modularAllosteric.ipynb

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    "***Note: this is the modularAllosteric.ipynb notebook. The\n",
    "PDF version \"Allosteric inhibition as a control actuator - modular approach: passive and active\n",
    "feedback\"\n",
    "is available [here](modularAllosteric.pdf).***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Introduction\n",
    "Using the methods of control theory to examine and reexamine the behaviour of living systems is well-established\n",
    "<cite data-cite=\"Cra47a\">(Craik, 1947)</cite>\n",
    "<cite data-cite=\"Wie61\">(Weiner, 1961)</cite>\n",
    "<cite data-cite=\"Bay66\">(Bayliss, 1966)</cite>\n",
    "<cite data-cite=\"Sav09\">(Savageau, 1976)</cite>\n",
    "<cite data-cite=\"JagFla03\">(Jagacinski and Flach, 2003)</cite>\n",
    "<cite data-cite=\"IglIng10\">(Inglesias and Ingalls, 2010)</cite>\n",
    "<cite data-cite=\"WelBulKalMasVer08\">(Wellstead et al, 2008)</cite>\n",
    "<cite data-cite=\"DriLeaDet15\">(Drion et al, 2015)</cite>\n",
    "<cite data-cite=\"Vec13\">(Del Veccio, 2013)</cite>.\n",
    "This notebook examines the enzyme-catalysed reaction as a control actuator and its behavior within a feedback loop controlling product concentration. The feedback mechanism used is *Allosteric inhibition* - see section 1.4.3\n",
    "<cite data-cite=\"KeeSne09\">(Keener and Sneyd, 2009)</cite>. \n",
    "\n",
    "- The notebook [fECR](https://github.com/gawthrop/BondGraphTools-Biomolecular/blob/master/fECR.ipynb) looks at an alternative feedback mechanism : competitive inhibition.\n",
    "- As discussed in the notebook [Allosteric](https://github.com/gawthrop/BondGraphTools-Biomolecular/blob/master/Allosteric.ipynb), competitive inhibition is a special case of allosteric inhibition.\n",
    "- As discussed in the notebook [fECR](fECR.pdf), the control methodology is based on \n",
    "    [Linearisation](https://github.com/gawthrop/BondGraphTools-Biomolecular/blob/master/Linearisation.ipynb).\n",
    "- This notebook introduces a novel method based on *chemostats* for deducing the *feedback loop-gain* $L(s)$ from the bond graph describing the biomolecular system. $L(s)$ is a crucial component of feedback control analysis.\n",
    "- The presence of *active* feedback via allosteric inhibition and *passive* feedback via the admittance of the reaction chain at the product is noted. The passive feedback has a stabilising effect."
   ]
  },
  {
   "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,
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    "## Some useful imports\n",
    "import BondGraphTools as bgt\n",
    "import numpy as np\n",
    "import sympy as sym\n",
    "import matplotlib.pyplot as plt\n",
    "import IPython.display as disp\n",
    "import copy\n",
    "\n",
    "## Stoichiometric analysis\n",
    "import stoich as st\n",
    "\n",
    "## SVG bg representation conversion\n",
    "import svgBondGraph as sbg\n",
    "\n",
    "## Modularity\n",
    "import modularBondGraph as mbg\n",
    "\n",
    "## Control systems package\n",
    "import control as con\n",
    "\n",
    "## Stoichiometry to BG\n",
    "import stoichBondGraph as stbg\n",
    "\n",
    "## Set quiet=False for verbose output\n",
    "quiet = True\n",
    "\n",
    "## Set slycot=True if slycot is installed (see control module)\n",
    "slycot=True\n",
    "\n",
    "## For reimporting: use imp.reload(module)\n",
    "import importlib as imp\n",
    "\n",
    "## Printing options\n",
    "np.set_printoptions(precision=3)\n",
    "fmt = '{:5.3f}'\n",
    "\n",
    "## Allow output from within functions\n",
    "from IPython.core.interactiveshell import InteractiveShell\n",
    "InteractiveShell.ast_node_interactivity = \"all\"\n",
    "\n",
    "## Minreal (minimum realisation algorithm) tolerance\n",
    "tol = 1e-2\n",
    "\n",
    "## Chemostat EM and CM\n",
    "chemostatEMCM = False\n",
    "\n",
    "## Use fixed-length reaction chain (N_reac=3)\n",
    "## Fixed = False allows arbitary length reaction chains using N_reac = int.\n",
    "Fixed = True"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Derive stoichiometry from bond graph"
   ]
  },
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   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def stoichiometry(abg,chemostats=[]):\n",
    "    s = st.stoich(abg,quiet=quiet)\n",
    "    sc = st.statify(s,chemostats=chemostats)    \n",
    "    return s,sc"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Enzme catalysed reaction with allosteric inhibition"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bond graph model\n",
    "\n",
    "-  **Ce:A**: substrate\n",
    "-  **Ce:B**: product\n",
    "-  **Ce:B0**: product sink\n",
    "-  **Ce:E**: enzyme\n",
    "-  **Ce:C**: enzyme bound to A\n",
    "-  **Ce:F** and **Ce:G**: species pumping the reaction\n",
    "-  **Ce:B**: product\n",
    "-  **Ce:EM**: enzyme bound to M\n",
    "-  **Ce:CM**: complex C bound to M\n",
    "-  Corresponding reactions are:\n",
    "\n",
    "\\begin{align}\n",
    "\\ch{A + E + F &<>[ r1 ] C }\\\\\n",
    "\\ch{C &<>[ r2 ] B + E + G }\\\\\n",
    "\\ch{B &<>[ r3 ] B0 }\\\\\n",
    "\\ch{CM &<>[ ra ] A + EM }\\\\\n",
    "\\ch{5 B + C &<>[ rc ] CM }\\\\\n",
    "\\ch{EM &<>[ re ] 5 B + E }\n",
    "\\end{align}"
   ]
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   ],
   "source": [
    "sbg.model('aiRE_abg.svg',quiet=quiet)\n",
    "import aiRE_abg\n",
    "#abg = aiRE_abg\n",
    "disp.SVG('aiRE_abg.svg')"
   ]
  },
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   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
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     "text": [
      "Reactions:\n"
     ]
    },
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       "\\begin{align}\n",
       "\\ch{A + E + F &<>[ r1 ] C }\\\\\n",
       "\\ch{C &<>[ r2 ] B + E + G }\\\\\n",
       "\\ch{CM &<>[ ra ] A + EM + F }\\\\\n",
       "\\ch{C + 5 M &<>[ rc ] CM }\\\\\n",
       "\\ch{EM &<>[ re ] E + 5 M }\n",
       "\\end{align}\n"
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   "source": [
    "## Stoichiometry\n",
    "chemostats=['A','M','F','G']\n",
    "if chemostatEMCM:\n",
    "    chemostats += ['EM','CM']\n",
    "\n",
    "s,sc = stoichiometry(aiRE_abg.model(),chemostats=chemostats)\n",
    "\n",
    "print('Reactions:')\n",
    "disp.Latex(st.sprintrl(s,chemformula=True))\n",
    "sp = st.path(s,sc)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Controlled system bond graph "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Arbitrary length $N_{reac}$\n",
    "This corresponds to the arbitary length chain when Fixed=False\n",
    "It is the same as the fixed length chain when N_reac=3."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
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   "source": [
    "sbg.model('BB_abg.svg',quiet=quiet)\n",
    "import BB_abg\n",
    "disp.SVG('BB_abg.svg')"
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  {
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   "source": [
    "def CLBG(aiRE_abg,abg,N=1):\n",
    "\n",
    "    if N is None:\n",
    "        NBB = abg.model()\n",
    "    else:\n",
    "        ## Create chain\n",
    "        NBB = mbg.chain(abg.model(),inport='B',outport='B0',N=N,quiet=quiet)\n",
    "        if N>1:\n",
    "            ## Rename penultimate state\n",
    "            ISN1 = 'IS'+str(N-1)\n",
    "            mbg.rename(NBB,{ISN1:'P'})\n",
    "        else:\n",
    "            mbg.rename(NBB,{'B':'P'})\n",
    "\n",
    "    ## Create composite system\n",
    "    aiRE = aiRE_abg.model()\n",
    "    if N is 1:\n",
    "        mbg.rename(aiRE,{'B':'P'})\n",
    "\n",
    "    mbg.rename(aiRE,{'M':'P'})\n",
    "\n",
    "    Allosteric = bgt.new(name='Allosteric') \n",
    "    Allosteric.add(aiRE,NBB)\n",
    "    if N is 1:\n",
    "        common = ['P']\n",
    "    else:\n",
    "        common = ['B','P']\n",
    "\n",
    "\n",
    "    mbg.unify(Allosteric,common=common,quiet=quiet)\n",
    "    \n",
    "    return Allosteric"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fixed length $N_{reac}=3$\n",
    "\n",
    "This corresponds to the fixed-length chain when Fixed=True"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<svg height=\"145pt\" viewBox=\"1283 435 10118 2291\" width=\"638pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       "<g fill=\"none\">\n",
       "<!-- Line -->\n",
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       "<!-- Line -->\n",
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       "<!-- Line -->\n",
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       "<!-- Text -->\n",
       "<text fill=\"#000000\" font-family=\"Times\" font-size=\"240\" font-style=\"normal\" font-weight=\"normal\" text-anchor=\"middle\" x=\"1575\" xml:space=\"preserve\" y=\"2385\">0</text>\n",
       "<!-- Text -->\n",
       "<text fill=\"#000000\" font-family=\"Times\" font-size=\"240\" font-style=\"normal\" font-weight=\"normal\" text-anchor=\"middle\" x=\"1575\" xml:space=\"preserve\" y=\"675\">Ce:B</text>\n",
       "<!-- Text -->\n",
       "<g transform=\"translate(3060,2250) rotate(-270)\">\n",
       "<text fill=\"#000000\" font-family=\"Times\" font-size=\"240\" font-style=\"normal\" font-weight=\"normal\" text-anchor=\"middle\" x=\"0\" xml:space=\"preserve\" y=\"0\">Re:r_0</text>\n",
       "</g><!-- Text -->\n",
       "<text fill=\"#000000\" font-family=\"Times\" font-size=\"240\" font-style=\"normal\" font-weight=\"normal\" text-anchor=\"middle\" x=\"4725\" xml:space=\"preserve\" y=\"2385\">0</text>\n",
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       "<text fill=\"#000000\" font-family=\"Times\" font-size=\"240\" font-style=\"normal\" font-weight=\"normal\" text-anchor=\"middle\" x=\"4725\" xml:space=\"preserve\" y=\"675\">Ce:B1</text>\n",
       "<!-- Text -->\n",
       "<g transform=\"translate(6210,2250) rotate(-270)\">\n",
       "<text fill=\"#000000\" font-family=\"Times\" font-size=\"240\" font-style=\"normal\" font-weight=\"normal\" text-anchor=\"middle\" x=\"0\" xml:space=\"preserve\" y=\"0\">Re:r_1</text>\n",
       "</g><!-- Text -->\n",
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       "<text fill=\"#000000\" font-family=\"Times\" font-size=\"240\" font-style=\"normal\" font-weight=\"normal\" text-anchor=\"middle\" x=\"7875\" xml:space=\"preserve\" y=\"675\">Ce:P</text>\n",
       "<!-- Text -->\n",
       "<g transform=\"translate(9360,2250) rotate(-270)\">\n",
       "<text fill=\"#000000\" font-family=\"Times\" font-size=\"240\" font-style=\"normal\" font-weight=\"normal\" text-anchor=\"middle\" x=\"0\" xml:space=\"preserve\" y=\"0\">Re:r_2</text>\n",
       "</g><!-- Text -->\n",
       "<text fill=\"#000000\" font-family=\"Times\" font-size=\"240\" font-style=\"normal\" font-weight=\"normal\" text-anchor=\"middle\" x=\"11025\" xml:space=\"preserve\" y=\"2385\">0</text>\n",
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       "<text fill=\"#000000\" font-family=\"Times\" font-size=\"240\" font-style=\"normal\" font-weight=\"normal\" text-anchor=\"middle\" x=\"11025\" xml:space=\"preserve\" y=\"675\">Ce:B0</text>\n",
       "</g>\n",
       "</svg>"
      ],
      "text/plain": [
       "<IPython.core.display.SVG object>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sbg.model('ReacChain_abg.svg',quiet=quiet)\n",
    "import ReacChain_abg\n",
    "disp.SVG('ReacChain_abg.svg')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Stoichiometry and reactions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Renaming components within aiRE\n",
      "\tRenaming M to P\n",
      "Reactions:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "\\begin{align}\n",
       "\\ch{A + E + F &<>[ r1 ] C }\\\\\n",
       "\\ch{C &<>[ r2 ] E + G + B }\\\\\n",
       "\\ch{CM &<>[ ra ] A + EM + F }\\\\\n",
       "\\ch{C + 5 P &<>[ rc ] CM }\\\\\n",
       "\\ch{EM &<>[ re ] E + 5 P }\\\\\n",
       "\\ch{B &<>[ r_0 ] B1 }\\\\\n",
       "\\ch{B1 &<>[ r_1 ] P }\\\\\n",
       "\\ch{P &<>[ r_2 ] B0 }\n",
       "\\end{align}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pathway reactions:\n",
      "2 pathways\n",
      "0:  + r1 + ra + rc + re\n",
      "1:  + r1 + r2 + r_0 + r_1 + r_2\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "\\begin{align}\n",
       " &\\Leftrightarrow \\\\\n",
       "A + F  &\\Leftrightarrow G + B0 \n",
       "\\end{align}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "if Fixed:\n",
    "    abg = ReacChain_abg\n",
    "    N_reac = None\n",
    "else:\n",
    "    abg = BB_abg\n",
    "    ## Number of reactions in the chain \n",
    "    N_reac = 3\n",
    "\n",
    "\n",
    "## Create composite closed-loop system\n",
    "Allosteric = CLBG(aiRE_abg,abg,N=N_reac)\n",
    "\n",
    "## Stoichiometry\n",
    "chemostats=['A','B0','F','G']\n",
    "if chemostatEMCM:\n",
    "    chemostats += ['EM','CM']\n",
    "s,sc = stoichiometry(Allosteric,chemostats=chemostats)\n",
    "\n",
    "print('Reactions:')\n",
    "disp.Latex(st.sprintrl(s,chemformula=True))\n",
    "sp = st.path(s,sc)\n",
    "print('Pathway reactions:')\n",
    "print(st.sprintp(sc))\n",
    "disp.Latex(st.sprintrl(sp,chemformula=False))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Utility functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plotStep(tf,chemo,spec,T):\n",
    "    \n",
    "    t,y = con.step_response(tf,T=T)\n",
    "    plt.plot(t,y)\n",
    "    plt.grid()\n",
    "    plt.xlabel('t')\n",
    "    plt.ylabel('x_B')\n",
    "    plt.title('Step response from '+chemo+' to '+spec)\n",
    "    plt.show()\n",
    "    \n",
    "def showTF(tf):\n",
    "    ## Show info\n",
    "    print(tf)\n",
    "    in_gain_X = con.dcgain(tf)\n",
    "    print('\\tgain:',fmt.format(in_gain_X))\n",
    "    print('\\tpoles:', con.pole(tf))\n",
    "    print('\\tzeros:', con.zero(tf))\n",
    "    print('\\n')\n",
    "\n",
    "def extractTF(TF,chemo,spec):\n",
    "    \n",
    "    ## Index of product\n",
    "    species = s['species']\n",
    "    i_prod = species.index(spec)\n",
    "    \n",
    "    ## Index of input\n",
    "    i = chemostats.index(chemo)\n",
    "    \n",
    "    ## Extract tf\n",
    "    #print('\\nTransfer function from','x_'+chemo,'to','x_'+spec)\n",
    "    tf = con.minreal(TF[i_prod,i],tol=tol,verbose=True)\n",
    "    \n",
    "    #showTF(tf)\n",
    "    \n",
    "    return tf\n",
    "\n",
    "def extractTFflow(TF,chemo,chemostats,reac):\n",
    "    \n",
    "    ## Index of reaction\n",
    "    reaction = s['reaction']\n",
    "    i_v = reaction.index(reac)\n",
    "    \n",
    "    ## Index of input\n",
    "    i = chemostats.index(chemo)\n",
    "    \n",
    "    ## Extract tf\n",
    "    #print('\\nTransfer function from','x_'+chemo,'to','v_'+reac)\n",
    "    tf = con.minreal(TF[i_v,i],tol=tol,verbose=True)\n",
    "    \n",
    "    #showTF(tf)\n",
    "    \n",
    "    return tf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Closed-loop analysis\n",
    "The function **ClosedLoop** derives the closed-loop properteis of the system from the bond graph model in the following steps:\n",
    "\n",
    "- Extract stoichiometry\n",
    "- Simulate the system to give a steady state\n",
    "- linearise the closed-loop system about this steady state to give:\n",
    "   - the multivariable transfer function relating chemostats to species states\n",
    "   - the multivariable transfer function relating chemostats to reaction flows\n",
    "- extract the scalar transfer functions relating the 'disturbance' $x_{B0}$ to\n",
    "    - the product state $x_P$\n",
    "    - the 'actuator' flow $v_{r2}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ClosedLoop(abg,chemostats,parameter,X0,t_ss,t_step,quiet=False):\n",
    "    ## Analyse the system\n",
    "    \n",
    "    cabg = copy.copy(abg)\n",
    "    \n",
    "    ## Stoichiometry\n",
    "    s,sc = stoichiometry(cabg,chemostats=chemostats)\n",
    "    \n",
    "    print('Closed-loop. Order = ',sc['n_x'])\n",
    "    \n",
    "    ## Steady-state simulation\n",
    "    t = np.linspace(0,t_ss,1000)\n",
    "    ssdat = st.sim(s,sc=sc,t=t,parameter=parameter,X0=X0,quiet=quiet)\n",
    "    #st.plot(s,ssdat,species=['E','C','EM','CM'],reaction = ['r2'])\n",
    "    \n",
    "    ## Use the final value as the steady-state\n",
    "    x_ss = ssdat['X'][-1,:]\n",
    "    v_ss = ssdat['V'][-1,:]\n",
    "    \n",
    "    if not quiet:\n",
    "        print(s['species'])\n",
    "        print('x_ss =', x_ss)  \n",
    "        print(s['reaction'])\n",
    "        print('v_ss = ', v_ss)\n",
    "    \n",
    "    ##Linearise\n",
    "    SysX = st.lin(s,sc,x_ss=x_ss,parameter=parameter,outvar='X',quiet=quiet) \n",
    "    SysV = st.lin(s,sc,x_ss=x_ss,parameter=parameter,outvar='V',quiet=quiet)\n",
    "\n",
    "    ## Multivariable transfer functions\n",
    "    TF = con.ss2tf(SysX)\n",
    "    TFV = con.ss2tf(SysV)\n",
    "\n",
    "    ## Scalar transfer function to x_M\n",
    "    tf_B0 = extractTF(TF,'B0','P')\n",
    "    t,x_B = con.step_response(tf_B0,T=t_step)\n",
    "\n",
    "    return x_ss,v_ss,tf_B0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Loop-gain analysis\n",
    "- The function LoopGain deduces the feedback loop-gain from the (closed-loop) bondgraph.\n",
    "- The product component **Ce:P** is converted into a chemostat. This 'breaks the loop' and enables the open-loop transfer functions relating $x_P$ to the various flows impinging on the corresponding **0** junction to be computed. In this case the relevant flows are:\n",
    "    - $v_{r1}$ - the main feedback path\n",
    "    - $v_{r2}$ - the product flow flow absorbed by  **Ce:B0**\n",
    "    - $5v_{re}$ - the flow transiently absorbed by **Ce:EM**\n",
    "    - $5v_{ce}$ - the flow transiently absorbed by **Ce:CM**\n",
    "- As will be seen, the the main feedback path to $v_{r1}$ is the sum of two transfer functions:\n",
    "    - an *active* path via the allosteric inhibition module\n",
    "    - a *passive* path via the admittance of the reaction chain at the product **Ce:P**\n",
    "    \n",
    "- The function LoopGain follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def LoopGain(abg,chemostats,parameter,x_ss,quiet=False):\n",
    "    \"\"\"Compute the loop gain tf\"\"\"\n",
    "    \n",
    "    ## Add the chemostat for B and recompute stoichiometry\n",
    "    chemostatsL = chemostats+['P']\n",
    "    sL,scL = stoichiometry(copy.copy(abg),chemostats=chemostatsL)\n",
    "    \n",
    "    print('Open-loop. Order = ',scL['n_x'])\n",
    "    ## Linearise using the appropriate steady-state x_ss\n",
    "    SysL = st.lin(sL,scL,x_ss=x_ss,parameter=parameter,outvar='V',quiet=quiet)\n",
    "    \n",
    "    ## The multivariable transfer function\n",
    "    TFL = con.ss2tf(SysL)\n",
    "    \n",
    "    ## Stoichiometry of feedback\n",
    "    N = sL['N'] # Stoichiometric matrix\n",
    "    i_P = sL['species'].index('P')\n",
    "    N_P = N[i_P,:] # Row of N corresponding to B\n",
    "    \n",
    "    ## Indices of reactions impinging on Ce:\n",
    "    j_FB = np.nonzero(N_P)[0][:]\n",
    "    \n",
    "    ## Reactions impinging on B and the transfer functions\n",
    "    reaction = sL['reaction']\n",
    "    R = []\n",
    "    FB = {}\n",
    "    fb = 0\n",
    "    for j in j_FB:\n",
    "        r = reaction[j]\n",
    "        R.append(r)\n",
    "        \n",
    "        ## Transfer function from product P to reaction r\n",
    "        FB_r = extractTFflow(TFL,'P',chemostatsL,r)\n",
    "        FB_r *= -N_P[j]\n",
    "        \n",
    "        ## Extract active and passive components of main feedback TF\n",
    "        if r in [r_last_1]:\n",
    "            #print('Doing',r_last_1)\n",
    "            num = FB_r.num[0][0]\n",
    "            #print('num',num)\n",
    "            den = FB_r.den[0][0]\n",
    "            #print('den',den)\n",
    "            n_num = len(num)\n",
    "            num_act = [num[n_num-1]]\n",
    "            FB['fb_act'] = con.tf(num_act,den)\n",
    "            print('\\nActive feedback from P to',r)\n",
    "            showTF(FB['fb_act'])\n",
    "            num_pas = copy.copy(num)\n",
    "            num_pas[n_num-1] = 0\n",
    "            FB['fb_pas'] = con.tf(num_pas,den)\n",
    "            print('\\nPassive feedback from P to',r)\n",
    "            showTF(FB['fb_pas'])\n",
    "        FB[r] = FB_r\n",
    "        fb = con.parallel(fb,FB[r])\n",
    "        print('\\nFeedback from P to ',r)\n",
    "        showTF(FB[r])\n",
    "    #print('\\nRelevant reactions:', R)\n",
    "    \n",
    "    if N_reac is None:\n",
    "        r_N1 = 'r_2'\n",
    "    else:\n",
    "        r_N1 = 'r_'+str(N_reac-1)\n",
    "    print('\\nGain from B0 to', r_N1)\n",
    "    FF = -extractTFflow(TFL,'B0',chemostatsL,r_N1)\n",
    "    showTF(FF)\n",
    "    \n",
    "    ## Total feedback transfer function \n",
    "    print('\\nNet feedback')\n",
    "    fb = con.minreal(fb,tol=tol,verbose=not quiet)    \n",
    "    showTF(fb)\n",
    "    \n",
    "    ## More tfs into FB\n",
    "    FB['net'] = fb\n",
    "    FB['rec'] = con.parallel(FB['re'],FB['rc'])\n",
    "    \n",
    "    ## Transfer function of CE:P\n",
    "    G = con.tf([1],[1,0])\n",
    "    print(\"\\nForward gain to P\")\n",
    "    showTF(G)\n",
    "    \n",
    "    ## The loop gains: feedbacks from P to r multiplied by G: TF of P\n",
    "    L = {}\n",
    "    for key,tf in FB.items():\n",
    "        L[key] = con.series(G,FB[key])\n",
    "        \n",
    "    ## Compute the closed-loop TF from the open-loop TF\n",
    "    print(\"\\nClosed loop\")\n",
    "    CL = con.minreal(con.feedback(G,sys2=FB['net']),tol=tol,verbose=not quiet)\n",
    "    CL = con.series(CL,FF)\n",
    "    #showTF(CL)\n",
    "    \n",
    "    return CL,L"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Loop gain analysis of Allosteric feedback"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Utility functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plotCL(CL,CLL,t_step):\n",
    "    \n",
    "    t_CL,y_CL = con.step_response(CL,T=t_step)\n",
    "    t_CLL,y_CLL = con.step_response(CLL,T=t_step)\n",
    "    plt.plot(t_CL,y_CL,label='Direct')\n",
    "    plt.plot(t_CLL,y_CLL,label='Computed')\n",
    "    plt.grid()\n",
    "    plt.xlabel('$t$')\n",
    "    plt.ylabel('$x_P$')\n",
    "    plt.legend()\n",
    "    plt.show()\n",
    "    return t_CL,y_CL \n",
    "\n",
    "def plotOL(L):\n",
    "\n",
    "    w = np.logspace(-1,1,200)\n",
    "    #w = None\n",
    "    Legend = []\n",
    "    plt.figure(figsize=(10,10))\n",
    "    print('Bode diagram: loop gain components')\n",
    "    for key,tf in L.items():\n",
    "        if not key in ['re','rc','fb_pas','fb_act']:\n",
    "            mag,phase,ww = con.bode(tf,w,Plot=True)\n",
    "            Legend += [key]\n",
    "    plt.legend(Legend)\n",
    "    plt.title('Loop gain componenents')\n",
    "    plt.show()\n",
    "    \n",
    "\n",
    "    Legend = []\n",
    "    plt.figure(figsize=(10,10))\n",
    "    print('Bode diagram: Passive and active loop-gain components')\n",
    "    for key,tf in L.items():\n",
    "        if key in ['fb_pas','fb_act',r_last_1]:\n",
    "            mag,phase,ww = con.bode(tf,w,Plot=True)\n",
    "            Legend += [key]\n",
    "    plt.legend(Legend)\n",
    "    plt.show()\n",
    "\n",
    "    re,im,ww = con.nyquist(L['net'],Plot=False)\n",
    "    plt.title('Nyquist Diagram')\n",
    "    plt.plot(re,im)\n",
    "    plt.axis('equal')\n",
    "    lim = 2\n",
    "    plt.xlim(-lim,lim)\n",
    "    plt.ylim(-lim,lim)\n",
    "    plt.grid()\n",
    "    theta = np.linspace(0,2*np.pi)\n",
    "    plt.plot(np.sin(theta),np.cos(theta))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Numerical parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "kappa_r_2 = 1\n",
      "X0_A = 1\n",
      "X0_B0 = 1\n",
      "X0_E = 0.01\n",
      "X0_C = 0.01\n"
     ]
    }
   ],
   "source": [
    "## Parameters\n",
    "X0_A = 1\n",
    "K_A = 1\n",
    "K_B = 1\n",
    "K_P = 1\n",
    "K_C = 1\n",
    "K_E = 1\n",
    "K_F = 1000\n",
    "K_G = 1/K_F\n",
    "\n",
    "K_EM = 1\n",
    "K_CM = 1\n",
    "\n",
    "kappa = 1000\n",
    "kappa_r1 = kappa\n",
    "kappa_r2 = kappa\n",
    "\n",
    "## Closed-loop allosteric inhibition\n",
    "## Set kappa_ra = kappa_rc = 0 for feedback inhibition\n",
    "kappa_ra = 1\n",
    "kappa_rc = 1\n",
    "kappa_re = 1\n",
    "\n",
    "K_B0 = K_P\n",
    "X0_B0 = 1\n",
    "#kappa_r3 = 1\n",
    "\n",
    "X0_E = 0.01\n",
    "X0_C = 0.01\n",
    "\n",
    "pars = ['K_A','K_B','K_P','K_C','K_E','K_F','K_G',\n",
    "        'K_EM','K_CM',\n",
    "        'kappa_r1','kappa_r2','kappa_ra','kappa_rc','kappa_re',\n",
    "        'K_B0']\n",
    "parameter = {}\n",
    "for par in pars:\n",
    "    parameter[par] = eval(par)\n",
    "\n",
    "if N_reac is  None:\n",
    "    r_last = 'r_2'\n",
    "    r_last_1 = 'r_1'\n",
    "else:\n",
    "    r_last = 'r_'+str(N_reac-1)\n",
    "\n",
    "    if N_reac>1:\n",
    "        r_last_1 = 'r_'+str(N_reac-2)\n",
    "        kappa_last_1 = 'kappa_'+r_last_1\n",
    "        parameter[kappa_last_1] = 1\n",
    "        print(kappa_last_1,'=', parameter[kappa_last_1])\n",
    "        \n",
    "kappa_last = 'kappa_'+r_last\n",
    "parameter[kappa_last] = 1\n",
    "print(kappa_last,'=', parameter[kappa_last])\n",
    "\n",
    "states = ['A','B0','E','C']\n",
    "X0 = np.ones(s['n_X'])\n",
    "for state in states:\n",
    "    X0_ = 'X0_'+state\n",
    "    val = eval(X0_)\n",
    "    print(X0_,'=',val)\n",
    "    X0[s['species'].index(state)] = val\n",
    "\n",
    "if not quiet:\n",
    "    print('Parameters',parameter)\n",
    "    print(s['species'])\n",
    "    print(X0)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Transfer function analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Closed-loop. Order =  6\n",
      "2 states have been removed from the model\n",
      "Open-loop. Order =  5\n",
      "4 states have been removed from the model\n",
      "\n",
      "Feedback from P to  rc\n",
      "\n",
      "13.45 s - 0.006295\n",
      "------------------\n",
      "    s + 735.1\n",
      "\n",
      "\tgain: -0.000\n",
      "\tpoles: [-735.097]\n",
      "\tzeros: [0.]\n",
      "\n",
      "\n",
      "2 states have been removed from the model\n",
      "\n",
      "Feedback from P to  re\n",
      "\n",
      "0.02689 s^3 + 2.699e+04 s^2 + 2.701e+07 s + 6.469e+06\n",
      "-----------------------------------------------------\n",
      "    s^3 + 1.004e+06 s^2 + 1.743e+09 s + 7.386e+11\n",
      "\n",
      "\tgain: 0.000\n",
      "\tpoles: [-1.003e+06 -1.002e+03 -7.351e+02]\n",
      "\tzeros: [-1.003e+06 -1.002e+03 -2.396e-01]\n",
      "\n",
      "\n",
      "3 states have been removed from the model\n",
      "\n",
      "Active feedback from P to r_1\n",
      "\n",
      "    3.659\n",
      "-------------\n",
      "s^2 + 3 s + 1\n",
      "\n",
      "\tgain: 3.659\n",
      "\tpoles: [-2.618 -0.382]\n",
      "\tzeros: []\n",
      "\n",
      "\n",
      "\n",
      "Passive feedback from P to r_1\n",
      "\n",
      "s^2 + 1.995 s\n",
      "-------------\n",
      "s^2 + 3 s + 1\n",
      "\n",
      "\tgain: 0.000\n",
      "\tpoles: [-2.618 -0.382]\n",
      "\tzeros: [-1.995  0.   ]\n",
      "\n",
      "\n",
      "\n",
      "Feedback from P to  r_1\n",
      "\n",
      "s^2 + 1.995 s + 3.659\n",
      "---------------------\n",
      "    s^2 + 3 s + 1\n",
      "\n",
      "\tgain: 3.659\n",
      "\tpoles: [-2.618 -0.382]\n",
      "\tzeros: [-0.998+1.632j -0.998-1.632j]\n",
      "\n",
      "\n",
      "5 states have been removed from the model\n",
      "\n",
      "Feedback from P to  r_2\n",
      "\n",
      "1\n",
      "-\n",
      "1\n",
      "\n",
      "\tgain: 1.000\n",
      "\tpoles: []\n",
      "\tzeros: []\n",
      "\n",
      "\n",
      "\n",
      "Gain from B0 to r_2\n",
      "5 states have been removed from the model\n",
      "\n",
      "1\n",
      "-\n",
      "1\n",
      "\n",
      "\tgain: 1.000\n",
      "\tpoles: []\n",
      "\tzeros: []\n",
      "\n",
      "\n",
      "\n",
      "Net feedback\n",
      "\n",
      "15.48 s^3 + 1516 s^2 + 3690 s + 3425\n",
      "------------------------------------\n",
      "  s^3 + 738.1 s^2 + 2206 s + 735.1\n",
      "\n",
      "\tgain: 4.659\n",
      "\tpoles: [-7.351e+02 -2.618e+00 -3.820e-01]\n",
      "\tzeros: [-95.462+0.j     -1.237+0.888j  -1.237-0.888j]\n",
      "\n",
      "\n",
      "\n",
      "Forward gain to P\n",
      "\n",
      "1\n",
      "-\n",
      "s\n",
      "\n",
      "\tgain:   inf\n",
      "\tpoles: [0.]\n",
      "\tzeros: []\n",
      "\n",
      "\n",
      "\n",
      "Closed loop\n",
      "Closed-loop: direct\n",
      "\n",
      "     s^3 + 738.1 s^2 + 2206 s + 735.1\n",
      "------------------------------------------\n",
      "s^4 + 753.6 s^3 + 3722 s^2 + 4425 s + 3425\n",
      "\n",
      "\tgain: 0.215\n",
      "\tpoles: [-7.486e+02+0.j    -3.703e+00+0.j    -6.305e-01+0.915j -6.305e-01-0.915j]\n",
      "\tzeros: [-7.351e+02 -2.618e+00 -3.820e-01]\n",
      "\n",
      "\n",
      "Closed-loop: from loop-gain\n",
      "\n",
      "     s^3 + 738.1 s^2 + 2206 s + 735.1\n",
      "------------------------------------------\n",
      "s^4 + 753.6 s^3 + 3722 s^2 + 4425 s + 3425\n",
      "\n",
      "\tgain: 0.215\n",
      "\tpoles: [-7.486e+02+0.j    -3.703e+00+0.j    -6.305e-01+0.915j -6.305e-01-0.915j]\n",
      "\tzeros: [-7.351e+02 -2.618e+00 -3.820e-01]\n",
      "\n",
      "\n",
      "Closed-loop: direct (reduced)\n",
      "\n",
      "  0.9824 s^2 + 2.958 s + 0.9859\n",
      "---------------------------------\n",
      "s^3 + 4.978 s^2 + 5.925 s + 4.594\n",
      "\n",
      "\tgain: 0.215\n",
      "\tpoles: [-3.717+0.j    -0.631+0.915j -0.631-0.915j]\n",
      "\tzeros: [-2.629 -0.382]\n",
      "\n",
      "\n",
      "Closed-loop: from loop-gain (reduced)\n",
      "\n",
      "  0.9824 s^2 + 2.958 s + 0.9859\n",
      "---------------------------------\n",
      "s^3 + 4.978 s^2 + 5.925 s + 4.594\n",
      "\n",
      "\tgain: 0.215\n",
      "\tpoles: [-3.717+0.j    -0.631+0.915j -0.631-0.915j]\n",
      "\tzeros: [-2.629 -0.382]\n",
      "\n",
      "\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "t_step = np.linspace(0,1000,100)\n",
    "t_step = None\n",
    "t_ss = 1e2\n",
    "\n",
    "x_ss,v_ss,CL = ClosedLoop(Allosteric,chemostats,parameter,X0,t_ss,t_step,quiet=quiet)\n",
    "\n",
    "CLL,L = LoopGain(Allosteric,chemostats,parameter,x_ss,quiet=quiet)\n",
    "\n",
    "print('Closed-loop: direct')\n",
    "showTF(CL)\n",
    "print('Closed-loop: from loop-gain')\n",
    "showTF(CLL)\n",
    "\n",
    "## Find reduced-order systems using balanced reduction\n",
    "print('Closed-loop: direct (reduced)')\n",
    "showTF(con.tf(con.balred(con.tf2ss(CL),3)))\n",
    "print('Closed-loop: from loop-gain (reduced)')\n",
    "showTF(con.tf(con.balred(con.tf2ss(CLL),3)))\n",
    "\n",
    "t_CL,y_CL = plotCL(CL,CLL,t_step)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Discussion\n",
    "Transfer function orders are reduced in two ways:\n",
    "\n",
    "- Using con.minreal (minimal realisation) to cancel approximately identical poles and zeros (using tolerance tol). This is used each time a transfer function is extracted.\n",
    "      \n",
    "- Using con.balred (balanced reduction) to give a transfer function of given order.\n",
    "\n",
    "In this case there are four transfer functions relating the product concentration $x_P$ to the  to the four flows\n",
    "which add to drive the product concentration $x_P$ \n",
    "\n",
    "- $v_{r1}$ - the main feedback path. \n",
    "This is $\\dfrac{s^2 + 1.995 s + 3.659}{s^2 + 3 s + 1}$\n",
    "\n",
    "- This is the sum of two transfer functions:\n",
    "    - an *active* path via the allosteric inhibition module: $\\dfrac{3.659}{s^2 + 3 s + 1}$\n",
    "    - a *passive* path via the admittance of the reaction chain at the product **Ce:P**: $\\dfrac{s^2 + 1.995 s}{s^2 + 3 s + 1}$\n",
    "\n",
    "- $v_{r2}$ - the product flow absorbed by  **Ce:B0**. This is the unit transfer function in this case.\n",
    "\n",
    "- $5v_{re}$ and $5v_{ce}$ - the flow transiently absorbed by **Ce:EM** and  **Ce:CM**. With reference to the bode diagram, this is small and can be ignored.\n",
    "\n",
    "The closed-loop transfer function relating the disturbance concentration $x_{B0}$ to product concentration $x_P$ can be derived in two ways: directly, and from the loop gain. When reduced to third order, the closed-loop transfer function is $\\dfrac{0.9824 s^2 + 2.958 s + 0.9859}{s^3 + 4.978 s^2 + 5.925 s + 4.594}$. \n",
    "\n",
    "- This has a real pole at $s = - 3.7$ and a complex pair of poles at $s =  -0.631 \\pm 0.915j$. This gives a stable but oscillatory response.\n",
    "\n",
    "- the steady-state gain is $0.215$. Thus a unit disturbance gives a 21.5% change in product concentration, without feedback this would be 100%.\n",
    "\n",
    "- The step response plot verifies this."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Frequency response analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Bode diagram: loop gain components\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 720x720 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Bode diagram: Passive and active loop-gain components\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 2 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": [
    "plotOL(L)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Phase margins"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Phase margin of loop-gain is 75.95006861540071 at omega = 1.581685736613151\n",
      "Phase margin of fb_act+fb_r_last is 42.172473898898204 at omega = 1.2668858916825174\n"
     ]
    }
   ],
   "source": [
    "gm, pm, wg, wp = con.margin(L['net'])\n",
    "#print('Gain margin',gm)\n",
    "print('Phase margin of loop-gain is',pm,'at omega =',wp)\n",
    "\n",
    "# gm, pm, wg, wp = con.margin(L['fb_act'])\n",
    "# print('Phase margin of fb_act is',pm,'at omega =',wp)\n",
    "\n",
    "gm, pm, wg, wp = con.margin(con.parallel(L['fb_act'],L[r_last]))\n",
    "print('Phase margin of fb_act+fb_r_last is',pm,'at omega =',wp)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Discussion\n",
    "\n",
    "- A control systems discussion is needed here\n",
    "- Active feedback dominates at low fequencies , and passive feedback at high frequencies.\n",
    "- The active feedback reduces the effect of disturbances at low frequencies\n",
    "- The passive feedback has no effect at zero frequency but has a phase advance effect at high frequencies thus improving phase margin and thence stability.\n",
    "- even long reaction chains, which would be destabilised by the active feedback alone, are stabilised by the passive feedback."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compare linear and non-linear responses"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'Linear and normalised non-linear step responses')"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fe1342176d8>]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fe1341647f0>,\n",
       " <matplotlib.lines.Line2D at 0x7fe134164978>]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5,0,'$t$')"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'x_P/amp')"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fe149ecf4e0>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t_max = int(11)\n",
    "t = np.linspace(0,t_max,1000)\n",
    "t_0 = 1\n",
    "\n",
    "\n",
    "AMP = [0.1,1]\n",
    "Legend = ['Linear']\n",
    "for amp in AMP:\n",
    "    ## Chemostat\n",
    "    x_B0 = x_ss[s['species'].index('B0')]\n",
    "    x_chemo = '{0}*(1+{2}*np.heaviside(t-{1},1))'.format(str(x_B0),str(t_0),str(amp))\n",
    "    x_chemo_lin = '{0}*(np.heaviside(t-{1},1))'.format(str(x_B0),str(t_0))\n",
    "    X_chemo = {'B0':x_chemo}\n",
    "    X_chemo_lin = {'B0':x_chemo}\n",
    "\n",
    "    ## Non linear simulation (from steady state)\n",
    "    ndat = st.sim(s,sc=sc,t=t,parameter=parameter,X0=x_ss,X_chemo=X_chemo,quiet=quiet)\n",
    "    i_P = s['species'].index('P')\n",
    "    x_P = ndat['X'][:,i_P] - x_ss[i_P]\n",
    "    if amp is AMP[0]:\n",
    "        X_P = x_P/amp\n",
    "    else:\n",
    "        X_P = np.vstack((X_P,x_P/amp))\n",
    "    Legend.append('non-linear, amp = '+str(amp))\n",
    "                     \n",
    "##Plot\n",
    "plt.title('Linear and normalised non-linear step responses')\n",
    "plt.plot(t_CL,y_CL,linewidth=4,linestyle='--')\n",
    "plt.plot(t-t_0,X_P.T)\n",
    "plt.xlabel('$t$')\n",
    "plt.ylabel('x_P/amp')\n",
    "plt.legend(Legend)\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Discussion\n",
    "\n",
    "The full non-linear simulation verifies that a disturbance step change of \n",
    "\n",
    "- 0.1 gives a close fit\n",
    "\n",
    "- 1.0 gives a reasonable fit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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