As described previously, the Na+,K+-ATPase and K+-selective channels in the plasma membrane are important determinants of the membrane potential (Vm) of the cell. For all cells within the body, the resting Vm is oriented with the interior of the cell electrically negative in relation to the ECF. However, the magnitude of the Vm can vary widely.
To understand what determines the magnitude of the Vm, it is important to recognize that any transporter that transfers charge across the membrane has the potential to influence the Vm. Such transporters are said to be fIn muscle cells, in which contraction is regulated by the intracellular [Ca++], the maintenance of a low intracellular [Ca++] during the relaxed state involves not only the activity of the plasma membrane 3Na+-Ca++ antiporter and the Ca++-ATPase but also a Ca++-ATPase molecule located in the smooth endoplasmic reticulum (see
Chapters 12 to 14 electrogenic. As might be expected, the contribution of various electrogenic transporters to the Vm is highly variable from cell to cell. For example, the Na+,K+-ATPase channel transports three Na+ and two K+ ions and thus transfers one net positive charge across the membrane. However, the direct contribution of the Na+,K+-ATPase to the Vm of most cells is only a few millivolts at the most. Similarly, the contribution of other electrogenic transporters, such as the 3Na+-Ca++ antiporter and the Na+-glucose symporter is minimal. The major determinants of the Vm are ion channels. The type (e.g., selectivity), number, and activity (e.g., gating) of these channels determine the magnitude of the Vm. As described in , rapid changes in ion channel activity underlies the action potential in neurons and other excitable cells, such as those of skeletal and cardiac muscle (see
As ions move across the membrane through a channel, they generate a current. As described in , this current can be measured, even at the level of a single channel. By convention, the current generated by the movement of cations into the cell, or the movement of anions out of the cell, is defined as negative current. Conversely, the movement of cations out of the cell, or the movement of anions into the cell, is defined as positive current. Also by convention, the magnitude of the Vm is expressed in relation to the outside of the cell; thus for a cell with a Vm of −80 mV, the interior of the cell is electrically negative in relation to the outside of the cell.
The current carried by ions moving through a channel depends on the driving force for that ion and on the conductance of the channel. As described in , the driving force is determined by the energy in the concentration gradient for the ion across the membrane (Ei), as calculated by the Nernst equation (Eq. 1.5a ) and the Vm:
Equation 2.3
Driving force = Vm − Ei.
Thus as defined by Ohm’s law, the ion current through the channel (Ii) is determined as follows:
Equation 2.4 where gi is the conductance of the channel. For a cell, the conductance of the membrane to a particular ion (Gi) is determined by the number of ion channels in the membrane and by the amount of time each channel is in the open state.
Fig. 2.4 , the Vm is the voltage at which there is no net ion flow into or out of the cell. Thus for a cell that has ion channels selective for Na+ , K+ , and Cl− ,
Equation 2.5
Equation 2.6 + [(Vm − E − )× G − ]= 0.