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I'm currently reading the book, "An Introduction to Nervous Systems" by Ralph J. Greenspan. On page 20, there is a sentence that confused me. It was, "Electrical signaling has the advantage of being able to cover large distances very quickly, much more quickly than chemical diffusion". It is in the context of the primitive signaling mechanism in Paramecium. My doubt was, isn't the electrical signal caused by the movement of ions? Then how is it any different from chemical diffusion? And again, it's not a electrical signal that travels, but a changing potential, right? Then how does it move at a faster pace than diffusion?

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Membrane potential is a directed force, while diffusion is a random walk

Your confusion is entirely justified, as you're correct that both diffusion and depolarization rely on the speed of ion travel. Where they differ is that depolarization is a directed force, occuring only in one direction along the membrane, whereas diffusion is subject to the stochastic walk of ions in water.

When membranes depolarize, the whole membrane begins with a certain amount of "pressure" built up behind it. As the signal propagates, a small area of this pressure is released at a time and triggers the next section to trip. That next section is essentially identical to the previous one, with the same amount of pressure behind it initially. In this way, you can imagine membranes "conserving" the initial concentration, so that the signal strength isn't dependent on the distance from the signal itself.

Diffusion, on the other hand, is stronger initially and decays over distance because of its stochastic nature. It's a probabilistic force, and so depends in general on something like the square root of the distance. If you imagine a thousand ions taking a step forward in one moment, in the next it's equally likely that five hundred take a step backward even as an equal amount moves forward. So the signal degrades over time and distance from the source.

If that was confusing, the following metaphor may help. Depolarization acts like a line of dominos, while diffusion acts like a complex dance. Check out this video of the largest human mattress dominos: the speed they're falling over is pretty constant when they're not turning. Compare that to two dancing humans who are equally likely to move forward and backward, and hopefully you can see that the mattress dominos is the faster way to go, even though each one is theoretically limited by how fast a human could move.

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Electrons are >100,000 times lighter than the atom nucleus. For chemical diffusion the entire atom moves, it moves >100,000 times times slower.

Molecular diffusion moves at ~500m/s

Electron signals move at ~50,000,000, m/s

In saline, electrons move at 10% speed of light.

In silver, they move at 95% speed of light.

Crowds of electrons drift very slowly, ~1mm per second. It's called electron "drift". Individuals orbiting and free electrons move at nearly the speed of light.

Conductive materials have free electrons that hop between atoms. If you introduce extra electrons at one end of the conductor, it will push free electrons at the speed of light from one atom to another, while the electron drift stays very slow.

Saltatory conduction travels at 10% the speed of light. Like Dubukay sais, the electrons travel like dominos. The dominos don't travel far/fast but the signal does.

Electrical signals are like a sound pressure wave, where the medium/the atoms stays nearly in the same place, but the electron excess propagates very fast with a wave-front, on a conductive line. only a very small number of electrons move, and they don't move very far at all, i.e. one micron each. The electrons travel like a sound pressure wave. The electrons hardly move but the pressure imbalance moves fast. for chemical diffusion I imagine two colors of paint mixing, atoms travel all through the medium, used by the brain to breach micron distances.

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