ENGR 093: Biomedical Directed Reading Spring 2004  
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  Sodium & Potassium Conductances

This page is devoted to examining the effects of changing sodium and potassium ion concentrations in order to better understand sodium and potassium conductances. Hodgkin and Huxley ran two sets of experiments, one that was concerned with the movement of sodium ions and the other devoted to the movement of potassium ions. It was found that both sodium and potassium conductance rise along an inflected curve during depolarization and fall without any inflection during repolarization. However, the rate that the sodium conductance rises and falls is at least 10 times faster than the rate of rise and fall for potassium conductance. Also, if the axon is depolatized, the potassium conductance is maintained but the sodium conductance declines after reaching it's peak. The identity of the effects of ion conductances on the membrane current were later used to help Hodgkin and Huxley develop their mathmatical model of the action potential in a neuron.

Experiments

Sodium Experiment

Potassium Experiment

Conclusions


From “The Components of Membrane Conductance in the Giant Axon of Loligo” (third paper)

Categorizing the Experiments

This article is concerned with the situation where the membrane potential is suddenly restored from the depolarized level back to the resting potential. The experiments that Hodgkin and Huxley ran can be characterized into two categories. The first is largely concerned with the movement of sodium ions and the second is concerned with the movement of potassium ions. Again, the voltage clamp apparatus was used in this set of experiments.

The Sodium Experiment

In one set of experiments Hodgkin and Huxley inputted a single step down from 0mV to –41mV into the membrane of the axon. As expected, they noticed that the membrane current had a wave of inward current followed by a maintained phase of outward current. They then inputted a step down from 0 to –41mv followed by a step up in the middle of the action potential from –41 mV to 0mV. The sudden change in potential is associated with a change in the capacity current followed by a “tail” of ionic current. Repolariztion during the period of high sodium permeability is associated with a large inward current with declines rapidly along an exponential curve. The tail disappears if sodium ions are removed from the external medium. These results can be explored quantitatively by supposing that the sodium conductance is continuous which rises when the membrane is depolarized and falls when the membrane is repolarized. The total period of inward current is greatly reduced by cutting the period of depolarization. This suggests that the process underlying sodium permeability is reversible and repolarization causes the sodium current to fall more rapidly than it would with a maintained depolarization. It was also found that large discontinuties could be induced with a sudden change in membrane potential (see figure2) Previous experimentation revealed that the inward current is carried by sodium ions. THe tail of inward current can also be associated with the sodium current. (see figure3) The time course of the sodium conductance during voltage clamp can be calculated the variation of the tail of inward current during depolarization.


The results of these experiments also suggest that the membrane obeys Ohm’s law if the ionic current is measured directly after a change in the membrane potential. To verify this, two rectangular pulses were fed into the feedback amplifier in order to produce a double step. The first step lasted 52ms and had amplitude of 29mV. The second step lasts longer and has an amplitude between –60 and +30mV. Hodgkin and Huxley were able to find that the instantaneous behavior of the membrane is linear when the nerve is in sea water. However, it is not clear whether this is the case in a sodium free environment. In fact, it probably is not the case in a sodium free environment since the method of defining conductance breaks down when there is no sodium in the external environment. In a sodium-free environment, the instantaneous current-voltage relationship shows a marked curvature and is very different from the linear relationship in a sodium rich environment. Hence, the linear relationship between current and voltage that is found in sea water is not a property of the membrane, since it is no longer present in a sodium free environment. However, the linear relationship that was observed is still a useful observation, since the primary concern of these studies is to understand the laws governing an action potential in normal circumstances. A sodium rich environment is a normal condition for an action potential to propagate in. When the membrane potential is returned to normal, it was found that the sodium conductance reverts rapidly to its original low level.

The Potassium Experiment

Potassium ions are largely responsible for maintaining the outward current during a prolonged depolarization of the membrane. In order to fully investigate the instantaneous relationship between potassium current and membrane potential, longer depolarization must be used. Like sodium potassium also returns to the same lower conductance when the membrane is repolarized. Repolarization of the membrane during high potassium permeability is associated with a tail of outward current at the resting potential and an inward current above the critical potential. The relationship between the potassium current and the membrane potential is linear passing through zero at 10-20mV above the resting potential. This suggests that potassium conductance is a continuous function of time which rises when the nerve is depolarized and falls when the nerve is repolarized. The rate at which the potassium conductance is reduced on repolarization increases with membrane potential. The critical potential at which the potassium current appears to reverse sign varies with the external concentration of potassium but less steeply than in the case of a potassium electrode.

The Final Conclusions
It was found that there were similarities and differences between sodium and potassium conductance. Both sodium and potassium conductance rise along an inflected curve when the membrane is depolarized. They both fall without any appreciable inflections when the membrane is repolarized. The rate of rise of conductance increases continuously as the membrane potential is reduced. The rate of fall of conductance decreases when the membrane potential is increased. The instantaneous relationship between sodium or potassium current and membrane potential normally consists of a straight line with zero current at the sodium or potassium potential. On the other hand, the rise and fall of the sodium conductance occurs 10-30 times faster than the corresponding rates for potassium. The variation of peak conductance with membrane potential is greater for sodium than for potassium. If the axon is depolarized, the potassium conductance is maintained but the sodium conductance declines after reaching its peak.

(Figure 1: On the left hand column, time course of the potential difference between the internal and external electrode. The right hand column shows the membrane current time course for the associated membrane potential shown in the left hand column)

(Figure 2: Membrane current time courses associated with depolarization of 97.5mV lastking 0.05, 0.08, 0.19, 0.32, 0.91, 1.6, and 2.6 msec)

(Figure 3: Membrane current associated with depolarization of 110mV, lasting 0.28 msec. Nerve A is in sea water. Nerve B is in chlorine water. Nerve C had a depolarization of 220mV and is in chlorine water)

(Figure 4:Time course of the sodium conductance estimated from records C and D from figure 2)

(Figure 5: A is the ionic current associated with depolarization of 25mV, lasting 4.9 msec. B is the potassium conductance estimated from A.)


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