Читать книгу Neurobiology For Dummies - Frank Amthor - Страница 103

The Nernst equation (refer to the previous section) tells you what the reversal potential would be for a single ion. But multiple ionic concentration differences exist across the neural membrane, and the most important are sodium, potassium, and chloride. But another question is, given the concentration differences of these different ions, what is the actual membrane potential for a given set of permeabilities to the different ions?

The Goldman–Hodgkin–Katz equation determines the voltage that results from ionic currents across the membrane. It expands on the Nernst equation by taking into account multiple ions and their individual permeabilities (that is, if you eliminate all but one ion from the Goldman equation, you get the Nernst equation). What the Goldman equation shows is that, for a given set of ionic concentration gradients across the membrane, the voltage inside the cell (across the membrane) will be driven toward the Nernst equilibrium potential of the most permeable ion.

The Goldman–Hodgkin–Katz equation is as follows:

 

The chloride versus terms are reversed in the numerator and denominator of the Goldman-Hodgkin-Katz equation. This takes into account that z for chloride is –1, while it is +1 for sodium and potassium.

The Goldman–Hodgkin–Katz equation was derived from the Nernst equation but takes into account the important fact that the membrane potential tends to move toward the reversal potential of the ion to which the membrane is most permeable. Note that, if you set the permeabilities of two of the ions to zero, the Goldman–Hodgkin–Katz equation reduces to the Nernst equation for the remaining ion that has some finite permeability.

The neuron is at its resting potential when it isn’t being stimulated, or excited. The permeability for chloride tends to be high in the resting state of neurons, so the chloride current contribution is relatively dominant then.

The potassium current also pulls the membrane potential toward the potassium reversal potential because the resting membrane permeability is much higher to potassium than sodium. The reversal potential for potassium is generally more negative than the resting potential (–75 mV versus –65 mV).

During an action potential, however, the sodium permeability becomes much higher than the potassium permeability, so the intracellular potential is driven toward the positive sodium equilibrium potential. In the next section, I show you what happens when the membrane permeability for sodium and potassium ions are regulated by voltage-gated ion channels.