Hill-Model-X1.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Regulation kinetics of Na+-Ca2+ exchange current in guinea-pig ventricular myocytes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Import libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 192,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.integrate import odeint\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "sns.set()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Define Constant"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 193,
   "metadata": {},
   "outputs": [],
   "source": [
    "Na = 10000\n",
    "Ca = 10000\n",
    "K_ci = 0.01*1e-3\n",
    "K_4ni = 8*1e-3\n",
    "K_3ni = 9*1e-3\n",
    "K_2ni = 9*1e-3\n",
    "K_1ni = 700*1e-3\n",
    "asym = 80*1e-3 \n",
    "V_m = 0*1e-3\n",
    "kvm = np.exp(2.0*V_m/53.08)\n",
    "K_Ca_act = 0.004*1e-3\n",
    "\n",
    "alpha1_Ca_on = 2.0\n",
    "alpha1_Ca_off = 1.5\n",
    "beta1_Ca_on = 1.2\n",
    "beta1_Ca_off = 0.0005\n",
    "\n",
    "alpha2_Ca_on = 0.03\n",
    "alpha2_Ca_off = 10\n",
    "beta2_Ca_on = 90\n",
    "beta2_Ca_off = 0.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 194,
   "metadata": {},
   "outputs": [],
   "source": [
    "D_i = (Na**4)*K_ci +\\\n",
    "      (Na**3)*K_ci*K_4ni +\\\n",
    "      (Na**2)*K_ci*K_4ni*K_3ni + \\\n",
    "      (Na**1)*K_ci*K_4ni*K_3ni*K_2ni + \\\n",
    "      K_ci*K_4ni*K_3ni*K_2ni*K_1ni + \\\n",
    "      Ca*K_4ni*K_3ni*K_2ni*K_1ni"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 195,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "100000080000072.0"
      ]
     },
     "execution_count": 195,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "D_i"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 209,
   "metadata": {},
   "outputs": [],
   "source": [
    "F_E14Na = (Na**4)*K_ci/D_i\n",
    "F_E1Ca = Ca*K_1ni*K_2ni*K_3ni*K_4ni/D_i\n",
    "\n",
    "F_E24Na = (Na**4)*K_ci/D_i\n",
    "F_E2Ca = Ca*K_1ni*K_2ni*K_3ni*K_4ni/D_i"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 210,
   "metadata": {},
   "outputs": [],
   "source": [
    "K_1no = (asym**0.25)*K_1ni\n",
    "K_2no = (asym**0.25)*K_2ni\n",
    "K_3no = (asym**0.25)*K_3ni\n",
    "K_4no = (asym**0.25)*K_4ni\n",
    "K_co =  (asym**0.25)*K_ci"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 211,
   "metadata": {},
   "outputs": [],
   "source": [
    "k1 = F_E14Na*1000*kvm\n",
    "k2 = F_E24Na*1000/kvm\n",
    "k3 = F_E2Ca*1000\n",
    "k4 = F_E1Ca*1000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 212,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[999.99919999992,\n",
       " 999.99919999992,\n",
       " 4.535996371199639e-14,\n",
       " 4.535996371199639e-14]"
      ]
     },
     "execution_count": 212,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[k1,k2,k3,k4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "metadata": {},
   "outputs": [],
   "source": [
    "F_Ca_act = Ca/(Ca+K_Ca_act)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 201,
   "metadata": {},
   "outputs": [],
   "source": [
    "alpha1 = F_E14Na*((F_Ca_act*alpha1_Ca_on) + (1-F_Ca_act)*alpha1_Ca_off)\n",
    "beta1 = F_Ca_act*beta1_Ca_on + (1-F_Ca_act)*beta1_Ca_off"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 202,
   "metadata": {},
   "outputs": [],
   "source": [
    "alpha2 = F_Ca_act*alpha2_Ca_on + (1-F_Ca_act)*alpha2_Ca_off\n",
    "beta2 = F_Ca_act*beta2_Ca_on + (1-F_Ca_act)*beta2_Ca_off"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---------"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 203,
   "metadata": {},
   "outputs": [],
   "source": [
    "k = {\"alpha1\":alpha1,\"beta1\":beta1,\\\n",
    "    \"alpha2\":alpha2,\"beta2\":beta2,\\\n",
    "    \"k1\":k1,\"k2\":k2,\"k3\":k3,\"k4\":k4}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 204,
   "metadata": {},
   "outputs": [],
   "source": [
    "# function that returns dy/dt\n",
    "def model(y,t,k):\n",
    "    \n",
    "    '''y[0] = FE1, y[1] = FI1, y[2] = FI2, y[3]=FE2'''\n",
    "    \n",
    "    dy1dt = y[3]*(k[\"k2\"]+k[\"k3\"]) + y[1]*k[\"beta1\"] +\\\n",
    "            y[2]*k[\"beta2\"] - y[0]*(k[\"k1\"]+\\\n",
    "            k[\"k4\"]+k[\"alpha1\"]+k[\"alpha2\"])\n",
    "    \n",
    "    dy2dt = y[0]*k[\"alpha1\"] - y[1]*k[\"beta1\"]\n",
    "    dy3dt = y[0]*k[\"alpha2\"] - y[2]*k[\"beta2\"]\n",
    "    dy4dt = 1 - (y[0] + y[1] + y[2])\n",
    "    \n",
    "    dydt = [dy1dt,dy2dt,dy3dt,dy4dt]\n",
    "    return dydt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 205,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 1\n",
    "T = 10\n",
    "\n",
    "# initial condition\n",
    "y0 = [1,0,0,0]\n",
    "\n",
    "\n",
    "# time points\n",
    "t = np.linspace(0,T)\n",
    "\n",
    "\n",
    "'''solve ODEs'''\n",
    "y = odeint(model,y0,t,args=(k,))\n",
    "\n",
    "\n",
    "y1 = np.empty_like(t)\n",
    "y2 = np.empty_like(t)\n",
    "y3 = np.empty_like(t)\n",
    "y4 = np.empty_like(t)\n",
    "I  = np.empty_like(t)\n",
    "\n",
    "for i in range(len(t)):\n",
    "    y1[i] = y[i][0]\n",
    "    y2[i] = y[i][1]\n",
    "    y3[i] = y[i][2]\n",
    "    y4[i] = y[i][3]\n",
    "    I[i] = y[i][0]*k1 - y[i][3]*k2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 207,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot results\n",
    "plt.figure(figsize = [15,5])\n",
    "plt.plot(t,y1,linewidth=2,label='FE1')\n",
    "plt.plot(t,y2,linewidth=2,label='FI1')\n",
    "plt.plot(t,y3,linewidth=2,label='FI2')\n",
    "plt.plot(t,y4,linewidth=2,label='FE2')\n",
    "#plt.plot(t,I,linewidth=2,label='I')\n",
    "plt.xlabel('time')\n",
    "plt.ylabel('y(t)')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 208,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot results\n",
    "plt.figure(figsize = [15,5])\n",
    "plt.plot(t,I,linewidth=2,label='I')\n",
    "plt.xlabel('time')\n",
    "plt.ylabel('y(t)')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "----------"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 187,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 40\n",
    "T = 10\n",
    "\n",
    "# initial condition\n",
    "y0 = [1,0,0,0]\n",
    "t = np.linspace(0,10,10)\n",
    "\n",
    "y1,y2,y3,y4 = [],[],[],[]\n",
    "\n",
    "for i in range(len(t)):\n",
    "    tspan = [t[i-1],t[i]]\n",
    "    \n",
    "    '''solve ODEs'''\n",
    "    y = odeint(model,y0,tspan,args=(k,))\n",
    "    \n",
    "    y1.append(y[1][0])\n",
    "    y2.append(y[1][1])\n",
    "    y3.append(y[1][2])\n",
    "    y4.append(y[1][3])\n",
    "    \n",
    "    y0 = y[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 188,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot results\n",
    "plt.figure(figsize = [15,5])\n",
    "plt.plot(t,y1,linewidth=2,label='c3')\n",
    "plt.plot(t,y2,linewidth=2,label='C2')\n",
    "plt.plot(t,y3,linewidth=2,label='C1')\n",
    "plt.plot(t,y4,linewidth=2,label='O')\n",
    "plt.xlabel('time')\n",
    "plt.ylabel('y(t)')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  }
 ],
 "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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}