cobrapy-02-genome-scale-metabolic-models.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Genome-scale metabolic 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": "markdown",
   "metadata": {},
   "source": [
    "## What is in a genome-scale metabolic model? (10 + 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "        <table>\n",
       "            <tr>\n",
       "                <td><strong>Name</strong></td>\n",
       "                <td>iJO1366</td>\n",
       "            </tr><tr>\n",
       "                <td><strong>Memory address</strong></td>\n",
       "                <td>0x07f60d9887080</td>\n",
       "            </tr><tr>\n",
       "                <td><strong>Number of metabolites</strong></td>\n",
       "                <td>1805</td>\n",
       "            </tr><tr>\n",
       "                <td><strong>Number of reactions</strong></td>\n",
       "                <td>2583</td>\n",
       "            </tr><tr>\n",
       "                <td><strong>Objective expression</strong></td>\n",
       "                <td>-1.0*BIOMASS_Ec_iJO1366_core_53p95M_reverse_5c8b1 + 1.0*BIOMASS_Ec_iJO1366_core_53p95M</td>\n",
       "            </tr><tr>\n",
       "                <td><strong>Compartments</strong></td>\n",
       "                <td>periplasm, cytosol, extracellular space</td>\n",
       "            </tr>\n",
       "          </table>"
      ],
      "text/plain": [
       "<Model iJO1366 at 0x7f60d9887080>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Metabolites"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The model contains a list of metabolites. Here are the first ten."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<Metabolite 10fthf_c at 0x7f608bbae358>,\n",
       " <Metabolite 12dgr120_c at 0x7f60d5e6d9b0>,\n",
       " <Metabolite 12dgr140_c at 0x7f60a1a52be0>,\n",
       " <Metabolite 12dgr141_c at 0x7f608bbaee48>,\n",
       " <Metabolite 12dgr160_c at 0x7f608bbc0208>,\n",
       " <Metabolite 12dgr161_c at 0x7f608bbc0588>,\n",
       " <Metabolite 12dgr180_c at 0x7f608bbc0908>,\n",
       " <Metabolite 12dgr181_c at 0x7f608bbc0c88>,\n",
       " <Metabolite 12ppd__R_c at 0x7f608bbc0f98>,\n",
       " <Metabolite 12ppd__S_c at 0x7f608bbc8358>]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.metabolites[0:10]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are 1805 metabolites in the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1805"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(model.metabolites)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One can access a specific metabolite using dot notation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "        <table>\n",
       "            <tr>\n",
       "                <td><strong>Metabolite identifier</strong></td><td>g3p_c</td>\n",
       "            </tr><tr>\n",
       "                <td><strong>Name</strong></td><td>Glyceraldehyde 3-phosphate</td>\n",
       "            </tr><tr>\n",
       "                <td><strong>Memory address</strong></td>\n",
       "                <td>0x07f608ba64b00</td>\n",
       "            </tr><tr>\n",
       "                <td><strong>Formula</strong></td><td>C3H5O6P</td>\n",
       "            </tr><tr>\n",
       "                <td><strong>Compartment</strong></td><td>c</td>\n",
       "            </tr><tr>\n",
       "                <td><strong>In 14 reaction(s)</strong></td><td>\n",
       "                    F6PA, TKT2, EDA, TALA, DRPA, DXPS, TPI, TRPS1, TGBPA, GAPD, TKT1, DDPGALA, FBA, TRPS3</td>\n",
       "            </tr>\n",
       "        </table>"
      ],
      "text/plain": [
       "<Metabolite g3p_c at 0x7f608ba64b00>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.metabolites.g3p_c"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-warning\">\n",
    "\n",
    "**Warning:** One cannot use dot notation to access metabolites, reactions, or genes if their identifiers do not resemble proper Python variable names.\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# the line below results in an error, uncomment to try\n",
    "# model.metabolites.10fthf_c\n",
    "\n",
    "\n",
    "#  File \"<ipython-input-5-2772b042e9ed>\", line 1\n",
    "#     model.metabolites.10fthf_c\n",
    "#                        ^\n",
    "# SyntaxError: invalid syntax"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-success\">\n",
    "\n",
    "**Solution:** Use the method `get_by_id` instead!\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "        <table>\n",
       "            <tr>\n",
       "                <td><strong>Metabolite identifier</strong></td><td>10fthf_c</td>\n",
       "            </tr><tr>\n",
       "                <td><strong>Name</strong></td><td>10-Formyltetrahydrofolate</td>\n",
       "            </tr><tr>\n",
       "                <td><strong>Memory address</strong></td>\n",
       "                <td>0x07f608bbae358</td>\n",
       "            </tr><tr>\n",
       "                <td><strong>Formula</strong></td><td>C20H21N7O7</td>\n",
       "            </tr><tr>\n",
       "                <td><strong>Compartment</strong></td><td>c</td>\n",
       "            </tr><tr>\n",
       "                <td><strong>In 9 reaction(s)</strong></td><td>\n",
       "                    BIOMASS_Ec_iJO1366_WT_53p95M, FMETTRS, AICART, FTHFD, MTHFC, FTHFLi, GARFT, ULA4NFT, BIOMASS_Ec_iJO1366_core_53p95M</td>\n",
       "            </tr>\n",
       "        </table>"
      ],
      "text/plain": [
       "<Metabolite 10fthf_c at 0x7f608bbae358>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.metabolites.get_by_id('10fthf_c')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Metabolites are associated with compartments in the cell. Glyceraldehyde 3-phosphate (`g3p_c`) is associated with the `c` (Cytosol) compartment."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'c'"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.metabolites.g3p_c.compartment"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The _E. coli_ model has three compartments."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'c': 'cytosol', 'e': 'extracellular space', 'p': 'periplasm'}"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.compartments"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Some metabolites (like Glucose for example) can be associated with multiple compartments."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'c'"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.metabolites.glc__D_c.compartment"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'p'"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.metabolites.glc__D_p.compartment"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The full name of the metabolite is available via the `.name` attribute. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'D-Glucose'"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.metabolites.glc__D_c.name"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One can look up the molecular formula of glucose."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'C3H5O6P'"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.metabolites.g3p_c.formula"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `.elements` attribute returns a dictionary representation of the formula."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'C': 3, 'H': 5, 'O': 6, 'P': 1}"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.metabolites.g3p_c.elements"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Furthermore, one can look up the molecular weight of a metabolite."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "168.041961"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.metabolites.g3p_c.formula_weight"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One can gather additional information (like references to external datbases) about the metabolite through the annotation attribute."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'SBO': 'SBO:0000247',\n",
       " 'bigg.metabolite': 'g3p',\n",
       " 'biocyc': 'META:GAP',\n",
       " 'chebi': ['CHEBI:12983',\n",
       "  'CHEBI:12984',\n",
       "  'CHEBI:14333',\n",
       "  'CHEBI:17138',\n",
       "  'CHEBI:181',\n",
       "  'CHEBI:18324',\n",
       "  'CHEBI:21026',\n",
       "  'CHEBI:29052',\n",
       "  'CHEBI:5446',\n",
       "  'CHEBI:58027',\n",
       "  'CHEBI:59776'],\n",
       " 'hmdb': 'HMDB01112',\n",
       " 'kegg.compound': ['C00118', 'C00661'],\n",
       " 'metanetx.chemical': 'MNXM2378',\n",
       " 'reactome': '29578',\n",
       " 'seed.compound': 'cpd00102',\n",
       " 'unipathway.compound': ['UPC00118', 'UPC00661']}"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.metabolites.g3p_c.annotation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One can use these annotations to look up the compound on [KEGG](http://www.genome.jp/dbget-bin/www_bget?cpd:C00118) for example."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Metabolites are not isolated things. They participate in reactions as substrates and products."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "frozenset({<Reaction F6PA at 0x7f608b51d828>,\n",
       "           <Reaction TKT2 at 0x7f608b25f630>,\n",
       "           <Reaction EDA at 0x7f608b4eb240>,\n",
       "           <Reaction TALA at 0x7f608b2c9e48>,\n",
       "           <Reaction DRPA at 0x7f608b52f860>,\n",
       "           <Reaction DXPS at 0x7f608b501470>,\n",
       "           <Reaction TPI at 0x7f608b278a58>,\n",
       "           <Reaction TRPS1 at 0x7f608b2f8860>,\n",
       "           <Reaction TGBPA at 0x7f608b2f44e0>,\n",
       "           <Reaction GAPD at 0x7f608b558ef0>,\n",
       "           <Reaction TKT1 at 0x7f608b25f0f0>,\n",
       "           <Reaction DDPGALA at 0x7f608b5cb940>,\n",
       "           <Reaction FBA at 0x7f608b519978>,\n",
       "           <Reaction TRPS3 at 0x7f608b2f8be0>})"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.metabolites.g3p_c.reactions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Reactions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The model contains a list of reactions. Here are the first 10 of them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<Reaction DM_4crsol_c at 0x7f608b684be0>,\n",
       " <Reaction DM_5drib_c at 0x7f608b684da0>,\n",
       " <Reaction DM_aacald_c at 0x7f608b684dd8>,\n",
       " <Reaction DM_amob_c at 0x7f608b684f98>,\n",
       " <Reaction DM_mththf_c at 0x7f608b684fd0>,\n",
       " <Reaction DM_oxam_c at 0x7f608b6891d0>,\n",
       " <Reaction BIOMASS_Ec_iJO1366_WT_53p95M at 0x7f608b689208>,\n",
       " <Reaction BIOMASS_Ec_iJO1366_core_53p95M at 0x7f608b6893c8>,\n",
       " <Reaction EX_12ppd__R_e at 0x7f608b6895f8>,\n",
       " <Reaction EX_12ppd__S_e at 0x7f608b689cf8>]"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.reactions[0:10]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are 2583 reactions in the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2583"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(model.reactions)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's take a closer look at the reactions associated with Glyceraldehyde 3-phosphate (`g3p`)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "F6PA: f6p_c <=> dha_c + g3p_c Fructose 6-phosphate aldolase\n",
      "TKT2: e4p_c + xu5p__D_c <=> f6p_c + g3p_c Transketolase\n",
      "EDA: 2ddg6p_c --> g3p_c + pyr_c 2-dehydro-3-deoxy-phosphogluconate aldolase\n",
      "TALA: g3p_c + s7p_c <=> e4p_c + f6p_c Transaldolase\n",
      "DRPA: 2dr5p_c --> acald_c + g3p_c Deoxyribose-phosphate aldolase\n",
      "DXPS: g3p_c + h_c + pyr_c --> co2_c + dxyl5p_c 1-deoxy-D-xylulose 5-phosphate synthase\n",
      "TPI: dhap_c <=> g3p_c Triose-phosphate isomerase\n",
      "TRPS1: 3ig3p_c + ser__L_c --> g3p_c + h2o_c + trp__L_c Tryptophan synthase (indoleglycerol phosphate)\n",
      "TGBPA: tagdp__D_c <=> dhap_c + g3p_c Tagatose-bisphosphate aldolase\n",
      "GAPD: g3p_c + nad_c + pi_c <=> 13dpg_c + h_c + nadh_c Glyceraldehyde-3-phosphate dehydrogenase\n",
      "TKT1: r5p_c + xu5p__D_c <=> g3p_c + s7p_c Transketolase\n",
      "DDPGALA: 2dh3dgal6p_c <=> g3p_c + pyr_c 2-dehydro-3-deoxy-6-phosphogalactonate aldolase\n",
      "FBA: fdp_c <=> dhap_c + g3p_c Fructose-bisphosphate aldolase\n",
      "TRPS3: 3ig3p_c --> g3p_c + indole_c Tryptophan synthase (indoleglycerol phosphate)\n"
     ]
    }
   ],
   "source": [
    "for reaction in model.metabolites.g3p_c.reactions:\n",
    "    print(reaction, reaction.name)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The second reaction in this list is Glyceraldehyde-3-phosphate dehydrogenase (GAPD)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Glyceraldehyde-3-phosphate dehydrogenase'"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.reactions.GAPD.name"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A reaction has a flux expression, which in cobrapy is coded as the forward flux + the reverse flux (a convenient way to represent the mathematical problem)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0*GAPD - 1.0*GAPD_reverse_459c1"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.reactions.GAPD.flux_expression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Genes and gene-protein-reaction associations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The model also contains genes (perhaps more appropriately gene products) and they belong to reactions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<Gene b2215 at 0x7f608b7fe3c8>,\n",
       " <Gene b1377 at 0x7f608b7fe6a0>,\n",
       " <Gene b0241 at 0x7f608b7fe710>,\n",
       " <Gene b0929 at 0x7f608b7fe780>,\n",
       " <Gene b4035 at 0x7f608b7fe7f0>]"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.genes[0:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "frozenset({<Reaction E4PD at 0x7f608b501748>,\n",
       "           <Reaction GAPD at 0x7f608b558ef0>})"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.genes.b1779.reactions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The gapA (b1779) gene is the only one associated to reaction glyceraldehyde-3-phosphate dehydrogenase."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'b1779'"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.reactions.GAPD.gene_reaction_rule"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Phosphofructokinase (PFK) on the other hand seems to be associated with to isozymes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'b3916 or b1723'"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.reactions.PFK.gene_reaction_rule"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One can display the gene names (typical 4 letter gene codes) instead of the identifiers (Blattner numbers in this case)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'pfkA or pfkB'"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.reactions.PFK.gene_name_reaction_rule"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Reactions are functional if all genes are functional"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "        <table>\n",
       "            <tr>\n",
       "                <td><strong>Reaction identifier</strong></td><td>PFK</td>\n",
       "            </tr><tr>\n",
       "                <td><strong>Name</strong></td><td>Phosphofructokinase</td>\n",
       "            </tr><tr>\n",
       "                <td><strong>Memory address</strong></td>\n",
       "                <td>0x07f608b341ef0</td>\n",
       "            </tr><tr>\n",
       "                <td><strong>Stoichiometry</strong></td>\n",
       "                <td>\n",
       "                    <p style='text-align:right'>atp_c + f6p_c --> adp_c + fdp_c + h_c</p>\n",
       "                    <p style='text-align:right'>ATP + D-Fructose 6-phosphate --> ADP + D-Fructose 1,6-bisphosphate + H+</p>\n",
       "                </td>\n",
       "            </tr><tr>\n",
       "                <td><strong>GPR</strong></td><td>b3916 or b1723</td>\n",
       "            </tr><tr>\n",
       "                <td><strong>Lower bound</strong></td><td>0.0</td>\n",
       "            </tr><tr>\n",
       "                <td><strong>Upper bound</strong></td><td>1000.0</td>\n",
       "            </tr>\n",
       "        </table>\n",
       "        "
      ],
      "text/plain": [
       "<Reaction PFK at 0x7f608b341ef0>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.reactions.PFK"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True True True\n"
     ]
    }
   ],
   "source": [
    "print(model.genes.b3916.functional, model.genes.b1723.functional, model.reactions.PFK.functional)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we knock out one of the isozymes, the PFK reaction stays functional, but not if we knock both."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "False\n"
     ]
    }
   ],
   "source": [
    "model_copy = model.copy()\n",
    "model_copy.genes.b3916.knock_out()\n",
    "print(model_copy.reactions.PFK.functional)\n",
    "\n",
    "model_copy = model.copy()\n",
    "model_copy.genes.b3916.knock_out()\n",
    "model_copy.genes.b1723.knock_out()\n",
    "print(model_copy.reactions.PFK.functional)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Objective"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the iJO1366 model, the default objective is to maximize the flux through the biomass reaction (i.e. growth). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Maximize\n",
      "-1.0*BIOMASS_Ec_iJO1366_core_53p95M_reverse_5c8b1 + 1.0*BIOMASS_Ec_iJO1366_core_53p95M\n"
     ]
    }
   ],
   "source": [
    "print(model.objective)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Querying"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "One can use `.query('search term', 'attribute_to_search_in')` to search in model metabolites, reactions, and genes. For example, one can search metabolites that contain the term _glucose_ in their name."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6-Acetyl-D-glucose\n",
      "ADPglucose\n",
      "DTDP-4-dehydro-6-deoxy-D-glucose\n",
      "DTDPglucose\n",
      "UDPglucose\n",
      "UDPglucose\n",
      "UDPglucose\n"
     ]
    }
   ],
   "source": [
    "for metabolite in model.metabolites.query('glucose', 'name'):\n",
    "    print(metabolite.name)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Convert the cells below to code and fill in the blanks"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "# which reactions includes cytosolic atp?\n",
    "model.____.atp_c.____"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "# which metabolite is named adenosine\n",
    "model.metabolites.____(____, ____)"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "# which genes are necessary for PFK reaction?\n",
    "model.____.____.____"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simulating models with regular flux balance analysis (FBA) (5 + 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<strong><em>Optimal</em> solution with objective value 0.982</strong><br><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>fluxes</th>\n",
       "      <th>reduced_costs</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>DM_4crsol_c</th>\n",
       "      <td>2.1907e-04</td>\n",
       "      <td>0.0000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>DM_5drib_c</th>\n",
       "      <td>2.2103e-04</td>\n",
       "      <td>0.0000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>DM_aacald_c</th>\n",
       "      <td>0.0000e+00</td>\n",
       "      <td>0.0000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>DM_amob_c</th>\n",
       "      <td>1.9647e-06</td>\n",
       "      <td>0.0000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>DM_mththf_c</th>\n",
       "      <td>4.4010e-04</td>\n",
       "      <td>0.0000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ZN2abcpp</th>\n",
       "      <td>0.0000e+00</td>\n",
       "      <td>-0.0083</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ZN2t3pp</th>\n",
       "      <td>0.0000e+00</td>\n",
       "      <td>-0.0021</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ZN2tpp</th>\n",
       "      <td>3.3499e-04</td>\n",
       "      <td>0.0000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ZNabcpp</th>\n",
       "      <td>0.0000e+00</td>\n",
       "      <td>-0.0083</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Zn2tex</th>\n",
       "      <td>3.3499e-04</td>\n",
       "      <td>0.0000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>2583 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "<Solution 0.982 at 0x7f608bf848d0>"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.optimize()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sometimes a solution cannot be found. For example, setting the lower bound of the objective function to a very high value that the model cannot achieve will trigger a warning when trying to optimize the model. Parameters reported from an infeasible model are not meaningful to interpret (except in rare occasions when you may want to figure out why a model is infeasible)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "cobra/util/solver.py:419 \u001b[1;31mUserWarning\u001b[0m: solver status is 'infeasible'\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<strong><em>infeasible</em> solution</strong>"
      ],
      "text/plain": [
       "<Solution infeasible at 0x7f608d20ac18>"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "infeasible_model = model.copy()\n",
    "infeasible_model.reactions.BIOMASS_Ec_iJO1366_core_53p95M.lower_bound = 100000\n",
    "infeasible_model.optimize()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Mathematical solvers are now so fast that for computing the solution can be even faster than it takes to collect the values from the solver. If we are only interested in the flux value of a single reaction or the objective, it is faster to use `model.slim_optimize` which only does the optimization and returnsm the objective value leaving it up to you to fetch other values that you may need. For example, let's optimize and get the flux value of the `ATPM` reaction."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 20 ms, sys: 0 ns, total: 20 ms\n",
      "Wall time: 19.3 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "solution = model.optimize()\n",
    "solution.fluxes['ATPM']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 0 ns, sys: 0 ns, total: 0 ns\n",
      "Wall time: 1.72 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "model.slim_optimize()\n",
    "model.reactions.ATPM.flux"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Convert the cell below to code and fill in the blanks."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Optimize for acetate production at minimum 0.1 $h^{-1}$ growth rate"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "model.____.BIOMASS_Ec_iJO1366_core_53p95M.____ = ____\n",
    "____.____ = ___.____.EX_ac_e\n",
    "____.____()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The math (5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The mathematical problem"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can calculate fluxes using our model by formulating it as a mathematical problem. There, fluxes through reactions become variables and metabolites become constraints. By deciding that fluxes in and out of the system must add up to zero, we can then compute possible flux values for all reactions (if the model is feasible). We can inspect the whole equation by:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\\* Problem: Unknown *\\\n",
      "\n",
      "Maximize\n",
      " obj: + BIOMASS_Ec_iJO1366_core_53p95M\n",
      " - BIOMASS_Ec_iJO1366_core_53p95M_reverse_5c8b1\n",
      "\n",
      "Subject To\n",
      " r_1: + FMETTRS_reverse_3b6c6 + FTHFD_reverse_44321\n",
      " - MTHFC_reverse_f6fcc\n",
      " + 0.000223 BIOMASS_Ec_iJO1366_WT_53p95M_reverse_06c4a\n",
      " + AICART_reverse_b7b59 - 0.000223 BIOMASS_Ec_iJO1366_WT_53p95M - FTHFD\n",
      " + 0.000223 BIOMASS_Ec_iJO1366_core_53p95M_reverse_5c8b1 - FMETTRS\n",
      " + GARFT_reverse_7ecb6 - 0.000223 BIOMASS_Ec_iJO1366_core_53p95M - GARFT\n",
      " + FTHFLi - FTHFLi_reverse_a6dc7 + ULA4NFT_reverse_07217 - AICART\n",
      " - ULA4NFT + MTHFC = 0\n",
      " r_2: + PAPA120 + x_665 - PAPA120_reverse_75d70 - x_666 - DAGK120\n",
      " + DAGK120_reverse_7cd00 = 0\n",
      " r_3: - PAPA140_reverse_255f5 - DAGK140 + DAGK140_reverse_87f8f\n",
      " + PAPA140 - x_668 + x_667 = 0\n",
      " r_4: - x_670 + PAPA141 + x_669 - PAPA141_reverse_945ab\n",
      " + DAGK141_reverse_f6e5f - DAGK141 = 0\n",
      " r_5: - DAGK160 + DAGK160_reverse_0238d + x_671 + PAPA160 - x_672\n",
      " - PAPA160_reverse_c64df = 0\n",
      " r_6: - PAPA161_reverse_1bc33 + DAGK161_reverse_9bfe7 + PAPA161 + x_673\n",
      " - DAGK161 - x_674 = 0\n",
      " r_7: + x_675 - DAGK180 + PAPA180 - x_676 - PAPA180_reverse_9f7f6\n",
      " + DAGK180_reverse_eb3e3 = 0\n",
      " r_8: + DAGK181_reverse_8c0c8 - DAGK181 + x_677 - x_678 + PAPA181\n",
      " - PAPA181_reverse_fb09e = 0\n",
      " r_9: - x_682 - ALR4x_reverse_17ebf + LCARR - LCARR_reverse_9213d\n",
      " + x_681 + ALR4x = 0\n",
      " r_10: - LCARS_reverse_66c3d - x_686 + LCARS + x_685 = 0\n",
      " r_11: - GAPD_reverse_459c1 + GAPD + PGK - PGK_reverse_02696 = 0\n",
      " r_12: + DHNCOAT_reverse_58c26 - DHNCOAT + DHNCOAS\n",
      " - DHNCOAS_reverse_af3a9 = 0\n",
      " r_13: - AAMYL + AAMYL_reverse_58\n"
     ]
    }
   ],
   "source": [
    "print(str(model.solver)[0:1550])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Mostly, we luckily do not have to care much about this as cobrapy will use optlang and dedicated mathematical solvers to do the hard work for us, but it can be good know about the separation between the metabolic model and the mathematical problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5166"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(model.variables)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1805"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(model.constraints)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The stoichiometric matrix S"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from cobra.util import create_stoichiometric_matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.,  0.,  0., ...,  0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0., ...,  0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0., ...,  0.,  0.,  0.],\n",
       "       ..., \n",
       "       [ 0.,  0.,  0., ...,  0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0., ...,  0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0., ..., -1., -1.,  1.]])"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stoich_matrix = create_stoichiometric_matrix(model)\n",
    "stoich_matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is how the the stoichiometry matrix S looks like when visualized as a matrix plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.lines.Line2D at 0x7f608d98d668>"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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94kQohHJCiEbb5DhdMWcBlmCoIQytBZo/O/HDDX4jBamTX5Q6I0RjnGj5tF1iLsWhYlGo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\nMDBCSAsEAoGB+f8U+huVgAjUIAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f608d200cc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.spy(stoich_matrix, precision=0.01, markersize=.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-info\">\n",
    "\n",
    "**Question:** What are the diagonal and horizontal lines?\n",
    "</div>\n"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2+"
  },
  "toc": {
   "colors": {
    "hover_highlight": "#DAA520",
    "navigate_num": "#000000",
    "navigate_text": "#333333",
    "running_highlight": "#FF0000",
    "selected_highlight": "#FFD700",
    "sidebar_border": "#EEEEEE",
    "wrapper_background": "#FFFFFF"
   },
   "moveMenuLeft": true,
   "nav_menu": {
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}