HHmodel.ipynb

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      "source": [
        "\n",
        "# Hodgkin-Huxley model\n",
        "\n",
        "In this section you will interact with the famous Hodgkin-Huxley (HH) Neuron Model.\n",
        "This was a mathematical model of a neuron's membrane potential based on careful experiments that studied the electrical properties of a squid's giant axon, which is visible to the naked eye.\n",
        "\n",
        "\n",
        "![squid](https://live.staticflickr.com/3844/14356033761_a360af2143.jpg)\n",
        "\n",
        "<font size =1><i> Image credit: National Institute of Health, USA</i></font>\n",
        "\n",
        "\n",
        "\n",
        "The HH Model is more realistic than many commonly used models of neurons. and captures the rich dynamics of a neuron's membrane as a function of its transmembrane conductances.\n",
        "\n"
      ],
      "metadata": {
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      "source": [
        "!pip install interact --quiet\n",
        "!pip install interactive --quiet"
      ],
      "metadata": {
        "id": "dK7zScO0yTTH",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "b5e23653-01d2-473c-87fa-27b5e6814364"
      },
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "  Preparing metadata (setup.py) ... \u001b[?25l\u001b[?25hdone\n",
            "  Building wheel for interact (setup.py) ... \u001b[?25l\u001b[?25hdone\n",
            "  Preparing metadata (setup.py) ... \u001b[?25l\u001b[?25hdone\n",
            "  Building wheel for interactive (setup.py) ... \u001b[?25l\u001b[?25hdone\n"
          ]
        }
      ]
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        "id": "k-ve-uW4j3Q6",
        "outputId": "d129c4d5-1f47-4995-a914-ea1e1931ded2"
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      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "interactive(children=(FloatSlider(value=1.0, continuous_update=False, description='C membrane capacitance', ma…"
            ],
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              "version_major": 2,
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        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<function __main__.HH_model(C, Gna, Gk, Gleak, Iin)>"
            ]
          },
          "metadata": {},
          "execution_count": 7
        }
      ],
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "import ipywidgets as widgets\n",
        "from ipywidgets import interact, interactive, fixed, interact_manual\n",
        "from IPython.display import display\n",
        "\n",
        "def HH_model(C,Gna,Gk,Gleak,Iin):\n",
        "  dt      = 0.5; # all time units in ms\n",
        "  t_end = 1000;\n",
        "  num_timepoints = t_end/dt;\n",
        "  time    = int(num_timepoints);\n",
        "\n",
        "#  C       = 1; # (muF/cm^2)\n",
        "#  Gna     = 2.0; # (2mS/cm^2)\n",
        "#  Gk      = 1.44; # (1.44mS/cm^2)\n",
        "#  Gleak   = 0.2; # (0.2mS/cm^2)\n",
        "\n",
        "\n",
        "  Ena     = 50.0; # 50(mV)\n",
        "  Ek      = -80.0; # -77(mV)\n",
        "  Eleak   = -65.0; # -54(mV)\n",
        "\n",
        "  kn      = 15.0; # (mV)\n",
        "  km      = 7.0; # (mV);\n",
        "  tau     = 10.0; # (ms)\n",
        "  Vn      = -45.0; # (mV)\n",
        "\n",
        "  n       = np.zeros((time,1));      # this is our gating parameter\n",
        "  V       = Eleak*np.ones((time,1)); # this will store our membrane potential\n",
        "#  Iin     = 2.0;                     # and this is an input current (muA/cm^2)\n",
        "\n",
        "  x = np.arange(1, time, 1, dtype=int);\n",
        "\n",
        "\n",
        "  for t in x:\n",
        "      minf    = 1/(1+np.exp((-40.0-V[t-1])/km));\n",
        "      ninf    = 1/(1+np.exp((Vn-V[t-1])/kn));\n",
        "      h       = 0.89 - 1.1*n[t-1];\n",
        "\n",
        "      dvdt = (1/C)*(-Gna*minf**3*h*(V[t-1]-Ena) - Gk*n[t-1]**4*(V[t-1]-Ek) - Gleak*(V[t-1]-Eleak) + Iin);\n",
        "      dndt = (1/tau)*(ninf - n[t-1]);\n",
        "\n",
        "      V[t] = V[t-1] + dvdt*dt;\n",
        "      n[t] = n[t-1] + dndt*dt;\n",
        "\n",
        "  t = np.arange(0, t_end, 0.5, dtype=float);\n",
        "\n",
        "\n",
        "  plt.plot(t,V)\n",
        "  plt.ylabel('Voltage (mV)');\n",
        "  plt.xlabel('Time (ms)');\n",
        "  plt.ylim(-100,100);\n",
        "  plt.show\n",
        "\n",
        "\n",
        "interact_manual(HH_model, C = widgets.FloatSlider(\n",
        "    value=1.0,\n",
        "    min=0.1,\n",
        "    max=2.0,\n",
        "    step=0.1,\n",
        "    continuous_update=False,\n",
        "    style = {'description_width': 'initial'},\n",
        "    description='C membrane capacitance'),\n",
        "    Gna = widgets.FloatSlider(\n",
        "    value=2.0,\n",
        "    min=0.0,\n",
        "    max=5.0,\n",
        "    step=0.1,\n",
        "    continuous_update=False,\n",
        "    style = {'description_width': 'initial'},\n",
        "    description='gNa conductance'),\n",
        "    Gk = widgets.FloatSlider(\n",
        "    value=1.44,\n",
        "    min=0.0,\n",
        "    max=5.0,\n",
        "    step=0.1,\n",
        "    continuous_update=False,\n",
        "    style = {'description_width': 'initial'},\n",
        "    description='gK conductance'),\n",
        "    Gleak = widgets.FloatSlider(\n",
        "    value=0.2,\n",
        "    min=0.0,\n",
        "    max=1.0,\n",
        "    step=0.1,\n",
        "    continuous_update=False,\n",
        "    style = {'description_width': 'initial'},\n",
        "    description='gLeak conductance'),\n",
        "    Iin = widgets.FloatSlider(\n",
        "    value=2.0,\n",
        "    min=0.0,\n",
        "    max=10.0,\n",
        "    step=0.1,\n",
        "    continuous_update=False,\n",
        "    description='Input current')\n",
        ")"
      ]
    }
  ]
}