23 Aug
2023
23 Aug
'23
8:50 a.m.
Hi!
Just a comment on the spike emission for Hodgkin-Huxley models. This is a non-trivial
topic that requires the modeller to make a choice of what they want. Remember that the
original Hodgkin-Huxley model is not a model of a neuron but a model for spike propagation
down the squid axon. In this model, there is no such thing as a singular spike in the
sense we use it commonly when discussing integrate-and-fire point neuron models.
In the HH model, under certain conditions, we have a rapidly rising Na current
depolarizing the membrane up to around +30 mV, followed by a rapidly activating K current
repolarizing the memrane again towards -70 mV. The resulting memrane potential excursion
looks like a spike, but the dynamics are entirely continuous and described by the HH ODEs.
These ODEs also incorporate the refractory mechanism. If one creates a chain of
HH-compartments, activation will thus travel one way, again as an entirely continuous
process. Only when the activation reaches an axon terminal will something new happen:
exocytosis of transmitter substances into the synaptic cleft.
In typical point-neuron models, on the other hand, we have on the one hand the
sub-threshold membrane potential dynamics, described by continuous ODEs, and some
threshold condition. When the threshold condition is met, we say the neuron emits a spike
(in the sense of a singular event causing exocytosis at axon terminals) and typically some
reset mechanism applies, followed by some refractory mechanism.
When we now force the HH model into this point-neuron framework subthreshold dynamics +
threshold mechanism + reset + refractoriness, the modeller needs to make choices. For the
subthreshold dynamics, one will usually use the HH equations, since this is a HH model,
after all.
For the threshold mechanism, various choices would be possible, but somehow one needs to
detect the fast rise followed by fast fall of the membrane potential. In the built-in
hh_psc_alpha model, this is done by
else if ( S_.y_[ State_::V_M ] >= 0 and U_old > S_.y_[ State_::V_M ] ) // (
threshold and maximum )
The first criterion makes sure that we are well into the rising flank of the Na-driven
depolarization, the second that we have just passed the maximum of that excursion.
For the reset, hh_psc_alpha does nothing, which makes sense, since the subthreshold HH
dynamics have the reset built in—the K current.
For refractoriness, hh_psc_alpha has a fixed refractory time (2 ms by default). In this
model, the only effect of refractoriness is that it prohibits spiking. The subthreshold
dynamics evolve freely during refractoriness. This again makes sense, since the HH
dynamics have refractoriness built in. This is different in iaf-models, where the membrane
potential is typically clamped to a reset potential during refractoriness.
Now the latter point raises the question of why hh_psc_alpha has an explicit refractory
mechanism even though the HH-dynamics include refractory effects already. The reason is
technical. Given that the Na-current will push the membrane potential to around +30 mV,
it will take several time steps before the K-current will pull the potential to below 0 mV
again. Then, if
S_.y_[ State_::V_M ] >= 0 and U_old > S_.y_[ State_::V_M ]
is the criterion for spike emission, a spike would be emitted for every time step during
the downward flank of the membrane potential excursion until V_m < 0 again. This might
be the effect you see. The refractory period in NEST's hh_psc_alpha simply suppresses
these spikes during the downward flank.
A better criterion could be to not just compare V_m at two points in time but at three
time steps to look for an actual maximum.
Best regards,
Hans Ekkehard
--
Prof. Dr. Hans Ekkehard Plesser
Department of Data Science
Faculty of Science and Technology
Norwegian University of Life Sciences
PO Box 5003, 1432 Aas, Norway
Phone +47 6723 1560
Email hans.ekkehard.plesser@nmbu.no<mailto:hans.ekkehard.plesser@nmbu.no>
Home http://arken.nmbu.no/~plesser
From: Charl Linssen <nest-users(a)turingbirds.com>
Date: Tuesday, 22 August 2023 at 17:05
To: users(a)nest-simulator.org <users(a)nest-simulator.org>
Subject: [NEST Users] Re: asynchronicity between spikes and firing pattern
Hi,
No problem. The step current generator isn't showing any effect, because the first
timepoint of the current generator (in ``amplitude_times``) is set to 1000, and you're
also simulating for 1000 ms, so the simulation ends too soon (or the amplitude timepoint
should be set earlier).
As for the spiking behaviour, this is because of the way the NESTML model is formulated.
When the neuron reaches threshold, a spike is emitted, but the membrane potential is not
reset to a large negative value (like E_L), so it stays above threshold and the condition
remains active, triggering more spikes to be emitted. You can add the reset to make this
issue go away. If this reset is undesirable (because it does not match the way your model
should behave), the test that finds the peak in V_m should be improved, for instance by
storing one more "old" version of V_m as the model currently does on line 197.
Hope this helps!
Yours,
Charl
On Tue, Aug 22, 2023, at 15:47, atiye nejadebrahim wrote:
Hello Hans,
This is the scripts with step_current_generator that can't generate spikes:
import numpy as np
import nest
import shelve
import matplotlib.pyplot as plt
nest.Install('hh_motor_neuron_module')
neuron=nest.Create('hh_motor_neuron_nestml',1) #{'I_e':1000})
scg1 = nest.Create("step_current_generator", 1, params={
"amplitude_times": [1000],
"amplitude_values": [2000],
})
mm1 = nest.Create("multimeter", 1, params={
"interval": .1,
"start": 0,
"stop": 1000,
"record_from": ["I"],
})
multimeter = nest.Create("multimeter",
params={'record_from':['V_m'],'interval': .1})
spikerecorder = nest.Create("spike_recorder")
spike_times = nest.GetStatus(spikerecorder, keys='events')[0]['times']
nest.Connect(multimeter, neuron)
nest.Connect(neuron, spikerecorder)
nest.Connect(scg1, neuron)
nest.Connect(mm1, scg1)
sim_time = 1000.0 # Simulation time in milliseconds
dt = 0.1 # Simulation time step in milliseconds
nest.Simulate(sim_time)
fig, ax = plt.subplots(nrows=2)
ax[0].plot(multimeter.get("events")["times"],
multimeter.get("events")["V_m"])
ax[1].plot(mm1.get("events")["times"],
mm1.get("events")["I"])
ax[0].scatter(spike_times, np.zeros_like(spike_times), marker="d",
c="orange", alpha=.8, zorder=99)
ax[0].set_ylabel("v [mV]")
ax[1].set_ylabel("I")
ax[-1].set_xlabel("Time [ms]")
fig.show()
plt.show(block=True)
this is the code with injecting I_e that generates asysnchronous outputs between spikes
and AP:
import numpy as np
import nest
import shelve
import matplotlib.pyplot as plt
nest.Install('hh_motor_neuron_module')
neuron=nest.Create('hh_motor_neuron_nestml',1, {'I_e':2000})
multimeter = nest.Create("multimeter",
params={'record_from':['V_m'],'interval': .1})
spikerecorder = nest.Create("spike_recorder")
spike_times = nest.GetStatus(spikerecorder, keys='events')[0]['times']
nest.Connect(multimeter, neuron)
nest.Connect(neuron, spikerecorder)
sim_time = 1000.0 # Simulation time in milliseconds
dt = 0.1 # Simulation time step in milliseconds
nest.Simulate(sim_time)
dmm = multimeter.get()
Vms = dmm["events"]["V_m"]
ts = dmm["events"]["times"]
plt.figure(1)
plt.plot(ts, Vms)
events = spikerecorder.get("events")
the .nestml neuron model is attached. however it is clear in 'hh_psc_alpha' model,
too.
On Tuesday, August 22, 2023 at 03:33:35 PM GMT+2, Hans Ekkehard Plesser
<hans.ekkehard.plesser(a)nmbu.no> wrote:
Hello Atiye,
Please post a script that reproduces the behavior you describe. Without it, it is
impossible to provide good advice.
Best,
Hans Ekkehard
--
Prof. Dr. Hans Ekkehard Plesser
Department of Data Science
Faculty of Science and Technology
Norwegian University of Life Sciences
PO Box 5003, 1432 Aas, Norway
Phone +47 6723 1560
Email hans.ekkehard.plesser@nmbu.no<mailto:hans.ekkehard.plesser@nmbu.no>
Home http://arken.nmbu.no/~plesser
From: atiye nejadebrahim <atiye.nejadebrahim(a)yahoo.com>
Date: Tuesday, 22 August 2023 at 14:12
To: NEST User Mailing List <users(a)nest-simulator.org>
Subject: [NEST Users] asynchronicity between spikes and firing pattern
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Dear All,
I made a HH neuron model and I can get an action potential from it. but it seems there is
a problem in spikes. Action potential shape show one spike, but spike recorder shows
several spikes and there is not any synchronicity between them. can you help me why?
my second question is about spike generation, when I use I_e current for injecting current
to the neuron, I can record spikes, but when I use step current generators, no spike
shows. can you help me why?
Thank you for your consideration.
Best,
Atiyeh
[Inline image]
Dear All,
I made a HH neuron model and I can get an action potential from it. but it seems there is
a problem in spikes. Action potential shape show one spike, but spike recorder shows
several spikes and there is not any synchronicity between them. can you help me why?
my second question is about spike generation, when I use I_e current for injecting current
to the neuron, I can record spikes, but when I use step current generators, no spike
shows. can you help me why?
Thank you for your consideration.
Best,
Atiyeh
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Attachments:
· hh_motor_neuron.nestml
