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

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來自 Duke University 的課程

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.

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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 the instructor for

bio electricity and we're in week two and this is the ten lecture.

The question for this lecture is why is CM the membrane capacitance so big?

Way, way bigger than your would normally expect.

And the answer very briefly is because the membrane is so thin.

In biological membrane, the membrane capacitance is about one micro [inaudible]

for each square centimeter. Now, there is a lot of centimeters^2 of

membrane surface in just one person. So if you were to say that, in a person,

there's a million centimeters^2, that would say the total capacitance within a

person would be one farad. When I was in school, I remember a teacher

telling me that one farad is so much capacitance that you could not imagine it

existing in the whole entire world. Well, he meant that, as a good

illustration. But he was not thinking in terms of

bio-electricity. If you think in terms of body electricity,

each of us may carry around a whole farad of capacitance which is an enormous amount

To think about why Cm is so big, you have to think about why is the membrane so

thin? Let's just think about the following

experiment. We would say for flat plates, the

[inaudible] can be found by the formula, c = epsilon zero, a over d, where epsilon

zero or epsilon. Is a constant that has to do with the

material. The material can be air, the material can

be membrane, and Epsilon changes accordingly, according to what the

material is, but it, it has a value that is more or less known.

The point of looking at the equation is to see that the capacitance gets bigger when

the area gets bigger. And it also gets bigger when D gets

smaller. So bigger capacitance occurs with a bigger

A or a smaller D. So, you might, if you draw this out, you

might say, okay, here's our capacitance. Here's the outside.

Here's the inside. D is this thickness.

A is the area, surface area. Now, lets do a little comparison with an

ordinary object. Think about a stack of 1000 sheets of

office paper. You can do this experiment yourself.

Get two reams of ordinary office paper, like copier paper.

Stack one ream on the other. You know, ream is a package that has 500

sheets. So get two packages of office paper, like

copier paper. Put them on top of each other.

And then marry, measure how high the stack is.

I did that. I mean I actually did it in preparation

for this lecture and my stack was about four centimeters high.

That means that the thickness of one sheet of office paper can be found by going

through this calculation, four centimeters for a 1000 sheets.

And I think that results in about 400,000 Angstroms for one sheet.

400,000 angstroms for one sheet. So if now we compare the thickness of

paper to the thickness of membrane we'd say well these things are quite different

in thickness, because with paper it is 400,000 angstroms.

That's just a numeric conversion from 4cm into angstroms.

One angstrom is ten to the minus tenth meters.

About 40 angstroms that miss four membrane.

That is to say, the thickness of the non conducting region is about 40 angstroms.

So the ratio there is 10,000. Wow!

Take a piece of office paper, hold it up in front of you, look at it on the edge.

Now when I do that, my vision is not perfect, so I barely see anything when I

hold it and look right at along the edge to see the thickness of a single sheet of

paper. Nonetheless, it is 10,000 times the

thickness of membrane. Well whether or not we've done the

calculation exactly right, you get the point.

It's thousands of times thicker, to have a sheet of office paper, than it is to have

a sheet of membrane. So the, since the, capacitance, goes

inversely as to thickness. The thinner the membrane, the greater the

comparison, the capacitance, and the conclusion is, membranes have a lot of

capacitance. I don't bring that up just as a random

thought, the fact they have a lot of capacitance means that they can store a

lot of charge, and that's very important to their electrical function.

Another fascinating, item. Is that all electrically active membranes

from whatever organ or system within you or people, or animals, or other elective,

electrically active structure, they all seem to be built out of the same kind of

lipid baler, more or less. And the coral area of that is.

All electrically active. Membranes from whatever ore in our system,

have about the same amount of capacitance. So you read different problems, or

different situations, and they, in those you have to specify a lot of different

parameters. Often times the membrane capacitance is

one of them, you can almost think of it as a constant of nature, not quite like pi,

or some other mathematical constant, but you can just be sure it's gonna come out

to be a round-about one microferret per centimeter square.

Not too far from then. So thank you very much for your attention.

And in the next segment we'll move onto a problem session.