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| { | ||
| "cells": [ | ||
| { | ||
| "cell_type": "markdown", | ||
| "id": "e713df72-6ca2-4213-9278-f718f2fda642", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "---\n", | ||
| "title: Bursting Neuron\n", | ||
| "project:\n", | ||
| " type: website\n", | ||
| "format:\n", | ||
| " html:\n", | ||
| " code-fold: false\n", | ||
| " code-tools: true\n", | ||
| "jupyter: python 3\n", | ||
| "number-sections: false\n", | ||
| "---" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "id": "472ba20d-8461-41fe-9518-50c286f6b552", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "The goal in this notebook is to update the HH equations to include a new (slow) current and produce bursting activity.\n", | ||
| "\n", | ||
| "To do so, start with the [HH code available here](https://raw.githubusercontent.com/Mark-Kramer/BU-MA665-MA666/master/HH_functions.py).\n", | ||
| "\n", | ||
| "Update the HH model to include the **$\\bf{g_K-}$\"M\" current** listed in [**Table A2** of this publication](/Readings/Traub_J_Neurophysiol_2003.pdf).\n", | ||
| "\n", | ||
| "In the code below, we'll use the variable `B` to define the gate for this current.\n", | ||
| "\n", | ||
| "## Challenges\n", | ||
| "\n", | ||
| "#### 1. Plot the steady-state function and time constant for this new current.\n", | ||
| "\n", | ||
| "*HINT:* In [**Table A2** of this publication](/Readings/Traub_J_Neurophysiol_2003.pdf), the authors provide the forward rate function ($\\alpha[V]$) and backward rate function ($\\beta[V]$) for this current. Use these functions to compute the steady-state function and time constant, and plot both versus V. \n", | ||
| "\n", | ||
| "#### 2. Update the HH model to include this new current.\n", | ||
| "\n", | ||
| "*HINT:* Update the HH model to accept three inputs: `HH(I0, T0, gB0)`, where `gB0` is the maximal conductance of the new current.\n", | ||
| "\n", | ||
| "*HINT:* Update the HH model to return six outputs: `return V,m,h,n,B,t`, where `B` is the gate variable of the new current.\n", | ||
| "\n", | ||
| "#### 3. Find parameter settings so that the model produces bursting activity.\n", | ||
| "\n", | ||
| "*HINT:* Fix `I0=10` and `T0=500` and vary the maximal conductance of the new current, `gB0`, until you find a value that supports bursting in the voltage.\n", | ||
| "\n", | ||
| "*HINT:* Plot the voltage `V` and the new current gate `B` to visualize how the dynamics behave.\n", | ||
| "\n", | ||
| "#### 4. Compute the spectrum to characterize the dominant rhythms.\n", | ||
| "\n", | ||
| "*HINT:* Be sure to carefully define `T`." | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": null, | ||
| "id": "a21a66c6-93b9-43e6-ad92-5bf168cbdd97", | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [ | ||
| "import numpy as np\n", | ||
| "import matplotlib.pyplot as plt" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": null, | ||
| "id": "e4af71a7-49d8-4004-8947-6ebddef6cb76", | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [ | ||
| "def alphaM(V):\n", | ||
| " return (2.5-0.1*(V+65)) / (np.exp(2.5-0.1*(V+65)) -1)\n", | ||
| "\n", | ||
| "def betaM(V):\n", | ||
| " return 4*np.exp(-(V+65)/18)\n", | ||
| "\n", | ||
| "def alphaH(V):\n", | ||
| " return 0.07*np.exp(-(V+65)/20)\n", | ||
| "\n", | ||
| "def betaH(V):\n", | ||
| " return 1/(np.exp(3.0-0.1*(V+65))+1)\n", | ||
| "\n", | ||
| "def alphaN(V):\n", | ||
| " return (0.1-0.01*(V+65)) / (np.exp(1-0.1*(V+65)) -1)\n", | ||
| "\n", | ||
| "def betaN(V):\n", | ||
| " return 0.125*np.exp(-(V+65)/80)\n", | ||
| "\n", | ||
| "def alphaB(V):\n", | ||
| " return \"SOMETHING\"\n", | ||
| "\n", | ||
| "def betaB(V):\n", | ||
| " return \"SOMETHING\"\n", | ||
| "\n", | ||
| "def HHB(I0,T0,gB0):\n", | ||
| " \"SOMETHING\"" | ||
| ] | ||
| } | ||
| ], | ||
| "metadata": { | ||
| "kernelspec": { | ||
| "display_name": "Python 3 (ipykernel)", | ||
| "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": "3.8.18" | ||
| } | ||
| }, | ||
| "nbformat": 4, | ||
| "nbformat_minor": 5 | ||
| } |
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