## Spike synchronization through subthreshold oscillation

This script reproduces the spike synchronization behavior of integrate-and-fire neurons in response to a subthreshold oscillation. This phenomenon is shown in Fig. 1 of

C.D. Brody and J.J. Hopfield Simple Networks for Spike-Timing-Based Computation, with Application to Olfactory Processing Neuron 37, 843-852 (2003)

Neurons receive a weak 35 Hz oscillation, a gaussian noise current and an increasing DC. The time-locking capability is shown to depend on the input current given. The result is then plotted using pylab. All parameters are taken from the above paper.

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

import nest
import nest.raster_plot

Second, the simulation parameters are assigned to variables.

N = 1000           # number of neurons
bias_begin = 140.  # minimal value for the bias current injection [pA]
bias_end = 200.    # maximal value for the bias current injection [pA]
T = 600            # simulation time (ms)

driveparams = {'amplitude': 50., 'frequency': 35.}
noiseparams = {'mean': 0.0, 'std': 200.}
neuronparams = {'tau_m': 20.,  # membrane time constant
'V_th': 20.,  # threshold potential
'E_L': 10.,  # membrane resting potential
't_ref': 2.,  # refractory period
'V_reset': 0.,  # reset potential
'C_m': 200.,  # membrane capacitance
'V_m': 0.}      # initial membrane potential

Third, the nodes are created using Create. We store the returned handles in variables for later reference.

neurons = nest.Create('iaf_psc_alpha', N)
sd = nest.Create('spike_detector')
noise = nest.Create('noise_generator')
drive = nest.Create('ac_generator')

Set the parameters specified above for the generators using SetStatus.

nest.SetStatus(drive, driveparams)
nest.SetStatus(noise, noiseparams)

Set the parameters specified above for the neurons. Nurons getan internal current. The first neuron additionally receives the current with amplitude bias_begin, the last neuron with amplitude bias_end.

nest.SetStatus(neurons, neuronparams)
nest.SetStatus(neurons, [{'I_e':
(n * (bias_end - bias_begin) / N + bias_begin)}
for n in neurons])

Set the parameters for the spike_detector: recorded data should include the information about global IDs of spiking neurons and the time of individual spikes.

nest.SetStatus(sd, {"withgid": True, "withtime": True})

Connect alternative current and noise generators as well as spike_detectors. to neurons

nest.Connect(drive, neurons)
nest.Connect(noise, neurons)
nest.Connect(neurons, sd)

Simulate the network for time T.

nest.Simulate(T)

Plot the raster plot of the neuronal spiking activity.

nest.raster_plot.from_device(sd, hist=True)