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I have read two papers related to modeling neurons. The first one is the paper by Pinsky and Rinzel and the second one by Wang and Buzsaki. The first mentioned neuron model is a excitatory neuron based on NMDA and AMPA neurotransmitters. The second one is inhibitory neuron model based on GABA. So I modeled them individually. Now trying to couple such that pre synaptic PR neuron will connect to post synaptic WB neuron which also connects to PR neuron. That is in effect an excitatory-inhibitory coupling with feedback.

  • Now how would the action potentials of both neuron look like?

  • Will both oscillate, or only WB neuron alone oscillate?

  • Is there any specific conditions for the oscillations to occur?

Any speculations, ideas, references (like books, related papers) would be helpful.


NOTE : By action potentials, I mean the neuronal membrane voltage signal which varies with time.

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    $\begingroup$ your first link to Pinsky and Rinzel is invalid. Try linking DOI or the abstract page. $\endgroup$ – Memming May 5 '15 at 15:02
  • $\begingroup$ @Memming : corrected the link. $\endgroup$ – dexterdev May 5 '15 at 15:25
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    $\begingroup$ By "action potentials" you mean the pattern of firing, not the shape of the action potential itself? Also, what's driving these neurons? $\endgroup$ – Memming May 5 '15 at 15:29
  • $\begingroup$ @Memming : I have explained "action potential" too. $\endgroup$ – dexterdev May 5 '15 at 15:33
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    $\begingroup$ @dexterdev you need to simulate the coupled system for that. For non-linear systems the input-output relationship is not that straightforward (hence non-linear :P). Can you paste both the equations here. $\endgroup$ – WYSIWYG May 6 '15 at 12:31
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There is no straightforward answer to this. It completely depends on the properties of the neurons and the network they are in.

I would recommend you to study Central pattern generators. Those are usually small networks that can create a repetitive pattern of action potentials. However, the exact pattern they generate depends on how they are connected (number and type of synapses, network structure,...) and a presumably large number of neuronal properties (like the conductance, the shape of their dendrites, the expression level of various ion channels and all kinds of intracellular messengers/peptides/proteins/molecules). For example, there are "leaky" ion channels that can cause a neuron to spontaneously depolarize (and fire action potentials) regularly without requiring any synaptic input. This means that you can have a regularly firing neuron even without network feedback mechanisms. example

There are many different rhythms in the brain and they are all generated by smaller and/or larger networks of neurons with different properties. Neurons can even participate in multiple different rhythms, depending on the situation (e.g. theta rhythm vs. SPWs in the hippocampus). Thus, even the same neurons in the same network can generate different rhythms.

So, the rhythms that you can build depend on how you tune the neurons' properties and the way they are connected. With just the information you provided (simulated excitatory and inhibitory neurons, but no info on their excitability, network,...) I can't tell you what the resulting rhythm will look like.

I'm afraid I didn't really answer your question, but I hope this was still helpful.

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