ElectroChemical.ipynb

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    "***Note: This example is discussed in detail by \n",
    "    <cite data-cite=\"GawPan20X\">(Gawthrop and Pan, 2020)</cite> \n",
    "    available [here](https://arxiv.org/abs/2009.02217).***\n",
    "\n",
    "***Note: this is the ElectroChemical.ipynb notebook. The\n",
    "PDF version \"Electrochemical Modelling and Ion Channels\"\n",
    "is available [here](Electrochemical.pdf).***\n"
   ]
  },
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    "# Introduction\n",
    "## Faraday equivalent potential\n",
    "The bond graph approach uses the notion of energy covariables: a pair\n",
    "of variables whose product is power. Thus, for example, electrical\n",
    "systems have voltage (with units \\si{\\volt}) and current (with units\n",
    "\\si{\\ampere}) as covariables and the product has units of power\n",
    "(\\si{\\watt} or \\si{\\joule\\per\\second}). Chemical system covariables\n",
    "are chemical potential $\\mu$ (with units \\si{\\joule\\per\\coulomb}) and\n",
    "molar flow $f$ (with units\n",
    "\\si{\\mole\\per\\second})\\citep{OstPerKat71,OstPerKat73,GawCra14}; again\n",
    "the product has units of power (\\si{\\watt} or \\si{\\joule\\per\\second}).\n",
    "\n",
    "The commonality of power over different physical domains makes the\n",
    "bond graph approach particularly appropriate to model multi-domain\n",
    "systems, in particular chemoelectrical systems\n",
    "\\citep{GawSieKam17}. Noting that the conversion factor relating the\n",
    "electrical and chemical domains is \\emph{Faraday's constant}\n",
    "$F\\approx\\SI{96485}{C.mol^{-1}}$. As discussed by \\citet{Kar90}\n",
    "and \\citet{GawSieKam17}, this conversion can be represented by the\n",
    "bond graph transformer (**TF**) component. An alternative approach\n",
    "introduced by \\citet{Gaw17a} is to divide the covariables $\\mu$ and\n",
    "$f$ by $F$ to give the pair of covariables $\\phi$ and $f$\n",
    "where:\n",
    "\\begin{align}\n",
    "  &\\text{Faraday-equivalent chemical potential}& \\phi &= \\frac{\\mu}{F} \\si{\\volt}\\label{eq:phi}\\\\   &\\text{Faraday-equivalent flow}& f &= F v \\si{\\ampere}\\label{eq:f} \n",
    "\\end{align}\n",
    "  \n",
    "## Chemical properties\n",
    "The **Ce** components representing chemical species generate Faraday-equivalent potential (FEP) $\\phi$ (measured in Volts) in terms of the amount of species $x$ as:\n",
    "\\begin{align}\n",
    "\\phi &= \\phi^\\ominus + \\phi_N \\ln \\frac{x}{x^\\ominus}\\\\\n",
    "&= \\phi_N \\ln K x\\\\\n",
    "\\text{where }\n",
    "K &= \\frac{K^\\ominus}{x^\\ominus}\\\\\n",
    "V_N &= \\frac{RT}{F} \\approx 26 mV\\\\\n",
    "\\text{and }\n",
    "K^\\ominus &= \\ln\\frac{\\phi^\\ominus}{\\phi_N}\n",
    "\\end{align}\n",
    "$\\phi^\\ominus$ in the standard potential at the standard amount $x^\\ominus$.\n",
    "$R$ is the universal gas constant and $F$ Faraday's constant.\n",
    "\n",
    "The amount of species $x$ is the integral of the species flow $f$:\n",
    "\\begin{equation}\n",
    "x = \\int^t f(\\tau)d\\tau\n",
    "\\end{equation}\n",
    "\n",
    "The formula can also be expressed in terms of concentration $c$ as:\n",
    "\\begin{align}\n",
    "\\phi &= \\phi_N \\ln K_C^\\prime c\\\\\n",
    "\\text{where }\n",
    "K_c^\\prime &= \\frac{K^\\ominus}{c^\\ominus}\\\\\n",
    "\\end{align}\n",
    "$c^\\ominus$ is the concentration at standard conditions.\n",
    "## Electrical properties\n",
    "The **C** components representing electrical capacitance generate electrical potential $\\phi$ (measured in Volts) in terms of the amount of positively charges $x$ and electrical capacitance $C$ as:\n",
    "\\begin{align}\n",
    "\\phi &= \\frac{x}{C}\\\\\n",
    "&= \\phi_N K_E x_E\\\\\n",
    "\\text{where }\n",
    "K_E &= \\frac{1}{x_N}\\\\\n",
    "\\text{and }\n",
    "x_N &= C\\phi_N \n",
    "\\end{align}\n",
    "The amount of charge $x_E$ is the integral of the charge flow (current) $f_E$:\n",
    "\\begin{equation}\n",
    "x_E = \\int^t f_E(\\tau)d\\tau\n",
    "\\end{equation}"
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      "In /home/peterg/.local/lib/python3.6/site-packages/matplotlib/mpl-data/stylelib/_classic_test.mplstyle: \n",
      "The text.latex.unicode rcparam was deprecated in Matplotlib 3.0 and will be removed in 3.2.\n",
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      "The savefig.frameon rcparam was deprecated in Matplotlib 3.1 and will be removed in 3.3.\n",
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      "The pgf.debug rcparam was deprecated in Matplotlib 3.0 and will be removed in 3.2.\n",
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    "## 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",
    "\n",
    "## Stoichiometric analysis\n",
    "import stoich as st\n",
    "\n",
    "## SVG\n",
    "import svgBondGraph as sbg\n",
    "\n",
    "## Display (eg disp.SVG(), disp.\n",
    "import IPython.display as disp\n",
    "\n",
    "quiet = True\n",
    "\n",
    "## Fix the concentrations via chemostats\n",
    "Fix_conc = False"
   ]
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    "## Concentrations in nM for Na and K in Giant Squid Axon\n",
    "## From Keener & Sneyd Table 2.1\n",
    "conc_e = {'Na':437, 'K':20}\n",
    "conc_i = {'Na':50, 'K':397}"
   ]
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   "source": [
    "# Electrodiffusion\n",
    "Cellular membranes have pores though which chemical species can diffuse. If the species are charged, the diffusion both depends on and creates an electrical potential.\n",
    "This section looks at a single ionic species with generic name \\ch{I+}; this can be thought of as \\ch{Na+} or \\ch{K+}.\n",
    "\n",
    "The bond graph representation of a charged ion has three components: a **Ce** component to represent the *chemical* properties of the ion, a **C** component to repesent the *electrical*   properties of the ion and a **1** junction to make the flow into the two components identical.\n",
    "\n",
    "The resultant potential is then the sum of the chemical and electrical components:\n",
    "\\begin{align}\n",
    "\\phi &= \\phi_C + \\phi_E\\\\\n",
    "\\text{where }\n",
    "\\phi_C &= \\phi_N \\ln K x\\\\\n",
    "\\text{and }\n",
    "\\phi_E = \\phi_N K_E x_E\n",
    "\\end{align}\n",
    "\n",
    "If the ion has *two* charges (\\ch{I^{++}}) the bold bonds in the diagram would each be replaced by *two* bonds; alternatively, if the ion had a *negative*  charge (\\ch{I-}) the bold bonds in the diagram would each be replaced by a bond with *reversed* direction.\n",
    "\n",
    "The bond graph of the pore itself has two pools of charged ions: internal and external connected by a reaction (**Re**) component. As the ion in each pool is the same, the property $K^\\prime$ is the same for each pool. Thus the reaction potential $\\Phi$ is the difference of the potentials of the internal and external ion pools:\n",
    "\\begin{equation}\n",
    "\\Phi = \\phi_N \\left ( \\ln K^\\prime c_i - \\ln K^\\prime c_e \\right )\n",
    "+ \\left ( \\phi_{Ei} - \\phi_{Ee} \\right ) \n",
    "\\end{equation}\n",
    "Defining $\\Delta E = \\phi_{Ei} - \\phi_{Ee}$ and noting that at equilibrium $\\Phi=0$:\n",
    "\\begin{equation}\n",
    "\\Delta E = \\phi_N \\ln\\frac{c_e}{c_i}\n",
    "\\end{equation}\n",
    "This is the expresion for the *Nernst potential* for a species with a single positive charge."
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   "source": [
    "## Electrodiffusion\n",
    "sbg.model('Electrodiffusion_abg.svg')\n",
    "import Electrodiffusion_abg\n",
    "disp.SVG('Electrodiffusion_abg.svg')"
   ]
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   "cell_type": "code",
   "execution_count": 4,
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   "source": [
    "## Stoichiometry: linear Re\n",
    "s = st.stoich(Electrodiffusion_abg.model(),linear=['Ei','Ee','r'],quiet=quiet)\n",
    "\n",
    "if Fix_conc:\n",
    "    chemostats = ['Ii','Ie']\n",
    "else:\n",
    "    chemostats = []\n",
    "    \n",
    "sc = st.statify(s,chemostats=chemostats)\n",
    "#print(s['species'])\n"
   ]
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   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
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     "data": {
      "text/latex": [
       "\\begin{align}\n",
       "N &=\n",
       "\\left(\\begin{matrix}1\\\\-1\\\\1\\\\-1\\end{matrix}\\right)\n",
       "\\end{align}\n"
      ],
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       "<IPython.core.display.Latex object>"
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   "source": [
    "## Stoichiometric matrix\n",
    "disp.Latex(st.sprintl(s,'N'))\n",
    "#print(st.sprintl(s,'species'))\n"
   ]
  },
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   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
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    {
     "data": {
      "text/latex": [
       "\\begin{align}\n",
       "\\ch{Ei + Ii &<>[ r ] Ee + Ie }\n",
       "\\end{align}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Reactions\n",
    "disp.Latex(st.sprintrl(s,chemformula=True,all=True))"
   ]
  },
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   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
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      "text/latex": [
       "\\begin{align}\n",
       "v_{r} &= \\kappa_{r} \\left(- K_{Ee} x_{Ee} + K_{Ei} x_{Ei} - V_{N} \\left(\\log{\\left(K_{Ie} x_{Ie} \\right)} - \\log{\\left(K_{Ii} x_{Ii} \\right)}\\right)\\right)\n",
       "\\end{align}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Flows\n",
    "disp.Latex(st.sprintvl(s))"
   ]
  },
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   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Stoichiometry: nonlinear Re\n",
    "s = st.stoich(Electrodiffusion_abg.model(),linear=['Ei','Ee'],quiet=quiet)\n",
    "\n",
    "if Fix_conc:\n",
    "    chemostats = ['Ii','Ie']\n",
    "else:\n",
    "    chemostats = []\n",
    "    \n",
    "sc = st.statify(s,chemostats=chemostats)\n",
    "#print(s['species'])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\begin{align}\n",
       "\\ch{Ei + Ii &<>[ r ] Ee + Ie }\n",
       "\\end{align}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Reactions\n",
    "disp.Latex(st.sprintrl(s,chemformula=True,all=True))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
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     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\\begin{align}\n",
      "v_{r} &= \\kappa_{r} \\left(- K_{Ie} x_{Ie} e^{\\frac{K_{Ee} x_{Ee}}{V_{N}}} + K_{Ii} x_{Ii} e^{\\frac{K_{Ei} x_{Ei}}{V_{N}}}\\right)\n",
      "\\end{align}\n",
      "\n"
     ]
    },
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     "data": {
      "text/latex": [
       "\\begin{align}\n",
       "v_{r} &= \\kappa_{r} \\left(- K_{Ie} x_{Ie} e^{\\frac{K_{Ee} x_{Ee}}{V_{N}}} + K_{Ii} x_{Ii} e^{\\frac{K_{Ei} x_{Ei}}{V_{N}}}\\right)\n",
       "\\end{align}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Flows\n",
    "print(st.sprintvl(s))\n",
    "disp.Latex(st.sprintvl(s))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "#disp.Latex(st.sprintl(s,'species'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "#disp.Latex(st.sprintl(s,'N'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Set non-unit parameters\n",
    "K_Ii = 1e-3\n",
    "K_Ie = 1e-3\n",
    "C = 1\n",
    "def setPar(s,C=1,conc_i=1,conc_e=1,prefix=['']):\n",
    "    \n",
    "    #V_N = st.V_N()\n",
    "    K_E = 1/C\n",
    "    #print(K_E)\n",
    "    \n",
    "    \n",
    "    ## Parameters\n",
    "    parameter = {}\n",
    "    parameter['K_Ei'] = 0\n",
    "    parameter['K_Ee'] = K_E\n",
    "    \n",
    "    ## Initial state\n",
    "    sp = s['species']\n",
    "    re = s['reaction']\n",
    "    X0 = np.ones(s['n_X'])\n",
    "    X0[sp.index('Ei')] = 0\n",
    "    X0[sp.index('Ee')] = 0\n",
    "    for p in prefix:\n",
    "        \n",
    "        ## Parameters\n",
    "        KK = 'K_'+p\n",
    "        kk = 'kappa_'+p\n",
    "        parameter[KK+'Ii'] = K_Ii\n",
    "        parameter[KK+'Ie'] = K_Ie\n",
    "        \n",
    "        ## States and kappa\n",
    "        if len(p) is 0:\n",
    "            Ion = 'Na'\n",
    "        else:\n",
    "            Ion = p[0:len(p)-1]\n",
    "            #X0[sp.index('Ee')] = 0.077/K_E\n",
    "        \n",
    "        print(Ion)    \n",
    "        X0[sp.index(p+'Ii')] = conc_i[Ion]/K_Ii\n",
    "        X0[sp.index(p+'Ie')] = conc_e[Ion]/K_Ie\n",
    "        parameter[kk+'r'] = 1/conc_i[Ion]\n",
    "        \n",
    "    return parameter,X0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
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   "source": [
    "def CheckTheory(dat):\n",
    "    \n",
    "    if 'Ii' in s['species']:\n",
    "        ## Check Nernst potential\n",
    "        t = dat['t']\n",
    "        phi_Ei = dat['phi'][:,s['species'].index('Ei')]\n",
    "        phi_Ee = dat['phi'][:,s['species'].index('Ee')]\n",
    "        x_Ii = dat['X'][:,s['species'].index('Ii')]\n",
    "        x_Ie = dat['X'][:,s['species'].index('Ie')]\n",
    "    #     v = dat['V'][:,s['reaction'].index('r')]\n",
    "        V_N = st.V_N()\n",
    "\n",
    "    #     v_ss = v[-1]\n",
    "        dV = (phi_Ei[-1]-phi_Ee[-1] )\n",
    "        dV_theory = V_N*np.log(x_Ie[-1]/x_Ii[-1])\n",
    "    #     print(f'Steady-state flow is {v_ss:0.2}')\n",
    "        print(f'dV = {dV*1000:4.1f}mV')\n",
    "        print(f'dV_Theory = {dV_theory*1000:4.1f}mV')\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
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   "outputs": [],
   "source": [
    "def Simulate(s,sc,T=1,X_chemo=None,prefix=['']):\n",
    "\n",
    "    ## Time\n",
    "    t = np.linspace(0,T,500)\n",
    "\n",
    "    ## Parameters and initial state\n",
    "    parameter,X0 = setPar(s,C=C,conc_i=conc_i,conc_e=conc_e,prefix=prefix)\n",
    "    \n",
    "    ## Simulate\n",
    "    dat = st.sim(s,sc=sc,t=t,parameter=parameter,X0=X0,X_chemo=X_chemo,quiet=True)\n",
    "\n",
    "    CheckTheory(dat)\n",
    "\n",
    "    return dat\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Na\n",
      "dV = 57.9mV\n",
      "dV_Theory = 57.9mV\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dat = Simulate(s,sc)\n",
    "#st.plot(s,dat)\n",
    "st.plot(s,dat,plotPhi=True,species=['Ei','Ee'])\n",
    "st.plot(s,dat,plotPhi=True,species=['Ei','Ee'],filename='Figs/electrodiffusion.pdf')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Voltage clamp\n",
    "The voltage agross the membrane is clamped by setting C:Ei and C_Ee as chemostats. This allows the voltage-current relationship to be plotted. It is compared with the Hodgkin-Huxley (linear) model and the Goldman-Huxley-Katz model.\n",
    "The bond graph model can be modified to reflect the other two models \\cite{GawSieKam17}."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Stoichiometry\n",
    "##chemostats = ['Ii','Ie','Ei','Ee']\n",
    "chemostats = chemostats + ['Ei','Ee']\n",
    "scc = st.statify(s,chemostats=chemostats)\n",
    "#print(s['species'])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Na\n",
      "dV = 57.9mV\n",
      "dV_Theory = 57.8mV\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X_chemo = {}\n",
    "V_Nernst = st.V_N()*np.log(conc_e['Na']/conc_i['Na'])\n",
    "#print(f'V_Nernst = {1000*V_Nernst:4.1f} mV')\n",
    "T = 100\n",
    "\n",
    "CV = C*V_Nernst\n",
    "# x_chemo = f'{CV}*(np.sin({2*np.pi/T}*t))'\n",
    "# #X_chemo['Ee'] = f'{-CV/2}-'+x_chemo\n",
    "# X_chemo['E'] = x_chemo\n",
    "x_chemo = f'-{CV}*(1+1.0*np.sin({2*np.pi/T}*t))'\n",
    "X_chemo['Ee'] = x_chemo\n",
    "\n",
    "\n",
    "#print(X_chemo)\n",
    "\n",
    "dat = Simulate(s,scc,T=T,X_chemo=X_chemo)\n",
    "#st.plot(s,dat)\n",
    "st.plot(s,dat,species=['Ei','Ee'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def PlotClamp():\n",
    "    t = dat['t']\n",
    "    phi_Ei = dat['phi'][:,s['species'].index('Ei')]\n",
    "    phi_Ee = dat['phi'][:,s['species'].index('Ee')]\n",
    "    x_Ii = dat['X'][:,s['species'].index('Ii')]\n",
    "    x_Ie = dat['X'][:,s['species'].index('Ie')]\n",
    "    v = dat['V'][:,s['reaction'].index('r')]\n",
    "    V_N = st.V_N()\n",
    "\n",
    "    dV = phi_Ei-phi_Ee\n",
    "\n",
    "    ## BG\n",
    "    v_BG = (1/x_Ii)*(x_Ii - x_Ie*np.exp(-dV/V_N))\n",
    "\n",
    "    ## GHK\n",
    "    v_GHK = 0.5*v_BG*(dV/V_N)/(1-np.exp(-dV/V_N))\n",
    "\n",
    "    ## HH\n",
    "    v_HH = (np.exp(-V_Nernst))*(dV - V_Nernst)/V_N\n",
    "\n",
    "    plt.plot(dV*1000,v,label='Clamp',lw = 6)\n",
    "    plt.plot(dV*1000,v_BG,label='BG')\n",
    "    plt.plot(dV*1000,v_GHK,label='GHK')\n",
    "    plt.plot(dV*1000,v_HH,label='HH')\n",
    "    plt.vlines(1000*V_Nernst,min(v),max(v),linestyle='dashed')\n",
    "    plt.grid()\n",
    "    plt.legend()\n",
    "    plt.xlabel('$\\Delta E$ mV')\n",
    "    plt.ylabel('$v/\\kappa$')\n",
    "    plt.savefig('Figs/clamp.pdf')\n",
    "    \n",
    "PlotClamp()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Gated ion channel\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<polyline points=\" 2250,3825 1575,3825 1800,4050\" stroke=\"#000000\" stroke-width=\"15px\"/>\n",
       "<!-- Line -->\n",
       "<polyline points=\" 3375,2475 2700,1800 2700,2025\" stroke=\"#000000\" stroke-width=\"15px\"/>\n",
       "<!-- Line -->\n",
       "<polyline points=\" 3825,2475 4500,1800 4500,2025\" stroke=\"#000000\" stroke-width=\"15px\"/>\n",
       "<!-- Line -->\n",
       "<polyline points=\" 3375,2925 2700,3600 2925,3600\" stroke=\"#000000\" stroke-width=\"15px\"/>\n",
       "<!-- Line -->\n",
       "<polyline points=\" 2700,5850 3375,5175 3375,5400\" stroke=\"#000000\" stroke-width=\"15px\"/>\n",
       "</g>\n",
       "</svg>"
      ],
      "text/plain": [
       "<IPython.core.display.SVG object>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Ion Channel\n",
    "sbg.model('IonChannel_abg.svg')\n",
    "import IonChannel_abg\n",
    "disp.SVG('IonChannel_abg.svg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['Ee', 'Ei', 'G', 'Ie', 'Ii']\n"
     ]
    }
   ],
   "source": [
    "## Stoichiometry\n",
    "s = st.stoich(IonChannel_abg.model(),linear=['Ei','Ee'],quiet=quiet)\n",
    "if Fix_conc:\n",
    "    chemostats = ['Ii','Ie','G']\n",
    "else:\n",
    "    chemostats = ['G']\n",
    "sc = st.statify(s,chemostats=chemostats)\n",
    "print(s['species'])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\begin{align}\n",
       "\\ch{Ei + G + Ii &<>[ r ] Ee + G + Ie }\n",
       "\\end{align}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Reactions\n",
    "disp.Latex(st.sprintrl(s,chemformula=True,all=True))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\begin{align}\n",
       "v_{r} &= K_{G} \\kappa_{r} x_{G} \\left(- K_{Ie} x_{Ie} e^{\\frac{K_{Ee} x_{Ee}}{V_{N}}} + K_{Ii} x_{Ii} e^{\\frac{K_{Ei} x_{Ei}}{V_{N}}}\\right)\n",
       "\\end{align}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Flows\n",
    "disp.Latex(st.sprintvl(s))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Na\n",
      "dV = 57.4mV\n",
      "dV_Theory = 57.9mV\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X_chemo = {'G':'0.1'}\n",
    "dat = Simulate(s,sc,X_chemo=X_chemo)\n",
    "#st.plot(s,dat)\n",
    "st.plot(s,dat,plotPhi=True,species=['Ei','Ee'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Interacting ion channels\n",
    "\n",
    "Two instances of the ion channel module are combined; one corresponds to \\ch{Na+} and one to \\ch{K+}. The species concentations are encapsulated in the individual modules, but the electrical capaciter are shared. This is a simplified version of the Hodgkin-Huxley model of the squid giant axon and the correponding \\ch{Na+} and \\ch{K+} concentrations are used.\n",
    "\n",
    "The simulations use piecewise constant gating variables $G_{Na}$ and $G_{K}$:\n",
    "\\begin{align}\n",
    "G_K &= \n",
    "\\begin{cases}\n",
    "10^{-6} & \\text{for $0.3<t<0.35$}\\\\\n",
    "1 & \\text{otherwise}\n",
    "\\end{cases}\\\\\n",
    "G_{Na} &= \n",
    "\\begin{cases}\n",
    "1 & \\text{for $0.3<t<0.35$}\\\\\n",
    "4.3 \\times 10^{-3} & \\text{otherwise}\n",
    "\\end{cases}\n",
    "\\end{align}\n",
    "\n",
    "The time course of the membrane potential $\\Delta E$ can be explained as follows.\n",
    "\n",
    "\\begin{description}\n",
    "\\item[$t<0.3$] $\\Delta E$ moves from the initial condition of zero to a *resting potential* of about $-65$mV.\n",
    "\n",
    "This corresponds to the value in Table 2.1 of Keener \\& Sneyd; the resting potential depends not only on Nernst potentials of ch{Na+} and \\ch{K+} (which in turn depends on the concentrations) but also on the values of the gating potential.\n",
    "\\item[$0.3<t<0.35$] $\\Delta E$ undergoes a typical action potential as the \\ch{Na+} gate opens and moves toward the Nernst potential for \\ch{Na+} until the gate closes.\n",
    "\\item[$t>0.35$] $\\Delta E$ \n",
    "returns to the resting potential.\n",
    "\\end{description}\n",
    "\n",
    "In this simple example the gating variables $G_{Na}$ and $G_{K}$ are independent variables, in reality, and in the HH model, the gating variables are modulated by the membrane potential $\\Delta E$. This is discussed in a bond graph context by \\citet{GawSieKam17}.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Creating subsystem: IonChannel:K\n",
      "Creating subsystem: IonChannel:Na\n"
     ]
    },
    {
     "data": {
      "image/svg+xml": [
       "<svg height=\"371pt\" viewBox=\"2238 -12 4524 5874\" width=\"285pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       "<g fill=\"none\">\n",
       "<!-- Line -->\n",
       "<rect height=\"5850\" rx=\"105\" stroke=\"#ffd600\" stroke-width=\"8px\" width=\"4500\" x=\"2250\" y=\"0\"/>\n",
       "<!-- Text -->\n",
       "<text fill=\"#000000\" font-family=\"Helvetica\" font-size=\"216\" font-style=\"normal\" font-weight=\"bold\" text-anchor=\"middle\" x=\"4500\" xml:space=\"preserve\" y=\"4395\">0</text>\n",
       "<!-- Text -->\n",
       "<text fill=\"#000000\" font-family=\"Helvetica\" font-size=\"216\" font-style=\"normal\" font-weight=\"bold\" text-anchor=\"middle\" x=\"4500\" xml:space=\"preserve\" y=\"315\">C:Ee</text>\n",
       "<!-- Text -->\n",
       "<text fill=\"#000000\" font-family=\"Helvetica\" font-size=\"216\" font-style=\"normal\" font-weight=\"bold\" text-anchor=\"middle\" x=\"4500\" xml:space=\"preserve\" y=\"5715\">C:Ei</text>\n",
       "<!-- Text -->\n",
       "<text fill=\"#000000\" font-family=\"Helvetica\" font-size=\"216\" font-style=\"normal\" font-weight=\"bold\" text-anchor=\"middle\" x=\"4500\" xml:space=\"preserve\" y=\"1665\">0</text>\n",
       "<!-- Text -->\n",
       "<text fill=\"#000000\" font-family=\"Helvetica\" font-size=\"216\" font-style=\"normal\" font-weight=\"bold\" text-anchor=\"middle\" x=\"3150\" xml:space=\"preserve\" y=\"3015\">IonChannel:Na</text>\n",
       "<!-- Text -->\n",
       "<text fill=\"#000000\" font-family=\"Helvetica\" font-size=\"216\" font-style=\"normal\" font-weight=\"bold\" text-anchor=\"middle\" x=\"5850\" xml:space=\"preserve\" y=\"3015\">IonChannel:K</text>\n",
       "<!-- Text -->\n",
       "<text fill=\"#ff0000\" font-family=\"Helvetica\" font-size=\"168\" font-style=\"normal\" font-weight=\"bold\" text-anchor=\"middle\" x=\"5850\" xml:space=\"preserve\" y=\"3375\">[Ei]</text>\n",
       "<!-- Text -->\n",
       "<text fill=\"#ff0000\" font-family=\"Helvetica\" font-size=\"168\" font-style=\"normal\" font-weight=\"bold\" text-anchor=\"middle\" x=\"5850\" xml:space=\"preserve\" y=\"2700\">[Ee]</text>\n",
       "<!-- Text -->\n",
       "<text fill=\"#ff0000\" font-family=\"Helvetica\" font-size=\"168\" font-style=\"normal\" font-weight=\"bold\" text-anchor=\"middle\" x=\"3150\" xml:space=\"preserve\" y=\"2700\">[Ee]</text>\n",
       "<!-- Text -->\n",
       "<text fill=\"#ff0000\" font-family=\"Helvetica\" font-size=\"168\" font-style=\"normal\" font-weight=\"bold\" text-anchor=\"middle\" x=\"3150\" xml:space=\"preserve\" y=\"3375\">[Ei]</text>\n",
       "<!-- Line -->\n",
       "<polyline points=\" 4500,1350 4500,450 4725,675\" stroke=\"#000000\" stroke-width=\"15px\"/>\n",
       "<!-- Line -->\n",
       "<polyline points=\" 4500,4500 4500,5400 4725,5175\" stroke=\"#000000\" stroke-width=\"15px\"/>\n",
       "<!-- Line -->\n",
       "<polyline points=\" 3375,2700 4275,1800 4275,2025\" stroke=\"#000000\" stroke-width=\"15px\"/>\n",
       "<!-- Line -->\n",
       "<polyline points=\" 4275,4050 3375,3150 3375,3375\" stroke=\"#000000\" stroke-width=\"15px\"/>\n",
       "<!-- Line -->\n",
       "<polyline points=\" 5625,2700 4725,1800 4725,2025\" stroke=\"#000000\" stroke-width=\"15px\"/>\n",
       "<!-- Line -->\n",
       "<polyline points=\" 4725,4050 5625,3150 5625,3375\" stroke=\"#000000\" stroke-width=\"15px\"/>\n",
       "</g>\n",
       "</svg>"
      ],
      "text/plain": [
       "<IPython.core.display.SVG object>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Ion Channels\n",
    "sbg.model('IonChannels_abg.svg')\n",
    "import IonChannels_abg\n",
    "disp.SVG('IonChannels_abg.svg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['Ee', 'Ei', 'K_G', 'K_Ie', 'K_Ii', 'Na_G', 'Na_Ie', 'Na_Ii']\n"
     ]
    }
   ],
   "source": [
    "## Stoichiometry\n",
    "s = st.stoich(IonChannels_abg.model(),linear=['Ei','Ee'],quiet=quiet)\n",
    "if Fix_conc:\n",
    "    chemostats = ['Na_Ii','Na_Ie','Na_G', 'K_Ii','K_Ie','K_G']\n",
    "else:\n",
    "    chemostats = ['Na_G','K_G']\n",
    "sc = st.statify(s,chemostats=chemostats)\n",
    "print(s['species'])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\begin{align}\n",
       "\\ch{Ei + K_G + K_Ii &<>[ K_r ] Ee + K_G + K_Ie }\\\\\n",
       "\\ch{Ei + Na_G + Na_Ii &<>[ Na_r ] Ee + Na_G + Na_Ie }\n",
       "\\end{align}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Reactions\n",
    "disp.Latex(st.sprintrl(s,chemformula=True,all=True))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\begin{align}\n",
       "v_{K r} &= K_{K G} \\kappa_{K r} x_{K G} \\left(- K_{K Ie} x_{K Ie} e^{\\frac{K_{Ee} x_{Ee}}{V_{N}}} + K_{K Ii} x_{K Ii} e^{\\frac{K_{Ei} x_{Ei}}{V_{N}}}\\right)\\\\\n",
       "v_{Na r} &= K_{Na G} \\kappa_{Na r} x_{Na G} \\left(- K_{Na Ie} x_{Na Ie} e^{\\frac{K_{Ee} x_{Ee}}{V_{N}}} + K_{Na Ii} x_{Na Ii} e^{\\frac{K_{Ei} x_{Ei}}{V_{N}}}\\right)\n",
       "\\end{align}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Flows\n",
    "disp.Latex(st.sprintvl(s))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Na\n",
      "K\n"
     ]
    },
    {
     "data": {
      "image/png": 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NiKz0v97MasZUoe9f+j0n713Ok/XvYub4bcC2cLxNjdm9+wDPLw/Ln6pGRUo5ABrujOZ54LFPfmBOXO0+R7B79wFeXvYtD27/A2k+D38+cAM7X/7R6bCCEinfsXqlhWRlhf51Az0H8jqwF3jav36lf1t15mltDmwot54D9DnaPsaYEhHZA6T6t8864rnNK3oTERkNjAZIT08nOzu7SkFKaQlNdv7ERM9gPi/sBoW7q/R8N/L5fOzereVwE0+pPe8Rnb+Z3QW1u0w+n49Lcp+nlW8V98Xcweq8aKB2lilSvmPx8b4q/+8LRKAJ5ARjTKdy61NFZMlR93YRY8xLwEsAvXr1MlnBpOFBWWz5diqTB0dG3/Xs7GyC+ju4TKSUA+Dbb76CaXDbyY24Letsp8OploXjH6PLos+h9w387Zx7nQ6nWiLlOxaucgQ6mOJPItK3bEVE+lD9q9M3Ai3KrWf4t1W4j4hEASnAjgCfGzreKIwnOmwvr5TxRENCGuRtcjqU6tm7mY7LnoL0LnDGA05Ho8Is0ATSE5ghImtFZC32XMNJIrJQRBYE+d6zgXYi0kpEYrAnxSccsc8E4Br/8iXAN8YY499+ub+XViugHVA7G1mVKlOvKeRtcTqK4JX64MPr8ZQWwSWvameTOiDQJqyzQv3G/nMaNwOTAS/wqjFmsYg8AMwxxkwAXgHe9J8k34lNMvj3ew97wr0EuClsPbCUqinJTWFvLa6BTH8c1n7HLx1uoWOj9k5Ho2pAQAnEGLMuHG9ujJkETDpi2/+VWy4ALj3Kcx8C9IIMFTmSm9opkWujnLkw9Z/Q+SK2pJ1GR6fjUTVCJ5RSyi3qNYd9ubVvWPfCfPhwlE2A5z0RmWN5qQrV+QmliouLycnJoaDg2LPBpaSksHTp0mPuU9Pi4uLIyMggOlpP8EeEhq3s/a510LgW/Yb/8m7YuQaumQjx9Z2ORtWgOp9AcnJySE5OJjMzEznGL6e8vDySk5NrMLJjM8awY8cOcnJyaNWqldPhqFAoG5xz15rak0CWfw5z/wv9b4VWpzgdjaphdb4Jq6CggNTU1GMmDzcSEVJTUyutOalapCyB7FztbByByt8Gn9xsu+wOvsfpaJQD6nwNBKh1yaNMbY1bHUV8A4hLgR0rnY6kcsbY5FGYB9d+qvPi1FGaQJRyCxFIPwG2LHI6ksrNfQ1+mQxnPQyNj3c6GuWQOt+E5QZer5fu3bsfvD388MMAjBo1iiVLasWIMSpUmnazs/eVuviypu2/wBd/hdanQu8bnI5GOUhrIC4QHx/PvHnzfrV97NixDkSjHNW0G5QcsP+k3Xgi3VcMH15vrzK/4Hnw6G/Qukw/fRfLyspizpzqDjmmapUmXe395vnOxnE03z5qL3Y870k79Iqq07QGUs7fJi5myaa9FT7m8/nweqs+T0OnZvW47/zOx9znwIEDdO/e/eD6XXfdxWWXXVbl91IRIK09RMXZBNLNZd+B9T/Ad/+CbldC5wucjka5gCYQFzhaE5aqg7xR9kS622oghXnw0WhIyYCzH3E6GuUSmkDKOVZNwW0XEqoI1qIPzB4LRfshJsHpaKwv7oTd6+HaSRBXz+lolEvoORCl3KbtYPAVwroZTkdiLfsMfn4LBvwBWvZzOhrlIppAXKDsHEjZ7c4773Q6JOWklieDNxZWTXE6Eti3HSb+Hpp0gUH6vVSH0yYsF/D5Ku7zH445jFUtEB0PLfvDqm+cjcMY+PQPULAHrv4EomKcjUe5jtZAlHKjdmdA7jLY7uCwJgvfh6UT4NS/QvqxexKqukkTiFJu1PkiEA8sGOfM++/dBJPusCf0+9/qTAzK9TSBKOVG9ZpC6yyY/y6UltbsexsDE26xV51f8Dx4qn79k6obNIEo5VbdroA962HNtzX7vnNfg5VfwxkPQGqbmn1vVatoAlHKrY4fComNYcYzNfeeO9fA5Hts7afXyJp7X1UraQJRyq2i46DvGNudd/OC8L9fqQ8+/p1tshr2nA6UqCql3xAXONpw7krRayTEpsA3fw//e836D6yfYYcqSckI//upWk+vA3EBHQtLHVV8fRj0J/jyHvjla2h3enjeZ9symPJ36HCuPfeiVAC0BuJic+fOZdCgQfTs2ZMhQ4awefNmp0NSTuh9g50vfdLtUJgf+tf3FcNHN0BsEpz/pJ0ZUakAaA2kvM/vtLPBVSDeV2JHSq2qJl3g7GM3SVU0nPtFF13ELbfcwieffEKjRo149913ufvuu3n11VerHoOq3aJi7DmJ186ByX+FoU+H9vW/+zdsngfD34CkxqF9bRXRNIG4QEVNWIsWLWLRokWcccYZgB3upGlTncCnzmrZHwbcBtOfgKZd4aRRoXndTT/DtMegy3DoNCw0r6nqDE0g5R2jpnCghodzN8bQuXNnZs6cWWPvqVxu8L2wdQlM+jM0yIS21TwfUlwAH42BxEZwzqMhCVHVLXoOxKU6dOhAbm7uwQRSXFzM4sWLHY5KOcrjhUtegcbHw7irYMXk6r3e1AfteFtDn4X4BqGJUdUpmkBcoKLh3GNiYhg/fjx/+ctf6NatG927d2fGDJfMD6GcE5tsR8Zt1AHGXQk/vRnc66ybCTOehZ7Xha9nl4p4jjRhiUhD4F0gE1gLDDfG7Kpgv2uAe/yrDxpjXvdvzwaaAgf8j51pjNkW3qjD52jDuXfv3p1p06bVcDTK9RLT4JpP4d3fwISbYf0s2wQVkxjY8wvz4eMxUP84OPPB8MaqIppTNZA7gSnGmHbAFP/6YfxJ5j6gD9AbuE9EytezrzLGdPffam3yUCoocfVgxEcw8E8w7214ri8s/9wOhFiZr+6FXevgwhds112lguRUAhkGvO5ffh24oIJ9hgBfGWN2+msnXwFn1VB8SrmfxwuD74HrJtm50/93Ofz3XFgz7eiJZOXXMOdV6HeT7dmlVDWICeQXS6jfVGS3Maa+f1mAXWXr5fa5A4gzxjzoX78XOGCM+Ze/CSsV8AEfYJu3KiyIiIwGRgOkp6f3HDfu8PkVUlJSaNOmDVLJxVM+nw+v113DWhtjWLVqFXv27KnS8/Lz80lKqv2/PCOlHFD9skhpMc02Tea49eOJLdrF3uR2bGo2hNxGA/BFxQMQVbyXk2bfSklUEnN7Pk6pNzwzDOrn4j7VLcepp5461xjT68jtYUsgIvI10KSCh+4GXi+fMERklzHmsG4glSSQ5saYjSKSjE0gbxlj3qgspl69epk5c+Yctm3NmjUkJyeTmpp6zCSSV8PdeCtjjGHHjh3k5eXRqlWrKj03OzubrKys8ARWgyKlHBDCshQXwM9vwuyxtodVdCK0HWyHKFn+GSz/Aq6fAk27Vf+9jkI/F/epbjlEpMIEEraT6MaYo3btEJGtItLUGLNZRJoCFZ3D2AhklVvPALL9r73Rf58nIu9gz5FUmkAqkpGRQU5ODrm5ucfcr6CggLi4uGDeImzi4uLIyNBB71Q50XHQ+3p7oeGGH2D+OHtuZOlE+/hp94U1eai6xakLCScA1wAP++8/qWCfycA/yp04PxO4S0SigPrGmO0iEg2cB3wdbCDR0dEB/YLPzs6mR48ewb6NUjVLBI7ra2/nPg6bf4bcFdB1uNORqQjiVAJ5GHhPREYC64DhACLSCxhjjBlljNkpIn8HZvuf84B/WyIw2Z88vNjk8XLNF0GpWsLjgeY97U2pEHIkgRhjdgCnVbB9DjCq3PqrwKtH7LMP0CNBKaUcpleiK6WUCooj3XidIiK52CazYKQB20MYjpMipSyRUg7QsrhVpJSluuVoaYxpdOTGOpVAqkNE5lTUja02ipSyREo5QMviVpFSlnCVQ5uwlFJKBUUTiFJKqaBoAgncS04HEEKRUpZIKQdoWdwqUsoSlnLoORCllFJB0RqIUkqpoGgCUUopFRRNIEcQkbNEZLmIrBSRiia6ihWRd/2P/yAimTUfZeUCKMdAEflJREpE5BInYgxUAGX5o4gsEZEFIjJFRFo6EWcgAijLGBFZKCLzRGS6iHRyIs5AVFaWcvtdLCLGP1SR6wTwmVwrIrn+z2SeiIyq6HXcIJDPRESG+4+Xxf7BaINnjNGb/4YdW2sV0BqIAeYDnY7Y53fAC/7ly4F3nY47yHJkAl2xoxhf4nTM1SzLqUCCf/lGN34mVShLvXLLQ4EvnI472LL490sGpgGzgF5Oxx3kZ3It8KzTsYaoLO2An4EG/vXG1XlPrYEcrjew0hiz2hhTBIzDzp5YXvnZFMcDp0lls1HVvErLYYxZa4xZAJQ6EWAVBFKWqcaY/f7VWdih/90okLLsLbeaCLi1l0sgxwrA34FHgIKaDK4KAi1HbRBIWa4HnjN2lldMNacD1wRyuObAhnLrOf5tFe5jjCkB9mBnR3STQMpRW1S1LCOBz8MaUfACKouI3CQiq4BHgVtrKLaqqrQsInIi0MIY81lNBlZFgX6/LvY3kY4XkRY1E1qVBVKW9kB7EfleRGaJSLWmCdcEoiKGiPwG6AU85nQs1WGMec4Y0wb4C3CP0/EEQ0Q8wOPA7U7HEgITgUxjTFfgKw61QNRGUdhmrCzgCuBlEal/zGccgyaQw20Eyv+6yPBvq3Af/+RWKcCOGokucIGUo7YIqCwicjp2uuShxpjCGoqtqqr6uYwDLghrRMGrrCzJwAlAtoisBfoCE1x4Ir3Sz8QYs6Pcd2os7p1OIpDvVw4wwRhTbIxZA6zAJpSgaAI53GygnYi0EpEY7EnyCUfsUzabIsAlwDfGfzbKRQIpR21RaVlEpAfwIjZ5VKtNN8wCKUv5g/lc4JcajK8qjlkWY8weY0yaMSbTGJOJPTc11Ng5f9wkkM+kabnVocDSGoyvKgI57j/GP1W4iKRhm7RWB/2OTvcccNsNOAeblVcBd/u3PYD98gPEAe8DK4EfgdZOxxxkOU7C/hrZh61BLXY65mqU5WtgKzDPf5vgdMzVKMtTwGJ/OaYCnZ2OOdiyHLFvNi7shRXgZ/JP/2cy3/+ZdHQ65mqURbBNi0uAhcDl1Xk/HcpEKaVUULQJSymlVFA0gSillAqKJhCllFJBiXI6gJqUlpZmMjMzg3ruvn37SExMDG1ADomUskRKOUDL4laRUpbqlmPu3LnbTQVzotepBJKZmcmcOcH1IszOziYrKyu0ATkkUsoSKeUALYtbRUpZqlsOEVlX0XZtwlJKKRUUTSBKRbgDRT6Wb8njp/W70G77KpTqVBOWUpFu0+4DLMjZzeJNe1m0cQ/LtuSxec+hgXAHtm/Ewxd1oVn9eAejVJFCE4hStVhhiY9pK7YzbUUu01duZ832fQB4PUK7xkn0a51Kq7REMtMS2bq3gH9/uYIhT0zj3vM6cWmvDNw3E4E7FRcXk5OTQ0GBW0elP7aUlBSWLq18BJa4uDgyMjKIjo4O6HU1gShVCy3etIe3f1jPZws2s+dAMQkxXvq2TmVE35b0bNmADk2SiYv2/up5Z3Zqwp/Gz+fPHyzgi8Vb+OdFXUivF+dACWqXnJwckpOTyczMrJVJNy8vj+Tk5GPuY4xhx44d5OTk0KpVq4BeVxOIUrXIoo17eHTycqatyCU+2suQzukM69Gck9ukERNV+SnN41IT+N/1fXlj5loe/mIZZz4xjb8N7cyw7s1q5T/GmlJQUFBrk0egRITU1FRyc3MDfo4mEKVqgfzCEv4xaSn/+3E9DRNi+PNZHbiqT0tS4gNraijP4xGuPbkVgzo05o7353Pbu/P4fNFmHrygC42SY8MQfWSI5ORRpqpl1ASilMv9sjWPMW/NZc32ffz25Fb8/vR21IureuI4Uqu0RN67oR+vTF/Nv75cwZAnp/H3YSdwbtemlT9ZKbQbr1KuNmftTi547nv2HCjm7VF9ufe8TiFJHmW8HmH0wDZ8dssAWjSI56Z3fuLmd35i176ikL2HilyaQJRyqUUb93DNqz+SXi+OibcMoF+b1LC9V7v0ZD64sT93nNmeyYu3cMYT0/hqydawvZ+quqSkpIPLkyZNon379qxbV+EF4jVGm7CUcqFd+4q44c251IuP5n+j+9ZIT6kor4ebB7djcMd0bn9/Pte/MYeLTmzOfed3DupcS6T628TFLNm0N6Sv2alZPRQP26EAACAASURBVO47v3NA+06ZMoVbb72VyZMn07Jly0r3LykpqW54R+XKGoiInCUiy0VkpYjcWcHjA0XkJxEpEZFLnIhRqXD628TF5OYV8sJvetZ4N9tOzerxyU0nc+vgtnwybxNDnphG9nI3zxRcd0ybNo3rr7+eTz/9lDZt2hx1v2uvvZYxY8bQp08f/vznP4ctHtfVQETECzwHnIGdcnW2iEwwxiwpt9t64FrgjpqPUKnw+mH1Dj6et4lbB7elW4v6jsQQE+Xhj2d24PRO6dz+3nyufW02V/Ruwd3ndiIp1nX/NmpUoDWFUCssLOSCCy4gOzubjh07Vrp/Tk4OM2bMwOv1kpeXF5aY3FgD6Q2sNMasNsYUAeOAYeV3MMasNcYsAEqdCFCpcHps8nKa14/nxqy2TodC14z6TLxlAGMGteHd2RsY8sQ0Zqzc7nRYdVJ0dDT9+/fnlVdeCWj/Sy+9FK/31xeThpIbf0o0BzaUW88B+gT7YiIyGhgNkJ6eTnZ2dlCvk5+fH/Rz3SZSyhIp5YBDZVm318ecdQVc0TGGH2Z853RYB/WNh7TecYxdWMCVY39gcIsoLu0QQ3zUr68biMTPJSUlJWy/4gPl8Xh45ZVXOP/887nvvvu4446jN8AUFxfj8XgOxuzz+QKOv6CgIODPz40JJKSMMS8BLwH06tXLBDsmfqTMCwCRU5ZIKQccKstfxi8gPnoTd16W5boT11nAVef6+NeXy3n1+zUs2xvFQxd24dSOjQ/bLxI/l6VLl1Y6FEhNSE9P54svvuCUU07huOOOY+TIkRXuFx0dTXx8/MGYAxnKpExcXBw9evQIaF83NmFtBFqUW8/wb1MqohUU+5i4YBNDuzVzXfIoEx/j5d7zOvHBjf1JjI3iuv/O5g/vzmOnXjdSYxo2bMgXX3zBgw8+yIQJExyNxY01kNlAOxFphU0clwNXOhuSUuE3c/UO9hf5OKtLE6dDqdSJxzXg01sH8NzUVfxn6kqmrcjlb8M6c24XvYo9XPLz8w8ut2jRgjVr1hx13//+9781EJELayDGmBLgZmAysBR4zxizWEQeEJGhACJykojkAJcCL4rIYuciVio0pq3IJS7aQ7/W4btgMJRio7z88Yz2TLxlAM0bxHPzOz8z+s257CrQvi11hRtrIBhjJgGTjtj2f+WWZ2ObtpSKGD+t20XXjPoVDsPuZsc3rceHN/bn1e/X8O8vVzB9RSlFqesZ3qtFnRiA0EkPPfQQ77///mHbLr30Uu6+++4aeX9XJhC3GfvdavZuLSHL6UBUxCryGRZv2suoU1o7HUpQorweRg9sw5mdmnDDK9P4ywcLmTB/Ew9e0IVWaYlOhxex7r777hpLFhVxXROW25T4Svl43kae/rmQUa/PIWfXfqdDUhFoU34pJaWGrhkpTodSLZlpifyldxwPXXgCCzbsYciT03jq618oLPE5HZoKA00glYjyevjodydzWYcYvl+5nTMen8YL366i2KftvCp0tuw3ALRuVPt/rXtEuKpPS6bcPoghnZvwxNcrOPvJ7/heL0CMOJpAAhDt9XB2q2i+vn0QA9ql8fDnyzjv6enMXrvT6dBUhNi6rxQRyEyt/QmkTON6cTxzRQ/e+G1vfMZw1dgf+P24n9mWVzvnFVe/pgmkCprXj+flq3vx8tW9yC8s4dIXZvLn8fO1D7yqts37SmmWEl/rTqAHYmD7Rky+bSC/P60dny/cwmn//pY3Z63DV2qcDk1VkyaQIJzRKZ2v/jiQMYPa8OFPGxn872xen7GWEm3WUkHaWWBo0TDe6TDCJi7ayx/OaM8Xt51C14wU7v14EcOem86Pa7QWHygR4fbbbz+4/q9//Yv777/fuYDQXlhBS4iJ4s6zO3Jhj+b8beJi7puwmLdmrePe8zoxsH0jp8NTtUxekaFdYuTPR966URJvjezDxAWb+eekpQx/cSbndm3KXWd3JKNBgtPhBebzO2HLwtC+ZpMucPbDx9wlNjaWDz/8kLvuuou0tLSQvG1JSQlRUcGnAa2BVFOHJsm8PaoPL47oSWFJKVe/+iMj/zub1bn5lT9ZKb/8IkP9BHcOXxJqIsLQbs345vYsbju9HVOWbuW0f3/L418uZ39R+CY/qu2ioqIYPXo0TzzxxK8emzhxIn369KFHjx6cfvrpbN169Nkk77//fkaMGMHJJ5/MiBEjqhdTtZ6tAHtADOnchKwOjXjt+7U8+81Khjw5jWv6ZXLTqW1pkBjjdIjKxUpLDfnF0LCOfU/iY7zcdnp7hvdqwcOfL+Ppb1by3pwc7hjSgQt7NMfrcelFiJXUFMLppptuomvXrr+aJGrAgAHMmjULEWHs2LE8+uij/Pvf/z7q6yxZsoTp06cTH1+9ZlOtgYRQbJSXMYPa8M0dg7ioRwavfL+GgY9O5ekpv5BfqL+sVMX2FhRjgAYJdSuBlGlWP56nr+jBBzf2I71eLHe8P5+znpzGF4u2YIyeaC+vXr16XH311Tz99NOHbc/JyWHIkCF06dKFxx57jMWLjz2609ChQ6udPEATSFg0To7jkUu6Mvm2gfRrk8rjX61g0KNTeWX6GgqK9YIqdbiyXnx1rQZypJ4tG/LxTSfzn6tOxGcMY96aywX/maHXjxzhtttu45VXXmHfvn0Ht91yyy3cfPPNLFy4kBdffJGCgmN3lU5MDE13cU0gYdQ+PZmXru7FxzedTMemyfz90yUM/lc2b/+wThOJOmjXfptAtKnTNgef06UpX942kEcv7kru3gKuGvsDV748i5mrdmiNBDuc+/Dhww+bmXDPnj00b94cgNdff73GYtEEUgO6t6jP26P68vaoPjSuF8fdHy1i4KNTefHbVdq0pdi5rxiABnXkJHogorwehp/Ugm/uyOLe8zqxYmseV7w8i4uen8FXS7ZSWsevIbn99tvZvv1Qzez+++/n0ksvpWfPniHroRUIPYleg05um0b/NqnMXLWD/2Sv4p+fL+O5qSu5pn8mV/fLpFFy5HfjVL+254BNIPXjtQZypLhoLyMHtOKqPsfx/pwNvDhtNde/MYcO6cmMyWrNuV2aERNVN34Hl58PJD09nf37D43LN2zYMIYNGxbQ64Ty2hFNIDVMROjfNo3+bdOYv2E3z2ev4tmpK3nh21Wc06UpV/dryYnHNdBhsOuQ/AKbQJLj9HA8mrhoLyP6ZXJ57+P4dMEmns9exR/enc9Dny3jyt4tuLJPS5qkxDkdZp2j31gHdWtRnxdG9GR1bj5vzlrH+Lk5fDJvE52a1uPKPsdxftdmpGizRsTLK7DNmImxejhWJtrr4cIeGQzr1pzvVm7nzZlreWbqSp7LXsWZndIZflILTmmbRpS3btRKjuW1117jqaeeAqC0tBSPx8PJJ5/Mc889F7L30G+sC7RulMR953fmjjM78PG8jbw5cx33fLyIByYu4bTjG3Nhj+ZkdWhcZ6rqdU1+YQnRHvTzrQKPRxjUvhGD2jdiw879vDVrHe/N2cDni7aQlhTLBd2bcdGJGXRqVi9k72mMqVUtA9dddx3XXXcdAHl5eSQnJ1f6nKp2UtAE4iKJsVFc1aclV/Y+jkUb9/LhzzlMmLeJzxdtISU+mtM6NubMzukMbN+IhBj96CJFXmEJ8fpxBq1FwwTuOud4bj+zA1OXb+PDn3J4feZaxk5fQ+tGiZzZqQlndk6ne0Z9PEFenBgXF8eOHTtITU2tVUmkKowx7Nixg7i4wJsC9WvrQiJCl4wUumSk8Ndzjue7X3L5dP5mpizbxoc/byQmysOAtmmc0i6N/m3SaJ+eFLFf6rogv6CE+Cj9/KorJsrDkM5NGNK5Cbv2FfHpgk1MXryVsd+t5oVvV9EoOZbBHRrTv20q/dukVanTSkZGBjk5OeTm5oaxBOFTUFAQUGKIi4sjIyPw2cI1gbhctNfD4I7pDO6YTomvlB/X7uSrJVuZsnQb3yzbBkBaUgz92qTR87j6dG1Rn05N60XksOCRKq+gWBNIiDVIjGFEv0xG9Mtkz/5ipi7fxpdLtjBp0WbenbMBgPbpSfRrnUr34+rTNaM+rVITj1pDiY6OplWrVjVZhJDKzs6mR48eIX9dTSC1SJTXQ/82ttZx3/md2bBzPzNX72Dmqh3MWLWdifM32f08Qvv0ZLq1SKF9ejJtGiXRtnESTVPitKbiQvnahBVWKQnRXNCjORf0aI6v1LBo4x5m+I+Z9+bk8PrMdYDtBdeleQpdmqfQprE9ZvYV1+3rTSqjX9tarEXDBFo0TGB4rxYYY9i6t5D5ObtZkLObBTl7+HzRFv7344aD+yfEeGndKJHYkgK+zVtM8/rxNKsfT9OUONLrxdEwMUZrLg7IKyghQWsgNcLrEbq1qE+3FvW5MasNJb5SVubmsyBnz8Hj5rXv11JUbm6f+3/8mlapiTSrH0cz/zHTvH48TevHkZYUS/346Drb60sTSIQQEZqkxNEkxbYBgz0ptj2/iJXb8lmVm8/Kbfms3r6PlRvzWDp7A/uLfj2cSkKMlwYJMTRMjKFBYgwNE6JJjosmMTaKxBgvCbFRJMV6SYiJIjHWS2JMFDFRHmKiPMRGeYj22uWy+xivvQV78rIuyCsoITVB/z5OiPJ66NikHh2b1GN4rxYA+EoNG3buZ1VuPpNnzcckNWLdzv3MWbeLLQs2U3LEVfAikBIfTcPEGFITY2iQEENyXDRJsV573MRGkXTw3m6LjfIeOj78x0759ZgoD1EecX2LQVAJREQGG2O+EZGLKnrcGPNh9cJSoSAiNEqOpVFyLP3apB7cnp2dzaBBg9h7oISNuw+wafcBtucXsmNfEbv2FbFzf9l9MWu255NfUMK+Ih9FJcHPuBjlEbxlNxFEOLguYrfZZX61j0f8N/+PPMEeVPl5B3h80XQOHmL+g00OXy23frTHD9/xaI8fXA/xMb0tr4CO9bTm5xZej5CZlkhmWiLerTFkZXU7+Jiv1JCbV8imPfa42bmviB35Rezcd+i2bsd+8gtLyC8sYV9hya8STqBEINrjOeyY8PiPGY+AR+Tg8XHoWOLgseTxH0Mi9liZPMBHbFRov2fB1kAGAd8A51fwmAE0gbiciJCSEE1KQnTAfeWLfaXsL/SRX1TC/kKbVPYVllBUUkphSSnFvlKKSkop8h2+XOR/rMRn8JUaSg2UmrJlU27Zzo3hM4eWy+9njP1ygb9PfpEcHMG2rPt6+cfLO/S4OXz9aNvLlk3Zo4c/HkrdW9SnR9qB0L+wCjmvp6ymH8eJxzWodH9jDIUlpQeTib33+Y8N38Fjp/yxUlRuvaTU2GOi7LjwHydly8faXv6Y8RTtwxOG2kxQCcQYc5///rrQhqPcLNrrISXB45qr47Ozs8nK6u10GCGRnZ3tdAgqDESEuGgvcdFe0pKcG+suOzub6DCcp6nWORARiQUuBjLLv5Yx5oHqhQUichbwFOAFxhpjHj7i8VjgDaAnsAO4zBiztrrvq5RSKjDVTUmfAMOAEmBfuVu1iIgXeA44G+gEXCEinY7YbSSwyxjTFngCeKS676uUUipw1e2FlWGMOSskkRyuN7DSGLMaQETGYRPVknL7DAPu9y+PB54VETE644xSStUIqc7/WxF5CXjGGLMwdCGBiFwCnGWMGeVfHwH0McbcXG6fRf59cvzrq/z7bD/itUYDowHS09N7jhs3LqiY8vPzSUpKCuq5bhMpZYmUcoCWxa0ipSzVLcepp5461xjT68jtwXbjXYg9uR8FXCciq4FCbA9IY4zpGnSkIWaMeQl4CaBXr14mKysrqNexJ2yDe67bREpZIqUcEOKyFO2DLYtg83zYugh2rra3onzIugt638DBPtFhoJ+L+4SrHME2YZ0X0ih+bSPQotx6hn9bRfvkiEgUkII9ma5U3VKYB2u/h9VTYc00yF0Gxn/NTnxDSG0LrQZC3hb44k5YMgGGPQupbZyNW9V6wSaQrcAYoC2wEHjFGBPKyb1nA+1EpBU2UVwOXHnEPhOAa4CZwCXAN3r+Q9UZvmL45SuY/z9Y8QX4iiAqDlr2h07DoElXaNoN6jU7dOWjMXb/z++EFwbA6X+Dk0aFtTaiIluwCeR1oBj4jkM9pX4fqqCMMSUicjMwGduN91VjzGIReQCYY4yZALwCvCkiK4Gd2CSjVGQrPgBz/wsznoW9OZCQBj2vg47nQIu+EH2MIbtFoPuV0GoQTLgFPv8TLJsIQ5+FBi1rrAgqcgSbQDoZY7oAiMgrwI+hC8kyxkwCJh2x7f/KLRcAl4b6fZVyrWWf2Sao3evhuP5wzmPQ7gzwVvHCzpTm8JsP4KfXYfLd8Hx/GPIQnHhN6MdpUREt2LprcdlCiJuulFJHKi6ACbfCuCshOhGu/gR++7mtdVQ1eZQRgZ7Xwo0zoFkPmPh7eOti2HPkqUalji7YBNJNRPb6b3lA17JlEdkbygCVqtP27YDXzrK1hQF/hDHfQeus0L1+g5Zw9QQ451+wfib8px/Meyc8g36piBPsWFg6dKhS4XZgF7wxFHashMvfgY7nhud9PB7ofT20GQyf3AQf32h7ap3/FCSnh+c9VUTQ7hdKuVGpDz4YBbnL4Yr/hS95lJfaBq79DM58CFZ9A//pAwvHa21EHZUmEKXcaMYzsPJrOOdRWzOoKR4v9L8ZxkyHhq3hg5Hw/jWwb3vlz1V1jiYQpdxmTw58+wh0ONd20XVCo/bw2y/htP+DZZPguT6wdKIzsSjX0gSilNtM+bu9kvysfzrbrdYbBafcDjd8ay9IfPc38MH1sH+nczEpV9EEopSb5G2FRR/YmodbLu5L7wzXfwOD7oTFH9qeWss/dzoq5QKaQJRyk59eh9Ji2yvKTbzRcOpdMGoKJKTC/y6H8SP13EgdpwlEKbcwxg5T0mawewc6bNYdRmdD1l9hySfw7Emw4H3tqVVHaQJRyi02z4O9G6GLy0foiYqBrL/YixobtoYPR9kaiV7FXudoAlHKLX75ChBod6bTkQSm8fEw8ksY8g9Y/S38py/Mee3QUPIq4mkCUcot1s+0J6wT05yOJHAeL/S7CX430zZvfXob3ebfCztWOR2ZqgGaQAKx/geii3Y7HYWKZKYUcuZAxklORxKchq3smFrnP01y3mp4/mR7MaRPx1qNZMEO5153+Ergg5H03rcTGu6EE6/VCXhUyMUf2AyFeyHjV9NO1x4i0PMaftyeRP+d4+HLe2DBu3Dek7W7XOqo9D9hZbxR8JsPyU9qDZ/+AV45AzYvcDoqFWES9vtPQKd1cDaQECiKTbWDPw5/w44mPPZ0e+wc2OV0aCrENIEEolF75nf7O1z0MuxeBy8Ngi/usnNRKxUC8Qc22QW3dt+tKhE7te7NP0Lf39nuyc+eBPPf1S6/EUQTSKBEoOtwuHm2nYhn1vPwbG9Y/LEeEKraEvZvtBfoJTR0OpTQik2Gs/5hrx2p3xI+Gg2vnw/bf3E6MhUCmkCqKr4BnPcEjPoaElPtSKVvXwK5K5yOTNVi8Qe22GsqIlXTbjDyK3vsbFlgp9H9+m9ai6/lNIEEK6MXXJ8NZz0MG36E5/vZZi1t51VBiC7eA4mNnQ4jvDwe6PVbuHkOnHAxTH8cnukJP78NpXrtSG2kCaQ6vFHQ90a45Sfo8RvbrPX0iTB7rHZfVFUSXZwXec1XR5PUGC58wY6rldICPvkdjB0M639wOjJVRZpAQiGpkZ3+c8x39kKwz26HF0+B1dlOR6ZqA2OILt5rz4HUJRm9bLPWhS9B3hZ49Uw7QOPuDU5HpgKkCSSUmnSBaybC8DehaB+8MQzeuAA2/uR0ZMrNivLxmJK6UwMpz+OBbpfZZq2Bf4Jln8IzJ9rmYB3p1/U0gYSaCHQaCjf9aOeW3jwfXj7VTsaTu9zp6JQblU3QVNdqIOXFJsHge2wi6TocfngBnuoGU/8BBXucjk4dhSaQcImOs3NL/34+ZN0Fq7LtYHMf3Qg71zgdnXKT/TvsfV1OIGXqt4Bhz8HvfoC2p9mpfZ/qBt8/bWv1ylU0gYRbXD3IutMmkr6/s7PNPdMTPhgFWxc7HZ1yA62B/Fqj9vZK9tHZ0KwHfHUvPHECZD+iU+q6iOsSiIg0FJGvROQX/32Do+z3hYjsFpFPazrGoCSmwpCH/InkRlg2yfaFf+cy7X1S1x3w/0OMr/CrXrc16wEjPoLffgktekP2P+DJLnacrb2bnY6uznNdAgHuBKYYY9oBU/zrFXkMGFFjUYVKvaY2kfxhkZ3VbcOPtvfJ2NPtMA8lhU5HqGpa4V57H1vP2Tjc7Lg+cOW7MOZ7aH8WzHzOJpIPRtljSEeDcIQbE8gw4HX/8uvABRXtZIyZAtTey1gTGtpZ3f6wCM56xF6A+NFoeLwTTHkAdq93OkJVU8quxo7TBFKpJifAJa/ALXPhpJGwYrId4PTFgfDTG1CY73SEdYoYl2VuEdltjKnvXxZgV9l6BftmAXcYY847xuuNBkYDpKen9xw3blxQceXn55OUlBTUcwNiSmmwawHNN04idcdshFJ2p5zAlianktuoP76ohJC9VdjLUkMipRytVr9Jiw0fMW3gB7YXXy1Xk5+Lt+QA6Vuzab5xEon71+PzxJLbqB9b009lV4MuIN5qvX6kfMeqW45TTz11rjHmV2PyO5JARORroEkFD90NvF4+YYjILmPM0c6DZFFJAimvV69eZs6cOUFEDNnZ2WRlZQX13CrbvQEWjIP542DHSoiKgw5nQ8fzoN0ZEJdSrZev0bKEUaSUg8/uoPjncUTfk+N0JCHhyOdiDKyfBfP/Zwc4LdwDyc2g8wXQ8Vxo0deOHFFFkfIdq245RKTCBOLIhFLGmNOP9piIbBWRpsaYzSLSFNhWg6G5Q/0W9qKqU+6AjXMPHRSLPwJPNLQ6BTqcA20G2wH4IuBXa51WmEdJVALRTsdRm4lAy372dvYjsPxzO5nV7LEw6z+2h1v7s6H9EMgcUDcv2gwDN85IOAG4BnjYf/+Js+E4SMQO95DRC85+FHJmw7LP7G3SHXafehnQaqC9teitCaU2KtyLzxu6Jso6LzoeTrjI3grzYOUUe8wsnQjz3gIEmna1x0zmQHt8aUIJihsTyMPAeyIyElgHDAcQkV7AGGPMKP/6d0BHIElEcoCRxpjJDsUcfh4vHNfX3s54AHasgjXf2tuKL2D+O3a/uPq262PzE+194052HoYgqu+qhhTmURIV73QUkSk22TZjdb4AfMW2Rr/6W1gzDX540c7bDvYYaX4iNDsRmnW3M0MmRfjoyCHguv8qxpgdwGkVbJ8DjCq3fkpNxuUqIpDW1t5OGmmHwt622B4cG3+CTT/B9CfB+Oz+3hho2AbS2kFae5puPQArfXYk1JTmEJPobHnqusK9lETpZxB23uhDP8Ky/gJF+2HjnEPHTM5c20xcJi6FHjFNYPdJkNoaUo6DlAx7S26qP8pwYQJRQfB47ECOTbrY2RIBig/YK91zl8H2FXYGuK2LYdmndDClsOK5Q8+Pb2APiITUim9x9WySiUny3xIPrXvc2BO8linYiy+6hdNR1D0xCYeaf8vk58LWhXaCuO0rKF35A/zyJcw74lSseOwxk9jIHiOJaZCQZi8YTki11/TEJttjJDbp0LETm2Q7xURIM7MmkEgVHX/o/El5vmJmfvUR/Y7PgD05/tsGyN9mx2TatsTe798JBNBDLzrB1nCiYsEba3/lRfnvvbH+x2Lsssdrb+K1B+Bhy55jbC/3GBw8+DLXrYPS78sdjHLY40dfp4r7H229MgHut287JWkdAnxNFVZJjSBpsO2gAswv671UmA97N9pjZc/GQ8fO/u121OAdv8C+HVAcwHhd4rVJpOy4OHgfW+5Y8t97ou33reyYqOiYOewxzxHHkABC5vr1cMrJ9rgMIU0gdY03msK4xtCy/7H3K/XZUVD3bbcnIovy7WB2RfmHlgv9y74iewW9rxh8hYcv+4qhYK/dp7TEvq4ptc1rpT7b/fLgcgXbTal/3b+tLKkZQ0uAde66jilY+xO0BuJqsUnQqIO9HUvxAfsDrDDPf3zkHTpOyq8fPGYKoaToiPtCKCmwx1/Zd/+w+9LDj4uDx0epbc4+bJs9ZloaA6XPaAJRNcTjtT1TXNw75duK+rYbc/g9YVoPRKDXWImwceZc2gX+ysqtouPtORKX+TY7m6zouJC/riYQFVmkqs1MSqlg6RlQpZRSQdEEopRSKiiuG0wxnEQkF3txYjDSgEiZpDlSyhIp5QAti1tFSlmqW46WxphGR26sUwmkOkRkTkWDidVGkVKWSCkHaFncKlLKEq5yaBOWUkqpoGgCUUopFRRNIIF7yekAQihSyhIp5QAti1tFSlnCUg49B6KUUiooWgNRSikVFE0gSimlgqIJ5AgicpaILBeRlSJyZwWPx4rIu/7HfxCRzJqPsnIBlGOgiPwkIiUicokTMQYqgLL8UUSWiMgCEZkiIi2diDMQAZRljIgsFJF5IjJdRDo5EWcgKitLuf0uFhHjnxTOdQL4TK4VkVz/ZzJPREZV9DpuEMhnIiLD/cfLYhF5p1pvaIzRm/8GeIFVQGsgBpgPdDpin98BL/iXLwfedTruIMuRCXQF3gAucTrmapblVCDBv3yjGz+TKpSlXrnlocAXTscdbFn8+yUD04BZQC+n4w7yM7kWeNbpWENUlnbAz0AD/3rj6ryn1kAO1xtYaYxZbYwpAsYBw47YZxjwun95PHCaiOtG7qu0HMaYtcaYBUCpEwFWQSBlmWqM2e9fnQW4bzhUK5Cy7C23mkiVhv+tUYEcKwB/Bx4BCmoyuCoItBy1QSBluR54zhizC8AYc8RMWVWjCeRwzYEN5dZz/Nsq3McYUwLsAVJrJLrABVKO2qKqZRkJfB7WiIIXUFlE5CYRWQU8CtxaQ7FVVaVlEZETgRbGmM9qMrAqCvT7dbG/iXS8iLh18pZAytIeD7+AeQAAApRJREFUaC8i34vILBE5qzpvqAlERQwR+Q3QC3jM6ViqwxjznDGmDfAX4B6n4wmGiHiAx4HbnY4lBCYCmcaYrsBXHGqBqI2isM1YWcAVwMsiUj/YF9MEcriNQPlfFxn+bRXuIyJRQAqwo0aiC1wg5agtAiqLiJwO3A0MNcYU1lBsVVXVz2UccEFYIwpeZWVJBk4AskVkLdAXmODCE+mVfibGmB3lvlNjgZ41FFtVBfL9ygEmGGOKjTFrgBUQ/FxmmkAONxtoJyKtRCQGe5J8whH7TACu8S9fAnxj/GejXCSQctQWlZZFRHoAL2KTR7XadMMskLKUP5jPBX6pwfiq4phlMcbsMcakGWMyjTGZ2HNTQ40xc5wJ96gC+UyallsdCiytwfiqIpDj/mNs7QMRScM2aa0O+h2d7jngthtwDjYrrwLu9m97APvlB4gD3gdWAj8CrZ2OOchynIT9NbIPW4Na7HTM1SjL18BWYJ7/NsHpmKtRlqeAxf5yTAU6Ox1zsGU5Yt9sXNgLK8DP5J/+z2S+/zPp6HTM1SiLYJsWlwALgcur8346lIlSSqmgaBOWUkqpoGgCUUopFRRNIEoppYKiCUQppVRQNIEopZQKiiYQpZRSQdEEopRSKiiaQJRymIhkiMhlTsehVFVpAlHKeacBJzodhFJVpVeiK+UgERkAfALsBvKAi4wxwY9NpFQN0gSilMNE5AvgDmPMIqdjUaoqtAlLKed1AJY5HYRSVaUJRCkH+YfU3mPs7JZK1SqaQJRyViawyekglAqGJhClnLUMSBORRSLS3+lglKoKPYmulFIqKFoDUUopFRRNIEoppYKiCUQppVRQNIEopZQKiiYQpZRSQdEEopRSKiiaQJRSSgXl/wHdutktg4QaEwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t0_Na = 0.3\n",
    "t1_Na = 0.35\n",
    "t0_K = 0.35\n",
    "t1_K = 1.0\n",
    "\n",
    "G_K_0 = 1e-6\n",
    "G_Na_0 = 4.3e-3\n",
    "\n",
    "G_K = f'{G_K_0}+np.heaviside(t,1)-np.heaviside(t-{t0_Na},1)+np.heaviside(t-{t0_K},1)-np.heaviside(t-{t1_K},1)'\n",
    "G_Na = f'{G_Na_0}+np.heaviside(t-{t0_Na},1)-np.heaviside(t-{t1_Na},1)'\n",
    "# G_K = '1e-1'\n",
    "# G_Na = '1e-6'\n",
    "X_chemo = {'Na_G':G_Na,'K_G':G_K}\n",
    "dat = Simulate(s,sc,X_chemo=X_chemo,prefix=['Na_','K_'],T=0.6)\n",
    "#st.plot(s,dat)\n",
    "st.plot(s,dat,plotPhi=True,species=['Ei','Ee'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Resting potential = -64.90 mV\n"
     ]
    },
    {
     "data": {
      "image/png": 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MCUeb2lm285jVoagYizhJiIhLRK4Qkb8DC4DNwDUxiyzkLKDWGLPdGNMOzAfmRnsnJ1t9LDvgxxidbkDFTmsAMjyJ3R/RYdrIYjLcThZok1PSO23jqIjMIFRzuAxYRugP9TxjTFOMYwMoA/Z0er4XmHJKfPOAeQBer5eampoe7+SdfT7uX9tOfsbrDMtL/F/ixsbGXv0/2FEylaW5zYcEAglfnsbGRt5b8hbV+fDcyt1Mzz2CI0FrR8l0fsWqLJH0oN0JPALcYYw5HvUI+sgYcx9wH8CkSZPMtGnTevwdE1t9PLT+FfY7S/nStMRvzaqpqaE3/w92lExl+d3KheTlZDJt2gVWh9InHcfkZP/9fP3RlWRXjuOswflWh9UryXR+xaoskXRcX2SMecCiBLEPqOj0vDz8WlTlpLsZW+jkpbUHCAa1yUnFhi8Iae7E7rTubPqoYtJcDh1Yl+R60icxSUSeFpEPRGSNiKwVkTWxDA54HxguIoNFxANcBzwXix1NKXFxsKGV5btsV1lSScIXMAl/Z1Nn2WkuLhxRxIJ1enGVzHpyxv4deAj4DHAFMCf8b8wYY/zA/wFeJnQn1ePGmPWx2Nf4YifpbgcvrNkfi69XKlSTcCV+n1dnl59RyqGGNr24SmI9SRJHjDHPGWN2hG+H3WWM2RWzyMKMMS8ZY0YYY4YaY34Sq/2ku4SLRhXz0tqDBPSqSMVAKEkkT00C4JLRXr24SnI9OWN/ICIPiMj1InJNx0/MIrPA5WMHUNfYxns7dLoBFX2+oEmqPgkIjR6/eJSXl9Ye0IF1SaonZ+y/AOOB2YSamTqanJLGRaOKyfQ4eWGNdsSp6PMFkq+5CWDOGaXUNbbz3g4dWJeMejKJzGRjzMiYRWIDGR4nF4/2snDdQf7rympczuS66lPWSsbmJgjd5ZTlcfL86v2cO6zQ6nBUlPXkjF2SClNizDmjlGNN7SzZpk1OKrp8weS6u6lDutvJjCovC9cfpN2vTU7Jpidn7FRgVXiyvXjdAht3F44oIjvNxYva5KSizBeANHfyNTcBXDFuACeafbxTW2d1KCrKepIkZgPDgZnE6RZYK+hVkYoFY0zSNjcBnD+8iH7pLp7Xu5ySTk9ngf3ETyyDs8qcM0qpb9GrIhU9voDBkLxJwuNyMHtMCa+sP0SrL2B1OCqKkvOM7aPzhxeRo1dFKora/KE/nMl4d1OHK8YNoLHNT83mI1aHoqJIk0QXPC4Hs6pLeFWvilSUtIWbLpNtnERnZw8poCDLowPrkkwka1xXxyMQu5lzRikn2/y8uUWvilTffZgkkrS5CcDldHDp2BIWbTxMc7vf6nBUlERyxv6t44GIfKnzBhHJjHpENnHusEL6Z7p5Xu9yUlHQ5kv+5iaAOWcMoMUXYNHGw1aHoqIkkiTReTWRr52y7a0oxmIrbqeDS8eW8tqGQzS16VWR6puOmkR6Ejc3AUyuzMfbL43nV2uTU7KI5IztPNvdqctPJfUZf9X4Mlp8AV7ZoEs0qr75qLkpuWsSTodw2dhSarYcoaHVZ3U4Kgoi+SNfIiK3iMgEPpkkknq61EmD+lOWl8EzK/WqSPVNx5gbdwpM9XLFuAG0+4O8sv6Q1aGoKIjkjP0hMBH4NVAuIhtE5EkR+SmQ1BO1OBzCleMH8HZtHXWNbVaHoxKYPxhKEi5nYq4F3RMTKvKoyM/g2VVRX0RSWSCS5UvvM8Z83RhzoTGmkNCI6weBFmBtrAO02lXjywgEDS9oG6vqA38gVOl2OZI/SYgIV48v453aOg43tFodjuqjHtV9w01O3wDuJTQtx3mxCMpORpbkMKokh2dWaZJQvdexkJUzBZIEwNwJZQQNPKcXVwkvknESI0TkByKyGXgAOApcaIyZAqTEBPJXTShj1Z4T7KxrsjoUlaD84SSRCn0SAEOLshlXnsvTK7XJKdFFcsZuAi4DrjXGTDTG/NwYsyO8Lak7rjtcOW4AIvCs1iZULwXCfRKpUpOA0MXV+v0NbDl00upQVB9EkiSuAXYAr4jI30TkChFxxzguWxmQl8FZlfk8u2ofxqREXlRR1lGTSIU+iQ5zzhiA0yE8o7WJhBZJx/UzxpjrgGHAAmAesFdEHgL6xTg+27hqQhnb65pYu6/e6lBUAkq1PgmAopw0zh9eyLOr9hMM6sVVourJVOFNxphHjDFXAKOAd4GkW3SoO5eNKcXjdOiYCdUrH93dlBp9Eh2unlDGvhMtLNuZEt2XSalXZ6wx5nj41tiLoh2QXeVmupk2sojn1+z/8KpQqUh1jJNwpsA4ic5mVpWQ5XFqk1MCS63Lmj66ekIZR062sWSbLkakeiYV+yQAMjxOZo0p4cW1B3Ta/QSlSaIHpo8qJifdxVMf6FWR6plAiiYJCF1cnWz1s3iTzgybiCxNEiLy3yKySUTWiMjTIpLXadudIlIrIptFZJaVcXZIdzu5YtwAFqw7wEmdvEz1QKr2SQCcM7SQopw0HTORoKw+Y18FxhhjzgC2AHcCiEgVcB1QDcwG/iAitpg+89qJ5bT6gry0VteZUJH78O6mFOuTgNAdXXPHDWDx5sOcaG63OhzVQ5YmCWPMK8aYjsUalgLl4cdzgfnGmLbwwL1a4CwrYjzVhIo8hhZl8Y/le60ORSWQVO2T6HDVhDJ8AaPTdCQgl9UBdPIF4LHw4zJCSaPD3vBrnyAi8wiN3cDr9VJTU9OrnTc2Nkb82TP7t/OPLU3Mf/F1SrKsrox9Uk/KYnfJUpat20JX0G+/9WbCJ4reHpOBOQ7+vHgjA9t2Rj2m3kqW8wtiV5aYJwkReQ0o6WLTXcaYZ8PvuQvwA3/v6fcbY+4D7gOYNGmSmTZtWq/irKmpIdLPjj6zlSfvXsQe1wCumzaqV/uLpZ6Uxe6SpSwrfVtg61YumjYNR4Inid4eky+4d/DD5zdQPOJMqgbYYxxuspxfELuyxPwy2BhziTFmTBc/HQniFkIzyt5oPprzYh9Q0elrysOv2YK3XzoXjCjiqQ/26ZgJFZFA0CCQ8AmiL+aOL8PjdPCPFXusDkX1gNV3N80GvgNcaYxp7rTpOeA6EUkTkcHAcGCZFTF2558mVnCgvpV3anXMhDo9f9CQIhPAdqt/locZ1V6eWbmPNr+OmUgUVp+29wA5wKsiskpE7gUwxqwHHgc2AAuB24wxtjqrLh5dTG6GmydWaAe2Or1AMEgK3tj0CZ+dVMHxZh+LNuqYiURhace1MWbYp2z7CfCTOIbTI+luJ3PHD+Cx9/dQ3+IjNyOlJsZVPeQPGlK4pelD5w0rpDQ3ncfe38NlY0utDkdFwOqaREK7dmI5bf4gL6zR2/rUpwsEjdYkCI2ZuHZiOW9uPcL+Ey1Wh6MioEmiD8aW5TLSm8PjOmZCnUaoJqFZAkL9ecbAUx/o700i0CTRByLCZydXsHrPCTbsb7A6HGVj/oD2SXQYWJDJ2UMKeHz5Xl1nIgFokuijz5xZhsfl4JFlu6wORdmY9kl83Gcnl7P7WLOuM5EANEn0UV6mhzljS3lm5X6a2vyn/4BKSYGgwaW/bR+aXV1KTpqL+ct2Wx2KOg09baPg+ikDaWzzawe26pbWJD4uw+Pk6jPLeGntQY416aR/dqZJIgomDerP8OJsHnlPr4pU1wIBvbvpVDdNHUR7IMg/lusIbDvTJBEFIsINUwayem896/bVWx2OsiG9u+mTRnhzOKsyn0eW7dYObBvTJBEl10woJ83l4BFtY1Vd0BHXXbtx6kB2HW3mLZ3exrY0SURJbqabOWcM4NmV+2jUDmx1Cu2T6NrsMSUUZHl4eKneHWhXmiSi6IYpFTS1B3h2lW0mrFU24Q/oBH9dSXM5+ezkChZtPKQjsG1KT9soOnNgf6pK+/GXJTv5aNZzpXRajk9zw1kDMaC3w9qUJokoEhFuObeSLYcaWbLtqNXhKBvxB4Pa3NSNivxMpo0oYv77e/AFglaHo06hSSLKrhw3gIIsDw+9s9PqUJSNhGoSmiW6c9PUQRw+2cbCdQetDkWdQpNElKW7ndwwZSCLNh1i19Emq8NRNqEd159u+shiKgsy+fM7O6wORZ1Ck0QM3DR1EE4R/vqu3rGhQgK6Mt2ncjiEfzl3MCt3n+CD3cetDkd1oqdtDHj7pXPZ2FIef3+P3g6rAK1JROLaieXkpLt48G2tTdiJJokY+ZdzKznZ5tc58xUQqknoL9uny0pzcf1ZA1m47iD79HZY29DzNkYmDOzPuIo8/vednTrlgAolCa1JnNbN51QC8NclOy2NQ31Ek0QMfeHcSrbXNbFoky76nuoCOndTRMryMphdXcIjy3br1Ps2oUkihi4fW0p5/wz+UFOrg+tSXNBoTSJSXzx/MCdb/cx/X2eHtQNNEjHkcjr4ygVDWLn7BMt26ApcqcwfNGhFIjJnDuzPlMH53P/mdtr9OrjOapokYuyfJlVQkOXhj29sszoUZaGg9kn0yNemD+NgQytPr9QbP6ymSSLG0t1OvnDeYGo2H2HD/garw1EWCWhzU49cMLyQMWX9uPeN7QT0xg9L2SJJiMgdImJEpDD8XETktyJSKyJrRORMq2Psi5umDiI7zaW1iRSmt8D2jIhw27Rh7KhrYsG6A1aHk9IsP29FpAKYCXSeAvJSYHj4Zx7wRwtCi5rcDDc3ThnIi2v2s7NOp+pIRdrc1HOzqksYUpTF7xdv0xs/LGR5kgD+B/gO0PksmAv81YQsBfJEpNSS6KLki+cPxuNy8NtFW60ORVlAm5t6zuEQbr1wKBsPNLB4s95GbhWXlTsXkbnAPmPMavn4rR9lQOf73/aGX/tEvVNE5hGqbeD1eqmpqelVLI2Njb3+bKSmlTl5euU+JmUdY0B27PJzPMoSL8lSFr8/iN8XSIqyxPOY9A8aijKE//vUB3B2etTHmiTL+QWxK0vMk4SIvAaUdLHpLuDfCTU19Zox5j7gPoBJkyaZadOm9ep7ampq6O1nIzV2Uhtv/mIxSxryuGdO7LpZ4lGWeEmWsphXXiI9zZ0UZYn3MWnI28vtj6+mrXAUl46NboNCspxfELuyxLy5yRhziTFmzKk/wHZgMLBaRHYC5cAHIlIC7AMqOn1Nefi1hFaQncYt51Ty4toDbDqodzqlkoCOk+i1uePLGFaczf97dYve6WQBy/okjDFrjTHFxphKY0wloSalM40xB4HngH8O3+U0Fag3xiTFLQ7zLhhCtsfFr1/VvolU0TF3lx06ABOR0yHcPmMEtYcbdf14C9j1vH2JUE2jFrgf+Jq14URPXqaHL5w3mIXrD7Jm7wmrw1FxEAjfmaMd1703u7qE6gH9+PVrW3WJ0zizTZII1yjqwo+NMeY2Y8xQY8xYY8xyq+OLpi+dP5iCLA8/fnGj3tqXAjqaSJyaJHrN4RDumDmC3ceamb9s9+k/oKLGNkkileSku/nWjBEs23GMl9cfsjocFWNBrUlExfSRxUwdks+vXt1CfbPP6nBShiYJi1w3uYIR3mzuXrBRJzFLch01CdGe6z4REf5zThUnWnz89nXt04sXTRIWcTkd3HV5FbuONvPXd3daHY6KoWD4GkBrEn1XPSCX6yZX8JclO9l2pNHqcFKCJgkLXTiiiAtHFPGbRVs51tRudTgqRrTjOrrumDmSDLeTn7640epQUoImCYvddfloWtoD/GyBnvDJqqO5SZNEdBRmp/H1i4exaNNhanS6jpjTJGGxEd4cvnj+YB5fvpf3th+1OhwVAx92XFscRzK55ZzBDCnK4vvPrqelPWB1OElNz1sb+ObFwynvn8Fdz6zTTuwkpDWJ6PO4HPz06rHsPtbMrxdtsTqcpKZJwgYyPS5+NHcMtYcb+ZOuOZF0NEnExtQhBVw3uYIH3trB+v31VoeTtDRJ2MT0UcVcfkYpv319q65gl2R0nETs3HnpaPpnevjek2t1JHaMaJKwkR/NHUNuhofbH19Fm1/bWZOFjpOIndxMNz++qpq1++r5na7VEhOaJGwkP8vDzz8zlk0HT/Kb1/SETxZak4it2WNK+cyZ5dyzuJYVu45ZHU7S0SRhMxeP9vK5SRXc+8Y2lurdTkkhoIPpYu6HV1YxIC+Dbz22msY2v9XhJBVNEjb0n1dUUVmYxdcfXemu+VMAAA4NSURBVMnhk61Wh6P6KKBThcdcTrqb//ncePYeb+Z7T67RiTOjSM9bG8pOc/HHGydystXHNx9dpQutJDhtboqPyZX5fHvWSF5Yc4CH3tlpdThJQ5OETY0syeHHV43l3e1H+cXLm6wOR/WB3gIbP7deOJSZVV5++tJG3t+p/RPRoEnCxq6dWM6NUwbypze28/jyPVaHo3pJ526KHxHhl58dR0V+Jrc+vII9x5qtDinhaZKwuR9eWc35wwv596fWsmRbndXhqF4Iak0irvqlu3ng5kn4AoabH1rGiWadPLMvNEnYnNvp4J4bzqSyMIuv/m2FDrRLQB81N2mWiJehRdnc/8+T2HushXl/W0GrT8cd9ZYmiQSQm+HmoVsmk5Xm4vMPvkft4ZNWh6R6oKO5SVNEfJ01OJ9ffnYc7+88xlcfXqEDVHtJk0SCqMjP5O9fmoKIcMP977GjrsnqkFSEdNEh61w5bgB3Xz2Wms1H+NrDH+gEmr2gSSKBDCnK5u9fmoI/aPine9/VSc0ShHZcW+u6swbyk6vHsGjTYeb9bTnN7TrYric0SSSYkSU5PP6VqXicwnV/WqprUCQA7bi23o1TBnH3NWN5c8sRrr9vKUcb26wOKWFokkhAw4pzeOLWc/DmpvP5B5cxf9luq0NSn0LHSdjD9WcN5N6bJrLp4Emu+eMSthzSvr1IaJJIUAPyMnjiq2czZUg+33tqLf/xzFptb7UpbW6yj5nVJTzy5ak0tQWYe887vHdAm55Ox/IkISJfF5FNIrJeRH7R6fU7RaRWRDaLyCwrY7SrvEwPD90yma9cMISHl+7mqt+/o1dHNhTUW2BtZeKg/rz4jfOoHtCPP65u49+fXkuTTgrYLUuThIhMB+YC44wx1cAvw69XAdcB1cBs4A8i4rQsUBtzOR3cedlo7vv8RA41tDLnd2+zYIcPvy7AYhsBXePadrz90nl03lQuHezm0WW7ufQ3b+msy92w+ry9FfiZMaYNwBhzOPz6XGC+MabNGLMDqAXOsijGhDCzuoSF/3oBFwwv4rHN7cz53ds6d41NfLTokMWBqI9xOx18bqSHx79yNgDX3beUbz22ikMNOvNyZ2LllLoisgp4llBtoRX4tjHmfRG5B1hqjHk4/L4HgQXGmCe6+I55wDwAr9c7cf78+b2KpbGxkezs7N4VxEaMMSzZ1cSTOx0cazVMKHZy9TA3A/slZkUsGY7Lkv1+7lvTxvcnGoYUJXZZIDmOSYeOsrT5DS9s97Fghw+nA2ZWupk1yE22J3Eye1+Oy/Tp01cYYyZ1tc3Vp6giICKvASVdbLorvP98YCowGXhcRIb05PuNMfcB9wFMmjTJTJs2rVdx1tTU0NvP2o3U1PCtG87jgbd2cP9b2/n+klYuG1vCl88fwviKvIRaRjMZjkvdir2wZjXZWZkJXxZIjmPSoXNZZgG7jjbx84WbeH7tQV7fE+Tmcyq55dxKinPSLY0zErE6LjFPEsaYS7rbJiK3Ak+ZUHVmmYgEgUJgH1DR6a3l4ddUhDI9Lr5x8XBuPruSB9/ezp/f2clLaw8ytiyXz589iMvHlpKVFvPDr9BxEolkUEEWf7hxIpsPnuS3r2/lj29s4743tzNrTAk3ThnI2UMKEuoiKxqs/ivxDDAdWCwiIwAPUAc8BzwiIr8CBgDDgWWWRZnAcjPd3D5zJPMuHMrTH+zlr+/u4jtPrOH7z67j4lFerhhXyvnDizRhxJDeApt4Rpbk8PsbzmT7kUYeeW83/1ixlxfXHGBAbjqXji3l8jNKGV+ehyMFDqrVfxn+DPxZRNYB7cDN4VrFehF5HNgA+IHbjDE6O1cfZKe5+PzZldw0dRDv7zzO86v389LaA7y49gBupzBxUH8uGFHEecMKGV3aD7fT6nsakocuX5q4hhRl8x9zqvj2rJEsXHeQ51fv52/v7uLBt3dQkOXhnGGFnDesgHOGFlLePyMpaxmWJgljTDtwUzfbfgL8JL4RJT8R4azB+Zw1OJ8fXFHFsh3HeGPLEd7cWscvFm7mF2wmzeVgTFku4yvyqB7Qj+HFOQwtziLTY/U1RWL6aPnS5PsDkirS3U6umlDGVRPKaGj1sWjjId7aUsfbtXU8v3o/AIXZHsaW5YZ+yvMY4c2mvH8mzgSvbehvfQpzOR2cM6yQc4YVcidw+GQr720/xqo9J1i15wQPL91FW6dR3GV5GQwpyqK8fwYDcjMYkBf6KclNJz/TQ066KyWq3z2l03Ikl37pbq6eUM7VE8oxxlB7uJF3tx9lzd561u6t540tR+hYlt7jdDCwIJMhhVlU5GdSmpuOt186JbnplPQLPfa47F3H1CShPlSck84V4wZwxbgBAPgCQXYdbWLroUZqDzdSe6SRHXVNbDxwkrouJkhzOoT+mR7ys9z0z/SQl+kmK81FlsdFZpqTbI+LzDQXWR4nmWkuMtxOPC4HbqeQ5nLgdoZ+PC4HnvDjk+2Gk60+nA7BIR0/oavyRElIOk4ieYkIw705DPfmfPhac7ufjQca2Ha4iW11jew40sT2uibe2lpHSxeLH2V5nORleuiX4SYvw01eppvcDDf9Mtyku51kuJ1kuB1keJxkeFzh504yPA48zo9+hxrbYzOcQZOE6pbb6WBYcQ7DinM+sa3VF+BAfSv7T7RwqKGV480+jjW1cazJx/Gmdo41t7Ozrpmmdj9NbX6a2gO9n1vq9Ve63eSQUHISEZynJJDO2zrnEwkv/9PxR7tj06ntyR9ul64/19Vn5ZQNAtS3+D6MVSW/TI+LiYPymTgo/2OvG2NoaPVzsL6Vgw2tHKpv5VBDKydafNS3+DjR7KO+pZ1tRxo50eyjodVHqy/y35nLBruZE+3CoElC9VK628ngwiwGF2ZF/BlfIEhzW4Cmdj/N7X6a2wP4AkHa/Sb8bzD074ePDRs2bWbQ4KEEjSFgDMaEbikNGEMw/LirbcaEruCDJvRjDHQeN2oIPel4rWPTR88/vuGj7aab93e9veNBeX4G6c6DEf9fqeQjIuRmhGoJI0s+eeHVFWMMbf4gze0BWnwBWtoDtPpCj5vDF14dvzcndm+KSdyaJFTcuJ0OcjMd5Ga6I/5MTct2pl3Qo/GVtlVTc8jqEFSCERHS3U7S3aefMaGmfmtMYrB3j4lSSilLaZJQSinVLU0SSimluqVJQimlVLc0SSillOqWJgmllFLd0iShlFKqW5oklFJKdcvS5UujTUSOALt6+fFCQmtZJAMtiz0lS1mSpRygZekwyBhT1NWGpEoSfSEiy7tb4zXRaFnsKVnKkizlAC1LJLS5SSmlVLc0SSillOqWJomP3Gd1AFGkZbGnZClLspQDtCynpX0SSimluqU1CaWUUt3SJKGUUqpbKZckRGS2iGwWkVoR+V4X29NE5LHw9vdEpDL+UUYmgrJcICIfiIhfRK61IsZIRVCW20Vkg4isEZFFIjLIijhPJ4JyfFVE1orIKhF5W0SqrIgzEqcrS6f3fUZEjIjY9lbSCI7LLSJyJHxcVonIl6yI83QiOSYi8tnw78p6EXmkzzs1xqTMD+AEtgFDAA+wGqg65T1fA+4NP74OeMzquPtQlkrgDOCvwLVWx9zHskwHMsOPb7XjcYmwHP06Pb4SWGh13L0tS/h9OcCbwFJgktVx9+G43ALcY3WsUSjHcGAl0D/8vLiv+021msRZQK0xZrsxph2YD8w95T1zgb+EHz8BXCwdq9zby2nLYozZaYxZA0S+mro1IinLYmNMc/jpUqA8zjFGIpJyNHR6mkWn5bBtJpLfFYAfAT8HWuMZXA9FWha7i6QcXwZ+b4w5DmCMOdzXnaZakigD9nR6vjf8WpfvMcb4gXqgIC7R9UwkZUkUPS3LF4EFMY2odyIqh4jcJiLbgF8A34hTbD112rKIyJlAhTHmxXgG1guRnl+fCTdnPiEiFfEJrUciKccIYISIvCMiS0Vkdl93mmpJQiU4EbkJmAT8t9Wx9JYx5vfGmKHAd4H/sDqe3hARB/Ar4A6rY4mS54FKY8wZwKt81JqQaFyEmpymAdcD94tIXl++MNWSxD6g8xVCefi1Lt8jIi4gFzgal+h6JpKyJIqIyiIilwB3AVcaY9riFFtP9PSYzAeuimlEvXe6suQAY4AaEdkJTAWes2nn9WmPizHmaKdz6gFgYpxi64lIzq+9wHPGGJ8xZgewhVDS6D2rO2Pi3PHjArYDg/mo46f6lPfcxsc7rh+3Ou7elqXTe/8Xe3dcR3JcJhDqtBtudbx9LMfwTo+vAJZbHXdfz6/w+2uwb8d1JMeltNPjq4GlVsfdy3LMBv4SflxIqHmqoE/7tbrgFvxHX0You24D7gq/9l+Erk4B0oF/ALXAMmCI1TH3oSyTCV1ZNBGqDa23OuY+lOU14BCwKvzznNUx97IcvwHWh8uw+NP+8Fr9c7qynPJe2yaJCI/L3eHjsjp8XEZZHXMvyyGEmgE3AGuB6/q6T52WQymlVLdSrU9CKaVUD2iSUEop1S1NEkoppbqlSUIppVS3NEkopZTqliYJpZRS3dIkoZRSqluaJJSKMREpF5HPWR2HUr2hSUKp2LsYONPqIJTqDR1xrVQMich5wLPACeAkcI0xZru1USkVOU0SSsWYiCwEvm2MWWd1LEr1lDY3KRV7I4FNVgehVG9oklAqhkSkEKg3oVUOlUo4miSUiq1KYL/VQSjVW5oklIqtTUChiKwTkXOsDkapntKOa6WUUt3SmoRSSqluaZJQSinVLU0SSimluqVJQimlVLc0SSillOqWJgmllFLd0iShlFKqW/8fHlUSNOXEekEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def PlotAction():\n",
    "    t = dat['t']\n",
    "    phi_Ei = dat['phi'][:,s['species'].index('Ei')]\n",
    "    phi_Ee = dat['phi'][:,s['species'].index('Ee')]\n",
    "    dE = phi_Ei-phi_Ee\n",
    "    \n",
    "    print(f'Resting potential = {1000*dE[-1]:.2f} mV')\n",
    "    \n",
    "    X_G_K = dat['X'][:,s['species'].index('K_G')]\n",
    "    X_G_Na = dat['X'][:,s['species'].index('Na_G')]\n",
    "\n",
    "    v_Na = dat['V'][:,s['reaction'].index('Na_r')]\n",
    "    v_K  = dat['V'][:,s['reaction'].index('K_r')]\n",
    "    \n",
    "    \n",
    "    conc_Na_e = K_Ie*dat['X'][:,s['species'].index('Na_Ie')]\n",
    "    conc_Na_i = K_Ii*dat['X'][:,s['species'].index('Na_Ii')]\n",
    "    conc_Na_e_0 = conc_Na_e[0]\n",
    "    conc_Na_i_0 = conc_Na_i[0]\n",
    "\n",
    "    conc_K_e = K_Ie*dat['X'][:,s['species'].index('K_Ie')]\n",
    "    conc_K_i = K_Ii*dat['X'][:,s['species'].index('K_Ii')]\n",
    "    conc_K_e_0 = conc_K_e[0]\n",
    "    conc_K_i_0 = conc_K_i[0]\n",
    "\n",
    "    plt.plot(t,1000*dE)\n",
    "    plt.grid()\n",
    "    plt.ylabel('$\\Delta E$ mV')\n",
    "    plt.xlabel('$t$')\n",
    "    plt.savefig('Figs/action.pdf')\n",
    "    plt.show()\n",
    "    \n",
    "    plt.plot(t,v_Na,label='Na')\n",
    "    plt.plot(t,v_K,label='K')\n",
    "    plt.grid()\n",
    "    plt.legend()\n",
    "    plt.ylabel('$i$ mA')\n",
    "    plt.xlabel('$t$')\n",
    "    plt.savefig('Figs/action_current.pdf')\n",
    "    plt.show()\n",
    "    \n",
    "    plt.plot(t,100*(conc_Na_e-conc_Na_e_0)/conc_Na_e_0,label='Na_e')\n",
    "    plt.plot(t,100*(conc_Na_i-conc_Na_i_0)/conc_Na_i_0,label='Na_i')\n",
    "    plt.plot(t,100*(conc_K_e-conc_K_e_0)/conc_K_e_0,label='K_e')\n",
    "    plt.plot(t,100*(conc_K_i-conc_K_i_0)/conc_K_i_0,label='K_i')\n",
    "\n",
    "    plt.legend()\n",
    "    plt.grid()\n",
    "    plt.ylabel(r'$\\Delta c (\\%)$')\n",
    "    plt.xlabel('$t$')\n",
    "    plt.savefig('Figs/action_conc.pdf')\n",
    "    plt.show()\n",
    "    \n",
    "    plt.plot(t,X_G_K,label='G_K')\n",
    "    plt.plot(t,X_G_Na,label='G_Na')\n",
    "    plt.legend()\n",
    "    plt.grid()\n",
    "    plt.ylabel('Gating')\n",
    "    plt.xlabel('$t$')\n",
    "    plt.savefig('Figs/action_gating.pdf')\n",
    "    plt.show()\n",
    "    \n",
    "    \n",
    "\n",
    "PlotAction()"
   ]
  }
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