Electrical Current and the Movement of Ions Across Membranes

An electrical current is the movement of charge through space. In a wire like that carrying electricity in your house, the electrical current is a flow of

Electrical Current and the Movement of Ions Across Membranes 49

electrons; in a solution of ions, however, a flow of current is carried by movement of ions. That is, in a solution, the charges that move during an electrical current flow are the charges on the ions in solution. Thus, the movement ofions through space such as from the outside of a cell to the inside of a cell constitutes an electrical current, just as the movement of electrons through a wire constitutes an electrical current.

By thinking of ion flows as electrical currents, we can get a different perspective on the factors governing the steady-state membrane potential of cells. We have seen that at the steady-state value of membrane potential, there is a steady influx of sodium ions into the cell and a steady efflux of potassium ions out of the cell. This means that there is a steady electrical current, carried by sodium ions, flowing across the cell membrane in one direction and another current, carried by potassium ions, flowing across the membrane in the opposite direction. By convention, it is assumed that electrical current flows from the plus to the minus terminal of a battery; that is, we talk about currents in a wire as though the current is carried by positive charges. By extension, this convention means that the sodium current is an inward membrane current (the transfer of positive charge from the outside to the inside of the membrane), and the potassium current is an outward membrane current.

As we saw in our discussion of the Goldman equation above, a steady value of membrane potential will be achieved when the influx of sodium is exactly balanced by the efflux of potassium. In electrical terms, this means that in the steady state the sodium current, iNa, is equal and opposite to the potassium current iK. In equation form, this can be written

Thus, at the steady state the net membrane current is zero. This makes electrical sense, if we keep in mind that the cell membrane can be treated as an electrical capacitor (see Chapter 4). If the sum of iNa and iK were not zero, there would be a net flow of current across the membrane. Thus, there would be a movement of charge onto (or from) the membrane capacitor. Any such movement of charge would change the voltage across the capacitor (the membrane potential); that is, from the relation q = CV, if q changes and C remains constant then V must of necessity change. Equation (5-4), then, is a requirement of the steady-state condition; if the equation is not true, the membrane potential cannot be at a steady level.

In cells in which there is an appreciable flow of chloride ions across the membrane, Equation (5-4) must be expanded to include the chloride current, iCl:

Equation (5-5) is, in fact, the starting point in the derivation of the Goldman equation (see Appendix B). Note that because of the negative charge ofchloride and because of the electrical convention for the direction ofcurrent flow, an outward movement of chloride ions is actually an inward membrane current.

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