SGLT.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 SGLT.ipynb notebook. The\n",
    "PDF version \"Sodium Glucose Symporter\"\n",
    "is available [here](SGLT.pdf).***\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Introduction\n",
    "The Sodium-Glucose Transport Protein 1 (SGLT1) (also known as the\n",
    "\\ch{Na+}-glucose symporter \\citep[\\S~2.4.2]{KeeSne09}) was studied experimentally by\n",
    "\\citet{ParSupLoo92} and explained by a biophysical model\n",
    "\\citep{ParSupLoo92a}; further experiments and modelling were conducted\n",
    "by \\citet{CheCoaJac95}.  \\citet{EskWriLoo05} examined the kinetics of\n",
    "the reverse mode using similar experiments and analysis to\n",
    "\\citet{ParSupLoo92,ParSupLoo92a} but with reverse transport and\n",
    "currents.\n",
    "\n",
    "This note looks at a bond graph based model\n",
    "of SGLT1 based on the model of \\citet{EskWriLoo05}.\n",
    "\n",
    "The model of Figure 6B of\n",
    " \\citet{EskWriLoo05} is based on the six-state\n",
    "biomolecular cycle of Figure 2 of \\citet{ParSupLoo92a}. When operating\n",
    "normally, sugar is transported from the outside to the inside of the\n",
    "membrane driven against a possibly adverse gradient by the\n",
    "concentration gradient of \\ch{Na+}. \n",
    "\n",
    "A similar situation is analysed in \\S~1.1 of the book by \\citet{Hil89}\n",
    "and the corresponding bond graph of the biomolecular cycle is\n",
    "described by \\citet{GawCra17}."
   ]
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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",
    "## Data file\n",
    "import json\n",
    "\n",
    "## Save the figure\n",
    "SaveFig = False\n",
    "\n",
    "TranslateSVG = False"
   ]
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     "text": [
      "([-149.08132530120483, -128.50492880613362, -108.26396495071195, -88.92935377875138, -68.92045454545456, -49.776150054764514, -29.841182913472096, -9.930859802847777, 11.341730558597988, 30.71741511500545], [1.3909090909090907, 1.8090909090909086, 3.409090909090909, 3.6636363636363636, 4.236363636363636, 4.9818181818181815, 5.2272727272727275, 5.363636363636363, 4.863636363636363, 5.3])\n"
     ]
    }
   ],
   "source": [
    "## Load data from Eskandari et. al. Fig 3A\n",
    "## Digitised using  https://apps.automeris.io/wpd/\n",
    "\n",
    "def loadData():\n",
    "    \n",
    "    with open('SGLT_data.json') as f:\n",
    "        Dict = json.load(f)\n",
    "        \n",
    "    List = Dict['datasetColl'][0]['data']\n",
    "\n",
    "    X = []\n",
    "    Y = []\n",
    "    for item in List:\n",
    "        xy = item['value']\n",
    "        X.append(xy[0])\n",
    "        Y.append(xy[1])\n",
    "\n",
    "    return X,Y\n",
    "\n",
    "print(loadData())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Sodium-Glucose Symporter - zero membrane potential.\n",
    "This non-electrogenic version is used to compute species and reaction parameters from the \n",
    "published model values."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bond graph"
   ]
  },
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   "cell_type": "code",
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    "scrolled": true
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   "source": [
    "## Sodium-Glucose tranporter - no E\n",
    "if TranslateSVG:\n",
    "    sbg.model('SGLT_abg.svg')\n",
    "import SGLT_abg\n",
    "disp.SVG('SGLT_abg.svg')"
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "## Stoichiometry"
   ]
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   "source": [
    "## Stoichiometry\n",
    "s0 = st.stoich(SGLT_abg.model(),quiet=quiet)\n",
    "chemostats = ['Nai','Nao','Si','So']\n",
    "sc0 = st.statify(s0,chemostats=chemostats)\n",
    "#print(s['species'])\n",
    "#disp.Latex(st.sprint(s0,'K'))\n",
    "#print(st.sprints(s))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Convert parameters\n",
    "The model of \\citet{EskWriLoo05} is based on rate constants. The following code converts this into the parameters required for the bond graph model."
   ]
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   "source": [
    "def Keq2K(K_eq,N,K,tol=1e-6):\n",
    "    ## Compute BG C parameters K_c from equilibrium constants K_eq.\n",
    "    ## NB K_eq must be thremodynamically consistent.\n",
    "    \n",
    "    logK_eq = np.log(K_eq)\n",
    "    #print(K_eq)\n",
    "    #print(logK_eq)\n",
    "    \n",
    "    if len(K) != 0:\n",
    "        ##First check that Keq is thermodynamically consistent.\n",
    "        check = np.linalg.norm(K.T*logK_eq)/np.linalg.norm(logK_eq)\n",
    "        print(check)\n",
    "    \n",
    "    ## Transformation of mu to affinities\n",
    "    NN = -N.T\n",
    "    \n",
    "    ## Pseudo inverse\n",
    "    pNN = np.linalg.pinv(NN)\n",
    "    \n",
    "    ## BG C constants\n",
    "    K_c = np.exp(pNN@logK_eq)\n",
    "    \n",
    "    return K_c"
   ]
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   "cell_type": "code",
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     "text": [
      "Error in kappa: 1.2e-05\n",
      "K_CNai = 0.149\n",
      "K_CNao = 49.12\n",
      "K_Ci = 0.3457\n",
      "K_Co = 40.33\n",
      "K_Nai = 13.93\n",
      "K_Nao = 13.96\n",
      "K_SCNai = 0.099\n",
      "K_SCNao = 0.099\n",
      "K_Si = 10.12\n",
      "K_So = 10.08\n",
      "r12 K_eq = 160.0000; kappa = 982183.7246\n",
      "r23 K_eq = 5000.0000; kappa = 19492291.8173\n",
      "r25 K_eq = 329.6703; kappa = 589.3102\n",
      "r34 K_eq = 1.0000; kappa = 48730729.5432\n",
      "r45 K_eq = 0.0656; kappa = 779691672.6910\n",
      "r56 K_eq = 0.0022; kappa = 6475936.6454\n",
      "r61 K_eq = 0.0086; kappa = 837303.6199\n"
     ]
    }
   ],
   "source": [
    "## Set non-unit parameters using data from EskWriLoo05\n",
    "def setPar(s,tol=1e-6):\n",
    "    \n",
    "    ## Extract stoichiometry\n",
    "    N = s['N']\n",
    "    Nf = s['Nf']\n",
    "    Nr = s['Nr']\n",
    "    K = s['K']\n",
    "    \n",
    "    n_V = s['n_V']\n",
    "    \n",
    "    \n",
    "    ## Rate constants from Fig 6.\n",
    "    kf = {}\n",
    "    kr = {}\n",
    "    \n",
    "    ## Rate constants from Fig 6.\n",
    "    kf['r12'] = 8e4;\n",
    "    kr['r12'] = 500;\n",
    "\n",
    "    kf['r23'] = 1e5;\n",
    "    kr['r23'] = 20;\n",
    "\n",
    "    kf['r34'] = 50;\n",
    "    kr['r34'] = 50;\n",
    "\n",
    "    kf['r45'] = 800;\n",
    "    kr['r45'] = 12190;\n",
    "\n",
    "    kf['r56'] = 10;\n",
    "    kr['r56'] = 4500;\n",
    "\n",
    "    kf['r61'] = 3;\n",
    "    kr['r61'] = 350;\n",
    "\n",
    "    kf['r25'] = 0.3;\n",
    "    kr['r25'] = 9.1e-4;\n",
    "\n",
    "    ## Equilibrium constants.\n",
    "    K_eq = np.zeros(n_V)\n",
    "    k_f = np.zeros(n_V)\n",
    "    k_r = np.zeros(n_V)\n",
    "    for i,reac in enumerate(s['reaction']):\n",
    "        K_eq[i] = kf[reac]/kr[reac]\n",
    "        k_f[i] = kf[reac]\n",
    "        k_r[i] = kr[reac]\n",
    "    \n",
    "    ## Compute Ce constants from equilibrium constants\n",
    "    K_c = Keq2K(K_eq,N,K)\n",
    "    \n",
    "#     print(K_eq)\n",
    "#     print(s['n_X'], K_c.shape)\n",
    "        \n",
    "    # Forward rates induced by Cs\n",
    "    k_f0 = np.exp(Nf.T@np.log(K_c))\n",
    "    \n",
    "    ## Rate constants kappa (Amps)\n",
    "    kappa = (k_f/k_f0)*st.F()\n",
    "    \n",
    "    ## Sanity check\n",
    "    k_r0 = np.exp(Nr.T@np.log(K_c))\n",
    "    kappa_r = (k_r/k_r0)*st.F()\n",
    "    check = np.linalg.norm(kappa-kappa_r)\n",
    "    \n",
    "    if check>tol:\n",
    "        print(f'Error in kappa: {check:.2}')\n",
    "    \n",
    "    \n",
    "    ## Parameters\n",
    "    parameter = {}\n",
    "    \n",
    "    ## Ce constants\n",
    "    for i,spec in enumerate(s['species']):\n",
    "        print(f'K_{spec} = {K_c[i]:.4}')\n",
    "        parameter['K_'+spec] = K_c[i]\n",
    "        \n",
    "    ## Re constants\n",
    "    for i,reac in enumerate(s['reaction']):\n",
    "        print(f'{reac} K_eq = {K_eq[i]:.4f}; kappa = {kappa[i]:.4f}')\n",
    "        parameter['kappa_'+reac] = kappa[i]\n",
    "      \n",
    "    return parameter\n",
    "\n",
    "par = setPar(s0)\n",
    "#print(par)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Electrogenic Sodium-Glucose Symporter\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bond graph\n",
    "The component C:E is added to express the effect of the charged \\ch{Na+} ion crossing the membrane."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
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       "<text xml:space=\"preserve\" x=\"0\" y=\"4590\" fill=\"#000000\" font-family=\"Helvetica\" font-style=\"normal\" font-weight=\"bold\" font-size=\"216\" text-anchor=\"middle\">0</text>\n",
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       "<text xml:space=\"preserve\" x=\"0\" y=\"5715\" fill=\"#000000\" font-family=\"Helvetica\" font-style=\"normal\" font-weight=\"bold\" font-size=\"216\" text-anchor=\"middle\">C:Nao</text>\n",
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       "<text xml:space=\"preserve\" x=\"0\" y=\"10215\" fill=\"#000000\" font-family=\"Helvetica\" font-style=\"normal\" font-weight=\"bold\" font-size=\"216\" text-anchor=\"middle\">C:So</text>\n",
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       "<text xml:space=\"preserve\" x=\"9000\" y=\"9105\" fill=\"#000000\" font-family=\"Helvetica\" font-style=\"normal\" font-weight=\"bold\" font-size=\"216\" text-anchor=\"middle\">0</text>\n",
       "<!-- Text -->\n",
       "<text xml:space=\"preserve\" x=\"9000\" y=\"10245\" fill=\"#000000\" font-family=\"Helvetica\" font-style=\"normal\" font-weight=\"bold\" font-size=\"216\" text-anchor=\"middle\">C:Si</text>\n",
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       "<text xml:space=\"preserve\" x=\"4500\" y=\"5715\" fill=\"#000000\" font-family=\"Helvetica\" font-style=\"normal\" font-weight=\"bold\" font-size=\"216\" text-anchor=\"middle\">C:E</text>\n",
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       "<text xml:space=\"preserve\" x=\"1215\" y=\"3465\" fill=\"#000000\" font-family=\"Helvetica\" font-style=\"normal\" font-weight=\"bold\" font-size=\"216\" text-anchor=\"end\">C:Co</text>\n",
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     },
     "execution_count": 7,
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   ],
   "source": [
    "## Sodium-Glucose tranporter - electrogenic\n",
    "if TranslateSVG:\n",
    "    sbg.model('ESGLT_abg.svg')\n",
    "import ESGLT_abg\n",
    "disp.SVG('ESGLT_abg.svg')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Stoichiometry"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "K:\n",
      " [[ 0  1]\n",
      " [ 1  0]\n",
      " [-1  1]\n",
      " [ 1  0]\n",
      " [ 1  0]\n",
      " [ 0  1]\n",
      " [ 0  1]]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Stoichiometry\n",
    "s = st.stoich(ESGLT_abg.model(),linear=['E'], quiet=quiet)\n",
    "chemostats = ['Nai','Nao','Si','So','E']\n",
    "sc = st.statify(s,chemostats=chemostats)\n",
    "\n",
    "disp.Latex(st.sprint(sc,'K'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Reactions and flows"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\begin{align}\n",
       "\\ch{Co + 2 Nao &<>[ r12 ] CNao + E }\\\\\n",
       "\\ch{CNao + So &<>[ r23 ] SCNao }\\\\\n",
       "\\ch{CNao &<>[ r25 ] CNai }\\\\\n",
       "\\ch{SCNao &<>[ r34 ] SCNai }\\\\\n",
       "\\ch{SCNai &<>[ r45 ] CNai + Si }\\\\\n",
       "\\ch{CNai &<>[ r56 ] Ci + 2 Nai }\\\\\n",
       "\\ch{Ci &<>[ r61 ] Co }\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": [
    {
     "data": {
      "text/latex": [
       "\\begin{align}\n",
       "v_{r12} &= \\kappa_{r12} \\left(- K_{CNao} x_{CNao} e^{\\frac{K_{E} x_{E}}{V_{N}}} + K_{Co} K_{Nao}^{2} x_{Co} x_{Nao}^{2}\\right)\\\\\n",
       "v_{r23} &= \\kappa_{r23} \\left(K_{CNao} K_{So} x_{CNao} x_{So} - K_{SCNao} x_{SCNao}\\right)\\\\\n",
       "v_{r25} &= \\kappa_{r25} \\left(- K_{CNai} x_{CNai} + K_{CNao} x_{CNao}\\right)\\\\\n",
       "v_{r34} &= \\kappa_{r34} \\left(- K_{SCNai} x_{SCNai} + K_{SCNao} x_{SCNao}\\right)\\\\\n",
       "v_{r45} &= \\kappa_{r45} \\left(- K_{CNai} K_{Si} x_{CNai} x_{Si} + K_{SCNai} x_{SCNai}\\right)\\\\\n",
       "v_{r56} &= \\kappa_{r56} \\left(K_{CNai} x_{CNai} - K_{Ci} K_{Nai}^{2} x_{Ci} x_{Nai}^{2}\\right)\\\\\n",
       "v_{r61} &= \\kappa_{r61} \\left(K_{Ci} x_{Ci} e^{- \\frac{K_{E} x_{E}}{V_{N}}} - K_{Co} x_{Co}\\right)\n",
       "\\end{align}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Flows\n",
    "disp.Latex(st.sprintvl(s))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sdet up initial conditions for simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def setX(s):\n",
    "    \n",
    "    sp = s['species']\n",
    "    X0 = np.zeros(s['n_X'])\n",
    "    X0[sp.index('So')] = 1e-6\n",
    "    X0[sp.index('Si')] = 1e-3\n",
    "    X0[sp.index('Nao')] = 1e-2\n",
    "    X0[sp.index('Nai')] = 0.5\n",
    "    \n",
    "#     X0 *= st.F()\n",
    "    \n",
    "    ## Normalised value\n",
    "    C_T = 1\n",
    "    others = ['Co','CNao','SCNao','Ci','CNai','SCNai']\n",
    "    for spec in others:\n",
    "        X0[sp.index(spec)] = C_T/len(others)\n",
    "        \n",
    "    #N_C = 3e6\n",
    "    N_C = 7.5e7\n",
    "    N_avo = 6.022e23\n",
    "    C_T_0 = N_C/N_avo\n",
    "    \n",
    "    I_0_pA = 1e12*C_T_0/C_T\n",
    "    \n",
    "    print(f'N_C = {N_C}; i_0 = {I_0_pA}pA')\n",
    "    \n",
    "    #X0 *= st.F()\n",
    "        \n",
    "    return X0,I_0_pA\n",
    "\n",
    "#print(setX(s))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Comparison with experimental data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Error in kappa: 1.2e-05\n",
      "K_CNai = 0.149\n",
      "K_CNao = 49.12\n",
      "K_Ci = 0.3457\n",
      "K_Co = 40.33\n",
      "K_Nai = 13.93\n",
      "K_Nao = 13.96\n",
      "K_SCNai = 0.099\n",
      "K_SCNao = 0.099\n",
      "K_Si = 10.12\n",
      "K_So = 10.08\n",
      "r12 K_eq = 160.0000; kappa = 982183.7246\n",
      "r23 K_eq = 5000.0000; kappa = 19492291.8173\n",
      "r25 K_eq = 329.6703; kappa = 589.3102\n",
      "r34 K_eq = 1.0000; kappa = 48730729.5432\n",
      "r45 K_eq = 0.0656; kappa = 779691672.6910\n",
      "r56 K_eq = 0.0022; kappa = 6475936.6454\n",
      "r61 K_eq = 0.0086; kappa = 837303.6199\n",
      "N_C = 75000000.0; i_0 = 0.00012454334108269677pA\n",
      "-0.17\n",
      "-0.17 + 0.00022000000000000003*t\n",
      "-0.17 0.05000000000000002\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Vary E\n",
    "E0 = -170/1000\n",
    "E1 = 50/1000\n",
    "#E1 = 200/1000\n",
    "X_chemo = {'E':str(E0)}\n",
    "\n",
    "## Simulation\n",
    "t = np.linspace(0,1e3,100)\n",
    "parameter = setPar(s0)\n",
    "X0,I_0_pA = setX(s)\n",
    "dat = st.sim(s,sc=sc,t=t,parameter=parameter,X_chemo=X_chemo,X0=X0)\n",
    "\n",
    "## Extract data\n",
    "spec = s['species']\n",
    "reac = s['reaction']\n",
    "X_ss = dat['X'][-1,:]\n",
    "print(X_ss[spec.index('E')])\n",
    "\n",
    "\n",
    "x_E = f'{E0} + {(E1-E0)/max(t)}*t'\n",
    "print(x_E)\n",
    "X_chemo = {'E':x_E}\n",
    "\n",
    "dat = st.sim(s,sc=sc,t=t,parameter=parameter,X0=X_ss,X_chemo=X_chemo)\n",
    "f_E = dat['dX'][:,spec.index('E')]\n",
    "E = dat['X'][:,spec.index('E')]\n",
    "\n",
    "print(E[0],E[-1])\n",
    "\n",
    "X,Y = loadData()\n",
    "plt.plot(1000*E,-f_E*I_0_pA, label='Model')\n",
    "plt.scatter(X,Y,label='Experimental')\n",
    "plt.legend()\n",
    "plt.grid()\n",
    "plt.xlabel('$E$ mV')\n",
    "plt.ylabel('$-f$ pA')\n",
    "if SaveFig:\n",
    "    plt.savefig('Figs/sglt.pdf')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
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