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Hi guys, looking at your average neuron, it is very difficult for me to imagine how this could be translated into a core-conductor model

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On the neuron above, where would be the intracellular space and where would be the extracellular space? Also, where is this membrane we are talking about?

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What may be confusing is that the myelin is wrapped around the membrane of the axon.

The easiest way to see this is in cross-section:

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From here.

The axon is indicated by #1 in the diagram and the myelin sheath is #4

The intracellular space (as represented by the horizontal resistors in the case of your model of the axon) is the fluid, replete with ions, that is contained within the membrane of the axons.

At the nodes of Ranvier, there is a break in the myelin sheath, exposing the underlying membrane of the axon. In membrane in those gaps of the sheath, there are sodium channels (voltage gated) and potassium channels that facilitate the influx and efflux of ions that "refresh" the action potential as it travels down the axon. The extracellular space is simply the milieu of fluid in the space between the axon and any adjoining cells. For the purposes of analyzing the currents of the neuron, the sodium and potassium ions (and the conductances of the channels) are all that you really need to be concerned with.

What is confusing about your diagram is that it represents the conductance -- the inverse of the resistance of the channels -- of the channels (inwards and outwards) as a single vertical resistor in between the horizontal resistors of the intracellular membrane. This oversimplification is handy when doing the cable theory-type analysis, but it betrays the actual physiology of the neuron.

From a model standpoint, I'm breaking all the rules here, but you can think of things like this:

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where one "rung" of your resistor ladder has $r_m$ broken out into the 2 components and drawn differently.

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  • $\begingroup$ That's probably clear as mud, and I've glossed over a lot, so feel free to ask questions and I'll fill in the gaps. $\endgroup$ – jonsca Sep 7 '14 at 1:38
  • $\begingroup$ Hi just to clarify. So the membrane is the axon membrane, the intracellular space is lies within the axon (so the cytoplasm within the axon) and the extracellular space lies outside of the axon and between the neurons (another type of fluid I guess). The breaks between the myelin sheath is used to refresh the action potential and is not modelled. could you provide a realistic example of core-conductor cable model of a neuron? You said the verticle resistors are not realistic and does not represent a part of the neuron. $\endgroup$ – Carlos - the Mongoose - Danger Sep 7 '14 at 15:10
  • $\begingroup$ @IllegalImmigrant The breaks (nodes of Ranvier) on the myelin sheath are modeled by the electrical nodes between the horizontal resistors in your model. These are the only places between the hillock of the axon (the pointy part at the end of the cell body) and the terminal where ions are being exchanged. At the other points along the axon, the receptors are covered over by the myelin, so no current leaks out with the movement of the ions. The vertical resistors are realistic, they just betray the complexity of the actual voltage-gated influx through sodium channels $\endgroup$ – jonsca Sep 7 '14 at 17:04
  • $\begingroup$ and the potassium efflux. There are different subtypes of these potassium channels as well (so Rm take a lot of information about conductances/resistances and jams it down into one component). My "grounds" in my circuit are a bit exaggerated, since the currents leaving and entering the axon can propagate through the ions in the extracellular milieu. I just wanted to illustrate that the conductances could be split off into the different components, but it was still justifiable to combine them. $\endgroup$ – jonsca Sep 7 '14 at 17:06
  • $\begingroup$ The core conductor model is very limited in scope. It may be helpful for you to take a look at Hodgkin and Huxley's work with the compartmental models as a way of exploring the limitations of cable theory. $\endgroup$ – jonsca Sep 7 '14 at 17:10

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