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Merge pull request #2919 from HanjiaJiang/astrocyte_lr_1994
Add astrocyte_lr_1994 to NEST for the modeling of astrocytes and neuron-astrocyte interactions
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doc/htmldoc/model_details/astrocyte_model_implementation.ipynb
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| { | ||
| "cells": [ | ||
| { | ||
| "cell_type": "markdown", | ||
| "id": "17ef5228", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "# NEST implementation of the `astrocyte_lr_1994` model\n", | ||
| "\n", | ||
| "The purpose of this notebook is to provide a reference solution for the the _astrocyte_lr_1994_ model in NEST. The model is based on Li, Y. X., & Rinzel, J. (1994), De Young, G. W., & Keizer, J. (1992), and Nadkarni, S., & Jung, P. (2003).\n", | ||
| "\n", | ||
| "This notebook demonstrates how the dynamics of _astrocyte_lr_1994_ is implemented, and generates a recording of the dynamics (test_astrocyte.dat). This recording serves as a reference for the verification of _astrocyte_lr_1994_ using test_astrocyte.py in the PyNEST tests.\n", | ||
| "\n", | ||
| "## The problem\n", | ||
| "\n", | ||
| "The equations governing the evolution of the astrocyte model are\n", | ||
| "\n", | ||
| "$$\\left\\lbrace\\begin{array}{rcl}\n", | ||
| " \\frac{d[\\mathrm{Ca^{2+}}](t)}{dt} &=& J_{\\mathrm{channel}}(t) - J_{\\mathrm{pump}}(t) + J_{\\mathrm{leak}}(t) \\\\\n", | ||
| " J_{\\mathrm{channel}}(t) &=& \\mathrm{r_{ER,cyt}} \\cdot \\mathrm{v_{IP_3R}} \\cdot m_{\\infty}(t)^3 \\cdot n_{\\infty}(t)^3\\cdot h_{\\mathrm{\\mathrm{IP_3R}}}(t)^3 \\cdot \\left([\\mathrm{Ca^{2+}}]_{\\mathrm{ER}} - [\\mathrm{Ca^{2+}}](t)\\right) \\\\\n", | ||
| " J_{\\mathrm{pump},k}(t) &=& \\frac{\\mathrm{v_{SERCA}} \\cdot [\\mathrm{Ca^{2+}}](t)^2}{K_{\\mathrm{m,SERCA}}^2+[\\mathrm{Ca^{2+}}](t)^2} \\\\\n", | ||
| " J_{\\mathrm{leak}}(t) &=& \\mathrm{r_{ER,cyt}} \\cdot \\mathrm{v_L} \\cdot \\left( [\\mathrm{Ca^{2+}}]_{\\mathrm{ER}}(t) - [\\mathrm{Ca^{2+}}](t) \\right) \\\\\n", | ||
| " m_{\\infty}(t) &=& \\frac{[\\mathrm{IP_3}](t)}{[\\mathrm{IP_3}](t) + \\mathrm{K_{d,IP_3,1}}} \\\\\n", | ||
| " n_{\\infty}(t) &=& \\frac{[\\mathrm{Ca^{2+}}](t)}{[\\mathrm{Ca^{2+}}](t) + \\mathrm{K_{d,act}}} \\\\\n", | ||
| " [\\mathrm{Ca^{2+}}]_{\\mathrm{ER}}(t) &=& \\frac{[\\mathrm{Ca^{2+}}]_{\\mathrm{tot}}-[\\mathrm{Ca^{2+}}](t)}{\\mathrm{r_{ER,cyt}}} \\\\\n", | ||
| " \\frac{dh_{\\mathrm{IP_3}}(t)}{dt} &=& \\alpha_{h_{\\mathrm{IP_3}}}(t) \\cdot (1-h_{\\mathrm{IP_3}}(t)) - \\beta_{h_{\\mathrm{IP_3}}}(t) \\cdot h_{\\mathrm{IP_3}} (t) \\\\\n", | ||
| " \\alpha_{h_{\\mathrm{IP_3}}}(t) &=& \\mathrm{k_{IP_3R}} \\cdot \\mathrm{K_{d,inh}} \\cdot \\frac{[\\mathrm{IP_3}](t) + \\mathrm{K_{d,IP_3,1}}}{[\\mathrm{IP_3}](t)+\\mathrm{K_{d,IP_3,2}}} \\\\\n", | ||
| " \\beta_{h_{\\mathrm{IP_3}}}(t) &=& \\mathrm{k_{IP_3R}} \\cdot [\\mathrm{Ca^{2+}}](t) \\\\\n", | ||
| " \\frac{d[\\mathrm{IP_3}](t)}{dt} &=& \\frac{[\\mathrm{IP_3}]^{*} - [\\mathrm{IP_3}](t)}{\\tau_\\mathrm{IP_3}} + \\Delta_\\mathrm{IP3} \\cdot J_\\mathrm{syn}(t)\n", | ||
| "\\end{array}\\right.$$\n", | ||
| "\n", | ||
| "where $[\\mathrm{IP_3}]$, $[\\mathrm{Ca^{2+}}]$, and $h_{\\mathrm{IP_3}}$ are the state variables of interest." | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "id": "622a93cb", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "## Technical details and requirements\n", | ||
| "\n", | ||
| "### Implementation of the functions\n", | ||
| "\n", | ||
| "* The reference solution is implemented through [scipy](http://www.scipy.org/).\n", | ||
| "\n", | ||
| "### Requirements\n", | ||
| "\n", | ||
| "To run this notebook, you need:\n", | ||
| "\n", | ||
| "* [numpy](http://www.numpy.org/) and [scipy](http://www.scipy.org/)\n" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": 1, | ||
| "id": "76d05384", | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [ | ||
| "import numpy as np\n", | ||
| "from scipy.integrate import odeint" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "id": "17cecb4d", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "## Reference solution\n", | ||
| "### Right hand side function" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": 2, | ||
| "id": "967b18fb", | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [ | ||
| "def rhs(y, _, p):\n", | ||
| " \"\"\"\n", | ||
| " Implementation of astrocyte dynamics.\n", | ||
| "\n", | ||
| " Parameters\n", | ||
| " ----------\n", | ||
| " y : list\n", | ||
| " Vector containing the state variables [IP3, Ca, h_IP3R]\n", | ||
| " _ : unused var\n", | ||
| " p : Params instance\n", | ||
| " Object containing the astrocyte parameters.\n", | ||
| "\n", | ||
| " Returns\n", | ||
| " -------\n", | ||
| " dCa : double\n", | ||
| " Derivative of Ca\n", | ||
| " dIP3 : double\n", | ||
| " Derivative of IP3\n", | ||
| " dh_IP3R : double\n", | ||
| " Derivative of h_IP3R\n", | ||
| " \"\"\"\n", | ||
| " IP3 = y[0]\n", | ||
| " Ca = y[1]\n", | ||
| " h_IP3R = y[2]\n", | ||
| "\n", | ||
| " Ca = max(0, min(Ca, p.Ca_tot * (1 + p.ratio_ER_cyt)))\n", | ||
| " alpha = p.k_IP3R * p.Kd_inh * (IP3 + p.Kd_IP3_1) / (IP3 + p.Kd_IP3_2)\n", | ||
| " beta = p.k_IP3R * Ca\n", | ||
| " Ca_ER = (p.Ca_tot - Ca) / p.ratio_ER_cyt\n", | ||
| " m_inf = IP3 / (IP3 + p.Kd_IP3_1)\n", | ||
| " n_inf = Ca / (Ca + p.Kd_act)\n", | ||
| " J_ch = p.ratio_ER_cyt * p.rate_IP3R * ((m_inf * n_inf * h_IP3R) ** 3) * (Ca_ER - Ca)\n", | ||
| " J_pump = p.rate_SERCA * (Ca**2) / (p.Km_SERCA**2 + Ca**2)\n", | ||
| " J_leak = p.ratio_ER_cyt * p.rate_L * (Ca_ER - Ca)\n", | ||
| "\n", | ||
| " dCa = J_ch - J_pump + J_leak\n", | ||
| " dIP3 = (p.IP3_0 - IP3) / p.tau_IP3\n", | ||
| " dh_IP3R = alpha * (1 - h_IP3R) - beta * h_IP3R\n", | ||
| "\n", | ||
| " return dIP3, dCa, dh_IP3R" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "id": "6f9246f9", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "### Complete model" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": 3, | ||
| "id": "6276334c", | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [ | ||
| "def scipy_astrocyte(p, f, simtime, dt, spk_ts, spk_ws):\n", | ||
| " \"\"\"\n", | ||
| " Complete astrocyte model using scipy `odeint` solver.\n", | ||
| "\n", | ||
| " Parameters\n", | ||
| " ----------\n", | ||
| " p : Params instance\n", | ||
| " Object containing the astrocyte parameters.\n", | ||
| " f : function\n", | ||
| " Right-hand side function\n", | ||
| " simtime : double\n", | ||
| " Duration of the simulation (will run between\n", | ||
| " 0 and tmax)\n", | ||
| " dt : double\n", | ||
| " Time increment.\n", | ||
| " spk_ts, spk_ws : list\n", | ||
| " Times and weights of spike input to the astrocyte\n", | ||
| "\n", | ||
| " Returns\n", | ||
| " -------\n", | ||
| " t : list\n", | ||
| " Times at which the astrocyte state was evaluated.\n", | ||
| " y : list\n", | ||
| " State values associated to the times in `t`\n", | ||
| " fos : list\n", | ||
| " List of dictionaries containing additional output\n", | ||
| " information from `odeint`\n", | ||
| " \"\"\"\n", | ||
| " t = np.arange(0, simtime, dt) # time axis\n", | ||
| " n = len(t)\n", | ||
| " y = np.zeros((n, 3)) # state variables: IP3, Ca, h_IP3R\n", | ||
| " # for the state variables, assign the same initial values as in test_astrocyte.py\n", | ||
| " y[0, 0] = 1.0\n", | ||
| " y[0, 1] = 1.0\n", | ||
| " y[0, 2] = 1.0\n", | ||
| " fos = [] # full output dict from odeint()\n", | ||
| " delta_ip3 = 5.0 # parameter determining the increase in IP3 induced by synaptic input\n", | ||
| "\n", | ||
| " # update time-step by time-step\n", | ||
| " for k in range(1, n):\n", | ||
| " # solve ODE from t_k-1 to t_k\n", | ||
| " d, fo = odeint(f, y[k - 1, :], t[k - 1 : k + 1], (p,), full_output=True)\n", | ||
| " y[k, :] = d[1, :]\n", | ||
| "\n", | ||
| " # apply synaptic inputs (spikes)\n", | ||
| " if t[k] in spk_ts:\n", | ||
| " y[k, 0] += delta_ip3 * spk_ws[spk_ts.index(t[k])]\n", | ||
| "\n", | ||
| " fos.append(fo)\n", | ||
| "\n", | ||
| " return t, y, fos" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "id": "246ef086", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "### Parameters" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": 4, | ||
| "id": "3fb81ba9", | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [ | ||
| "astro_param = {\n", | ||
| " \"Ca_tot\": 2.0,\n", | ||
| " \"IP3_0\": 0.16,\n", | ||
| " \"Kd_act\": 0.08234,\n", | ||
| " \"Kd_inh\": 1.049,\n", | ||
| " \"Kd_IP3_1\": 0.13,\n", | ||
| " \"Kd_IP3_2\": 0.9434,\n", | ||
| " \"Km_SERCA\": 0.1,\n", | ||
| " \"ratio_ER_cyt\": 0.185,\n", | ||
| " \"delta_IP3\": 5.0,\n", | ||
| " \"k_IP3R\": 0.0002,\n", | ||
| " \"rate_L\": 0.00011,\n", | ||
| " \"tau_IP3\": 7142.0,\n", | ||
| " \"rate_IP3R\": 0.006,\n", | ||
| " \"rate_SERCA\": 0.0009,\n", | ||
| "}\n", | ||
| "\n", | ||
| "\n", | ||
| "class Params:\n", | ||
| " \"\"\"\n", | ||
| " Class giving access to the astrocyte parameters.\n", | ||
| " \"\"\"\n", | ||
| "\n", | ||
| " def __init__(self):\n", | ||
| " self.params = astro_param\n", | ||
| " self.Ca_tot = astro_param[\"Ca_tot\"]\n", | ||
| " self.IP3_0 = astro_param[\"IP3_0\"]\n", | ||
| " self.Kd_act = astro_param[\"Kd_act\"]\n", | ||
| " self.Kd_inh = astro_param[\"Kd_inh\"]\n", | ||
| " self.Kd_IP3_1 = astro_param[\"Kd_IP3_1\"]\n", | ||
| " self.Kd_IP3_2 = astro_param[\"Kd_IP3_2\"]\n", | ||
| " self.Km_SERCA = astro_param[\"Km_SERCA\"]\n", | ||
| " self.ratio_ER_cyt = astro_param[\"ratio_ER_cyt\"]\n", | ||
| " self.delta_IP3 = astro_param[\"delta_IP3\"]\n", | ||
| " self.k_IP3R = astro_param[\"k_IP3R\"]\n", | ||
| " self.rate_L = astro_param[\"rate_L\"]\n", | ||
| " self.tau_IP3 = astro_param[\"tau_IP3\"]\n", | ||
| " self.rate_IP3R = astro_param[\"rate_IP3R\"]\n", | ||
| " self.rate_SERCA = astro_param[\"rate_SERCA\"]\n", | ||
| "\n", | ||
| "\n", | ||
| "p = Params()" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "id": "854edc71", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "### Simulate the implementation" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": 5, | ||
| "id": "c83f56f0", | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [ | ||
| "# Parameters for the simulation\n", | ||
| "simtime = 100.0\n", | ||
| "resolution = 0.1\n", | ||
| "spike_times = [10.0]\n", | ||
| "spike_weights = [1.0]\n", | ||
| "\n", | ||
| "# Simulate and get the recording\n", | ||
| "t, y, fos = scipy_astrocyte(p, rhs, simtime, resolution, spike_times, spike_weights)\n", | ||
| "data = np.concatenate((np.array([t]).T, y), axis=1)\n", | ||
| "\n", | ||
| "# Save the recording (excluding the initial values)\n", | ||
| "np.savetxt(\n", | ||
| " \"test_astrocyte.dat\",\n", | ||
| " data[1:, :],\n", | ||
| " header=\"\"\"\\ntest_astrocyte.dat\\n\n", | ||
| "This file is part of NEST.\\n\n", | ||
| "This .dat file contains the recordings of the state variables of an\n", | ||
| "astrocyte, simulated using the ODEINT solver of SciPy, with the\n", | ||
| "implementation detailed in\n", | ||
| "``doc/htmldoc/model_details/astrocyte_model_implementation.ipynb``.\n", | ||
| "This data is used as reference for the tests in ``test_astrocyte.py``.\\n\n", | ||
| " Times IP3 Ca h_IP3R \"\"\",\n", | ||
| ")" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "id": "df8ff655", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "-----------------------------\n", | ||
| "### License\n", | ||
| "\n", | ||
| "This file is part of NEST. Copyright (C) 2004 The NEST Initiative\n", | ||
| "\n", | ||
| "NEST is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 2 of the License, or (at your option) any later version.\n", | ||
| "\n", | ||
| "NEST is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details." | ||
| ] | ||
| } | ||
| ], | ||
| "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": "3.10.10" | ||
| } | ||
| }, | ||
| "nbformat": 4, | ||
| "nbformat_minor": 5 | ||
| } |
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