Neuroscience Online (i,1,2)

Before examining the ionic mechanisms of action potentials, it is first necessary to understand the ionic mechanisms of the resting potential. The two phenomena are intimately related. The story of the resting potential goes back to the early 1900's when Julius Bernstein suggested that the resting potential (Vm) was equal to the potassium equilibrium potential (E_K). Where

The key to understanding the resting potential is the fact that ions are distributed unequally on the inside and outside of cells, and that cell membranes are selectively permeable to different ions. K⁺ is particularly important for the resting potential. The membrane is highly permeable to K⁺. In addition, the inside of the cell has a high concentration of K⁺ ([K⁺]_i) and the outside of the cell has a low concentration of K⁺ ([K⁺]_o). Thus, K⁺ will naturally move by diffusion from its region of high concentration to its region of low concentration. Consequently, the positive K⁺ ions leaving the inner surface of the membrane leave behind some negatively charged ions. That negative charge attracts the positive charge of the K⁺ ion that is leaving and tends to "pull it back". Thus, there will be an electrical force directed inward that will tend to counterbalance the diffusional force directed outward. Eventually, an equilibrium will be established; the concentration force moving K⁺ out will balance the electrical force holding it in. The potential at which that balance is achieved is called the Nernst Equilibrium Potential.

Figure 1.4

An experiment to test Bernstein's hypothesis that the membrane potential is equal to the Nernst Equilibrium Potential (i.e., V_m = E_K) is illustrated to the left.

The K⁺ concentration outside the cell was systematically varied while the membrane potential was measured. Also shown is the line that is predicted by the Nernst Equation. The experimentally measured points are very close to this line. Moreover, because of the logarithmic relationship in the Nernst equation, a change in concentration of K⁺ by a factor of 10 results in a 60 mV change in potential.

Note, however, that there are some deviations in the figure at left from what is predicted by the Nernst equation. Thus, one cannot conclude that V_m = E_K. Such deviations indicate that another ion is also involved in generating the resting potential. That ion is Na⁺. The high concentration of Na⁺ outside the cell and relatively low concentration inside the cell results in a chemical (diffusional) driving force for Na⁺ influx. There is also an electrical driving force because the inside of the cell is negative and this negativity attracts the positive sodium ions. Consequently, if the cell has a small permeability to sodium, Na⁺ will move across the membrane and the membrane potential would be more depolarized than would be expected from the K⁺ equilibrium potential.

Goldman-Hodgkin and Katz (GHK) Equation

Note that

is the ratio of Na⁺ permeability (P_Na) to K⁺ permeability (P_K). Note also that if the permeability of the membrane to Na⁺ is 0, then alpha in the GHK is 0, and the Goldman-Hodgkin-Katz equation reduces to the Nernst equilibrium potential for K⁺. If the permeability of the membrane to Na⁺ is very high and the potassium permeability is very low, the [Na⁺] terms become very large, dominating the equation compared to the [K⁺] terms, and the GHK equation reduces to the Nernst equilibrium potential for Na⁺.

If the GHK equation is applied to the same data in Figure 1.4, there is a much better fit. The value of alpha needed to obtain this good fit was 0.01. This means that the potassium K⁺ permeability is 100 times the Na⁺ permeability. In summary, the resting potential is due not only to the fact that there is a high permeability to K⁺. There is also a slight permeability to Na⁺, which tends to make the membrane potential slightly more positive than it would have been if the membrane were permeable to K⁺ alone.

Figure 1.5

Membrane Potential Laboratory

Click here to go to the interactive Membrane Potential Laboratory to experiment with the effects of altering external or internal potassium ion concentration and membrane permeability to sodium and potassium ions. Predictions are made using the Nernst and the Goldman, Hodgkin, Katz equations.

Test Your Knowledge

Question 1
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B
C
D
E

If a nerve membrane suddenly became equally permeable to both Na⁺ and K⁺, the membrane potential would:

A. Not change
B. Approach the new K⁺ equilibrium potential
C. Approach the new Na⁺ equilibrium potential

D. Approach a value of about 0 mV

E. Approach a constant value of about +55 mV

If a nerve membrane suddenly became equally permeable to both Na⁺ and K⁺, the membrane potential would:

A. Not change This answer is INCORRECT.

A change in permeability would depolarize the membrane potential since alpha in the GHK equation would equal one. Initially, alpha was 0.01. Try substituting different values of alpha into the GHK equation and calculate the resultant membrane potential.

B. Approach the new K⁺ equilibrium potential

C. Approach the new Na⁺ equilibrium potential

D. Approach a value of about 0 mV

E. Approach a constant value of about +55 mV

If a nerve membrane suddenly became equally permeable to both Na⁺ and K⁺, the membrane potential would:

A. Not change

B. Approach the new K⁺ equilibrium potential This answer is INCORRECT.

The membrane potential would approach the K+ equilibrium potential only if the Na⁺ permeability was decreased or the K⁺ permeability was increased. Also there would be no "new" equilibrium potential. Changing the permeability does not change the equilibrium potential.

C. Approach the new Na⁺ equilibrium potential

D. Approach a value of about 0 mV

E. Approach a constant value of about +55 mV

If a nerve membrane suddenly became equally permeable to both Na⁺ and K⁺, the membrane potential would:

A. Not change

B. Approach the new K⁺ equilibrium potential

C. Approach the new Na⁺ equilibrium potential This answer is INCORRECT.

The membrane potential would approach the Na⁺ equilibrium potential only if alpha in the GHK equation became very large (e.g., decrease PK or increase PNa). Also, there would be no "new" Na⁺ equilibrium potential. Changing the permeability does not change the equilibrium potential; it changes the membrane potential.

D. Approach a value of about 0 mV

E. Approach a constant value of about +55 mV

If a nerve membrane suddenly became equally permeable to both Na⁺ and K⁺, the membrane potential would:

A. Not change

B. Approach the new K⁺ equilibrium potential

C. Approach the new Na⁺ equilibrium potential

D. Approach a value of about 0 mV This answer is CORRECT!

Roughly speaking, the membrane potential would move to a value half way between E_K and E_Na. The GHK equation could be used to determine the precise value.

E. Approach a constant value of about +55 mV

If a nerve membrane suddenly became equally permeable to both Na⁺ and K⁺, the membrane potential would:

A. Not change

B. Approach the new K⁺ equilibrium potential

C. Approach the new Na⁺ equilibrium potential

D. Approach a value of about 0 mV

E. Approach a constant value of about +55 mV This answer is INCORRECT.

The membrane potential would not approach a value of about +55 mV (the approximate value of E_Na) unless there was a large increase in the sodium permeability without a corresponding change in the potassium permeability. Alpha in the Goldman equation would need to approach a very high value.

Question 2
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B
C
D
E