5 - Constitutive equations.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Dynamic simulations of enzyme cycles using generalised rate laws\n",
    "BondGraphTools provides tools for modelling biochemical networks. The package contains a library with storage and dissipative components that enable the specification of models under the mass action framework. While support for rate laws corresponding to enzyme-catalysed reactions is not supported by default, the package provides an interface for defining components with new constitutive equations. In this notebook we define a constitutive relationship corresponding to Michaelis-Menten kinetics and use this to simulate dynamic networks of enzymes described by these rate laws. First we import the necessary packages."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import BondGraphTools as bgt\n",
    "from matplotlib import pyplot as plt\n",
    "import sympy as sp\n",
    "\n",
    "sp.init_printing()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Defining the Michaelis-Menten rate law\n",
    "In this section we show how an enzyme catalysed reaction $S \\rightleftharpoons P$ can be described using Michaelis-Menten kinetics. The **C** components corresponding to the species can be defined as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "C_S = bgt.new(component=\"Ce\",name=\"S\",library=\"BioChem\")\n",
    "C_P = bgt.new(component=\"Ce\",name=\"P\",library=\"BioChem\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that in the above block of code, the `Ce` components are defined within the `BioChem` library. Therefore, it is possible to define our own libaries with arbitrary components. We show an example of this in the code below, which defines a component corresponding to Michaelis-Menten enzyme kinetics:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{\n",
      "    \"description\": \"Enzyme catalysed reactions\",\n",
      "    \"id\":\"Enzyme\",\n",
      "    \"components\":{\n",
      "      \"R_MM\":{\n",
      "        \"description\": \"Michaelis-Menten reaction\",\n",
      "        \"class\": \"Component\",\n",
      "        \"metamodel\":\"R\",\n",
      "        \"ports\":{\n",
      "          \"0\":{\"description\":\"Substrate\"},\n",
      "          \"1\":{\"description\":\"Product\"}\n",
      "        },\n",
      "        \"params\":{\n",
      "          \"r1\":{\"description\":\"Rate of reaction 1\"},\n",
      "          \"r2\":{\"description\":\"Rate of reaction 2\"},\n",
      "          \"k_c\":{\"description\":\"Affinity of complex relative to free enzyme\"},\n",
      "          \"e_T\":{\"description\":\"Total amount of enzyme\"},\n",
      "          \"R\":{\"description\":\"Universal Gas Constant\"},\n",
      "          \"T\":{\"description\": \"Temperature\"}\n",
      "        },\n",
      "        \"constitutive_relations\":[\n",
      "          \"f_0 + f_1\",\n",
      "          \"f_0 - e_T*r1*r2*k_c*(exp(e_0/R/T) - exp(e_1/R/T)) / (r1*exp(e_0/R/T) + r2*exp(e_1/R/T) + k_c*(r1+r2))\"\n",
      "        ]\n",
      "      }\n",
      "    }\n",
      "  }\n"
     ]
    }
   ],
   "source": [
    "with open(\"enzymes.json\") as f:\n",
    "    print(f.read())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In terms of the chemical potentials $\\mu_S$ and $\\mu_P$ of the substrate and product, the rate law has been defined as\n",
    "\n",
    "$$\n",
    "v(\\mu_S,\\mu_P) = e_T \\frac{r_1 r_2 k_C (e^{\\mu_S/RT} - e^{\\mu_P/RT})}{r_1 e^{\\mu_S/RT}+r_2e^{\\mu_P/RT} + k_C(r_1 + r_2)}\n",
    "$$\n",
    "\n",
    "where $e_T$ (total amount of enzyme), $r_1$ (normalised rate of the first reaction), $r_2$ (normalised rate of the second reaction) and $k_C$ (affinity of the complex relative to the free enzyme) are the parameters of the equation.\n",
    "\n",
    "Therefore if the substrate corresponds to the 0 port and the product corresponds to the 1 port the constitutive equations of the model are\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "f_0 + f_1 &= 0 \\\\\n",
    "f_0 - v(e_0,e_1) &= 0\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "The library can be loaded into BondGraphTools using the code below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bgt.component_manager.load_library('enzymes.json')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now a new dissapative component with Michaelis-Menten kinetics can be created:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "R_MM = bgt.new(component=\"R_MM\",name=\"E\",library=\"Enzyme\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The constitutive equations for this components are as expected:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/latex": [
       "$$\\left [ f_{0} + f_{1}, \\quad - \\frac{e_{T} k_{c} r_{1} r_{2} \\left(e^{\\frac{e_{0}}{R T}} - e^{\\frac{e_{1}}{R T}}\\right)}{k_{c} \\left(r_{1} + r_{2}\\right) + r_{1} e^{\\frac{e_{0}}{R T}} + r_{2} e^{\\frac{e_{1}}{R T}}} + f_{0}\\right ]$$"
      ],
      "text/plain": [
       "⎡                            ⎛  e₀     e₁⎞        ⎤\n",
       "⎢                            ⎜ ───    ───⎟        ⎥\n",
       "⎢                            ⎜ R⋅T    R⋅T⎟        ⎥\n",
       "⎢              e_T⋅k_c⋅r₁⋅r₂⋅⎝ℯ    - ℯ   ⎠        ⎥\n",
       "⎢f₀ + f₁, - ───────────────────────────────── + f₀⎥\n",
       "⎢                                e₀        e₁     ⎥\n",
       "⎢                               ───       ───     ⎥\n",
       "⎢                               R⋅T       R⋅T     ⎥\n",
       "⎣           k_c⋅(r₁ + r₂) + r₁⋅ℯ    + r₂⋅ℯ        ⎦"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R_MM.constitutive_relations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now make a new model of the network $S \\rightleftharpoons P$. The bond graph of the model is drawn below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 960x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = bgt.new(name=\"Enzyme network\")\n",
    "bgt.add(model,C_S,C_P,R_MM)\n",
    "bgt.connect(C_S,(R_MM,0))\n",
    "bgt.connect((R_MM,1),C_P)\n",
    "\n",
    "C_S.set_param(\"k\",1)\n",
    "C_S.set_param(\"R\",1)\n",
    "C_S.set_param(\"T\",1)\n",
    "\n",
    "C_P.set_param(\"k\",1)\n",
    "C_P.set_param(\"R\",1)\n",
    "C_P.set_param(\"T\",1)\n",
    "\n",
    "R_MM.set_param(\"r1\",200)\n",
    "R_MM.set_param(\"r2\",200)\n",
    "R_MM.set_param(\"k_c\",1)\n",
    "R_MM.set_param(\"e_T\",1)\n",
    "R_MM.set_param(\"R\",1)\n",
    "R_MM.set_param(\"T\",1)\n",
    "\n",
    "bgt.draw(model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The constitutive equations of the model are below. Note that it is specified in a differential algebraic equation (DAE) form. It appears that the symbolic manipulation has not fully simplified the equations. However, we will develop a workaround for this in the next section."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAqEAAAAzBAMAAABVvcwMAAAAMFBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEN2ZRGYyze9UiSJ2u6vH0KEdAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAIN0lEQVR4Ae1cW2gcZRT+JtlNsru5bCxKkdaErQUvYGJDqdSiRSgqKI3tg0ofuj4JVWhUBAtKg5dSUXHRtyp08UGxRl3bN4V2q9CHWmoexD54awV9KjShWklTiOe/nJn/n/03uzszzQUzkPPPOf+5fOfbmd3N5BD09/dj5UiIAa+/P4+hucsJpVtJg565uUncWo+ISr2N+eyRguZL2ORepLqRghoAStdntLvUINa5/YjTet2NSweswejTr9l9H7LVxlpu5JUialqTVhz5jq4HKerkadJNR3e8NGznWViwxzb9BGQn7tXCgmIwihlrxxuz1CaU48j+DTwX8pTWzpJ3J6QI7fpqk27s32ffQAsLNnceX27FPtxQUYJBydVgNDVt7bSPWqpQUrUm6bNNeV4ADgI7leI7S+sO4HNIoXdrlibdOG57ns/k6gCrQVlupHAPNlj2aoBCB/fm0TWeHkR2UgoOVqvBaHbQ2uqyNKlkqrU2YflQmd/N41IFXbpXdpbW34DDeSncGYAm3Tj8Iz5RqwOsBmX7ARYsHyx7NUChg7um0Tvbcx6ZaSk4WK0Go53D1taDliYVRhPe0eD/AC4V0akvZHaWVvp+tr0kRTiW9Sbd2P0FPlGrA2wDRm2wnK0BCt1T7yB6r/QNIzUjBQer1Wf02MTeEtacvelISTtsptXUSWWSvDMX9nyq3cQSgB+i9+rzaoedSRvyBJmPCTEajlXOUjbpBuQ2n5qBlcgBlkHV6UHACsA2iSLoqW1qgBj9RwqbJmY09RZ+z2O4+2L7oM7+Iq2mTionbMfZ6gbtJhYGj45rQHpM7bAzyJq7Cuz9XohqODZI06QbBTxU6ZmGlcgBlkHV6UHACsA2iSLoaW/1RJkySGHTxIyuHsUmpCvds72jOHJaFLid6pk6mTjhLvxQ+RPe44yDwaON3jgyg8rMziCrZPQzwWhZxWYnyhzsrw63oITvRSfeG2gfgwXCAVaD0j3cqF9nvwcBKwAbpHegCMAGPa2DIPOqFHYJZvT+PO5AB3qocLaamqQKr9OraOrthcJtrxYK52mriHMkn/2WBLChUDhYKNwlz0dIdkyRMJyBEXhE5vaTQlRV7AQeFQHe8wVxFMW5y02XkNuBaJ9GW9kGEQYbgFI9dJwZFPEhWBpsIxQarBncPoyBMlLXpLBKgBl9Bx59l0RfFegqYpZOCaSlkxa8RHTDAO8JIQ6+RtP0qiM1ToIO31lY6S30sPhkOlwCROwB9FWkVyBcbkGJwI8ATmJgKxkMEA6wDEr25N85NiykximPebhQBGD9nnYSNcPIiE+mDH2NF7RxCc0oXUTpKbJur3j5ExW8Saf76MfUSfMTpmZBz6tqGD2EXIUTB87C+iuwOy8FRGxuFl3ErXU43IwSpitdGLtJN0E4wPqMip58VDaswMz5HSgMsExApoxveiaRnpZC0cS5mNEZ9Ix9sHbrJWSxN4/1VOAXwNLJpBN6P/ZOoWy0q8F3lNGdF1e9PLi6tD4BepsWQsV20H07qtxYutyMEuwm1oESzmW+skA4wGpQqgdu1+8BNlhO70JhgOWe9gAn0+P0bi6FXYLv+pexY7h8+Kl78LBg9G2q8AXdo6ZOJp0wc2XVeIousfA1enRkhL7PtVcVPK4urW0l7wCEULEEsku7KWfA5WaUYDexdlbT67I2CAdYzajqoZZRGyynd6EwwOqecutG7hukj+7VRSnsEszoLaefuVhcdSazsQS668Vv+A8Alk4mndDbUn3/SVLDjO6fm/uXPkIrCh4zKq3exNkihFCxdCOFfjGHy80ooXIq6V38+PgpG4QDrGZU9VDLqA2W07tQGGB1T51zc3NjuPnMX5DCLsGMckpa9SdTW1HbtE4ak6Q3wowq81G9G3LWVr0Eb/a2Paz5JcIbvq48HGA1o9qRv9OFemCwfjrXSQB23p50CQej9O1pjBLLD25RQOt0xk8ZhJUOv91tSldyo1ZCzqYLMAHH7422i9T8Eo49ZVIeDrAWqOAatWEx2LrpxUYA1g4OBdVnlB5j5oXzzxyhdVZ5/Xr/Fj411tykodQ9zU7cXXfP2HCXMBzAHg3A5j65XDXD9HmSYLmE4xrlymv5pKW1R74aLYUk4bx0wM7DaG40Squ7ogTFj1k6YOdhNH6b/8sMK4wm/bKvMHqdGO2j76xL9ahpeakCJVxT9K2z/t/razpZMTTDwAqjzbDUis+yYHRxvuK2QqPhuxwY9ej5y/I5lgOjKCyni3ThGFWDTZGutcyCMxoD7MIxqqaiIjGajRQVJygG2AQZrfeoSz9WuyCnoiK1uSZS1LxB9rM+35V7iAE2QUbrPY7Vj37lSJEPvaWT0Za8m3K2n0f7IdxDDLALxyj9CYqmopbK0YDRGGDjMFpnosgaSCIGA/BDi8hnCCyDCpn5GiWgUcHGYbTORJE1kGQyKgaNFu0IgWVGQ+aA0chgYzAaaSpqsRgNg9WM2iNL5t8m24YjQo3BaKSpqIgwY4dZYJudiopUNQajkaaiIoFMJMgY6aJ8fNdbI0vGNer/cbXl2rEYNaakqLD/HmQOJBng5VRUywATC7DB+ozONxUVqXYMRiNNRUUCmUBQGKxm1B5ZCq4KNRUVqW4MRiNNRUUCmUBQGKxm1B5ZChhVU1GR6sZgNNJUVCSQCQSFwWpG7ZGlgNH9coQrUt0YjKp6LU5FRQKZWFAA1n8flbnrTEVFqhub0RanoiKBTCwoAGs/KfEZ5SclMSrGZpSnpMIYeCApbF9c3T3CxSNLiWAjRtev/MeCRKiUSbz+NZMr/7EgOT4h/2PBfx99utuF9ADUAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\left [ \\frac{dx_{0} \\left(x_{0} + x_{1} + 2\\right) + 200 x_{0} - 200 x_{1}}{x_{0} + x_{1} + 2}, \\quad \\frac{dx_{1} \\left(x_{0} + x_{1} + 2\\right) - 200 x_{0} + 200 x_{1}}{x_{0} + x_{1} + 2}\\right ]$$"
      ],
      "text/plain": [
       "⎡dx₀⋅(x₀ + x₁ + 2) + 200⋅x₀ - 200⋅x₁  dx₁⋅(x₀ + x₁ + 2) - 200⋅x₀ + 200⋅x₁⎤\n",
       "⎢───────────────────────────────────, ───────────────────────────────────⎥\n",
       "⎣            x₀ + x₁ + 2                          x₀ + x₁ + 2            ⎦"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.constitutive_relations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Despite the equations being specified as DAEs, they can still be simulated by the package."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1ba0dcabf98>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "t,x = bgt.simulate(model,timespan=(0.,5.), x0=[200,100])\n",
    "plt.plot(t,x)\n",
    "plt.xlabel(\"Time\")\n",
    "plt.ylabel(\"Amount\")\n",
    "plt.legend([\"S\",\"P\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below we create a model with the full mass action equations, then simulate it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1ba70175ac8>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from BondGraphTools import reaction_builder\n",
    "\n",
    "def mass_action_model():\n",
    "    reactions = [\n",
    "        (\"E + S = C\",\"R1\"),\n",
    "        (\"C = E + P\",\"R2\")\n",
    "    ]\n",
    "    \n",
    "    rn = reaction_builder.Reaction_Network()\n",
    "    for r in reactions:\n",
    "        rn.add_reaction(r[0],name=r[1])\n",
    "    \n",
    "    model = rn.as_network_model()\n",
    "    \n",
    "    for s in rn.species:\n",
    "        (model/f\"C:{s}\").set_param(\"k\",1)\n",
    "        \n",
    "    for r in rn._reactions.keys():\n",
    "        (model/f\"R:{r}\").set_param(\"r\",200)\n",
    "    \n",
    "    return model\n",
    "\n",
    "def species_order(model):\n",
    "    return [v[0].name for v in model.state_vars.values()]\n",
    "def biochemical_ic(model,ic):\n",
    "    return [ic[s] for s in species_order(model)]\n",
    "\n",
    "ma_model = mass_action_model()\n",
    "initial_conditions = {\"E\":0.5,\"C\":0.5,\"S\":200,\"P\":100}\n",
    "     \n",
    "t_ma,x_ma = bgt.simulate(ma_model,\n",
    "                         timespan=(0.,5.), \n",
    "                         x0=biochemical_ic(ma_model,initial_conditions))\n",
    "plt.plot(t_ma,x_ma)\n",
    "plt.xlabel(\"Time\")\n",
    "plt.ylabel(\"Amount\")\n",
    "plt.legend(species_order(ma_model))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To verify that the Michaelis-Menten approximation is appropriate in this case, we compare the simulation results between the two models. As expected, the results from the two simulations are similar, owing to the relatively small amount of enzyme relative to metabolites."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1ba0e3f9320>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "\n",
    "l1,l2 = plt.plot(t,x,'g')\n",
    "\n",
    "idx_metabolites = [species_order(ma_model).index(s) for s in [\"S\",\"P\"]]\n",
    "l3, l4 = plt.plot(t_ma,x_ma[:,idx_metabolites],'ro',markersize=1.5)\n",
    "\n",
    "plt.xlabel(\"Time\")\n",
    "plt.ylabel(\"Amount\")\n",
    "plt.legend((l1,l3),(\"MM model\",\"Mass action model\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simplifying network constitutive equations\n",
    "As noted in the previous section, the equations for the Michaelis-Menten model were not fully simplified. While this did not cause any issues during simulation (BondGraphTools uses a DAE solver to simulate all models), it may be useful to remove redundant terms for ease of interpretability and computational efficiency. Below we show one possible workaround that enables this simplification.\n",
    "\n",
    "We define a new class (`ODEModel`) that inherits the standard bond graph functions, but with a modification to how constitutive equations are derived. Note that this new class does not check for correctness, and will likely produce incorrect results for models that are not ODEs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "from BondGraphTools import BondGraph\n",
    "\n",
    "class ODEModel(BondGraph):\n",
    "    def __init__(self, name, components=None, **kwargs):\n",
    "        super().__init__(name,components,**kwargs)\n",
    "        \n",
    "    @property\n",
    "    def constitutive_relations(self):\n",
    "        equations = super().constitutive_relations\n",
    "        dx = [rate_symbol(expr) for expr in equations]\n",
    "        ode_constraints = [r-sp.solve(expr,r)[0] for expr,r in zip(equations,dx)]\n",
    "        \n",
    "        return ode_constraints\n",
    "    \n",
    "def rate_symbol(x):\n",
    "    return next(filter(lambda s: str(s)[0:3] == 'dx_',x.free_symbols))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Michaelis-Menten model in the previous section can then be defined using this new class in exactly the same manner, but initialised using the `ODEModel` class."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 960x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "species_params = params={'k':1,'R':1,'T':1}\n",
    "reaction_params = params={'r1':200,'r2':200,'k_c':1,'e_T':1,'R':1,'T':1}\n",
    "\n",
    "ode_model = ODEModel(name=\"Michaelis-Menten model\")\n",
    "bgt.add(ode_model,\n",
    "    bgt.new(component=\"Ce\",name=\"S\",library=\"BioChem\",value=species_params),\n",
    "    bgt.new(component=\"Ce\",name=\"P\",library=\"BioChem\",value=species_params),\n",
    "    bgt.new(component=\"R_MM\",name=\"E\",library=\"Enzyme\",value=reaction_params)\n",
    ")\n",
    "bgt.connect(ode_model/\"C:S\",(ode_model/\"R:E\" , 0))\n",
    "bgt.connect((ode_model/\"R:E\" , 1),ode_model/\"C:P\")\n",
    "bgt.draw(ode_model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The constitutive equations for this model are now simplified so that the common positive denominator has been removed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\left [ dx_{0} - \\frac{200 \\left(- x_{0} + x_{1}\\right)}{x_{0} + x_{1} + 2}, \\quad dx_{1} - \\frac{200 \\left(x_{0} - x_{1}\\right)}{x_{0} + x_{1} + 2}\\right ]$$"
      ],
      "text/plain": [
       "⎡      200⋅(-x₀ + x₁)        200⋅(x₀ - x₁)⎤\n",
       "⎢dx₀ - ──────────────, dx₁ - ─────────────⎥\n",
       "⎣       x₀ + x₁ + 2           x₀ + x₁ + 2 ⎦"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ode_model.constitutive_relations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Simulation of this model gives rise to the same results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1ba153e9470>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "t,x = bgt.simulate(model,timespan=(0.,5.), x0=[200,100])\n",
    "plt.plot(t,x)\n",
    "plt.xlabel(\"Time\")\n",
    "plt.ylabel(\"Amount\")\n",
    "plt.legend([\"S\",\"P\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Coupled enzyme-catalysed reactions\n",
    "Because the Michaelis-Menten rate law has been defined in a bond graph components, it is now possible to use this describe biochemical pathways. Below we define a relatively simple example for the network $A \\rightleftharpoons B \\rightleftharpoons C$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 960x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def pathway():\n",
    "    species_params = {'k':1,'R':1,'T':1}\n",
    "    reaction_params ={'r1':100,'r2':100,'k_c':1,'e_T':1,'R':1,'T':1}\n",
    "    \n",
    "    C_A = bgt.new(component=\"Ce\",name=\"A\",library=\"BioChem\",value=species_params)\n",
    "    C_B = bgt.new(component=\"Ce\",name=\"B\",library=\"BioChem\",value=species_params)\n",
    "    C_C = bgt.new(component=\"Ce\",name=\"C\",library=\"BioChem\",value=species_params)\n",
    "    \n",
    "    R1 = bgt.new(component=\"R_MM\",name=\"R1\",library=\"Enzyme\",value=reaction_params)\n",
    "    R2 = bgt.new(component=\"R_MM\",name=\"R2\",library=\"Enzyme\",value=reaction_params)\n",
    "    \n",
    "    effort_B = bgt.new(\"0\")\n",
    "    \n",
    "    model = ODEModel(name=\"Enzyme catalysed pathway\")\n",
    "    \n",
    "    bgt.add(model,C_A,C_B,C_C,R1,R2,effort_B)\n",
    "    \n",
    "    bgt.connect(effort_B,C_B)\n",
    "    bgt.connect(C_A,(R1,0))\n",
    "    bgt.connect((R1,1),effort_B)\n",
    "    bgt.connect(effort_B,(R2,0))\n",
    "    bgt.connect((R2,1),C_C)\n",
    "    \n",
    "    return model\n",
    "    \n",
    "m = pathway()\n",
    "bgt.draw(m)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The constitutive equations for the model are below"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/latex": [
       "$$\\left [ dx_{0} - \\frac{100 \\left(- x_{0} + x_{1}\\right)}{x_{0} + x_{1} + 2}, \\quad dx_{1} - \\frac{200 \\left(x_{0} x_{2} + x_{0} - x_{1}^{2} - 2 x_{1} + x_{2}\\right)}{x_{0} x_{1} + x_{0} x_{2} + 2 x_{0} + x_{1}^{2} + x_{1} x_{2} + 4 x_{1} + 2 x_{2} + 4}, \\quad dx_{2} - \\frac{100 \\left(x_{1} - x_{2}\\right)}{x_{1} + x_{2} + 2}\\right ]$$"
      ],
      "text/plain": [
       "⎡                                         ⎛               2            ⎞      \n",
       "⎢      100⋅(-x₀ + x₁)                 200⋅⎝x₀⋅x₂ + x₀ - x₁  - 2⋅x₁ + x₂⎠      \n",
       "⎢dx₀ - ──────────────, dx₁ - ─────────────────────────────────────────────────\n",
       "⎢       x₀ + x₁ + 2                                   2                       \n",
       "⎣                            x₀⋅x₁ + x₀⋅x₂ + 2⋅x₀ + x₁  + x₁⋅x₂ + 4⋅x₁ + 2⋅x₂ \n",
       "\n",
       "                        ⎤\n",
       "           100⋅(x₁ - x₂)⎥\n",
       "───, dx₂ - ─────────────⎥\n",
       "            x₁ + x₂ + 2 ⎥\n",
       "+ 4                     ⎦"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m.constitutive_relations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1ba1ad16a20>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "t,x = bgt.simulate(m,timespan=(0.,20.),x0=[200,50,100])\n",
    "plt.plot(t,x)\n",
    "plt.xlabel(\"Time\")\n",
    "plt.ylabel(\"Amount\")\n",
    "plt.legend([\"A\",\"B\",\"C\"])"
   ]
  }
 ],
 "metadata": {
  "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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}