Channel Diversity and Evolution

Humans have about 400 genes that encode channel proteins. The historical channel nomenclature based variously on the ion transported, mode of regulation, physiological role, or drug sensitivity is often ambiguous. Fortunately, knowledge of channel protein structures clarified evolutionary relationships and provided a framework to classify most plasma membrane channels into a few large families (Fig. 10-2).

Figure 10-2 classification of channel proteins. This scheme is based on primary structure, atomic structures (where known), and postulated evolutionary origins. The predicted transmembrane topology has the extracellular side at the top and uses rectangles to indicate helices labeled “S.” P loops are shown as a short helix and loop between two transmembrane helices. S4 voltage-sensing helices are pink; pore positions are yellow. The last column shows the known (or likely) subunit compositions. In many cases, it is possible to trace the origins of a channel family back to prokaryotes. In other cases, family members are known only in vertebrate organisms. In most families, relatively recent gene duplications and divergence have given rise to multiple isoforms of each type of channel. Channel nomenclature is not uniform. Some names indicate the transported ion (Na⁺, K⁺, Ca²⁺, Cl⁻), whereas others signify the regulatory modality (i.e., voltage-gated [VG] or neurotransmitter-gated), a physiologic role (intracellular calcium release), drug binding (ryanodine receptor), or some other feature. ClC, chloride channel; ENaC, epithelial sodium channel; GABA, γ-amino butyric acid; 5-HT, 5-hydroxytryptamine; IC, intracellular ligand; IP₃, inositol triphosphate; Kir, potassium inward rectifier; nAch, nicotinic acetylcholine; R, receptor; Ryanodine, a chemical that binds calcium-release channels; TRP, transient receptor potential; VG, voltage-gated; XC-ATP, extracellular ATP-gated channel.

Channels are integral membrane proteins, usually with two or more a-helices crossing the lipid bilayer. Porins are an exception; they are built from transmembrane β-strands (see Fig. 7-8C). Channels generally consist of two to six subunits, but some are single, large polypeptides. The transmembrane pores for conducting ions or other substrates are often located in the middle of a group of subunits or subunit-like domains, but the pores of chloride, water, and ammonia channels are located within single subunits.

A limited number of genes in early forms of life appear to have given rise to most channel genes. For example, the gene for a simple prokaryotic channel with just two transmembrane segments (called S5 and S6) was the progenitor of a huge family of channels with 2 to 24 transmembrane segments. Some channels with two transmembrane segments acquired features to produce rectified ion fluxes (see later section), extracellular ligand binding (neuropeptides and ATP), and intracellular ligand binding (cyclic adenosine monophosphate [cAMP], G proteins). A simple duplication of one of these genes yielded channels with four segments. Even before the emergence of eukaryotes, the addition of four segments (S1 to S4) yielded channels with six transmembrane segments. Acquisition of positive charges by S4 provided for voltage sensitivity. Two rounds of gene duplication and divergence produced voltage-gated channels consisting of four domains, each with six transmembrane segments, such as voltage-gated Na⁺ channels. Water channels originated in prokaryotes by duplication of a gene that encoded three hydrophobic transmembrane segments. The extracellular domain of glutamate-gated channels originated as a bacterial glutamate-binding protein. Ammonia channels and double-barreled Cl⁻ channels also had bacterial ancestors. The origins of ligand-gated neurotransmitter receptors related to the nicotinic acetylcholine receptor, gap junction connexins, and calcium release channels are still obscure.

Channels in higher eukaryotes are products of multigene families that arose from multiple rounds of gene duplication and divergence. Alternative splicing also enriches the variety of channels. Combining different subunit isoforms in one channel creates increased specialization. All of this diversity suggests a sophistication of function that is difficult to demonstrate with current assays. For example, it is not known why the sodium channels that produce action potentials in neurons cannot substitute for their counterparts in skeletal muscle.

Channel Structure

The K⁺ channel KcsA from the Bacterium Streptomyces lividans serves the model for channels in general and the whole family of S5/S6 channels in particular (Fig. 10-3). Four identical subunits are composed of two transmembrane helices connected by a P loop (for pore)—a short third helix and a crucial strand that makes the selectivity filter. The transmembrane helices are packed close together on the cytoplasmic side of the bilayer but splay apart on the extracellular side to make room for the pore helices and selectivity filter.

Figure 10-3 Atomic structure of KcsA, a K⁺ channel from Streptomyces lividans. A, Transmembrane topology. The short helix and loop between the two transmembrane helices are called a P loop because they form the pore. B, Space-filling model with each subunit shaded a different color and with a cutaway view to expose the central pore, which contains three K⁺ ions (blue). C, Ribbon model of KcsA with the front subunit removed to reveal the central pore. Starting on the extracellular side, the 4.5-nm-long pore consists of a negatively charged vestibule; the 1.2-nm-long selectivity filter with binding sites for four dehydrated K⁺ ions (each site is partially occupied at any time); a central cavity with space for a single hydrated K⁺; a gate (closed here); and a negatively charged cytoplasmic vestibule. D, Views from outside the cell. Aromatic side chains (shown as stick figures) at both ends of the transmembrane helices of each subunit project radially into the lipid.

(PDB file: 1BL8. References: Doyle DA, Morais-Cabral J, Pfuetzner RA: The structure of the potassium channel: Molecular basis of K⁺ conduction and selectivity. Science 280:69–77, 1998; Zhou Y, Morais-Cabral JH, MacKinnon R: Chemistry of ion coordination and hydration revealed by a K⁺-channel-Fab complex at 2.0 Å resolution. Nature 414:43–48, 2001.)

The selectivity filter is a centrally located pore where the four identical subunits meet, each subunit contributing a quarter of the wall. Highly conserved residues (GYG) in an unusual linear conformation line the pore. The backbone carbonyl oxygens (C=O) of four successive residues all point toward the pore. The pore is 1.2 nm long and about 0.2 nm in diameter, just wide enough to accommodate a dehydrated K⁺ ion. This passage distinguishes between K⁺ and Na⁺ with a fidelity of 1000 to 1 even though Na⁺ (with a diameter of 0.095 nm) is smaller than K⁺ (0.133 nm in diameter). A simple explanation is that K⁺ fits so perfectly into the pore that the carbonyl oxygens replace the water shell of K⁺ without an energy penalty, whereas the smaller Na⁺ binds more strongly to its hydration shell than to the pore. However, the protein is not sufficiently rigid to discriminate a difference of 0.38 Å, so local electrostatic interactions between ions and carbonyl oxygens and between carbonyl oxygens themselves contribute to selectivity. Carbonyl oxygens carry the optimal electric dipole to favorably counterbalance the hydration free energy of K⁺ over that of Na⁺, thereby giving robust selectivity despite thermal fluctuations of the protein.

The selectivity filter accommodates two K⁺ ions, a local concentration exceeding that inside or outside the cell by more than 10-fold, so it actually concentrates K⁺. However, it does not impede diffusion through the pore, since electrostatic repulsion between these closely spaced ions forces them apart. Outside the filter, the pore is lined with hydrophobic groups, but a cavity in the middle of this passage accommodates a hydrated K⁺ in an environment with a negative electrostatic potential that is thought to reduce the electrostatic barrier to the ion as it crosses the membrane, as predicted by earlier physiological studies.

Channel Activity

Single-channel electrical recordings show that channel pores are either open or closed (Figs. 10-4 and 10-5). Open channels, also called the active state, pass selected ions across the membrane at rates approaching their diffusion in water. Closed channels have a different conformation that does not pass ions, small solutes, or water. Many channels also have an inactivated state in which part of the channel protein or an impermeant ion blocks the pore of an otherwise open channel, preventing diffusion of ions through the pore. Inactivation makes a channel unresponsive to conditions that favor the active state. Voltage-gated Na⁺ channels provide a good example; they cycle from closed to open and then inactivate before returning to the closed state.

Figure 10-4 patch recording of a single-cation channel molecule. This time course shows the current that results when a single channel opens and closes at random. When open, it conducts Na⁺ ions at a rate of about 36 × 10⁶ per second, yielding a current of -6 pA. The transitions between open and closed are so fast that they appear instantaneous on this time scale.

Figure 10-5 functional states of a typical ion channel embedded in a lipid bilayer. A, Drawings of three functional states. Closed channels are inactive. Open channels are active, forming a selective pore for particular ions across the bilayer. The pore rejects other ions because of inappropriate size or charge. Either the channel protein itself or a large ion can inactivate channels by blocking the pore. In this example, an inactivation ball blocks the pore to inactivate the channel. Simple channels switch between two conformations: open and closed. Complex channels switch from closed to open to inactivated and then back to closed without returning to the open state. B–C, Drawings of side and top views of the polypeptide backbones of two potassium channels. Red is KcsA from Streptomyces lividans with the gate closed. Blue is a calcium-gated MthK K-channel from Methanobacterium autotrophicum with the gate open. The selectivity filters are identical in the closed and open states.

(Reference: Jiang Y, Lee A, Chen J, et al: Crystal structure and mechanism of a calcium-gated potassium channel. Nature 417:515–522, 2002.)

Channels with One Transmembrane Segment

The simplest known channel is found in the membrane envelope of influenza virus. This M₂ channel consists of four small subunits, each with but one transmembrane helix. After an infected cell takes the virus into an endosome (see Chapter 22), the acidic environment opens the channel, allowing protons to enter the virus and to begin to disassemble the protein shell that surrounds the genome. The antiviral drug amantadine blocks these channels. Bacteria secrete peptides (gramicidin, alamethicin, and colicins) that are designed to kill other species by forming highly selective and conductive channels. Only 13 amino acids are required for gramicidin A to form β-helical homodimers that function as K⁺-selective channels.

Vertebrates also have simple channel proteins of about 130 residues with a single transmembrane segment and no sequence homology with other known channels. These minK molecules do not form channels on their own but are accessory subunits for a conventional P loop, voltage-gated, K⁺-specific channel. Both subunits contribute to the pore of the channel. Mice that lack the minK gene have defects in hearing and balance. Epithelial cells in the inner ear fail to secrete the K⁺-rich fluid required for the function and viability of hair cells that transduce sound waves.

Channels with Two Transmembrane Segments

Mechanosensitive Channels

MscL from Mycobacterium tuberculosis (Fig. 10-6) is a simple channel of five subunits. One of the two transmembrane helices forms the wall of the pore. A third C-terminal helix extends the pore 4 nm into the cytoplasm. The central pore is lined with polar residues except for a gate at its narrowest constriction, where an isoleucine and a value reduce the diameter to about 0.2 nm. Tension in the plane of the membrane created by osmotic stress is believed to rearrange these helices and open the channel. Cations pass through the open channels indiscriminately at high rates, since they lack a selectivity filter like that of KcsA. This response avoids osmotic lysis of the cell. Such channels are widespread in prokaryotes and are also found in eukaryotes.

Figure 10-6 Atomic structure of MscL, a mechanosensitive channel from Mycobacterium tuberculosis. A, Subunit topology. Ribbon model with each subunit shaded a different color. B, Space-filling model with each subunit shaded a different color and a cutaway view to expose the central pore, which is 8 nm long. C–F, Space-filling and ribbon models. The arrow indicates the probable ion entry site on the cytoplasmic side of the pore.

(PDB file: 1MSL. Reference: Chang G, Spencer RH, Lee AT, et al: Structure of the MscL homolog from Mycobacterium tuberculosis: A gated mechanosensitive ion channel. Science 282:2220–2226, 1998.)

Channels with Four Transmembrane Helices

K⁺ channels with four transmembrane segments and two P loops (Fig. 10-2, TWIK) are abundant in animal genomes, with 40 to 50 genes in C. elegans. Two of these subunits form a channel with four domains similar to KcsA. They help to establish the resting potential of the plasma membrane by allowing K⁺ to leak out of the cell, independent of the membrane potential. These leak channels are activated by volatile anesthetics, leading to hyperpolarization of the membrane and reduced excitability.

Voltage-Gated Cation Channels

Voltage-gated channels have two main functions. First, voltage-gated K⁺ and Na⁺ channels produce action potentials in excitable cells (see Fig. 11-6). Depolarization of the membrane opens these channels transiently, driving the membrane potential first toward the Na⁺ equilibrium potential (Appendix 10-2) and then back toward the K⁺ equilibrium potential. Second, voltage-gated Ca²⁺ channels convert electrical signals into chemical signals when they admit Ca²⁺ to the cytoplasm, where it acts as a second messenger (see Figs. 11-8, 11-9, and 26-12) to stimulate secretion, activate protein kinases, trigger muscle contraction, or influence gene expression.

Voltage-gated channels share a common domain organization (Fig. 10-2). Crystal structures of voltage-gated K⁺ channels from a thermophilic Archaea and rat brain (Fig. 10-7) confirmed that hydrophobic segments S5 and S6 are transmembrane helices with a P loop just like KcsA. The P loop is the selectivity filter, since transplantation of the P loop from one channel to another can yield a chimeric channel with the ion conductance of the foreign P loop. Hydrophobic segments S1 to S4 form a separate domain lateral to the central pore.

Figure 10-7 voltage-gated potassium channel. Crystal structure of the Kv1.2 K⁺ channel with b2-subunits from rat brain. A, Ribbon diagram of two of the four α-subunits and two of the four β-subunits viewed from the side. Each of the four α-subunits contributes an S5 helix, P loop, and S6 helix to form a channel similar to KcsA. Helices S1 through S4 form a separate domain connected to the channel domain by the S4–S5 linker helix. Movements of the S4 helix in response to the membrane potential pull the channel gate open and closed. The N-terminal T1 domains of each α-polypeptide are located in the cytoplasm, interacting with the tetrameric β-subunit. B, Ribbon diagram viewed from outside the cell, illustrating the central channel domains and the peripheral voltage-sensing domains. C, Side view of a space-filling model of three of the four subunits, showing K⁺ ions (blue), one above the membrane, four in the selectivity pore, and one in the vestibule. D, Space-filling model with an artist’s conception of the N-terminal “ball and chain” plugging the open gate of an inactivated channel.

(PDB file: 2A79. Reference: Long SB, Campbell EB, MacKinnon R: Crystal structure of a mammalian voltage-dependent Shaker Family K⁺ channel. Science 309:897–902, 2005.)

In voltage-gated K⁺ channels, the domains consisting of S1 to S6 are four separate polypeptides that associate noncovalently as homo-oligomers or hetero-oligomers. Animal voltage-gated Na⁺ and Ca²⁺ channels consist of four similar but nonidentical domains (each with S1 to S6) linked in a single polypeptide (Fig. 10-2). Voltage-gated channels have additional specialized domains and/or subunits, but the four main domains carry out the basic functions.

The probability that a voltage-sensitive channel is open depends on the membrane potential (Fig. 10-8). The transition is sharp, likely because all four domains respond cooperatively. A negative internal membrane potential stabilizes the closed state. A voltage sensor couples membrane depolarization to channel opening, physically moving charged residues a small distance across the lipid bilayer. Helix S4 is a key part of the sensor. One side of this helix has a spiral of positively charged lysines or arginines. Spectroscopic measurements suggest that the S4 helix makes a subtle motion such as a rotation in response to membrane depolarization. This movement would bring positive charges on S4 closer to the external side of the membrane, accounting for the charge movement that is detected as a “gating current.” Movement of S4 pulls on the helix connecting S4 and S5 (Fig. 10-7A), producing force to open the gate of the channel.

Figure 10-8 Graph of the open probability (P_o) of a voltage-gated Na⁺ channel as a function of membrane potential (E_m). Essentially, all channels are closed at the resting potential of -70 mV, and all are open above a threshold potential of about -40 mV.

Inactivation is accomplished by flexible parts of these channels, either a ball and chain at the N-terminus of some K⁺ channels (Fig. 10-7D) or a loop between the domains of Na⁺ channels. Inactivation depends on membrane depolarization in the sense that the channel must first open to expose a binding site for the inactivation peptide, which then occludes the pore and blocks conduction. As a result, the channel opens only transiently. Less is known about the transition from the inactivated state to the closed state, but a conformational change must occlude the pore before the ball dissociates from the cytoplasmic side of the pore.

TRP Channels

Organisms from most parts of the phylogenetic tree use the TRP family of channels for sensation of diverse stimuli, including chemicals, osmolarity of their environment, and temperature. TRP channels enable humans to sense bitter and sweet tastes, high temperature (and hot spices), and cool temperatures (and cooling chemicals). Mutations that cause defects in fly photoreception led to the first known TRP (transient receptor potential) channel. Some of the large family of nearly 30 mammalian TRP genes were subsequently discovered by sequence homology and assigned function by physiological tests. Other TRP channels were found by expression cloning of cDNAs that allowed test cells to respond to hot spices or cooling chemicals by admitting Ca⁺².

No high-resolution structures are available, but the sequences of TRP channels indicate six transmembrane helices and a possible P-loop (Fig. 10-9). These subunits form tetrameric channels that are thought to be similar in architecture to voltage-sensitive K-channels, including a gate on the cytoplasmic side of the ion-conduct-ing pore.

Figure 10-9 trp channels. Topology of three temperature-sensitive TRP channel subunits. Note the similar transmembrane segments coupled to cytoplasmic domains that vary in size. The blue to red shading indicates the range of temperatures that activates each of these channels. The cooling chemical menthol activates CMR1. Capsaicin, the active ingredient of hot chili peppers, activates VRL-1.

(Reference: McKemy DD, Neuhausser WM, Julius D: Identification of a cold receptor reveals a general role for TRP channels in thermosensation. Nature 416:52–58, 2002.)

All TRP family members are cation channels, admitting modest amounts of both extracellular Na⁺ and Ca⁺² when active. Diverse stimuli activate the various TRP channels, but the mechanisms are still poorly understood and subject to controversy. In the simplest case, extracellular ligands such as hot spices or cooling chemicals open particular channels. High temperature also activates the hot spice channels, accounting for the perception of such spices as being “hot.” The brain cannot discern whether the TRP channels in a sensory nerve are activated by heat or a spice. Similarly, cold temperatures activate another TRP channel that responds also to cooling chemicals such as menthol. Signaling mechanisms downstream from seven-helix receptors and receptors tyrosine kinases (see Chapter 24) activate other TRP channels, in some cases by producing a second messenger (see Chapter 26) such as the membrane lipids PIP₂ and diacylglycerol.

Channels Gated by Intracellular Ligands

Genes for families of channels gated by cytoplasmic Ca²⁺, cyclic nucleotides, or β/γ-subunits of trimeric γ-proteins (see Fig. 25-9) diverged from K⁺ channels relatively recently in evolution, about the time when animals diverged from fungi. Their sequences are similar to each other (LC ligand-gated [Fig. 10-2]).

Ca²⁺-activated K⁺ channels are first cousins of voltage-gated K⁺ channels. They have six transmembrane segments and a P loop. The Ca²⁺-binding protein, cal-modulin (see Fig. 3-12C), binds constitutively to the cytoplasmic tail following S6. Ca²⁺, entering the cytoplasm through the plasma membrane or released from intracellular stores (see Fig. 26-12), binds this associated calmodulin and activates the channel by making it more sensitive to membrane depolarization. Expression from different genes and alternative splicing produce a variety of these channels with different physiological properties.

Cyclic nucleotide–gated ion channels have six membrane-spanning segments with a P loop and a C-terminal cyclic nucleotide–binding domain homologous with bacterial cyclic nucleotide–binding proteins (Fig. 10-10). Four of these subunits, some of which may be different isoforms, form a functional channel. Binding of cyclic adenosine monophosphate (cAMP) to the cytoplasmic receptor domain opens a pore for Na⁺ and Ca²⁺ and depolarizes the membrane. Changes in cyclic nucleotide concentration provide a sharp on/off switch, as ligand must occupy at least three of the four subunits to open the channel. Ca²⁺ entering the cytoplasm binds to calmodulin associated with the N-terminal cytoplasmic part of the protein. This provides negative feedback to the channel.

Figure 10-10 cyclic nucleotide–gated cation channels. A, Domain architecture with six predicted transmembrane helices (S1 to S6), a P loop, and a C-terminal cyclic nucleotide–binding domain. B, Predicted transmembrane topology of each of the four identical subunits. The N-terminal cytoplasmic domain has a binding site for calcium-calmodulin. C, Atomic structure of the bacterial cyclic nucleotide–binding protein, CAP, which is homologous to the ligand-binding domains of these channels. cGMP, cyclic guanosine monophosphate. (PDB file: 3GAP.)

Ion channels gated by intracellular cyclic nucleotides are particularly important in sensory systems, including olfaction (see Fig. 27-1) and vision (see Fig. 27-2). Odorant molecules stimulate olfactory sensory neurons by binding seven-helix receptors in the plasma membrane. These receptors work through trimeric γ-proteins to increase the cytoplasmic concentration of cAMP. cAMP opens cAMP-gated cation channels, depolarizes the membrane, and activates voltage-gated Na⁺ channels to fire an action potential. Visual transduction also uses a cyclic nucleotide–gated channel. Light activates a seven-helix receptor, leading to a decline in cytoplasmic cyclic guanosine monophosphate (cGMP). This closes cGMP-gated channels, hyperpolarizing the photoreceptor plasma membrane and reducing the secretion of neurotransmitter (see the next section).

Ion Channels Gated by Extracellular Ligands

Channels that are gated by chemicals mediate communication between nerve terminals and other nerves or muscles. This communication takes place at specializations called synapses, which facilitate chemical transmission (see Figs. 11-8 and 11-9). On the sending side, presynaptic terminals are specialized for exocytosis of chemicals called neurotransmitters, which they package in small synaptic vesicles. Neurotransmitters include acetylcholine, serotonin, glutamic acid, glycine, and γ-aminobutyric acid (GABA) (see Fig. 11-7). When an action potential arrives at a nerve terminal, voltage-gated Ca²⁺ channels admit Ca²⁺ to the cytoplasm, causing synaptic vesicles to fuse with the plasma membrane, releasing transmitter outside the cell. Transmitters diffuse to the postsynaptic membrane in micro-seconds.

On the receiving side, the transmitter activates ligand-gated ion channels in the postsynaptic membrane. Many of these receptor-channels appear to have diverged from a still mysterious common ancestor, but glutamate receptors had a separate origin in bacteria. Some ligand-gated channels trigger action potentials in the postsynaptic membrane by admitting cations, which drive the membrane potential toward threshold. Others inhibit action potentials by admitting Cl⁻, which hyperpolarizes the postsynaptic membrane.

Stimulation of ligand-gated channels is transient because of an inactivating conformational change called desensitization and because neurotransmitters are rapidly removed from the synaptic cleft between the cells (see Figs. 11-8 and 11-9). An extracellular enzyme degrades acetylcholine. Carriers (see Chapter 9) remove all other neurotransmitters by pumping them back into the presynaptic cell.

Glutamate Receptors

Glutamate receptors depolarize the postsynaptic membrane when glutamate binding opens a cation channel that is permeable to both Na⁺ and K⁺ (see Fig. 11-9). This depolarization of the plasma membrane excites the cell by activating voltage-sensitive sodium channels to trigger an action potential. Eukaryotic glutamate receptor channels (Fig. 10-11) have an extracellular ligand-binding domain and four hydrophobic segments: M2 is a P loop between transmembrane helices M1 and M3. Four subunits form a channel with their P loops on the cytoplasmic side of the plasma membrane rather than outside, like KcsA and its many relatives. A change in the conformation of the extracellular domain induced by glutamate binding opens a pore through the middle of the channel. Successive binding of glutamate to each of the four subunits opens the pore in steps (although binding is usually too fast to resolve these partially open states).

Figure 10-11 glutamate-gated ion channels. A, Domain organization with the glutamate-binding domain between a and b and four predicted transmembrane segments, M1 to M4. M2 is probably a cytoplasmically oriented P loop. B, Transmembrane topology and orientation of the atomic structure of the glutamate-binding domain. The N-terminal domain is shown approximately to scale. Four of these subunits are thought to constitute a channel similar to an inverted K⁺ channel. C, Atomic structure of the ligand-binding extracellular domain from the vertebrate kainate (KA) receptor.

(PDB file: 1GR2. From Armstrong N, Sun Y, Chen γ-Q, Gouaux E: Structure of a glutamate-receptor ligand-binding core in complex with kainate. Nature 395:913–917, 1998.)

Multiple genes, alternative splicing, and RNA editing (see Fig. 16-7) all provide a diversity of glutamate receptor subunits, which assemble into homomeric and heteromeric channels used in different parts of the nervous system. Three families of isoforms are sensitive to different pharmacologic agonists in addition to glutamate: N-methyl-d-aspartate (NMDA), α-amino-3-hydroxy-5-methyl-4-isoxazole propionate (AMPA), or kainate. NMDA receptors are more permeable to Ca²⁺ than to Na⁺ and K⁺. Because excess intracellular Ca²⁺ can be damaging, overstimulation of NMDA receptors by glutamate released from cells during strokes or constitutive activation of NMDA receptors by point mutations can kill nerve cells.

Eukaryotic glutamate receptor channels apparently originated in Bacteria by fusion of genes for a periplasmic amino acid–binding protein (similar to Escherichia coli glutamine-binding protein) and an S5/P/S6 potassium channel similar to KcsA. The domain organiza-tion of plant glutamate receptors is similar to that of animal brain glutamate receptors. Glutamate receptors participate in the response of developing plants to light.

Nicotinic Acetylcholine Receptor

The best-characterized ligand-gated channel is an excitatory cation channel—the nicotinic acetylcholine receptor from the plasma membrane of skeletal muscle cells. This receptor triggers action potentials that stimulate muscle contraction (see Figs. 11-8 and 39-14). It is called the nicotinic acetylcholine receptor because it also binds the tobacco alkaloid nicotine. Related nicotinic acetylcholine receptors in the central nervous system are the targets in tobacco addiction.

The muscle nicotinic acetylcholine receptor is a pentamer of four different, but homologous, subunits with the composition a₂bge (Fig. 10-12). Each subunit has a large N-terminal extracellular segment, four transmembrane α-helices (M1 to M4), and a large cytoplasmic segment between M3 and M4. M2 α-helices from the five subunits line a central transmembrane pore like staves of a barrel. Hydrophobic side chains line this pore except for a few negative charges that may contribute to cation selectivity. Three other α-helices of each subunit separate the M2 helices from the surrounding lipid. The N-terminal segments of each subunit form massive extracellular domains, each folded into similar, highly twisted β-sandwiches. The α-subunits have deep cavities that bind acetylcholine.

Figure 10-12 nicotinic acetylcholine receptor. A, Domain organization of the acetylcholine receptor and related receptors gated by neurotransmitters. All four hydrophobic segments, M1 to M4, form transmembrane helices. B–C, Structure of the pentameric nicotinic acetylcholine receptor from the electric organ of the electric ray determined by electron microscopy. B, Reconstruction at a resolution of 0.46 nm. C, Ribbon diagrams of the nicotinic acetylcholine receptor from a structure at a resolution of 0.40 nm. Left, View from the extracellular side, showing five M2 helices lining the central pore. Right, Side view of model. The extracellular domains of two red α-subunits bind acetylcholine. D, Space-filling surface representation. E, Central section through the pore. F, Diagram showing the acetylcholine-binding sites, the proposed conformational changes following activation, and the passages for Na⁺ into the cell and K⁺ out of the cell. A 43-kD protein called rapsyn (blue) binds on the cytoplasmic side.

(PDB file: 1OED. Reference: Miyazawa A, Fujiyoshi Y, Unwin N: Structure and gating mechanism of the acetylcholine receptor pore. Nature 423:949–955, 2003.)

Gating and ion selectivity of acetylcholine receptors differ in concept from the P-loop family of channels. In closed channels, the narrowest part of the closed pore is less than 7 Å in diameter, too small for hydrated K⁺ and Na⁺ ions, and the hydrophobic pore does not provide a passage for unhydrated ions. Acetylcholine binding to the two α-subunits changes the conformations of the extracellular domains, which rotate the M2 helices and open a channel that is more permeable to K⁺ and Na⁺ than to Ca²⁺. The resulting permeability to all three ions causes the membrane potential to collapse toward a reversal potential (see the section titled “Net Current through Ion-Selective Channels”) around 0 mV. This triggers voltage-gated Na⁺ channels to initiate a self-propagating action potential in the muscle plasma membrane with nearly 100% efficiency (see Fig. 11-8).

Muscle cells and some central nervous system neurons express more than two dozen different isoforms of nicotinic acetylcholine receptors, most with a mixture of subunits but some with five identical subunits.

Many toxins bind nicotinic acetylcholine receptors, blocking transmission of impulses between motor nerves and skeletal muscle (Table 10-1). -Bungarotoxin has been used to characterize the receptor. Curare is a powerful muscle relaxant that is used during surgery because it blocks acetylcholine-binding sites without opening the channel. Local anesthetics, such as procaine, bind within the channel and block ion conductance.

Some people produce autoimmune antibodies to nicotinic acetylcholine receptors, resulting in a disease called myasthenia gravis. When antibody binds to the receptor, the skeletal muscle internalizes the receptor, reducing its response to acetylcholine and causing weakness.

ClC Chloride Channels

Organisms ranging from bacteria to yeast and animals have genes for members of a large family of ClC chloride channels. ClCs control membrane excitability and contribute to volume regulation and epithelial transport. Like P-loop cation channels, ClCs are selective for a particular ion, Cl⁻ in this case, and are gated by the membrane potential. Nevertheless, P-loop cation channels and ClCs differ in evolutionary origins and structure.

ClC subunits are triangular transmembrane proteins formed from 18 α-helices (Fig. 10-13). These helices surround a pore that passes through the middle of each subunit, like the pores of ammonia channels (Fig. 10-14), aquaporins (Fig. 10-15), and porins (see Fig. 7-8C). Several helices around the pore extend only part way across the lipid bilayer. Highly conserved residues in the loops between these helices form the selectivity filter for Cl⁻ in the middle of the protein and the membrane bilayer. Two subunits associate tightly in the lipid bilayer, so each channel has two pores.

Figure 10-13 structure of clc chloride channel. Ribbon diagrams of the crystal structure of StClC isolated from the bacterium Salmonella typhimurium. One subunit is red; the other is blue. The white sphere shows the position of a Cl⁻ ion in the selectivity filter. This structure is the model for other chloride channels, but it actually works more like a carrier than a channel.

(PDB file: 1KPK. Reference: Dutzler R, Campbell EB, Cadene M, et al: X-ray structure of a CIC chloride channel at 3.0 Å reveals the molecular basis of anion selectivity. Nature 415:287–294, 2002.)

Figure 10-14 ammonia channels. A, Ribbon diagram of one subunit of the trimeric AmtB ammonia channel from E. coli with the extracellular side at the top. B, Ribbon and space-filling diagram of the channel viewed from outside the cell. Each of the three identical subunits has a pore for ammonia to cross the lipid bilayer. C, Space-filling cutaway drawing of one subunit exposing the channel for passage of ammonia (blue). In the vestibule facing outside the cell, an ammonium ion gives up a proton to an amino acid side chain before passing through the hydrophobic pore through the core of the protein as uncharged ammonia. At the narrowest point of the pore, hydrogen bonds between the ammonia and two histidines contribute to the specificity.

(PDB file: 1U77. Reference: Khademi S, O’Connell J, Remis J, et al: Mechanism of ammonia transport by Amt/MEP/Rh: Structure of AmtB at 1.35 Å. Science 305:1587–1594, 2004.)

Figure 10-15 water channels. A, Membrane topology of aquaporin-1 deduced from the primary structure. The two halves of the polypeptide have similar sequences but are inverted relative to each other. B, Structure determined by electron crystallography, showing four identical units, each with a pore (red asterisk). Helices are depicted as cylinders. C, Detail of the water pore, with a chain of water molecules crossing the membrane. Two asparagines in the middle of the pore hydrogen bond one water.

(PDB file: 1FQY. Courtesy of P. Agre, Johns Hopkins Medical School, Baltimore, Maryland. Reference: Murata K, Mitsuoka K, Hirai T, et al: Structural determinants of water permeation through aquaporin-1. Nature 407:599–605, 2000.)

The best-known member of the family is ClC0 from skeletal muscle. Like voltage-gated cation channels, ClC0 channels open when the membrane depolarizes and subsequently inactivate. In contrast to cation channels, which have a single conductance state, active Cl⁻ channels conduct at two levels: 10 or 20 pS (picosiemens; see the section titled “Net Current through Ion-Selective Channels”). The pairing of two subunits, each with a pore capable of conducting at 10 pS, explains this behavior. When active, either one or both subunits conduct Cl⁻. A negatively charged glutamate side chain is believed to block the pore of inactive channels and to swing out of the way in active channels. In an unexpected turn of events, physiological analysis of the bacterial ClC channel used for structural studies revealed many features of a carrier that exchanges Cl⁻ for H⁺ rather than features of a typical ion channel behavior like other members of this family. This is one of several examples of blurred distinctions among channels, carriers, and pumps.

Mutations in Cl⁻ channel genes cause several human diseases. Defective skeletal muscle ClC1 channels cause recessive and dominant myotonias. Mutations in kidney ClC5 channels predispose individuals to the formation of kidney stones.

Ammonia Channels

One ancient channel family evolved in early prokaryotes to conduct ammonia across the cell membrane. Ammonia can directly penetrate lipid bilayers, but these channels allow low concentrations of ammonia to serve as a source of nitrogen that prokaryotes use to synthesize proteins and nucleic acids. Bacteria, Archaea, and eukaryotes still depend on these channels. In humans, these channels conduct both ammonia and carbon dioxide across the plasma membranes of red blood cells, where they are known as Rh antigens (Box 10-1). These channels are also important for ammonia transport in the human kidney and liver.

Ammonia channels consist of three identical subunits, each composed of 11 transmembrane helices and having its own conducting pore (Fig. 10-14). These are the only known trimeric channels (Fig. 10-2). The interfaces between these subunits are tightly sealed, but each subunit has a narrow internal pore that is highly selective for ammonia and methylammonium. Chloride channels (Fig. 10-13) and aquaporins (Fig. 10-15) also have conducting pores through subunits rather than the more common strategy of forming pores at a central interface among subunits. Both substrates (ammonium NH₄⁺ and methylammonium CH₃NH₃⁺) are charged in aqueous solution and must leave behind a proton to pass through the pore as uncharged species (NH₃, CH₃NH₂). They pick up a replacement proton on the other side of the membrane as they exit the channel. Selectivity is achieved by the tight fit of the substrates in the hydrophobic pore and by transient formation of an unusual hydrogen bond within the pore. With millimolar ammonium on one side of a membrane, these channels conduct hundreds of ammonia molecules per second without leaking water, protons, or other charged species.

Water Channels

Water diffuses relatively slowly across lipid bilayers, so membranes are barriers to water movement unless the membranes contain water channels. Such channels were postulated years ago to explain the water permeability of certain cell membranes, but they eluded identification until investigators tested a small hydrophobic protein from red blood cells for water channel activity. When expressed in frog eggs, this protein made the eggs permeable to water, so they swelled and burst when placed in hypotonic media. Knowledge of this aquaporin rapidly led to the characterization of a family of related water channels from many species, including bacteria, fungi, and plants. A related channel transports glycerol across bacterial membranes.

Aquaporins provide highly permeable pores for water to cross membranes. Four identical subunits form a stable tetramer in the plane of the membrane (Fig. 10-15). Each subunit has a narrow pore that is selective for water passing through the middle of a bundle of α-helices. About 10 water molecules line up in a pore about 0.3 nm in diameter. Hydrogen bonding of waters with a pair of asparagine residues at a narrow point in the pore allows the channel to be selective for water. The two halves of the protein arose by a gene duplication, since their sequences are remarkably similar.

Osmotic pressure created by pumps, carriers, and the macromolecular composition of the cytoplasm drives water through aquaporins at rates exceeding 10⁹ molecules per second. This explains why red blood cells rapidly swell and shrink passively, depending on the osmolarity of the surrounding fluid (see Fig. 7-6). Water channels have no gates, so they are open constitutively.

Various human tissues express 12 different aquaporin isoforms. Aquaporin-1 is found in red blood cells, renal proximal tubules, blood vessel endothelial cells, and the choroid plexus (which makes spinal fluid in the brain). A few humans carry mutations that inactivate aquaporin-1; remarkably, homozygotes have no symptoms, despite the low water permeability of their red blood cells (and presumably other tissues that depend on this isoform). Aquaporin-2 is required for renal collecting ducts to reabsorb water. A patient with inactivating mutations in both aquaporin-2 genes suffered from severe water loss, called nephrogenic diabetes insipidus. Antidiuretic hormone (vasopressin) controls the placement of aquaporin-2 in the collecting duct membrane. It activates a seven-helix receptor, causing cytoplasmic vesicles storing aquaporin-2 to fuse with the plasma membrane. This increases the permeability of apical plasma membranes to water, allowing it to move from the urine into the hypertonic extracellular space of the renal medulla. Reaction of sensitive cysteine residues with mercuric chloride closes the water pores of aquaporins. This explains how mercurials, used therapeutically as diuretics in the past, inhibit the reabsorption of water filtered by the kidney. The reversible inhibition of aquaporins with mercurials provides a test for their participation in physiological processes.

Aquaporins are also important in plants, which depend on water to maintain turgor and to expand cells in growing tissues. When the stomata in leaves open, water moves continuously from roots through xylem vessels and cells in tissues to exit from leaves as vapor. The movement across cell and tonoplast membranes depends on aquaporins. Water deprivation induces expression of tonoplast aquaporins in some plants and may provide a mechanism for plants to compete for water when it is scarce.

Porins

Porins are channels with wide, water-filled pores found in the outer membranes of gram-negative bacteria and mitochondria. The subunits are composed of an antiparallel barrel of 16 or 18 β-strands that cross the membrane (see Fig. 6-8C). One to three of the loops connecting the strands extend into the center of the barrel and line the pore. The functional molecule consists of three identical subunits.

Most porins are relatively nonselective pores for small, water-soluble molecules, although some are specific for certain solutes, such as sugars. E. coli uses a related protein with 22 transmembrane β-strands to transport iron complexes across the outer membrane. A central “cork” domain occludes the lumen of this β-barrel. Interactions across the periplasmic space with plasma membrane proteins open and close the pore. A variety of viruses use bacterial porins as receptors.

ACKNOWLEDGMENTS

Thanks go to Fred Sigworth for material used in the first edition and to Fred Sigworth and Benoit Roux for their suggestions on revisions to this chapter.

APPENDIX 10-1 Electrical Recordings in Biology

Analysis of electrical activity across biological membranes requires sensitive methods to detect electrical potential differences and the flow of current on a rapid time scale. Physiologists and clinicians use four general methods, with different sensitivities, to detect electrical activity of single channels (patch electrodes), cell membranes (microelectrodes and fluorescent dyes), and whole tissues (extracellular electrodes).

Single-Channel Recordings with Patch Electrodes

Patch-clamp microelectrodes (Fig. 10-16A) provide the best way to characterize the behavior of individual channels. A small-diameter, fire-polished glass capillary is pressed onto the surface of a cell and suction is used to form a high-resistance seal (10 to -50 gigaohms). The membrane patch is small enough to contain just a few ion channels. The electrode becomes part of an electric circuit that can measure current or voltage across the membrane. The high-resistance seal between micropipette and membrane ensures that more electrical current (composed of ions) flows through a single open channel than leaks in around the side of the electrode. When a channel opens, a sensitive ammeter connected to the micropipette records the direction and magnitude of ion flow through the channel as an electrical current. Patch electrodes give direct information about both current and the time that individual channels spend open or closed.

Figure 10-16 electrophysiological measurements. A, Patch electrode. Fine-tipped glass micropipettes form a tight seal with a small patch of plasma membrane. The salt solution inside the pipette conducts current flowing through an open channel in the patch for recording. Lifting the patch of membrane off the cell exposes the cytoplasmic surface of the membrane to experimental manipulation from the bath. Solutes in the micropipette can stimulate the extracellular face of the membrane. B, Measurement of membrane potentials and currents with microelectrodes. A fine-tipped micropipette penetrates the plasma membrane of a cell and is part of a circuit that can record either membrane potential or current flowing across the membrane. To measure membrane potential, a voltmeter in the circuit records the voltage inside the cell relative to the bath and follows any changes that occur when ion channels open and close. To measure current, an electronic feedback device is placed in the circuit to hold the membrane potential at a constant value. Under these “voltage-clamped” conditions, the feedback device provides current to balance any current that results from opening of membrane channels. The current from the feedback device is a record of current across the membrane channels. The membrane potential is an ensemble property of a large number of individual molecules. Microelectrodes can measure the membrane potential on a submillisecond time scale.

Variations of the patch-clamp technique provide access to channel properties. Leaving the membrane patch on the cell (cell-attached configuration) reveals properties of the channels in their cellular context. Lifting the membrane patch off the cell (excised-patch configuration) exposes the cytoplasmic surface of the membrane to ions, enzymes, or second messengers that the investigator adds to the bath. Similarly, the investigator can test the effects of potential ligands, drugs, and ions in the micropipette.

Measurement of Membrane Potentials with Intracellular Microelectrodes and Fluorescent Dyes

A glass capillary is drawn to a fine tip (˜0.5 mm), filled with a conducting solution (3 M KCl), and inserted through the plasma membrane. The tip penetrates the cell with minimal damage, and the membrane seals tightly around it. The microelectrode is connected to a meter to record current and voltage (Fig. 10-16B). Alternatively, the investigator can apply a patch electrode to the cell surface and suck forcefully to breach the membrane, putting the micropipette in continuity with the cytoplasm for recordings from the rest of the membrane.

Two microelectrodes inserted into a beaker of saline register no potential difference. If one electrode is inserted into a cell, the meter registers a potential difference of -60 to -90 mV inside the cell relative to the bath. This membrane potential arises from the combined action of many membrane pumps, carriers, and channels.

New fluorescent dyes provide an optical signal that is sensitive to membrane potential. This is the only convenient approach for acquiring information about the spatial distribution of potential charges within cells.

Extracellular Electrical Measurements

Synchronous electrical activity of thousands of cells produces small electrical currents outside the cells, which can be recorded with extracellular electrodes or even with electrodes on the surface of the body. Physicians take advantage of this phenomenon to record the ensemble electrical activity of the heart (electrocardiogram [ECG]), brain (electroencephalogram [EEG]), and muscle (electromyogram [EMG]). These recordings reflect the behavior of thousands of cells, so they provide little information about events at molecular or cellular levels.

APPENDIX 10-2 The Biophysical Basis of Membrane Potentials

The membrane potential arises from separation of charges across an insulating surface (Fig. 10-17). The lipid bilayer provides the insulation required to separate charges. Either pumps or channels can produce unpaired charges. Pumps that transport unpaired ions generate membrane potentials directly. Channels that pass un-paired ions can use ion concentration gradients across membranes to generate membrane potentials. The concentration gradient provides a diffusional force to drive ions through channels. Because channels are ion specific, an excess of charge builds up after very few ions cross a membrane. This excess charge creates a membrane potential and stops the net movement of additional ions across the membrane.

Figure 10-17 membrane potential. A, Production of a membrane potential, E_m, by a K⁺-selective ion channel and a 10-fold potassium chloride concentration gradient across a membrane. The three panels illustrate the situations without a channel, when a channel first opens, and at equilibrium. B, Dependence of K⁺ fluxes out of the vesicle (J_o) and into the vesicle (J_i) as a function of membrane potential (E_m). K⁺ passes into the vesicle (driven by the concentration gradient) and out of the vesicle (driven by the voltage across the membrane). At a potential of -60 mV, these fluxes are balanced. This is called the resting potential, or E_K. If the membrane potential is greater than -60 mV, the flux of K⁺ into the vesicle (driven by the concentration gradient) exceeds the flux out of the vesicle (driven by the voltage across the membrane). This pushes the potential toward E_K.

This discussion starts with a qualitative description of forces behind membrane potentials and then develops a quantitative account of membrane potentials with single or multiple types of ion channels.

Diffusion Potentials

An impermeable membrane enclosing concentrated potassium chloride is suspended in a bath of more dilute potassium chloride (Fig. 10-17). If the mem-brane contains a pore that is selectively permeable for bidirectional diffusion of K⁺, the concentration gradient drives K⁺ out of the membrane compartment. Because Cl⁻ cannot pass through this selective pore or the membrane bilayer, the inside compartment loses positive charge. Charge imbalance creates an electrical field, negative inside, called the membrane potential. By convention, extracellular voltage is de-fined as zero.

Force provided by the membrane potential influences the diffusion of ions through the pore in both directions. The positive potential outside opposes the diffusion of K⁺ out of the vesicle and drives K⁺ into the vesicle, up its concentration gradient. Net K⁺ efflux continues until a charge imbalance builds up a membrane potential large enough to drive K⁺ influx at the same rate that the concentration gradient drives K⁺ efflux. The electrical potential required to stop net ion movement is called the equilibrium potential for K⁺, or Nernst potential, E_K.

Quantitative Relationships

The quantitative description of membrane potentials by the Nernst equation is the central concept of electrophysiology. This relationship between an ion concentration gradient and a balancing membrane potential is derived as follows, using K⁺ as an example.

The concentration gradient provides the first force. J_o is the rate (expressed in ions per second) of efflux through the K⁺-selective pore. J_i is the rate of influx. The fluxes are proportionate to the concentrations on the side from which the ions come. The ratio of these rates is equal to the ratio of the inside and outside K⁺ concentrations, K_i and K_o:

A typical cell has a K_i:K_o ratio of about 35.

The membrane potential provides a second force. A positive potential gives a positive ion a higher energy, driving it down the electrical gradient. A negative potential has the opposite effect. The difference in electrical energy per mole of ions is equal to zFE, where z is the valence (+1 for K⁺), F is the faraday constant (10⁵ coulombs/mol), and E is the potential in volts. This difference in energy enters the equation for the flux ratio as an exponential term (the “Boltzmann factor”), with the electrical energy difference divided by the thermal energy:

where R is the gas constant and T is the absolute temperature.

The K⁺ fluxes in and out are equal when

This famous Nernst equation can be rearranged to give the equilibrium (Nernst) potential in terms of the ion concentrations.

RT is the thermal energy of a mole of particles. The ratio RT/zF has the dimensions of voltage and provides the electrical potential that gives a mole of charged particles with valence z an electrical energy (zFE) equal to the thermal energy (RT). At physiological temperatures, its value is about 25 mV for univalent ions where z = 1. The ratio of RT/zF establishes the range of potentials (tens of millivolts) that occur in cells.

Another form of the Nernst equation is more convenient. Since ln(x) = 2.3 log(x) and 2.3 RT/F = 60 mV at 30°C, the Nernst equation can be rewritten as

Thus, the membrane potential is -60 mV when the K⁺ concentration inside is 10 times the concentration outside.

Nernst Potential for Various Ions

The Nernst potential can be calculated for each ion known to have a selective channel in cell membranes: Na⁺, K⁺, Ca²⁺, and Cl⁻ (Fig. 10-18). Given physiological gradients of these ions across the plasma membrane, the membrane potential could range from -98 to +128 mV, depending on which channels are open. In resting cells, only K⁺ channels are open, so the resting membrane potential is close to E_K. Thus, variation of extracellular K⁺ concentration changes the membrane potential. In vertebrates, the normal extracellular K⁺ concentration is about 4 mM, but it varies from 2 mM to >8 mM in disease states. This fourfold variation in K_o changes the membrane potential by 30 to 37 mV, enough to affect cellular processes that are sensitive to the membrane potential. Other channels open and close selectively in response to extracellular or intracellular ligands, membrane potential, physical forces, or other factors (see text). Selective activation of channels is responsible for action potentials and other behavior of excitable membranes (see Fig. 11-6).

Figure 10-18 physiological ion concentrations and membrane potentials. Ion concentrations in the cytoplasm and outside a vertebrate muscle cell. The scale on the right shows the corresponding equilibrium membrane potentials (Nernst potentials) that would result if channels for each one of these ions opened.

APPENDIX 10-3 Charging and Discharging the Membrane

Opening or closing ion channels influences the membrane potential and the flux of ions across the membrane. This discussion explains how movement of just a few ions allows cells to change their membrane potential without dissipating ion gradients across the membrane. Consequently, flux through a few ion channels rapidly changes the membrane potential during action potentials. The result of opening multiple channels with different ion selectivities and concentration gradients is also explained.

Membrane Capacitance

The membrane potential (E) produced by a given net charge inside the cell (Q) depends on the physical properties of the membrane, summarized in a constant called capacitance (C):

Capacitance depends on membrane area, thickness (physical separation between internal and external charges), and dielectric constant. If the capacitance is large, many ions must move to change the membrane potential. For cell membranes, the capacitance is approximately 1 mF/cm ². One farad is 6 × 10¹⁸ charges per volt.

Charge Movement for a Small Cell

The following calculation shows why ion concentration gradients change little during most electrical events in cells. This is important to obviate the requirement for excessive energy to restore ion gradients. A cell that is 18 mm in diameter might have a capacitance of 10⁻¹¹ F, or 6 × 10⁷ charges per volt of membrane potential. Thus, movement of 6 million positive charges out of the cell produces a membrane potential of -0.1 V, or -100 mV. A cell of this size with an internal concentration of 150 mM K⁺ contains about 2.7 × 10¹¹ K⁺, so movement of fewer than one out of 40,000 K ions from inside to outside creates a large membrane potential. This fraction of ions is far less for large cells, owing to their smaller ratio of surface area to volume. Thus, little energy is required for a large change in membrane potential, such as an action potential. When ion channels open, few ions cross the membrane before an opposing electrical field develops and retards fur-ther flux.

In Chapters 8 and 9, pumps and carriers were also noted to produce opposing membrane potentials when moving ions across membranes. This can be avoided by opening ion channels that short-circuit the change in membrane potential by providing pathways for counterions to move in the same direction or similar ions to move in the opposite direction across the membrane.

Rate of Charge Movement through Channels

A current is the rate of movement of charge. The ionic current (I) across a membrane is taken as positive when charges move outward. According to this definition, the equation for conservation of charge in a cell is

A positive current reduces the net charge inside the cell, and vice versa. Including the relationship for capacitance (E = Q/C), the equation relates the current to the rate of change of membrane potential:

Because channels conduct about 6 × 10⁶ charges per second, a single open channel changes E at a rate of -100 mV/sec on this 18-μm cell.

Because most channels occur at densities of 50–200/μm ², an 18-μm cell will have 50,000 to 200,000 channels. If a few channels open together, the membrane potential rapidly approaches the Nernst potential for the selected ion. This explains why most electrical events in cells transpire in a millisecond time frame. Because the rate of current flow through ion channels is not limiting, the time course of electrical events depends on the kinetics of channel opening and closing. This focuses attention on factors that control whether channels are open or closed, also known as gating.

Net Current through Ion-Selective Channels

Another way to describe ionic current across a membrane is

where e_o is the elementary charge. The dependence of current on membrane potential for real channels is complicated (Fig. 10-17B), so electrophysiologists approximate this current-voltage relationship of channels by a linear relationship, such as Ohm’s law (E = IR):

where g is conductance (inverse of resistance) and E_ion is the reversal potential of a particular ion channel (the potential at which current reverses from out to in). For perfectly selective pores, the reversal potential for each ion equals its Nernst potential, even in the face of other ionic gradients. The unit used for current is siemens (equivalent to 1 ampere per volt). Most channels have currents in the picosiemens range (10⁻¹² S).

For a simple pore, a plot of current versus mem-brane potential is linear, with no current at E_ion; real channels are more complicated. Typical plots of current versus voltage deviate from a straight line. This is called rectification. Deviation may be attributable to voltage-dependent conformational changes in the channel protein or to nonpermeant ions blocking the pore.

Each channel contributes independently to the total current, so given n channels on a cell membrane, the total current is

Opening Na⁺ and K⁺ channels has opposite effects because the ion concentration gradients are reversed. The Nernst potential for Na⁺ is about +65 mV in a typical cell, given a 10-fold excess of Na⁺ outside the cell. Current through an Na⁺ channel is negative (i.e., inward) at membrane potentials below E_Na. Thus, if a Na⁺ channel opens on a cell in which E equals 0, the membrane potential rises toward E_Na.

Consequence of Multiple Channel Types Opening Simultaneously

More than one type of open channel creates a situation more complicated than the equilibrium described by the Nernst potential for a single-ion species (Figs. 10-18 and 10-19). Consider a cell with physiological ion gradients and two channels—one open K⁺ channel and one open Na⁺ channel—having conductances of g_K and g_Na. The total current through these two channels is the sum of the individual currents:

Figure 10-19 membrane potential and currents across a membrane with two types of channels. A, Dependence of currents on membrane potential resulting from opening either K⁺ channels or Na⁺ channels individually or together. In contrast to Figure 10-17, which shows ion fluxes in each direction, this is a plot of net current. E_K and E_Na are the equilibrium potentials (zero current) when only potassium or sodium channels are open. When both types of channels are open, the equilibrium potential (E_eff) is midway between the equilibrium potentials of the two types of channels. B, Distribution of positive (red) and negative (blue) ions across the plasma membrane and around a cell having a negative membrane potential. Excess negative charge builds up near the inside of the membrane, with the excess positive charge near the outside.

Note from this relationship that current is zero at the midpoint between E_K and E_Na, and the line has twice the slope of a single channel (i.e., twice the conductance).

Which channel predominates? The equation for I_total can also be written as

where the effective conductance geff and reversal potential E_eff are given by

and

The two channels together act like a single channel with an effective conductance equal to the sum of their conductances and a reversal potential that is the weighted average of their reversal potentials, that is, weighted by their relative conductances (Fig. 10-19A).

Goldman, Hodgkin, and Katz formulated another equation for E. It uses permeability (P, in units of cm/sec) to describe the membrane potential:

This equation summarizes the concepts presented here about membrane potentials. Just two factors determine the membrane potential: (1) the concentration gradients of different ions (e.g., the Nernst potentials for each ion) and (2) the relative permeabilities of the membrane to these ions. When all Na⁺ and Cl⁻ channels are closed (P_Na, P_Cl = 0), the equation reduces to the Nernst relationship for K. When all K⁺ and Cl⁻ channels are closed (P_K, P_Cl = 0), the equation collapses to the Nernst relationship for Na⁺.

In nerve cells, the resting membrane is most permeable to K⁺ but also slightly permeable to Na⁺, so the resting potential is near E_K. Opening more K⁺ channels or lowering extracellular K⁺ makes the resting potential more negative. Opening more Na⁺ channels or raising extracellular Na⁺ makes the resting potential more positive.

Charge Redistribution by Electrical Conduction

Most cellular ions have balancing counterions, whereas unpaired ions contributing to membrane potentials are confined to boundary layers near the membrane (Fig. 10-19B). Like-charged ions repel one another, so unpaired ions tend to accumulate at boundaries where they can move no farther.

During electrical events, unpaired ions redistribute over membrane surfaces by electrical conduction at rates much faster than diffusion. This works as follows: Ions are always in motion, exchanging places. Introduction of extra ions sets off a chain of movements as neighbors repel each other, resulting in rapid spread of unbalanced charge near the membrane. Diffusion of the entering ions over to the membrane would take much longer than this electrical wave. Thus, electrical signaling is the fastest signaling process in cells.