Phosphorylation.ipynb

{
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***Note: this is the Phosphorylation.ipynb notebook. The\n",
    "PDF version is available [here](Phosphorylation.pdf).***\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "# Introduction\n",
    "The Mitogen-activated Protein Kinase (MAPK) cascade is a well-studied\n",
    "signalling pathway with ultrasensitive components \n",
    "<cite data-cite=\"AlbJohLew15,KliLieWie16\"></cite>. However, the use of the  Michaelis-Menten\n",
    "approximation to enzyme-catalysed reactions can be misleading in this\n",
    "context <cite data-cite='Voi13'></cite>.\n",
    "\n",
    "Following <cite data-cite=\"GawCra16\"></cite>, each phosphorylation step is built out of\n",
    "reversible mass-action reactions using the bond graph approach of\n",
    "<cite data-cite=\"GawCra14\"></cite>. This resolves the potential problems\n",
    "mentioned above as well as giving a thermodynamically compliant model\n",
    "which explicitly accounts for energy consumption via ATP hydrolysis.\n",
    "\n",
    "This notebook presents, analyses and simulates three bond graph models\n",
    "using [BondGraphTools](https://pypi.org/project/BondGraphTools/) and extensions:\n",
    "\n",
    "1. A phosphorylation/dephosphorylation system (PD).\n",
    "\n",
    "2. A double phosphorylation/dephosphorylation system (DPD).\n",
    "\n",
    "3. A Mitogen-activated Protein Kinase (MAPK)\n",
    "   cascade using a cascade of one PD systems and two DPD systems.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Import some python code\n",
    "The bond graph analysis uses a number of Python modules:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Some useful imports\n",
    "import BondGraphTools as bgt\n",
    "import numpy as np\n",
    "import sympy as sp\n",
    "import matplotlib.pyplot as plt\n",
    "import IPython.display as disp\n",
    "\n",
    "## Stoichiometric analysis\n",
    "import stoich as st\n",
    "\n",
    "## SVG bg representation conversion\n",
    "import svgBondGraph as sbg\n",
    "\n",
    "## Modular bond graphs\n",
    "import modularBondGraph as mbg\n",
    "\n",
    "## Export stoichiometry as bond graph\n",
    "import stoichBondGraph as stbg\n",
    "\n",
    "## Data structure copy\n",
    "import copy\n",
    "\n",
    "## Set quiet=False for verbose output\n",
    "quiet = True"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Phosphorylation/dephosphorylation\n",
    "A biomolecular cycle involving both phosphorylation and\n",
    "dephosphorylation is a basic element of cell signalling\n",
    "<cite data-cite=\"AlbJohLew15\"></cite>. A bond graph model of this cycle\n",
    "<cite data-cite=\"GawCra14,GawCra16\"></cite> is given in the Figure.\n",
    "\n",
    "1. The upper part of the   bond graph  represents an enzyme-catalysed\n",
    "reaction phosphorylating protein M to give MP driven by the\n",
    "dephosphorylation of ATP to ADP.\n",
    "\n",
    "2. The lower part of the bond graph  represents an enzyme-catalysed\n",
    "reaction dephosphorylating protein MP to give M and P.\n",
    "\n",
    "This forms a biochemical switch <cite data-cite=\"BeaQia10\"></cite> with input the net\n",
    "amount of E1 and C1 and output the  phosphorylated protein MP. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Convert bond graph in SVG format to BGT format and display"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
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   ],
   "source": [
    "## Phosphorylation/dephosphorylation\n",
    "sbg.model('PD_abg.svg',quiet=quiet)\n",
    "import PD_abg\n",
    "disp.SVG('PD_abg.svg')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## A flowstat is used to add to the pool of enzyme formed by E1 and C1\n",
    "\n",
    "The flowstat is formed from a simple reaction A$\\Leftrightarrow$B where A is a chemostat and B is unified with E1. The flow in this reaction is set in the simulation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def addFlowstat(model,species,quiet=False):\n",
    "    \n",
    "    ## Creat a simple reaction\n",
    "    sbg.model('AB_abg.svg',quiet=quiet)\n",
    "    import AB_abg\n",
    "    AB = AB_abg.model()\n",
    "    mbg.rename(AB,{'A':'Aflow','B':species},quiet=quiet)\n",
    "    \n",
    "    ## Create composite model\n",
    "    modelF = bgt.new(name='modelF')\n",
    "    modelF.add(model,AB)\n",
    "    mbg.unify(modelF,[species],quiet=quiet)\n",
    "    \n",
    "    return modelF\n",
    "    \n",
    "PDF = addFlowstat(PD_abg.model(),'E1',quiet=quiet)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Reactions, pathways and pools\n",
    "The coresponding reactions and pathways are generated using stoich.\n",
    "\n",
    "1. The four reactions r1-r4 correspond to the four Re components in the\n",
    "bond graph.\n",
    "\n",
    "2. The reaction r corresponds to the added flowstat: the flow in r is\n",
    "externally specified and provides a way to change the amount of enzyme\n",
    "in the E1/P1 pool.\n",
    "\n",
    "3. There is a single pathway though the four components r1-r4\n",
    "corresponding the the flow around the loop driven by the reaction\n",
    "ATP = ADP + P.\n",
    "\n",
    "4. The two enzyme catalysed reactions are modulated by {E1} and\n",
    "E2 which therfore determine the flows and the relative amounts of\n",
    "M and MP.\n",
    "\n",
    "5. Apart from the chemostats which are themselves conserved moieties, there are two pools:\n",
    "\n",
    "    a) C2 + E2 \n",
    "    \n",
    "    b) C1 + C2 + M + MP\n",
    "    \n",
    "   Note that C1+E1 is not a pool due to the input flow from the flowstat."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Reactions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\begin{align}\n",
       "\\ch{ATP + M + E1 &<>[ r1 ] C1 }\\\\\n",
       "\\ch{C1 &<>[ r2 ] ADP + MP + E1 }\\\\\n",
       "\\ch{E2 + MP &<>[ r3 ] C2 }\\\\\n",
       "\\ch{C2 &<>[ r4 ] E2 + M + P }\\\\\n",
       "\\ch{Aflow &<>[ r ] E1 }\n",
       "\\end{align}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s = st.stoich(PDF,quiet=quiet)\n",
    "disp.Latex(st.sprintrl(s,chemformula=True))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Pathways\n",
    "The ATP hydrolysis species are set as chemostats together with Aflow from the flowstat reaction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 pathways\n",
      "0:  + r1 + r2 + r3 + r4\n",
      "\n"
     ]
    }
   ],
   "source": [
    "chemostats = ['Aflow','ATP','ADP','P']\n",
    "sc = st.statify(s,chemostats=chemostats)\n",
    "print(st.sprintp(sc))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\begin{align}\n",
       "ATP  &\\Leftrightarrow ADP + P \n",
       "\\end{align}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp = st.path(s,sc)\n",
    "disp.Latex(st.sprintrl(sp))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Pools: Conserved moieties"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\begin{align}\n",
       "\\ch{&<>[ m_0 ] ADP }\\\\\n",
       "\\ch{&<>[ m_1 ] ATP }\\\\\n",
       "\\ch{&<>[ m_2 ] C2 + E2 }\\\\\n",
       "\\ch{&<>[ m_3 ] C1 + C2 + M + MP }\\\\\n",
       "\\ch{&<>[ m_4 ] P }\\\\\n",
       "\\ch{&<>[ m_5 ] Aflow }\n",
       "\\end{align}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "disp.Latex(st.sprintml(sc,chemformula=True))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Set up parameters for PD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def setParameterPD(s,x_M=1,x_E2=0.1):\n",
    "    \"\"\"Set up parameters and states for simulation of PD module\"\"\"\n",
    "    \n",
    "    parameter = {}\n",
    "    \n",
    "    # Ce components: set non-unity parameters\n",
    "    K_ATP = 1e2\n",
    "    K_ADP = 1e-3\n",
    "    K_P = 1e-3\n",
    "    parameter['K_ATP'] = K_ATP\n",
    "    parameter['K_ADP'] = K_ADP\n",
    "    parameter['K_P'] = K_P\n",
    "    parameter['K_E1'] = 1\n",
    "    parameter['K_E2'] = 1\n",
    "    parameter['K_C1'] = 100\n",
    "    parameter['K_C2'] = 100\n",
    " \n",
    "    ## Initial states\n",
    "    small = 1e-10\n",
    "    \n",
    "    ## Small initial values\n",
    "    smallStates = ['E1','C1','C2','MP']\n",
    "    for smallState in smallStates:\n",
    "        parameter['X0_'+smallState] = small\n",
    "    \n",
    "    ## Initial values of other states\n",
    "    parameter['X0_M'] = x_M\n",
    "    parameter['X0_E2'] = x_E2  \n",
    "    \n",
    "    return parameter"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plotting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def inPool(s,X,species):\n",
    "    \"\"\"Find total amount in pool specified by species\"\"\"\n",
    "    \n",
    "    index = []\n",
    "    for spec in species:\n",
    "        index.append(s['species'].index(spec))\n",
    "        \n",
    "    total = np.sum(X[:,index],axis=1)\n",
    "\n",
    "    return total\n",
    "\n",
    "def Plot(s,dat,M=['M','MP'],E=['E1','C1'],i0=0):\n",
    "    \"\"\"Plot relevant data\"\"\"\n",
    "    \n",
    "    ## Extract data\n",
    "    X = dat['X']\n",
    "    V = dat['V']\n",
    "    N = s['N']\n",
    "    dX = (N@V.T).T\n",
    "    dX_ATP = dX[:,s['spec_index']['ATP']]\n",
    "    dX_ADP = dX[:,s['spec_index']['ADP']]\n",
    "    dX_P = dX[:,s['spec_index']['P']]\n",
    "\n",
    "\n",
    "    st.plot(s,dat,species=M,reaction = [],i0=10)\n",
    "\n",
    "\n",
    "    plt.plot(t,dX_ATP,t,dX_ADP,t,dX_P)\n",
    "    plt.grid()\n",
    "    plt.ylabel('Flow $v$')\n",
    "    plt.xlabel('$t$')\n",
    "    plt.legend(['ATP','ADP','P'])\n",
    "    plt.show()\n",
    "    \n",
    "    e_tot = inPool(s,X,E)\n",
    "    \n",
    "    plt.plot(t,e_tot)\n",
    "    plt.grid()\n",
    "    plt.xlabel('$t$')\n",
    "    plt.show()\n",
    "    \n",
    "    st.plot(s,dat,species=M,reaction = [],x=e_tot,xlabel='$e_{tot}$',i0=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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+xsxKBq270Mw2mlmtmW03s8zIlS9BMRB2yX6+nXOpLMtTX1/GbcTQN7NU4EHgRmARcIeZLRqy2ReA4865cuAB4H5v3zTg34D/6pxbDFQBPRGrXgJjU0MrM3MymT01y+9SfFNZls+J0+rry/iE80x/CVDvnGtwznUDjwKrhmyzCnjIu/0EcJ2FGq83ANucc28BOOdanXP6PLmMinOOmoY2KsvyA9nPHzDQ2tqoFo+MQ1oY28wC3hn0/SFg6dm2cc71mtkJIB84D3Bm9ixQCDzqnPvW0Acws7uAuwCKioqorq4e5TB+r6OjY1z7J5ogjLexo5/Wzm5ye5qprq4OxJiH6ujoYPebNUybaDz9Wh3zeg/4XVLUBfU4R3vM4YT+eO9/BXA5cAp4wcy2OOdeGLyRc241sBqgoqLCVVVVjfkBq6urGc/+iSYI4/3Fxv1ALZ+9cTlz8icGYsxDDYz5mpZtPFN7lKuuujqprxoGwfjdHioWYw6nvdMIFA/6fra3bNhtvD5+DtBK6FXBy865FufcKWAtcOl4i5Zg2dTQxsycTIrzgtvPH1A5L48Tp3vYefSk36VIggon9DcD882s1MzSgduBNUO2WQPc6d2+BVjnnHPAs8AFZjbR+2NwNbAjMqVLEITm57cGvp8/YKCvv6mhzedKJFGNGPrOuV7gbkIBvhN43DlXa2b3mdnN3mY/BvLNrB74MnCPt+9x4DuE/nC8CWx1zv0m8sOQZFXf1EFrZzdLA3L+/JHMyMmiJF/z9WXswurpO+fWEmrNDF5276DbZ4Bbz7LvvxGatikyakE7f344KsvyWbv9CH39jtQk7+tL5OkTuRLXNjW0MSMnkzkBOn/+SCrL8jl5ppedR9TXl9FT6Evccs5Rs0/9/KF+39dXi0dGT6EvcWtvcwctHd2BuR5uuKbnZFJakK03c2VMFPoStzZ6oaZ+/geFzsPTSp/OwyOjpNCXuLWpoZXpU9TPH05lWT7t6uvLGCj0JS6FzrfTSmVAz58/kqWl6uvL2Cj0JS79vp+v1s5wpudkUpI/kZp96uvL6Cj0JS5tUj9/RJVl+bym8+vLKCn0JS4N9PPn5quffzZLy3QeHhk9hb7EnYHr4aqff24Dff0aTd2UUVDoS9zZ29xJS0cXS9XaOaeZuVnM1Xl4ZJQU+hJ3dL6d8C0tzeO1/errS/gU+hJ3NjW0UjQlgxL180dUWZbPu6d6qDum6+ZKeBT6EldC59vR9XDDtVTn4ZFRUuhLXGlo6aS5vUutnTDNys2iOC9LoS9hU+hLXFE/f/QqSzVfX8Kn0Je4sqmhjWmT1c8fjaVl+Rw/1cPuJvX1ZWQKfYkbuh7u2CwtDZ16etNetXhkZAp9iRvq549Ncd5EZk/N0vn1JSwKfYkbv+/n66Ipo7W0NF/z9SUsCn2JGzVeP7+0INvvUhJOZVkebZ3d7Gnq8LsUiXMKfYkL6uePj66bK+FS6Etc2NfSSVN7F0vV2hmT4ryJzMrNomafQl/OTaEvcUHnzx+/pWV5bGpowzn19eXsFPoSFzY1tFI4OYMy9fPHrLIsX319GZFCX3ynfn5kVL53fn21eOTsFPriu/2tp2hq79JUzXEqzstiZk6m5uvLOSn0xXcbvU+SDlwJSsbGzKgsy6dmX6v6+nJWCn3x3UA/f16h+vnjtbQsj5aObvY2q68vw1Poi6+cc2xsaGWZ+vkRMTD7aaNaPHIWYYW+ma00szozqzeze4ZZn2Fmj3nra8ysZMj6OWbWYWZ/E5myJVnofDuRNSdvIjNyMvUhLTmrEUPfzFKBB4EbgUXAHWa2aMhmXwCOO+fKgQeA+4es/w7w2/GXK8lmoJ+/bJ5CPxLMjKWledRovr6cRTjP9JcA9c65BudcN/AosGrINquAh7zbTwDXmfda3cw+DuwDaiNTsiQTXQ838irL8mnp6GJvc6ffpUgcCif0ZwHvDPr+kLds2G2cc73ACSDfzCYBfwv8w/hLlWQTmp/fpn5+hOk8PHIuaVG+/78HHnDOdZzrP7WZ3QXcBVBUVER1dfWYH7Cjo2Nc+yeaRB7v4Y5+Wjq6mNrTMqoxJPKYx2o0Y3bOkZth/HrTTmaf2RfdwqJIxzk6wgn9RqB40PezvWXDbXPIzNKAHKAVWArcYmbfAnKBfjM745z7l8E7O+dWA6sBKioqXFVV1RiGElJdXc149k80iTzeX2zcD9Ty2Y9ewdz88KdrJvKYx2q0Y7762Bu8ureVq6++OmFfRek4R0c47Z3NwHwzKzWzdOB2YM2QbdYAd3q3bwHWuZArnXMlzrkS4LvA/x4a+BJcmxramJGTyZw89fMjrbIsn+b2Lhpa1NeX9xsx9L0e/d3As8BO4HHnXK2Z3WdmN3ub/ZhQD78e+DLwgWmdIoMNnG9H/fzoGLhubo3m68sQYfX0nXNrgbVDlt076PYZ4NYR7uPvx1CfJKndxzpo7ezW/PwoKS3IZtrkDDY1tPKppXP8LkfiiD6RK74YmFmi+fnRMXAenk0NOg+PvJ9CX3yxcW8rs3KzKFY/P2qWluXR1N7F/tZTfpcicUShLzHX3++o2deq1k6Uab6+DEehLzFXd6yd46d61NqJsrKCbAq9vr7IAIW+xNxACOmiKdGl8/DIcBT6EnMb97ZSnJfF7Knq50dbZVk+R0+e4YD6+uJR6EtM9fU7ava1vXc9V4ku9fVlKIW+xFTt4ROcON3DivkFfpcSCPMKsymYlMFGhb54FPoSU6/UtwBwxTyFfiyYGVfMy2dDvebrS4hCX2JqQ30LC6dPpnByht+lBMaK+QW0dHRRd6zd71IkDij0JWbO9PSxef9xlpfrWX4srfB+3q/safG5EokHCn2Jmc372+ju7Vc/P8Zm5mZRVpj9XmtNgk2hLzHzSn0LE1KNJSWanx9rK8oLqGkI/dGVYFPoS8xsqG/hkjlTyc6I9gXbZKgV5QWc7ulj68HjfpciPlPoS0y0dXZTe/jke/1lia3Kefmkphgb1OIJPIW+xMTGva04h97E9cmUzAlcNDuH9XozN/AU+hITr9S3MCkjjYtm5/hdSmCtKC9g26F3OXG6x+9SxEcKfYmJDfUtVJblk5aqXzm/rJhfSL8LveqS4NL/QIm6g62nONh2ihXlOt+Ony4uzmVieqr6+gGn0Jeo27A3FDKan++v9LQUKsvyNV8/4BT6EnUv1TUzfUom8won+V1K4C0vL2BfSyeHjutUy0Gl0Jeo6unrZ0N9C1ULCjEzv8sJvKu8V1sv79az/aBS6EtUbTlwnPauXqoWFPpdigDl0yYxKzeL6romv0sRnyj0Jaqq65pJSzHNz48TZsbVCwrZUN+iUzIElEJfoqq6ronL5k5lcuYEv0sRzzULptHZ3cfr+9v8LkV8oNCXqDl64gy7jrZTtWCa36XIIFfMyyc9NYUX1eIJJIW+RM1Lu0Ohon5+fMnOSGNJaR7Vdc1+lyI+UOhL1FR7UzUXTp/sdykyRNWCQvY0dWjqZgAp9CUqevr6eWVPC1efp6ma8Wig5aZn+8Gj0Jeo2KqpmnFtXmE2xXmauhlECn2Jiurd3lRNnXohLpkZVedNY0N9K129fX6XIzEUVuib2UozqzOzejO7Z5j1GWb2mLe+xsxKvOXXm9kWM9vu/XttZMuXePX8jmNcXpLHFE3VjFvXLCzkdE8fNQ2auhkkI4a+maUCDwI3AouAO8xs0ZDNvgAcd86VAw8A93vLW4A/cM5dANwJ/CJShUv82tfSyZ6mDq5fVOR3KXIOy8oKyJyQwvM7j/ldisRQOM/0lwD1zrkG51w38Ciwasg2q4CHvNtPANeZmTnn3nDOHfaW1wJZZpYRicIlfj234yiAQj/OZaWnctX8Qn5XewznnN/lSIyEc4XqWcA7g74/BCw92zbOuV4zOwHkE3qmP+CTwFbnXNfQBzCzu4C7AIqKiqiurg63/g/o6OgY1/6JJh7H+0TNaYonp7B322vsjcL9x+OYoy1aY56T2sPvTnbzszXrKM1Jjfj9j4eOc3SEE/rjZmaLCbV8bhhuvXNuNbAaoKKiwlVVVY35saqrqxnP/okm3sbb2tFF/bPPc/e186mqOi8qjxFvY46FaI35os5ufvL2c7RmzuZzVQsifv/joeMcHeG0dxqB4kHfz/aWDbuNmaUBOUCr9/1s4FfAZ5xz0XjiJ3HkhV1N9Du4Qa2dhDA1O50lpXn8zmvJSfILJ/Q3A/PNrNTM0oHbgTVDtllD6I1agFuAdc45Z2a5wG+Ae5xzGyJVtMSv53YcY2ZOJotnTvG7FAnTDYums/tYB/tbOv0uRWJgxNB3zvUCdwPPAjuBx51ztWZ2n5nd7G32YyDfzOqBLwMD0zrvBsqBe83sTe9LZ99KUqe7+1i/p5nrFxXpU7gJZOAN9+d2aBZPEITV03fOrQXWDll276DbZ4Bbh9nvG8A3xlmjJIj1e5o509PP9Yum+12KjEJx3kQWzZjC73Yc5c+uKvO7HIkyfSJXIuY3248wdeIElpbl+V2KjNINi4t4/cBxmtrP+F2KRJlCXyLiTE8fz+84xsrzpzMhVb9WieamC2bgHPx2u97QTXb63ykR8eKuJjq7+/jYhTP9LkXGYH7RZBZOn8yv3zo88saS0BT6EhFPbztCwaR0lpaqtZOo/uCimbx+4DiN7572uxSJIoW+jFtnVy8v7DrGjefPIE2tnYT1sQtnAPCbbXq2n8z0P1TGbd2uJs709L8XGpKY5uZnc9HsHH791hG/S5EoUujLuP36rcNMm5zB5SVq7SS6j104k+2NJ/RBrSSm0Jdxaevs5sW6Jv7gopmkpOgDWYnuJu/V2hq9oZu0FPoyLmvebKSnz3HLZbP9LkUiYGZuFsvK8nliyyH6+3W65WSk0JdxeXJrI+fPmsKHZuhcO8ni1orZHGw7xWv7dUWtZKTQlzHbdfQk2xtPcMulepafTG48fwaTMtL4j9cP+V2KRIFCX8bsyS2HmJBq3HzxLL9LkQjKSk/lYxfOYO32I3R09fpdjkSYQl/GpKu3j1+90ci1C6eRl53udzkSYbdWFHO6p09z9pOQQl/G5Jm3j9LS0c2nls71uxSJgkvn5DKvMJuHX3tn5I0loSj0ZUx+vvEAJfkTubK8wO9SJArMjM8sK+Gtd97lzXfe9bsciSCFvoza240n2HLgOH9cOVdz85PYJy+bzaSMNB56db/fpUgEKfRl1H6x8QBZE1K59bLikTeWhDUpI41bLpvN09sO09ze5Xc5EiEKfRmVts5unnqrkY9fMpOciRP8Lkei7DPL5tLT53jktYN+lyIRotCXUfnZhn2c6enn88tL/S5FYqCscBJXn1fIzzfu50xPn9/lSAQo9CVs7Wd6+Nmr+/nI4iLmF032uxyJkS9WzaOlo5tH9Ww/KSj0JWwP1xzk5JlevlhV7ncpEkNLy/JZUpLHD19uoKtXz/YTnUJfwtLZ1cuP1u9jeXk+FxXn+l2OxNjd15Zz5MQZntzS6HcpMk4KfQnLj9Y30NLRxX+/YYHfpYgPrpxfwCVzcvneC7s53a1n+4lMoS8jam7vYvXLDdx4/nQunTPV73LEB2bG3330Qxw72cWP1jf4XY6Mg0JfRvTd53fT1dvP//iInuUH2eUleaxcPJ0fvLSXpvYzfpcjY6TQl3PacuA4D792kD+pnEtZ4SS/yxGf3XPjQnr6+vnG0zv9LkXGSKEvZ9XT18/XfrWd6VMy+Rs9yxegpCCbL11Tzpq3DvPCzmN+lyNjoNCXs/r2s3XsOtrOfavOZ1JGmt/lSJz4YlU5C4om83e/2k5rh07PkGgU+jKsF3c18cOXG/j00jlcv6jI73IkjqSnpfCd2y7i+Kke/vLRN+nTtXQTikJfPqD28An+4pE3WDh9Mv/rY4v8Lkfi0OKZOfzjqsW8Ut/CPz69A+cU/IkirNA3s5VmVmdm9WZ2zzDrM8zsMW99jZmVDFr3VW95nZl9JHKlSzTUN7Xz2Z9uZlJmGj/57OVkTkj1uySJU7ddPofPLy/lZ6/u59u/q1PwJ4gRG7Vmlgo8CFwPHAI2m9ka59yOQZt9ATjunCs3s9uB+4HbzGwRcDuwGJgJPG9m5znn9OmOOPRiXRN/+cgbpKel8vPPL2FmbpbfJUm6VSKEAAAH/klEQVSc+583fYjOrl4efHEvx052cd+qxUxM1/s/8Syco7MEqHfONQCY2aPAKmBw6K8C/t67/QTwL2Zm3vJHnXNdwD4zq/fub2Nkypfx6u931B4+yer1Dfz6rcMsKJrMv95ZQXHeRL9LkwSQkmL80ycuYHpOJt97YQ+bGlr5i+vmc9MFM8jWm/9xKZyjMgsYfKHMQ8DSs23jnOs1sxNAvrd805B9Z4252nPYdfQkdz/8Bqc6TzFx60vve6n5gRedbtiboe/Psd/QV69u0BYfWHeOV7rhPoYbstYNU3d3dzfpG54f8ngj7zegu7efjq5eJqan8qVr5vHn185XS0dGJSXF+Ovrz2N5eQFfX1PLV57Yxj1PbmNmbhYZaSmk2NiurtZ56hTZW1+KcLXxbd7ELqqqovsYcfGn2MzuAu4CKCoqorq6etT3cayzn6kp3UzO6ict5XTofs/1mO97/BHqO+s3YIMWnPPxPrBf+NuebT8Denr7mZDWd5bazvF49vt/Sqakc8m0NCalH2XThqPnqCw+dHR0jOl3JJElypi/cqFjd3Emta19NJ/uprf/3E+AzmVSRj+pdjqyBca5idYb9eMcTug3AoOvizfbWzbcNofMLA3IAVrD3Bfn3GpgNUBFRYWrGuOfutuA6upqxrp/IgraeEFjjnfXROh+EmnMkRKLMYcze2czMN/MSs0sndAbs2uGbLMGuNO7fQuwzoV6GGuA273ZPaXAfOC1yJQuIiKjNeIzfa9HfzfwLJAK/MQ5V2tm9wGvO+fWAD8GfuG9UdtG6A8D3naPE3rTtxf4kmbuiIj4J6yevnNuLbB2yLJ7B90+A9x6ln2/CXxzHDWKiEiE6BO5IiIBotAXEQkQhb6ISIAo9EVEAkShLyISIBZvZ8Yzs2bgwDjuogBoiVA5iSBo4wWNOSg05tGZ65wrHGmjuAv98TKz151zFX7XEStBGy9ozEGhMUeH2jsiIgGi0BcRCZBkDP3VfhcQY0EbL2jMQaExR0HS9fRFROTskvGZvoiInEXShP5IF29PJGZWbGYvmtkOM6s1s7/0lueZ2XNmtsf7d6q33Mzs+97Yt5nZpYPu605v+z1mdufZHjMemFmqmb1hZk9735eaWY03rse8U3vjnar7MW95jZmVDLqPr3rL68zsI/6MJDxmlmtmT5jZLjPbaWbLAnCM/9r7nX7bzB4xs8xkO85m9hMzazKztwcti9hxNbPLzGy7t8/3zUZ5aTLnXMJ/ETrl816gDEgH3gIW+V3XOMYzA7jUuz0Z2A0sAr4F3OMtvwe437v9UeC3hC6EVQnUeMvzgAbv36ne7al+j+8c4/4y8DDwtPf948Dt3u0fAP/Nu/1F4Afe7duBx7zbi7xjnwGUer8TqX6P6xzjfQj4U+92OpCbzMeY0KVS9wFZg47vZ5PtOANXAZcCbw9aFrHjSuiaJJXePr8FbhxVfX7/gCL0Q14GPDvo+68CX/W7rgiO7yngeqAOmOEtmwHUebd/CNwxaPs6b/0dwA8HLX/fdvH0Reiqai8A1wJPe7/QLUDa0GNM6NoOy7zbad52NvS4D94u3r4IXV1uH977akOPXZIe44Fraed5x+1p4CPJeJyBkiGhH5Hj6q3bNWj5+7YL5ytZ2jvDXbw9KhdgjzXvJe0lQA1Q5Jw74q06ChR5t882/kT6uXwX+ArQ732fD7zrnOv1vh9c+3vj8taf8LZPpPGWAs3AT72W1r+aWTZJfIydc43At4GDwBFCx20LyX2cB0TquM7ybg9dHrZkCf2kZGaTgCeBv3LOnRy8zoX+zCfF1Csz+xjQ5Jzb4nctMZRGqAXw/5xzlwCdhF72vyeZjjGA18deRegP3kwgG1jpa1E+8Pu4Jkvoh3UB9kRiZhMIBf6/O+d+6S0+ZmYzvPUzgCZv+dnGnyg/l+XAzWa2H3iUUIvne0CumQ1c3W1w7e+Ny1ufA7SSOOOF0DO0Q865Gu/7Jwj9EUjWYwzwYWCfc67ZOdcD/JLQsU/m4zwgUse10bs9dHnYkiX0w7l4e8Lw3o3/MbDTOfedQasGX4D+TkK9/oHln/FmAlQCJ7yXks8CN5jZVO9Z1g3esrjinPuqc262c66E0LFb55z7NPAicIu32dDxDvwcbvG2d97y271ZH6XAfEJvesUd59xR4B0zW+Atuo7QtaST8hh7DgKVZjbR+x0fGHPSHudBInJcvXUnzazS+xl+ZtB9hcfvNzwi+MbJRwnNctkLfM3vesY5lhWEXv5tA970vj5KqJ/5ArAHeB7I87Y34EFv7NuBikH39Xmg3vv6nN9jC2PsVfx+9k4Zof/M9cB/ABne8kzv+3pvfdmg/b/m/RzqGOWsBh/GejHwunec/5PQLI2kPsbAPwC7gLeBXxCagZNUxxl4hNB7Fj2EXtF9IZLHFajwfn57gX9hyGSAkb70iVwRkQBJlvaOiIiEQaEvIhIgCn0RkQBR6IuIBIhCX0QkQBT6IiIBotAXEQkQhb5ImMxstpnd5ncdIuOh0BcJ33WEzo8jkrD0iVyRMJjZCkLnOHkXaAc+4Zxr8LcqkdFT6IuEycyeAf7GOff2iBuLxCm1d0TCt4DQycJEEpZCXyQMZlZA6LS3vSNuLBLHFPoi4SkBDvtdhMh4KfRFwrMLKDCzt83sCr+LERkrvZErIhIgeqYvIhIgCn0RkQBR6IuIBIhCX0QkQBT6IiIBotAXEQkQhb6ISIAo9EVEAuT/A1D8K7GvEwpuAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def setFlow(e_max,t_max):\n",
    "    \"\"\"Set the flow stat flow (as a string)\n",
    "    \n",
    "    Flow is non-zero between 0.25 and 0.75 t_max\n",
    "    and is sinusoidal. \n",
    "    The integrated flow has a maximum at e_tot = e_max\n",
    "    \n",
    "    \"\"\"\n",
    "    r_flow = ('2*{0}*( (t>(0.25*{1}))*(t<(0.75*{1})) )'\n",
    "              '*np.sin(4*np.pi*(t-0.25*{1})/{1})'\n",
    "                .format(np.pi*e_max/(t_max),t_max)\n",
    "              )\n",
    "    V_flow = {'r':r_flow}\n",
    "    \n",
    "    return V_flow\n",
    "    \n",
    "    \n",
    "##Time\n",
    "quiet = True\n",
    "#t_max = int(8e2)\n",
    "t_max = 1e4\n",
    "t = np.linspace(0,t_max,1000)\n",
    "t_0 = 100\n",
    "t_1 = t_max-t_0\n",
    "i_max = len(t)\n",
    "i_0 = int(i_max*t_0/t_max)\n",
    "i_1 = i_max-i_0\n",
    "\n",
    "## Flow\n",
    "x_M = 1\n",
    "e_max = 1e-1\n",
    "V_flow = setFlow(e_max,t_max)\n",
    "\n",
    "## Parameters\n",
    "x_E2=0.5*x_M\n",
    "parameter = setParameterPD(s,x_M=x_M,x_E2=x_E2)\n",
    "\n",
    "## Simulate\n",
    "dat = st.sim(s,sc=sc,t=t,parameter=parameter,V_flow=V_flow,quiet=quiet)\n",
    "\n",
    "## Plot\n",
    "Plot(s,dat,M=['M','MP'],E=['E1','C1'])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Discussion\n",
    "The PD module acts and a high-gain saturating amplifier, or switch <cite data-cite=\"BeaQia10\"></cite>, with the total  enzyme  associated with the first reaction $e_{tot}= x_{E1}+x_{c1}$ as the input and the amount of the phosphorylated protein MP as output. Note that $e_{tot}$ is varied using the flowstat."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Double Phosphorylation/dephosphorylation\n",
    "Double phosphorylation/dephosphorylation is an important building block of signalling cascades\n",
    "<cite data-cite=\"AlbJohLew15,KliLieWie16\"></cite>. A model can be built by combining two copes of the PD module using [BondGraphTools](https://pypi.org/project/BondGraphTools/) <cite data-cite=\"CudGawPanCra19X\"></cite>."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Set up parameters for DPD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def copyNames(names,same=[],changed={},prefix=''):\n",
    "    \n",
    "    rename = {}\n",
    "    for name in names:\n",
    "        if not name in same:\n",
    "            if name in changed.keys():\n",
    "                rename[name] = changed[name]\n",
    "            else:\n",
    "                rename[name] = prefix+name\n",
    "\n",
    "    return rename\n",
    "\n",
    "def copyParameters(parameter,rename):\n",
    "    \n",
    "    sep = '_' # parameter seperator\n",
    "    Parameter = {}\n",
    "    for key,val in parameter.items():\n",
    "        Key = key.split(sep)\n",
    "        #print(key,Key)\n",
    "        if len(Key)<2:\n",
    "            print(key,'should contain _')\n",
    "        else:\n",
    "            prefix = Key[0]\n",
    "            name = Key[1]\n",
    "            for nam in Key[2:]:\n",
    "                name += sep+nam\n",
    "            \n",
    "        if name not in rename.keys():\n",
    "            Parameter[key] = val\n",
    "        else:\n",
    "            Parameter[prefix+sep+rename[name]] = val\n",
    "    return Parameter\n",
    "\n",
    "def mergeParameters(par1,par2):\n",
    "\n",
    "#    par = par1.copy()\n",
    "    par = {}\n",
    "    for key,val in par2.items():\n",
    "        par[key] = val\n",
    "    for key,val in par1.items():\n",
    "        par[key] = val\n",
    "    return par\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create DPD from two copies of PD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def makeDPD(x_M=x_M,x_E2=x_E2,quiet=False):\n",
    "    \"\"\"Create Double Phosphorylation/dephosphorylation\"\"\"\n",
    "    \n",
    "    \n",
    "    ## Components not to be renamed\n",
    "    same = ['E1','ATP','ADP','P']\n",
    "    \n",
    "    ## Common components to be unified\n",
    "    unified = same + ['MP']\n",
    "    \n",
    "    ## Create two copies of PD, renaming as appropriate\n",
    "    PD1 = PD_abg.model()\n",
    "    sPD = st.stoich(PD_abg.model(),quiet=quiet)\n",
    "    PD1.name = 'PD1'\n",
    "\n",
    "    names = sPD['species'] + sPD['reaction']\n",
    "    rename = copyNames(names,prefix='PD1__',same=same+['M','MP'])\n",
    "    mbg.rename(PD1,rename,quiet=quiet)\n",
    "    \n",
    "    ## Parameters of PD\n",
    "    parameterPD = setParameterPD(sPD,x_M=x_M,x_E2=x_E2)\n",
    "    \n",
    "    ## Parameters of P1\n",
    "    parameter_P1 = copyParameters(parameterPD,rename)\n",
    "    \n",
    "    PD2 = PD_abg.model()\n",
    "    PD2.name = 'PD2'\n",
    "    rename = copyNames(names,prefix='PD2__',same=same, changed={'M':'MP_','MP':'MPP'})\n",
    "    mbg.rename(PD2,rename,quiet=quiet)\n",
    "    mbg.rename(PD2,{'MP_':'MP'},quiet=quiet)\n",
    "    \n",
    "    ## Parameters of P2\n",
    "    parameter_P2 = copyParameters(parameterPD,rename)\n",
    "    \n",
    "    ## DPD parameters\n",
    "    parameter_DPD = mergeParameters(parameter_P1,parameter_P2)\n",
    "\n",
    "    ## Create DPD\n",
    "    DPD = bgt.new(name='DPD')\n",
    "    DPD.add(PD1,PD2)\n",
    "    \n",
    "    ## Unify common species\n",
    "    mbg.unify(DPD,unified,quiet=quiet)\n",
    "    \n",
    "    ## Stoichiometry of DPD\n",
    "    sDPD = st.stoich(DPD,quiet=quiet)\n",
    "    \n",
    "    ## Save as flattened bond graph for later use\n",
    "    sDPD['name'] = 'DPD_abg'\n",
    "    stbg.model(sDPD)\n",
    "    \n",
    "    ## Add in the flowstat\n",
    "    DPDF = addFlowstat(DPD,'E1',quiet=quiet)\n",
    "    \n",
    "    ## Stoichiometry\n",
    "    s = st.stoich(DPDF,quiet=quiet)\n",
    "    chemostats = ['Aflow','ATP','ADP','P']\n",
    "    sc = st.statify(s,chemostats=chemostats)\n",
    "    \n",
    "    return s,sc,parameter_DPD,sPD,sDPD\n",
    "\n",
    "x_E2 = 0.1*x_M\n",
    "S,Sc,Parameter,sPD,sDPD = makeDPD(x_M=x_M,x_E2=x_E2,quiet=quiet)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Reactions, pathways and pools\n",
    "The dot (.) notation is used to represent species and reactions within each submodule. Thus PD1.C1 and PD2.C2 represent the C2 species associated with each submodule and PD1.r1 and PD2.r1 reaction r1 associated with each submodule.\n",
    "\n",
    "1. There is a pathway though the four components r1-r4 within each submodule\n",
    "corresponding the the flow around the loop driven by the reaction\n",
    "ATP = ADP + P.\n",
    "\n",
    "2. Apart from the chemostats which are themselves conserved moieties, there are three pools:\n",
    "\n",
    "    a) PD1.C2 + PD1.E2 \n",
    " \n",
    "    b) PD2.C2 + PD2.E2 \n",
    "     \n",
    "    c) PD1.C1 + PD1.C2 + PD2.C1 + PD2.C2 + M + MP + MPP\n",
    "    \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Reactions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\begin{align}\n",
       "\\ch{M + ATP + E1 &<>[ PD1.r1 ] PD1.C1 }\\\\\n",
       "\\ch{PD1.C1 &<>[ PD1.r2 ] ADP + MP + E1 }\\\\\n",
       "\\ch{PD1.E2 + MP &<>[ PD1.r3 ] PD1.C2 }\\\\\n",
       "\\ch{PD1.C2 &<>[ PD1.r4 ] PD1.E2 + M + P }\\\\\n",
       "\\ch{ATP + MP + E1 &<>[ PD2.r1 ] PD2.C1 }\\\\\n",
       "\\ch{PD2.C1 &<>[ PD2.r2 ] MPP + ADP + E1 }\\\\\n",
       "\\ch{PD2.E2 + MPP &<>[ PD2.r3 ] PD2.C2 }\\\\\n",
       "\\ch{PD2.C2 &<>[ PD2.r4 ] PD2.E2 + P + MP }\\\\\n",
       "\\ch{Aflow &<>[ r ] E1 }\n",
       "\\end{align}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "disp.Latex(st.sprintrl(S,chemformula = True))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Pathways"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2 pathways\n",
      "0:  + PD1.r1 + PD1.r2 + PD1.r3 + PD1.r4\n",
      "1:  + PD2.r1 + PD2.r2 + PD2.r3 + PD2.r4\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "\\begin{align}\n",
       "\\ch{ATP &<>[ pr1 ] ADP + P }\\\\\n",
       "\\ch{ATP &<>[ pr2 ] ADP + P }\n",
       "\\end{align}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(st.sprintp(Sc))\n",
    "Sp = st.path(S,Sc)\n",
    "disp.Latex(st.sprintrl(Sp,chemformula = True))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Pools"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\begin{align}\n",
       "\\ch{&<>[ m_0 ] PD1.C2 + PD1.E2 }\\\\\n",
       "\\ch{&<>[ m_1 ] PD2.C2 + PD2.E2 }\\\\\n",
       "\\ch{&<>[ m_2 ] ATP }\\\\\n",
       "\\ch{&<>[ m_3 ] ADP }\\\\\n",
       "\\ch{&<>[ m_4 ] P }\\\\\n",
       "\\ch{&<>[ m_5 ] PD1.C1 + PD1.C2 + M + PD2.C1 + PD2.C2 + MPP + MP }\\\\\n",
       "\\ch{&<>[ m_6 ] Aflow }\n",
       "\\end{align}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "disp.Latex(st.sprintml(Sc,chemformula=True))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Unused parameters: ['X0_MP_']\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Simulation\n",
    "\n",
    "# Copy parameters and states to each sub module\n",
    "# common = ['E1','M','MP','ATP','ADP','P','Aflow']\n",
    "\n",
    "\n",
    "## Simulate\n",
    "Dat = st.sim(S,sc=Sc,t=t,parameter=Parameter,V_flow=V_flow,quiet=quiet)\n",
    "\n",
    "## Plot\n",
    "Plot(S,Dat,M=['M','MP','MPP'],E=['E1','PD1__C1','PD2__C1'])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Discussion\n",
    "In a similar way to the PD module, the DPD module acts and a high-gain saturating amplifier, or switch <cite data-cite=\"BeaQia10\"></cite>, with the total  enzyme  associated with the first reaction of the first PD $e_{tot}= x_{E1}+x_{c1}$ as the input and the amount of the double-phosphorylated protein MPP as output. Note that the gain is giher, and the behavior more switch-like compared to the PD module."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# MAPK cascade"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create cascade from one PD and two DPD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['PD1__C1', 'PD1__C2', 'PD1__E2', 'M', 'PD2__C1', 'PD2__C2', 'PD2__E2', 'MPP', 'E1', 'ATP', 'ADP', 'P', 'MP', 'PD1__r1', 'PD1__r2', 'PD1__r3', 'PD1__r4', 'PD2__r1', 'PD2__r2', 'PD2__r3', 'PD2__r4']\n"
     ]
    }
   ],
   "source": [
    "def makeMAPK(sPD,S,Parameter,useDPD=True,quiet=quiet):\n",
    "    \"\"\"Create the MAPK cascade\"\"\"\n",
    "   \n",
    "    ## Components not to be renamed\n",
    "    same = ['ATP','ADP','P']\n",
    "    \n",
    "    ## Amount of M in each layer\n",
    "    X_M = np.array([1,7,50])\n",
    "    X_E2 = 0.5*X_M\n",
    "\n",
    "    ## Phosphorylation layer 1\n",
    "    names = sPD['species'] + sPD['reaction']\n",
    "    P1 = PD_abg.model()\n",
    "    P1.name = 'P1'\n",
    "    rename = copyNames(names,prefix='L1__',same=same, \n",
    "                       changed={'M':'MKKK','MP':'MKKKP','E1':'MKKKK'})\n",
    "    mbg.rename(P1,rename,quiet=quiet)\n",
    "    parameter_P1 = copyParameters(setParameterPD(s,x_M=X_M[0],x_E2=X_E2[0]),rename)\n",
    "    \n",
    "    if not useDPD:\n",
    "        ## Use PD in place of DPD\n",
    "        ## Phosphorylation layer 2\n",
    "        names = sPD['species'] + sPD['reaction']\n",
    "        P2 = PD_abg.model()\n",
    "        P2.name = 'P2'\n",
    "        rename = copyNames(names,prefix='L2__',same=same, \n",
    "                           changed={'M':'MKK','MP':'MKKP','E1':'MKKKP'})\n",
    "        mbg.rename(P2,rename,quiet=quiet)\n",
    "        parameter_P2 = copyParameters(setParameterPD(s,x_M=X_M[1],x_E2=X_E2[1]),rename)\n",
    "        \n",
    "        ## Phosphorylation layer 3\n",
    "        P3 = PD_abg.model()\n",
    "        P3.name = 'P3'\n",
    "        rename = copyNames(names,prefix='L3__',same=same, \n",
    "                           changed={'M':'MK','MP':'MKP','E1':'MKKP'})\n",
    "        mbg.rename(P3,rename,quiet=quiet)\n",
    "        parameter_P3 = copyParameters(setParameterPD(s,x_M=X_M[2],x_E2=X_E2[2]),rename)\n",
    "        \n",
    "        connections = ['MKKKK','MKKKP','MKKP']\n",
    "    else: \n",
    "    ## Use DPD \n",
    "        import DPD_abg\n",
    "        ## Phosphorylation layer 2\n",
    "        S,Sc,Parameter,sPD,sDPD = makeDPD(x_M=X_M[1],x_E2=X_E2[1],quiet=quiet)\n",
    "        names = sDPD['species'] + sDPD['reaction']\n",
    "        P2 = DPD_abg.model()\n",
    "        P2.name = 'P2'\n",
    "        rename = copyNames(names,prefix='L2__',same=same, \n",
    "                           changed={'M':'MKK','MP':'MKKP','MPP':'MKKPP','E1':'MKKKP'})\n",
    "        mbg.rename(P2,rename,quiet=quiet)\n",
    "        parameter_P2 = copyParameters(Parameter,rename)\n",
    "        \n",
    "        ## Phosphorylation layer 3\n",
    "        S,Sc,Parameter,sPD,sDPD = makeDPD(x_M=X_M[2],x_E2=X_E2[2],quiet=quiet)\n",
    "        names = sDPD['species'] + sDPD['reaction']\n",
    "        print(names)\n",
    "        P3 = DPD_abg.model()\n",
    "        P3.name = 'P3'\n",
    "        rename = copyNames(names,prefix='L3__',same=same, \n",
    "                           changed={'M':'MK','MP':'MKP','MPP':'MKPP','E1':'MKKPP'})\n",
    "        mbg.rename(P3,rename,quiet=quiet)\n",
    "        parameter_P3 = copyParameters(Parameter,rename)\n",
    "        \n",
    "        connections = ['MKKKK','MKKKP','MKKPP']\n",
    "    \n",
    "    ## Flowstat\n",
    "    import AB_abg\n",
    "    AB = AB_abg.model()\n",
    "    mbg.rename(AB,{'A':'Aflow','B':'MKKKK'},quiet=quiet)\n",
    "    \n",
    "    ## Create the MAPK cascade with flowstat\n",
    "    MAPK = bgt.new(name='MAPK')\n",
    "    MAPK.add(AB,P1,P2,P3)\n",
    "    unify = same + connections\n",
    "    mbg.unify(MAPK,unify,quiet=quiet)\n",
    "    \n",
    "    parameter_P12 = mergeParameters(parameter_P1,parameter_P2)\n",
    "    parameterM = mergeParameters(parameter_P12,parameter_P3)\n",
    "\n",
    "    ## Stoichiometry\n",
    "    sM = st.stoich(MAPK,quiet=quiet)\n",
    "    chemostats = ['Aflow','ATP','ADP','P']\n",
    "    scM = st.statify(sM,chemostats=chemostats)\n",
    "    \n",
    "    return sM,scM,parameterM\n",
    "\n",
    "useDPD = True\n",
    "sM,scM,ParameterM = makeMAPK(sPD,S,Parameter,useDPD=useDPD,quiet=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Reactions, pathways and pools\n",
    "The dot (.) notation is used to represent species and reactions within each submodule. Thus L2.PD1.C1 and L2.PD2.C2 represent the C2 species associated with each submodule within level 2 and L2.PD1.r1 and L2.PD2.r1  represent reaction r1 associated with each submodule within level 2.\n",
    "\n",
    "1. There is a pathway though the four components r1-r4 within each of the five submodule\n",
    "corresponding the the flow around the loop driven by the reaction\n",
    "ATP = ADP + P.\n",
    "\n",
    "2. Apart from the chemostats which are themselves conserved moieties, there are eight pools:\n",
    "\n",
    "    a) C2 and E2 within each of the 5 submodules\n",
    " \n",
    "    b) L1.C1 + L1.C2 + L2.PD1.C1 + L2.PD2.C1 + MKKK + MKKKP \n",
    "     \n",
    "    c) L3.PD1.C1 + L3.PD1.C2 + L3.PD2.C1 + L3.PD2.C2 + MKPP + MKP + MK\n",
    "    \n",
    "    d) L2.PD1.C1 + L2.PD1.C2 + L2.PD2.C1 + L2.PD2.C2 + L3.PD1.C1 + L3.PD2.C1 + MKKPP + MKKP + MKK\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Reactions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\begin{align}\n",
       "\\ch{Aflow &<>[ r ] MKKKK }\\\\\n",
       "\\ch{MKKK + ATP + MKKKK &<>[ L1.r1 ] L1.C1 }\\\\\n",
       "\\ch{L1.C1 &<>[ L1.r2 ] ADP + MKKKK + MKKKP }\\\\\n",
       "\\ch{L1.E2 + MKKKP &<>[ L1.r3 ] L1.C2 }\\\\\n",
       "\\ch{L1.C2 &<>[ L1.r4 ] L1.E2 + MKKK + P }\\\\\n",
       "\\ch{MKK + ATP + MKKKP &<>[ L2.PD1.r1 ] L2.PD1.C1 }\\\\\n",
       "\\ch{L2.PD1.C1 &<>[ L2.PD1.r2 ] MKKP + ADP + MKKKP }\\\\\n",
       "\\ch{L2.PD1.E2 + MKKP &<>[ L2.PD1.r3 ] L2.PD1.C2 }\\\\\n",
       "\\ch{L2.PD1.C2 &<>[ L2.PD1.r4 ] L2.PD1.E2 + MKK + P }\\\\\n",
       "\\ch{MKKP + ATP + MKKKP &<>[ L2.PD2.r1 ] L2.PD2.C1 }\n",
       "\\end{align}\n",
       "\n",
       "\\begin{align}\n",
       "\\ch{L2.PD2.C1 &<>[ L2.PD2.r2 ] ADP + MKKKP + MKKPP }\\\\\n",
       "\\ch{L2.PD2.E2 + MKKPP &<>[ L2.PD2.r3 ] L2.PD2.C2 }\\\\\n",
       "\\ch{L2.PD2.C2 &<>[ L2.PD2.r4 ] L2.PD2.E2 + MKKP + P }\\\\\n",
       "\\ch{MK + ATP + MKKPP &<>[ L3.PD1.r1 ] L3.PD1.C1 }\\\\\n",
       "\\ch{L3.PD1.C1 &<>[ L3.PD1.r2 ] MKP + ADP + MKKPP }\\\\\n",
       "\\ch{L3.PD1.E2 + MKP &<>[ L3.PD1.r3 ] L3.PD1.C2 }\\\\\n",
       "\\ch{L3.PD1.C2 &<>[ L3.PD1.r4 ] L3.PD1.E2 + MK + P }\\\\\n",
       "\\ch{MKP + ATP + MKKPP &<>[ L3.PD2.r1 ] L3.PD2.C1 }\\\\\n",
       "\\ch{L3.PD2.C1 &<>[ L3.PD2.r2 ] MKPP + ADP + MKKPP }\\\\\n",
       "\\ch{L3.PD2.E2 + MKPP &<>[ L3.PD2.r3 ] L3.PD2.C2 }\n",
       "\\end{align}\n",
       "\n",
       "\\begin{align}\n",
       "\\ch{L3.PD2.C2 &<>[ L3.PD2.r4 ] L3.PD2.E2 + MKP + P }\n",
       "\\end{align}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "disp.Latex(st.sprintrl(sM,chemformula = True))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Pathways"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5 pathways\n",
      "0:  + L1.r1 + L1.r2 + L1.r3 + L1.r4\n",
      "1:  + L2.PD1.r1 + L2.PD1.r2 + L2.PD1.r3 + L2.PD1.r4\n",
      "2:  + L2.PD2.r1 + L2.PD2.r2 + L2.PD2.r3 + L2.PD2.r4\n",
      "3:  + L3.PD1.r1 + L3.PD1.r2 + L3.PD1.r3 + L3.PD1.r4\n",
      "4:  + L3.PD2.r1 + L3.PD2.r2 + L3.PD2.r3 + L3.PD2.r4\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "\\begin{align}\n",
       "\\ch{ATP &<>[ pr1 ] ADP + P }\\\\\n",
       "\\ch{ATP &<>[ pr2 ] ADP + P }\\\\\n",
       "\\ch{ATP &<>[ pr3 ] ADP + P }\\\\\n",
       "\\ch{ATP &<>[ pr4 ] ADP + P }\\\\\n",
       "\\ch{ATP &<>[ pr5 ] ADP + P }\n",
       "\\end{align}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(st.sprintp(scM))\n",
    "sMp = st.path(sM,scM)\n",
    "disp.Latex(st.sprintrl(sMp,chemformula = True))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Pools"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\begin{align}\n",
       "\\ch{&<>[ m_0 ] Aflow }\\\\\n",
       "\\ch{&<>[ m_1 ] L1.C2 + L1.E2 }\\\\\n",
       "\\ch{&<>[ m_2 ] L2.PD1.C2 + L2.PD1.E2 }\\\\\n",
       "\\ch{&<>[ m_3 ] L2.PD2.C2 + L2.PD2.E2 }\\\\\n",
       "\\ch{&<>[ m_4 ] L3.PD1.C2 + L3.PD1.E2 }\\\\\n",
       "\\ch{&<>[ m_5 ] L3.PD2.C2 + L3.PD2.E2 }\\\\\n",
       "\\ch{&<>[ m_6 ] L3.PD1.C1 + L3.PD1.C2 + MK + L3.PD2.C1 + L3.PD2.C2 + MKPP + MKP }\\\\\n",
       "\\ch{&<>[ m_7 ] ATP }\\\\\n",
       "\\ch{&<>[ m_8 ] ADP }\\\\\n",
       "\\ch{&<>[ m_9 ] P }\n",
       "\\end{align}\n",
       "\n",
       "\\begin{align}\n",
       "\\ch{&<>[ m_10 ] L1.C1 + L1.C2 + MKKK + L2.PD1.C1 + L2.PD2.C1 + MKKKP }\\\\\n",
       "\\ch{&<>[ m_11 ] L2.PD1.C1 + L2.PD1.C2 + MKK + L2.PD2.C1 + L2.PD2.C2 + MKKP + L3.PD1.C1 + L3.PD2.C1 + MKKPP }\n",
       "\\end{align}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "disp.Latex(st.sprintml(scM,chemformula=True))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Unused parameters: ['X0_MP_']\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Flows\n",
    "e_max = 1e-3\n",
    "V_flow = setFlow(e_max,t_max)\n",
    "\n",
    "## Simulate\n",
    "Dat = st.sim(sM,sc=scM,t=t,parameter=ParameterM,V_flow=V_flow,quiet=quiet)\n",
    "\n",
    "## Plot\n",
    "if useDPD:\n",
    "    Plot(sM,Dat,M=['MKKKP','MKKPP','MKPP'],E=['MKKKK','L1__C1'])\n",
    "else:\n",
    "    Plot(sM,Dat,M=['MKKKP','MKKP','MKP'],E=['MKKKK','L1__C1'])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Discussion\n",
    "In a similar way to the PD and DPD modules, the MAPK cascade module acts and a high-gain saturating amplifier, or switch with the total  enzyme  associated with the first reaction of the PD $e_{tot}= x_{E1}+x_{c1}$ of the first layer as the input and the amount of the double-phosphorylated protein MKPP of the third layer as output. \n",
    "Here, the maximum value (0.001) of the input is 100 times smaller than that of the simulations of PD and DPD and so the gain is much higher, and the behavior more switch-like compared to the PD and DPD modules."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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