Physics of Myelin: Resistance & Capacitance

[Sakha]

This post might be in the wrong subforum, I wasn't sure where to put it, sorry.

Quoting another website:

The main purpose of a myelin layer (or ''sheath'') is to increase in the speed at which impulses propagate along the ''myelinated'' fiber. Along ''unmyelinated'' fibers, impulses move continuously as waves, but, in myelinated fibers, they hop or "propagate by saltation."

Myelin increases electrical resistance across the cell membrane by a factor of 5,000 and decreases capacitance by a factor of 50. Thus, myelination helps prevent the electrical current from leaving the axon.

For me this two paragraphs contradict. The first saying that the myelin increase the speed of the impulses, and the second says that "myelination helps prevent the electrical current from leaving the axon.", which sound contradictory to me.

Viewing it from the physics side, how does an increase in resistance and a decrease in capacitance accelerate (or slows down) the speed of the impulses?

 

[Bob S]

Here is a simple electrical engineering approach. This is a standard RC transmission (delay) line. Consider N cells, each composed of a series resistance R followed by a shunt capacitance C. In the case of the nerve signals, the signal amplitude is regenerated (amplified by the regenerative spiking nerve cells), but the associated delay is not corrected, and accumulates.

Using complex variables in the frequency domain, the impedance of the capacitor alone is 1/jωC, and for the resistor and capacitor in series, the impedance is R +1/jωC. Here, ω represents the ω (frequency) component of the transmitted signal.

So for a single RC cell, the transfer function is 1-jωRC/(1+ω²R²).

The delay phase angle (at frequency ω) is θ₁ = tan^-1(ωRC).

So for N cells, the cumulative phase delay is θ_N = N·tan^-1(ωRC).

So for a particular frequency component ω, increasing either R or C will increase the delay. The myelination increases the thickness of the dielectric around the nerve, and reduces the capacitance C. [FYI-Mylar is a thin polyester film developed by DuPont in the 1950's].

Bob S

 

[Sakha]

So for a particular frequency component ω, increasing either R or C will increase the delay. The myelination increases the thickness of the dielectric around the nerve, and reduces the capacitance C.

According to the EE approach then the myelin, which increses R by 5000 and decreases C by 50 should cause the impulses to delay by a factor of 100.

I'm just having trouble how grasping that a dielectric (myelin) can actually increase impulse speed, which is the basic function of myelin.

 

[Bob S]

See attached thumbnail of an RC delay line with a series resistance and shunt capacitance. The purpose of the myelin layer is to increase the radial spacing between the nerve and the surrounding tissue. If we look at the equation for a cylindrical capacitor,

C = 2πεε₀/Ln(b/a)

where ε is the relative permittivity of the myelin layer, ε₀ is the permittivity of free space, Ln is the natural logarithm, and b and a are the outer radius and inner radius of the myelin layer. So as the myelin layer gets thicker (ratio b/a gets larger), the shunt capacitance decreases. A thicker myelin layer may also increase the leakage (shunt) resistance (Not series resistance).

The resistance R in my model is the series resistance from one nerve cell to the next, not the shunt resistance from the nerve cell through the myelin layer to the surrounding tissue. See thumbnail. My model shows that if the series resistance decreases, the time delay decreases. Increasing the myelin layer thickness probably has little effect on the series resistance.

So reducing either the shunt capacitance C and/or the series resistance R will reduce the phase delay, and therefore increase the nerve signal velocity (impulse speed).

[Question: What is the nerve signal velocity in a reptile? What is the reaction time if you tickle the tail of a python?]

Bob S

[Thumbnail from http://www.swarthmore.edu/NatSci/echeeve1/Ref/trans/Infinite.html]

 

[Sakha]

Thanks Bob, I think I'm understanding it. You explained it in a very understandable way.

[Question: What is the nerve signal velocity in a reptile? What is the reaction time if you tickle the tail of a python?]

Did a quick search about that question but didn't found anything.
What you meant with those?

 

[Bob S]

Thanks Bob, I think I'm understanding it. You explained it in a very understandable way.

From Bob S:
[Question: What is the nerve signal velocity in a reptile? What is the reaction time if you tickle the tail of a python?]

Did a quick search about that question but didn't found anything.
What you meant with those?

The action potential velocity in myelinated nerves is ~ 40 meters to ~100 meters per second. In unmyelinated nerves, the action potential is much slower, perhaps as slow as ~1 meter per second. Do reptiles (cold-blooded animals) have unmyelinated nerves? For a long reptile (e.g., python, dinasaour) what is the nerve signal impulse propagation time from the tail to the head, and back?

Bob S

 

[jbsteele]

OK - it's an old thread, but I felt like the physics nerds are overlooking the real advantage of myelin - it prevents depolarization of the membrane by direct leakage. There is no simple analogy to this in electricity that I can think of. On bare axonal membrane, a depolarization event triggers adjacent depolarizations in all directions, presumably via an electric field detected by ion channels very close by. This is generally described as propagation with a direction since the initial depolarization should begin at the "beginning" of the nerve fiber. At any rate, depolarization "waves" are a lot more like dominoes tipping each other over. It's pretty slow.

Wrap myelin around the axon, depolarize the cell at the beginning of axon, and there is no adjacent depolarization, since even though adjacent membrane might pick up on the change in the field, there is no way for ions to flow in and out. In this sense it's not insulation any more than you would describe a garden hose as "insulating" the water in the hose. Still, there is an electric field between the beginning of the axon and points more distant. That field gets detected at a node much further away than the distance between two ion channels in the axon's bare membrane. That "node" being uninsulated, or unwrapped, depolarizes, but now we are talking about real speed - the speed at which the electric field itself is propagated and detected.

Well, that's my recollection from memory anyway - I'm fascinated about the underlying physics of the dielectric nature of multiple wraps of plasma membrane. I wonder how fast the signals would travel if the myelin was not a dielectric per se but just a barrier, or if this is just icing from the nerve's point of view.