Measuring Changes in Membrane Ionic Conductance Using the Voltage Clamp

By inserting a current monitor into the output line of the amplifier, we can measure the amount of current that the amplifier is passing to keep the membrane voltage equal to the command voltage. How does this measured current give information about changes in ionic current and, therefore, changes in ionic conductance of the membrane? First of all, let's review what happens to membrane current and membrane potential without the voltage clamp, using the principles we discussed in Chapters 5 and 6. This is illustrated in Figure 7-2a, which shows the changes in transmembrane ionic current and membrane potential in response to a stepwise increase in pNa, with pK remaining constant. Under resting conditions, we have seen that the steady-state membrane potential will be between ENa and EK, at the membrane voltage at which the inward sodium current exactly balances the outward potassium current, so that the total membrane current is zero (iNa + iK = 0). When pNa is suddenly increased, the steady state is perturbed, and there will be an increase in iNa. This greater sodium

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Figure 7-2 The ionic currents flowing in response to a stepwise change in pNa, either without voltage clamp (a) or with voltage clamp (b). Without voltage clamp, both /Na and iK increase in response to the increase in pNa, and a new steady-state membrane potential is reached at a more depolarized level. With voltage clamp, the membrane potential remains constant because the voltage-clamp apparatus injects current (/clamp) that compensates for the increased sodium current. Potassium current remains constant because neither pK nor Em changes.

PNa clamp

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Na influx causes Em to move positive from its original resting value. With depolarization, however, potassium current increases because of the increasing difference between Em and EK. The membrane potential will reach a new steady state, governed by the new ratio of pNa/pK, at which both iNa and iK are larger than they were initially, but once again exactly balance each other. This is just a restatement of the basis of resting membrane potential discussed in detail in Chapter 5. Let's consider now what happens if the same change in pNa occurs under voltage clamp, as shown in Figure 7-2b. Now we must consider an additional source of current: the current provided by the voltage-clamp apparatus (iclamp). Suppose we set the command voltage, EC, to be equal to the normal steady-state membrane potential of the cell and turn on the voltage-clamp apparatus. In this situation, Em is already equal to EC and the current injected by the voltage-clamp apparatus will be zero. Suppose that at some time after we turn on the apparatus, there is a sudden increase in the sodium permeability of the membrane. As we have just seen, this would normally cause the membrane potential to take up a new steady-state value closer to the sodium equilibrium potential; that is, the cell would depolarize because of the increase in inward sodium current across the membrane. However, now the voltage-clamp circuit will detect the depolarization as soon as it begins, and the voltage-clamp amplifier will inject negative current into the axon to counter the increased sodium current (see trace labeled iclamp in Figure 7-2b). The voltage clamp will continue to inject this holding current to maintain Em at its usual resting value for as long as the increased sodium permeability persists, so that Em remains equal to EC. Thus, the injected current will be equal in magnitude to the increase in sodium current resulting from the increase in sodium permeability. Notice that there is now no change in i'K, because there is now no change in Em (as well as no change in pK). If the potassium permeability, rather than the sodium permeability, were to undergo a stepwise increase from its normal resting value, then the voltage-clamp apparatus will respond as shown in Figure 7-3. In this case, the increased potassium permeability would normally drive Em more negative, toward EK, and the cell would hyperpolarize. However, the voltage-clamp amplifier will inject a depolarizing current of the right magnitude to counteract the hyperpolarizing potassium current leaving the cell. The point is that the current injected by the voltage clamp gives a direct measure of the change in ionic current resulting from a change in membrane permeability to an ion.

How do we relate the measured change in membrane current to the underlying change in membrane permeability? Recall from Chapter 5 that the ionic current carried by a particular ion is given by the product of the membrane conductance to that ion and the voltage driving force for that ion, which is the difference between the actual value of membrane potential and the equilibrium potential for the ion. For example, for sodium ions iNa = gNa(Em - ENa)

Thus, we can calculate gNa from the measured iNa according to the relation

In this calculation, Em is equal to the value set by the voltage clamp, and ENa can be computed from the Nernst equation or measured experimentally by setting EC to different values and determining the setting that produces no change in ionic current upon a change in gNa (that is, Em - ENa = 0). In this way, it is straightforward to obtain a measure of the time-course of a change in membrane ionic conductance from the time-course of the change in ionic current. As discussed in Chapter 5, conductance is not the same as permeability. However, for rapid changes in permeability like those underlying the action potential, we can treat the two as having the same time-course.

PNa clamp

Figure 7-3 The changes in ionic current and injected current after a stepwise change in pK under voltage clamp. Potassium current increases because of the increase in pK, but the voltage-clamp amplifier injects compensating current to keep Em constant.

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