    "gene_deletions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A gene/reaction can be considered essential if removing it leads to an infeasible model, or a model with very low growth rate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'b0003',\n",
       " 'b0004',\n",
       " 'b0009',\n",
       " 'b0025',\n",
       " 'b0029',\n",
       " 'b0031',\n",
       " 'b0052',\n",
       " 'b0071',\n",
       " 'b0072',\n",
       " 'b0073',\n",
       " 'b0074',\n",
       " 'b0085',\n",
       " 'b0086',\n",
       " 'b0087',\n",
       " 'b0088',\n",
       " 'b0090',\n",
       " 'b0091',\n",
       " 'b0096',\n",
       " 'b0103',\n",
       " 'b0109',\n",
       " 'b0131',\n",
       " 'b0133',\n",
       " 'b0134',\n",
       " 'b0142',\n",
       " 'b0154',\n",
       " 'b0159',\n",
       " 'b0166',\n",
       " 'b0173',\n",
       " 'b0174',\n",
       " 'b0175',\n",
       " 'b0179',\n",
       " 'b0180',\n",
       " 'b0181',\n",
       " 'b0182',\n",
       " 'b0185',\n",
       " 'b0369',\n",
       " 'b0386',\n",
       " 'b0414',\n",
       " 'b0415',\n",
       " 'b0417',\n",
       " 'b0420',\n",
       " 'b0421',\n",
       " 'b0423',\n",
       " 'b0475',\n",
       " 'b0522',\n",
       " 'b0523',\n",
       " 'b0524',\n",
       " 'b0639',\n",
       " 'b0720',\n",
       " 'b0750',\n",
       " 'b0774',\n",
       " 'b0775',\n",
       " 'b0776',\n",
       " 'b0777',\n",
       " 'b0778',\n",
       " 'b0781',\n",
       " 'b0783',\n",
       " 'b0784',\n",
       " 'b0785',\n",
       " 'b0826',\n",
       " 'b0827',\n",
       " 'b0907',\n",
       " 'b0908',\n",
       " 'b0914',\n",
       " 'b0915',\n",
       " 'b0918',\n",
       " 'b0928',\n",
       " 'b1062',\n",
       " 'b1069',\n",
       " 'b1091',\n",
       " 'b1092',\n",
       " 'b1093',\n",
       " 'b1094',\n",
       " 'b1096',\n",
       " 'b1098',\n",
       " 'b1131',\n",
       " 'b1136',\n",
       " 'b1208',\n",
       " 'b1210',\n",
       " 'b1215',\n",
       " 'b1260',\n",
       " 'b1261',\n",
       " 'b1262',\n",
       " 'b1263',\n",
       " 'b1264',\n",
       " 'b1277',\n",
       " 'b1281',\n",
       " 'b1288',\n",
       " 'b1415',\n",
       " 'b1662',\n",
       " 'b1693',\n",
       " 'b1740',\n",
       " 'b1812',\n",
       " 'b2019',\n",
       " 'b2020',\n",
       " 'b2021',\n",
       " 'b2022',\n",
       " 'b2023',\n",
       " 'b2024',\n",
       " 'b2025',\n",
       " 'b2026',\n",
       " 'b2103',\n",
       " 'b2153',\n",
       " 'b2311',\n",
       " 'b2312',\n",
       " 'b2315',\n",
       " 'b2316',\n",
       " 'b2320',\n",
       " 'b2323',\n",
       " 'b2329',\n",
       " 'b2400',\n",
       " 'b2472',\n",
       " 'b2476',\n",
       " 'b2478',\n",
       " 'b2499',\n",
       " 'b2507',\n",
       " 'b2515',\n",
       " 'b2530',\n",
       " 'b2557',\n",
       " 'b2564',\n",
       " 'b2574',\n",
       " 'b2585',\n",
       " 'b2599',\n",
       " 'b2600',\n",
       " 'b2615',\n",
       " 'b2687',\n",
       " 'b2746',\n",
       " 'b2747',\n",
       " 'b2750',\n",
       " 'b2751',\n",
       " 'b2752',\n",
       " 'b2762',\n",
       " 'b2763',\n",
       " 'b2764',\n",
       " 'b2780',\n",
       " 'b2818',\n",
       " 'b2827',\n",
       " 'b2838',\n",
       " 'b2942',\n",
       " 'b3018',\n",
       " 'b3040',\n",
       " 'b3041',\n",
       " 'b3058',\n",
       " 'b3172',\n",
       " 'b3176',\n",
       " 'b3177',\n",
       " 'b3187',\n",
       " 'b3189',\n",
       " 'b3196',\n",
       " 'b3198',\n",
       " 'b3199',\n",
       " 'b3200',\n",
       " 'b3201',\n",
       " 'b3255',\n",
       " 'b3256',\n",
       " 'b3359',\n",
       " 'b3360',\n",
       " 'b3368',\n",
       " 'b3389',\n",
       " 'b3412',\n",
       " 'b3433',\n",
       " 'b3607',\n",
       " 'b3608',\n",
       " 'b3633',\n",
       " 'b3634',\n",
       " 'b3639',\n",
       " 'b3642',\n",
       " 'b3648',\n",
       " 'b3729',\n",
       " 'b3730',\n",
       " 'b3770',\n",
       " 'b3771',\n",
       " 'b3774',\n",
       " 'b3804',\n",
       " 'b3805',\n",
       " 'b3807',\n",
       " 'b3809',\n",
       " 'b3843',\n",
       " 'b3850',\n",
       " 'b3857',\n",
       " 'b3939',\n",
       " 'b3941',\n",
       " 'b3957',\n",
       " 'b3958',\n",
       " 'b3959',\n",
       " 'b3960',\n",
       " 'b3967',\n",
       " 'b3972',\n",
       " 'b3974',\n",
       " 'b3990',\n",
       " 'b3991',\n",
       " 'b3992',\n",
       " 'b3993',\n",
       " 'b3994',\n",
       " 'b3997',\n",
       " 'b4005',\n",
       " 'b4006',\n",
       " 'b4013',\n",
       " 'b4039',\n",
       " 'b4040',\n",
       " 'b4160',\n",
       " 'b4177',\n",
       " 'b4214',\n",
       " 'b4245',\n",
       " 'b4261',\n",
       " 'b4262',\n",
       " 'b4407',\n",
       " 's0001'}"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "set(gene_deletions[(gene_deletions.flux < 0.01) | (gene_deletions.status != 'optimal')].index)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Or use the convenience function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{<Gene b0523 at 0x7fca17fda048>,\n",
       " <Gene b0783 at 0x7fca17fac048>,\n",
       " <Gene b4039 at 0x7fca17ffe048>,\n",
       " <Gene b4261 at 0x7fca18027c18>,\n",
       " <Gene b4013 at 0x7fca1808dfd0>,\n",
       " <Gene b3990 at 0x7fca17fbf9e8>,\n",
       " <Gene b0907 at 0x7fca17f44208>,\n",
       " <Gene b2615 at 0x7fca17f50208>,\n",
       " <Gene b2746 at 0x7fca17f2a208>,\n",
       " <Gene b3634 at 0x7fca17f3e208>,\n",
       " <Gene b3639 at 0x7fca17efc208>,\n",
       " <Gene b3648 at 0x7fca18008240>,\n",
       " <Gene b3805 at 0x7fca17f19dd8>,\n",
       " <Gene b3972 at 0x7fca17eb0208>,\n",
       " <Gene b4005 at 0x7fca17fa95f8>,\n",
       " <Gene b4262 at 0x7fca18027630>,\n",
       " <Gene b3994 at 0x7fca17ff4828>,\n",
       " <Gene b0185 at 0x7fca1804a3c8>,\n",
       " <Gene b0182 at 0x7fca17f2e400>,\n",
       " <Gene b1069 at 0x7fca17f32400>,\n",
       " <Gene b2827 at 0x7fca17f4c400>,\n",
       " <Gene b0774 at 0x7fca17ff4438>,\n",
       " <Gene b3368 at 0x7fca17e9ddd8>,\n",
       " <Gene b3974 at 0x7fca17edddd8>,\n",
       " <Gene b2564 at 0x7fca17edfdd8>,\n",
       " <Gene b2316 at 0x7fca1804a5c0>,\n",
       " <Gene b0784 at 0x7fca17fdc5f8>,\n",
       " <Gene b0908 at 0x7fca17f605f8>,\n",
       " <Gene b1210 at 0x7fca17f5a5f8>,\n",
       " <Gene b0785 at 0x7fca17f325f8>,\n",
       " <Gene b1096 at 0x7fca17fd2630>,\n",
       " <Gene b1263 at 0x7fca18002630>,\n",
       " <Gene b0031 at 0x7fca17fec630>,\n",
       " <Gene b1281 at 0x7fca17f445f8>,\n",
       " <Gene b1740 at 0x7fca17f505f8>,\n",
       " <Gene b2507 at 0x7fca17f905f8>,\n",
       " <Gene b3256 at 0x7fca1804a630>,\n",
       " <Gene b3771 at 0x7fca18008630>,\n",
       " <Gene b3198 at 0x7fca17f23dd8>,\n",
       " <Gene b0009 at 0x7fca17f8ffd0>,\n",
       " <Gene b1261 at 0x7fca17f0ffd0>,\n",
       " <Gene b0524 at 0x7fca17f027f0>,\n",
       " <Gene b0826 at 0x7fca17f327f0>,\n",
       " <Gene b0174 at 0x7fca17eb07f0>,\n",
       " <Gene b0914 at 0x7fca17fa0828>,\n",
       " <Gene b1264 at 0x7fca18002828>,\n",
       " <Gene b0639 at 0x7fca17f6a7f0>,\n",
       " <Gene b0417 at 0x7fca17f4c7f0>,\n",
       " <Gene b0086 at 0x7fca181047f0>,\n",
       " <Gene b1812 at 0x7fca17fd2828>,\n",
       " <Gene b2400 at 0x7fca17f5a7f0>,\n",
       " <Gene b2478 at 0x7fca17fec828>,\n",
       " <Gene b2763 at 0x7fca180bc828>,\n",
       " <Gene b3255 at 0x7fca1804a828>,\n",
       " <Gene b0096 at 0x7fca181049e8>,\n",
       " <Gene b3993 at 0x7fca17f4c9e8>,\n",
       " <Gene b2557 at 0x7fca17fa9dd8>,\n",
       " <Gene b0131 at 0x7fca1800aa20>,\n",
       " <Gene b0776 at 0x7fca18002a20>,\n",
       " <Gene b2599 at 0x7fca18004a20>,\n",
       " <Gene b2764 at 0x7fca180bca20>,\n",
       " <Gene b3360 at 0x7fca17fd2a20>,\n",
       " <Gene b0004 at 0x7fca180b2ba8>,\n",
       " <Gene b2023 at 0x7fca17f6cbe0>,\n",
       " <Gene b2311 at 0x7fca17f44be0>,\n",
       " <Gene b2585 at 0x7fca17f60be0>,\n",
       " <Gene b0173 at 0x7fca17feac18>,\n",
       " <Gene b0827 at 0x7fca17fe8c18>,\n",
       " <Gene b2103 at 0x7fca17f19fd0>,\n",
       " <Gene b2600 at 0x7fca18004c18>,\n",
       " <Gene b3196 at 0x7fca17f96c18>,\n",
       " <Gene b3642 at 0x7fca17f3d5f8>,\n",
       " <Gene b3730 at 0x7fca17f94c18>,\n",
       " <Gene b4407 at 0x7fca17fbf5f8>,\n",
       " <Gene s0001 at 0x7fca18024da0>,\n",
       " <Gene b0133 at 0x7fca17f3add8>,\n",
       " <Gene b2025 at 0x7fca17f6cdd8>,\n",
       " <Gene b3843 at 0x7fca17f44dd8>,\n",
       " <Gene b3850 at 0x7fca17efcdd8>,\n",
       " <Gene b0420 at 0x7fca17feae10>,\n",
       " <Gene b0781 at 0x7fca17fa0e10>,\n",
       " <Gene b2315 at 0x7fca17fece10>,\n",
       " <Gene b2329 at 0x7fca18004e10>,\n",
       " <Gene b3941 at 0x7fca17f32dd8>,\n",
       " <Gene b4245 at 0x7fca1800ae10>,\n",
       " <Gene b3960 at 0x7fca17fff630>,\n",
       " <Gene b0052 at 0x7fca17edffd0>,\n",
       " <Gene b0166 at 0x7fca17e9ffd0>,\n",
       " <Gene b3804 at 0x7fca17f1b9e8>,\n",
       " <Gene b1092 at 0x7fca17fa8fd0>,\n",
       " <Gene b0109 at 0x7fca17f6afd0>,\n",
       " <Gene b1262 at 0x7fca17f6cfd0>,\n",
       " <Gene b1136 at 0x7fca17f6efd0>,\n",
       " <Gene b2515 at 0x7fca17f8efd0>,\n",
       " <Gene b3187 at 0x7fca17fb0fd0>,\n",
       " <Gene b0475 at 0x7fca17ff1048>,\n",
       " <Gene b1091 at 0x7fca18027048>,\n",
       " <Gene b3018 at 0x7fca18041048>,\n",
       " <Gene b3433 at 0x7fca17fe7048>,\n",
       " <Gene b3857 at 0x7fca1800d048>,\n",
       " <Gene b1215 at 0x7fca17f23fd0>,\n",
       " <Gene b0180 at 0x7fca181451d0>,\n",
       " <Gene b0085 at 0x7fca17ea9208>,\n",
       " <Gene b0087 at 0x7fca17edf208>,\n",
       " <Gene b2020 at 0x7fca17f19208>,\n",
       " <Gene b2021 at 0x7fca17fcf208>,\n",
       " <Gene b3040 at 0x7fca18013240>,\n",
       " <Gene b3389 at 0x7fca17fa5240>,\n",
       " <Gene b3607 at 0x7fca17f01208>,\n",
       " <Gene b3770 at 0x7fca17f13208>,\n",
       " <Gene b3957 at 0x7fca18027240>,\n",
       " <Gene b3958 at 0x7fca18041240>,\n",
       " <Gene b4214 at 0x7fca1800d240>,\n",
       " <Gene b3807 at 0x7fca17f6ebe0>,\n",
       " <Gene b2747 at 0x7fca17f2a5f8>,\n",
       " <Gene b3991 at 0x7fca17ee39e8>,\n",
       " <Gene b0073 at 0x7fca17f23400>,\n",
       " <Gene b0423 at 0x7fca17fbf400>,\n",
       " <Gene b0091 at 0x7fca17ea9fd0>,\n",
       " <Gene b0103 at 0x7fca1805b438>,\n",
       " <Gene b0154 at 0x7fca17f63438>,\n",
       " <Gene b1693 at 0x7fca17fa5438>,\n",
       " <Gene b2022 at 0x7fca17f19400>,\n",
       " <Gene b2024 at 0x7fca17fa9fd0>,\n",
       " <Gene b2320 at 0x7fca17eef400>,\n",
       " <Gene b2762 at 0x7fca17edf400>,\n",
       " <Gene b2838 at 0x7fca17fb7438>,\n",
       " <Gene b3200 at 0x7fca18027438>,\n",
       " <Gene b3359 at 0x7fca18047438>,\n",
       " <Gene b3939 at 0x7fca17f8d5f8>,\n",
       " <Gene b4160 at 0x7fca17f607f0>,\n",
       " <Gene b4177 at 0x7fca18091c18>,\n",
       " <Gene b0159 at 0x7fca1807f5c0>,\n",
       " <Gene b0750 at 0x7fca17f055f8>,\n",
       " <Gene b0915 at 0x7fca17e9f5f8>,\n",
       " <Gene b0072 at 0x7fca17f235f8>,\n",
       " <Gene b3633 at 0x7fca17fdc7f0>,\n",
       " <Gene b0414 at 0x7fca18087630>,\n",
       " <Gene b0421 at 0x7fca17fa5630>,\n",
       " <Gene b0720 at 0x7fca1804f630>,\n",
       " <Gene b0775 at 0x7fca1800d630>,\n",
       " <Gene b1288 at 0x7fca17fab630>,\n",
       " <Gene b2019 at 0x7fca17ff7630>,\n",
       " <Gene b2574 at 0x7fca180bb630>,\n",
       " <Gene b3058 at 0x7fca17fb1630>,\n",
       " <Gene b3774 at 0x7fca1805b630>,\n",
       " <Gene b3809 at 0x7fca17fb7630>,\n",
       " <Gene b3176 at 0x7fca17eeffd0>,\n",
       " <Gene b3992 at 0x7fca17fbf7f0>,\n",
       " <Gene b1093 at 0x7fca181457b8>,\n",
       " <Gene b0071 at 0x7fca17f237f0>,\n",
       " <Gene b0181 at 0x7fca17ea97f0>,\n",
       " <Gene b0777 at 0x7fca17f3b7f0>,\n",
       " <Gene b0029 at 0x7fca17fa5828>,\n",
       " <Gene b0175 at 0x7fca17fb7828>,\n",
       " <Gene b1208 at 0x7fca18013828>,\n",
       " <Gene b1415 at 0x7fca17f5b7f0>,\n",
       " <Gene b2472 at 0x7fca17eeb7f0>,\n",
       " <Gene b2499 at 0x7fca17fa97f0>,\n",
       " <Gene b2750 at 0x7fca18091828>,\n",
       " <Gene b3172 at 0x7fca17fff828>,\n",
       " <Gene b3199 at 0x7fca18027828>,\n",
       " <Gene b3967 at 0x7fca17fb3fd0>,\n",
       " <Gene b3997 at 0x7fca17f1bbe0>,\n",
       " <Gene b2323 at 0x7fca181459b0>,\n",
       " <Gene b0074 at 0x7fca17f239e8>,\n",
       " <Gene b0142 at 0x7fca1808d9e8>,\n",
       " <Gene b1662 at 0x7fca17f059e8>,\n",
       " <Gene b2026 at 0x7fca17fa99e8>,\n",
       " <Gene b0928 at 0x7fca180bba20>,\n",
       " <Gene b1062 at 0x7fca17fb1a20>,\n",
       " <Gene b1131 at 0x7fca18091a20>,\n",
       " <Gene b2687 at 0x7fca17f119e8>,\n",
       " <Gene b3041 at 0x7fca17fb7a20>,\n",
       " <Gene b3189 at 0x7fca17ea99e8>,\n",
       " <Gene b3201 at 0x7fca18027a20>,\n",
       " <Gene b3412 at 0x7fca17eddbe0>,\n",
       " <Gene b3959 at 0x7fca17fd7a20>,\n",
       " <Gene b1094 at 0x7fca1807fba8>,\n",
       " <Gene b0090 at 0x7fca17ea9be0>,\n",
       " <Gene b0415 at 0x7fca17f05be0>,\n",
       " <Gene b0918 at 0x7fca17f23be0>,\n",
       " <Gene b1098 at 0x7fca18033c18>,\n",
       " <Gene b0778 at 0x7fca17fb7c18>,\n",
       " <Gene b2153 at 0x7fca17fa7be0>,\n",
       " <Gene b2476 at 0x7fca17fa9be0>,\n",
       " <Gene b2751 at 0x7fca17f0ddd8>,\n",
       " <Gene b2752 at 0x7fca17f0dbe0>,\n",
       " <Gene b2818 at 0x7fca17fd7c18>,\n",
       " <Gene b3177 at 0x7fca17fb1c18>,\n",
       " <Gene b4006 at 0x7fca18041c18>,\n",
       " <Gene b3608 at 0x7fca17f6f438>,\n",
       " <Gene b3729 at 0x7fca17f71400>,\n",
       " <Gene b2942 at 0x7fca17f2a7f0>,\n",
       " <Gene b1277 at 0x7fca17fa7dd8>,\n",
       " <Gene b1260 at 0x7fca17f0fdd8>,\n",
       " <Gene b0003 at 0x7fca1808ddd8>,\n",
       " <Gene b0088 at 0x7fca17ea9dd8>,\n",
       " <Gene b0025 at 0x7fca1801de10>,\n",
       " <Gene b0134 at 0x7fca17f8fdd8>,\n",
       " <Gene b0369 at 0x7fca17ee5dd8>,\n",
       " <Gene b0386 at 0x7fca17f3dfd0>,\n",
       " <Gene b0522 at 0x7fca18041e10>,\n",
       " <Gene b2312 at 0x7fca17fb3dd8>,\n",
       " <Gene b2780 at 0x7fca1804fe10>,\n",
       " <Gene b4040 at 0x7fca17f75400>,\n",
       " <Gene b2530 at 0x7fca17f6e7f0>,\n",
       " <Gene b0179 at 0x7fca17ee3fd0>}"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from cobra.flux_analysis import find_essential_genes\n",
    "find_essential_genes(model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. Find the essential reactions instead of genes.\n",
    "2. MOMA is a common approach simulation approach to use instead of FBA when doing knock-out simulations. Briefly, MOMA adds constraints to minimize the deviation from the state without the knock-out, causing smaller effects. Use `method='linear moma'` to simulate MOMA gene deletions."
   ]
  }
 ],
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