How is passive current propagated?

Matt Jones jonesmat at ohsu.edu
Wed Oct 30 13:54:35 EST 1996


In article <leipzjn9-301096000943 at rts0107.ppp.wfu.edu> Jeremy Leipzig,
leipzjn9 at wfu.edu writes:
>Does anyone know exactly how passive current spreads down a dendrite or
>myelinated axon. One of my professors says the depolarization moves in
>successive collisions of repelling cations, in a manner not unlike the
>propagation of sound waves. Another one says that the electric field
>created by incoming cations is enough to depolarize adjoining regions,
>implying that passive current spreads close to the speed of light. I have
>also heard in intro courses that simple diffusion of the cations is
>responsible. Which, if any, is the correct explanation?

Ok, I'll take a stab at this. It'll be fun having my errors corrected.

I think all of the mechanisms you listed are involved, but you can't get
the whole picture by considering any of them alone. Suppose you inject
positive current into a *purely* passive dendrite, using a typical
silver/silver chloride electrode. The electrode forms an electron sink
(but a conventional current source), chloride ions are attracted to it
and interact with it, depleting the nearby solution of negative charges
and leaving a bunch of potassium ions behind in the dendrite. These
potassium ions are a local concentration of positive charge, and thus
raise the potential positive with respect to distant points in the
dendrite and external ground. 

So the incoming ions create an instantaneous voltage peak, which
depolarizes the surrounding solution (the amount of depolarization falls
off with distance according to Coulomb's law, but propagates *in the
solution* at almost the speed of light, and requires almost no time to
attain its final level at each location). The depolarization of the
solution drives positive charges to the membrane at distant points, which
charge the membrane. This takes time as the voltage rises e-fold
according to the membrane time constant, which is determined by the
membrane capacitance and the resistance of the solution. The charges are
ions that have to diffuse through a resistive solution in an electric
field before accumulating on the membrane and charging it. The diffusion
is aided by the fact that the charges are are repelling each other, so
the electrostatic forces add and give direction to the diffusional
"forces". This is probably what your instructor was referring to by
"collisions of repelling charges", although that's pretty loose language.
The charging of the membrane also drops off with distance, but not as
Coulomb's law predicts. The length constant is shortened if charge leaks
out through the membrane resistance instead of charging the membrane
capacitance at distance points. In a myelinated axon, the membrane
resistance is huge, so hardly any charge leaks out. Thus, the
depolarization falls off very slowly with distance, and the next node
down the axon sees almost the same voltage as the initial site of current
injection. It sees that voltage in the time it takes for the electric
field to propagate (at almost the speed of light). The propagation of
*current* is slower, because it depends on the movement of ions in
solution, and the usual lag introduced by having to charge a capacitor. 

Ok, now somebody point out where I went wrong.

Cheers,
Matt



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