07-Theoretical-maximum-yields.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Calculating yields"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from cobra.io import read_sbml_model\n",
    "model_original = read_sbml_model('data/iJO1366.xml.gz')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Product yield"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "model = model_original.copy()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculating the yield of a product is straigtforward. First one sets the producing reaction a new objective of the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "model.objective = model.reactions.EX_ac_e"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then one determines the maximum production flux by solving the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "29.093467336683354"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solution = model.optimize()\n",
    "solution.fluxes['EX_ac_e']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dividing the production flux by the uptake flux of the carbon source (in this case glucose) yields the molar yield (mol product / mol glucose)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.9093467336683352"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solution.fluxes['EX_ac_e'] / (-1. * solution.fluxes['EX_glc__D_e'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise (15 min)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Convert the yield into a C-mol (product) / C-mol (carbon source) yield.\n",
    "* Calculate a mass yield instead of molar yield (g (product) / g (carbon source))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Biomass yield"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "model = model_original.copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.098237181272697788"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solution = model.optimize()\n",
    "g_dw_biomass_per_mmol_glucose = solution.objective_value / (-1. * solution.fluxes['EX_glc__D_e'])\n",
    "g_dw_biomass_per_mmol_glucose"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "## Excercise (10 min)\n",
    "\n",
    "The units of this yield are gDW (Biomass) / mmol (glucose). Convert this number into a mass yield."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Growth vs. Product yield"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise (30 min)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the previous section we calculated theoretical maximum yields in the absence of competing objectives. But how does product yield vary with growth for example?\n",
    "\n",
    "* Determina molar, mass, and c-mol yields of acetate for the following growth rates (plot them using the code snippet below).\n",
    "* How do the yields looks like for anaerobic conditions?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "model = model_original.copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "growth_rates = [0.0, 0.10915242, 0.21830485, 0.32745727, 0.43660969, 0.54576212, 0.65491454, 0.76406697, 0.87321939, 0.98237181]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fill in your own product fluxes here (needs to be a list)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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shHmWAIe224cC/zFDmzOB/duHQrcA9m+PkeS9wGbAG0eYSZK0mrrOXXY7cDtwSL9xeD9w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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f4295c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "product_fluxes = [0] * len(growth_rates) # replace this\n",
    "import matplotlib.pyplot as plt\n",
    "plt.plot(growth_rates, product_fluxes)\n",
    "plt.xlabel('Growth [$h^{-1}$]')\n",
    "plt.ylabel('Product flux [$mmol gDW^{-1} h^{-1}$]')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fill in your own product yields here (needs to be a list)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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YPt/2PNsnABdTTGz8QGPJIiKi1YZswUiS+41ltn3GUGUiImLZVqUFc4WkwySN6zwpaSVJ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\nIiIa8f8BIIzf2LD9+lUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f606198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "yields = [0] * len(growth_rates) # replace this\n",
    "plt.plot(growth_rates, yields)\n",
    "plt.xlabel('Growth [$h^{-1}$]')\n",
    "plt.ylabel('Product yield [$mmol(acetate) / mmol(glucose)$]')\n",
    "plt.show()"
   ]
  }
 ],
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