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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From the lesson

Hodgkin-Huxley Membrane Models

This week we will examine the Hodgkin-Huxley model, the Nobel-prize winning set of ideas describing how membranes generate action potentials by sequentially allowing ions of sodium and potassium to flow. The learning objectives for this week are: (1) Describe the purpose of each of the 4 model levels 1. alpha/beta, 2. probabilities, 3. ionic currents and 4. trans-membrane voltage; (2) Estimate changes in each probability over a small interval $$\Delta t$$; (3) Compute the ionic current of potassium, sodium, and chloride from the state variables; (4) Estimate the change in trans-membrane potential over a short interval $$\Delta t$$; (5) State which ionic current is dominant during different phases of the action potential -- excitation, plateau, recovery.

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

Biomedical Engineering, Pediatrics

Well, hello again. This is the Bioelectricity course, Week

number four, Segment number eight. Here, we want to talk a little bit about

reviewing where we are so far in the Hodgkin-Huxley model.

It has lots of different parts, we want to talk about putting these all together.

Let's see what we got. What were Hodgkin and Huxley trying to do?

They were trying to explain the big response that occurs in active tissue

after a very small stimulus. So, they had observed that with a little

stimulus, you get a big response. They were trying to explain, where does

all that come from. They provided us with a mechanism by which

a single current, a single current through the tissue, single current through a

resistant tissue. Or was, in fact, replaced with three

currents, okay Na, iL and these three currents together were the components of

the actual current flow in the model. Hodgkin and Huxley said the total of these

three components. These three altogether, should be thought

of as the ionic current because each of them is an ion and they add to be the

total current. So, if you look at this diagrammatically,

we start off with ir, a resistive current, and what we wound up doing is we wound up

replacing ir over here with i ionic and i ionic was found in a completely different

way. All the currents are dependent on the

probabilities of particle openings. And the probabilities were designated n,

m, and h. So, let's just say that one more time, for

INa, we have a channel. Channel has four particles.

Three of them are m particles and the fourth one is an h particle.

Probabilities that each of these particles will be open at the same time is the

probability that the channel will be open. Now, here's the power.

What we are trying to do, is we are trying to be here at our present time.

You're trying to project over into the future.

So, I've drawn a dot indicating present time, and then an arrow over to another

dot, indicating a time in the future. We think of that time shift, delta T, as

being short, a microsecond or just a few microseconds.

What Hodgkin actually showed us was that to make that projection from present time

into future time we have to know, at the present time, we have to know Vm, n, m and

h. We also know, have to know about current

conditions in terms of membrane current I'm, or stimulus current, I-stem.

So, if we know about the stimuli, we know about Vm, n, m, and h, then we can project

over to a future time as long as delta T is short.

Because if delta T is short, our projection will be fairly accurate.

If you think about the meaning of this process as a whole, you would say, look,

finding individual currencies are a nice thing to do, because it allows us to

understand the tissue and its mechanisms and we want to do that.

However, you would say being able to project forward from one time to the next,

time shifting is absolutely essential. That is really the big jump that we have

made in our understanding because now, for active tissue, we can move forward from

one time to the next time. So, if we repeat that process over and

over, we can move forward step by step throughout a, a long time.

We can move forward for a millisecond or a second, or hours and hours as long as

we're willing to keep going, keep computing.

You might think, well that's a big job. On the other hand, that's what we are

doing in our tissues every second of our lives.

Over and over and over, we're taking our state variables and Vm and projecting

forward into the future. Thank you for watching this segment.

We'll come back and talk about that projection in a little more detail

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