In article <34E4F163.343505A1 at mindspring.com>, jeremyl at mindspring.com
says...
>>Yes, sorry, my paragraph should read that myelin _decreases_
>capacitance, as many of you have pointed out. I also have no dispute
>with the part of the theory that myelin insulates the areas between the
>Nodes of Ranvier, effectively reducing the electric field experienced by
>ions on either side and allowing more charge to reach the Nodes of
>Ranvier. But this insulation point is made in textbooks in addition to
>the point about capacitance. It's as though they're implying that less
>charge is necessary to depolarize the "present" node, as opposed to less
>charge is necessary to depolarize the subsequent node. Would all of you
>agree that myelin does not affect the capacitance of the membrane at the
>nodes and that its only function is insulation?
>--
>Jeremy Leipzig
>
There is no such thing as capacitance at "this point" as opposed to
capacitance at "an adjacent point". The axon is an electrical cable
with transmembrane resistance and capacitance. Calculate the space
constant of the cable. Then the resistance or capacitance measured at
one point, say at a node, is no different from the resistance or
capacitance
measured at a different point, say under the myelin, provided the two
points are separated by a fraction of the space constant.
Myelin simultaneously increases the resistance and decreases the
capacitance. Plug both factors into the cable equation. Plug the
Hodgkin-Huxley equations in, also, and solve for the piecewise continuous
myelinated axon. The conduction velocity went up.
Of course, solving these equations is far too difficult, so here is an
interpretation in words.
The action potential propagates because local current loops depolarize
neighboring sections of action to threshold. The speed of propagation
depends on two factors: how far down the axon the current loops travel
and how quickly the membrane depolarizes. Increasing the transmembrane
resistance increases the distance the current loops travel (space
constant
calculation). Decreasing the transmembrane capacitance increases the
rate
of depolarization caused by current (definition of capacitance: i = C
dV/dt,
getting into electric field calculations is irrelevant).
Does this do it for you?
Incidentally, many textbooks don't treat this subject well because few
students have any background in either the physics of RC circuits or the
mathematics (partical differential equations) necessary to go into it.