Medical Physiology A Cellular and Molecular Approach, Updated 2nd Ed.

ELECTROPHYSIOLOGY OF THE CELL MEMBRANE

Edward G. Moczydlowski

Physics is concerned with the fundamental nature of matter and energy, whereas the goal of medical physiology is to understand the workings of living tissue. Despite their different perspectives, physics and physiology share common historical roots in the early investigations of charge and electricity. In the late 1700s, Luigi Galvani, a professor of anatomy in Bologna, Italy, used the leg muscles of a dissected frog to assay the presence of electrical charge stored in various ingenious devices that were the predecessors of modern capacitors and batteries. He observed that frog legs vigorously contracted when electrical stimulation was applied either directly to the leg muscle or to the nerves leading to the muscle (Fig. 6-1). Such early physiological experiments contributed to the development of electromagnetic theory in physics and electrophysiological theory in biology.

Figure 6-1 Early electrophysiological experiments of Galvani. A, Electrical stimulation of a dissected frog with diverse sources of electricity. On the center of the table is a board with a dissected frog that has been prepared for an experiment (Fig. Ω). A hand with a charged metal rod (G) is about to touch the sacral nerves (D), contracting the limbs (C). A metal wire (F) penetrates the spinal cord; a second metal wire (K) grounds the first wire to the floor. On the left side of the table (Fig. 1) is a large “electrical machine” with a rotating disk (A), a conductor (C), and a hand holding a metal rod (B) that is about to be charged. On the extreme left of the room (Fig. 2), a dissected frog is suspended from an iron wire that penetrates the spinal cord (F); the wire is attached to the wall by a hook. A hand with a charged metal rod (G) is touching the wire, stimulating the sacral nerves (D) and causing the legs (C) to twitch. Outside the room on the extreme right side (Fig. 3) is a frog in a glass jar (A). Emerging from the glass jar is an iron wire (B) that is attached at one end to a hook on the frog and ends in a hook (C) in the air. A silk loop (D) near this hook connects to a long conductor (F) that runs near the ceiling to a hook in the wall at the extreme left of the main room. At the far right/front of the table in the main room (Fig. 4) is a dissected frog with one conductor connected to a nerve (C) and another connected to a muscle (D). Just behind this frog (Fig. 5) is a “Leiden jar” (A) containing small lead shot used by hunters. A hand with a charged metal rod (C) is about to touch a conductor (B) emerging from the jar. To the left of the Leiden jar (Fig. 6) is an inverted jar (A) with lead shot (C). This jar sits on top of a similar jar (B) containing a suspended, dissected frog and is connected by a conductor to the lead shot in the upper jar. The legs of the frog are grounded to lead shot near the bottom of the jar. B, Electrical stimulation of the leg muscles of a dissected frog by “natural electricity” (i.e., lightning). In one experiment (Fig. 7), an iron wire (A) runs from near the roof, through several insulating glass tubes (B), to a flask (C) that contains a freshly dissected frog. A second wire (D) grounds the frog’s legs to the water in the well. In a second experiment (Fig. 8), a noninsulated wire extends from an iron hook fastened to the wall and to the spinal cord of a frog (E), which is on a table coated with oil. (From Galvani L: De viribus electricitatis in motu musculari commentarius Aloysii Galvani, Bononiae. New Haven, CT: Yale University, Harvey Cushing/John Hay Whitney Medical Library, 1791.)

The phenomenon of “animal electricity” is central to the understanding of physiological processes. Throughout this book, we will describe many basic functions of tissues and organs in terms of electrical signals mediated by cell membranes. Whereas electrical currents in a metal wire are conducted by the flow of electrons, electrical currents across cell membranes are carried by the major inorganic ions of physiological fluids: Ca²⁺, Na⁺, K⁺, Cl⁻, and HCO⁻₃. Many concepts and terms used in cellular electrophysiology are the same as those used to describe electrical circuits. At the molecular level, electrical current across cell membranes flows through three unique classes of integral membrane proteins (see Chapter 2): ion channels, electrogenic ion transporters, and electrogenic ion pumps. The flow of ions through specific types of channels is the basis of electrical signals that underlie neuronal activity and animal behavior. Opening and closing of such channels is the fundamental process behind electrical phenomena such as the nerve impulse, the heartbeat, and sensory perception. Channel proteins are also intimately involved in hormone secretion, ionic homeostasis, osmoregulation, and regulation of muscle contractility.

This chapter begins with a review of basic principles of electricity and introduces the essentials of electrophysiology. We also discuss the molecular biology of ion channels and provide an overview of channel structure and function.

IONIC BASIS OF MEMBRANE POTENTIALS

Principles of electrostatics explain why aqueous pores formed by channel proteins are needed for ion diffusion across cell membranes

The plasma membranes of most living cells are electrically polarized, as indicated by the presence of a transmembrane voltage—or a membrane potential—in the range of 0.1 V. In Chapter 5, we discussed how the energy stored in this miniature battery can drive a variety of transmembrane transport processes. Electrically excitable cells such as brain neurons and heart myocytes also use this energy for signaling purposes. The brief electrical impulses produced by such cells are called action potentials. To explain these electrophysiological phenomena, we begin with a basic review of electrical energy.

Atoms consist of negatively (⁻) and positively (⁺) charged elementary particles, such as electrons (e⁻) and protons (H⁺), as well as electrically neutral particles (neutrons). Charges of the same sign repel each other, and those of opposite sign attract. Charge is measured in units of coulombs (C). The unitary charge of one electron or proton is denoted by e₀ and is equal to 1.6022 × 10⁻¹⁹ C. Ions in solution have a charge valence (z) that is an integral number of elementary charges; for example, z = +2 for Ca²⁺, z = +1 for K⁺, and z = −1 for Cl⁻. The charge of a single ion (q₀), measured in coulombs, is the product of its valence and the elementary charge:

In an aqueous solution or a bulk volume of matter, the number of positive and negative charges is always equal. Charge is also conserved in any chemical reaction.

The attractive electrostatic force between two ions that have valences of z₁ and z₂ can be obtained from Coulomb’s law. This force (F) is proportional to the product of these valences and inversely proportional to the square of the distance (r) between the two. The force is also inversely proportional to a dimensionless term called the dielectric constant (): (See Note: Coulomb’s Law)

Because the dielectric constant of water is ~40-fold greater than that of the hydrocarbon interior of the cell membrane, the electrostatic force between ions is reduced by a factor of ~40 in water compared with membrane lipid.

If we were to move the Na⁺ ion from the extracellular to the intracellular fluid without the aid of any proteins, the Na⁺ would have to cross the membrane by “dissolving” in the lipids of the bilayer. However, the energy required to transfer the Na⁺ ion from water (high ) to the interior of a phospholipid membrane (low ) is ~36 kcal/mol. This value is 60-fold higher than molecular thermal energy at room temperature. Thus, the probability that an ion would dissolve in the bilayer (i.e., partition from an aqueous solution into the lipid interior of a cell membrane) is essentially zero. This analysis explains why inorganic ions cannot readily cross a phospholipid membrane without the aid of other molecules such as specialized transporters or channel proteins, which provide a favorable polar environment for the ion as it moves across the membrane (Fig. 6-2).

Figure 6-2 Formation of an aqueous pore by an ion channel. The dielectric constant of water ( = 80) is ~40-fold higher than the dielectric constant of the lipid bilayer ( = 2).

Membrane potentials can be measured by use of microelectrodes and voltage-sensitive dyes

The voltage difference across the cell membrane, or the membrane potential (V_m), is the difference between the electrical potential in the cytoplasm (γ_i) and the electrical potential in the extracellular space (Ψ_o). Figure 6-3A shows how to measure V_m with an intracellular electrode. The sharp tip of a microelectrode is gently inserted into the cell and measures the transmembrane potential with respect to the electrical potential of the extracellular solution, defined as ground (i.e., γ_o = 0). If the cell membrane is not damaged by electrode impalement and the impaled membrane seals tightly around the glass, this technique provides an accurate measurement of V_m. Such a voltage measurement is called an intracellular recording.

Figure 6-3 Recording of membrane potential. (C and D, Data modified from Grinvald A: Real-time optical mapping of neuronal activity: From single growth cones to the intact mammalian brain. Annu Rev Neurosci 1985; 8:263-305. © Annual Reviews www.annualreviews.org.)(See Note: Methods for Recording Membrane Potential)

For an amphibian or mammalian skeletal muscle cell, resting V_m is typically about –90 mV, meaning that the interior of the resting cell is ~90 mV more negative than the exterior. There is a simple relationship between the electrical potential difference across a membrane and another parameter, the electrical field (E): (See Note: Electrical Fields and Potentials)

Accordingly, for a V_m of –0.1 V and a membrane thickness of a = 4 nm (i.e., 40 × 10⁻⁸ cm), the magnitude of the electrical field is ~250,000 V/cm. Thus, despite the small transmembrane voltage, cell membranes actually sustain a very large electrical field. Later, we discuss how this electrical field influences the activity of a particular class of membrane signaling proteins called voltage-sensitive ion channels (see Chapter 7).

Skeletal muscle cells, cardiac cells, and neurons typically have resting membrane potentials of approximately –60 to –90 mV; smooth muscle cells have membrane potentials in the range of –55 mV; and the V_m of the human erythrocyte is only about –9 mV. However, certain bacteria and plant cells have transmembrane voltages as large as –200 mV. For very small cells such as erythrocytes, small intracellular organelles such as mitochondria, and fine processes such as the synaptic endings of neurons, V_m cannot be directly measured with a microelectrode. Instead, spectroscopic techniques allow the membrane potentials of such inaccessible membranes to be measured indirectly (Fig. 6-3B). This technique involves labeling of the cell or membrane with an appropriate organic dye molecule and monitoring of the absorption or fluorescence of the dye. The optical signal of the dye molecule can be independently calibrated as a function of V_m. Whether V_m is measured directly by a microelectrode or indirectly by a spectroscopic technique, virtually all biological membranes have a nonzero membrane potential. This transmembrane voltage is an important determinant of any physiological transport process that involves the movement of charge.

Measurements of V_m have shown that many types of cells are electrically excitable. Examples of excitable cells are neurons, muscle fibers, heart cells, and secretory cells of the pancreas. In such cells, V_mexhibits characteristic time-dependent changes in response to electrical or chemical stimulation. When the cell body, or soma, of a neuron is electrically stimulated, electrical and optical methods for measuring V_m detect an almost identical response at the cell body (Fig. 6-3C). The optical method provides the additional insight that the V_m changes are similar but delayed in the more distant neuronal processes that are inaccessible to a microelectrode (Fig. 6-3D). When the cell is not undergoing such active responses, V_m usually remains at a steady value that is called the resting potential. In the next section, we discuss the origin of the membrane potential and lay the groundwork for understanding its active responses.

Membrane potential is generated by ion gradients

In Chapter 5, we introduced the concept that some integral membrane proteins are electrogenic transporters in that they generate an electrical current that sets up an electrical potential across the membrane. One class of electrogenic transporters includes the adenosine triphosphate (ATP)–dependent ion pumps. These proteins use the energy of ATP hydrolysis to produce and to maintain concentration gradients of ions across cell membranes. In animal cells, the Na-K pump and Ca²⁺ pump are responsible for maintaining normal gradients of Na⁺, K⁺, and Ca²⁺. The reactions catalyzed by these ion transport enzymes are electrogenic because they lead to separation of charge across the membrane. For example, enzymatic turnover of the Na-K pump results in the translocation of three Na⁺ ions out of the cell and two K⁺ ions into the cell, with a net movement of one positive charge out of the cell. In addition to electrogenic pumps, cells may express secondary active transporters that are electrogenic, such as the Na⁺/glucose cotransporter (see Chapter 5).

It may seem that the inside negative V_m originates from the continuous pumping of positive charges out of the cell by the electrogenic Na-K pump. The resting potential of large cells—whose surface-to-volume ratio is so large that ion gradients run down slowly—is maintained for a long time even when metabolic poisons block ATP-dependent energy metabolism. This finding implies that an ATP-dependent pump is not the immediate energy source underlying the membrane potential. Indeed, the squid giant axon normally has a resting potential of –60 mV. When the Na-K pump in the giant axon membrane is specifically inhibited with a cardiac glycoside (see Chapter 5), the immediate positive shift in V_m is only 1.4 mV. Thus, in most cases, the direct contribution of the Na-K pump to the resting V_m is very small.

In contrast, many experiments have shown that cell membrane potentials depend on ionic concentration gradients. In a classic experiment, Paul Horowicz and Alan Hodgkin measured the V_m of a frog muscle fiber with an intracellular microelectrode. The muscle fiber was bathed in a modified physiological solution in which SO²⁻₄ replaced Cl⁻, a manipulation that eliminates the contribution of anions to V_m. In the presence of normal extracellular concentrations of K⁺ and Na⁺ for amphibians ([K⁺]_o = 2.5 mM and [Na⁺]_o = 120 mM), the frog muscle fiber has a resting V_m of approximately –94 mV. As [K⁺]_o is increased above 2.5 mM by substitution of K⁺ for Na⁺, V_m shifts in the positive direction. As [K⁺]_o is decreased below 2.5 mM, V_m becomes more negative (Fig. 6-4). For [K⁺]_o values greater than 10 mM, the V_mmeasured in Figure 6-4 is approximately a linear function of the logarithm of [K⁺]_o. Numerous experiments of this kind have demonstrated that the immediate energy source of the membrane potential is not the active pumping of ions but rather the potential energy stored in the ion concentration gradients themselves. Of course, it is the ion pumps—and the secondary active transporters that derive their energy from these pumps—that are responsible for generating and maintaining these ion gradients.

Figure 6-4 Dependence of resting potential on extracellular K⁺ concentration in a frog muscle fiber. The slope of the linear part of the curve is 58 mV for a 10-fold increase in [K⁺]_o. Note that the horizontal axis for [K⁺]_o is plotted using a logarithmic scale. (Data from Hodgkin AL, Horowicz P: The influence of potassium and chloride ions on the membrane potential of single muscle fibers. J Physiol [Lond] 1959; 148:127-160.)

One way to investigate the role of ion gradients in determining V_m is to study this phenomenon in an in vitro (cell-free) system. Many investigators have used an artificial model of a cell membrane called a planar lipid bilayer. This system consists of a partition with a hole ~200 μm in diameter that separates two chambers filled with aqueous solutions (Fig. 6-5). It is possible to paint a planar lipid bilayer having a thickness of only ~4 nm across the hole, thereby sealing the partition. By incorporating membrane proteins and other molecules into planar bilayers, one can study the essential characteristics of their function in isolation from the complex metabolism of living cells. Transmembrane voltage can be measured across a planar bilayer with a voltmeter connected to a pair of Ag/AgCl electrodes that are in electrical contact with the solution on each side of the membrane through salt bridges. This experimental arrangement is much like an intracellular voltage recording, except that both sides of the membrane are completely accessible to manipulation.

Figure 6-5 Diffusion potential across a planar lipid bilayer containing a K⁺-selective channel. (See Note: Planar Lipid Bilayers)

The ionic composition of the two chambers on opposite sides of the bilayer can be adjusted to simulate cellular concentration gradients. Suppose that we put 4 mM KCl on the left side of the bilayer and 155 mM KCl on the right side to mimic, respectively, the external and internal concentrations of K⁺ for a mammalian muscle cell. To eliminate the osmotic flow of water between the two compartments (see Chapter 5), we also add a sufficient amount of a nonelectrolyte (e.g., mannitol) to the side with 4 mM KCl. We can make the membrane selectively permeable to K⁺ by introducing purified K⁺ channels or K⁺ionophores into the membrane. Assuming that the K⁺ channels are in an open state and are impermeable to Cl⁻, the right (“internal”) compartment quickly becomes electrically negative with respect to the left (“external”) compartment because positive charge (i.e., K⁺) diffuses from high to low concentration. However, as the negative voltage develops in the right compartment, the negativity opposes further K⁺efflux from the right compartment. Eventually, the voltage difference across the membrane becomes so negative as to halt further net K⁺ movement. At this point, the system is in equilibrium, and the transmembrane voltage reaches a value of 92.4 mV, right-side negative. In the process of generating the transmembrane voltage, a separation of charge has occurred in such a way that the excess positivecharge on the left side (low [K⁺]) balances the same excess negative charge on the right side (high [K⁺]). Thus, the stable voltage difference (⁻92.4 mV) arises from the separation of K⁺ ions from their counterions (in this case Cl⁻) across the bilayer membrane. (See Note: An Impermeant Bilayer; Ionophores)

For mammalian cells, nernst potentials for ions typically range from –100 mV for K⁺ to +100 mV for Ca²⁺

The model system of a planar bilayer (impermeable membrane), unequal salt solutions (ionic gradient), and an ion-selective channel (conductance pathway) contains the minimal components essential for generating a membrane potential. The hydrophobic membrane bilayer is a formidable barrier to inorganic ions and is also a poor conductor of electricity. Poor conductors are said to have a high resistance to electrical current, in this case, ionic current. On the other hand, ion channels act as molecular conductors of ions. They introduce a conductance pathway into the membrane and lower its resistance.

In the planar bilayer experiment of Figure 6-5, V_m originates from the diffusion of K⁺ down its concentration gradient. Membrane potentials that arise by this mechanism are called diffusion potentials. At equilibrium, the diffusion potential of an ion is the same as the equilibrium potential (E_X) given by the Nernst equation previously introduced as Equation 5-8.

The Nernst equation predicts the equilibrium membrane potential for any concentration gradient of a particular ion across a membrane. E_X is often simply referred to as the Nernst potential. The Nernst potentials for K⁺, Na⁺, Ca²⁺, and Cl⁻, respectively, are written as E_K, E_Na, E_Ca, and E_Cl.

The linear portion of the plot of V_m versus the logarithm of [K⁺]_o for a frog muscle cell (Fig. 6-4) has a slope that is ~58.1 mV for a 10-fold change in [K⁺]_o, as predicted by the Nernst equation. Indeed, if we insert the appropriate values for R and F into Equation 6-4, select a temperature of 20°C, and convert the logarithm base e (ln) to the logarithm base 10 (log₁₀), we obtain a coefficient of –58.1 mV, and the Nernst equation becomes

For a negative ion such as Cl⁻, where z = –1, the sign of the slope is positive:

For Ca²⁺ (z = +2), the slope is half of –58.1 mV, or approximately –30 mV. Note that a Nernst slope of 58.1 mV is the value for a univalent ion at 20°C. For mammalian cells at 37°C, this value is 61.5 mV.

At [K⁺]_o values above ~10 mM, the magnitude of V_m and the slope of the plot in Figure 6-4 are virtually the same as those predicted by the Nernst equation (Equation 6-5), suggesting that the resting V_m of the muscle cell is almost equal to the K⁺ diffusion potential. When V_m follows the Nernst equation for K⁺, the membrane is said to behave like a potassium electrode because ion-specific electrodes monitor ion concentrations according to the Nernst equation.

Table 6-1 lists the expected Nernst potentials for K⁺, Na⁺, Ca²⁺, Cl⁻, and HCO⁻₃ as calculated from the known concentration gradients of these physiologically important inorganic ions for mammalian skeletal muscle and a typical non-muscle cell. For a mammalian muscle cell with a V_m of –80 mV, E_K is ~15 mV more negative than V_m, whereas E_Na and E_Ca are about +67 and +123 mV, respectively, far more positive than V_m. E_Cl is ~9 mV more negative than V_min muscle cells but slightly more positive than the typical V_m of –60 mV in most other cells.

Table 6-1 Ion Concentration Gradients in Mammalian Cells

What determines whether the cell membrane potential follows the Nernst equation for K⁺ or Cl⁻ rather than that for Na⁺ or Ca²⁺? As we shall see in the next two sections, the membrane potential is determined by the relative permeabilities of the cell membrane to the various ions.

Currents carried by ions across membranes depend on the concentration of ions on both sides of the membrane, the membrane potential, and the permeability of the membrane to each ion

Years before ion channel proteins were discovered, physiologists devised a simple but powerful way to predict the membrane potential, even if several different kinds of permeable ions are present at the same time. The first step, which we discuss in this section, is to compute an ionic current, that is, the movement of a single ion species through the membrane. The second step, which we describe in the following section, is to obtain V_m by summating the currents carried by each species of ion present, assuming that each species moves independently of the others.

The process of ion permeation through the membrane is called electrodiffusion because both electrical and concentration gradients are responsible for the ionic current. To a first approximation, the permeation of ions through most channel proteins behaves as though the flow of these ions follows a model based on the Nernst-Planck electrodiffusion theory, which was first applied to the diffusion of ions in simple solutions. This theory leads to an important equation in medical physiology called the constant-field equation, which predicts how V_m will respond to changes in ion concentration gradients or membrane permeability. Before introducing this equation, we first consider some important underlying concepts and assumptions.

Without knowing the molecular basis for ion movement through the membrane, we can treat the membrane as a “black box” characterized by a few fundamental parameters (Fig. 6-6). We must assume that the rate of ion movement through the membrane depends on (1) the external and internal concentrations of the ion X ([X]_o and [X]_i, respectively), (2) the transmembrane voltage (V_m), and (3) a permeability coefficient for the ion X (P_X). In addition, we make four major assumptions about how the ion X behaves in the membrane:

The membrane is a homogeneous medium with a thickness a.

The voltage difference varies linearly with distance across the membrane (Fig. 6-6). This assumption is equivalent to stating that the electrical field—that is, the change in voltage with distance—is constant throughout the thickness of the membrane. This requirement is therefore called the constant-field assumption (See Note: Electrical Fields and Potentials)

The movement of an ion through the membrane is independent of the movement of any other ions. This assumption is called the independence principle.

The permeability coefficient P_X is a constant (i.e., it does not vary with the chemical or electrical driving forces). P_X (units: cm/s) is defined as P_X = D_Xβ/a. D_X is the diffusion coefficient for the ion in the membrane, β is the membrane/water partition coefficient for the ion, and a is the thickness of the membrane. Thus, P_X describes the ability of an ion to dissolve in the membrane (as described by β) and to diffuse from one side to the other (as described by D_X) over the distance a.

Figure 6-6 Electrodiffusion model of the cell membrane.

With these assumptions, we can calculate the current carried by a single ion X (I_X) through the membrane by using the basic physical laws that govern (1) the movement of molecules in solution (Fick’s law of diffusion; see Equation 5-13), (2) the movement of charged particles in an electrical field (electrophoresis), and (3) the direct proportionality of current to voltage (Ohm’s law). The result is the Goldman-Hodgkin-Katz (GHK) current equation, named after the pioneering electrophysiologists who applied the constant-field assumption to Nernst-Planck electrodiffusion:

I_X, or the rate of ions moving through the membrane, has the same units as electrical current: amperes (coulombs per second). Thus, the GHK current equation relates the current of ion X through the membrane to the internal and external concentrations of X, the transmembrane voltage, and the permeability of the membrane to X. The GHK equation thus allows us to predict how the current carried by X depends on V_m. This current-voltage (I-V) relationship is important for understanding how ionic currents flow into and out of cells. (See Note: Calculating an Ionic Current from an Ionic Flow)

Figure 6-7A shows how the K⁺ current (I_K) depends on V_m, as predicted by Equation 6-7 for the normal internal (155 mM) and external (4.5 mM) concentrations of K⁺. By convention, a current of ions flowing into the cell (inward current) is defined in electrophysiology as a negative-going current, and a current flowing out of the cell (outward current) is defined as a positive current. (As in physics, the direction of current is always the direction of movement of positive charge. This convention means that an inward flow of Cl⁻ is an outward current.) For the case of 155 mM K⁺ inside the cell and 4.5 mM K⁺ outside the cell, an inward current is predicted at voltages that are more negative than –95 mV, and an outward current is predicted at voltages that are more positive than –95 mV (Fig. 6-7A). The value of –95 mV is called the reversal potential (V_rev) because it is precisely at this voltage that the direction of current reverses (i.e., the net current equals zero). If we set I_K equal to zero in Equation 6-7 and solve for V_rev, we find that the GHK current equation reduces to the Nernst equation for K⁺ (Equation 6-5). Thus, the GHK current equation for an ion X predicts a reversal potential (V_rev) equal to the Nernst potential (E_X) for that ion; that is, the current is zero when the ion is in electrochemical equilibrium. At V_m values more negative than V_rev, the net driving force on a cation is inward; at voltages that are more positive than V_rev, the net driving force is outward. (See Note: Shape of the I-V Relationship)

Figure 6-7 Current-voltage relationships predicted by the GHK current equation. A, The curve is the K⁺ current predicted from the GHK equation (Equation 7)—assuming that the membrane is perfectly selective for K⁺—for a [K⁺]_i of 155 mM and a [K⁺]_o of 4.5 mM. The dashed line represents the current that can be expected if both [K⁺]_i and [K⁺]_o were 155 mM (Ohm’s law). B, The curve is the Na⁺ current predicted from the GHK equation—assuming that the membrane is perfectly selective for Na⁺—for a [Na⁺]_i of 12 mM and a [Na⁺]_o of 145 mM. The dashed line represents the current that can be expected if both [Na⁺]_i and [Na⁺]_o were 145 mM.

Figure 6-7B shows the analogous I-V relationship predicted by Equation 6-7 for physiological concentrations of Na⁺. In this case, the Na⁺ current (I_Na) is inward at V_m values more negative than V_rev (⁺67 mV) and outward at voltages that are more positive than this reversal potential. Here again, V_rev is the same as the Nernst potential, in this case, E_Na.

Membrane potential depends on ionic concentration gradients and permeabilities

In the preceding section, we discussed how to use the GHK current equation to predict the current carried by any single ion, such as K⁺ or Na⁺. If the membrane is permeable to the monovalent ions K⁺, Na⁺, and Cl⁻—and only to these ions—the total ionic current carried by these ions across the membrane is the sum of the individual ionic currents:

The individual ionic currents given by Equation 6-7 can be substituted into the right-hand side of Equation 6-8. Note that for the sake of simplicity, we have not considered currents carried by electrogenic pumps or other ion transporters; we could have added extra “current” terms for such electrogenic transporters. At the resting membrane potential (i.e., V_m is equal to V_rev), the sum of all ion currents is zero (i.e., I_total = 0). When we set I_total to zero in the expanded Equation 6-8 and solve for V_rev, we get an expression known as the GHK voltage equation or the constant-field equation:

Because we derived Equation 6-9 for the case of I_total = 0, it is valid only when zero net current is flowing across the membrane. This zero net current flow is the steady-state condition that exists for the cellular resting potential, that is, when V_m equals V_rev. The logarithmic term of Equation 6-9 indicates that resting V_m depends on the concentration gradients and the permeabilities of the various ions. However, resting V_m depends primarily on the concentrations of the most permeant ion. (See Note: Contribution of Ions to Membrane Potential)

The principles underlying Equation 6-9 show why the plot of V_m versus [K⁺]_o in Figure 6-4, which summarizes data obtained from a frog muscle cell, bends away from the idealized Nernst slope at very low values of [K⁺]_o. Imagine that we expose a mammalian muscle cell to a range of [K⁺]_o values, always substituting extracellular K⁺ for Na⁺, or vice versa, so that the sum of [K⁺]_o and [Na⁺]_o is kept fixed at its physiological value of 4.5 + 145 = 149.5 mM. To simplify matters, we assume that the membrane permeability to Cl⁻ is very small (i.e., P_Cl ≅ 0). We can also rearrange Equation 6-9 by dividing the numerator and denominator by P_K and representing the ratio P_Na/P_K as α. At 37°C, this simplified equation becomes

Figure 6-8 shows that when α is zero—that is, when the membrane is impermeable to Na⁺—Equation 6-10 reduces to the Nernst equation for K⁺ (Equation 6-4), and the plot of V_m versus the logarithm of [K⁺]_ois linear. If we choose an α of 0.01, however, the plot bends away from the ideal at low [K⁺]_o values. This bend reflects the introduction of a slight permeability to Na⁺. As we increase this P_Na further by increasing α to 0.03 and 0.1, the curvature becomes even more pronounced. Thus, as predicted by Equation 6-10, increasing the permeability of Na⁺ relative to K⁺ tends to shift V_m in a positive direction, toward E_Na. In some skeletal muscle cells, an α of 0.01 best explains the experimental data.

Figure 6-8 Dependence of the resting membrane potential on [K⁺]_o and on the P_Na/P_K ratio, α. The blue line describes an instance in which there is no Na⁺ permeability (i.e., P_Na/P_K = 0). The three orange curves describe the V_m predicted by Equation 6-10 for three values of α greater than zero and assumed values of [Na⁺]_o, [Na⁺]_i, and [K⁺]_i for skeletal muscles, as listed in Table 6-1. The deviation of these orange curves from linearity is greater at low values of [K⁺]_o, where the [Na⁺]_o is relatively larger.

The constant-field equation (Equation 6-9) and simplified relationships derived from it (e.g., Equation 6-10) show that steady-state V_m depends on the concentrations of all permeant ions, weighted according to their relative permeabilities. Another very useful application of the constant-field equation is determination of the ionic selectivity of channels. If the I-V relationship of a particular channel is determined in the presence of known gradients of two different ions, one can solve Equation 6-10 to obtain the permeability ratio, α, of the two ions from the measured value of the reversal potential, V_rev.

In general, the resting potential of most vertebrate cells is dominated by high permeability to K⁺, which accounts for the observation that the resting V_m is typically close to E_K. The resting permeability to Na⁺and Ca²⁺ is normally very low. Skeletal muscle cells, cardiac cells, and neurons typically have resting membrane potentials ranging from –60 to –90 mV. As discussed in Chapter 7, excitable cells generate action potentials by transiently increasing Na⁺ or Ca²⁺ permeability and thus driving V_m in a positive direction toward E_Na or E_Ca. A few cells, such as vertebrate skeletal muscle fibers, have high permeability to Cl⁻, which therefore contributes to the resting V_m. This high permeability also explains why the Cl⁻ equilibrium potential in skeletal muscle is essentially equivalent to the resting potential (Table 6-1).

ELECTRICAL MODEL OF A CELL MEMBRANE

The cell membrane model includes various ionic conductances and electromotive forces in parallel with a capacitor

The current carried by a particular ion varies with membrane voltage, as described by the I-V relationship for that ion (e.g., Fig. 6-7). This observation suggests that the contribution of each ion to the electrical properties of the cell membrane may be represented by elements of an electrical circuit. The various ionic gradients across the membrane provide a form of stored electrical energy, much like that of a battery. In physics, the voltage source of a battery is known as an emf (electromotive force). The equilibrium potential of a given ion can be considered an emf for that ion. Each of these batteries produces its own ionic current across the membrane, and the sum of these individual ionic currents is the total ionic current (Equation 6-8). According to Ohm’s law, the emf or voltage (V) and current (I) are directly related to each other by the resistance (R)—or inversely to the reciprocal of resistance, conductance(G):

Thus, the slopes of the lines in Figure 6-7 represent conductances because I = GV. In a membrane, we can represent each ionic permeability pathway with an electrical conductance. Ions with high permeability or conductance move through a low-resistance pathway; ions with low permeability move through a high-resistance pathway. For cell membranes, V_m is measured in millivolts, membrane current (I_m) is given in amps per square centimeter of membrane area, and membrane resistance (R_m) has the units of ohms × square centimeter. Membrane conductance (G_m), the reciprocal of membrane resistance, is thus measured in units of ohms⁻¹ per square centimeter, which is equivalent to siemens per square centimeter. (See Note: Electrical Units)

Currents of Na⁺, K⁺, Ca²⁺, and Cl⁻ generally flow across the cell membrane through distinct pathways. At the molecular level, these pathways correspond to specific types of ion channel proteins (Fig. 6-9A). It is helpful to model the electrical behavior of cell membranes by a circuit diagram (Fig. 6-9B). The electrical current carried by each ion flows through a separate parallel branch of the circuit that is under the control of a variable resistor and an emf. For instance, the variable resistor for K⁺ represents the conductance provided by K⁺ channels in the membrane (G_K). The emf for K⁺ corresponds to E_K. Similar parallel branches of the circuit in Figure 6-9B represent the other physiologically important ions. Each ion provides a component of the total conductance of the membrane, so G_K + G_Na + G_Ca + G_Cl sum to G_m.

Figure 6-9 Electrical properties of model cell membranes. A, Four different ion channels are arranged in parallel in the cell membrane. B, The model represents each channel in A with a variable resistor. The model represents the Nernst potential for each ion as a battery in series with each variable resistor. Also shown is the membrane capacitance, which is parallel with each of the channels. C, On the left is an idealized capacitor, which is formed by two parallel plates, each with an area A and separated by a distance d. On the right is a capacitor that is formed by a piece of lipid membrane. The two plates are, in fact, the electrolyte solutions on either side of the membrane.

The GHK voltage equation (Equation 6-9) predicts steady-state V_m, provided the underlying assumptions are valid. We can also predict steady-state V_m (i.e., when the net current across the membrane is zero) with another, more general equation that assumes channels behave like separate ohmic conductances:

Thus, V_m is the sum of equilibrium potentials (E_X), each weighted by the ion’s fractional conductance (e.g., G_X/G_m).

One more parallel element, a capacitor, is needed to complete our model of the cell membrane as an electrical circuit. A capacitor is a device that is capable of storing separated charge. Because the lipid bilayer can maintain a separation of charge (i.e., a voltage) across its ~4-nm width, it effectively functions as a capacitor. In physics, a capacitor that is formed by two parallel plates separated by a distance acan be represented by the diagram in Figure 6-9C. When the capacitor is charged, one of the plates bears a charge of +Q and the other plate has a charge of –Q. Such a capacitor maintains a potential difference (V) between the plates. Capacitance (C) is the magnitude of the charge stored per unit potential difference: (See Note: Charge Carried by a Mole of Monovalent Ions)

Capacitance is measured in units of farads (F); 1 farad = 1 coulomb/volt. For the particular geometry of the parallel-plate capacitor in Figure 6-9C, capacitance is directly proportional to the surface area (A) of one side of a plate, to the dielectric constant of the medium between the two plates (), and to the permittivity constant (_o), and it is inversely proportional to the distance (a) separating the plates. (See Note: Electrical Units)

Because of its similar geometry, the cell membrane has a capacitance that is analogous to that of the parallel-plate capacitor. The capacitance of 1 cm² of most cell membranes is ~1 μF; that is, most membranes have a specific capacitance of 1 μF/cm². We can use Equation 6-14 to estimate the thickness of the membrane. If we assume that the average dielectric constant of a biological membrane is = 5 (slightly greater than the value of 2 for pure hydrocarbon), Equation 6-14 gives a value of 4.4 nm for a—that is, the thickness of the membrane. This value is quite close to estimates of membrane thickness that have been obtained by other physical techniques.

The separation of relatively few charges across the bilayer capacitance maintains the membrane potential

We can also use the capacitance of the cell membrane to estimate the amount of charge that the membrane actually separates in generating a typical membrane potential. For example, consider a spherical cell with a diameter of 10 μm and a [K⁺]_i of 100 mM. This cell needs to lose only 0.004% of its K⁺ to charge the capacitance of the membrane to a voltage of –61.5 mV. This small loss of K⁺ is clearly insignificant in comparison with a cell’s total ionic composition and does not significantly perturb concentration gradients. In general, cell membrane potentials are sustained by a very small separation of charge. (See Note: Charge Separation Required to Generate the Membrane Potential)

Because of the existence of membrane capacitance, total membrane current has two components (Fig. 6-9), one carried by ions through channels, and the other carried by ions as they charge the membrane capacitance.

Ionic current is directly proportional to the electrochemical driving force (Ohm’s law)

Figure 6-10 compares the equilibrium potentials for Na⁺, K⁺, Ca²⁺, and Cl⁻ with a resting V_m of –80 mV. In our discussion of Figure 6-7, we saw that I_K or I_Na becomes zero when V_m equals the reversal potential, which is the same as the E_X or emf for that ion. When V_m is more negative than E_X, the current is negative or inward, whereas when V_m is more positive than E_X, the current is positive or outward. Thus, the ionic current depends on the difference between the actual V_m and E_X. In fact, the ionic current through a given conductance pathway is proportional to the difference (V_m – E_X), and the proportionality constant is the ionic conductance (G_X):

Figure 6-10 Electrochemical driving forces acting on various ions. For each ion, we represent both the equilibrium potential (e.g., E_Na = +67 mV) as a horizontal bar and the net driving force for the ion (e.g., V_m – E_Na = –147 mV) as an arrow assuming a resting potential (V_m) of –80  mV. The values for the equilibrium potentials are those for mammalian skeletal muscle in Table 6-1 as well as a typical value for E_Cl in a non-muscle cell. (See Note: Electrochemical Driving Forces and Predicted Direction of Net Fluxes)

This equation simply restates Ohm’s law (Equation 6-11). The term (V_m – E_X) is often referred to as the driving force in electrophysiology. In our electrical model of the cell membrane (Fig. 6-9), this driving force is represented by the difference between V_m and the emf of the battery. The larger the driving force, the larger the observed current. Returning to the I-V relationship for K⁺ in Figure 6-7A, when V_m is more positive than E_K, the driving force is positive, producing an outward (i.e., positive) current. Conversely, at V_m values more negative than E_K, the negative driving force produces an inward current. (See Note: Conductance Varies with Driving Force)

In Figure 6-10, the arrows represent the magnitudes and directions of the driving forces for the various ions. For a typical value of the resting potential (⁻80 mV), the driving force on Ca²⁺ is the largest of the four ions, followed by the driving force on Na⁺. In both cases, V_m is more negative than the equilibrium potential and thus draws the positive ion into the cell. The driving force on K⁺ is small. V_m is more positive than E_K and thus pushes K⁺ out of the cell. In muscle, V_m is slightly more positive than E_Cl and thus draws the anion inward. In most other cells, however, V_m is more negative than E_Cl and pushes the Cl⁻ out.

Capacitative current is proportional to the rate of voltage change

The idea that ionic channels can be thought of as conductance elements (G_X) and that ionic current (I_X) is proportional to driving force (V_m – E_X) provides a framework for understanding the electrical behavior of cell membranes. Current carried by inorganic ions flows through open channels according to the principles of electrodiffusion and Ohm’s law, as explained above. However, when V_m is changing—as it does during an action potential—another current due to the membrane capacitance also shapes the electrical responses of cells. This current, which flows only while V_m is changing, is called the capacitative current. How does a capacitor produce a current? When voltage across a capacitor changes, the capacitor either gains or loses charge. This movement of charge onto or off the capacitor is an electrical (i.e., the capacitative) current.

The simple membrane circuit of Figure 6-11A, which is composed of a capacitor (C_m) in parallel with a resistor (R_m) and a switch, can help illustrate how capacitative currents arise. Assume that the switch is open and that the capacitor is initially charged to a voltage of V₀, causing a separation of charge (Q) across the capacitor. According to the definition of capacitance (Equation 6-13), the charge stored by the capacitor is a product of capacitance and voltage.

Figure 6-11 Capacitative current through a resistance-capacitance (RC) circuit.

As long as the switch in the circuit remains open, the capacitor maintains this charge. However, when the switch is closed, the charge on the capacitor discharges through the resistor, and the voltage difference between the circuit points labeled “In” and “Out” decays from V₀ to a final value of zero (Fig. 6-11B). This voltage decay follows an exponential time course. The time required for the voltage to fall to 37% of its initial value is a characteristic parameter called the time constant (τ), which has units of time: (See Note: Units for the “Time Constant”)

Thus, the time course of the decay in voltage is

Figure 6-11C shows that the capacitative current (I_C) is zero before the switch is closed, when the voltage is stable at V₀. When we close the switch, charge begins to flow rapidly off the capacitor, and the magnitude of I_C is maximal. As the charge on the capacitor gradually falls, the rate at which charge flows off the capacitor gradually falls as well until I_C is zero at “infinite” time. Note, however, that V and I_Crelax with the same time constant.

In Figure 6-11, current and voltage change freely. Figure 6-12 shows two related examples in which either current or voltage is abruptly changed to a fixed value, held constant for a certain time, and returned to the original value. This pattern is called a square pulse. In Figure 6-12A, we control, or “clamp,” the current and allow the voltage to follow. When we inject a square pulse of current across the membrane, the voltage changes to a new value with a rounded time course determined by the RC value of the membrane. In Figure 6-12B, we clamp voltage and allow the current to follow. When we suddenly change voltage to a new value, a transient capacitative current flows as charge flows onto the capacitor. The capacitative current is maximal at the beginning of the square pulse, when charge flows most rapidly onto the capacitor, and then falls off exponentially with a time constant of RC. When we suddenly decrease the voltage to its original value, I_C flows in the direction opposite that observed at the beginning of the pulse. Thus, I_C appears as brief spikes at the beginning and end of the voltage pulse. (See Note: Time Constant of Capacitative Current)

Figure 6-12 Voltage and current responses caused by the presence of a membrane capacitance. (See Note: Two-Electrode Voltage Clamping)

A voltage clamp measures currents across cell membranes

Electrophysiologists use a technique called voltage clamping to deduce the properties of ion channels. In this method, specialized electronics are used to inject current into the cell to set the membrane voltage to a value that is different from the resting potential. The device then measures the total current required to clamp V_m to this value. A typical method of voltage clamping involves impaling a cell with two sharp electrodes, one for monitoring V_m and one for injecting the current. Figure 6-13A illustrates how the technique can be used with a Xenopus (i.e., frog) oocyte. When the voltage-sensing electrode detects a difference from the intended voltage, called the command voltage, a feedback amplifier rapidly injects opposing current to maintain a constant V_m. The magnitude of the injected current needed to keep V_mconstant is equal, but opposite in sign, to the membrane current and is thus an accurate measurement of the total membrane current (I_m). (See Note: Voltage and Current Transients Due to Membrane Capacitance)

Figure 6-13 Two-electrode voltage clamp. A, Two microelectrodes impale a Xenopus oocyte. One electrode monitors membrane potential (V_m) and the other passes enough current (I_m) through the membrane to clamp V_m to a predetermined command voltage (V_command). B, In the left panel, the membrane is clamped for 10 ms to a hyperpolarized potential (40 mV more negative). Because a hyperpolarization does not activate channels, no ionic currents flow. Only transient capacitative currents flow after the beginning and end of the pulse. In the right panel, the membrane is clamped for 10 ms to a depolarized potential (40 mV more positive). Because the depolarization opens voltage-gated Na⁺ channels, a large inward Na⁺ current flows, in addition to the transient capacitative current. Adding the transient capacitative currents in the left panel to the total current in the right panel, thereby canceling the transient capacitative currents (I_c), yields the pure Na⁺ current shown at the bottom in the right panel.

I_m is the sum of the individual currents through each of the parallel branches of the circuit in Figure 6-9B. For a simple case in which only one type of ionic current (I_X) flows through the membrane, I_m is simply the sum of the capacitative current and the ionic current:

Equation 6-19 suggests a powerful way to analyze how ionic conductance (G_X) changes with time. For instance, if we abruptly change V_m to another value and then hold V_m constant (i.e., we clamp the voltage), the capacitative current flows for only a brief time at the voltage transition and disappears by the time that V_m reaches its new steady value (Fig. 6-12B). Therefore, after I_C has decayed to zero, any additional changes in I_m must be due to changes in I_X. Because V_m is clamped and the ion concentrations do not change (i.e., E_X is constant), only one parameter on the right side of Equation 6-19 is left free to vary, G_X. In other words, we can directly monitor changes in G_X because this conductance parameter is directly proportional to I_m when V_m is constant (i.e., clamped).

Figure 6-13B shows examples of records from a typical voltage-clamp experiment on an oocyte expressing voltage-gated Na⁺ channels. In this experiment, a cell membrane is initially clamped at a resting potential of –80 mV. V_mis then stepped to –120 mV for 10 ms (a step of –40 mV) and finally returned to –80 mV. Such a negative-going V_m change is called a hyperpolarization. With this protocol, only brief spikes of current are observed at the beginning and end of the voltage step and are due to the charging of membrane capacitance. No current flows in between these two spikes.

What happens if we rapidly change V_m in the opposite direction by shifting the voltage from –80 to –40 mV (a step of +40 mV)? Such a positive-going change in V_m from a reference voltage is called a depolarization. In addition to the expected transient capacitative current, a large, inward, time-dependent current flows. This current is an ionic current and is due to the opening and closing kinetics of a particular class of channels called voltage-gated Na⁺channels, which open only when V_m is made sufficiently positive. We can remove the contribution of the capacitative current to the total current by subtracting the inverse of the rapid transient current recorded during the hyperpolarizing pulse of the same magnitude. The remaining slower current is inward (i.e., downward) and represents I_Na, which is directly proportional to G_Na (Equation 6-19).

The ionic current in Figure 6-13B (lower right panel) is called a macroscopic current because it is due to the activity of a large population of channels sampled from a whole cell. Why did we observe Na⁺current only when we shifted V_m in a positive direction from the resting potential? As described later, such Na⁺ channels are actually members of a large family of voltage-sensitive ion channels that are activated by depolarization. A current activated by depolarization is commonly observed when an electrically excitable cell, such as a neuron, is voltage clamped under conditions in which Na⁺ is the sole extracellular cation.

A modern electrophysiological method called whole-cell voltage clamping involves the use of a single microelectrode both to monitor V_m and to pass current into the cell. In this method, a glass micropipette electrode with a smooth, fire-polished tip that is ~1 μm in diameter is pressed onto the surface of a cell (Fig. 6-14A). One then applies slight suction to the inside of the pipette, forming a high-resistance seal between the circular rim of the pipette tip and the cell membrane. The piece of sealed membrane is called a patch, and the pipette is called a patch pipette. Subsequent application of stronger suction causes the patch to rupture, creating a continuous, low-resistance pathway between the inside of the cell and the pipette. In this configuration, whole-cell currents can be recorded (Fig. 6-14B). Because single cells can be dissociated from many different tissues and studied in culture, this method has proved very powerful for analyzing the physiological roles of various types of ion channels and their regulation at the cellular level. The approach for recording whole-cell currents with a patch pipette was introduced by Erwin Neher and Bert Sakmann, who received the Nobel Prize in Physiology or Medicine in 1991. (See Note: Erwin Neher and Bert Sakmann)

Figure 6-14 Patch-clamp methods. (Data from Hamill OP, Marty A, Neher E, et al: Improved patch-clamp techniques for high-resolution current recording from cells and cell-free membrane patches. Pflugers Arch 1981; 391:85-100.)

The patch-clamp technique resolves unitary currents through single-channel molecules

Voltage-clamp studies of ionic currents at the whole-cell (i.e., macroscopic) level led to the question of how many channels are involved in the production of a macroscopic current. Electrophysiologists realized that if the area of a voltage-clamped membrane was reduced to a very small fraction of the cell surface area, it might be possible to observe the activity of a single channel.

This goal was realized when Neher and Sakmann developed the patch-clamp technique. Applying suction to a patch pipette creates a high-resistance seal between the glass and the cell membrane, as described in the preceding section for whole-cell voltage clamping. However, instead of rupturing the enclosed membrane patch as in the whole-cell approach, the tiny membrane area within the patch is kept intact so that one can record current from channels within the patch. A current recording made with the patch pipette attached to a cell is called a cell-attached recording (Fig. 6-14A). After a cell-attached patch is established, it is also possible to withdraw the pipette from the cell membrane to produce an inside-out patch configuration by either of two methods (Fig. 6-14E or Fig. 6-14F–H). In this configuration, the intracellular surface of the patch membrane faces the bath solution. One can also arrive at the opposite orientation of the patch of membrane by starting in the cell-attached configuration (Fig. 6-14A), rupturing the cell-attached patch to produce a whole-cell configuration (Fig. 6-14B), and then pulling the pipette away from the cell (Fig. 6-14C). When the membranes reseal, the result is an outside-out patch configuration in which the extracellular patch surface faces the bath solution (Fig. 6-14D).

The different patch configurations summarized in Figure 6-14 are useful for studying drug-channel interactions, receptor-mediated processes, and biochemical regulatory mechanisms that take place at either the inner or external surface of cell membranes.

Single-channel currents sum to produce macroscopic membrane currents

Figure 6-15 illustrates the results of a patch-clamp experiment that is analogous to the macroscopic experiment on the right-hand side of Figure 6-13B. Under the diagram of the voltage step in Figure 6-15Aare eight current records, each of which is the response to an identical step of depolarization lasting 45 ms. The smallest, nearly rectangular transitions of current correspond to the opening and closing of a single Na⁺ channel. When two or three channels in the patch are open simultaneously, the measured current level is an integral multiple of the single-channel or “unitary” transition.

Figure 6-15 Outside-out patch recordings of Na⁺ channels. A, Eight single-current responses—in the same patch on a myotube (a cultured skeletal muscle cell)—to a depolarizing step in voltage (cytosolic side of patch negative). B, Average current. The record in black shows the average of many single traces, such as those in A. The blue record shows the average current when tetrodotoxin blocks the Na⁺ channels. (Data from Weiss RE, Horn R: Single-channel studies of TTX-sensitive and TTX-resistant sodium channels in developing rat muscle reveal different open channel properties. Ann NY Acad Sci 1986; 479:152-161.)

The opening and closing process of ion channels is called gating. Patch-clamp experiments have demonstrated that macroscopic ionic currents represent the gating of single channels that have discrete unitary currents. Averaging consecutive, microscopic Na⁺ current records produces a time-dependent current (Fig. 6-15B) that has the same shape as the macroscopic I_m shown in Figure 6-13B. If one does the experiment in the same way but blocks Na⁺channels with tetrodotoxin, the averaged current is equivalent to the zero current level, indicating that Na⁺ channels are the only channels present within the membrane patch.

Measuring the current from a single channel in a patch at different clamp voltages reveals that the size of the discrete current steps depends on voltage (Fig. 6-16A). Plotting the unitary current (i) of single channels versus the voltage at which they were measured yields a single-channel I-V relationship (Fig. 6-16B) that is similar to the one we discussed earlier for macroscopic currents (Fig. 6-7). This single-channel I-V relationship reverses direction at a certain potential (V_rev), just like a macroscopic current does. If a channel is permeable to only one type of ion present in the solution, the V_rev equals the equilibrium potential for that ion (E_X). However, if the channel is permeable to more than one ion, the single-channel reversal potential depends on the relative permeabilities of the various ions, as described by the GHK voltage equation (Equation 6-9).

Figure 6-16 Voltage dependence of currents through single Cl⁻ channels in outside-out patches. A, The channel is a γ-aminobutyric acid A (GABA_A) receptor channel, which is a Cl⁻ channel activated by GABA. Identical solutions, containing 145 mM Cl⁻, were present on both sides of the patch. B, The magnitudes of the single-channel current transitions (y-axis) vary linearly with voltage (x-axis). (Data from Bormann J, Hamill OP, Sakmann B: Mechanism of anion permeation through channels gated by glycine and γ-aminobutyric acid in mouse cultured spinal neurones. J Physiol [Lond] 1987; 385:243-286.)

The slope of a single-channel I-V relationship is a measure of the conductance of a single channel, the unitary conductance (g). Every type of ion channel has a characteristic value of g under a defined set of ionic conditions. The single-channel conductance of most known channel proteins is in the range of 1 to 500 picosiemens (pS), where 1 pS is equal to 10⁻¹² ohm⁻¹.

How do we know that the unitary current in fact corresponds to just a single channel? One good indication is that such conductance measurements are close to the theoretical value expected for ion diffusion through a cylindrical, water-filled pore that is long enough to span a phospholipid membrane and that has a diameter large enough to accept an ion. The unitary conductance of typical channels corresponds to rates of ion movement in the range of 10⁶ to 10⁸ ions per second per channel at 100 mV of driving force. These rates of ion transport through single channels are many orders of magnitude greater than typical rates of ion transport by ion pumps (~500 ions/s) or by the fastest ion cotransporters and exchangers (~50,000 ions/s). The high ionic flux through channels places them in a unique class of transport proteins whose unitary activity can be resolved by patch-clamp current recordings.

Single channels can fluctuate between open and closed states

When a channel has opened from the closed state (zero current) to its full unitary conductance value, the channel is said to be in the open state. Channel gating thus represents the transition between closed and open states. A single-channel record is actually a record of the conformational changes of a single protein molecule as monitored by the duration of opening and closing events.

Examination of the consecutive records of a patch recording, such as that in Figure 6-15A, shows that the gating of a single channel is a probabilistic process. On average, there is a certain probability that a channel will open at any given time, but such openings occur randomly. For example, the average record in Figure 6-15B indicates that the probability that the channels will open is highest ~4 ms after the start of the depolarization.

The process of channel gating can be represented by kinetic models that are similar to the following hypothetical two-state scheme.

This scheme indicates that a channel can reversibly change its conformation between closed (C) and open (O) states according to first-order reactions that are determined by an opening rate constant (k_o) and a closing rate constant (k_c). The probability of channel opening (P_o) is the fraction of total time that the channel is in the open state.

We already have seen in Figure 6-15 that the average of many single-channel records from a given patch produces a time course that is similar to a macroscopic current recorded from the same cell. The same is true for the sum of the individual single-channel current records. This conclusion leads to an important principle: macroscopic ionic current is equal to the product of the number of channels (N) within the membrane area, the unitary current of single channels, and the probability of channel opening:

Comparison of the magnitude of macroscopic currents recorded from large areas of voltage-clamped membrane with the magnitude of unitary current measured by patch techniques indicates that the surface density of ion channels typically falls into the range of 1 to 1000 channels per square micrometer of cell membrane, depending on the channel and cell type.

MOLECULAR PHYSIOLOGY OF ION CHANNELS

Classes of ion channels can be distinguished on the basis of electrophysiology, pharmacological and physiological ligands, intracellular messengers, and sequence homology

Mammalian cells express a remarkable array of ion channels. One way of making sense of this diversity is to classify channels according to their functional characteristics. Among these characteristics are electrophysiological behavior, inhibition or stimulation by various pharmacological agents, activation by extracellular agonists, and modulation by intracellular regulatory molecules. In addition, we can classify channels by structural characteristics, such as amino acid sequence homology and the kinds of subunits of which they are composed.

Electrophysiology This approach consists of analyzing ionic currents by voltage-clamp techniques and then characterizing channels on the basis of ionic selectivity, dependence of gating on membrane potential, and kinetics of opening and closing.

One of the most striking differences among channels is their selectivity for various ions. Indeed, channels are generally named according to which ion they are most permeable to—for example, Na⁺ channels, Ca²⁺ channels, K⁺channels, and Cl⁻ channels.

Another major electrophysiological characteristic of channels is their voltage dependence. In electrically excitable cells (e.g., nerve, skeletal muscle, heart), a major class of channels becomes activated—and often inactivated—as a steep function of V_m. For example, the Na⁺ channel in nerve and muscle cells is increasingly more activated as V_m becomes more positive (see Chapter 7). Such voltage-gated channels are generally highly selective for Na⁺, Ca²⁺, or K⁺.

Channels are also distinguished by the kinetics of gating behavior. For example, imagine two channels, each with an open probability (P_o) of 0.5. One channel might exhibit openings and closures with a duration of 1 second each on average, whereas the other may have the same P_o with openings and closures of 1 ms each on average. Complex gating patterns of some channels are characterized by bursts of many brief openings, followed by longer silent periods.

Pharmacological Ligands Currents that are virtually indistinguishable by electrophysiological criteria can sometimes be distinguished pharmacologically. For example, subtypes of voltage-gated Na⁺ channels can be distinguished by their sensitivity to the peptide toxin μ-conotoxin, which is produced by Conus geographus, a member of a family of venomous marine mollusks called Cone snails. This toxin strongly inhibits the Na⁺ channels of adult rat skeletal muscle but has little effect on the Na⁺ channels of neurons and cardiac myocytes. Another conotoxin (ω-conotoxin) from another snail specifically inhibits voltage-gated Ca²⁺ channels in the spinal cord. A synthetic version of this conotoxin (ziconotide) is available for treatment of neuropathic pain in patients.

Physiological Ligands Some channels are characterized by their unique ability to be activated by the binding of a particular molecule termed an agonist. For example, at the vertebrate neuromuscular junction, a channel called the nicotinic acetylcholine (ACh) receptor opens in response to the binding of ACh released from a presynaptic nerve terminal. Other agonist-gated channels are activated directly by neurotransmitters such as glutamate, serotonin (5-hydroxytryptamine [5-HT]), γ-aminobutyric acid (GABA), and glycine.

Intracellular Messengers Channels can be categorized by their physiological regulation by intracellular messengers. For example, increases in [Ca²⁺]_i stimulate some ionic currents, in particular K⁺ and Cl⁻currents. Channels underlying such currents are known as Ca²⁺-gated K⁺ channels and Ca²⁺-gated Cl⁻ channels, respectively. Another example is seen in the plasma membrane of light-sensitive rod cells of the retina, in which a particular type of channel is directly activated by intracellular cyclic guanosine monophosphate.

The four functional criteria—electrophysiology, pharmacology, extracellular agonists, and intracellular regulators—for characterizing channels are not mutually exclusive. For example, one of the major types of Ca²⁺-activated K⁺channels is also voltage-gated.

Sequence Homology The diversity of channels implied by functional criteria ultimately requires a molecular biological approach to channel classification. Such an approach began in the 1970s and 1980s with the biochemical purification of channel proteins. Membrane biochemists originally used rich, natural sources of ion channels, such as the electrical organs of the torpedo ray and Electrophorus eel, to isolate channel proteins such as the nicotinic ACh receptor (see Chapter 8) and the voltage-gated Na⁺ channel, respectively. Amino acid sequencing of purified channel proteins provided the information needed to prepare oligonucleotide probes for isolating the coding sequences of channels from cDNA clones, in turn derived from mRNA. Genes coding for many different types of ion channel proteins have been cloned in this way. This work has confirmed that the diversity of channels foreshadowed by physiological assays corresponds to an enormous diversity at the molecular level.

When annotation of the human genome is completed, a definitive catalogue of ion channels of significance to medical physiology will eventually be available. On the basis of the data bank of mammalian channel protein sequences, we recognize at least 24 distinct families of channel proteins (Table 6-2). Despite rapid progress in the cloning of channels, detailed knowledge of the three-dimensional structures of channels is emerging more slowly because of the difficulty in crystallizing membrane proteins for x-ray crystallographic analysis. However, molecular information gleaned from sequence analysis and structural information on several channel proteins has revealed a number of important themes that we discuss in the remainder of this chapter.

Table 6-2 Major Families of Human Ion Channel Proteins

Many channels are formed by a radially symmetric arrangement of subunits or domains around a central pore

The essential function of a channel is to facilitate the passive flow of ions across the hydrophobic membrane bilayer according to the electrochemical gradient. This task requires the channel protein to form an aqueous pore. The ionophore gramicidin is a small peptide that forms a unique helix dimer that spans the membrane; the hollow cylindrical region inside the helix is the channel pore. Another interesting type of channel structure is that of the porinchannel proteins (see Chapter 5), which are present in the outer membranes of mitochondria and gram-negative bacteria. This protein forms a large pore through the center of a barrel-like structure; the 16 staves of the barrel are formed by 16 strands of the protein, each of which are in a β-sheet conformation. However, the structural motifs of a hole through a helix (gramicidin) or a hole through a 16-stranded β barrel (porin) appear to be exceptions rather than the rule.

For the majority of eukaryotic channels, the aqueous pores are located at the center of an oligomeric rosette-like arrangement of homologous subunits in the plane of the membrane (Fig. 6-17). Each of these subunits, in turn, is a polypeptide that weaves through the membrane several times. In some cases, the channel is not a true homo-oligomer or hetero-oligomer but rather a pseudo-oligomer: the subunits are replaced by a single polypeptide composed of repetitive homologous domains. The rosette-like arrangement of these domains surrounds a central pore. In the case of gap junction channels and ACh receptor channels, which we discuss in the following two sections, it has been possible to use cryoelectron microscopy to construct images of the channel from membrane preparations in which the proteins exist in a densely packed two-dimensional crystalline array. This technique has provided low-resolution pictures that show how the polypeptide chains of the channel proteins weave through the membrane. (See Note: Rosette Arrangement of Channel Subunits)

Figure 6-17 Structure of ion channels. Most ion channels consist of four to six subunits that are arranged like a rosette in the plane of the membrane. The channel can be made up of (1) identical, distinct subunits (homo-oligomer); (2) distinct subunits that are homologous but not identical (hetero-oligomer); or (3) repetitive subunit-like domains within a single polypeptide (pseudo-oligomer). In any case, these subunits surround the central pore of the ion channel. Note that each subunit is itself made up of several transmembrane segments.

Gap junction channels are made up of two connexons, each of which has six identical subunits called connexins

Gap junctions are protein channels that connect two cells with a large, unselective pore (~1.5 nm in diameter) that allows ions and small molecules as large as 1 kDa to pass between cells. These channels have been found in virtually all mammalian cells with only a few exceptions, such as adult skeletal muscle and erythrocytes. For example, gap junctions interconnect hepatocytes of the liver, cardiac muscle fibers of the heart and smooth muscle of the gut, β cells of the pancreas, and epithelial cells in the cornea of the eye, to name just a few. Gap junctions provide pathways for chemical communication and electrical coupling between cells. The basic structure deduced for a gap junction from the liver is shown in Figure 6-18A. The gap junction comprises two apposed hexameric structures called connexons, one contributed by each cell. These connexons contact each other to bridge a gap of ~3 nm between the two cell membranes. Each connexon has six identical subunits surrounding a central pore, so-called radial hexameric symmetry. Each of these subunits is an integral membrane protein called connexin (Cx) that has a molecular mass of 26 to 46 kDa. The aqueous pore formed at the center of the six connexin subunits has a diameter that is estimated to be 1.2 to 2 nm. At the cytoplasmic end of the connexon, the pore appears to open to a wider funnel-shaped entrance.

Figure 6-18 Gap junction channels. In C, the left panel shows the preparation of the two cells, each of which is voltage clamped by means of a patch pipette in the whole-cell configuration (see Fig. 6-14). Because Cell 1 is clamped to –40 mV and Cell 2 is clamped to –80 mV, current flows through the gap junctions from Cell 1 to Cell 2. The right panel shows that the current recorded by the electrode in Cell 1 is the mirror image of the current recorded in Cell 2. The fluctuating current transitions represent the openings and closings of individual gap junction channels. (Data from Veenstra RD, DeHaan RL: Measurement of single channel currents from cardiac gap junctions. Science 1986; 233:972-974.)

A given connexon hexamer in a particular cell membrane may be formed from a single connexin (homomeric) or a mixture of different connexin proteins (heteromeric). The apposition of two identical connexon hexamers forms a homotypic channel; the apposition of dissimilar connexon hexamers forms a heterotypic channel. Such structural variation in the assembly of connexons provides for greater diversity of function and regulation.

In one mode of regulation, increases in [Ca²⁺]_i can cause gap junctions to close. For Ca²⁺-dependent gating, it is possible to visualize a structural change in the conformation of the connexon. In the absence of Ca²⁺, the pore is in an open configuration and the connexin subunits are tilted 7 to 8 degrees from an axis perpendicular to the plane of the membrane. After the addition of Ca²⁺, the pore closes and the subunits move to a more parallel alignment (Fig. 6-18B). The gating of the gap junction channel may thus correspond to a conformational change that involves concerted tilting of the six connexin subunits to widen (open) or to constrict (close) the pore.

The gating properties of gap junctions can be studied by measuring electrical currents through gap junctions, using two patch electrodes simultaneously placed in a pair of coupled cells (Fig. 6-18C). When the two cells are clamped at different values of V_m, so that current flows from one cell to the other through the gap junctions, the current measured in either cell fluctuates as a result of the opening and closing of individual gap junction channels. Because the amount of current that enters one cell is the same as the amount of current that leaves the other cell, the current fluctuations in the two cells are mirror images of one another. Studies of this type have shown that increases in [Ca²⁺]_i or decreases in intracellular pH generally favor the closing of gap junction channels. In addition, gating of gap junction channels can be regulated by the voltage difference between the coupled cells as well as by phosphorylation.

Nicotinic acetylcholine receptor channels are α₂βγδ pentamers made up of four homologous subunits

In contrast to the gap junction channel, which is a hexamer made up of six identical subunits, the nicotinic ACh receptor is a pentameric channel comprising four different homologous subunits. The α subunit is represented twice; therefore, the pentamer has a subunit composition of α₂βγδ. The nicotinic ACh receptor channel is located in a specialized region of the skeletal muscle membrane, at the postsynaptic nerve terminal. The receptor responds to ACh released from the nerve terminals by opening and allowing cations to flow through its pore (see Chapter 8). Images of the ACh receptor show a pentameric radial symmetry that corresponds to a rosette-like arrangement of the five subunits (Fig. 6-19). When viewed from the extracellular face of the membrane, a hole with a diameter of 2 to 2.5 nm is observed in the center of the rosette and corresponds to the extracellular entrance to the cation-selective channel. The structural changes induced by ACh binding that control opening and closing of the channel appear to occur in a central region of the protein that lies within the plane of the lipid bilayer. We discuss the structure and function of this particular class of channels, an example of ligand-gated channels (or agonist-gated channels), in more detail in Chapter 8. (See Note: The Nicotinic Acetylcholine Receptor)

Figure 6-19 Three-dimensional image of the nicotinic ACh receptor channel. (Data from Toyoshima C, Unwin N: Ion channel of acetylcholine receptor reconstructed from images of postsynaptic membranes. Nature 1988; 336:247-250.)

An evolutionary tree called a dendrogram illustrates the relatedness of ion channels

A comparison of amino acid sequences of channels and the nucleotide sequences of genes that encode them provides insight into the molecular evolution of these proteins. The current human genome database contains at least 256 different genes encoding channel proteins. Like other proteins, specific isoforms of channels are differentially expressed in different parts of cells in various tissues and at certain stages of development. In particular, many different kinds of channels are expressed in the brain. In the central nervous system, the great diversity of ion channels provides a means of specifically and precisely regulating the complex electrical activity of a huge number of neurons that are connected in numerous functional pathways.

As an example of the diversity and species interrelatedness of a channel family, consider the connexins. Figure 6-20A compares 14 sequences of homologous proteins that are members of the connexin family. Like many other proteins, connexins are encoded by a family of related genes that evolved by gene duplication and divergence. In the connexin family, various subtypes are named according to their protein molecular masses. Thus, rat Cx32 refers to a rat connexin with a protein molecular mass of ~32 kDa. The various connexins differ primarily in the length of the intracellular C-terminal domain.

Figure 6-20 Family tree of hypothetical evolutionary relationships among connexin sequences of gap junction channels. In A, The dendrogram is based on amino acid sequence differences among 14 connexins in various species. The summed length of the horizontal line segments connecting two connexins is a measure of the degree of difference between the two connexins. In B, the dendrogram is based strictly on human sequences. (A, Data from Dermietzel R, Spray DC: Gap junctions in the brain: Where, what type, how many and why? Trends Neurosci 1993; 16:186-192. B, Data from White TW: Nonredundant gap junction functions. News Physiol Sci 2003; 18:95-99.)

By aligning connexin sequences according to identical amino acids and computing the relative similarity of each pair of connexin sequences, it is possible to reconstruct a hypothetical family tree of evolutionary relationships. Such a tree is called a dendrogram. The one in Figure 6-20A includes 9 rat, 2 human, 1 chicken, and 2 frog (Xenopus) connexins. The branch lengths of the tree correspond to relative evolutionary distances as measured by sequence divergence. Clusters of sequences in the tree represent highly related groups of proteins. The connexin tree indicates that the Cx32 genes from rats and humans are very closely related, differing by only 4 amino acids of a total of 284 residues. Thus, these Cx32 proteins probably represent the same functional genes in these two species—orthologous genes. The closely related Cx43 genes from the rat and human are also likely to be orthologues.

Charcot-Marie-Tooth Disease

Many human genetic diseases have been identified in which the primary defect has been mapped to mutations of ion channel proteins. For example, Charcot-Marie-Tooth disease is a rare form of hereditary neuropathy that involves the progressive degeneration of peripheral nerves. Patients with this inherited disease have been found to have various mutations in the human gene for one of the gap junction proteins, connexin 32 (Cx32), which is located on the X chromosome. Cx32 appears to be involved in forming gap junctions between the folds of Schwann cell membranes. These Schwann cells wrap around the axons of peripheral nerves and form a layer of insulating material called myelin, which is critical for the conduction of nerve impulses. Apparently, mutations in Cx32 interfere with the normal function of these cells and result in the disruption of myelin and axonal degeneration. Some of these mutations have been identified at the amino acid level by gene sequencing. Many other human diseases involve either a genetic defect of a particular channel protein or an autoimmune response directed against a channel protein (Table 6-2). (See Note: Charcot-Marie-Tooth Disease; Genetic and Autoimmune Ion Channel Defects)

A sequence analysis restricted to only human connexin genes reveals three families (Fig. 6-20B): CJA, CJB, and CJC. Members of a family of channel proteins often exhibit different patterns of tissue expression. For example, Cx32 is expressed in the liver, Schwann cells, and oligodendrocytes, whereas Cx43 is expressed in heart and many other tissues.

The functional properties of cloned channel genes are generally consistent with the classification of channel subtypes based on molecular evolution. For example, ion channels that share the property of being voltage gated also share sequence homology of their voltage-sensing domain. We discuss voltage-gated channels in Chapter 7.

Hydrophobic domains of channel proteins can predict how these proteins weave through the membrane

From sequence information of many ion channels, a number of common structural principles emerge. Like other integral membrane proteins (see Chapter 2), channel proteins generally have several segments of hydrophobic amino acids, each long enough (~20 amino acids) to span the lipid bilayer as an α helix. If the channel has N membrane-spanning segments, it also has N + 1 hydrophilic domains of variable length that connect or terminate the membrane spans. Putative transmembrane segments are normally identified by hydropathy analysis (see Table 2-1), which identifies long segments of hydrophobic amino acid residues. In some cases, supporting biochemical evidence indicates that such domains are actually embedded in the membrane. By analogy to a few membrane proteins of known three-dimensional structure, such as the bacterial photosynthetic reaction center, it is generally presumed that such hydrophobic transmembrane domains have an α-helical conformation. The intervening hydrophilic segments that link the transmembrane regions together are presumed to form extracellular and intracellular protein domains that contact the aqueous solution.

The primary sequences of channel proteins are often schematically represented by hypothetical folding diagrams, such as that shown in Figure 6-21A for Cx32, one of the connexins that we have already discussed. Cx32 is a polypeptide of 284 amino acids that contains four identifiable hydrophobic transmembrane segments. In connexins, these transmembrane segments are known as M1, M2, M3, and M4. Biochemical evidence indicates that the N-terminal and C-terminal hydrophilic segments of connexin are located on the cytoplasmic side of the membrane and that the M3 domain is involved in forming part of the gap junction pore. Mutations in Cx32 can lead to a rare hereditary neuropathy known as Charcot-Marie-Tooth disease (see the box on this disease).

Figure 6-21 Membrane topology features of ion channel proteins.

Protein superfamilies, subfamilies, and subtypes are the structural bases of channel diversity

Table 6-2 summarizes the basic functional and structural aspects of currently recognized families of the pore-forming subunits of human ion channel proteins. The table (1) groups these channels into structurally related protein families; (2) describes their properties; (3) lists the assigned human gene symbols, number of genes, and protein names; (4) summarizes noted physiological functions; (5) lists human diseases associated with the corresponding ion channels; and (6) provides a reference to Figure 6-21 that indicates the hypothetical membrane topology. Because the membrane topology diagrams in Figure 6-21 are based primarily on hydropathy analysis, they should be considered “best-guess” representations unless the structure has been confirmed by direct approaches (e.g., inward rectifier K⁺ channels and ClC chloride channels). We briefly summarize major aspects of the molecular physiology of human ion channel families, in the order of their presentation in Table 6-2. More detailed functional information on many of these channels is discussed in numerous chapters of this text. (See Note: Voltage-Gated Channels)

Connexins We discussed these channels earlier in the section on gap junctions, in Figures 6-18 and 6-20, and in the box on Charcot-Marie-Tooth disease.

K⁺ Channels These channels form the largest and most diverse family of ion channels and share a common K⁺-selective pore domain containing two transmembrane segments (TMs). The family includes five distinct subfamilies, all of which we will discuss in Chapter 7: (1) Kv voltage-gated K⁺ channels, (2) small- and intermediate-conductance Ca²⁺-activated K⁺ channels (SK_Ca and IK_Ca), (3) large-conductance Ca²⁺-and voltage-activated K⁺ channels (BK_Ca), (4) inward rectifier K⁺ channels (Kir), and (5) dimeric tandem two-pore K⁺ channels (K2P). For the first two subfamilies, the pore-forming complex consists of four subunits, each of which contains six TMs denoted S1 to S6 (Fig. 6-21Band 6-21C). BK_Ca channels are similar to Kv channels but have an additional S0 TM (Fig. 6-21D). The Kir channels consist of four subunits, each of which contains two TMs analogous to S5 and S6 in the Kv channels (Fig. 6-21E). The K2P channels appear to be a tandem duplication of Kir channels (Fig. 6-21F).

HCN, CNG, and TRP Channels Hyperpolarization-activated, cyclic nucleotide–gated cation channels (HCN channels, Fig. 6-21G) play a critical role in electrical automaticity of the heart (see Chapter 21) and rhythmically firing neurons of the brain. CNG channels form a family of cation-selective channels that are directly activated by intracellular cyclic guanosine monophosphate (cGMP) or cyclic adenosine monophosphate (cAMP). These channels play an important role in visual and olfactory sensory transduction. The CNGs have the same basic S1 through S6 motif as K⁺ channels, but they contain a unique cyclic nucleotide–binding domain at the C terminus (Fig. 6-21H). Transient receptor potential cation channels (TRP channels, Fig. 6-21I) are divided into at least six subfamilies: TRPA (for ankyrin like), TRPC (for canonical), TRPM (for melastatin), TRPML (for mucolipin), TRPP (for polycystin 2), and TRPV (for vanilloid). One TRPV is activated by capsaicin, the “hot” ingredient of chili peppers; a TRPM responds to menthol, the “cool”-tasting substance in eucalyptus leaves. The capsaicin receptor TRP channel appears to function in pain and temperature sensation.

Voltage-Gated Na⁺ Channels The pore-forming subunits of voltage-gated Na⁺ channels (Nav, see Chapter 7) comprise four domains (I, II, III, and IV), each of which contains the S1 to S6 structural motif (Fig. 6-21J) that is homologous to Kv K⁺ channel monomers. Because domains I to IV of Nav channels are organized as four tandem repeats within the membrane, these domains are referred to as pseudosubunits. The Nav channels are associated with a unique family of auxiliary β-subunits, which are known to modify the gating behavior and membrane localization of the channel-forming α-subunit.

Voltage-Gated Ca²⁺ Channels The pore-forming subunits of voltage-gated Ca²⁺ channels (Cav, see Chapter 7) are analogous to those for the Nav channels. Like Nav channels, Cav channels (Fig. 6-21K) are multisubunit complexes consisting of accessory proteins in addition to the channel-forming subunits.

Ligand-Gated Channels The agonist-activated channels are also represented by three large and diverse gene families. The pentameric Cys-loop receptor family (Fig. 6-21L) includes cation-or Cl⁻-selective ion channels that are activated by binding of ACh (see Chapter 8), serotonin, GABA, and glycine (see Chapter 13). Glutamate-activated cation channels (Fig. 6-21M) include two subfamilies of excitatory AMPA-kainate and NMDA receptors (see Chapter 13). Purinergic ligand-gated cation channels (Fig. 6-21N) are activated by binding of extracellular ATP and other nucleotides (see Chapters 20 and 34).

Other Ion Channels Amiloride-sensitive Na⁺ channels (ENaC) are prominent in Na⁺-transporting epithelia (Fig. 6-21O). The cystic fibrosis transmembrane conductance regulator (CFTR, see Chapter 5) is a Cl⁻channel (Fig. 6-21P) that is a member of the ABC protein family. The unrelated ClC family of Cl⁻ channels are dimeric (Fig. 6-21Q). Table 6-2 includes two types of Ca²⁺ release channels. ITPR (see Chapter 3) is present in the endoplasmic reticulum membrane and is gated by the intracellular messenger inositol 1,4,5-trisphosphate (Fig. 6-21R). RYR (see Chapter 9) is located in the sarcoplasmic reticulum membrane of muscle and plays a critical role in the release of Ca²⁺ during muscle contraction (Fig. 6-21S). Finally, a recently discovered family of Ca²⁺-selective channel proteins known as ORAI store-operated Ca²⁺ channels (Fig. 6-21T) has been found to play a role in entry of extracellular Ca²⁺ across the plasma membrane linked to IP₃ metabolism and depletion of intracellular Ca²⁺ from the endoplasmic reticulum of non-excitable cells (see p. 257). (See Note: Structure of ClC Channels)

REFERENCES

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Wei CJ, Xu X, Lo CW: Connexins and cell signaling in development and disease. Annu Rev Cell Dev Biol 2004; 20:811-838.

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Ho K, Nichols CG, Lederer J, et al: Cloning and expression of an inwardly rectifying ATP-regulated potassium channel. Nature 1993; 362:31-38.

Sigworth FJ, Neher E: Single Na-channel currents observed in cultured rat muscle cells. Nature 1980; 287:447-449.

Ressot C, Bruzzone R: Connexin channels in Schwann cells and the development of the X-linked form of Charcot-Marie-Tooth disease. Brain Res Rev 2000; 32:192-202.