Behavior of Single Ion Channels

At this point, it is worthwhile considering the properties of the ion current flowing through an individual ion channel. We have already seen that the total membrane permeability of a cell to a particular ion depends on the number of channels the cell has that allow the ion to cross. But in addition, the total permeability will also depend on how readily ions go through a single channel. In Equations (5-6) through (5-8), we showed that the ion current across a membrane is equal to the product of the electrical driving force and the membrane conductance. Similar considerations apply to the ion current flowing through a single open ion channel, and we can write (for a potassium channel, for example):

where is is the single-channel current and gs is the single-channel conductance for the potassium channel in question. Analogous equations could be written for single sodium or chloride channels.

What would we expect to see if we could measure directly the electrical current flowing through a single ion channel in a cell membrane? Up to now, we have treated ion channels as simple open pores or holes that allow ions to cross the membrane. But real ion channels show somewhat more complex behavior: the protein molecule that makes up the channel can apparently exist in two conformational states, one in which the pore is open and ions are free to move through it, and one in which the pore is closed and ions are not allowed through. (Actually, channels frequently show more than two functional states, but for our purposes in this book, we can treat channels as being either open or closed.) Thus, channels behave as though access to the pore is controlled by a "gate" that can be open or closed; for this reason, we refer to the opening and closing of the channel as channel gating. The electrical behavior of such a gated ion channel is illustrated in Figure 5-6, which shows the electrical current we would measure through a small patch of cell membrane containing a single potassium channel. We find that when the channel is in the closed state, there is no current across the membrane patch because potassium ions have no path across the membrane; however, when the channel protein abruptly undergoes

Outward

Membrane current

Open

State of channel

Closed

Figure 5-6 The electrical current flowing through a single potassium channel. The bottom trace shows the state of the channel (either open or closed), and the top trace shows the resulting ionic current through the channel. At the beginning of the trace, the channel is closed and so there is no ionic current flowing. When the channel opens, potassium ions begin to exit the cell through the channel, carrying an outward membrane current. The magnitude of the current (/S) is given by Equation (5-9).

a transition to the open state, an outward current will suddenly appear as potassium ions begin to exit the cell through the open pore. When the channel makes a transition back to the closed state, the current will abruptly disappear again. As we will see in the next section of this book, the control of ion channel gating, and thus of the ionic conductance of the cell membrane, is an important way in which biological signals are passed both within a cell and between cells.

The amplitude of the current that flows through the open channel will be given by Equation (5-9); that is, the single-channel current will depend on the electrical driving force and on the single-channel conductance. How big is the single-channel current in real life? That depends on exactly what particular kind of ion channel we are talking about, because there is considerable variation in single-channel conductance among the various kinds of channel we would encounter in a cell membrane (however, all of the individual channels of a particular kind would have the same single-channel conductance). But a value of about 20 pS might be considered typical (pS is the abbreviation for picoSiemen, or 10-12 Siemen). If the conductance is 20 pS and the driving force is 50 mV, then Equation (5-9) tells us that the single-channel current would be 10-12 A (or 1 pA; this corresponds to about 6 million monovalent ions per second). A small current indeed! Nevertheless, it has proved possible, using a measurement technique called the patch clamp, to measure directly the electrical current flowing through a single open ion channel. This technique, invented by Erwin Neher and Bert Sakmann, will be discussed in more detail in Chapter 8. The ability to make such measurements from single channels has revolutionized the study of ion channels and made possible a great deal of what we know about how channels work.

What is the relationship between the total conductance of the cell membrane to an ion (Equations (5-6), (5-7), and (5-8)) and the single-channel conductance? If a cell has only one type of potassium channel with single-channel conductance gS, then the total membrane conductance to potassium, gK, would be given by:

where N is the number of potassium channels in the entire cell membrane and Po is the average proportion of time that an individual channel is in the open state. You can see that if the individual channels are always closed, then Po is zero and gK would also be zero. Conversely, if individual channels are always open, then Po is 1 and gK will simply be the sum of all the individual singlechannel conductances (i.e., N x gs).

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