{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "92b0779a",
   "metadata": {},
   "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:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "6e0b739b25395649",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-13T09:24:03.790903Z",
     "start_time": "2025-10-13T09:24:03.787694Z"
    },
    "execution": {
     "iopub.execute_input": "2026-05-25T09:59:30.542884Z",
     "iopub.status.busy": "2026-05-25T09:59:30.542687Z",
     "iopub.status.idle": "2026-05-25T09:59:33.882200Z",
     "shell.execute_reply": "2026-05-25T09:59:33.881138Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "An NVIDIA GPU may be present on this machine, but a CUDA-enabled jaxlib is not installed. Falling back to cpu.\n"
     ]
    }
   ],
   "source": [
    "import braintools\n",
    "import brainunit as u\n",
    "import matplotlib.pyplot as plt\n",
    "import braincell"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9565ec89c36cdcf6",
   "metadata": {},
   "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, `CaT_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://brainx.chaobrain.com/braincell/apis/braincell.channel.html).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "318d6844ce18da5a",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-13T09:24:03.895568Z",
     "start_time": "2025-10-13T09:24:03.893364Z"
    },
    "execution": {
     "iopub.execute_input": "2026-05-25T09:59:33.886280Z",
     "iopub.status.busy": "2026-05-25T09:59:33.885408Z",
     "iopub.status.idle": "2026-05-25T09:59:36.470740Z",
     "shell.execute_reply": "2026-05-25T09:59:36.469819Z"
    }
   },
   "outputs": [],
   "source": [
    "# Create Low-Threshold T-Type Calcium Channel (ICaT)\n",
    "cat = braincell.channel.CaT_HP1992(1)\n",
    "\n",
    "# Create High-Threshold Calcium Channel (ICaHT)\n",
    "caht = braincell.channel.CaHT_HM1992(1)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2bca175f485d43b1",
   "metadata": {},
   "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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "846d8c8bb3eda503",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-13T09:24:04.013533Z",
     "start_time": "2025-10-13T09:24:04.010411Z"
    },
    "execution": {
     "iopub.execute_input": "2026-05-25T09:59:36.474446Z",
     "iopub.status.busy": "2026-05-25T09:59:36.473913Z",
     "iopub.status.idle": "2026-05-25T09:59:36.598875Z",
     "shell.execute_reply": "2026-05-25T09:59:36.597756Z"
    }
   },
   "outputs": [],
   "source": [
    "# Generate Voltage Sequence\n",
    "vs = u.math.arange(-100 * u.mV, 0 * u.mV, 0.1 * u.mV)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "903f53c8ccbecc75",
   "metadata": {},
   "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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "6f249daa8ece8649",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-13T09:24:04.608638Z",
     "start_time": "2025-10-13T09:24:04.119006Z"
    },
    "execution": {
     "iopub.execute_input": "2026-05-25T09:59:36.601003Z",
     "iopub.status.busy": "2026-05-25T09:59:36.600760Z",
     "iopub.status.idle": "2026-05-25T09:59:37.121503Z",
     "shell.execute_reply": "2026-05-25T09:59:37.120392Z"
    }
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 900x300 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# These channels' steady-state gates depend only on voltage, but the API\n",
    "# requires a calcium IonInfo argument; supply a resting calcium state.\n",
    "ca = braincell.IonInfo(Ci=5e-5 * u.mM, Co=2. * u.mM, E=120. * u.mV, valence=2)\n",
    "\n",
    "# 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, ca)\n",
    "p_inf = cat.f_p_inf(vs, ca)\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, ca)\n",
    "p_inf = caht.f_p_inf(vs, ca)\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"
   ]
  },
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   "id": "e85ded496cf19afd",
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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"
   ]
  }
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