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Dear all,

Hi, I have a problem to apply current controlled stimulation.

Background is,
There are animal experiments, which apply epidural cortical stimulation with 0.2 ms rectangular pulses. And I try to explain excitability patterns through simulations.
Thus, I constructed a 3D volume conductor model representing the head/brain and then calculated potential/electrical field distributions induced by the epidural electrode. In my previous work, I used multicompartmental neuronal models and thus I could apply extracellular stimulation using 'extracellular' function. However, in this case, I implement single-compartment models and thus I use IClamp and determined stimulus amplitude by calculating 'activating function'. For the waveform, since in experiments they used voltage-controlled stimulation, I made exponentially increase and decrease biphasic waveform which represents a derivative of the rectangular waveform.
For the single-compartment model, I use the model in Mahmud et al., Frontiers in Neuroscience 2016. (for ted, I think you remember my previous question of how to reproduce this paper results. I use this model due to the finding that lower excitation threshold of inhibitory neurons compared to excitatory neurons).

The problem is, when I apply 'exponentially increase and decrease biphasic wave' to excitatory neuron, it showed linearly increased membrane potential according to IClamp.amp, even for supra-threshold stimulation.
Here is the peak membrane potential according to IClamp.amp.
[amp, peak membrane potential]
[10, -48.8661]
[20, -32.7343]
[30, -16.6026]
[40. 0.89375]
[50, 19.15727]
[60, 31.79305]
[70, 42.92485]

When I applied this waveform to the original HH model or inhibitory model, they showed action potentials for some amplitude. However, when I additionally tested this biphasic current pulse to other single-compartment models (Pospischil et al., Minimal HH type models for different classes of cortical and thalamic neurons, Biological Cybernetics, 2008), they also showed this weird linear increase pattern.
Thus, I am confused about this weird activation of the excitatory neuron.
Could you explain this phenomenon or how to fix it?

I haven't seen anything like that. It will be necessary for me to be able to reproduce the phenomenon with the same code you are using. If you zip it up (hoc, Python, ses, NMODL, whatever else is needed) and email it to ted dot carnevale at yale dot edu, I'll see what I can find out and be able to advise you properly.

There are two problems. The first problem is that your model cell is not very excitable. If you reduce the amplitude of the biphasic stimulus to 0 (by executing run_exp(0)), then attach an IClamp with del 1, dur 0.1, you can do some exploratory simulations. I'll send you a session file that recreates a RunControl panel, a PointProcessManager configured to be an IClamp, a parameter panel for adjusting gl, gnabar, and gkbar, and graphs that show ina, ik, and your model cell's membrane potential. I'll also include a hoc file that reads your own epidural_PN_square_wave.hoc, loads the session file, and executes run_exp(0). You can adjust the IClamp's amp and run some simulations that will show that a 6 nA current pulse is required to elicit a spike, and the spike that you get is not very impressive--it is preceded by a long latency while the cell hovers at about -35 mV, and finally, after about 5 or 6 ms, membrane potential gradually sweeps up to a brief peak at about 20 mV before it crashes down to about -90 mV. You may find it helpful to use the current graphs' "View = plot" to rescale them.

So what do you think is likely to happen if you inject a brief depolarizing current pulse that is followed almost immediately by a brief hyperpolarizing pulse of the same magnitude? The cell isn't likely to produce a recognizable spike, because the hyperpolarizing phase of the stimulus current will pull membrane potential right back down. It won't have 5 or 6 ms to sit around at -35 mV waiting for inward current to outweigh outward current.

And that's exactly what happens. Reduce the IClamp's amp to 0. Now you can adjust the "extracellular stimulus" by executing run_exp() with an appropriate argument at the oc> prompt, and you'll see the resulting stimulus and what happens to ina, ik, and membrane potential.

Your nicely synthesized stimulus current is a balanced biphasic pair of current pulses. The duration of each pulse is much shorter than membrane time constant, and the interval between them is also much shorter than membrane time constant. The first pulse injects depolarizing charge into the cell, and the second pulse removes that charge. If all ionic conductances are reduced to 0 (you can do that by changing the values of gnabar, gkbar, and gl in the parameter panel), the cell ends at the same potential as its initial potential, which confirms that the injected current is "charge balanced." The depolarizing phase of the injected current charges membrane capacitance, and the hyperpolarizing phase removes that charge. The peak amplitude of the depolarization is proportional to the charge injected by the depolarizing phase of the stimulus.

Restore the leak conductance to its original value and use the RunControl's Init & Run to launch a new simulation. You'll see that the peak depolarization produced by the depolarizing phase of the stimulus is slightly reduced. That's because some of the depolarizing charge escapes through the leak conductance. Then the hyperpolarizing phase of the stimulus pulls membrane potential slightly below the model's initial potential--slightly below because depolarizing charge is not only being removed by the stimulus current--it is also escaping through the leak conductance. After the stimulus current returns to 0, the hyperpolarization decays slowly (governed by membrane time constant which is much longer than the duration of the stimulus).

What happens if the voltage-gated conductances are also restored? Not much, if the stimulus is small. Why? Because the depolarization is very brief--not long enough for the sodium and potassium channels to activate. Use the GUI to bring up a graph of stim.i and another graph that shows ina and ik, and you'll see that run_exp(20) makes ina appear, but peak ina coincides with the hyperpolarizing phase of the stimulus.

So the second problem is the time course of the stimulus. The biphasic stimulus current isn't going to elicit a nice spike from this model cell.

Thanks for your kind reply, Ted.

I understood why the model did not activate, well.
The reason why I applied short duration biphasic current pulse is that I want to apply a monophasic square pulse of voltage stimulation.
(Since I use the value of the activating function, it is right to use IClamp. Alternatively, I want to understand SEClamp.)
Thus, I see the 'SEClamp' which control voltage input. I set a monophasic square voltage pulse and see the induced current (SEClamp.i (nA)).
I thought the current stimulation can be considered as the derivative of voltage stimulation. However, in SEClamp, i = (vc-v)/rs.
In addition, when I set SEClamp.dur1 = 0, SEClamp.amp1 = 0, according to i=(vc-v)/rs I know there exist some stimulus, but I wonder what indicates it since stimulus amplitude is zero.

I see a SEClamp example in Programmer's Reference, svclmp.mod, and 'the NEURON book'. However, I do not fully understand SEClamp mechanisms.
is there more explanation for the beginner like me?

The short biphasic current does produce a monophasic pulse of membrane potential. And, just like an extracellular stimulus, it does not affect the model's equations (doesn't introduce a shunting conductance). A voltage clamp has a _very_ low source impedance, and is not electrically equivalent to extracellular stimulation.

Thanks for the reply, Ted.
Though I still do not fully understand SEClamp mechanism, it is a good opportunity to understand NEURON detail.

SEClamp is extremely simple--just a voltage source in series with a resistance.