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

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From the course by Duke University

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.

From the lesson

Passive and Active Resonses, Channels

This week we'll be discussing channels and the remarkable experimental findings on how membranes allow ions to pass through specialized pores in the membrane wall. The learning objectives for this week are: (1) Describe the passive as compared to active responses to stimulation; (2) Describe the opening and closing of a channel in terms of probabilities; (3) Given the rate constants alpha and beta at a fixed Vm, determine the channel probabilities; (4) Compute how the channel probabilities change when voltage Vm changes.

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

Biomedical Engineering, Pediatrics

So, hello again. This is the Bioelectricity course, I'm

Roger Coke Barr. And this is Week three, segment ten.

We were talking about channels, and how channels go open and closed.

Because they're just opening and closing seemingly randomly, the more frequently

under some circumstances than others, we really need to think about channel

openings in terms of probabilities. But first, let's just think about what we

have said. It is really amazing, the critical

functions of humans depend on probabilities.

There's not a mechanism, not a deterministic mechanism, A causes B, but

rather probabilities. The channel is probably open, but then it

may be closed. The channel is probably closed, but then

it may be open. Of course, it'll work out in a statistical

sense if there are enough channels because we can rely on their average behavior.

But, it is still quite remarkable. So, the issue is, how can this channels be

understood quantitatively? Which turns into, how can these

probabilities be determined quantitatively?

So, I'll just make a little sketch here. We're not going to try to analyze this

problem in detail right now. But, let's just make a little sketch as to

how we might think about it. First, we can say that in some patch,

there are a total of N channels, and at a certain moment, NO are open and NC are

closed. Now, the number that are open and closed

is dynamic and changing randomly. We can, we can write what is happening as

an equation by saying that the number that are open is changing as a function of tab,

dN0 / dt, the rate of change of the number that are opened by two processes.

First, there's a process where channels that are closed are reopening that's

associated with this rate cost an alpha. And there's a process by which those that

are open are going closed, and that's associated with this right constant, beta.

You notice that alpha and beta, somehow are there built into the membrane.

We are supposing that alpha and beta are not constants, rather alpha and beta

change. And, in particular, they change when the

transmembrane voltage changes but they're constant for, for a constant vm.

So, let's go through that again. As long as the membrane potential is

constant, alpha and beta are constant. But, if the membrane voltage changes, then

alpha and beta change. They change with vm.

We're not working on this problem quantitatively right now, but if you were,

do work on it quantitatively, solve the differential equation for constant vm,

that is to say, for alpha and beta constants.

Then, the fraction of channels that are open will become alpha over alpha plus

beta. So, let me ask you, can you do that

problem? Can you solve that, that differential

equation and find what the actual solution is?

If you do, you can see not only that ultimately the fraction becomes alpha over

alpha plus beta, you can also see how long it takes for that to occur.

So, the crucial result here is if you framed it this way, the channels that are

open will on the average be alpha over alpha plus beta.

And alpha over alpha plus beta will be a function of vm.

Or, as we saw in the channel segment, if you have a higher voltage with a potassium

channel, there's a higher fraction that will be open when the trans-membrane

voltage is greater. Now, how do we get specific values for

alpha and alpha plus beta? We have not provided any way to do it.

So, the fact is, up until now nobody has figured out how to get specific values for

alpha and beta except by measurement. So, what we have is we have measurements

for different kinds of tissues and the different kinds of tissues, the

measurements have been captured in equations that we can use for further

analysis. But so far as I know, nobody yet knows how

to find values for alpha and beta based on some underlying principle.

We will discuss this further as we go forward in the course.

Here's some trees in the North Carolina woods.

I thought you might enjoy seeing them. Thank you for watching.

See you in the next segment.

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