{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "### Quickstart\n", "To run the code below:\n", "\n", "1. Click on the cell to select it.\n", "2. Press `SHIFT+ENTER` on your keyboard or press the play button\n", " () in the toolbar above.\n", "\n", "Feel free to create new cells using the plus button\n", "(), or pressing `SHIFT+ENTER` while this cell\n", "is selected." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Appendix 4: multicompartmental modeling\n", "\n", "This example demonstrates multicompartmental modeling in Brian 2. It partly reproduces Figure 9C from the following paper:\n", "\n", "Dendritic Low-Threshold Calcium Currents in Thalamic Relay Cells\n", "Alain Destexhe, Mike Neubig, Daniel Ulrich, John Huguenard\n", "Journal of Neuroscience 15 May 1998, 18 (10) 3574-3588\n", "\n", "The original NEURON code is available on ModelDB: \n", "https://senselab.med.yale.edu/modeldb/ShowModel.cshtml?model=279 \n", "\n", "Reference for the original morphology: \n", "Rat VB neuron (thalamocortical cell), given by J. Huguenard, stained with\n", "biocytin and traced by A. Destexhe, December 1992. The neuron is described\n", "in: J.R. Huguenard & D.A. Prince, A novel T-type current underlies prolonged\n", "calcium-dependent burst firing in GABAergic neurons of rat thalamic reticular\n", "nucleus. J. Neurosci. 12: 3804-3817, 1992.\n", "\n", "Available at NeuroMorpho.org:\n", "http://neuromorpho.org/neuron_info.jsp?neuron_name=tc200 \n", "NeuroMorpho.Org ID :NMO_00881" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The code makes use of physical constants defined in Brian's `brian2.units.constants` package, and of a plotting function defined as parts of the external `brian2tools` package (https://brian2tools.readthedocs.io ):" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "from brian2 import *\n", "from brian2.units.constants import (zero_celsius, faraday_constant as F,\n", " gas_constant as R)\n", "from brian2tools import plot_morphology" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We switch on plotting in the notebook:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "%matplotlib notebook" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We set the integration time step and set a couple of constants:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "defaultclock.dt = 0.01*ms\n", "\n", "VT = -52*mV\n", "El = -76.5*mV \n", "gl = 0.0379*msiemens/cm**2\n", "\n", "E_Na = 50*mV\n", "E_K = -100*mV\n", "\n", "T = 34*kelvin + zero_celsius # 34 degC (current-clamp experiments)\n", "tadj_HH = 3.0**((34-36)/10.0) # temperature adjustment for Na & K (original recordings at 36 degC)\n", "tadj_m_T = 2.5**((34-24)/10.0)\n", "tadj_h_T = 2.5**((34-24)/10.0)\n", "\n", "shift_I_T = -1*mV\n", "\n", "gamma = F/(R*T) # R=gas constant, F=Faraday constant\n", "Z_Ca = 2 # Valence of Calcium ions\n", "Ca_i = 240*nM # intracellular Calcium concentration\n", "Ca_o = 2*mM # extracellular Calcium concentration" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The neuron's membrane equations are described in the same formalism used for single compartment models with three exceptions:\n", "1. The membrane potential is automatically defined as `v`\n", "2. The user has to provide an equation for the transmembrane current `Im` (as a current per area)\n", "3. Currents injected at a particular point (e.g. provided by electrodes or synapses), can be declared as a `point current` and will be automatically added to the membrane equations (divided by the area of the respective compartment)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "eqs = Equations('''\n", "Im = gl*(El-v) - I_Na - I_K - I_T: amp/meter**2\n", "I_inj : amp (point current)\n", "\n", "# HH-type currents for spike initiation\n", "g_Na : siemens/meter**2\n", "g_K : siemens/meter**2\n", "I_Na = g_Na * m**3 * h * (v-E_Na) : amp/meter**2\n", "I_K = g_K * n**4 * (v-E_K) : amp/meter**2\n", "v2 = v - VT : volt # shifted membrane potential (Traub convention)\n", "dm/dt = (0.32*(mV**-1)*(13.*mV-v2)/\n", " (exp((13.*mV-v2)/(4.*mV))-1.)*(1-m)-0.28*(mV**-1)*(v2-40.*mV)/\n", " (exp((v2-40.*mV)/(5.*mV))-1.)*m) / ms * tadj_HH: 1\n", "dn/dt = (0.032*(mV**-1)*(15.*mV-v2)/\n", " (exp((15.*mV-v2)/(5.*mV))-1.)*(1.-n)-.5*exp((10.*mV-v2)/(40.*mV))*n) / ms * tadj_HH: 1\n", "dh/dt = (0.128*exp((17.*mV-v2)/(18.*mV))*(1.-h)-4./(1+exp((40.*mV-v2)/(5.*mV)))*h) / ms * tadj_HH: 1\n", "\n", "# Low-threshold Calcium current (I_T) -- nonlinear function of voltage\n", "I_T = P_Ca * m_T**2*h_T * G_Ca : amp/meter**2\n", "P_Ca : meter/second # maximum Permeability to Calcium\n", "G_Ca = Z_Ca**2*F*v*gamma*(Ca_i - Ca_o*exp(-Z_Ca*gamma*v))/(1 - exp(-Z_Ca*gamma*v)) : coulomb/meter**3\n", "dm_T/dt = -(m_T - m_T_inf)/tau_m_T : 1\n", "dh_T/dt = -(h_T - h_T_inf)/tau_h_T : 1\n", "m_T_inf = 1/(1 + exp(-(v/mV + 56)/6.2)) : 1\n", "h_T_inf = 1/(1 + exp((v/mV + 80)/4)) : 1\n", "tau_m_T = (0.612 + 1.0/(exp(-(v/mV + 131)/16.7) + exp((v/mV + 15.8)/18.2))) * ms / tadj_m_T: second\n", "tau_h_T = (int(v<-81*mV) * exp((v/mV + 466)/66.6) +\n", " int(v>=-81*mV) * (28 + exp(-(v/mV + 21)/10.5))) * ms / tadj_h_T: second\n", "''')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Multicompartment models have to specify the morphology of the cell, either by loading them from a file or by constructing it. The model is then instantiated by creating a `SpatialNeuron`:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "# Load morphology from SWC file\n", "morpho = Morphology.from_file('tc200.CNG.swc')\n", "neuron = SpatialNeuron(morpho, eqs, Cm=0.88*uF/cm**2, Ri=173*ohm*cm,\n", " method='exponential_euler')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Compartment-specific values, such as the initial membrane potential, or the densitities of ion channels, can be set for the whole neuron or for individual compartments:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "neuron.v = -74*mV\n", "# Only the soma has Na/K channels\n", "neuron.main.g_Na = 100*msiemens/cm**2\n", "neuron.main.g_K = 100*msiemens/cm**2\n", "\n", "neuron.m_T = 'm_T_inf'\n", "neuron.h_T = 'h_T_inf'\n", "\n", "neuron.P_Ca = 1.7e-5*cm/second\n", "# Distal dendrites\n", "neuron.P_Ca['(distance + length/2) > 11*um'] = 8.5e-5*cm/second\n", "\n", "mon = StateMonitor(neuron, ['v'], record=morpho[0]) # Record at soma\n", "cutoff = 100*ms # we'll ignore the first 100ms\n", "# Switch off monitor during initial transient\n", "mon.active = False\n", "run(cutoff)\n", "mon.active = True\n", "run(80 * ms)\n", "neuron.main.I_inj = 75*pA\n", "run(320*ms)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "application/javascript": [ "/* Put everything inside the global mpl namespace */\n", "window.mpl = {};\n", "\n", "\n", "mpl.get_websocket_type = function() {\n", " if (typeof(WebSocket) !== 'undefined') {\n", " return WebSocket;\n", " } else if (typeof(MozWebSocket) !== 'undefined') {\n", " return MozWebSocket;\n", " } else {\n", " alert('Your browser does not have WebSocket support.' +\n", " 'Please try Chrome, Safari or Firefox ≥ 6. 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