## Intrinsic currents subthreshold

This example illustrates how to record from a model with multiple intrinsic currents and visualize the results. This is illustrated using the ht_neuron which has four intrinsic currents: I_NaP, I_KNa, I_T, and I_h. It is a slightly simplified implementation of neuron model proposed in Hill and Tononi (2005) Modeling Sleep and Wakefulness in the Thalamocortical System J Neurophysiol 93:1671 http://dx.doi.org/10.1152/jn.00915.2004 .

The neuron is driven by DC current, which is alternated between depolarizing and hyperpolarizing. Hyperpolarization intervals become increasingly longer.

We imported all necessary modules for simulation, analysis and plotting.

import nest
import numpy as np
import matplotlib.pyplot as plt

Additionally, we set the verbosity using set_verbosity to suppress info messages. We also reset the kernel to be sure to start with a clean NEST.

nest.set_verbosity("M_WARNING")
nest.ResetKernel()

We define simulation parameters:

• The length of depolarization intervals
• The length of hyperpolarization intervals
• The amplitude for de- and hyperpolarizing currents
• The end of the time window to plot

n_blocks = 5 t_block = 20. t_dep = [t_block] * n_blocks t_hyp = [t_block * 2 ** n for n in range(n_blocks)] I_dep = 10. I_hyp = -5.

t_end = 500.

We create the one neuron instance and the DC current generator and store the returned handles.

nrn = nest.Create('ht_neuron')
dc = nest.Create('dc_generator')

We create a multimeter to record

• membrane potential V_m
• threshold value theta
• intrinsic currents I_NaP, I_KNa, I_T, I_h

by passing these names in the record_from list.

To find out which quantities can be recorded from a given neuron, run::

nest.GetDefaults('ht_neuron')['recordables']

The result will contain an entry like::

<SLILiteral: V_m>

for each recordable quantity. You need to pass the value of the SLILiteral, in this case V_m in the record_from list.

We want to record values with 0.1 ms resolution, so we set the recording interval as well; the default recording resolution is 1 ms.

mm = nest.Create('multimeter',
params={'interval': 0.1,
'record_from': ['V_m', 'theta',
'I_NaP', 'I_KNa', 'I_T', 'I_h']}
)

We connect the DC generator and the multimeter to the neuron. Note that the multimeter, just like the voltmeter is connected to the neuron, not the neuron to the multimeter.

nest.Connect(dc, nrn)
nest.Connect(mm, nrn)

We are ready to simulate. We alternate between driving the neuron with depolarizing and hyperpolarizing currents. Before each simulation interval, we set the amplitude of the DC generator to the correct value.

for t_sim_dep, t_sim_hyp in zip(t_dep, t_hyp):

nest.SetStatus(dc, {'amplitude': I_dep})
nest.Simulate(t_sim_dep)

nest.SetStatus(dc, {'amplitude': I_hyp})
nest.Simulate(t_sim_hyp)

We now fetch the data recorded by the multimeter. The data are returned as a dictionary with entry 'times' containing timestamps for all recorded data, plus one entry per recorded quantity.

All data is contained in the 'events' entry of the status dictionary returned by the multimeter. Because all NEST function return arrays, we need to pick out element 0 from the result of GetStatus.

data = nest.GetStatus(mm)[0]['events']
t = data['times']

The next step is to plot the results. We create a new figure, add a single subplot and plot at first membrane potential and threshold.

fig = plt.figure()
Vax.plot(t, data['V_m'], 'b-', lw=2, label=r'$V_m$')
Vax.plot(t, data['theta'], 'g-', lw=2, label=r'$\Theta$')
Vax.set_ylim(-80., 0.)
Vax.set_ylabel('Voltageinf [mV]')
Vax.set_xlabel('Time [ms]')

To plot the input current, we need to create an input current trace. We construct it from the durations of the de- and hyperpolarizing inputs and add the delay in the connection between DC generator and neuron:

1. We find the delay by checking the status of the dc->nrn connection.
2. We find the resolution of the simulation from the kernel status.
3. Each current interval begins one time step after the previous interval, is delayed by the delay and effective for the given duration.
4. We build the time axis incrementally. We only add the delay when adding the first time point after t=0. All subsequent points are then automatically shifted by the delay.

delay = nest.GetStatus(nest.GetConnections(dc, nrn))[0]['delay'] dt = nest.GetKernelStatus('resolution')

t_dc, I_dc = [0], [0]

for td, th in zip(t_dep, t_hyp): t_prev = t_dc[-1] t_start_dep = t_prev + dt if t_prev > 0 else t_prev + dt + delay t_end_dep = t_start_dep + td t_start_hyp = t_end_dep + dt t_end_hyp = t_start_hyp + th

t_dc.extend([t_start_dep, t_end_dep, t_start_hyp, t_end_hyp])
I_dc.extend([I_dep, I_dep, I_hyp, I_hyp])

The following function turns a name such as I_NaP into proper TeX code INaP for a pretty label.

def texify_name(name):
return r'${}_{{\mathrm{{{}}}}}$'.format(*name.split('_'))

Next, we add a right vertical axis and plot the currents with respect to that axis.

Iax = Vax.twinx()
Iax.plot(t_dc, I_dc, 'k-', lw=2, label=texify_name('I_DC'))

for iname, color in (('I_h', 'maroon'), ('I_T', 'orange'),
('I_NaP', 'crimson'), ('I_KNa', 'aqua')):
Iax.plot(t, data[iname], color=color, lw=2, label=texify_name(iname))

Iax.set_xlim(0, t_end)
Iax.set_ylim(-10., 15.)
Iax.set_ylabel('Current [pA]')
Iax.set_title('ht_neuron driven by DC current')

We need to make a little extra effort to combine lines from the two axis into one legend.

lines_V, labels_V = Vax.get_legend_handles_labels()
lines_I, labels_I = Iax.get_legend_handles_labels()
try:
Iax.legend(lines_V + lines_I, labels_V + labels_I, fontsize='small')
except TypeError:
# work-around for older Matplotlib versions
Iax.legend(lines_V + lines_I, labels_V + labels_I)

Note that I_KNa is not activated in this example because the neuron does not spike. I_T has only a very small amplitude.