Medical Physiology, 3rd Edition

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:

image

(6-1)

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. imageN6-1 This force () is proportional to the product of these valences and inversely proportional to the square of the distance (a) between the two. The force is also inversely proportional to a dimensionless term called the dielectric constant (εr):

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Coulomb's Law

Contributed by Ed Moczydlowski

The attractive electrostatic force between two charged particles of opposite sign and the repulsive electrostatic force between two charged particles of the same sign are described by Coulomb's law. The coulombic force between two interacting particles with charges of q1 and q2 is

image

(NE 6-1)

The above equation shows that the electrostatic force is directly proportional to the product of the charges and is inversely proportional to the square of the distance, a, between them. ε0 is a physical constant called the permittivity of free space (or the vacuum permittivity) and is equal to 8.854 × 10−12 C2N−1m−2, where C is coulomb, N is newton, and m is meter. The denominator of the equation also includes a dimensionless parameter called the dielectric constant (εr), also known as the relative permittivity. The dielectric constant of a vacuum is defined as 1.0. The dielectric constant is a property that depends on the polarizability of the medium surrounding the two charges. Polarizability refers to the ability of molecules of the medium to orient themselves around ions to reduce electrostatic interactions. Polar water molecules are able to solvate ions effectively by orienting themselves around ions in solutions and thereby reducing coulombic forces between neighboring ions. The dielectric constant of water is therefore relatively high and has a value of ~80. For a nonpolar hydrocarbon, such as decane or the alkyl-chain interior of a phospholipid bilayer, ε is comparatively low and has a value of ~2.

image

(6-2)

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 an 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 an Na+ ion from water (high ε) to the interior of a phospholipid membrane (low ε) is ~36 kcal/mole. 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).

image

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

Membrane potentials can be measured with microelectrodes as well as dyes or fluorescent proteins that are voltage sensitive

The voltage difference across the cell membrane, or the membrane potential (Vm), is the difference between the electrical potential in the cytoplasm (ψi) and the electrical potential in the extracellular space (ψo). Figure 6-3A shows how to measure Vm 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., ψo = 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 Vm. Such a voltage measurement is called an intracellular recording.

image

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 8:263–305, 1985. © Annual Reviews www.annualreviews.org.)imageN6-1

For an amphibian or mammalian skeletal muscle cell, resting Vm is typically about −90 mV, which means 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 electric field (E):imageN6-2

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Electric Fields and Potentials

Contributed by Ed Moczydlowski

A useful way to represent the electrical force () acting on a charged particle is by the concept of an electric field. The electric field (E) is defined as the force that a particle with positive charge q0 would sense in the vicinity of a charge source. Forces are vector parameters that are described by a magnitude and a direction. The direction of an electrostatic force is defined by the direction in which a positive charge would move: namely, away from a positively charged source or toward a negatively charged source. Similarly, the direction of an electric field is the direction in which a positive test charge would move within the field. The definition of an electric field is

image

(NE 6-2)

Although the net charge of any bulk system must be equal to zero, other forms of energy, such as chemical energy, can be used to separate positive and negative charges. The electrical potential (ψ) describes the potential energy that arises from such a separation of charge. The electrical potential difference (Δψ) is a measure of the work (W12) needed to move a test charge q0 between two points (1 and 2) in an electric field:

image

The electrical potential difference (V) is measured in volts (i.e., joules per coulomb). Because work is also equal to force times distance, the electrical potential difference may also be expressed in terms of the magnitude of the force required to move a test charge (q0) over a distance (d, in centimeters), along the same direction as the force. With the help of the preceding two equations, we can therefore define the electrical potential difference in terms of the electric field (volts per centimeter):

image

(NE 6-4)

Thus, the voltage difference between two points is the product of electric field and the distance between those points. Conversely, the electric field is the voltage difference divided by the distance:

image

(NE 6-5)

image

(6-3)

Accordingly, for a Vm of −0.1 V and a membrane thickness of a = 4 nm (i.e., 40 × 10−8cm), the magnitude of the electric field is ~250,000 V/cm. Thus, despite the small transmembrane voltage, cell membranes actually sustain a very large electric field. Below, we discuss how this electric field influences the activity of a particular class of membrane signaling proteins called voltage-gated ion channels (see pp. 182–199).

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 Vmof 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, Vm cannot be directly measured with a microelectrode. Instead, spectroscopic techniques allow the membrane potentials of such inaccessible membranes to be measured indirectly (see Fig. 6-3B). Such techniques involve 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 Vm.

Another approach for monitoring changes in Vm optically is to use cells that express genetically engineered voltage-sensing proteins that have been coupled to a modified version of the jellyfish green fluorescent protein (GFP). imageN6-3 For their work on GFP, Osamu Shimomura, Martin Chalfie, and Roger Tsien shared the 2008 Nobel Prize in Chemistry. imageN6-4 Whether Vm is measured directly by a microelectrode or indirectly by a spectroscopic technique, virtually all biological membranes are found to have a nonzero membrane potential. This transmembrane voltage is an important determinant of any physiological transport process that involves the movement of charge.

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Measuring Membrane Potential with Fluorescent Proteins

Contributed by Ed Moczydlowski

Figure 6-3 illustrates well-established methods for measuring the membrane potential of cells with a sharp intracellular microelectrode connected to a voltage amplifier or with the use of voltage-sensitive membrane dyes that can be calibrated to known values of Vm. In recent years it has become possible to express a genetically engineered fluorescent voltage-sensing protein in a cell of interest and record changes in Vm such as neuronal action potential signals by measuring the fluorescence signal. This method became feasible with the discovery of proteins that exhibit natural fluorescence in the visible spectral region of light. One such fluorescent protein is the green fluorescent protein (GFP) of the luminescent jellyfish Aequorea victoria. The discovery, determination of the mechanism of fluorescence, and wide application of GFP in biotechnology was recognized with the awarding of the 2008 Nobel Prize in Chemistry to Osamu Shimomura, Martin Chalfie, and Roger Tsien. imageN6-4

So that GFP could be used to measure Vm, the GFP gene was inserted into a nonconducting mutant of the Drosophila K+ channel, Shaker. Expression of the GFP-tagged Shaker results in observable green fluorescence in the membrane of a transfected cell, which changes fluorescence intensity in response to changes in Vm. More recently, a pair of GFP variants called CYP for cyan (blue) and YFP for yellow fluorescent protein were fused to the C terminus of a voltage-sensor domain of a voltage-sensing phosphatase enzyme (Ci-VSP) of Ciona intestinalis. The voltage-sensing domain of VSP is homologous to the S1 to S4 domains of voltage-gated channels. Expression of such fluorescent Ci-VSP in neurons allows Vm changes corresponding to a fast action potential to be recorded optically. The mechanism of Vmmeasurement by these engineered proteins involves voltage-dependent conformational changes of the protein that result in a spectroscopic change of the fluorescent protein tag. With improvement of these methods, it should be possible to optically record electrical signals from cells of appropriately engineered transgenic animals. This technique thus has the potential to greatly advance understanding of cellular electrophysiology.

References

Baker BJ, Mutoh H, Dimitrov D, et al. Genetically encoded fluorescent sensors of membrane potential. Brain Cell Biol. 2008;36:53–67.

Newman RH, Fosbrink MD, Zhang J. Genetically encodable fluorescent biosensors for tracking signaling dynamics in living cells. Chem Rev. 2011;111:3614–3666.

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Osamu Shimomura, Martin Chalfie, and Roger Tsien

For more information about Osamu Shimomura, Martin Chalfie, and Roger Tsien and the work that led to their Nobel Prize, visit http://www.nobelprize.org/nobel_prizes/chemistry/laureates/2008 (accessed October 2014).

Measurements of Vm 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, Vm exhibits 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 Vm detect an almost identical response at the cell body (see Fig. 6-3C). The optical method provides the additional insight that Vm changes are similar but delayed in the more distant neuronal processes inaccessible to a microelectrode (see Fig. 6-3D). When the cell is not undergoing such active responses, Vm 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

Chapter 5 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 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 Ca 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 (see pp. 115–117) 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 pp. 121–122).

It may seem that the inside negative Vm 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 p. 117), the immediate positive shift in Vm is only 1.4 mV. Thus, in most cases, the direct contribution of the Na-K pump to the resting Vm 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 Vm of a frog muscle fiber with an intracellular microelectrode. The muscle fiber was bathed in a modified physiological solution in which image replaced Cl, a manipulation that eliminates the contribution of anions to Vm. 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 Vm of approximately −94 mV. As [K+]o is increased above 2.5 mM by substitution of K+ for Na+Vm shifts in the positive direction. As [K+]o is decreased below 2.5 mM, Vm becomes more negative (Fig. 6-4). For [K+]o values >10 mM, the Vm measured 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.

image

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 148:127–160, 1959.)

One way to investigate the role of ion gradients in determining Vm 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 via salt bridges. This experimental arrangement is much like an intracellular voltage recording, except that both sides of the membrane are completely accessible to manipulation.

image

FIGURE 6-5 Diffusion potential across a planar lipid bilayer containing a K+-selective channel. imageN6-28

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Planar Lipid Bilayers

Contributed by Ed Moczydlowski

Planar bilayers can be readily formed by spreading a solution of phospholipids across a small hole in a thin plastic partition that separates two chambers filled with aqueous solution. The lipid solution seals the hole and spontaneously thins to produce a stable phospholipid bilayer. This artificial membrane, by itself, is structurally much like a cell membrane, except that it is completely devoid of protein. In the example in Figure 6-5, purified K+ channels have been incorporated into the membrane. Because of the large K+ gradient across this K+-permeable membrane, a transmembrane voltage of 92.4 mV (right-side negative) develops spontaneously across the membrane.

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 p. 128), we also add a sufficient amount of a nonelectrolyte (e.g., mannitol) to the side with 4 mM KCl. imageN6-5 We can make the membrane selectively permeable to K+ by introducing purified K+ channels or K+ionophores into the membrane. imageN6-6 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 that further net K+ movement halts. 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 positive charge 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.

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An Impermeant Bilayer

Contributed by Ed Moczydlowski

If a totally impermeant bilayer were not separating the two solutions, the unequal concentrations of KCl would lead to diffusion of the salt in the direction of high to low [KCl]. However, by sealing the hole in the partition with a pure lipid bilayer having no permeability to K+ or Cl, we ensure that the system does not have any separation of charge, and therefore the measured transmembrane voltage is 0 mV.

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Ionophores

Contributed by Ed Moczydlowski

We can create a perfectly K+-selective membrane by adding certain organic molecules, known as K+ ionophores, to a planar lipid bilayer. Examples are valinomycin and gramicidin. These molecules have the ability to partition into bilayers and catalyze the diffusion of K+ across phospholipid membranes. Valinomycin and gramicidin act by different mechanisms, but both allow a current of K+ ions to flow across membranes. Valinomycin, which is isolated from Streptomyces fulvissimus, is an example of a carrier molecule that binds K+ and literally ferries it across the lipid bilayer. On the other hand, gramicidin catalyzes K+ movement by the same basic mechanism that has been established for ion channel proteins in cell membranes. Gramicidin, a small, unusual peptide produced by Bacillus brevis, forms a water-filled pore across the membrane with a very small diameter (0.4 nm). The pore is small enough to permit only water molecules or K+ ions to move through in single file. Both gramicidin and valinomycin share another property of channel proteins, called ionic selectivity. These ionophores are strongly cation selective: they accept certain inorganic cations but not Cl or other anions.

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 6-5Vm 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 (EX) given by the Nernst equation previously introduced as Equation 5-8.

image

(6-4)

The Nernst equation predicts the equilibrium membrane potential for any concentration gradient of a particular ion across a membrane. EX is often simply referred to as the Nernst potential. The Nernst potentials for K+, Na+, Ca2+, and Cl are written as EKENaECa, and ECl, respectively.

The linear portion of the plot of Vm versus the logarithm of [K+]o for a frog muscle cell (see 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

image

(6-5)

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

image

(6-6)

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 Vm and the slope of the plot in Figure 6-4 are virtually the same as those predicted by the Nernst equation (see Equation 6-5), which suggests that the resting Vmof the muscle cell is almost equal to the K+ diffusion potential. When Vm 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 image as calculated from the known concentration gradients of these physiologically important inorganic ions for mammalian skeletal muscle and typical nonmuscle cells. For a mammalian muscle cell with a Vm of −80 mV, EK is ~15 mV more negative than Vm, whereas ENa and ECa are about +67 and +123 mV, respectively, far more positive than VmECl is ~9 mV more negative than Vm in muscle cells but slightly more positive than the typical Vm of −60 mV in most other cells.

TABLE 6-1

Ion Concentration Gradients in Mammalian Cells

ION

OUT (mM)

IN (mM)

OUT/IN

EX* (mV)

Skeletal Muscle

K+

4.5

155

0.026

−95

Na+

145

12

12

+67

Ca2+

1.0

10−4

10,000

+123

Cl

116

4.2

28

−89

image

24

12

2

−19

Most Other Cells

K+

4.5

120

0.038

−88

Na+

145.4

15

9.67

+61

Ca2+

1.0

10−4

10,000

+123

Cl

116

20

5.8

−47

image

24

15

1.6

−13

*Nernst equilibrium potential of X at 37°C.

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, Vm depends on the relative permeabilities of the cell membrane to the various ions and the concentrations of ions on both sides of the membrane. Thus, the stability of Vm depends on the constancy of plasma ion concentrations—an important aspect of the homeostasis of the milieu intérieur (see pp. 3–4). Changes in the ionic composition of blood plasma can therefore profoundly affect physiological function. For example, conditions of low or high plasma [K+]—termed hypokalemia and hyperkalemia (see pp. 792–793), respectively—result in neurological and cardiac impairment (see Box 37-1) due to changes in Vm of excitable cells.

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 Vm by summing 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 Vm 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 (Vm), and (3) a permeability coefficient for the ion X (PX). In addition, we make four major assumptions about how the ion X behaves in the membrane:

1. The membrane is a homogeneous medium with a thickness a.

2. The voltage difference varies linearly with distance across the membrane (see Fig. 6-6). This assumption is equivalent to stating that the electric field—that is, the change in voltage with distance—is constant imageN6-2 throughout the thickness of the membrane. This requirement is therefore called the constant-field assumption.

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

4. The permeability coefficient PX is a constant (i.e., it does not vary with the chemical or electrical driving forces). PX (units: centimeters per second) is defined as PX = DXβ/a. DX 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, PX describes the ability of an ion to dissolve in the membrane (as described by β) and diffuse from one side to the other (as described by DX) over the distance a.

image

FIGURE 6-6 Electrodiffusion model of the cell membrane.

With these assumptions, we can calculate the current carried by a single ion X (IX) 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 electric 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:

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(6-7)

IX, or the rate of ions moving through the membrane, has the same units as electrical current: amperes (coulombs per second). imageN6-7 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 Vm. This current-voltage (I-V) relationship is important for understanding how ionic currents flow into and out of cells.

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Calculating an Ionic Current from an Ionic Flow

Contributed by Ed Moczydlowski

On page 147 of the text, we pointed out that the current carried by ion X through the membrane (Ix) has the units of amperes, which is the same as coulombs per second (the coulomb is the fundamental unit of charge). In order to compute how many moles per second of X are passing through the membrane, we need to convert from coulombs to moles. We can compute a macroscopic quantity of charge by using a conversion factor called the Faraday (F). The Faraday is the charge (in coulombs) of a mole of univalent ions. Put another way, F is the product of the elementary charge (e0; see p. 141) and Avogadro's number:

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(NE 6-6)

Thus, given an ionic current, we can easily compute the flow of the ion:

image

(NE 6-7)

Figure 6-7A shows how the K+ current (IK) depends on Vm, 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 (see Fig. 6-7A). The value of −95 mV is called the reversal potential (Vrev), because it is precisely at this voltage that the direction of current reverses (i.e., the net current equals zero). If we set IK equal to zero in Equation 6-7 and solve for Vrev, we find that the GHK current equation reduces to the Nernst equation for K+ (see Equation 6-5). Thus, the GHK current equation for an ion X predicts a reversal potential (Vrev) equal to the Nernst potential (EX) for that ion; that is, the current is zero when the ion is in electrochemical equilibrium. At Vm values more negative than Vrev, the net driving force on a cation is inward; at voltages that are more positive than Vrev, the net driving force is outward. imageN6-8

image

FIGURE 6-7 Current-voltage relationships predicted by the GHK current equation. A, The solid curve is the K+ current predicted from the GHK equation (see Equation 6-7)—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 would be expected if both [K+]i and [K+]o were 155 mM (Ohm's law). B, The solid curve is the Na+ current predicted from the GHK equation—assuming that the membrane is perfectly selective for Na+—for an [Na+]i of 12 mM and an [Na+]o of 145 mM. The dashed line represents the current that would be expected if both [Na+]i and [Na+]o were 145 mM.

N6-8

Shape of the I-V Relationship

Contributed by Ed Moczydlowski

In the text, we introduced the GHK current equation as Equation 6-7 (shown here as Equation NE 6-8):

image

(NE 6-8)

In the nonphysiological case in which [K+]i and [K+]o are equal to [K+], the above equation reduces to

image

(NE 6-9)

In this case, the relationship between the K+ current (IK) and Vm should be a straight line that passes through the origin, as shown by the dashed line in Figure 6-7A.

Similarly, in the nonphysiological case in which [Na+]i and [Na+]o are equal to [Na+], the GHK current equation reduces to

image

(NE 6-10)

Again, the preceding equation predicts that the relationship between the Na+ current (INa) and Vm also should be a straight line, as shown by the dashed line in Figure 6-7B in the text. These relationships are “ohmic” because they follow Ohm's law: ΔI = ΔV/R,imageN6-31 where R in this equation represents resistance. Thus, the slope of the line is 1/R or the conductance:

image

(NE 6-11)

Comparing the above equation with the two that precede it, we see that—for the special case in which the ion concentrations ([X]) are identical on both sides of the membrane—the conductance is

image

(NE 6-12)

Thus, according to the GHK current equation, the membrane's conductance to an ion is proportional to the membrane's permeability and also depends on ion concentration.

What does the GHK current equation predict for more realistic examples in which [K+]i greatly exceeds [K+]o, or [Na+]i is much lower than [Na+]o? The solid curve in Figure 6-7A in the text is the prediction of the GHK current equation 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 means that an inward flow of Cl is an outward current.) The nonlinear behavior of the I-V relationship in Figure 6-7A in the text is solely due to the asymmetric internal and external concentrations of K+. Because K+ is more concentrated inside than outside, the outward K+ currents will tend to be larger than the inward K+ currents. That is, the K+ current will tend to exhibit outward rectification, as shown by the solid I-V curve in Figure 6-7A. Such I-V rectification is known as Goldman rectification. It is due solely to asymmetric ion concentrations and does not reflect an asymmetric behavior of the channels through which the ion moves.

For the case of 155 mM K+ inside the cell and 4.5 mM K+ outside the cell, the GHK current equation predicts an inward current at voltages more negative than −95 mV and an outward current for voltages more positive than −95 mV. The value of −95 mV is called the reversal potential (Vrev) because it is precisely at this voltage that the direction of current reverses (i.e., the net current equals zero). If we set IKequal to zero in the GHK current equation and solve for Vrev, we find that this rather complicated equation reduces to the Nernst equation for K+ (see Equation 6-5 in the text, shown here as Equation NE 6-13):

image

(NE 6-13)

Thus, the GHK current equation for an ion X predicts a reversal potential (Vrev) equal to the Nernst potential (EX) for that ion; that is, the current is zero when the ion is in electrochemical equilibrium. At voltages more negative than Vrev, the net driving force on a cation is inward; at voltages more positive than Vrev, the net driving force is outward.

Figure 6-7B in the text shows a similar treatment for Na+. Again, the dashed line that passes through the origin refers to the artificial situation in which [Na+]i and [Na+]o are each equal to 145 mM. This line describes an ohmic relationship. The solid curve in Figure 6-7B shows the I-V relationship for a physiological set of Na+ concentrations: [Na+]o = 145 mM, [Na+]i = 12 mM. The relationship is nonlinear solely because of the asymmetric internal and external concentrations of Na+. Because Na+ is more concentrated outside than inside, the inward Na+ currents will tend to be larger than the outward Na+ currents. That is, the Na+ current will tend to exhibit inward rectification. Again, such I-V rectification is known as Goldman rectification.

N6-31

Ohmic I-V Curve

Contributed by Ed Moczydlowski

According to Ohm's law (I = V/R), the I-V relationship is a straight line if 1/R (i.e., the conductance) is constant. The slope is positive. For a simple electrical circuit consisting of a resistor and a voltage source, the line passes through the origin (i.e., I = 0 when V = 0). However, if the Na+ current (INa) were ohmic (i.e., we assume that the [Na+] is the same on both sides of the membrane), INa is zero when the driving force (Vm − ENa) is zero (see Equation 7-2 on p. 180 of the text). Therefore, the I-V plot for an Na+ current passes through the x-axis at the equilibrium potential for Na+ (ENa).

In real-life situations, the I-V curve for Na+ currents is much more complicated, following the Goldman-Hodgkin-Katz current equation, as discussed in imageN6-8.

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 (INa) is inward at Vm values more negative than Vrev (+67 mV) and outward at voltages that are more positive than this reversal potential. Here again, Vrev is the same as the Nernst potential, in this case, ENa.

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:

image

(6-8)

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., Vm is equal to Vrev), the sum of all ion currents is zero (i.e., Itotal = 0). When we set Itotal to zero in the expanded Equation 6-8 and solve for Vrev, we get an expression known as the GHK voltage equation or the constant-field equation:

image

(6-9)

Because we derived Equation 6-9 for the case of Itotal = 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 Vm equals Vrev. The logarithmic term of Equation 6-9 indicates that resting Vm depends on the concentration gradients and the permeabilities of the various ions. However, resting Vmdepends primarily on the concentrations of the most permeant ion. imageN6-9

N6-9

Contribution of Ions to Membrane Potential

Contributed by Ed Moczydlowski

In the text, we introduced Equation 6-9 (shown here as Equation NE 6-14)

image

(NE 6-14)

and pointed out that the resting Vm depends mostly on the concentrations of the most permeant ion. This last statement is only true on the condition that the most permeant ion is also present at a reasonable concentration. It would be more precise to state that Vm depends on a series of permeability-concentration products. Thus, an ion contributes to Vm to the extent that its permeability-concentration product dominates the above equation. An interesting example is the H+ ion, which we omit from Equation NE 6-14. Although its permeability PH may be quite high in some cells, H+ concentrations on both sides of the membrane are usually extremely low (at a pH of 7, [H+] is 10−7M). Thus, even though PH may be large, the product PH × [H+] is usually negligibly small, so that H+ usually does not contribute noticeably to Vm via a PH × [H+] term, which is why we omitted it from the above equation.

The principles underlying Equation 6-9 show why the plot of Vm 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., PCl ≅ 0). We can also rearrange Equation 6-9 by dividing the numerator and denominator by PK and representing the ratio PNa/PK as α. At 37°C, this simplified equation becomes

image

(6-10)

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+ (see Equation 6-4), and the plot of Vm versus the logarithm of [K+]o is 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 PNa 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 Vm in a positive direction, toward ENa. In some skeletal muscle cells, an α of 0.01 best explains the experimental data.

image

FIGURE 6-8 Dependence of the resting membrane potential on [K+]o and on the PNa/PK ratio, α. The blue line describes the instance in which there is no Na+ permeability (i.e., PNa/PK = 0). The three orange curves describe the Vm 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 (see Equation 6-9) and simplified relationships derived from it (e.g., Equation 6-10) show that steady-state Vm 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. For example, when [K+]o is in the normal range, a particular K+ channel in human cardiac myocytes (i.e., the TWIK-1 K2P channel introduced below in Table 6-2 and Fig. 6-20F) has an extremely low α—as we could calculate from Vrev and the ion concentrations using Equation 6-10. However, under conditions of hypokalemia (plasma [K+] < 3.5 mM), α becomes substantially larger, which causes a depolarization that can trigger cardiac arrhythmias that may lead to cardiac arrest and sudden death. imageN6-10

TABLE 6-2

Major Families of Human Ion-Channel Proteins

CHANNEL FAMILY

DESCRIPTION AND SUBFAMILIES

HUMAN GENE SYMBOLS (NUMBER OF GENES): PROTEIN NAMES

NOTED PHYSIOLOGICAL FUNCTIONS

KNOWN HUMAN GENETIC AND AUTOIMMUNE DISEASES

NOTES FOR TOPOLOGY FIGURE

1. Connexin channels

Hexameric gap junction channels

GJA (7)

Cell-cell communication, electrical coupling and cytoplasmic diffusion of molecules between interconnected cells; mediate Ca2+ waves of coupled cells

GJA1: oculodentodigital dysplasia
GJA3, 8: congenital cataract
GJA5: familial atrial standstill and fibrillation

Hexamer of 4-TM subunits
(Fig. 6-20A)

GJB (7)

 

GJB1: Charcot-Marie-Tooth disease
GJB2, 3, 6: keratitis-ichthyosis-deafness syndrome
GJB3, 4: erythrokeratodermia variabilis

GJC (3)
GJD (3)
GJE (1)

 

GJC2: spastic paraplegia, lymphedema

2. Potassium channels (canonical members of VGL channel superfamily)

Homo- or heterotetrameric voltage-gated channels (Kv channels)

KCNA (8): Shaker-related or Kv1
KCNB (2): Shab-related or Kv2

Electrical signaling; repolarization of action potentials; frequency encoding of action potentials

KCNA1: episodic ataxia 1 and myokymia 1
KCNA5: atrial fibrillation 7

Tetramer of 6-TM subunits
(Fig. 6-20B)

KCNC (4): Shaw-related or Kv3

KCNC3: spinocerebellar ataxia 3

KCND (3): Shal-related or Kv4
KCNF (1): modulatory
KCNG (4): modulatory

 

KCNH (8): eag-related

KCNH2 (cardiac HERG): promiscuously drug-sensitive K+ channel responsible for acquired long QT syndrome

KCNH2: long QT syndrome 2, short QT syndrome 1

KCNQ (5): KvLQT-related

 

KCNQ1 (cardiac KvLQT1): long QT syndrome 1, Romano-Ward syndrome, Jervell and Lange-Nielsen syndrome 1 and congenital deafness, atrial fibrillation 3, short QT syndrome 2
KCNQ2, 3: benign familial neonatal seizures, early infantile epileptic encephalopathy 7
KCNQ4: deafness 2A

KCNS (3): modulatory

   

KCNV (2)

 

KCNV2: cone dystrophy with night blindness

 

Tetrameric small- and intermediate-conductance Ca2+-activated K+ channels

KCNN (4)
KCNN1, 2, 3: SKCa1, 2, 3 = KCa2.1, 2.2, 2.3
KCNN4: IKCa = SKCa4 = KCa3.1

Repolarization of APs; slow phase of AP afterhyperpolarization; regulation of AP interspike interval and firing frequency; activated by Ca2+-calmodulin; voltage-insensitive

 

Tetramer of 6-TM subunits
(Fig. 6-20C)

           
 

Tetrameric large-conductance Ca2+-, Na+-, or H+- activated K+ channels

KCNMA (1): KCa1.1 = Slo1= BKCa

Slo1 (BKCa): voltage- and Ca2+-activated K+ channel; mediation of fast component of AP afterhyperpolarization; feedback regulation of contractile tone of smooth muscle; feedback regulation release of neurotransmitters at nerve terminals and auditory hair cells

KCNMA1: generalized epilepsy and paroxysmal dyskinesia

Tetramer of 7-TM subunits
(Fig. 6-20D)

KCNT1 (1): KCa4.1 = Slo2.1 = Slick
KCNT2 (1): KCa4.2 = Slo2.2 = Slack

Slo2.1 (Slick) and Slo2.2 (Slack): low intrinsic voltage dependence and synergistically activated by internal Na+ and Cl

   

KCNU (1): KCa5.1 = Slo3

Slo3: activated by voltage and internal pH; involved in sperm capacitation and acrosome; exclusively expressed in spermatocytes and mature spermatozoa

   
 

Homo- or heterotetrameric inward-rectifier channels

KCNJ (16): Kir

Genesis and regulation of resting membrane potential, regulation of electrical excitability

 

Tetramer of 2-TM subunits
(Fig. 6-20E)

KCNJ1, 10, 13: Kir1.1 = ROMK1, Kir1.2, 1.4

Renal outer medullary K+ channel

KCNJ1: Bartter syndrome 2
KCNJ10: SESAME complex disorder
KCNJ13: snowflake vitreoretinal degeneration

 

KCNJ2, 12, 4, 14: Kir2.1, 2, 3, 4 = IRK1, 2, 3, 4

IRK: strong inward rectifiers; blocked by intracellular Mg2+ and polyamines, activated by PIP2

KCNJ2: long QT syndrome 7 (Anderson syndrome), short QT syndrome 3, atrial fibrillation 9

 

KCNJ3, 6, 9, 5: Kir3.1, 2, 3, 4 = GIRK1, 2, 3, 4

GIRK: G protein–coupled K+ channels

KCNJ5: long QT syndrome 13, familial hyperaldosteronism 3

 

KCNJ8,11: Kir6.1, 2 = KATP

KATP: coupling of metabolism to excitability, release of insulin in pancreas

KCNJ11: familial persistent hyperinsulinemic hypoglycemia 2, neonatal diabetes mellitus

 

KCNJ18: Kir2.6

 

KCNJ18: thyrotoxic hypokalemic periodic paralysis

 
 

Dimeric 2-TM tandem two-pore channels

KCNK (15): K2P
KCNK1: TWIK-1

Genesis and regulation of resting membrane potential; regulation of AP firing frequency; sensory perception of touch, stretch, and temperature; involved in mechanism of general anesthesia; activated by chloroform, halothane, heat, internal pH, PIP2, fatty acids, G proteins

KCNK9: Birk-Barel mental retardation syndrome
KCNK18: Migraine with or without aura 13

Dimer of 4-TM subunits
(Fig. 6-20F)

3. Hyperpolarization-activated cyclic nucleotide–gated cation channels (VGL superfamily member)

Tetrameric cation-selective HCN channels

HCN (4)

Na+/K+ selective, cAMP- and cGMP-activated, If current in heart; hyperpolarization-activated Ih current in heart and neurons; generation of AP automaticity in heart and CNS neurons; mediate depolarizing current that triggers the next AP in rhythmically firing cells

HCN4: sick sinus syndrome 2, Brugada syndrome 8 (tachyarrhythmia)

Tetramer of 6-TM subunits
(Fig. 6-20G)

4. Cyclic nucleotide–gated cation channels (VGL superfamily member)

Tetrameric CNG channels

CNGA (4)

Cation nonselective channels permeable to Na+, K+, and Ca2+; sensory transduction mechanism in vision, and olfaction, cGMP- and cAMP-gated cation-selective channels in rods, cones, and olfactory receptor neurons

CNGA1CNGB1: retinitis pigmentosa
CNGA3: achromatopsia 2 (total colorblindness)

Tetramer of 6-TM subunits
(Fig. 6-20H)

CNGB (2)

CNGB3: Stargardt disease 1 (macular degeneration), achromatopsia 3

5. Transient receptor potential cation channels (VGL superfamily member)

Tetrameric TRP channels

TRPA (1)

Cation nonselective channels permeable to Na+, K+, and Ca2+; involved in polymodal sensory transduction of pain, itch, thermosensation, various chemicals, osmotic and mechanical stress, taste (TRPM5); TRPV family is also called the vanilloid receptor family, which includes the capsaicin receptor (TRPV1); TRPM8 is the menthol receptor

TRPA1: familial episodic pain syndrome

Tetramer of 6-TM subunits
(Fig. 6-20I)

TRPC (6)

TRPC6: focal segmental glomerulosclerosis (proteinuric kidney disease)

TRPV (6)

TRPV4: hereditary motor and sensory neuropathy

TRPM (8)

TRPM1: congenital stationary night blindness
TRPM4: progressive familial heart block
TRPM6, 7: hypomagnesia with secondary hypocalcemia

PKD (3)

PKD1, 2, 3: polycystic kidney disease

MCOLN (3)

MOCLN1: mucolipidosis IV

6. NAADP receptor Ca2+-release channels (VGL superfamily member)

Dimeric 6-TM tandem two-pore Ca2+ channels (related to TRP, CatSper, and Cav channels)

TPCN (2)

Ca2+-selective channels activated by NAADP that mediate release of Ca2+ from acidic stores and lysosomes

TPCN2: Genetic differences are linked to variations in human skin, hair, and eye pigmentation

Dimer of 12-TM subunits
(Fig. 6-20J)

7. Voltage-gated sodium channels (VGL superfamily member) (see Table 7-1)

Pseudo-tetrameric voltage-gated channels (Nav channels)

SCN (10): Nav

Na+ selective, voltage-activated channels that mediate the depolarizing upstroke of propagating APs in neurons and muscle; blocked by local anesthetics
SCN7A (Nax, Nav2.1) senses plasma [Na+] in brain circumventricular organs

SCN1A: generalized epilepsy with febrile seizures
SCN2A: infantile epileptic encephalopathy
SCN4A: hyperkalemic periodic paralysis, paramyotonia congenita, potassium-aggravated myotonia
SCN5A: cardiac long QT syndrome 3
SCN9A: primary erythermalgia, paroxysmal extreme pain disorder, congenital indifference to pain

Monomer of 4 × 6 TMs 
(Fig. 6-20K)

8. Voltage-gated calcium channels (VGL superfamily member) (see Table 7-2)

Pseudo-tetrameric voltage-gated channels (Cav channels)

CACNA (10): Cav

CACNA genes encode Ca2+-selective, voltage-activated channels that mediate prolonged depolarizing phase of APs in muscle and neurons; entry of Ca2+ via Cav triggers release of transmitter and hormone secretion; molecular target of Ca-blocker drugs

CACNA1A: episodic ataxia 2, familial hemiplegic migraine, spinocerebellar ataxia 6
CACNA1A, 1B: antibodies to channel proteins cause Lambert-Eaton syndrome
CACNA1C: Timothy syndrome arrhythmia, Brugada syndrome 3
CACNA1F: congenital stationary night blindness, X-linked cone-rod dystrophy 3
CACNA1H: idiopathic generalized epilepsy 6
CACNA1S: hypokalemic periodic paralysis, malignant hyperthermia

Monomer of 4 × 6 TMs 
(Fig. 6-20L)

   

NALCN (1): Na+ leak

NALCN gene encodes a voltage-insensitive cation channel that mediates a resting Na+ leak current in neurons

   

9. CatSper cation channels of sperm (VGL superfamily member)

Heterotetrameric 6-TM voltage-gated Ca2+-selective channels of sperm

CATSPER (4)

Essential for hyperactivation of sperm cell motility; located in sperm tail membrane; activated by high pH; required for male fertility

CATSPER1: spermatogenic failure
CATSPER2: deafness-infertility syndrome

Tetramer of 6-TM subunits
(Fig. 6-20M)

10. Hv voltage-gated proton channels (VGL superfamily member)

Dimeric 4-TM H+ channels

HVCN1

4-TM monomer is similar to S1–S4 region of voltage-gated channels; mediates H+ efflux from sperm flagellum, innate immune function of neutrophils where H+efflux compensates outward charge movement of electrons via NADPH oxidase in phagocytes; inhibited by Zn2+

 

Dimer of 4-TM subunits
(Fig. 6-20N)

11. Ligand-gated ion channels (pentameric Cys-loop receptor superfamily)

Pentameric nicotinic, cholinergic ionotropic receptors

CHRNA (10): α subunits
CHRNB (4): β subunits
CHRNG (1): γ subunits
CHRND (1): δ subunits
CHRNE (1): ε subunits

Na+, K+ non-selective cation channels activated by binding of ACh; mediate depolarizing postsynaptic potentials, EPSPs; site of action of nicotine

CHCRNA1, B1, E, D: slow-channel syndromes, fast-channel syndromes
CHRNA2, A4, B2: nocturnal frontal lobe epilepsy
CHRNA1: antibodies to channel proteins cause myasthenia gravis

Pentamer of 4-TM subunits
(Fig. 6-20O)

 

Pentameric serotonin 5HT3 ionotropic receptors

HTR3A (1)
HTR3B (1)
HTR3C (1)
HTR3D (1)
HTR3E (1)

Na+, K+ nonselective, cation channels activated by binding of serotonin; mediate depolarizing postsynaptic potentials, EPSPs

 

Same as above

 

Pentameric GABAA ionotropic receptors

GABRA (6)
GABRB (3)
GABRD (1)
GABRE (1)
GABRG (3)
GABRP (1)
GABRQ (1)
GABRR (3)

Cl-selective anion channels activated by binding of GABA; mediate hyperpolarizing postsynaptic potentials, IPSPs; site of action of benzodiazepines and barbiturates

 

Same as above

 

Pentameric glycine ionotropic receptors

GLRA (4)
GLRB (1)

Cl-selective anion channels activated by binding of glycine; mediate IPSPs

GLRA1, 1B: hyperekplexia or startle disease

Same as above

12. Glutamate-activated cation channels (see Fig. 13-15 and Table 13-2)

Tetrameric AMPA receptor cation-selective channels

GRIA (4)
GRIA1, 2, 3, 4: GluR1, 2, 3, 4 = GluA1, 2, 3, 4

Na+, K+ nonselective cation channels activated by binding of glutamate; mediate depolarizing postsynaptic potentials, EPSPs; involved in long-term potentiation of neuronal memory

 

Tetramer of 3-TM subunits
(Fig. 6-20P)

 

Tetrameric kainate receptor cation-selective channels

GRIK (5)
GRIK1: GluR5 = GluK1
GRIK2: GluR6 = GluK2
GRIK3: GluR7 = GluK3
GRIK4: KA1 = GluK4
GRIK5: KA2 = GluK5

Same as above

   
 

Tetrameric NMDA receptor cation-selective channels

GRIN (7)
GRIN1: NR1 = GluN1
GRIN2A: NR2A = GluN2A
GRIN2B: NR2B = GluN2B
GRIN2C: NR2C = GluN2C
GRIN2D: NR2D = GluN2D
GRIN3A: NR3A = GluN3A
GRIN3B: NR3B = GluN3B

Same as above but also permeable to Ca2+

 

Same as above

13. Purinergic ligand-gated cation channels

Trimeric P2X receptor cation channels

P2RX (7)
P2RX1, 2, 3, 4, 5, 6, 7: P2X1, P2X2, P2X3, P2X4, P2X5, P2X6, P2X7

ATP-activated cation channels permeable to Na+, K+, Ca2+; involved in excitatory synaptic transmission and nociception, regulation of blood clotting; channel activated by synaptic co-release of ATP in catecholamine-containing synaptic vesicles

 

Trimer of 2-TM subunits
(Fig. 6-20Q)

14. Epithelial sodium channels/degenerins

Heterotrimeric ENaC epithelial amiloride-sensitive Na+ channels and homotrimeric ASIC acid-sensing cation channels

SCNN1A (1): α subunit
SCNN1B (1): β subunit
SCNN1D (1): δ subunit
SCNN1G (1): γ subunit
ACCN (5)

SCNN1 genes encode amiloride-sensitive Na+-selective channels mediating Na+ transport across tight epithelia; ACCN genes encode ASIC cation channels activated by external H+, which are involved in pain sensation in sensory neurons following acidosis

SCNN1A, 1B: pseudohypoaldosteronism 1
SCNN1A, 1B, 1G: bronchiectasis with or without elevated sweat chloride
SCNN1B, 1G: Liddle syndrome (hypertension)

Trimer of 2-TM subunits
(Fig. 6-20R)

15. Cystic fibrosis transmembrane regulator (see Table 5-6)

CFTR; channel protein contains two internally homologous domains

ABCC7: CFTR
Part of the ABC family (49)

Cl-selective channel coupled to cAMP regulation; Cl transport pathway in secretory and absorptive epithelia; regulated by ATP binding and hydrolysis at two intracellular nucleotide-binding domains

ABCC7: cystic fibrosis

Monomer of 2 × 6 TMs
(Fig. 6-20S)

16. ClC chloride channels

Dimeric ClC Cl channels

CLCN (9)
CLCN1, 2, 3, 4, 5, 6, 7: CLC-1, 2, 3, 4, 5, 6, 7
CLCNKA: CLC-K1
CLCNKB: CLC-K2

Cl-selective, voltage-sensitive anion channels in muscle, neurons, and many other tissues; many ClC channels also function as H+/Cl exchange transporters in endosomes, synaptic vesicles, and lysosomes; involved in regulation of electrical excitability in skeletal muscle, mediation of Cl transport in epithelia, regulatory volume decrease

CLCN1: Becker disease, Thomsen disease (congenital myotonia)
CLCN2: idiopathic and juvenile epilepsy
CLCN5: Dent disease complex, nephrolithiasis
CLCN7: osteopetrosis
CLCNKA, CLCNKB: Bartter syndromes

Monomer of 14 TMs
(Fig. 6-20T)

17. CaCC Ca2+-activated chloride channels

Anoctamin family of Ca2+- and voltage-activated Cl channels

ANO (10)
ANO1, 2, 3, 4, 5, 6, 7, 8, 9, 10: TMEM16A, B, C, D, E, F, G, H, I, J

Present in epithelia, smooth muscle, photoreceptors, olfactory sensory neurons; activated at more than ~1 µM cytosolic Ca2+; involved in Cl secretion, smooth muscle contraction, amplification of olfactory stimulus

 

Dimer of 8-TM subunits
(Fig. 6-20U)

18. IP3-activated Ca2+ channels

Tetrameric IP3 receptor channels

ITPR (3)
ITPR1, 2, 3: IP3R1, 2, 3 = InsP3R-1, 2, 3

Intracellular cation channel permeable to Na+, K+, and Ca2+; activated by binding of IP3 and Ca2+; coupled to receptor activation of PLC and hydrolysis of PIP2; regulated by binding of ATP; mediates excitation-contraction coupling in smooth muscle and participates in intracellular Ca2+ release and signaling in many cells

ITPR1: spinocerebellar ataxia

Tetramer of 6-TM subunits
(Fig. 6-20V)

19. RYR Ca2+-release channels

Tetrameric ryanodine receptor Ca2+-release channels

RYR (3)
RYR1, 2, 3: RYR1, 2, 3

Intracellular cation channel permeable to Ca2+; intracellular Ca2+-release channel activated by mechanical coupling to Cav channel in skeletal muscle or by plasma membrane Ca2+ entry in heart and smooth muscle

RYR1: malignant hyperthermia, central core disease, congenital myopathy
RYR2: familial arrhythmogenic right ventricular dysplasia, catecholaminergic polymorphic ventricular tachycardia

Tetramer of 4-TM subunits
(Fig. 6-20W)

20. Orai store-operated Ca2+ channels

Multimeric Orai Ca2+-selective channels

ORAI (3)
(also known as ICRAC for Ca2+-release activated Ca2+ current or SOC channels for store-operated Ca2+ entry)

Plasma membrane, low-conductance Ca2+ channel predominantly found in nonexcitable cells such as epithelia and lymphocytes; activated via PLC-coupled pathways leading to IP3-activated Ca2+ release from ER; Ca2+ depletion in ER activates an ER membrane protein (STIM) which activates Orai, resulting in entry of extracellular Ca2+; functions in lymphocyte activation and epithelial secretion

ORAI1: severe combined immunodeficiency syndrome (SCID)

Tetramer of 4-TM subunits
(Fig. 6-20X)

AP, action potential; CNS, central nervous system; ER, endoplasmic reticulum; EPSP, excitatory postsynaptic potential; IPSP, inhibitory postsynaptic potential; PIP2, phosphatidylinositol 4,5-bisphosphate; PLC, phospholipase C; SESAME, seizures, sensorineural deafness, ataxia, mental retardation, and electrolyte imbalance; TM, transmembrane segment.

Data from references listed in imageN6-26.

N6-10

Role of TWIK-1 Channels in Cardiac Arrhythmias

Contributed by Ed Moczydlowski

As noted in the text, the resting Vm of many cells, particularly muscle cells and neurons, is dominated by high K+ permeability due to certain K+ channels that are spontaneously open at negative membrane potentials. Maintaining Na+ and Ca2+ channels in a predominantly closed state is an important aspect of cellular physiology since the transient opening of these channels allows their efficient function in membrane signaling processes dependent on intracellular Ca2+. Thus, in typical excitable cells we would expect K+ channels to maintain a negative Vm, close to EK, except when Na+ and Ca2+ channels are stimulated to open and trigger activation of cellular processes such as muscle contraction or secretion.

The human genome includes 79 genes that encode K+ channels, comprising five major families of K+-selective–channel proteins (see Table 6-2):

• Voltage-gated (Kv)

• Small-conductance Ca2+ activated (SK and IK)

• Large-conductance Ca2+ activated (BK)

• Inward rectifier (Kir)

• Two-pore (K2P)

Of these K+ channels, only the Kir and K2P channels show gating behavior compatible with significant open-state probability at negative Vm. Thus, these latter channels are expected to have the greatest role in determining the resting Vm.

Because the K+ channels that have been studied most extensively appear to conduct very little inward Na+ current under physiological conditions, it is not entirely clear why Vm deviates from strict Nernst behavior in experiments such as that for which results are shown in Figure 6-4, where the measured Vm is more positive than expected at low extracellular [K+]. It has often been assumed that this deviation is simply due to a low but finite permeability of K+ channels to Na+ (e.g., α ≅ 0.01 in Equation 6-10) or an unspecified Na+ leak. However, structural and biophysical studies of K+ channel proteins imageN7-13 indicate that K+ binding to the ion-selectivity filter actually stabilizes the filter in a K+-selective conformation. When K+ concentration is reduced to low-millimolar levels, the selectivity filter may deform and permit other ions such as Na+ to permeate the channel. Thus, at low extracellular K+ concentration it is possible that K+ channels in cell membranes could become less selective for K+ relative to Na+.

An example of this effect has been described in human cardiac myocytes, in which pathological conditions of blood hypokalemia (plasma [K+] < 3 mM) may lead to paradoxical depolarization, cardiac arrhythmia, and sudden death. Evidence suggests that this phenomenon may be caused by a certain K2P K+ channel called TWIK-1 (human gene KCNK1) that exhibits increased permeability to Na+ at low extracellular K+. Serum hypokalemia can be secondary to diuretic therapy, diarrhea (including laxative abuse) or vomiting, or starvation. Plasma K+ concentration should be raised to normal levels of 3.5 to 4.8 mM to prevent dangerous cardiac arrhythmia in such instances.

Reference

Ma L, Zhang X, Chen H. TWIK-1 two-pore domain potassium channels change ion selectivity and conduct inward leak sodium currents in hypokalemia. Sci Signal. 2011;4:ra37 [1–10].

N6-26

References for Major Families of Human Ion Channel Proteins (Table 6-2)

Contributed by Ed Moczydlowski

Data for Table 6-2 are from the following sources:

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Brailoiu E, Churamani D, Cai X, et al: Essential requirement for two-pore channel 1 in NAADP-mediated calcium signaling. J Cell Biol 186:201–209, 2009.

Calcraft PJ, Ruas M, Pan Z, et al: NAADP mobilizes calcium from acidic organelles through two-pore channels. Nature 459:596–600, 2009.

Chen TY: Structure and function of ClC channels. Annu Rev Physiol 67:809–839, 2005.

Clapham DE, Runnels LW, Strübing C: The TRP ion channel family. Nat Rev Neurosci 2:387–396, 2001.

Dorwart M, Thibodeau P, Thomas P: Cystic fibrosis: Recent structural insights. J Cyst Fibros 2:91–94, 2004.

Dutzler R: The structural basis of ClC chloride channel function. Trends Neurosci 27:315–320, 2004.

Dutzler R, Campbell ER, Cadene M, et al: X-ray structure of a ClC chloride channel at 3.0 Å reveals the molecular basis of anion selectivity. Nature 415:287–294, 2002.

Foskett JK, White C, Cheung K-H, Mak DD: Inositol trisphosphate receptor Ca2+ release channels. Physiol Rev 87:593–658, 2007.

Hamilton SL: Ryanodine receptors. Cell Calcium 38:253–260, 2005.

Jasti J, Furukawa H, Gonzales EB, Gouaux E: Structure of acid-sensing ion channel 1 at 1.9 Å resolution and low pH. Nature 449:316–324, 2007.

Khakh BS, North RA: P2X receptors as cell-surface ATP sensors in health and disease. Nature 442:527–532, 2006.

Kellenberger S, Schild L: Epithelial sodium channel/degenerin family of ion channels: A variety of functions for a shared structure. Physiol Rev 82:735–767, 2002.

Kim D: Fatty-acid sensitive two-pore domain K+ channels. Trends Pharm Sci 24:648–654, 2003.

Lewis RS: The molecular choreography of a store-operated calcium channel. Nature 446:284–287, 2007.

Lishko P, Kirichok Y, Ren D, et al: The control of male fertility by spermatozoan ion channels. Annu Rev Physiol 74:453–475, 2012. Epub October 13, 2011.

Lu B, Su Y, Das S, et al: The neuronal channel NALCN contributes resting sodium permeability and is required for normal respiratory rhythm. Cell 129:371–383, 2007.

Maylie J, Bond CT, Herson PS, et al: Small conductance Ca2+-activated K+ channels and calmodulin. J Physiol 554.2:255–261, 2003.

Mese G, Richard G, White TW: Gap junctions: Basic structure and function. J Invest Dermatol 127:2516–2524, 2007.

Montell C: The history of TRP channels, a commentary and reflection. Pflugers Arch 461:499–506, 2011.

Moran MM, McAlexander M, Biro T, Szallasi A: Transient receptor potential channels as therapeutic targets. Nat Rev Drug Discov 10:601–620, 2011.

Nilius B, Droogmans G: Amazing chloride channels: An overview. Acta Physiol Scand 177:119–147, 2003.

Nilius B, Owsianik G, Voets T, Peters JA: Transient receptor potential channels in disease. Physiol Rev 87:165–217, 2007.

Pederson SF, Owsianik G, Nilius B: TRP channels: An overview. Cell Calcium 38:233–252, 2005.

Pifferi S, Cenedese V, Menini A: Anoctamin2/TMEM16B: A calcium-activated chloride channel in olfactory transduction. Exp Physiol 97:193–199, 2012. Epub September 2, 2011.

Qi H, Moran MM, Navarro B, et al: All four CatSper ion channel proteins are required for male fertility and sperm cell hyperactivated motility. Proc Nat Acad Sci U S A 104:1219–1223, 2007.

Ramsey IS, Moran MM, Chong JA, Clapham DE: A voltage-gated proton-selective channel lacking the pore domain. Nature 440:1213–1216, 2006.

Riordan JR: Assembly of functional CFTR chloride channels. Annu Rev Physiol 67:701–718, 2005.

Rooslid TP, Le K-T, Choe S: Cytoplasmic gatekeepers of K+ channel flux: A structural perspective. Trends Biochem Sci 29:39–45, 2004.

Salkoff L, Butler A, Ferreira G, et al: High-conductance potassium channels of the SLO family. Nat Rev Neurosci 5:921–931, 2006.

Scudieri P, Sondo E, Ferrera L, Galietta LJV: The anoctamin family: TMEM16A and TMEM16B as calcium-activated chloride channels. Exp Physiol 97(2):177–183, 2012. Epub October 7, 2011.

Song MY, Yuan JXJ: Introduction to TRP channels: Structure, function, and regulation. Adv Exp Med Biol 661:99–108, 2010.

Stocker M: Ca2+-activated K+ channels: Molecular determinants and function of the SK family. Nat Rev Neurosci 5:758–770, 2004.

Taylor CW, da Fonseca PCA, Morris EP: IP3 receptors: The search for structure. Trends Biochem Sci 29:210–219, 2004.

Vial C, Roberts JA, Evans RJ: Molecular properties of ATP-gated P2X receptor ion channels. Trends Pharm Sci 25:487–493, 2004.

Williams AJ, West DJ, Sitsapesan R: Light at the end of the Ca2+-release channel tunnel: Structures and mechanisms involved in ion translocation in ryanodine receptor channels. Q Rev Biophys 34:61–104, 2001.

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In general, the resting potential of most vertebrate cells is dominated by high permeability to K+, which accounts for the observation that the resting Vm is typically close to EK. 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 Vm in a positive direction toward ENa or ECa. A few cells, such as vertebrate skeletal muscle fibers, have high permeability to Cl, which therefore contributes to the resting Vm. This high permeability also explains why the Cl equilibrium potential in skeletal muscle is essentially equivalent to the resting potential (see Table 6-1).