Linearisation.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***Note: this is the Linearisation.ipynb notebook. The\n",
    "PDF version \"Linearisation of Biomolecular Systems\"\n",
    "is available [here](Linearisation.pdf).***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Introduction\n",
    "As discussed by <cite data-cite=\"GawCra16\">(Gawthrop and Crampin, 2016)</cite>:\n",
    "\n",
    "\"The bond graph approach gives the set of *nonlinear* ordinary\n",
    "differential equations describing the biomolecular system being modelled.\n",
    "Linearisation of non-linear systems is a standard technique in control\n",
    "engineering: as discussed by \n",
    "<cite data-cite=\"GooGraSal01\">(Goodwin, Graebe and Salgado)</cite>, \n",
    "\"The incentive to\n",
    "try to approximate a nonlinear system by a linear model is that the\n",
    "science and art of linear control is vastly more complete and simpler\n",
    "than they are for the nonlinear case.\". Nevertheless, it is important\n",
    "to realise that conclusions drawn from linearisation can only be\n",
    "verified using the full *nonlinear* equations.\"\n",
    "\n",
    "This notebook tutorial examines the linearisation of bond graph models in the context of biomolecular systems using two simple examples:\n",
    "\n",
    "1. An enzyme-catalysed reaction \n",
    "2. An enzyme-catalysed reaction with product removal\n",
    "\n",
    "As will be seen, the first example is actually linear given the particular choce of chemostats; the second is non-linear the deviation from linearity is examined.\n",
    "\n",
    "Linearisation of a dynamic system $\\dot x = f(x,v)$ is with reference to a steady state defined by constant states $x=x_{ss}$ and constant flows $v=v_{ss}$ such that $f(x_{ss},v_{ss})=0$. In general, determination of steady-states is a difficult problem and can only be determined numerically. Some theoretical results are given by <cite data-cite=\"Gaw18\">(Gawthrop, 2018)</cite>. In this tutorial, steady-states can be determined theoretically."
   ]
  },
  {
   "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",
    "## Control systems package\n",
    "import control as con\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"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Example system: enzyme-catalysed reaction\n",
    "The bond graph representation of the (reversible) enzyme-catalysed reaction is given by\n",
    "<cite data-cite=\"GawCra14\">(Gawthrop and Crampin, 2014)</cite> and is discussed in the tutorial [ECR](ECR.ipynb).\n",
    "\n",
    "The additional species $E0$ represents a reservoir of enzyme coupled to the ECR via the reaction $r0$. \n",
    "$E0$ is used as a chemostat to adjust the total amount of enzyme associated with the ECR."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
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     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sbg.model('eRE_abg.svg')\n",
    "import eRE_abg\n",
    "disp.SVG('eRE_abg.svg')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Stoichiometry & reactions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\begin{align}\n",
       "E0  &\\Leftrightarrow E \\\\\n",
       "A + E  &\\Leftrightarrow C \\\\\n",
       "C  &\\Leftrightarrow B + E \n",
       "\\end{align}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s = st.stoich(eRE_abg.model(),quiet=quiet)\n",
    "disp.Latex(st.sprintrl(s))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Chemostats and pathways\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\begin{align}\n",
       "A  &\\Leftrightarrow B \n",
       "\\end{align}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "chemostats=['A','B','E0']\n",
    "sc = st.statify(s,chemostats=chemostats)\n",
    "sp =st.path(s,sc)\n",
    "disp.Latex(st.sprintrl(sp))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Steady state.\n",
    "In this particular case, the system steady state can be found theoretically assuming constant amounts of A and B\n",
    "<cite data-cite=\"GawCra14\">(Gawthrop and Crampin, 2014)</cite>. Function ssECR does this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x_ss = [2.e+00 1.e+00 6.e-01 4.e-01 4.e+03]\n",
      "v_ss = 0.2\n"
     ]
    }
   ],
   "source": [
    "def ssECR(x_A,x_B,e0=1,\n",
    "             K_A = 1,K_B=1,K_C=1,K_E=1, K_E0 = 1e-3,\n",
    "             kappa_r1 = 1,kappa_r2=1):\n",
    "    \"\"\"Theoretical steady state of Enzyme-catalysed Reactions\n",
    "    \"\"\"\n",
    "    \n",
    "    kappa_bar = (kappa_r1*kappa_r2)/(kappa_r1+kappa_r2)\n",
    "    delta = K_A*x_A - K_B*x_B\n",
    "    sigma = (kappa_r1*K_A*x_A + kappa_r2*K_B*x_B)/(kappa_r1 + kappa_r2)\n",
    "    K_m = K_C/K_E\n",
    "    \n",
    "    v = kappa_bar*e0*K_C*delta/(K_m+sigma)\n",
    "    x_E = e0/(1+(sigma/K_m))\n",
    "    x_C = e0 - x_E\n",
    "    x_E0 = (K_E/K_E0)*x_E\n",
    "    x = np.array([x_A,x_B,x_C,x_E,x_E0])\n",
    "    #x = [x_A,x_B,x_C,x_E,x_E0]\n",
    "    return x,v\n",
    "\n",
    "x_A = 2\n",
    "x_B = 1\n",
    "K_E0 = 1e-4\n",
    "K_C = 1\n",
    "x_ss,v_ss = ssECR(x_A,x_B,K_C=K_C,K_E0=K_E0)\n",
    "print('x_ss =',x_ss)\n",
    "print('v_ss =',v_ss)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Parameters\n",
    "x_E0 = x_ss[4]\n",
    "\n",
    "parameter = {}\n",
    "parameter['K_E0'] = K_E0\n",
    "parameter['K_C'] = K_C"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linearisation\n",
    "The function lin provides the linear transfer function sys in control toolbox format and puts the corresponding state-space matrices $a$, $b$, $c$ and $d$ into the data structure sc where $\\dot{x}=ax + bu$ and $y = cx + du$\n",
    "The system is the *reduced* form <cite data-cite=\"GawCra16\">(Gawthrop and Crampin, 2016)</cite>.\n",
    "The output $y$ corresponds to the flows $V$, the input $u$ to the chemostats $X_{chemo}$ and $x$ to the reduced state.\n",
    "In this case\n",
    "\\begin{align}\n",
    "y = V&= \\begin{pmatrix}\n",
    "    V_{r0}\\\\\n",
    "    V_{r1}\\\\\n",
    "    V_{r2}\\\\\n",
    "\\end{pmatrix}\\\\\n",
    "u= X_{chemo}&= \\begin{pmatrix}\n",
    "    X_{A}\\\\\n",
    "    X_{B}\\\\\n",
    "    X_{E0}\\\\\n",
    "\\end{pmatrix}\\\\\n",
    "x&= \\begin{pmatrix}\n",
    "    X_{C}\\\\\n",
    "    X_{E}\\\\\n",
    "\\end{pmatrix}\n",
    "\\end{align}\n",
    "\n",
    "It also gives the symbolic matrix dv/dx relating incremental flows to incremental states where the states $X$ are:\n",
    "\\begin{align}\n",
    "X&= \\begin{pmatrix}\n",
    "    X_{A}\\\\\n",
    "    X_{B}\\\\\n",
    "    X_{C}\\\\\n",
    "    X_{E}\\\\\n",
    "    X_{E0}\\\\\n",
    "\\end{pmatrix}\n",
    "\\end{align}\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[]\n",
      "[]\n"
     ]
    }
   ],
   "source": [
    "## imp.reload(st)\n",
    "sys = st.lin(s,sc,x_ss=x_ss,parameter=parameter,quiet=quiet)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\begin{align}\n",
       "dvdx &=\n",
       "\\left(\\begin{matrix}0 & 0 & 0 & - K_{E} \\kappa_{r0} & K_{E0} \\kappa_{r0}\\\\K_{A} K_{E} \\kappa_{r1} x_{E} & 0 & - K_{C} \\kappa_{r1} & K_{A} K_{E} \\kappa_{r1} x_{A} & 0\\\\0 & - K_{B} K_{E} \\kappa_{r2} x_{E} & K_{C} \\kappa_{r2} & - K_{B} K_{E} \\kappa_{r2} x_{B} & 0\\end{matrix}\\right)\n",
       "\\end{align}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "disp.Latex(st.sprintl(sc,'dvdx'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\begin{align}\n",
       "a &=\n",
       "\\left(\\begin{matrix}-2.0 & 3.0\\\\2.0 & -4.0\\end{matrix}\\right)\n",
       "\\end{align}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "disp.Latex(st.sprintl(sc,'a'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\begin{align}\n",
       "b &=\n",
       "\\left(\\begin{matrix}0.4 & 0.4 & 0.0\\\\-0.4 & -0.4 & 0.0001\\end{matrix}\\right)\n",
       "\\end{align}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "disp.Latex(st.sprintl(sc,'b'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\begin{align}\n",
       "c &=\n",
       "\\left(\\begin{matrix}0.0 & -1.0\\\\-1.0 & 2.0\\\\1.0 & -1.0\\end{matrix}\\right)\n",
       "\\end{align}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "disp.Latex(st.sprintl(sc,'c'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\begin{align}\n",
       "d &=\n",
       "\\left(\\begin{matrix}0.0 & 0.0 & 0.0001\\\\0.4 & 0.0 & 0.0\\\\0.0 & -0.4 & 0.0\\end{matrix}\\right)\n",
       "\\end{align}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "disp.Latex(st.sprintl(sc,'d'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Pole/zero analysis\n",
    "One advantage of dealing with linear systems is the possibility of using standard control system methods\n",
    "<cite data-cite=\"GooGraSal01\">(Goodwin, Graebe and Salgado)</cite>. One such method is examining the poles and zeros of the system transfer function relating inputs and outputs of interest. In this case, the transfer function relating input $X_{E0}$ to output $V_{r2}$ is examined.\n",
    "\n",
    "NB con.zero requires slycot to be installed; set slycot=False if slycot is not installed.\n",
    "\n",
    "Note that the positive zero ($s=1$) corresponds to the initial negative response of the flow - this is an non-minimum phase system"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "System gain = 0.20\n",
      "System poles =  [-0.35 -5.65]\n",
      "System zeros =  [1.]\n"
     ]
    }
   ],
   "source": [
    "i_E0 = chemostats.index('E0')\n",
    "reaction = sc['reaction']\n",
    "i_r = reaction.index('r2')\n",
    "np.set_printoptions(precision=2)\n",
    "aa = sc['a']\n",
    "bb = np.array([sc['b'][:,i_E0]]).T\n",
    "cc = sc['c'][i_r,:]\n",
    "dd = sc['d'][i_r,i_E0]\n",
    "siso = con.ss(aa,bb,cc,dd)\n",
    "np.set_printoptions(precision=2)\n",
    "gain = x_E0*con.dcgain(siso)\n",
    "print('System gain = {0:.2f}'.format(gain))\n",
    "print('System poles = ',con.pole(siso))\n",
    "if slycot:\n",
    "    ## This needs slycot\n",
    "    print('System zeros = ',np.real(con.zero(siso)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simulation\n",
    "1. As simulation starts at a steady-state value, states and flows remain constant until the chemostat E0 changes at time $t_0=5$.\n",
    "2. For each fixed chemostat value, the non-linear system is actually linear (but with parameters dependent on the steady-state).\n",
    "3. The flow in reaction r2 is the same for both linear and non-linear simulation.\n",
    "4. The flow in reaction r2 increases by the gain=0.2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "NON-LINEAR SIMULATION\n",
      "Setting K_C to 1\n",
      "Setting K_E0 to 0.0001\n"
     ]
    },
    {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LINEAR SIMULATION\n",
      "Setting K_C to 1\n",
      "Setting K_E0 to 0.0001\n",
      "Setting K_C to 1\n",
      "Setting K_E0 to 0.0001\n",
      "[]\n",
      "[]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/peterg/WORK/Research/SystemsBiology/lib/python/stoich.py:109: RuntimeWarning: divide by zero encountered in log\n",
      "  lx_i = np.log(xx_i)\n",
      "/home/peterg/WORK/Research/SystemsBiology/lib/python/stoich.py:1665: RuntimeWarning: invalid value encountered in matmul\n",
      "  Phi = -phi@N\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## imp.reload(st)\n",
    "##Time\n",
    "t_max = int(20)\n",
    "t = np.linspace(0,t_max,1000)\n",
    "t_0 = 5\n",
    "\n",
    "## Chemostat\n",
    "x_chemo =     '{0}*(1+np.heaviside(t-{1},1))'.format(str(x_E0),str(t_0))\n",
    "x_chemo_lin = '{0}*(np.heaviside(t-{1},1))'.format(str(x_E0),str(t_0))\n",
    "\n",
    "## Simulate\n",
    "print('NON-LINEAR SIMULATION')\n",
    "#X0 = x_ss\n",
    "X_chemo = {'E0':x_chemo}\n",
    "ndat = st.sim(s,sc=sc,t=t,parameter=parameter,X0=x_ss,X_chemo=X_chemo,quiet=False)\n",
    "st.plot(s,ndat,species=['A','B','C','E'])\n",
    "\n",
    "print('LINEAR SIMULATION')\n",
    "#X0 = x_ss\n",
    "X_chemo = {'E0':x_chemo_lin}\n",
    "V0 = [0,v_ss,v_ss] # Steady-state flows\n",
    "ldat = st.sim(s,sc=sc,t=t,linear=True,V0=V0,parameter=parameter,X0=x_ss,X_chemo=X_chemo,quiet=False)\n",
    "st.plot(s,ldat,species=['A','B','C','E'])\n",
    "#st.plot(s,ldat,species=[])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Compare linear and nonlinear"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def compare(ndat,ldat,v_ss,gain,i):\n",
    "\n",
    "    v_1_l = ldat['V'][:,i]\n",
    "    v_1_n = ndat['V'][:,i]\n",
    "\n",
    "    ax = plt.gca()  # gca stands for 'get current axis'\n",
    "    plt.plot(t,v_1_l,label='linear')\n",
    "    plt.plot(t,v_1_n,label='non-linear')\n",
    "    xlim = ax.get_xlim()\n",
    "    plt.hlines(v_ss+gain, xlim[1]/2, xlim[1],linestyles='dotted',label='asymptote')\n",
    "    plt.xlabel('$t$')\n",
    "    plt.ylabel('$v$')\n",
    "    plt.legend()\n",
    "    plt.grid\n",
    "    plt.show()\n",
    "    \n",
    "compare(ndat,ldat,v_ss,gain,i_r)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Example system: enzyme-catalysed reaction with product removal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
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       "<text fill=\"#000000\" font-family=\"Helvetica\" font-size=\"216\" font-style=\"normal\" font-weight=\"bold\" text-anchor=\"middle\" x=\"4050\" xml:space=\"preserve\" y=\"990\">Ce:C</text>\n",
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       "<!-- Text -->\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=\"675\" xml:space=\"preserve\" y=\"990\">Ce:A</text>\n",
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       "<IPython.core.display.SVG object>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## imp.reload(st)\n",
    "sbg.model('eREr_abg.svg')\n",
    "import eREr_abg\n",
    "disp.SVG('eREr_abg.svg')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Stoichiometry"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['A', 'B', 'B0', 'C', 'E', 'E0']\n"
     ]
    }
   ],
   "source": [
    "s = st.stoich(eREr_abg.model(),quiet=quiet)\n",
    "print(s['species'])\n",
    "chemostats=['A','B0','E0']\n",
    "disp.Latex(st.sprintrl(s))\n",
    "sc = st.statify(s,chemostats=chemostats)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Parameters\n",
    "# x_E0 = x_ss[4]\n",
    "# x_A = 2\n",
    "# x_B = 1\n",
    "\n",
    "parameter = {}\n",
    "parameter['K_E0'] = K_E0\n",
    "parameter['K_C'] = K_C\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Steady state.\n",
    "As a special case, the amount of B0 is taken to be very small and the parameter $\\kappa_3=v_{ss}$. This gives the same steady states a the previous section."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Steady states for ECR\n",
    "x_ss,v_ss = ssECR(x_A,x_B,K_C=K_C,K_E0=K_E0)\n",
    "\n",
    "## Steady states for this examples\n",
    "X_ss = np.array([x_ss[0],x_ss[1],1e-10,x_ss[2],x_ss[3],x_ss[4]])\n",
    "#print(X_ss)\n",
    "V_ss = np.array([0,v_ss,v_ss,v_ss])\n",
    "#print(V_ss)\n",
    "\n",
    "## Set appropriate  kappa3\n",
    "kappa_r3 = v_ss\n",
    "parameter['kappa_r3'] = kappa_r3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linearisation\n",
    "The function lin provides the linear transfer function sys in control toolbox format and puts the corresponding state-space matrices $a$, $b$, $c$ and $d$ into the data structure sc where $\\dot{x}=ax + bu$ and $y = cx + du$\n",
    "The system is the *reduced* form <cite data-cite=\"GawCra16\">(Gawthrop and Crampin, 2016)</cite>.\n",
    "The output $y$ corresponds to the flows $V$, the input $u$ to the chemostats $X_{chemo}$ and $x$ to the reduced state.\n",
    "In this case\n",
    "\\begin{align}\n",
    "y = V&= \\begin{pmatrix}\n",
    "    V_{r0}\\\\\n",
    "    V_{r1}\\\\\n",
    "    V_{r2}\\\\\n",
    "    V_{r3}\\\\\n",
    "\\end{pmatrix}\\\\\n",
    "U = X_{chemo} &= \\begin{pmatrix}\n",
    "    X_{A}\\\\\n",
    "    X_{B0}\\\\\n",
    "    X_{E0}\\\\\n",
    "\\end{pmatrix}\\\\\n",
    "x&= \\begin{pmatrix}\n",
    "    X_{B}\\\\\n",
    "    X_{C}\\\\\n",
    "    X_{E}\\\\\n",
    "\\end{pmatrix}\n",
    "\\end{align}\n",
    "\n",
    "\n",
    "It also gives the symbolic matrix dv/dx relating incremental flows to incremental states where the states $X$ are:\n",
    "\\begin{align}\n",
    "X&= \\begin{pmatrix}\n",
    "    X_{A}\\\\\n",
    "    X_{B}\\\\\n",
    "    X_{B0}\\\\\n",
    "    X_{C}\\\\\n",
    "    X_{E}\\\\\n",
    "    X_{E0}\\\\\n",
    "\\end{pmatrix}\n",
    "\\end{align}\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Setting K_C to 1\n",
      "Setting K_E0 to 0.0001\n",
      "Setting kappa_r3 to 0.2\n",
      "[]\n",
      "[]\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "\\begin{align}\n",
       "dvdx &=\n",
       "\\left(\\begin{matrix}0 & 0 & 0 & 0 & - K_{E} \\kappa_{r0} & K_{E0} \\kappa_{r0}\\\\K_{A} K_{E} \\kappa_{r1} x_{E} & 0 & 0 & - K_{C} \\kappa_{r1} & K_{A} K_{E} \\kappa_{r1} x_{A} & 0\\\\0 & - K_{B} K_{E} \\kappa_{r2} x_{E} & 0 & K_{C} \\kappa_{r2} & - K_{B} K_{E} \\kappa_{r2} x_{B} & 0\\\\0 & K_{B} \\kappa_{r3} & - K_{B0} \\kappa_{r3} & 0 & 0 & 0\\end{matrix}\\right)\n",
       "\\end{align}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## imp.reload(st)\n",
    "sys = st.lin(s,sc,x_ss=X_ss,parameter=parameter)\n",
    "disp.Latex(st.sprintl(sc,'dvdx'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\begin{align}\n",
       "a &=\n",
       "\\left(\\begin{matrix}-0.6 & 1.0 & -1.0\\\\0.4 & -2.0 & 3.0\\\\-0.4 & 2.0 & -4.0\\end{matrix}\\right)\n",
       "\\end{align}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "disp.Latex(st.sprintl(sc,'a'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\begin{align}\n",
       "b &=\n",
       "\\left(\\begin{matrix}0.0 & 0.2 & 0.0\\\\0.4 & 0.0 & 0.0\\\\-0.4 & 0.0 & 0.0001\\end{matrix}\\right)\n",
       "\\end{align}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "disp.Latex(st.sprintl(sc,'b'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\begin{align}\n",
       "c &=\n",
       "\\left(\\begin{matrix}0.0 & 0.0 & -1.0\\\\0.0 & -1.0 & 2.0\\\\-0.4 & 1.0 & -1.0\\\\0.2 & 0.0 & 0.0\\end{matrix}\\right)\n",
       "\\end{align}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "disp.Latex(st.sprintl(sc,'c'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\begin{align}\n",
       "d &=\n",
       "\\left(\\begin{matrix}0.0 & 0.0 & 0.0001\\\\0.4 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0\\\\0.0 & -0.2 & 0.0\\end{matrix}\\right)\n",
       "\\end{align}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "disp.Latex(st.sprintl(sc,'d'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Pole/zero analysis\n",
    "One advantage of dealing with linear systems is the possibility of using standard control system methods\n",
    "<cite data-cite=\"GooGraSal01\">(Goodwin, Graebe and Salgado)</cite>. One such method is examining the poles and zeros of the system transfer function relating inputs and outputs of interest. In this case, the transfer function relating input $X_{E0}$ to output $V_{r2}$ is examined.\n",
    "\n",
    "\n",
    "NB con.zero requires slycot to be installed; set slycot=False if slycot is not installed.\n",
    "\n",
    "Note that the positive zero ($s=1$) corresponds to the initial negative response of the flow - this is an non-minimum phase system."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "System gain = 0.10\n",
      "System poles =  [-5.8  -0.56 -0.25]\n",
      "System zeros =  [1.]\n"
     ]
    }
   ],
   "source": [
    "i_E0 = chemostats.index('E0')\n",
    "reaction = sc['reaction']\n",
    "i_r = reaction.index('r3')\n",
    "np.set_printoptions(precision=2)\n",
    "aa = sc['a']\n",
    "bb = np.array([sc['b'][:,i_E0]]).T\n",
    "cc = sc['c'][i_r,:]\n",
    "dd = sc['d'][i_r,i_E0]\n",
    "siso = con.ss(aa,bb,cc,dd)\n",
    "np.set_printoptions(precision=2)\n",
    "gain = x_E0*con.dcgain(siso)\n",
    "print('System gain = {0:.2f}'.format(gain))\n",
    "print('System poles = ',con.pole(siso))\n",
    "if slycot:\n",
    "    ## This needs slycot\n",
    "    print('System zeros = ',np.real(con.zero(siso)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simulation\n",
    "1. As simulation starts at a steady-state value, states and flows remain constant until the chemostat E0 changes at time $t_0=5$.\n",
    "2. For each fixed chemostat value, the non-linear system leads to an approximate linear system (but with parameters dependent on the steady-state).\n",
    "3. The flow in reaction r2 is the different for linear and non-linear simulation, but the difference is smaller for smaller step changes in $x_{E0}$.\n",
    "4. In the linear case, the flow in reaction r2 increases by gain=0.1 multiplied by the step.\n",
    "5. In both linear and non-linear cases, the flow in reaction r1 is zero in the steady-state. Thus flow from the input source E0 is transient; in other words *retroactivity* is zero in the steady state."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "NON-LINEAR SIMULATION: Step = 1\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LINEAR SIMULATION: Step = 1\n",
      "[]\n",
      "[]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/peterg/WORK/Research/SystemsBiology/lib/python/stoich.py:109: RuntimeWarning: divide by zero encountered in log\n",
      "  lx_i = np.log(xx_i)\n",
      "/home/peterg/WORK/Research/SystemsBiology/lib/python/stoich.py:1665: RuntimeWarning: invalid value encountered in matmul\n",
      "  Phi = -phi@N\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "COMPARE LINEAR & NONLINEAR: Step = 1\n"
     ]
    },
    {
     "data": {
      "image/png": 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KsCHKzXmpCeu4qLiE575w73bq374RL97Yhwsa1nO6LGP8gg1RbgzuGw/d9/46Vmw/yK2D2/G/13QnONA2qI05VxYWptZKOZzLrTNXkXokl+cm9OSG/m2dLsmYGsvCwtRKG/dmcdvbqykqKeH9OwcR2772ngJsTHWwsDC1zrfbD/Lb2WuoHxbEB1MG06m5DR9uzPmysDC1yldb0rh79lo6NI3gnd8MoGUDuxGRMVXBwsLUGks3p3H3e2vo1qo+7/5mIA3C7WpsY6qKnRZSB/z1r3/12iczM5NXX321GqrxjSVlg+J2CwpjqpqFRR1Q28Ni+bYM7nlvDd1PBEU9CwpjqpqFRTX4xS9+Qb9+/ejRowdvvPEGxcXF3HbbbcTExNCzZ0/+9re/kZycTN++fUuX2b59e2m7ffv2PPzww/Tu3ZvY2FjWrl3LqFGj6NixY+mV2MuWLeOKK67g6quvpmvXrvz2t7+lpKSEadOmkZeXR+/evbnpppsAeOGFF4iJiSEmJqZ0pNtp06aRnJxM7969eeihhwCYMWMG/fv3p1evXjzxxBPVucoqLCElk7tnr6FT8yj+bUFhjO+oaq149OvXT8vbvHnzKe0hQ4bo22+/raqqBQUFOmTIEH333XdVVTUnJ0eHDBmiH3zwgaqqZmZm6pAhQ/Tjjz9WVdWMjAwdMmSILliwQFVV9+/f/7PPO5NDhw6pqmpubq726NFD4+Pjdfjw4aXzjxw5oqqqLpdL161bp6qqDz/8sL700kuqqtquXTt99dVXVVX1gQce0J49e+rRo0c1PT1dmzdvrqqqcXFxGhoaqsnJyVpUVKTDhw/Xjz76SFVVIyIiSj8rPj5eY2JiNDs7W48dO6bdu3fXtWvX6s6dO7VHjx6l/RYvXqx33nmnlpSUaHFxsV599dW6fPlyr+u4OiWnH9M+T32plz33laZl5TlWhzE1GRCvFfiO9emWhYiMFpFEEUkSkWmnmf+giGwWkZ9E5CsRaVdm3nQR2SQiW0TkJanB97J86aWXSm9GlJKSQkFBATt27OC+++7jiy++oH599w127rjjDt5++22Ki4v58MMP+dWvflX6HmPHjgWgZ8+eDBw4kKioKJo1a0ZoaGjpKLYDBgzgwgsvJDAwkEmTJvHtt9/+rJZvv/2W8ePHExERQWRkJNddd91pb7D05Zdf8uWXX9KnTx/69u3L1q1b2b59uy9WT6WkHz3OrTNXIcC/fzOQ5vXtrCdjfMlnZ0OJSCDwCjACSAVWi8gCVS17s+h1QKyq5orI3cB04AYRuQS4FOjl6fctMARYdj41LVt2cvHg4OBT2uHh4ae0GzRocEq7adOmp7RbtmxZ4c9cunQpP/zwA+Hh4bhcLvLz81m/fj2LFy/mtddeY86cOcycOZMJEybw5JNPMmzYMPr160eTJidHQz0xbHlAQMApQ54HBASUDgBYPk/PJ19VlYcffpi77rqr0u/hK8cLi7nz3TUczinggymD6NC0dg6lbow/8eWWxQAgSVV3qGoB8AEwrmwHVY1T1VxPcyUQfWIWEAaEAKFAMJDmw1p9Jisri0aNGhEeHs7WrVtZuXIlBw8epKSkhAkTJvD000+zdu1aAMLCwhg1ahR33303v/71r8/5s1atWsXOnTspKSnhww8/5LLLLgPcwXjipkaXX345n3zyCbm5ueTk5DB//nwuv/xyoqKiOHbsWOl7jRo1ipkzZ5KdnQ3A3r17SU9PP9/Vcd5UlUfmbWB9SiYvXN+bXtENnS7JmDrBl9dZtAZSyrRTgYFn6X878DmAqv4gInHAfkCAf6jqFl8V6kujR4/mtddeo1u3bnTt2pVBgwaxd+9eXC4XJSUlAPzf//1faf+bbrqJ+fPnM3LkyHP+rP79+zN16lSSkpIYOnQo48ePB2DKlCn06tWLvn378t5773HbbbcxYMAAwL3rq0+fPgBceumlxMTEMGbMGGbMmMGWLVsYPHgw4L639+zZs2nevPl5rY/z9eaKHcxbt5cHR3RhdEzFtu6MMVWgIgc2KvMAJgJvlWnfgvtL/3R9b8a9ZRHqaXcC/gtEeh4/AJefZrkpQDwQ37Zt258duHHy4GtlzZgxQx977LFzXi4uLk6vvvpqH1R0dtW5juO2pmn7aZ/pPbPXaElJSbV9rjG1GRU8wO3LLYu9QJsy7WjPtFOIyHDgUWCIquZ7Jo8HVqpqtqfP58Bg4JQjsar6BvAGuO9nUdX/gOo2fvx4kpOT+frrr50uxe/sy8zjgQ8T6Noiihm/7HVex2OMMefOl8csVgOdRaSDiIQANwILynYQkT7A68BYVS27Q3wPMEREgkQkGPfB7Rq5G+pczJ8/n59++ommTZue87Iul4vPPvvMB1U5r7C4hN+9v47CohL+eXM/wkNslBpjqpvPwkJVi4CpwGLcX/RzVHWTiDwlImM93Wbg3s30kYgkiMiJMJkLJAMbgPXAelVdWMk6zuefYc6iutbtC0u2Eb/7CH+9rqed+WSMQ3z6J5qqLgIWlZv2eJnXw8+wXDFw3udshoWFcejQIZo0aWK7LaqYqnLo0CHCwnx7fcM32zL457JkbuzfhnG9W/v0s4wxZ1art+ejo6NJTU0lIyPD6VJqpbCwMKKjo713rKSs3EIemruezs0jeeLaHj77HGOMd7U6LIKDg+nQoYPTZZhKemLBRg5lF/DWrf2pFxLodDnG1Gk2kKDxS59v2M8nCfuYOqwTPaMbOF2OMXWehYXxOwez83n0k430bN2Ae4d2crocYwwWFsYPPbVwM9nHi3jh+osJDrQfUWP8gf0mGr+yfFsGC9bv456hHencIsrpcowxHhYWxm/kFRTz2CcbuLBpBHe7OjpdjjGmjFp9NpSpWV7+ejsph/N4/85BhAbZ2U/G+BPbsjB+YXvaMd74ZgcT+0UzuGMT7wsYY6qVhYVxnKry1GebCQ8J5JGrujldjjHmNCwsjOO+3prOiu0HeWB4FxpHhDhdjjHmNCwsjKMKikp45r9buLBZBLcMbud9AWOMIywsjKP+/cMudhzM4X+v7m7XVBjjx+y30zjmSE4BL361nSFdmjH0Imdv12qMOTsLC+OYV5clkZNfxKNX20FtY/ydhYVxxP6sPN75YTfX9Y2mi12pbYzfs7Awjnjpq+2oKvdf2dnpUowxFWBhYardzoM5zIlP5aaB7WjTONzpcowxFWBhYardC0u2ERIYYMOPG1OD2NhQplolHjjGwvX7uHdoR5pFhTpdjqluqlBSDCVFgIKWeB5lXsMZpp+uv57lfcpO5+R7oydrqZZ22Wnl2+WWuaAvRDY78/pzkIWFqVb/iEsiIiSQOy+/0OlSaqeSEijKg4JcKMxxPxfknHxdmAtF+VCcD0UF5Z7zobjg5HPZ10X57i/4nz1KyrWLQYtPbZd91mKn15B/u2kudB7hdBWnZWFhqk1yRjaf/bSPu67oSMNwG9bjtEpKIO8I5GRA7kE4ngV5me7n0ke5dv7Rk0FQmFv5zw4MhaBQCAw5/XNAMAQGQ3A9CAgCCYSAQPfr0sdppklAuT5BEBDgni4BgJx8LWVewxmmn66/nOV9yvXh5NPJtvi2XaFlgMb+OzS/hYWpNv9clkxoUAB3XN7B6VKqX0kxZKdBVurJx7EDkJPuDoacgyefz/bXd2h9CGvgeTSEhm0hNAqCwyEk4uRz6etwCI7wPHvmBYWWCYZg9+vA4DJfXsb8nIWFqRYph3OZv24vtw5uR9PIWnqsIj8bDifDoSQ4lOx+ZO72BMN+z376MoIj3PunI5q5v/Rb93O/jmgGEU3dj7CG7mCo19AdFAF2nw/jDAsLUy3+uTyZQBHuusJ/N7MrrPA4ZGyBAxshbSOkbYKD2yH7wKn96kdDo3bQ7hJoEA31W0ODNtCgtbsd1sCZ+o2pBAsL43Ppx44zNz6VibHRtGwQ5nQ556a4CNI3QcoqSF0N+9e7g+HErqLgCGjeDTpdCU06QpNO7v3OjS907/oxppawsDA+9+4PuyksKWFKTTgDqijfHQw7l0PKj5C6xn0mEUBkS7igD3S7FlrEQMue0KiD+2CtMbWchYXxqbyCYmav3M2Ibi1o3zTC6XJOL2MbJC2B5DjY/Z37jCIJhJYx0OcmaDMQ2gxw70Kyg8CmjrKwMD41b10qR3ILucOftipUYX8CbFnofhzc5p7epBP0vgk6DoX2l9kxBWPK8GlYiMho4EUgEHhLVZ8tN/9B4A6gCMgAfqOquz3z2gJvAW1wX954laru8mW9pmqVlCj/WrGTXtEN6N++kdPlwMEkWP8f+OkjyNrj3npofykMmAJdRrnPSDLGnJbPwkJEAoFXgBFAKrBaRBao6uYy3dYBsaqaKyJ3A9OBGzzz/g08o6pLRCQSKMHUKHGJ6ew4mMOLN/ZGnNp9k58NGz6ChP9A6ir3xVkdh4FrGnQdA+GNnanLmBrGl1sWA4AkVd0BICIfAOOA0rBQ1bgy/VcCN3v6dgeCVHWJp1+2D+s0PvLWip20ahDGVT1bVf+HH94Jq9+Cte9CfhY0uwiGPwm9boD6DtRjTA3ny7BoDaSUaacCA8/S/3bgc8/rLkCmiMwDOgBLgWmqNrBMTbF531F+2HGIaWMuqt57a+9bB988D1v/696K6D4OBv7WfYDaDk4bU2l+cYBbRG4GYoEhnklBwOVAH2AP8CFwG/CvcstNAaYAtG1r+5v9yewfdxMaFMCN/dtUzwfuXQvLn4NtX7gPTF/+IMTe7r4Azhhz3nwZFntxH5w+Idoz7RQiMhx4FBiiqvmeyalAQpldWJ8AgygXFqr6BvAGQGxsbNnxgI2Djh0v5JN1e7n24gt8P2DgwSRY8r+QuMg9NMbQx2DgFDuTyZgq5suwWA10FpEOuEPiRuBXZTuISB/gdWC0qqaXW7ahiDRT1QxgGBDvw1pNFfpk3V5yC4q5eVA7331I3hFYPgNWvQ5B9WDYYzDgLgir77vPNKYO81lYqGqRiEwFFuM+dXamqm4SkaeAeFVdAMwAIoGPPGfL7FHVsapaLCL/A3wl7hlrgDd9VaupOqrK7JV7iGldn4ujffDXvSqsfx8WP+oOjL63uoMisnnVf5YxppRPj1mo6iJgUblpj5d5Pfwsyy4BevmuOuML8buPkJh2jGev61n1p8se2Q2fPQDJX0ObQXDVDGhlPyLGVAe/OMBtao/ZK3cTFRbE2N4XVN2bqsKat2HxY+4zmq563n3w2sZkMqbaWFiYKnMoO5/PNxzgVwPbEh5SRT9auYdh4e/cw3J0HAbXvgQNq+kMK2NMKQsLU2U+XptKQXEJNw2sotOY9/wIc3/jvsPcyKdh0L22NWGMQywsTJVQVebEp9K3bUM6t4g6/zdc8w789w/umwTd/iW07nv+72mMqTT7M81UiYSUTJLSs7k+9jx3ERUXwaI/unc9dbgcpsRZUBjjB2zLwlSJj9akEhYcwNW9zmPcpfxj8OEtsCMOBk91j+UUaD+ixvgD+0005+14YTEL1+/jqphWRIUFV+5Ncg7BexPdty0d+w/oe0vVFmmMOS8WFua8Ld50gGPHi5gYG125N8hMgXfHQ1YK3Piee+hwY4xfsbAw5+2j+FSiG9VjUIcm575wZgrMugryMuGW+dDukqov0Bhz3uwAtzkvqUdy+S75IBP7RRMQcI5XbB/dB+9cC3lZMHmBBYUxfsy2LMx5mbfWPZDwxH7nuAvqWJo7KHIOwq2fwAV9fFCdMaaqWFiYSlNVPknYy8AOjYluFF7xBY8fhdkT4Oh+uPljiI71XZHGmCphu6FMpW3ce5QdGTn8ovc53GCouBDm3AoZW+CGd6HdYN8VaIypMrZlYSrt04S9BAcKY2IqeG2FKiy8330dxbhXoNOVvi3QGFNlbMvCVEpxibLwp324ujanQXgFr61Y8TwkvAdDpkGfm31boDGmSllYmEr5ccch0o7mM66iQ5FvXwJfPwM9rwfXNN8WZ4ypcl7DQkS+E5Gh1VGMqTk+TdhHREggV17Uwnvnwzvh49uhRQxc+6L7nhTGmBqlIlsWdwFTReQrEbGjkYb8omIWbdzPqJiW1AsJPHvnglz3eE/gPqAdcg5nTRlj/IbXA9yquhGYICJ9gac8t8p8VFXX+7o445+kIgmnAAAS+ElEQVSWJWZw7HgR4ypyFtQX0yBtI9z0ETTu4PvijDE+cS7HLJKAvwB7gTW+KcfUBAsS9tEkIoRLO3oZ3mPLQlj7Dlz2AHQeUT3FGWN8wuuWhYjEAZ2BPGCz53Gbb8sy/iq3oIivtqYxsV80QYFn+Vvj6H5YcB+06g2uR6qvQGOMT1TkOos/AFtUNc/XxRj/tywxg+OFJVzV8yzXVpSUwCd3Q1E+THgLgkKqr0BjjE9U5JjF2uooxNQMizbsp0lECAPaNz5zp/h/uS+8u+bv0LRz9RVnjPEZu87CVNjxwmK+3prOqJiWZ94FlZUKS/8MHa+EfrdVZ3nGGB+ysDAVtnxbBrkFxVx1puE9VOG/fwAtgWv+ZtdTGFOLWFiYCvt8w34ahQcz8MIz7ILaNA+2fQHDHoNG7aq3OGOMT1lYmAo5XljM0i3pjOzekuDT7YLKPQyf/8l9X4qBv63+Ao0xPmWjzpoK+Xb7QbLzixjTs+XpOyz7P8g9BDfPgwAvV3UbY2oc27IwFbJo437qhwVxScemP5+ZthlW/wtifwOtelV/ccYYn/NpWIjIaBFJFJEkEfnZUKMi8qCIbBaRnzxjT7UrN7++iKSKyD98Wac5u4KiEpZsTmNkj5aEBJX7kVF1D+kRGgVDH3WmQGOMz/ksLEQkEHgFGAN0ByaJSPdy3dYBsaraC5gLTC83/y/AN76q0VTM98kHOXa8iDExp9kFlbgIdi6HoY9A+FmuvTDG1Gi+3LIYACSp6g5VLQA+AMaV7aCqcaqa62muBKJPzBORfkAL4Esf1mgqYMnmNMJDArm0U7ldUEX5sPhRaHaRexeUMabW8mVYtAZSyrRTPdPO5HbgcwARCQD+H/A/PqvOVEhJibJ0SxpXdG5GWHC5A9drZsGRnTDyGQis4N3yjDE1kl+cDSUiNwOxwBDPpHuARaqaKme5sEtEpgBTANq2bevrMuukjfuySDuaz4ju5W5ylJ8N38yA9pfbvbSNqQN8GRZ7gTZl2tGeaacQkeHAo8AQVc33TB4MXC4i9wCRQIiIZKvqKQfJVfUN4A2A2NhYrfp/glmyOY3AAGHYRc1PnfHja5CTATf+x67UNqYO8GVYrAY6i0gH3CFxI/Crsh1EpA/wOjBaVdNPTFfVm8r0uQ33QXC7cbMDlmxOI7ZdIxpFlBk5Nu8IfPcSdBkDbQY4V5wxptr47JiFqhYBU4HFwBZgjqpuEpGnRGSsp9sM3FsOH4lIgogs8FU95tylHM5l64FjP98F9d1LkH/UPayHMaZO8OkxC1VdBCwqN+3xMq+HV+A9ZgGzqro2492SzWkAp4ZFdoZ7F1TPidAyxqHKjDHVza7gNme0ZHMaXVpE0q5JxMmJP/4TCvNgyJ+cK8wYU+0sLMxpZeYWsGrX4VO3KvIyYdWb0H2c3dTImDrGwsKcVlxiOsUlyvBuZcJi9VvuYxWXP+hcYcYYR1hYmNNaujmd5lGhXBzd0D2hIBdWvgqdR0Kri50tzhhT7SwszM/kFxWzLDGdK7u1ICDAcw3F2nfcQ5Bf/gdnizPGOMLCwvzMyh2HySkoZkR3z4V4xYXw/cvQ7lJoO8jZ4owxjrCwMD8TtzWdsOCAk/eu2PwpHN0Ll97vbGHGGMdYWJifWZaYzuALm7gHDlSFH16BJp2g0winSzPGOMTCwpxi58Ecdh3KZeiJsaBSV8O+te77agfYj4sxdZX99ptTLEt0D9Hl6uIJi5WvQlgDuHiSg1UZY5xmYWFOEZeYwYXNImjbJBwyU2DzAug7GUIjnS7NGOMgCwtTKq+gmJU7DjG0q2erYvWb7ucBU5wryhjjFywsTKkfdhykoKgEV9dm7vGf1rwD3a6Bhm28L2yMqdUsLEypuK0Z1AsOZECHxu7TZY9nQuztTpdljPEDFhYGAFUlLjGdSzs1ITQoEOLfhsYdocMVTpdmjPEDFhYGgOSMHFKP5OHq2hzSt0DKSuh3m90y1RgDWFgYj9JTZrs2c29VBIZA75u8LGWMqSssLAwAyxIz6Nw8kugIYP0H7ntWRDRxuixjjJ+wsDDk5Bexaudh91Xbm+ZDfhb0+7XTZRlj/IiFheH75EMUFJfg6tIM4mdC067Q7hKnyzLG+BELC0NcYjoRIYH0j0iDvfHQb7Id2DbGnMLCoo5TVZYnZnBpp6YEb3gfAoKg1w1Ol2WM8TMWFnXc9vRs9mbmMaxLY/hpDnQeBRFNnS7LGONnLCzquBOnzI4M2wzZadDbRpc1xvychUUdF7c1g4taRtF4+1yo19i9ZWGMMeVYWNRhx44XsnrXYUZ1DIOti6DnLyEoxOmyjDF+yMKiDvsu6RBFJcq44B+hON92QRljzsjCog5blphOVGgQ7VM/hebdoVVvp0syxvgpC4s6SlVZlpjBhPa5BKSudt821a6tMMacgU/DQkRGi0iiiCSJyLTTzH9QRDaLyE8i8pWItPNM7y0iP4jIJs88O/G/im09cIwDR49zffD3IAHQ63qnSzLG+DGfhYWIBAKvAGOA7sAkEelerts6IFZVewFzgeme6bnAraraAxgN/F1EGvqq1rooLjEdULpkLIYLXRDV0uGKjDH+zJdbFgOAJFXdoaoFwAfAuLIdVDVOVXM9zZVAtGf6NlXd7nm9D0gHmvmw1jpnWWIG45qlEZS1G2ImOF2OMcbP+TIsWgMpZdqpnmlncjvwefmJIjIACAGSq7S6Oiwrr5A1u49wS+Rq930rLrrG6ZKMMX4uyOkCAETkZiAWGFJueivgXWCyqpacZrkpwBSAtm3bVkOltcN3SQcpKSmmV9bX0GkE1LM9fMaYs/PllsVeoE2ZdrRn2ilEZDjwKDBWVfPLTK8P/Bd4VFVXnu4DVPUNVY1V1dhmzWwvVUXFbU3HFZZESG4a9LRdUMYY73wZFquBziLSQURCgBuBBWU7iEgf4HXcQZFeZnoIMB/4t6rO9WGNdY6qsmxbBr9psBaCw6HLaKdLMsbUAD4LC1UtAqYCi4EtwBxV3SQiT4nIWE+3GUAk8JGIJIjIiTC5HrgCuM0zPUFE7IqxKrBp31GOHMthQO430HUMhEQ4XZIxpgbw6TELVV0ELCo37fEyr4efYbnZwGxf1lZXxW1N59KATYQWZkLMRKfLMcbUEHYFdx0Tl5jO5Kh4CGsAna50uhxjTA1hYVGHHM4pYFNKOpcWrYRu10JQqNMlGWNqCAuLOmTF9gxcsp7Q4hy7EM8Yc04sLOqQuK3pTAxdiUY0g/ZXOF2OMaYGsbCoI4pLlNWJexjCWqT7LyDQL67HNMbUEBYWdURCSiax+SsJ0XzbBWWMOWcWFnXEssR0xgb+QElUa2gz0OlyjDE1jIVFHbF6SzJDAjcQ0PM6CLD/dmPMubFvjTog/ehx2qV/TRBFtgvKGFMpFhZ1wLJtGYwN+J78Bh3sPtvGmEqxsKgD1m7awuDAzYRcPNHus22MqRQLi1qusLiEBjv+SwCK2FhQxphKsrCo5VbtPMxI/Y5jDbpC84ucLscYU0NZWNRyq9cl0C9gO2F9bnC6FGNMDWZhUYupKqFb5wMQfLHtgjLGVJ6FRS22ad9RXIXfcLDhxdCondPlGGNqMAuLWmxN/A90C9hDWN/rnS7FGFPDWVjUYsFb5lNMAJF9ful0KcaYGs7CopZKPZzD4Nw49jeKhagWTpdjjKnhLCxqqXUr4+gQkEZoH9sFZYw5fxYWtVTApo8pJIhm/e0sKGPM+bOwqIXSs3Lom72MPY0GQ71GTpdjjKkFLCxqofUrFtJKDlMv9ldOl2KMqSUsLGqhsI0fcIwILhhwndOlGGNqCQuLWiY9I53YvO/Y2XIMBIc5XY4xppawsKhltn39LvWkgEaXTna6FGNMLWJhUcs0SZrL7oA2tIm53OlSjDG1iIVFLbJ723q6FW7mQIfxdpMjY0yVsrCoRfbHvU6RBtBx+O1Ol2KMqWV8GhYiMlpEEkUkSUSmnWb+gyKyWUR+EpGvRKRdmXmTRWS752E74L0oOp5Nt/2fkhBxGU1btXe6HGNMLeOzsBCRQOAVYAzQHZgkIt3LdVsHxKpqL2AuMN2zbGPgCWAgMAB4QkTs6rKz2P71OzQgm5LYO5wuxRhTC/lyy2IAkKSqO1S1APgAGFe2g6rGqWqup7kSiPa8HgUsUdXDqnoEWAKM9mGtNZsq9RLeJpk29L78GqerMcbUQkE+fO/WQEqZdiruLYUzuR34/CzLtq7S6jyOZOwn6B99Tp1YpceG5TSvvNsdeTEX3TePwNBwr333JnxJ+4LtfN1xGh2DAytRozHGnJ0vw6LCRORmIBYYco7LTQGmALRt27ZSnx0SVo8NLcaecb6ebWE9de7Z+v5snp6lmX+Uy459wYb3/kjP3/zjbBUAcPyr6aRrQ3pefbfXvsYYUxm+DIu9QJsy7WjPtFOIyHDgUWCIquaXWdZVbtll5ZdV1TeANwBiY2PP+r1+JhFRDRl0zxuVWdRnVJXlz9/AoD0fkJPxEBHNznxL1CPbvqdjdjwLW97NtY0bVmOVxpi6xJfHLFYDnUWkg4iEADcCC8p2EJE+wOvAWFVNLzNrMTBSRBp5DmyP9EyrE0SEplc/jmgJu+Y9ceaOqmQteIRDGkXPcQ9WX4HGmDrHZ2GhqkXAVNxf8luAOaq6SUSeEpET+31mAJHARyKSICILPMseBv6CO3BWA095ptUZPbrH8E39a+m6/1OOpmw+bZ+MVXNpn72OZRdMof0Fzau5QmNMXSKqldp743diY2M1Pj7e6TKq1LYdO7jgncGkNhrARQ8sPGWeZmeQ9cIA0osjiXrge1o1inKoSmNMTSYia1Q11ls/u4Lbj3W58EK+bXUrF2V+Q8ryd07OKCpg38ybqVd8jC2Dn7egMMb4nIWFnxtw05Osl4toEfcg6XGvUbJnFQdevYrWh1fyfrPfce3IkU6XaIypAyws/FzjqHCCbp7DRjrTfPmfCJg5gshDG3ij8f/wyzsfISDABgw0xvieX1xnYc6uR8d2HHjga9778lMKjmbQsucwbu/fg0ALCmNMNbGwqCFaNgznpusnOV2GMaaOst1QxhhjvLKwMMYY45WFhTHGGK8sLIwxxnhlYWGMMcYrCwtjjDFeWVgYY4zxysLCGGOMV7Vm1FkRyQB2n8dbNAUOVlE5tZGtH+9sHZ2drR/vnFhH7VS1mbdOtSYszpeIxFdkmN66ytaPd7aOzs7Wj3f+vI5sN5QxxhivLCyMMcZ4ZWFx0htOF+DnbP14Z+vo7Gz9eOe368iOWRhjjPHKtiyMMcZ4VefDQkRGi0iiiCSJyDSn6/EHIjJTRNJFZGOZaY1FZImIbPc8N3KyRieJSBsRiRORzSKySUTu90y3deQhImEiskpE1nvW0ZOe6R1E5EfP79uHIhLidK1OEpFAEVknIp952n67fup0WIhIIPAKMAboDkwSke7OVuUXZgGjy02bBnylqp2BrzztuqoI+IOqdgcGAfd6fm5sHZ2UDwxT1YuB3sBoERkEPAf8TVU7AUeA2x2s0R/cD2wp0/bb9VOnwwIYACSp6g5VLQA+AMY5XJPjVPUb4HC5yeOAdzyv3wF+Ua1F+RFV3a+qaz2vj+H+ZW+NraNS6pbtaQZ7HgoMA+Z6ptfpdSQi0cDVwFuetuDH66euh0VrIKVMO9UzzfxcC1Xd73l9AGjhZDH+QkTaA32AH7F1dArPLpYEIB1YAiQDmapa5OlS13/f/g78ESjxtJvgx+unroeFqQR1n0JX50+jE5FI4GPgAVU9WnaerSNQ1WJV7Q1E496Kv8jhkvyGiFwDpKvqGqdrqaggpwtw2F6gTZl2tGea+bk0EWmlqvtFpBXuvxbrLBEJxh0U76nqPM9kW0enoaqZIhIHDAYaikiQ56/nuvz7dikwVkSuAsKA+sCL+PH6qetbFquBzp4zEEKAG4EFDtfkrxYAkz2vJwOfOliLozz7lv8FbFHVF8rMsnXkISLNRKSh53U9YATuYztxwERPtzq7jlT1YVWNVtX2uL93vlbVm/Dj9VPnL8rzJPvfgUBgpqo+43BJjhOR9wEX7hEw04AngE+AOUBb3KP7Xq+q5Q+C1wkichmwAtjAyf3Nj+A+bmHrCBCRXrgP0Abi/qN0jqo+JSIX4j6RpDGwDrhZVfOdq9R5IuIC/kdVr/Hn9VPnw8IYY4x3dX03lDHGmAqwsDDGGOOVhYUxxhivLCyMMcZ4ZWFhjDHGKwsLY4wxXllYGGOM8crCwhgfE5FoEbnB6TqMOR8WFsb43pVAX6eLMOZ82BXcxviQZ2iQT4FM4BhwnarucLYqY86dhYUxPiYiX+Ae+2ej187G+CnbDWWM73UFtjpdhDHnw8LCGB8SkaZAVpm7nxlTI1lYGONb7YF9ThdhzPmysDDGt7YCTUVko4hc4nQxxlSWHeA2xhjjlW1ZGGOM8crCwhhjjFcWFsYYY7yysDDGGOOVhYUxxhivLCyMMcZ4ZWFhjDHGKwsLY4wxXv1/1aMASxyQvZYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "NON-LINEAR SIMULATION: Step = 0.1\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LINEAR SIMULATION: Step = 0.1\n",
      "[]\n",
      "[]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "COMPARE LINEAR & NONLINEAR: Step = 0.1\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## imp.reload(st)\n",
    "\n",
    "##Time\n",
    "t_max = int(40)\n",
    "t = np.linspace(0,t_max,1000)\n",
    "t_0 = 5\n",
    "\n",
    "for step in [1,0.1]:\n",
    "    \n",
    "    ## Chemostat\n",
    "    #step = 1\n",
    "    x_chemo =     '{0}*(1+{2}*np.heaviside(t-{1},1))'.format(str(x_E0),str(t_0),str(step))\n",
    "    x_chemo_lin = '{0}*({2}*np.heaviside(t-{1},1))'.format(str(x_E0),str(t_0),str(step))\n",
    "\n",
    "    ## Simulate\n",
    "    print('NON-LINEAR SIMULATION: Step = '+str(step))\n",
    "    #X0 = x_ss\n",
    "    X_chemo = {'E0':x_chemo}\n",
    "    ndat = st.sim(s,sc=sc,t=t,parameter=parameter,X0=X_ss,X_chemo=X_chemo,quiet=quiet)\n",
    "    st.plot(s,ndat,species=['A','B','C','E'])\n",
    "\n",
    "    print('LINEAR SIMULATION: Step = '+str(step))\n",
    "    #X0 = x_ss\n",
    "    X_chemo = {'E0':x_chemo_lin}\n",
    "    V0 = [0,v_ss,v_ss] # Steady-state flows\n",
    "    ldat = st.sim(s,sc=sc,t=t,linear=True,V0=V_ss,parameter=parameter,X0=X_ss,X_chemo=X_chemo,quiet=quiet)\n",
    "    st.plot(s,ldat,species=['A','B','C','E'])\n",
    "\n",
    "    print('COMPARE LINEAR & NONLINEAR: Step = '+str(step))\n",
    "    compare(ndat,ldat,v_ss,step*gain,i_r)\n",
    "    "
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.9"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}