Membrane Potential

From the previous pages, you have learned that cells usually have a negative membrane potential (inside being negative) and that there is an unequal distribution of ions across the membrane. For example, in a typical cell, the membrane potential is between -70 to -90 mV and the concentration of potassium outside the cell is lower than the concentration of potassium inside the cell. This means that diffusion is trying to drive potassium out of the cell (from high to low). Despite the presence of this force, potassium does not usually undergo any net movement as the electrical force (negative on the inside and remember that negative charges attract positive ones such as potassium ions) is trying to drag the potassium inward (toward the negative). As long as these two forces push potassium in opposite directions and push with equal force, there will be no net movement of potassium even though it is freely permeable. Under these conditions, potassium is said to be in equilibrium. The normal intracellular concentration of potassium is about 150 mM while the extracellular concentration is typically about 5 mM. Despite this large difference in concentrations (and thus a large diffusion force pushing potassium out), potassium does not undergo any net movement in a typical cell. This is because the inside of the cell has a negative membrane potential which exactly balances the outward diffusion of potassium. Physics can predict exactly what magnitude of membrane potential is needed to exactly balance the outward diffusion of potassium. In this case, the membrane potential would need to be -92 mV (take my word for it). This means that the -92 mV pulls the potassium with same force as does diffusion (due to the concentration gradient), but in the opposite direction, so that the sum of forces acting on the potassium is zero (0) and thus potassium is in equilibrium. The membrane potential which must occur to exactly balance the diffusion of the ion (and thus achieve equilibrium) is known as the equilibrium potential for that ion. Given the concentration gradient for potassium shown above, therefore, the equilibrium potential for potassium is -92 mV.

What happens if the membrane potential is no longer -92 mV but is -50 mV instead (still assuming that the extracellular potassium concentration is 5 mM and the intracellular concentration is 150 and that potassium is permeable)? Well, since the concentration of potassium has not changed, the diffusion force pushing potassium out will remain unchanged. However, the membrane potential is not as large as before (-50 mV compared to -92 mV). That means that the electrical force pushing potassium into the cell is not as large. Since the electrical force exactly balanced with the diffusion force when the membrane potential was -92 mV (the equilibrium potential for potassium), by setting the membrane potential -50, the diffusion force is stronger and is no longer balanced out by the electrical force. Since the diffusion force is stronger, potassium is no longer at equilibrium and it will begin to move outward.

When will potassium stop moving out? Well, the simplistic answer is AWhen reaches equilibrium@, but that doesn=t really tell us anything. Let=s analyze the situation. If the diffusion force is larger than the electrical force (given the conditions outlined above), then potassium will diffuse out of the cell. Since potassium is a positive ion, the intracellular space must lose positive charges (as potassium is moving out). Thus the inside of the cell must become more negative (and since the extracellular fluid is gaining the positive potassium ions, it must become more positive). This means that the membrane potential (which was -50mV) will become more negative. When enough potassium leaves so that the membrane potential reaches -92 mV, the electrical force will once again exactly balance the diffusion force and potassium will be in equilibrium again. So the correct answer to the question AWhen will potassium stop moving out?@ is simply when enough potassium ions move so that the membrane potential once again equals the equilibrium potential for potassium.

What if we set the membrane potential to -110 mV? What will happen? In this case the electrical force pulling potassium into the cell is now greater than the diffusion force, so potassium will move inward. This inward movement of positive charges with make the inside less negative (or more positive) and the membrane potential will begin to fall (become less negative). When enough potassium enters the cell to make the membrane potential -92 mV, potassium will once again be in equilibrium and it will no longer have any net movement.

What we have attempted to demonstrate is that potassium will always move in such a way to make the membrane potential of the cell equal to its equilibrium potential. Note, this is only possible IF potassium is permeable.

One word of caution, although we talk of potassium moving into or out of the cell, the actual number of ions that must move to change the membrane potential is very, very small so that even though potassium is moving, the concentrations of potassium are not changing. This is a hard concept to follow but take my word, very few ions ever move and we assume that the concentration of the ions do not change during these processes! Of course, in an experiment, we can change them

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