{
 "cells": [
  {
   "metadata": {},
   "cell_type": "raw",
   "source": [
    "# Comparison of Gating Properties of Low-Threshold and High-Threshold Calcium Channels\n",
    "\n",
    "This example demonstrates how to use the `braincell` library to analyze the steady-state properties of gating variables for low-threshold T-type calcium channels and high-threshold calcium channels. By comparing their gating curves, you will understand the functional differences of different calcium channels in neuronal electrical activity.\n",
    "\n",
    "## Preparation\n",
    "\n",
    "First, ensure that the necessary libraries (`braincell`, `brainunit`, `braintools`, `matplotlib`) are installed, and import the required modules:"
   ],
   "id": "11fab9ff781e91dd"
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "",
   "id": "79ad127b46878e9b"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-13T09:24:03.790903Z",
     "start_time": "2025-10-13T09:24:03.787694Z"
    }
   },
   "cell_type": "code",
   "source": [
    "import braintools\n",
    "import brainunit as u\n",
    "import matplotlib.pyplot as plt\n",
    "import braincell"
   ],
   "id": "6e0b739b25395649",
   "outputs": [],
   "execution_count": 8
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": [
    "## Code Explanation\n",
    "\n",
    "### Creating Calcium Channel Models\n",
    "\n",
    "`braincell` provides various ion channel models based on classical literature, named in the format `ChannelType_LiteratureID`, for example, `ICaT_HP1992` represents a T-type calcium channel based on Huguenard & Prince 1992.\n",
    "If you want to learn more about ion channel models, you can refer to our [Ion Channel Model Library](https://braincell.readthedocs.io/latest/apis/braincell.channel.html).\n"
   ],
   "id": "9565ec89c36cdcf6"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-13T09:24:03.895568Z",
     "start_time": "2025-10-13T09:24:03.893364Z"
    }
   },
   "cell_type": "code",
   "source": [
    "# Create Low-Threshold T-Type Calcium Channel (ICaT)\n",
    "cat = braincell.channel.ICaT_HP1992(1)\n",
    "\n",
    "# Create High-Threshold Calcium Channel (ICaHT)\n",
    "caht = braincell.channel.ICaHT_HM1992(1)\n"
   ],
   "id": "318d6844ce18da5a",
   "outputs": [],
   "execution_count": 9
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": [
    "### Generate Voltage Sequence\n",
    "\n",
    "To analyze how channel gating properties change with membrane potential, we generate a continuous voltage sequence from -100 mV to 0 mV:\n"
   ],
   "id": "2bca175f485d43b1"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-13T09:24:04.013533Z",
     "start_time": "2025-10-13T09:24:04.010411Z"
    }
   },
   "cell_type": "code",
   "source": [
    "# Generate Voltage Sequence\n",
    "vs = u.math.arange(-100 * u.mV, 0 * u.mV, 0.1 * u.mV)"
   ],
   "id": "846d8c8bb3eda503",
   "outputs": [],
   "execution_count": 10
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": [
    "### Calculate Steady-State Gating Variables and Plot\n",
    "\n",
    "The steady-state values of ion channel gating variables describe the probability that the channel gates are open at a given membrane potential. We calculate these values using the channel's `f_q_inf` and `f_p_inf` methods and visualize the comparison:\n"
   ],
   "id": "903f53c8ccbecc75"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-13T09:24:04.608638Z",
     "start_time": "2025-10-13T09:24:04.119006Z"
    }
   },
   "cell_type": "code",
   "source": [
    "# Create Figure and Subplot Layout\n",
    "fig, gs = braintools.visualize.get_figure(1, 2, 3., 4.5)\n",
    "\n",
    "# Compute steady-state values of activation and inactivation gates for low-threshold channel\n",
    "q_inf = cat.f_q_inf(vs)\n",
    "p_inf = cat.f_p_inf(vs)\n",
    "\n",
    "# Add subplot 1\n",
    "fig.add_subplot(gs[0, 0])\n",
    "plt.plot(vs / u.mV, q_inf, label='q_inf (activation gate)')  # Convert x-axis to mV for readability\n",
    "plt.plot(vs / u.mV, p_inf, label='p_inf (inactivation gate)')\n",
    "plt.legend()  # Show legend\n",
    "plt.fill_between([-80, -60], 1., alpha=0.2)  # Highlight typical activation range for low-threshold channel\n",
    "plt.title('Low-Threshold Calcium Channel (ICaT)')\n",
    "plt.xlabel('Membrane Potential (mV)')\n",
    "\n",
    "# Compute q_inf and p_inf for high-threshold channel\n",
    "q_inf = caht.f_q_inf(vs)\n",
    "p_inf = caht.f_p_inf(vs)\n",
    "\n",
    "# Add subplot 2\n",
    "fig.add_subplot(gs[0, 1])\n",
    "plt.plot(vs / u.mV, q_inf, label='q_inf (activation gate)')\n",
    "plt.plot(vs / u.mV, p_inf, label='p_inf (inactivation gate)')\n",
    "plt.fill_between([-60, -40], 1., alpha=0.2)  # Highlight typical activation range for high-threshold channel\n",
    "plt.legend()\n",
    "plt.xlabel('Membrane Potential (mV)')\n",
    "plt.title('High-Threshold Calcium Channel (ICaHT)')\n",
    "\n",
    "# Display figure\n",
    "plt.show()\n"
   ],
   "id": "6f249daa8ece8649",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 900x300 with 2 Axes>"
      ],
      "image/png": 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"
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    }
   ],
   "execution_count": 11
  },
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   "source": [
    "## Result Interpretation\n",
    "\n",
    "After running the code, you will see two plots of the gating characteristics.\n",
    "\n",
    "Analyzing the two gating characteristic plots, the key conclusions are as follows:\n",
    "\n",
    "Low-threshold calcium channel (ICaT):\n",
    "   - `q_inf` rises significantly at membrane potentials around -80 ~ -60 mV, indicating that the channel is easily activated within this range.\n",
    "   - This matches the shaded region, showing that the channel can be activated near the neuron's resting potential.\n",
    "\n",
    "High-threshold calcium channel (ICaHT):\n",
    "   - `q_inf` only rises significantly at membrane potentials around -60 ~ -40 mV, indicating a higher activation threshold.\n",
    "   - The shaded area corresponds to its typical activation range, requiring stronger depolarization to activate.\n",
    "\n",
    "## Extended Exercises\n",
    "\n",
    "- Try modifying the channel's conductance density parameter and observe whether the gating curves change.\n",
    "- Compare the gating characteristics of other ion channels to understand how different channels cooperate during action potentials.\n",
    "\n",
    "With these tools, you can quickly build channel models that align with electrophysiological properties, laying the foundation for complex neural dynamics simulations.\n"
   ],
   "id": "e85ded496cf19afd"
  }
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