04-analyze-models.ipynb

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    "# Analyzing models\n",
    "\n",
    "**cameo** uses and extends the model data structures defined by [cobrapy](https://opencobra.github.io/cobrapy/), our favorite **CO**nstraints-**B**ased **R**econstruction and **A**nalysis tool for **Py**thon. **cameo** is thus 100% compatible with **cobrapy**. For efficiency reasons though **cameo** implements its own analysis methods that take advantage of a more advanced solver interface."
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   "source": [
    "from cameo import models\n",
    "model = models.bigg.e_coli_core"
   ]
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   "source": [
    "## Flux Variability Analysis\n",
    "\n",
    "Flux variability analysis (FVA) enables the computation of lower and upper bounds of reaction fluxes."
   ]
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  {
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   "source": [
    "from cameo import flux_variability_analysis"
   ]
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>upper_bound</th>\n",
       "      <th>lower_bound</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>ACALD</th>\n",
       "      <td>9.375217e-16</td>\n",
       "      <td>-2.000000e+01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ACALDt</th>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>-2.000000e+01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ACKr</th>\n",
       "      <td>-1.862346e-15</td>\n",
       "      <td>-2.000000e+01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ACONTa</th>\n",
       "      <td>2.000000e+01</td>\n",
       "      <td>-4.825168e-16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ACONTb</th>\n",
       "      <td>2.000000e+01</td>\n",
       "      <td>-1.999683e-16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ACt2r</th>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>-2.000000e+01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ADK1</th>\n",
       "      <td>1.666100e+02</td>\n",
       "      <td>0.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SUCDi</th>\n",
       "      <td>1.000000e+03</td>\n",
       "      <td>0.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SUCOAS</th>\n",
       "      <td>-3.552714e-15</td>\n",
       "      <td>-2.000000e+01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TALA</th>\n",
       "      <td>2.000000e+01</td>\n",
       "      <td>-1.545362e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>THD2</th>\n",
       "      <td>3.332200e+02</td>\n",
       "      <td>0.000000e+00</td>\n",
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       "      <th>TKT1</th>\n",
       "      <td>2.000000e+01</td>\n",
       "      <td>-1.545362e-01</td>\n",
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       "    <tr>\n",
       "      <th>TKT2</th>\n",
       "      <td>2.000000e+01</td>\n",
       "      <td>-4.663728e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TPI</th>\n",
       "      <td>1.000000e+01</td>\n",
       "      <td>-1.000000e+01</td>\n",
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       "         upper_bound   lower_bound\n",
       "ACALD   9.375217e-16 -2.000000e+01\n",
       "ACALDt  0.000000e+00 -2.000000e+01\n",
       "ACKr   -1.862346e-15 -2.000000e+01\n",
       "ACONTa  2.000000e+01 -4.825168e-16\n",
       "ACONTb  2.000000e+01 -1.999683e-16\n",
       "ACt2r   0.000000e+00 -2.000000e+01\n",
       "ADK1    1.666100e+02  0.000000e+00\n",
       "...              ...           ...\n",
       "SUCDi   1.000000e+03  0.000000e+00\n",
       "SUCOAS -3.552714e-15 -2.000000e+01\n",
       "TALA    2.000000e+01 -1.545362e-01\n",
       "THD2    3.332200e+02  0.000000e+00\n",
       "TKT1    2.000000e+01 -1.545362e-01\n",
       "TKT2    2.000000e+01 -4.663728e-01\n",
       "TPI     1.000000e+01 -1.000000e+01\n",
       "\n",
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   "source": [
    "fva_result = flux_variability_analysis(model)\n",
    "fva_result.data_frame"
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    "One very useful application of FVA is determining if alternative optimal solution exist."
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       "      <th></th>\n",
       "      <th>upper_bound</th>\n",
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       "<p>95 rows × 2 columns</p>\n",
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       "         upper_bound  lower_bound\n",
       "ACALD   0.000000e+00   -12.602453\n",
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       "ACKr    0.000000e+00   -13.358852\n",
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       "ACt2r  -6.527569e-14   -13.358852\n",
       "ADK1    8.433833e+01     0.000000\n",
       "...              ...          ...\n",
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    "fva_result2 = flux_variability_analysis(model,fraction_of_optimum=0.5)\n",
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     "metadata": {},
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   ],
   "source": [
    "fva_result2.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from cameo.visualization import plotting"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Phenotpic Phase Plane\n",
    "--------------------\n",
    "\n",
    "The phenotypic phase plane is a modeling technique was developed to do a theoretical accessement of what cell can or cannot do in terms of the stoichiometric constraints [Edawards *et al.* 2001]. \n",
    "\n",
    "The phenotipic phase plane between growth and a product of interest yields the production envelope: a representation between the trade of between production of the desired product and growth."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from cameo import phenotypic_phase_plane"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "model.reactions.EX_o2_e.lower_bound = -10\n",
    "result = phenotypic_phase_plane(model, \n",
    "                                variables=[model.reactions.BIOMASS_Ecoli_core_w_GAM],\n",
    "                                objective=model.reactions.EX_succ_e,\n",
    "                                points=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
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    "The production envelope can show the coupling between growth and production. There is no stoichiometric couple between growth and production for succinate under aerobic conditions, but that is not the case for acetate under anaerobic conditions."
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       "      window._bokeh_onload_callbacks.forEach(function(callback) { callback() });\n",
       "      delete window._bokeh_onload_callbacks\n",
       "      console.info(\"Bokeh: all callbacks have finished\");\n",
       "    }\n",
       "  \n",
       "    function load_libs(js_urls, callback) {\n",
       "      window._bokeh_onload_callbacks.push(callback);\n",
       "      if (window._bokeh_is_loading > 0) {\n",
       "        console.log(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n",
       "        return null;\n",
       "      }\n",
       "      if (js_urls == null || js_urls.length === 0) {\n",
       "        run_callbacks();\n",
       "        return null;\n",
       "      }\n",
       "      console.log(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n",
       "      window._bokeh_is_loading = js_urls.length;\n",
       "      for (var i = 0; i < js_urls.length; i++) {\n",
       "        var url = js_urls[i];\n",
       "        var s = document.createElement('script');\n",
       "        s.src = url;\n",
       "        s.async = false;\n",
       "        s.onreadystatechange = s.onload = function() {\n",
       "          window._bokeh_is_loading--;\n",
       "          if (window._bokeh_is_loading === 0) {\n",
       "            console.log(\"Bokeh: all BokehJS libraries loaded\");\n",
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       "        };\n",
       "        s.onerror = function() {\n",
       "          console.warn(\"failed to load library \" + url);\n",
       "        };\n",
       "        console.log(\"Bokeh: injecting script tag for BokehJS library: \", url);\n",
       "        document.getElementsByTagName(\"head\")[0].appendChild(s);\n",
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       "    };var element = document.getElementById(\"d2c69e72-3bd3-48d2-97c1-30e99a9368e8\");\n",
       "    if (element == null) {\n",
       "      console.log(\"Bokeh: ERROR: autoload.js configured with elementid 'd2c69e72-3bd3-48d2-97c1-30e99a9368e8' but no matching script tag was found. \")\n",
       "      return false;\n",
       "    }\n",
       "  \n",
       "    var js_urls = [];\n",
       "  \n",
       "    var inline_js = [\n",
       "      function(Bokeh) {\n",
       "        Bokeh.$(function() {\n",
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   ],
   "source": [
    "result = phenotypic_phase_plane(model, \n",
    "                                variables=[model.reactions.BIOMASS_Ecoli_core_w_GAM],\n",
    "                                objective=model.reactions.EX_ac_e)\n",
    "result.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
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   },
   "outputs": [
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       "      <th></th>\n",
       "      <th>BIOMASS_Ecoli_core_w_GAM</th>\n",
       "      <th>objective_lower_bound</th>\n",
       "      <th>objective_upper_bound</th>\n",
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       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
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       "    BIOMASS_Ecoli_core_w_GAM  objective_lower_bound  objective_upper_bound\n",
       "0                   0.559051                9.90568              11.503269\n",
       "1                   0.529627                2.62796              11.950466\n",
       "2                   0.500203                0.00000              12.397662\n",
       "3                   0.470779                0.00000              12.844858\n",
       "4                   0.441356                0.00000              13.292055\n",
       "5                   0.411932                0.00000              13.739251\n",
       "6                   0.382508                0.00000              14.186448\n",
       "..                       ...                    ...                    ...\n",
       "13                  0.176542                0.00000              17.316822\n",
       "14                  0.147119                0.00000              17.764018\n",
       "15                  0.117695                0.00000              18.211215\n",
       "16                  0.088271                0.00000              18.658411\n",
       "17                  0.058847                0.00000              19.105607\n",
       "18                  0.029424                0.00000              19.552804\n",
       "19                  0.000000                0.00000              20.000000\n",
       "\n",
       "[20 rows x 3 columns]"
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   "source": [
    "result.plot(points=[(0.2, 8), (0.2, 2)], points_colors=[\"green\", \"red\"])"
   ]
  },
  {
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   "metadata": {},
   "source": [
    "The computed data can be inspected in the format of a pandas data frame by calling `result.data_frame`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>BIOMASS_Ecoli_core_w_GAM</th>\n",
       "      <th>objective_lower_bound</th>\n",
       "      <th>objective_upper_bound</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.559051</td>\n",
       "      <td>9.90568</td>\n",
       "      <td>11.503269</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.529627</td>\n",
       "      <td>2.62796</td>\n",
       "      <td>11.950466</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.500203</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>12.397662</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.470779</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>12.844858</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.441356</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>13.292055</td>\n",
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       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.411932</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>13.739251</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.382508</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>14.186448</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>0.176542</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>17.316822</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>0.147119</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>17.764018</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>0.117695</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>18.211215</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>0.088271</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>18.658411</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>0.058847</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>19.105607</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>0.029424</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>19.552804</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>20.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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       "<p>20 rows × 3 columns</p>\n",
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      "text/plain": [
       "    BIOMASS_Ecoli_core_w_GAM  objective_lower_bound  objective_upper_bound\n",
       "0                   0.559051                9.90568              11.503269\n",
       "1                   0.529627                2.62796              11.950466\n",
       "2                   0.500203                0.00000              12.397662\n",
       "3                   0.470779                0.00000              12.844858\n",
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     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.reactions.EX_o2_e.lower_bound = 0\n",
    "result2 = phenotypic_phase_plane(model, \n",
    "                                 variables=[model.reactions.BIOMASS_Ecoli_core_w_GAM],\n",
    "                                 objective=model.reactions.EX_ac_e,\n",
    "                                 points=10)\n",
    "result2.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Flux Balance Impact Degree"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from cameo.flux_analysis.analysis import flux_balance_impact_degree"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "model.reactions.EX_o2_e.lower_bound = -10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 312 ms, sys: 6.53 ms, total: 318 ms\n",
      "Wall time: 595 ms\n"
     ]
    }
   ],
   "source": [
    "%time fbid = flux_balance_impact_degree(model, [\"EX_o2_e\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "        <h3>Flux Balance Impact Degree</h3>\n",
       "        <ul>\n",
       "            <li> Degree: 9</li>\n",
       "            <li> Reactions: 62</li>\n",
       "        </ul>\n",
       "        <div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>perturbed</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>ACALD</th>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ACALDt</th>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ACKr</th>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ACt2r</th>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ADK1</th>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ALCD2x</th>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ATPM</th>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PYK</th>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PYRt2</th>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SUCCt2_2</th>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SUCCt3</th>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SUCDi</th>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>THD2</th>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TPI</th>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>62 rows × 1 columns</p>\n",
       "</div>\n",
       "        "
      ],
      "text/plain": [
       "<cameo.flux_analysis.analysis.FluxBalanceImpactDegreeResult at 0x10d8f3da0>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fbid"
   ]
  }
 ],
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