{ "cells": [ { "cell_type": "markdown", "id": "b1c93dcd460fce2c", "metadata": { "collapsed": true }, "source": [ "# Simulating excitatory-inhibitory spiking networks with ``brainpy``\n", "\n", "[![Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/chaobrain/brain-modeling-ecosystem/blob/main/docs/brainpy_EI_spiking_network.ipynb)\n", "[![Open in Kaggle](https://kaggle.com/static/images/open-in-kaggle.svg)](https://kaggle.com/kernels/welcome?src=https://github.com/chaobrain/brain-modeling-ecosystem/blob/main/docs/brainpy_EI_spiking_network.ipynb)" ] }, { "cell_type": "markdown", "id": "8dc3f2b8c5d20527", "metadata": {}, "source": [ "Implementation of the EI network from Brunel (1996) with the brainstate package.\n", "\n", "- Van Vreeswijk, Carl, and Haim Sompolinsky. “Chaos in neuronal networks with balanced excitatory and inhibitory activity.” Science 274.5293 (1996): 1724-1726." ] }, { "cell_type": "markdown", "id": "cc16760ad4bc0d39", "metadata": {}, "source": [ "This notebook demonstrates how to build and simulate a classic Excitatory–Inhibitory (E–I) spiking network using the BrainState backend. It walks through model assumptions, equations, parameters, connectivity, and analysis so you can adapt it to your own studies.\n", "\n", "## Model overview\n", "\n", "- Populations: one excitatory (E) and one inhibitory (I) population with leaky integrate-and-fire (LIF) neurons by default.\n", "- Synapses: current-based or conductance-based synapses (model-dependent), with E→E, E→I, I→E, I→I projections configurable.\n", "- External drive: constant background current and/or Poisson input can be enabled to elicit activity and oscillations.\n" ] }, { "cell_type": "markdown", "id": "b2b9f1eb00b000c2", "metadata": {}, "source": [ "## Network dynamics\n", "\n", "Dynamic of membrane potential is given as:\n", "\n", "$$ \\tau \\frac {dV_i}{dt} = -(V_i - V_{rest}) + I_i^{ext} + I_i^{net} (t) $$\n", "\n", "where $I_i^{net}(t)$ represents the synaptic current, which describes the sum of excitatory and inhibitory neurons.\n", "\n", "$$ I_i^{net} (t) = J_E \\sum_{j=1}^{pN_e} \\sum_{t_j^\\alpha < t} f(t-t_j^\\alpha ) - J_I \\sum_{j=1}^{pN_i} \\sum_{t_j^\\alpha < t} f(t-t_j^\\alpha )$$\n", "\n", "where\n", "\n", "$$\n", "f(t) = \\begin{cases} {\\rm exp} (-\\frac t {\\tau_s} ), \\quad t \\geq 0 \\\\\n", "0, \\quad t < 0 \\end{cases}\n", "$$\n", "\n", "Parameters: $J_E = \\frac 1 {\\sqrt {pN_e}}, J_I = \\frac 1 {\\sqrt {pN_i}}$" ] }, { "cell_type": "markdown", "id": "42fe6ea0851dd039", "metadata": {}, "source": [ "## Network" ] }, { "cell_type": "code", "execution_count": 1, "id": "b3997d66a37b2993", "metadata": { "ExecuteTime": { "end_time": "2025-09-16T03:06:16.563037Z", "start_time": "2025-09-16T03:06:15.077839Z" } }, "outputs": [], "source": [ "import brainunit as u\n", "import brainstate\n", "import braintools\n", "import brainpy.state" ] }, { "cell_type": "code", "execution_count": 2, "id": "c77810a2b1f8e761", "metadata": { "ExecuteTime": { "end_time": "2025-09-16T03:06:16.573387Z", "start_time": "2025-09-16T03:06:16.568152Z" } }, "outputs": [], "source": [ "class EINet(brainstate.nn.Module):\n", " def __init__(self, n_exc, n_inh, prob, JE, JI):\n", " super().__init__()\n", " self.n_exc = n_exc\n", " self.n_inh = n_inh\n", " self.num = n_exc + n_inh\n", "\n", " # neurons\n", " self.N = brainpy.state.LIF(\n", " n_exc + n_inh,\n", " V_rest=-52. * u.mV, V_th=-50. * u.mV, V_reset=-60. * u.mV, tau=10. * u.ms,\n", " V_initializer=braintools.init.Normal(-60., 10., unit=u.mV), spk_reset='soft'\n", " )\n", "\n", " # synapses\n", " self.E = brainpy.state.AlignPostProj(\n", " comm=brainstate.nn.EventFixedProb(n_exc, self.num, prob, JE),\n", " syn=brainpy.state.Expon.desc(self.num, tau=2. * u.ms),\n", " out=brainpy.state.CUBA.desc(),\n", " post=self.N,\n", " )\n", " self.I = brainpy.state.AlignPostProj(\n", " comm=brainstate.nn.EventFixedProb(n_inh, self.num, prob, JI),\n", " syn=brainpy.state.Expon.desc(self.num, tau=2. * u.ms),\n", " out=brainpy.state.CUBA.desc(),\n", " post=self.N,\n", " )\n", "\n", " def update(self, inp):\n", " spks = self.N.get_spike() != 0.\n", " self.E(spks[:self.n_exc])\n", " self.I(spks[self.n_exc:])\n", " self.N(inp)\n", " return self.N.get_spike()" ] }, { "cell_type": "markdown", "id": "98d6978794723c8e", "metadata": {}, "source": [ "## Simulation" ] }, { "cell_type": "code", "execution_count": 3, "id": "9008ea0bf71cbd63", "metadata": { "ExecuteTime": { "end_time": "2025-09-16T03:06:16.696359Z", "start_time": "2025-09-16T03:06:16.578847Z" } }, "outputs": [], "source": [ "# connectivity\n", "num_exc = 500\n", "num_inh = 500\n", "prob = 0.1\n", "# external current\n", "Ib = 3. * u.mA\n", "# excitatory and inhibitory synaptic weights\n", "JE = 1 / u.math.sqrt(prob * num_exc) * u.mS\n", "JI = -1 / u.math.sqrt(prob * num_inh) * u.mS" ] }, { "cell_type": "code", "execution_count": 4, "id": "3a7eb3f4d7fadfa9", "metadata": { "ExecuteTime": { "end_time": "2025-09-16T03:06:17.028007Z", "start_time": "2025-09-16T03:06:16.726864Z" } }, "outputs": [], "source": [ "# network\n", "brainstate.environ.set(dt=0.1 * u.ms)\n", "net = EINet(num_exc, num_inh, prob=prob, JE=JE, JI=JI)\n", "_ = brainstate.nn.init_all_states(net)" ] }, { "cell_type": "code", "execution_count": 5, "id": "c56bd478a86da34f", "metadata": { "ExecuteTime": { "end_time": "2025-09-16T03:06:18.684364Z", "start_time": "2025-09-16T03:06:17.033471Z" } }, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "8f60d01a41a447a2b2bd5d49e55d7cd9", "version_major": 2, "version_minor": 0 }, "text/plain": [ " 0%| | 0/10000 [00:00" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "\n", "# visualization\n", "t_indices, n_indices = u.math.where(spikes)\n", "plt.scatter(times[t_indices], n_indices, s=1)\n", "plt.xlabel('Time (ms)')\n", "plt.ylabel('Neuron index')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "ef40db69f3b8950e", "metadata": {}, "source": [ "## Analysis checklist\n", "\n", "- Plot spike raster for a subset of neurons from E and I.\n", "- Compute population-averaged firing rates with a 5–10 ms bin; smooth with a Gaussian window (σ≈5 ms).\n", "- Build an LFP proxy (e.g., mean V over E or total syn current to I) and compute its PSD (e.g., via Welch).\n", "- Inspect gamma peak frequency and bandwidth; relate to synaptic τ and weights.\n", "- Perform parameter sweeps over $J_\\mathrm{EI}$ and $J_{IE}$ to map oscillatory regimes." ] } ], "metadata": { "kernelspec": { "display_name": "Ecosystem-py", "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": "3.11.13" } }, "nbformat": 4, "nbformat_minor": 5 }