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Here is the original question which inspired my question. As explained by the answers there, the reason saltatory conduction in myelinated neurons is faster than non-myelinated conduction is because the capacitance of the membrane is lowered by reducing the number of channels (Channel density) or equivalently, increasing the spacing between channels. I also did a preliminary study of membrane electrodynamic modelling here and here.

From what I gathered from the linked question, the decreased capacitance overcompensates the effect of absence of channels reinforcing the sodium current, and on the whole, increases the speed of conduction by allowing the depolarizing potential to travel to the adjacent node faster than in case of an unmyelinated fibre. In view of this, I have a question:-

Why does lower capacitance increase "the effectiveness of nearby nodes" or allow the depolarizing voltage to "travel not by ion diffusion, but as an electric field"? I am comfortable with capacitors and related physics, but why would lower capacitance allow propagation of the changing voltage as an electric field, is still unclear to me? (The links I have placed also help quantify the problem mathematically. This allows us to say that $\lambda$, or the rate of spatial decay of potential, increases, decreasing the effective length of the neuron. Why should its decrease help faster conduction?)

And another question is, how would reduced density of sodium voltage gated channels cause a decreased capacitance?

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1 Answer 1

The Hodgkin-Huxley model:

$$I=C_m\frac{dV}{dt} + g_k(V_m - V_k) + g_{Na}(V_m - V_{Na}) + g_l(V_m- V_l)$$

Where $C_m$ is membrane capacitance per unit area and $g_i$ are membrane conductances.

Reducing the number of channels does not affect capacitance per se (it does in a way) but what it basically does is to reduce membrane conductance to leak channels (Voltage activated channels).

Capacitance also decreases as an inverse function of "inter-plate distance" (of parallel plates) which is the membrane thickness. This reduces the capacitative membrane current.It also prevents the build up charge and thereby allowing it to propagate forward.

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