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.

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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 Roger Coke Barr for

Bioelectricity. We are in week four and this is the third

segment in week four. In this segment, we are talking about the

specific way in which Hodgkin and Huxley replaced the membrane resistance with

several ion channels. Let us get right into it.

In the Hodgkin and Huxley model, the Hodgkin and Huxley model observes that

the, the passive model is limited in its representation of the pass through the

membrane that are called, caused by holes and channels in the membrane.

In the passive model all of that is put together into a single equivalent

resistance represented by RM. What Hodgkin and Huxley did is they

replaced that composite resistive model with what it really is underneath the

surface, so to speak. It is three different pathways or actually

its thousands of each of three different kinds of channels.

One for Potassium. One for Sodium, and one for everything

else. So called Leakage.

Let us look at each of these pathways in a little bit more detail.

Each ionic pathway now comes into the representation with a battery in it.

Wow, a battery. And these batteries have voltages that are

the Nernst potential for the concentrations for that particular ion.

So EK is the battery in the K path. Ena is the battery in the Sodium path.

El is the battery in the Leakage path. As you know EK and ENa are the equilibrium

voltages for Potassium and for Sodium. As you know from the work we did in the

earlier week EK is a negative number and ENa is a positive number.

So these batteries have quite different voltages.

That is to say, it may be so that the form of the path is similar.

So this one, this one, this one, they all have the same elements.

But the actual details of what's in there is quite different.

So EK is not equal to ENa, and that's not equal to EL.

These are three different numbers. We also need to notice that the resistance

in each of these pathways is marked with a line through it.

So here we have a line through that resistance, and that is a signifier that,

that resistance is a variable resistance. It is not the same resistance all the

time. So there is a line through GK.

A line through GNa, and a line through GL. These resistances are not linked to each

other. Because a part of the model is that each

of these three lines is operating independently.

It is the so called Independence Assumption.

So that means that there has to be some other additional rules that tell us how

these pathways operate. You will notice in the way that these

resistances are denoted here on the diagram.

That each of the, each of them is not actually written as a resistance.

It is written as a, conductance. Its reciprocal.

So rather than having an RK, RNa and RL. There is instead a GK, GNa, GL, and at one

level it is just notational. It could have been done the other way.

But here it has a little bit further significance because there are further

equations that are given for these conductenses.

So what are exactly GK, GNa and GL? Well, we will come back in the next

lecture and talk about those. Thank you for watching and I'll see you

again in a few minutes.

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