MWC.ipynb

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   "source": [
    "***Note: this is the MWC.ipynb notebook.***\n",
    " The PDF version \"The Monod-Wyman-Changeux model\"\n",
    "is available [here](modulatedCooperative.pdf).***\n",
    "\n",
    "*** Note: incomplete ***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Introduction\n",
    "\"For many enzymes, the reaction velocity is not a simple hyperbolic curve, as predicted\n",
    "by the Michaelis–Menten model, but often has a sigmoidal character. This can result from cooperative effects, in which the enzyme can bind more than one substrate\n",
    "molecule but the binding of one substrate molecule affects the binding of subsequent\n",
    "ones\" <cite data-cite=\"KeeSne09\">(Keener and Sneyd, 2009)</cite>, Section 1.4.4.\n",
    "\n",
    "This note gives a bond graph <cite data-cite=\"GawCra14\">(Gawthrop and Crampin, 2014)</cite> interpretation of such cooperativity and uses the iterative properties of [BondGraphTools](https://pypi.org/project/BondGraphTools/) <cite data-cite=\"CudGawPanCra19X\">(Cudmore et. al., 2019)</cite> to build high-order cooperative systems. These systems are simulated to give steady-state behavior as the order of cooperativity increases.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Import some python code\n",
    "The bond graph analysis uses a number of Python modules:"
   ]
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    "## Some useful imports\n",
    "\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",
    "## Stoichiometry to BG\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": [
    "# Enzyme-catalysed reaction\n",
    "The basic enzyme-catalysed reaction is given in this section. It is the basic building block of cooperative enzyme-catalysed reactions\n",
    "More details are given by <cite data-cite=\"GawCra14\">(Gawthrop and Crampin, 2014)</cite>.\n"
   ]
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  {
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       "'0.3.7'"
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   ],
   "source": [
    "bgt.version"
   ]
  },
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   "source": [
    "## Enzyme-catalysed reaction\n",
    "sbg.model('RE_abg.svg')\n",
    "import RE_abg\n",
    "disp.SVG('RE_abg.svg')"
   ]
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       "\\begin{align}\n",
       "\\ch{A + E &<>[ r1 ] C }\\\\\n",
       "\\ch{C &<>[ r2 ] B + E }\n",
       "\\end{align}\n"
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   "source": [
    "s = st.stoich(RE_abg.model(),quiet=quiet)\n",
    "disp.Latex(st.sprintrl(s,chemformula=True))"
   ]
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   "source": [
    "# Cooperative enzyme-catalysed reaction\n",
    "\n",
    "<cite data-cite=\"KeeSne09\">(Keener and Sneyd, 2009)</cite>, Section 1.4.4, discusses cooperativity. This section gives a bond graph interpretation. This is done in two ways:\n",
    "\n",
    "1. As a graphical representation of a two-stage cooperative enzyme-catalysed reaction.\n",
    "2. As a generic representation of an N-stage cooperative enzyme-catalysed reaction using  [bond-graph tools](https://pypi.org/project/BondGraphTools/)"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "## Two-stage cooperative enzyme-catalysed reaction (N=2) <a id='coop2'></a>\n"
   ]
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       "<!-- Text -->\n",
       "<text fill=\"#000000\" font-family=\"Helvetica\" font-size=\"216\" font-style=\"normal\" font-weight=\"bold\" text-anchor=\"middle\" x=\"13050\" xml:space=\"preserve\" y=\"11475\">Ce:T3</text>\n",
       "<!-- Text -->\n",
       "<text fill=\"#000000\" font-family=\"Helvetica\" font-size=\"216\" font-style=\"normal\" font-weight=\"bold\" text-anchor=\"middle\" x=\"14400\" xml:space=\"preserve\" y=\"6300\">Re:t12</text>\n",
       "<!-- Text -->\n",
       "<text fill=\"#000000\" font-family=\"Helvetica\" font-size=\"216\" font-style=\"normal\" font-weight=\"bold\" text-anchor=\"middle\" x=\"3600\" xml:space=\"preserve\" y=\"2250\">Re:r01</text>\n",
       "<!-- Text -->\n",
       "<text fill=\"#000000\" font-family=\"Helvetica\" font-size=\"216\" font-style=\"normal\" font-weight=\"bold\" text-anchor=\"middle\" x=\"6300\" xml:space=\"preserve\" y=\"2250\">Re:r02</text>\n",
       "<!-- Text -->\n",
       "<text fill=\"#000000\" font-family=\"Helvetica\" font-size=\"216\" font-style=\"normal\" font-weight=\"bold\" text-anchor=\"middle\" x=\"4950\" xml:space=\"preserve\" y=\"3375\">Ce:R1</text>\n",
       "<!-- Text -->\n",
       "<text fill=\"#000000\" font-family=\"Helvetica\" font-size=\"216\" font-style=\"normal\" font-weight=\"bold\" text-anchor=\"middle\" x=\"3600\" xml:space=\"preserve\" y=\"6300\">Re:r11</text>\n",
       "<!-- Text -->\n",
       "<text fill=\"#000000\" font-family=\"Helvetica\" font-size=\"216\" font-style=\"normal\" font-weight=\"bold\" text-anchor=\"middle\" x=\"4950\" xml:space=\"preserve\" y=\"7425\">Ce:R2</text>\n",
       "<!-- Text -->\n",
       "<text fill=\"#000000\" font-family=\"Helvetica\" font-size=\"216\" font-style=\"normal\" font-weight=\"bold\" text-anchor=\"middle\" x=\"3600\" xml:space=\"preserve\" y=\"10350\">Re:r21</text>\n",
       "<!-- Text -->\n",
       "<text fill=\"#000000\" font-family=\"Helvetica\" font-size=\"216\" font-style=\"normal\" font-weight=\"bold\" text-anchor=\"middle\" x=\"6300\" xml:space=\"preserve\" y=\"10350\">Re:r22</text>\n",
       "<!-- Text -->\n",
       "<text fill=\"#000000\" font-family=\"Helvetica\" font-size=\"216\" font-style=\"normal\" font-weight=\"bold\" text-anchor=\"middle\" x=\"4950\" xml:space=\"preserve\" y=\"11475\">Ce:R3</text>\n",
       "<!-- Text -->\n",
       "<text fill=\"#000000\" font-family=\"Helvetica\" font-size=\"216\" font-style=\"normal\" font-weight=\"bold\" text-anchor=\"middle\" x=\"6300\" xml:space=\"preserve\" y=\"6300\">Re:r12</text>\n",
       "<!-- Text -->\n",
       "<text fill=\"#000000\" font-family=\"Helvetica\" font-size=\"216\" font-style=\"normal\" font-weight=\"bold\" text-anchor=\"middle\" x=\"9000\" xml:space=\"preserve\" y=\"-450\">Re:rt</text>\n",
       "<!-- Text -->\n",
       "<text fill=\"#000000\" font-family=\"Helvetica\" font-size=\"216\" font-style=\"normal\" font-weight=\"bold\" text-anchor=\"middle\" x=\"13050\" xml:space=\"preserve\" y=\"-450\">Ce:T0</text>\n",
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       "<IPython.core.display.SVG object>"
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     },
     "execution_count": 5,
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   ],
   "source": [
    "## MWC model\n",
    "sbg.model('MWC_abg.svg',quiet=quiet)\n",
    "import MWC_abg\n",
    "disp.SVG('MWC_abg.svg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Chemostat Br is not a model species\n",
      "Chemostat Bt is not a model species\n"
     ]
    },
    {
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      "text/latex": [
       "\\begin{align}\n",
       "\\ch{A + Act + R0 &<>[ r01 ] R1 }\\\\\n",
       "\\ch{R1 &<>[ r02 ] B + R0 }\\\\\n",
       "\\ch{A + Act + R1 &<>[ r11 ] R2 }\\\\\n",
       "\\ch{R2 &<>[ r12 ] B + R1 }\\\\\n",
       "\\ch{A + Act + R2 &<>[ r21 ] R3 }\\\\\n",
       "\\ch{R3 &<>[ r22 ] B + R2 }\\\\\n",
       "\\ch{R0 &<>[ rt ] T0 }\\\\\n",
       "\\ch{A + Inh + T0 &<>[ t01 ] T1 }\\\\\n",
       "\\ch{T1 &<>[ t02 ] B + T0 }\\\\\n",
       "\\ch{A + Inh + T1 &<>[ t11 ] T2 }\n",
       "\\end{align}\n",
       "\n",
       "\\begin{align}\n",
       "\\ch{T2 &<>[ t12 ] B + T1 }\\\\\n",
       "\\ch{A + Inh + T2 &<>[ t21 ] T3 }\\\\\n",
       "\\ch{T3 &<>[ t22 ] B + T2 }\n",
       "\\end{align}\n"
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       "<IPython.core.display.Latex object>"
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     },
     "execution_count": 6,
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   ],
   "source": [
    "ss = st.stoich(MWC_abg.model(),quiet=quiet)\n",
    "ssc = st.statify(ss,chemostats=['A','Br','Bt','Act','Inh'])\n",
    "disp.Latex(st.sprintrl(ss,chemformula=True))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create cooperative enzyme-catalysed reaction of any degree N\n",
    "The following code builds an N-stage cooperative enzyme-catalysed reaction using  [bond-graph tools](https://pypi.org/project/BondGraphTools/).\n",
    "\n",
    "1. N+1 instances of the basic enzyme-catalysed reaction are created and the enzyme and complex renamed.\n",
    "2. The substrate A, product B  and enzymes E1-EN are unified."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Create cooperative enzyme-catalysed reaction of any degree N\n",
    "def makeCoop(N=3,R='R',quiet=True):\n",
    "    r = R.lower()\n",
    "    Coop = bgt.new(name='Coop')\n",
    "    for i in range(N+1):\n",
    "        RE = RE_abg.model()\n",
    "        RE.name = 'RE'+str(i)\n",
    "        mbg.rename(RE,{\n",
    "                    'E':R+str(i), \n",
    "                    'C':R+str(i+1),\n",
    "                    'r1':r+str(i)+'1',\n",
    "                    'r2':r+str(i)+'2'\n",
    "                    },\n",
    "                   quiet=quiet)\n",
    "        Coop.add(RE)\n",
    "\n",
    "    ## Unify common components\n",
    "    unified = ['A','B']\n",
    "    for i in range(N): \n",
    "        Ri = R+str(i+1)\n",
    "        unified.append(Ri)\n",
    "    print('unified =',unified)\n",
    "    mbg.unify(Coop,unified,quiet=quiet)\n",
    "\n",
    "        \n",
    "    ## Stoichiometry\n",
    "    chemostats = ['A','B']\n",
    "    s = st.stoich(Coop,quiet=quiet)\n",
    "    sc = st.statify(s,chemostats=chemostats)\n",
    "    if not quiet:\n",
    "        print(st.sprint(sc,'species'))\n",
    "        print(st.sprint(sc,'reaction'))\n",
    "        \n",
    "    ## Regenerate flat Coop BG from stoichiometry\n",
    "    s['name'] = R+'_abg'\n",
    "    stbg.model(s)\n",
    "    \n",
    "    return s,sc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
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     "execution_count": 8,
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   ],
   "source": [
    "## Connecting system\n",
    "sbg.model('RT_abg.svg',quiet=quiet)\n",
    "import RT_abg\n",
    "disp.SVG('RT_abg.svg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Chemostat R0 is not a model species\n",
      "Chemostat T0 is not a model species\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "\\begin{align}\n",
       "\\ch{R &<>[ rt ] T }\n",
       "\\end{align}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "srt = st.stoich(RT_abg.model(),quiet=quiet)\n",
    "srtc = st.statify(srt,chemostats=['R0','T0'])\n",
    "disp.Latex(st.sprintrl(srt,chemformula=True))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Create Monod-Wyman-Changeux model\n",
    "def makeMWC(N=3,quiet=False):\n",
    "    MWC = bgt.new(name='MWC')   \n",
    "    sR,sRc = makeCoop(N=N,R='R',quiet=quiet)\n",
    "    sT,sRT = makeCoop(N=N,R='T',quiet=quiet)\n",
    "    import R_abg\n",
    "    import T_abg\n",
    "    import RT_abg\n",
    "    \n",
    "    MWC.add(R_abg.model(),T_abg.model(),RT_abg.model())\n",
    "    \n",
    "#     ## Unify common components\n",
    "#     unified = ['A','B','R0','T0']\n",
    "    \n",
    "#    MWC.add(R_abg.model(),T_abg.model())\n",
    "    \n",
    "    ## Unify common components\n",
    "    unified = ['A','B','R','T']\n",
    "    \n",
    "    mbg.unify(MWC,unified,quiet=False)\n",
    "    \n",
    "    ## Stoichiometry\n",
    "    chemostats = ['A','B']\n",
    "    s = st.stoich(MWC,quiet=quiet)\n",
    "    sc = st.statify(s,chemostats=chemostats)\n",
    "    if not quiet:\n",
    "        print(st.sprint(sc,'species'))\n",
    "        print(st.sprint(sc,'reaction'))\n",
    "    \n",
    "    return s,sc,MWC"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generate equations for $N=2$\n",
    "Note that these equations are identical to those of the explicit bondgraph."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "unified = ['A', 'B', 'R1', 'R2']\n",
      "unified = ['A', 'B', 'T1', 'T2']\n",
      "Unifying components in: MWC\n",
      "Creating: Ce:A and 0:A_jun in MWC\n",
      "Creating: Ce:B and 0:B_jun in MWC\n",
      "Creating: Ce:R and 0:R_jun in MWC\n",
      "Creating: Ce:T and 0:T_jun in MWC\n",
      "Exposing: Ce:A in R_abg and connecting to 0:A_jun\n",
      "Exposing: Ce:B in R_abg and connecting to 0:B_jun\n",
      "Exposing: Ce:A in T_abg and connecting to 0:A_jun\n",
      "Exposing: Ce:B in T_abg and connecting to 0:B_jun\n",
      "Exposing: Ce:R in RT and connecting to 0:R_jun\n",
      "Exposing: Ce:T in RT and connecting to 0:T_jun\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "\\begin{align}\n",
       "\\ch{R0 + A &<>[ r01 ] R1 }\\\\\n",
       "\\ch{R1 &<>[ r02 ] R0 + B }\\\\\n",
       "\\ch{R1 + A &<>[ r11 ] R2 }\\\\\n",
       "\\ch{R2 &<>[ r12 ] R1 + B }\\\\\n",
       "\\ch{R2 + A &<>[ r21 ] R3 }\\\\\n",
       "\\ch{R3 &<>[ r22 ] R2 + B }\\\\\n",
       "\\ch{T0 + A &<>[ t01 ] T1 }\\\\\n",
       "\\ch{T1 &<>[ t02 ] T0 + B }\\\\\n",
       "\\ch{T1 + A &<>[ t11 ] T2 }\\\\\n",
       "\\ch{T2 &<>[ t12 ] T1 + B }\n",
       "\\end{align}\n",
       "\n",
       "\\begin{align}\n",
       "\\ch{T2 + A &<>[ t21 ] T3 }\\\\\n",
       "\\ch{T3 &<>[ t22 ] T2 + B }\\\\\n",
       "\\ch{R &<>[ rt ] T }\n",
       "\\end{align}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "### Generate equations for N=2\n",
    "s,sc,MWC = makeMWC(N=2,quiet=quiet)\n",
    "disp.Latex(st.sprintrl(s,chemformula=True))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generate pathway equations for $N=2$\n",
    "Pathways are generated using the approach of <cite data-cite=\"GawCra17\">Gawthrop and Crampin (2014)</cite>."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6 pathways\n",
      "0:  + r01 + r02\n",
      "1:  + r11 + r12\n",
      "2:  + r21 + r22\n",
      "3:  + t01 + t02\n",
      "4:  + t11 + t12\n",
      "5:  + t21 + t22\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "\\begin{align}\n",
       "A  &\\Leftrightarrow B \\\\\n",
       "A  &\\Leftrightarrow B \\\\\n",
       "A  &\\Leftrightarrow B \\\\\n",
       "A  &\\Leftrightarrow B \\\\\n",
       "A  &\\Leftrightarrow B \\\\\n",
       "A  &\\Leftrightarrow B \n",
       "\\end{align}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp = st.path(s,sc)\n",
    "print(st.sprintp(sc))\n",
    "disp.Latex(st.sprintrl(sp))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Steady-state properties\n",
    "\n",
    "The steady state properties are investigated using dynamic simulation where slowly varing exogenous quantities are used to induce quasi-steady-state behaviour. In each case, the variable is at a constant value to start with followed by a slowly increasing ramp. The response after the initial reponse is plotted to remove artefacts due to the initial transient.\n",
    "\n",
    "All parameters are unity except for $K_B=0.01$ (to approximate an irreversible reaction) and initial states are chosen so that the total enzyme is $e_0=1$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Set up some parameters for simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Set up some parameters for simulation\n",
    "def setParameter(ss,N,K_R0,K_T0,X_Act,X_Inh):\n",
    "    \n",
    "    e0 = 1/2\n",
    "        \n",
    "    ## Set up the non-unit parameters and states\n",
    "    parameter = {}\n",
    "\n",
    "    \n",
    "    K_i = 1/(K_R0**(N+1))\n",
    "    for i in range(N+2):\n",
    "        Ki = 'K_R'+str(i)\n",
    "        #print('Setting:', Ki)\n",
    "        parameter[Ki] = K_i\n",
    "        K_i *= K_R0\n",
    "    \n",
    "    K_i = 1/(K_T0**(N+1))\n",
    "    if 'T0' in s['species']: \n",
    "        for i in range(N+2):\n",
    "            Ki = 'K_T'+str(i)\n",
    "            #print('Setting:', Ki)\n",
    "            parameter[Ki] = K_i\n",
    "            K_i *= K_T0\n",
    "\n",
    "    ## Set product constant to a small value\n",
    "    ## to make the RCR approximately irreversible\n",
    "    K_B = 1e-10\n",
    "    parameter['K_B'] = K_B\n",
    "#     parameter['K_Br'] = K_B\n",
    "#     parameter['K_Bt'] = K_B\n",
    "    \n",
    "#     parameter['K_R00'] = parameter['K_R0'] \n",
    "#     parameter['K_T00'] = parameter['K_T0'] \n",
    "#    parameter['K_Inh'] = 100\n",
    "    \n",
    "    ## States\n",
    "    X0 = np.ones(ss['n_X'])\n",
    "    X0[ss['spec_index']['Act']] = X_Act\n",
    "    X0[ss['spec_index']['Inh']] = X_Inh\n",
    "    \n",
    "    ## Set total enzyme to e0\n",
    "    for i in range(N+2):\n",
    "        Ri = 'R'+str(i)\n",
    "        X0[ss['spec_index'][Ri]] = (e0/(N+2))  \n",
    "        \n",
    "    if 'T0' in s['species']:  \n",
    "        for i in range(N+2):\n",
    "            Ti = 'T'+str(i)\n",
    "            X0[ss['spec_index'][Ti]] = (e0/(N+2)) \n",
    "    \n",
    "    return parameter,X0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Vary substrate concentration  $x_A$ for various $K_{T0}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Simulation\n",
    "## Vary x_A\n",
    "\n",
    "##Time\n",
    "quiet = True\n",
    "t_max = int(1e5)\n",
    "t = np.linspace(0,t_max,100000)\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",
    "## Chemostats: vary x_A\n",
    "x_max = 1e3\n",
    "x_min = 1e-1\n",
    "    \n",
    "A_chemo = '{3} + ({0}-{3})*np.heaviside(t-{1},1)*((t-{1})/{2})'.format(x_max,t_0,t_1,x_min)\n",
    "X_chemo =  {'A':A_chemo}\n",
    "\n",
    "K_R0 = 1\n",
    "K_T0 = 1\n",
    "\n",
    "\n",
    "for K_T0 in [1,3,10,30]:\n",
    "    N = 2\n",
    "\n",
    "    X_Act = K_T0\n",
    "    X_Inh = 1\n",
    "    \n",
    "    parameter,X0 = setParameter(ss,N,K_R0,K_T0,X_Act,X_Inh)\n",
    "\n",
    "    dat = st.sim(ss,sc=ssc,t=t,parameter=parameter,X0=X0,X_chemo=X_chemo,quiet=quiet)\n",
    "    phi_A = dat['phi'][:,ss['spec_index']['A']]\n",
    "    dX = ss['N']@(dat['V'].T)\n",
    "    dX_B = dX[ss['spec_index']['B'],:]\n",
    "    V_B = dX_B[-i_1:]\n",
    "    \n",
    "    ## Plot flow v. x_A  \n",
    "    grey = '0.8'\n",
    "    plt.plot(phi_A[-i_1:],V_B,label = 'K_T0 ='+str(K_T0)) \n",
    "plt.grid()\n",
    "plt.legend()\n",
    "#plt.ylim((0,e0))\n",
    "#plt.xlim((0,x_max))\n",
    "#plt.legend(['N=0 (theory)']+['N='+str(i) for i in NN]+['MWC'])\n",
    "plt.xlabel('$\\phi_A$')\n",
    "plt.ylabel('$v$')\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
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  "language_info": {
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    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
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  "toc": {
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   "number_sections": true,
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   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  }
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}