Dax42 wrote:Prediction for nonmyelinated axon: Rm has no effect as long as membrane isn't grossly leaky.

In nonmyelinated axons. Why do you say that it won't have any effect?

Because the rate of spike propagation depends on the rate at which the part of the axon that is depolarized above rest can drive depolarization of "downstream" membrane. The half width of a spike is only about 1 ms, much shorter than membrane time constant, so almost all of the charge delivered from the depolarized part of the axon to downstream membrane is deposited on downstream membrane capacitance, and almost none is lost through downstream membrane's resistance. This means that propagation velocity will be independent of Rm, but will depend on specific membrane capacitance, cytoplasmic resistivity, and fiber diameter, in particular reflecting the facts that the rate of depolarization of downstream membrane will be:

(1) reduced by increasing specific membrane capacitance or cytoplasmic resistivity

(2) increased by increasing fiber diameter (which reduces axial resistance faster than it increases net downstream capacitance)

I see a decrease in R_input of around a third

(Under what condition?) That's substantial, but (1) how much of a decrease of axonal membrane resistance does it imply (could be more, or less), and (2) is it enough to have an experimentally measurable effect on conduction velocity?

If conduction velocity theta = 2*lambda/tau

Interesting. Don't recall seeing that before; where's that from?

It's from the Foundations of Cellular Neurophysiology book (Johnston and Wu)

Good book. In section 6.4 on page 156 I see theta = sqrt(K*a/(2*Ri*Cm)), where K is ~ 10.47/ms based on experimental observations (presumably one of the papers cited in the back of J&W). Notice that Rm doesn't appear. Where exactly in J&W is the formula theta = 2*lambda/tau?

if you don't recall seeing the above definition of theta before, how would you define it?

Ordinarily it wouldn't occur to me to define it. I'll accept the partially empirical formula on p. 156 of J&W. How did you arrive at theta = 2*lambda/tau, and how can predictions from it be reconciled with the very different predictions that come from the formula in J&W?

Effect of Cm: inversely proportional to Cm vs. inversely proportional to the square root of Cm

Effect of Rm: inversely proportional to the square root of Rm vs. no effect

These are big differences, and it should be relatively easy to empirically determine which is closer to what actually happens.

But even before doing a "real" or "computational" experiment, it's easy to do this Gedankenexperiment:

Suppose Rm is indeed an important determinant of conduction velocity.

What should happen to conduction velocity if Rm is increased?

Less of the charge that spreads from the depolarized zone to the downstream membrane will leak out through membrane resistance.

What happens to this charge that stays in the cell?

It must accumulate on local membrane capacitance.

So downstream membrane must charge faster, not slower.

This should accelerate spike propagation, not slow it down.

But theta = 2*lambda/tau predicts that a 10 fold increase of Rm should slow conduction velocity by a factor of about 3, which doesn't seem reasonable.