Nerves, the heart, and the brain are electrical. How do these things work? This course presents fundamental principles, described quantitatively.

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Bioelectricity: A Quantitative Approach

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Nerves, the heart, and the brain are electrical. How do these things work? This course presents fundamental principles, described quantitatively.

從本節課中

Energy into Voltage

This week we will examine energy, by which pumps and channels allow membranes to "charge their batteries" and thereby have a non-zero voltage across their membranes at rest. The learning objectives for this week are: (1) Describe the function of the sodium-potassium pump; (2) State from memory an approximate value for RT/F; (3) Be able to find the equilibrium potential from ionic concentrations and relative permeabilities; (4) Explain the mechanism by which membranes use salt water to create negative or positive trans-membrane voltages.

- Dr. Roger BarrAnderson-Rupp Professor of Biomedical Engineering and Associate Professor of Pediatrics

Biomedical Engineering, Pediatrics

Hello again. This is Roger Coke Barr for the

Bioelectricity course, Week two, and this is our ninth segment.

In this segment, we talk about membrane capacitance.

And the capacitance per unit area is designated C sub m.

First, it's just worth asking why does membrane have capacitance?

Somehow or other, it seems very reasonable that membrane has resistance, but

capacitance, well, we're not quite so sure about that.

However, think about the general definition of capacitance.

There is capacitance between one point and another when you have two conductors

separated by an insulating region. So, membranes are certainly an insulating

region. So, the question is, if capacitance comes

from two conductors separated by an insulating region, what are the

conductors? Well, let's make ourselves a sketch and

talk about that. So, let's suppose, this is a cell and

cross section. We said that the membrane [unknown] which

is diagrammed there in red, is a very good insulator.

And, this region in the interior, that's a conductor.

That's not a metal plate. We think of capacitors as having metal

plates because human-made capacitors are built that way.

But there's nothing about the phenomenon that requires that the conductors be

plates. And, in fact, this solution is quite a

good conductor because it's got a lot of ions floating around in it.

So, that's one of the plates. And then, the other plate is this reaching

outside. So, this exterior volume, which is also a

conductor, is the other side of the capacitor.

So, if we say to ourselves, capacitors have two conductors separated by an

insulating region, that's exactly what we have here.

A conductor inside, a conductor outside, insulating region in between.

So, of course, it has capacitance. Let's talk about capacitors and

capacitance and membrane current that flows through the capacitants as people

describe it. The definition of capacitance, C = Q/V.

Get that equation and turn it around, we'll have Q is equal to the membrane

capacitance times V. Q, of course, is the charge on the

capacitor. So, here's the charge right here.

It's on the capacitor. I better make a note of that.

Just write it in. Here is the charge.

If we now mathematically differentiate the second equation, we get the third.

And equation three says, that if things change as a function of time, the dQ/dt

here is equal to the amount of capacitance times the derivative of the voltage.

And if we rearranged that equation to get equation four, you could say dQ/dt is the

same thing as the membrane current, that's the change in charge that's present

membrane so that's like a current, a change in charge per time.

So, I am then as the, as the current through the membrane that's coming by

because of a, a current through the capacitor.

Now, I have made a mistake here. So, I should say that's a C, the current

through the capacitor. A C is equal to Cm times dVm / dt.

We use that equation all the time in later mathematical work, so it's very helpful.

Thank you for watching this segment and we'll go on to another one, having to do

of what the value of capacitance is.