Hodgkin-Huxley Neuron Model

hodgkin-huxley.ipynb

{
 "metadata": {
  "name": "Hodgkin-Huxley"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy.integrate import odeint\n",
      "\n",
      "C_m   =    1.0   # uF / cm^2\n",
      "I_ext =   10.0   # uA / cm^2\n",
      "\n",
      "g_Na  =  120.0   # in mS/cm^2\n",
      "g_K   =   36.0\n",
      "g_L   =    0.3\n",
      "\n",
      "E_Na  = + 45.0   # in mV\n",
      "E_K   = - 82.0\n",
      "E_L   = - 59.387\n",
      "\n",
      "def alpha_n(V): return 0.01 * (V + 60.0) / (1.0 - exp(-(V+60.0)/10.0)) # in msec^-1\n",
      "def beta_n (V): return 0.125 * exp(-(V+70.0) / 80.0)\n",
      "def alpha_m(V): return 0.1 * (V + 45.0) / (1.0 - exp(-(V+45.0)/10.0))\n",
      "def beta_m (V): return 4.0 * exp(-(V+70)/18.0)\n",
      "def alpha_h(V): return 0.07 * exp(-(V+70)/20.0)\n",
      "def beta_h (V): return 1.0 / (1.0 + exp(-(V+40.0)/10.0))\n",
      "\n",
      "def I_K (V, n):    return g_K  * n**4     * (V - E_K )  # uA / cm^2\n",
      "def I_Na(V, m, h): return g_Na * m**3 * h * (V - E_Na)\n",
      "def I_L(V):        return g_L             * (V - E_L)\n",
      "\n",
      "def HH(X, t):\n",
      "    V, n, m, h = X\n",
      "    dV_dt = (I_ext - I_K(V, n) - I_Na(V, m, h) - I_L(V)) / C_m\n",
      "    dn_dt = alpha_n(V) * (1.0 - n) - beta_n(V) * n\n",
      "    dm_dt = alpha_m(V) * (1.0 - m) - beta_m(V) * m\n",
      "    dh_dt = alpha_h(V) * (1.0 - h) - beta_h(V) * h\n",
      "    return dV_dt, dn_dt, dm_dt, dh_dt\n",
      "\n",
      "t = arange(0.0, 500.0, 0.1) # in msec\n",
      "X = odeint(HH, (-70.0, 0.32, 0.05, 0.6), t)\n",
      "\n",
      "V = X[:, 0]\n",
      "n = X[:, 1]\n",
      "m = X[:, 2]\n",
      "h = X[:, 3]\n",
      "\n",
      "figure()\n",
      "xlabel('Time (sec)')\n",
      "ylabel('Membrane Potential (mV)')\n",
      "plot(t, V)\n",
      "\n",
      "figure()\n",
      "xlabel('Time (sec)')\n",
      "ylabel('Gating Variable')\n",
      "plot(t, n)\n",
      "plot(t, m)\n",
      "plot(t, h)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}