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In Galvani's experiment with frog legs, he applies an electric potential across the muscles of a frog which causes the leg muscles to contract. What would happen if the polarity was reversed (I do not know the polarity he had originally used). Would the muscle still twitch?

voltage being applied to frog legs

Here the voltage is applied by using two different types of metals fused to each other

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A nerve fiber is something like a cylindrical tube: it has walls (cell membrane) on all sides, and at rest is a bit negative inside, like this:

enter image description here

There are channels in the membrane that are sensitive to voltage. They are oriented with an inside-side and an outside-side, and move according to voltage such that they are closed when the inside is more negative than the outside. Most or all will be closed when the membrane potential is around -70 mV. If the voltage gets closer to equal, though, say -55 mV or more positive, the channels open, let more positive ions come in, and this current flows down the fiber depolarizing more membrane and opening more channels.

When you stimulate electrically with an external shock like in an experiment like this, the situation looks more like this:

enter image description here

You've added some huge voltage in some direction, here I've drawn it assuming the positive terminal is somewhere to the left and negative is somewhere to the right. For that brief time that the stimulus is on (it better be brief or you'll start cooking your tissue), you can just about ignore the little charge inside and outside the membrane that set the membrane voltage. All the membrane "sees" is your big stimulus.

For the membrane on the left, it's going to see a strongly negative voltage inside (towards the negative terminal) versus outside (towards the positive), and the voltage-gated sodium channels will stay closed. It doesn't really matter to the channels that this is extremely negative compared to normal rest: closed is closed.

For the membrane on the right, though, it doesn't have a negative voltage inside relative to outside anymore: the outside is facing the negative terminal, and the inside is facing the positive terminal. This is going to open some channels and let in some sodium ions.

A brief moment later, the external stimulus is gone, but those channels were opened and some ions were let in, making the inside less negative than it was, opening more channels, etc.

So, what if we flipped the polarity? Well, just flip the image, and apply the logic the same way. You can put the positive terminal into the page, too, and the negative outside (remember, we really have a cylinder here): as long as you make a voltage across the combined membrane of the fiber, you're going to stimulate a response. Even if your voltage source was at the top and bottom of the page, nerve fibers aren't perfectly straight, and anywhere that there is a bend will be susceptible to the shock (though not as sensitive as if the whole fiber was exposed across the potential gradient).

In practical, non-theoretical terms, sometimes the polarity you use does change the effectiveness a bit, but it's usually a subtle effect. I'll admit I'm not entirely sure what is physically behind this, but I think it has to do mostly with the electrode material and an inductance/capacitance that reduces the intensity of the voltage gradient depending on which way the stimulus is applied.

It's common in electrophysiology also to use biphasic square-wave pulses; in that case, the polarity reverses in the middle of the stimulation. This helps keep the electrodes in good shape and not depositing salts on them (the way you'd get in a battery-style chemical reaction), but it works just as well for stimulation.

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