Comparing precise and grid-based neuron models

In traditional time-driven simulations, spikes are constrained to the time grid at a user-defined resolution. The precise spiking models overcome this by handling spikes in continuous time [1, 2]. The precise spiking neuron models in NEST include: iaf_psc_exp_ps, iaf_psc_alpha_canon, iaf_psc_alpha_presc, and iaf_psc_delta_canon. More detailed information about the precise spiking models can be found here: http://www.nest-simulator.org/simulations-with-precise-spike-times/ This example compares the conventional grid-constrained model and the precise version for an integrate-and-fire neuron model with exponential post-synaptic currents [2]. References: [1] Morrison A, Straube S, Plesser HE, Diesmann M (2007) Exact subthreshold integration with continuous spike times in discrete-time neural network simulations. Neural Comput. 19(1):47-79. doi: 10.1162/neco.2007.19.1.47 [2] Hanuschkin A, Kunkel S, Helias M, Morrison A and Diesmann M (2010) A general and efficient method for incorporating precise spike times in globally time-driven simulations. Front. Neuroinform. 4:113. doi:10.3389/fninf.2010.00113
First, we import all necessary modules for simulation, analysis and plotting.
import nest
import pylab
Second, we assign the simulation parameters to variables.
simtime      = 100.0           # ms
stim_current = 700.0           # pA
resolutions  = [0.1, 0.5, 1.0] # ms

Now, we simulate the two versions of the neuron models (i.e. discrete-time: iaf_psc_exp; precise: iaf_psc_exp_ps) for each of the defined resolutions. The neurons use their default parameters and we stimulate them by injecting a current using a dc_generator device. The membrane potential is recorded by a voltmeter, the spikes are recorded by a spike_detector, whose property 'precise_times' is set to True. The data is stored in a dictionary for later use.
data = {}

for h in resolutions:
    data[h] = {}
    for model in ["iaf_psc_exp", "iaf_psc_exp_ps"]:
        nest.ResetKernel()
        nest.SetKernelStatus({'resolution': h})
        
        neuron = nest.Create(model)
        voltmeter= nest.Create("voltmeter", params={"interval": h})
        dc = nest.Create("dc_generator", params={"amplitude": stim_current})
        sd = nest.Create("spike_detector", params={"precise_times": True})
        
        nest.Connect(voltmeter, neuron)
        nest.Connect(dc, neuron)        
        nest.Connect(neuron, sd)
    
        nest.Simulate(simtime)

        vm_status = nest.GetStatus(voltmeter, 'events')[0]
        sd_status = nest.GetStatus(sd, 'events')[0]
        data[h][model] = {"vm_times": vm_status['times'],
                          "vm_values": vm_status['V_m'],
                          "spikes": sd_status['times'],
                          "V_th": nest.GetStatus(neuron, 'V_th')[0]}

After simulation, we plot the results from the simulation. The figure illustrates the membrane potential excursion of the two models due to injected current simulated for 100 ms for a different timestep in each panel. The blue line is the voltage trace of the discrete-time neuron, the red line is that of the precise spiking version of the same model.Please note that the temporal differences between the traces in the different panels is caused by the different resolutions used.
        plot.set_xticklabels('')
  precise_spiking
                                # -*- coding: utf-8 -*-
#
# precise_spiking.py
#
# This file is part of NEST.
#
# Copyright (C) 2004 The NEST Initiative
#
# 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.
#
# 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.
#
# You should have received a copy of the GNU General Public License
# along with NEST.  If not, see <http://www.gnu.org/licenses/>.

'''
Comparing precise and grid-based neuron models
----------------------------------------------

In traditional time-driven simulations, spikes are constrained to the
time grid at a user-defined resolution. The precise spiking models
overcome this by handling spikes in continuous time [1, 2].

The precise spiking neuron models in NEST include: iaf_psc_exp_ps,
iaf_psc_alpha_canon, iaf_psc_alpha_presc, and iaf_psc_delta_canon.
More detailed information about the precise spiking models can be
found here:
  http://www.nest-simulator.org/simulations-with-precise-spike-times/

This example compares the conventional grid-constrained model and the
precise version for an integrate-and-fire neuron model with exponential
post-synaptic currents [2].

References:
[1] Morrison A, Straube S, Plesser HE, Diesmann M (2007) Exact
    subthreshold integration with continuous spike times in
    discrete-time neural network simulations. Neural
    Comput. 19(1):47-79. doi: 10.1162/neco.2007.19.1.47
[2] Hanuschkin A, Kunkel S, Helias M, Morrison A and Diesmann M (2010)
    A general and efficient method for incorporating precise spike
    times in globally time-driven simulations. Front. Neuroinform.
    4:113. doi:10.3389/fninf.2010.00113
'''

'''
First, we import all necessary modules for simulation, analysis and
plotting.
'''

import nest
import pylab

'''
Second, we assign the simulation parameters to variables.
'''

simtime      = 100.0           # ms
stim_current = 700.0           # pA
resolutions  = [0.1, 0.5, 1.0] # ms

'''
Now, we simulate the two versions of the neuron models (i.e.
discrete-time: `iaf_psc_exp`; precise: `iaf_psc_exp_ps`) for each of
the defined resolutions. The neurons use their default parameters and
we stimulate them by injecting a current using a `dc_generator`
device. The membrane potential is recorded by a `voltmeter`, the
spikes are recorded by a `spike_detector`, whose property
'precise_times' is set to True. The data is stored in a dictionary for
later use.
'''

data = {}

for h in resolutions:
    data[h] = {}
    for model in ["iaf_psc_exp", "iaf_psc_exp_ps"]:
        nest.ResetKernel()
        nest.SetKernelStatus({'resolution': h})
        
        neuron = nest.Create(model)
        voltmeter= nest.Create("voltmeter", params={"interval": h})
        dc = nest.Create("dc_generator", params={"amplitude": stim_current})
        sd = nest.Create("spike_detector", params={"precise_times": True})
        
        nest.Connect(voltmeter, neuron)
        nest.Connect(dc, neuron)        
        nest.Connect(neuron, sd)
    
        nest.Simulate(simtime)

        vm_status = nest.GetStatus(voltmeter, 'events')[0]
        sd_status = nest.GetStatus(sd, 'events')[0]
        data[h][model] = {"vm_times": vm_status['times'],
                          "vm_values": vm_status['V_m'],
                          "spikes": sd_status['times'],
                          "V_th": nest.GetStatus(neuron, 'V_th')[0]}

'''
After simulation, we plot the results from the simulation. The figure 
illustrates the membrane potential excursion of the two models due to
injected current simulated for 100 ms for a different timestep in each
panel. The blue line is the voltage trace of the discrete-time neuron,
the red line is that of the precise spiking version of the same model.

Please note that the temporal differences between the traces in the
different panels is caused by the different resolutions used.
'''

colors = ["#3465a4", "#cc0000"]

for v, h in enumerate(sorted(data)):
    plot = pylab.subplot(len(data), 1, v + 1)
    plot.set_title("Resolution: {0} ms".format(h))
    
    for i, model in enumerate(data[h]):
        times = data[h][model]["vm_times"]
        potentials = data[h][model]["vm_values"]
        spikes = data[h][model]["spikes"]
        spikes_y = [data[h][model]["V_th"]]*len(spikes)

        plot.plot(times, potentials, "-", c=colors[i], ms=5, lw=2, label=model)
        plot.plot(spikes, spikes_y, ".", c=colors[i], ms=5, lw=2)
    
    if v==2:
        plot.legend(loc=4)
    else:
        plot.set_xticklabels('')