Neuronal_Dynamics-STDP.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Spike-timing dependent plasticity\n",
    "\n",
    "Spike-timing dependent plasticity has a number of interesting and not entirely obvious effects when we include it into the dynamics of a neural network. \n",
    "\n",
    "We test some of these effects in one of the simplest possible networks: one (leaky integrate-and-fire) neuron receiving input from $N$ \"neurons\" modelled as emitting spikes as a Poisson process (essentially at random times with a fixed firing rate). "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The synapse from the input neurons to the output neuron has conductance that decays exponentially (with time constant $\\tau_e$) after each spike. \n",
    "Its efficacy changes according to a STDP rule.\n",
    "\n",
    "We follow the treatment in the paper by Song et al. [Competitive Hebbian learning through spike-timing-dependent synaptic plasticity](https://www.nature.com/articles/nn0900_919) and we make the STDP curve asymmetric, so that the area under the curve for the \"depressing\" part of the curve ($\\tau_{pre} - \\tau_{post} > 0$) is greater then the potentiating part ($\\tau_{pre} - \\tau_{post} < 0$). Synapses are initialized at random values\n",
    "\n",
    "The result will be that most synapses will be depressed at the beginning (because relative spike times are equally likely to fall in the depressing than in the potentiating part of the plasticity curve, and the depressing effect is stronger under these circumstances. (Look at Song et al. Figure 3)\n",
    "\n",
    "Only the few synapses that are stronger, for which the input is more likely to drive the output neuron, the post-synaptic neuron will tend to follow the pre-synaptic spike and we get a potentiation. As a result, there is a partition of synapses between a group that gets very high values of conductance, and the others that will go towards zero. \n",
    "\n",
    "The other effect is that the neuron gets in a state in which the excitatory (synaptic) current and the leakage current are balanced, and the neuron is driven by fluctuations. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from brian2 import *\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## setting the parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# this parameter determines the relative area-under-the-curve for depression vs potentiation in the STDP curve \n",
    "# (1 is perfect balance)\n",
    "inhibition_excess = 1.05\n",
    "\n",
    "# number of input \"neurons\" (random Poisson spike trains)\n",
    "N = 1000\n",
    "\n",
    "#membrane time constant for the output neuron\n",
    "taum = 10*ms\n",
    "\n",
    "# Time constants for the potentiation (pre) and depression (post) parts of the STDP curve\n",
    "taupre = 20*ms\n",
    "taupost = taupre\n",
    "\n",
    "# excitatory reversal potential\n",
    "Ee = 0*mV\n",
    "\n",
    "# threshold for the integrate-and-fire neuron\n",
    "vt = -54*mV\n",
    "\n",
    "# resting potential\n",
    "vr = -60*mV\n",
    "\n",
    "# leakage reversal potential \n",
    "El = -74*mV\n",
    "\n",
    "# synaptic time constant \n",
    "taue = 5*ms\n",
    "\n",
    "# input mean firing rate \n",
    "F = 15*Hz\n",
    "\n",
    "# maximal synaptic conductance \n",
    "gmax = .01\n",
    "\n",
    "# the synaptic increment after each spike \n",
    "syn_increment = .01\n",
    "\n",
    "dApre = None\n",
    "dApsot = None\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Defining the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "class STDP_model:\n",
    "    def __init__(self):\n",
    "\n",
    "        global dApre, dApost\n",
    "        # integrate and fire equations for the output neuron (including synaptic current decay)\n",
    "        eqs_neurons = '''\n",
    "        dv/dt = (ge * (Ee-vr) + El - v) / taum : volt\n",
    "        dge/dt = -ge / taue : 1\n",
    "        '''\n",
    "        dApre = syn_increment\n",
    "        dApost = -dApre * taupre / taupost * inhibition_excess\n",
    "        dApost *= gmax\n",
    "        dApre *= gmax\n",
    "        \n",
    "        \n",
    "        self.net = Network()\n",
    "        self.input = PoissonGroup(N, rates=F)\n",
    "        self.net.add(self.input)\n",
    "        self.neurons = NeuronGroup(1, eqs_neurons, threshold='v>vt', reset='v = vr',\n",
    "                              method='exact')\n",
    "        self.net.add(self.neurons)\n",
    "        # equations for the synapses\n",
    "        self.S = Synapses(self.input, self.neurons,\n",
    "                     '''w : 1\n",
    "                        dApre/dt = -Apre / taupre : 1 (event-driven)\n",
    "                        dApost/dt = -Apost / taupost : 1 (event-driven)''',\n",
    "                     on_pre='''ge += w\n",
    "                            Apre += dApre\n",
    "                            w = clip(w + Apost, 0, gmax)''',\n",
    "                     on_post='''Apost += dApost\n",
    "                             w = clip(w + Apre, 0, gmax)''',\n",
    "                     )\n",
    "        self.net.add(self.S)\n",
    "        self.S.connect()\n",
    "\n",
    "        # synapses are initialized to a random value between 0 and gmax\n",
    "        self.S.w = 'rand() * gmax'\n",
    "        self.mon = StateMonitor(self.S, 'w', record=[0, 1, 2, 3])\n",
    "        self.net.add(self.mon)\n",
    "        self.s_mon = SpikeMonitor(self.input)\n",
    "        self.net.add(self.s_mon)\n",
    "        \n",
    "        \n",
    "    def output_monitor(self):\n",
    "        self.o_mon = SpikeMonitor(self.neurons)\n",
    "        self.net.add(self.o_mon)\n",
    "        return self.o_mon\n",
    "    \n",
    "    def run(self, run_time):\n",
    "        self.net.run(run_time, report='text')\n",
    "        "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Running the model \n",
    "\n",
    "These simulations will take some minutes to run (on my laptop around 3 seconds for each second of simulated time. Please be patients and grab a cup of coffee while each run executes "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Varying the input rate \n",
    "\n",
    "in this simulation, we will run the network with different input firing rates, from 10 to 40 Hz. We will reproduce the result from the Song et al. paper, Figure 2a-c. (Ignore the warnings if you get any)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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   ],
   "source": [
    "out_rates = []\n",
    "w_matrices = []\n",
    "firing_rates = np.arange(10, 41, 5)\n",
    "for F in [f*Hz for f in firing_rates]:\n",
    "    # if we want to change some of the parameters from the default values, we have to do it here below\n",
    "    inhibition_excess = 1.05\n",
    "    \n",
    "    model = STDP_model()\n",
    "    \n",
    "    model.S.w = 'rand() * gmax'\n",
    "    o_mon = model.output_monitor()\n",
    "    model.run(100*second)\n",
    "    device.build(directory='STDP_standalone', compile=True, run=True, debug=False)\n",
    "    out_rates.append(o_mon.count[0])\n",
    "    w_matrices.append(model.S.w[:])\n",
    "\n",
    "out_rates = np.array(out_rates)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "let's plot the output firing rate as a function of the input firing rate. Similar to Song et al. (Figure 2c) the output activity increases only weakly when the firing rate increases (note that the plot is not exactly the same as in the paper, because the model parameters are slightly different, so that we can see the main effects in shorter simulations) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Output firing rate (Hz)')"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(firing_rates, out_rates/100)\n",
    "xlabel(\"Input firing rate (Hz)\")\n",
    "ylabel(\"Output firing rate (Hz)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's look at the distribution of the synaptic weights, for each of the runs (change run_no to look at the result for different firing rates)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "run_no = 6\n",
    "\n",
    "subplot(211)\n",
    "title(\"Firing rate: \" + str(firing_rates[run_no]) + \" Hz\")\n",
    "plot(w_matrices[run_no] / gmax, '.k')\n",
    "ylabel('Weight / gmax')\n",
    "xlabel('Synapse index')\n",
    "subplot(212)\n",
    "hist(w_matrices[run_no] / gmax, 20)\n",
    "xlabel('Weight / gmax')\n",
    "\n",
    "tight_layout()\n",
    "show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}