Spiking neuron models (ion current models)

  1. Pythagorean

    Pythagorean 4,472
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    Models like the Hodgkin-Huxley and Morris-Lecar include a current term: applied current.


    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:

    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.
  2. jcsd
  3. 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 in to 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?
  4. Pythagorean

    Pythagorean 4,472
    Gold Member

    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?
  5. I cant 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?"
  6. I don't get why it couldn't be 0. Would you mind to explain please?
  7. Pythagorean

    Pythagorean 4,472
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    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.
  8. Well, I'm not sure to understand, but wasn't it a question solved by the second paper you cited?

  9. Pythagorean

    Pythagorean 4,472
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    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.
  10. 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.
  11. Pythagorean

    Pythagorean 4,472
    Gold Member

    No, I'm still trying to understand where those components come in to 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)
  12. Pythagorean

    Pythagorean 4,472
    Gold Member

    I should also add that iPhone autocomplete is annoying...
  13. Pyth can you clarify what your question is about the HH model. I don't really understand what your first question is.
  14. Pythagorean

    Pythagorean 4,472
    Gold Member

    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.)


    b) a threshold setting (to make it easier for the neurons to fire).
  15. 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.
  16. Pythagorean

    Pythagorean 4,472
    Gold Member

    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.
  17. 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.
    Last edited: Feb 19, 2011
  18. Pythagorean

    Pythagorean 4,472
    Gold Member

    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).
  19. 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!
  20. Pythagorean

    Pythagorean 4,472
    Gold Member

    Oi! Thank you for the clarification, I never realized that.
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