Spiking neuron models (ion current models)

In summary, models like the Hodgkin-Huxley and Morris-Lecar include a current term: applied current. This current is a bifurcation parameter that changes the fixed points and geometry of the nullclines. In nature, these currents come from intrinsic passive or global currents or perturbations caused by a stimulus.
  • #1
Pythagorean
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Models like the Hodgkin-Huxley and Morris-Lecar include a current term: applied current.

http://cropsci.illinois.edu/faculty/gca/bioengin/Top/Lit/GENESIS_book/iBoGpdf/chapt4.pdf [Broken]

From what I understand, experimentally, this is the injected current, applied by the experimenter. But what is it in nature? This term can't be 0, or it must be replaced by a non zero term for the neuron model to remain excitatory or oscillatory (excitable vs. pacemaker cells, for example).

This is highlighted when we couple neurons together:

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.58.8157&rep=rep1&type=pdf
Bifurcations in a synaptically coupled Morris-Lecar neuron model
Rajesh G Kavasseri

Where the applied current is the bifurcation parameter (Tsumoto treats it the same in Bifurcations of the Morris Lecar neuron model)

But in a large network of say, 100 or so neurons, where we must have a significant current term applied to each neuron, it seems kind of silly to motivate from the point of view the experimenter injecting the current into each neuron.

So what, in nature, provides these currents? In the paper by Kavasseri, the synaptic coupling term is applied in addition to the applied current (as it should, the applied current is a steady state here, the coupling term is more of an impulse, a perturbation) so it's not from the coupling according to this treatment.

Are intrinsic, passive or global currents involved? What replaces "I applied" (aka "I external") in the system in nature? I'm also not counting perturbations caused by a stimulus. These currents must be more-or-less steady-state in comparison to the propagation of action potentials and significantly above 0 for the mathematical model to do what it's supposed to.
 
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  • #2
In the Kavasseri paper, I thought it was interesting that by making the coupling term (gs) greater than .5875, the neurons will fire, even when Iext=0.

I had trouble visualizing where gs fits into a natural system. I think that it relates to things like width of synaptic cleft and density of neurotransmitter in the synaptic vesicles? That makes sense to me because a high coupling could also be equated to a seizure type spasm or episode.

Sorry I don't have any clue for a clear answer to your question.

This also may seem silly, but are you thinking of the intrinsic potential maintained by the Na+/K+pump?
 
  • #3
The coupling constant was my first thought (instead of I ext coming from experimenter, it comes from neighboring neurons) but I notice a lot of papers treat them separately, so I'm not sure.

I wasnt thinking of the pumps. They don't seem to appear in any of the spiking models unless they're swept under the leak current. I'm guessing their contributions are insignificant?
 
  • #4
I can't see how the pumps are included mathematically. But they fit the description "intrinsic" "passive" and "global" so I thought I'd mention it.

"What came first, the coupling constant or the current?"
 
  • #5
Pythagorean said:
This term can't be 0, or it must be replaced by a non zero term for the neuron model to remain excitatory or oscillatory (excitable vs. pacemaker cells, for example).
I don't get why it couldn't be 0. Would you mind to explain please?
 
  • #6
Well, it's a bifurcation parameter so it changes the fixed points and the geometry of the nullclines. The result is dynamics that no longer match the actual neuron. There are of course, other parameters to change (v1 thru v4, conductances, capacitance) that might make the difference.
 
  • #7
Well, I'm not sure to understand, but wasn't it a question solved by the second paper you cited?

the analysis demonstrates the ability of coupled neurons to excite, (or fire ) despite the absence of a constant input dc current.
 
  • #8
Lievo said:
Well, I'm not sure to understand, but wasn't it a question solved by the second paper you cited?

Yes, they were able to make the synaptic coupling term makeup for the current. I'm currently using diffusive (gap junction) coupling. The reciprocal gap junction coupling causes the neurons at rest to drag the kicked neuron back to a rest state so the signal doesn't propagate through te network... Unless of course, I use a sufficient injected current, which drives the unstable point in the phaseplot to become an unstable focus.

They also reduced the membrane capacitance to 5 uF rather than the 20 uF of most other treatments.

There's also the possibility that gap junctions in nature are never enough to trigger action potentials on their own, in which case I could justify the injected current as inputs from numerous synaptic junctions, so what I really have is a small network embedded in a larger network.
 
  • #9
Pythagorean said:
I'm currently using diffusive (gap junction) coupling. The reciprocal gap junction coupling causes the neurons at rest to drag the kicked neuron back to a rest state so the signal doesn't propagate through te network...
Does your model treats separatly dendrits, soma and hillock? It seems that electrical synapses are found on the soma only, so maybe modelizing these three parts differently would improve the behavior of your net. I also wonder if an AP generated at hillock could not come back, pass through the gap junctions, and then trigger new APs in the neighbouring neurons, which would in turn come back, etc... might be the missing Iext... just one thought.
 
  • #10
No, I'm still trying to understand where those components come into play, but it appears to me that we are simply naively triggering action potetials in te neuron. My guess is that the experimenter with his Iext replaces the hillock, then evrything computed is a matter of the K and Na currents across the membrane as channels open close, and inactivate.

Also, in the single neuron case (going back a couple posts, here) if yu have Iext = 0, there is no hyperpolarization; the neuron goes back to memrane potential and stops. The action potential just doesn't look right.

Of corse if you know make Iext a function of time, you can trigger action potentials just like the experimenters do in vitro/vivo (ie not computer)
 
  • #11
I should also add that iPhone autocomplete is annoying...
 
  • #12
Pyth can you clarify what your question is about the HH model. I don't really understand what your first question is.
 
  • #13
mtc1973 said:
Pyth can you clarify what your question is about the HH model. I don't really understand what your first question is.

Question is really about the Morris Lecar, which is equivalent to a reduced (two-dimensional) HH (and you change Sodium current to a Calcium current for the barnacle). I think I've narrowed the question down though:

in a network of neurons, is it justifiable to treat Iext as:

a) a bunch of other synapses that you're not considering explicitly (i.e. you have a network of N neurons, but they're embedded in a larger network and the neurons in the larger network give an average, approximately constant current injection to each of the N neurons.)

OR

b) a threshold setting (to make it easier for the neurons to fire).
 
  • #14
I had a quick glance through the first article. Where in the first article does it refer to Iext - I can find the definition.

I can't access the second file.
 
  • #15
I_ext is the experimentally injected current (into the axon) leading to sufficient depolarization to trigger the voltage-gated sodium/potassiom channels to open (triggering the action potential).

I live on campus so sometimes I forget that I have subscriptions to these papers. I don't think I can repost it if it's not already available for free.
 
  • #16
Usually to trigger an action potential you voltage clamp (then depolarize) and record currents - if they are current clamping then they must be recording voltage, but I'd need to see the paper to see their protocol. IF it is current clamp then all Iext represents is the current that you have to inject to record the membrane potential.

Just cite the paper rather than providing link then I can get the paper.
 
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  • #17
My assumption was that the final formulation is of the neuron in nature, not under voltage or current clamp conditions (though they used those techniques to separate the currents involved and gain other insights in their 1952 papers; Hodgkin & Huxley). But the ideal is to have a model of neurons in nature, not under experimental voltage/current clamp.

I provided the author's name and the title of the paper right under the link. I think it's a manuscript, so it's not published yet, here's the other information included in the paper:

Department of Electrical and Computer Engineering
North Dakota State University

Realize that this is a theoretical treatment and motivation, not experimental; clamping isn't brought up (since we're trying to model them in nature, not the lab).
 
  • #18
No - can't track down paper.

Current clamp can be thought of as the 'natural' situation since we let the cell maintain its normal voltage and this ion fluxes are normal compared to voltage clamping.
Thats why in long term experiments its prefereable to current clamp rather than voltage clamp - becuase it is more natural!
 
  • #19
Oi! Thank you for the clarification, I never realized that.
 

1. What are spiking neuron models?

Spiking neuron models are mathematical models used to describe the behavior of neurons in the brain. They simulate the electrical activity of neurons by taking into account the flow of ions across the neuronal membrane.

2. How do spiking neuron models work?

Spiking neuron models work by representing the neuronal membrane as a circuit with various ion channels. These channels allow different types of ions, such as sodium and potassium, to flow in and out of the neuron, creating changes in electrical potential that result in the firing of an action potential.

3. What types of ion channels are included in spiking neuron models?

The most commonly included ion channels in spiking neuron models are sodium, potassium, and calcium channels. These channels play a crucial role in generating and regulating action potentials in neurons.

4. How are spiking neuron models useful in research?

Spiking neuron models are useful in research as they allow scientists to study the behavior of neurons and networks of neurons in a controlled and quantifiable manner. They can also be used to simulate and predict the effects of different drugs or stimuli on neuronal activity.

5. What are some limitations of spiking neuron models?

Some limitations of spiking neuron models include oversimplification of the complex interactions between ions and ion channels, as well as the inability to account for all the variables that may affect neuronal activity. They also require a significant amount of computational power and may not accurately reflect the behavior of real neurons in certain situations.

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