## Stephen G. Waxman, Jeffery D. Kocsis, and Peter K. Stys

Print publication date: 1995

Print ISBN-13: 9780195082937

Published to Oxford Scholarship Online: May 2009

DOI: 10.1093/acprof:oso/9780195082937.001.0001

# Voltage-clamp studies in axons: Macroscopic and single-channel currents

Chapter:
(p. 257 ) 13 Voltage-clamp studies in axons: Macroscopic and single-channel currents
Source:
The Axon
Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780195082937.003.0013

# Abstract and Keywords

This chapter describes macroscopic membrane currents measured in amphibian and mammalian nodes of Ranvier with the voltage-clamp method. These results are compared with those of single-channel recordings, which provide important data on channel characteristics in myelinated axons. The results obtained from the calculation of the action potentials with voltage-clamp data obtained from frog, rat, and human nerve fibers are also reviewed. It is shown that the properties of the various new ionic channel types detected with the patch-clamp technique help explain previously unsolved problems concerning the ionic basis of accommodation, resting potential, and various pathophysiological phenomena.

# ACTION POTENTIALS AND NODAL MEMBRANE CURRENTS

The first quantitative description of membrane currents recorded with the voltage-clamp method was made in single myelinated nerve fibers of the frog (Dodge and Frankenhaeuser, 1958 ). These studies showed that the ionic mechanisms underlying the generation of the action potential in a frog myelinated nerve fiber are very similar to those described in the unmyelinated giant axon of the squid by Hodgkin and Huxley ( 1952 ). Frankenhaeuser’s method of voltage clamping the node of Ranvier and analyzing the membrane currents subsequently was extended to other amphibian myelinated nerve fibers (Dodge, 1963 ; Hille, 1967 ; Nonner, 1969 ). These studies provided a conceptual framework in which the nodal membrane currents were composed both of currents flowing through ion-selective sodium and potassium channels and of leakage currents. The inter-nodal axolemma together with the myelin was conceived to be a passive resistive element, the main function of which was to provide an effective isolation for internodal current flow. In this “classical” view, the upstroke of the action potential is brought about by a rapid activation of sodium channels, and repolarization is due to sodium channel inactivation and to a delayed activation of potassium channels (Hille, 1992 ; Stämpfli and Hille, 1976 ).

Following a short communication by Horáckova et al. ( 1968 ), the first quantitative descriptions of membrane currents in mammalian nodes of Ranvier were published by Brismar in rat ( 1979, 1980 ) and by Chiu et al. in rabbit ( 1979 ). A voltage-clamp study in single human myelinated nerve fibers also has been reported (Schwarz et al., 1993 ). These studies showed that the mammalian node of Ranvier contains almost no delayed outward-rectifying fast potassium channels and indicated that, in mammalian nerve, the ionic mechanisms underlying the action potential must be different from those in amphibian myelinated nerve fibers. In addition, it became apparent that mammalian and amphibian nodes of Ranvier are very complex anatomical structures (Berthold and Rydmark, 1983 ; Rosenbluth, 1983 ; see also Chapters 2, 11, and 21 ) with a distinct distribution of more than three populations of ionic channels (Baker et al., 1987 ; Black et al., 1990 ; Dubois, 1981 ; Kocsis and Waxman, 1987 ). Further progress in the analysis of nodal ionic currents was achieved when it became possible to perform single-channel measurements in myelinated nerve fibers (Jonas et al., 1989 ) with the patch-clamp technique (Hamill et al., 1981 ; Neher and Sakmann, 1976 ). These studies provided direct evidence for the existence of various populations of ionic channels already known from the analysis of macroscopic currents. A multiplicity of ionic channels that had not been detected so far in macroscopic membrane current recordings also was observed in the node, paranode, and internode.

This chapter will describe macroscopic membrane currents as measured in amphibian and mammalian nodes of Ranvier with the voltage-clamp method. These results are compared with those of single-channel recordings, which have provided important data on channel characteristics in myelinated axons. We also review the results obtained from the calculation of action potentials with voltage-clamp data obtained from frog, rat, and human nerve fibers. It also will be shown that the properties of the various new ionic channel types detected with the patch-clamp technique help to explain previously unresolved problems concerning the ionic basis of accommodation, of the resting potential, and of various pathophysiological phenomena. Results of these studies also provide links between axoplasmic metabolism and excitability.

In order to perform voltage-clamp experiments on (p. 258 ) the node of Ranvier, a single myelinated nerve fiber must be isolated from a peripheral nerve (Stämpfli, 1952 ). Human nerve fibers can be dissected from nerve material obtained either from grafting operations or from amputated limbs. The review by Stämpfli and Hille ( 1976 ) gives a detailed description of how to dissect and mount a single myelinated nerve fiber isolated from the frog sciatic nerve. The same general dissecting procedure is used to isolate a single mammalian myelinated nerve fiber. Isolating a rat or human nerve fiber, however, is more difficult because of the considerable amount of connective tissue in mammalian nerve. Mammalian nerve fibers are also extraordinarily sensitive to mechanical stretch. Readers interested in further details should consult the review by Stämpfli and Hille ( 1976 ), which gives an overview of the various current- and voltage-clamp methods. Most of the data presented in this chapter were obtained with the voltage-clamp method designed by Nonner ( 1969 ).

Figure 13-1 shows action potentials measured in a rat nerve fiber. Blockage of potassium channels with external tetraethylammonium (TEA) ion and internal CsCl does not induce a major change in action potential duration (Figure 13-1A ), whereas in frog nerve fibers the duration is prolonged severalfold (compare Figures 13-18 and 13-19 ). This indicates that the ionic mechanisms underlying the action potential in rat and frog nerve fibers are different. The duration of rat action potentials at room temperature is about 1.5 milliseconds if measured near the threshold potential. At the higher body temperature of mammals, the action potential is shortened to a duration of about 0.3 milliseconds (Figure 13-1B ).

Membrane currents underlying the action potential in a frog and a rat nerve fiber are presented in Figure 13-2 . The holding potential was set close to the resting membrane potential, which is about −70 mV in frog (Stämpfli and Hille, 1976 ) and between −75 and −80 mV in rat (Neumcke and Stämpfli, 1982 ), rabbit (Chiu et al., 1979 ), and human (Schwarz et al., 1993 ) nodes of Ranvier. On depolarizing potential steps, a transient inward current is recorded that is carried by Na+ ions. This sodium current changes direction at potentials more positive than the sodium equilibrium potential. The potential-dependent parameters of sodium currents are similar in frog and rat nerve fibers (Neumcke et al., 1987 ), but the outward potassium currents are clearly different. Only a small maintained outward potassium current is present in the rat, whereas in the frog large outward potassium currents occur. The differences in potassium conductance result in different tail currents. On repolarization, there are only small tail currents in the rat but large tail currents in the frog nerve fiber.

An action potential of a single human ulnar nerve fiber recorded at 20°C is shown in Figure 13-3 . Its form and duration (1.5 milliseconds) are similar to those of a rat action potential recorded at the same temperature. Figure 13-3 also presents a family of membrane currents recorded in the same fiber. As in the rat nerve fiber, outward potassium currents are not present. The outward current consists mainly of a nonspecific leakage current.

# SODIUM CHANNELS

## Macroscopic Sodium Currents

### Activation and Inactivation of Sodium Currents.

The total membrane current in a node of Ranvier consists of a capacity current and an ionic current. The ionic current has three components: In addition to current flow through ionic channels selective for Na+ and K+, a leakage current of unknown origin regularly is present in nodal voltage-clamp recordings. By definition, the leakage current has a linear potential dependence and does not show activation and inactivation kinetics. Moreover, the leakage current as yet cannot be blocked by specific substances. Sodium currents can be isolated from the other membrane currents by measuring the tetrodotoxin (TTX)-sensitive current, as demonstrated in Figure 13-4 . TTX specifically blocks sodium currents in nodal membranes of frog (Hille, 1968 ) and rat (Neumcke et al., 1987 ) nerve fibers. After sodium channel blockage with TTX, a small-capacity current becomes

fig. 13-1. Action potentials recorded in a rat node of Ranvier. A, Action potentials recorded at 20°C. The action potentials were elicited with a 0.1 millisecond depolarizing current stimulus before and after exchange of the normal solutions with external TEA and internal CsCl. B, A local response and an action potential elicited at 37°C in Ringer’s solution with 30 μs sub- and suprathreshold current stimuli. Note the different time scales in A and B. (From Schwarz and Eikhof, 1987 ).

(p. 259 )

fig. 13-2. Membrane currents in a rat and a frog nerve fiber induced by depolarizing pulses in Ringer’s solution. Capacity and leakage currents have been subtracted. Each positive pulse was preceded by a 50 mV negative pulse of 50 milliseconds (Epre). EH, holding potential of −75 mV in the rat and −70 mV in the frog. (From Röper and Schwarz, 1989 .)

apparent upon depolarizing and repolarizing potential steps. The outward current is the sum of a very small outward potassium current and a leakage current. Separation of sodium currents is also possible by blockage of the potassium current with TEA and subtraction of the leakage and capacity currents (see Figure 13-19 ). TEA is known to block nodal outward potassium currents specifically (Hille, 1967 ; Koppenhöfer, 1967 ).

Sodium conductance of the nodal membrane increases upon depolarization and decreases upon repolarization. However, Figure 13-4 shows that the sodium current also decreases during a maintained depolarization. This process is called sodium conductance inactivation and leaves the membrane refractory for a few milliseconds. In the Hodgkin-Huxley model (Frankenhaeuser and Huxley, 1964 ; Hodgkin and Huxley, 1952 ), this behavior of sodium currents is described by assuming the existence of two independent gating processes, activation and inactivation, that involve two kinds of gating particles, called m and h. In the rat node of Ranvier three m particles control activation and one h particle controls inactivation (Neumcke and Stämpfli, 1982 ; Neumcke et al., 1987 ). The probability that a sodium channel is in its open state is therefore m 3 h, and the macroscopic sodium current (I Na) can be described by $Display mathematics$ where E = the membrane potential, E Na = the sodium equilibrium potential, and g Na = the sodium-limiting conductance. As will be shown below, single-channel recordings demonstrate that there is indeed a homogeneous population of sodium channels. With a single-channel conductance γNa and a given number of sodium channels N, the equation can be written as $Display mathematics$

To obtain standard data for the calculation of action potentials, a voltage-clamp analysis of sodium and potassium conductances within a potential range from E = −120 to +80 mV must be performed (Frankenhaeuser and Huxley, 1964 ). The design of the pulse protocols is very similar to that first described by Hodgkin and Huxley ( 1952 ). Frankenhaeuser ( 1960 ) described sodium currents in the node of Ranvier of the toad Xenopus laevis by equations similar to those used for the description of membrane currents in the squid giant axon by Hodgkin and Huxley ( 1952 ). These equations are still very useful for describing the macroscopic membrane currents of amphibian as well as mammalian myelinated axons.

Chiu et al. ( 1979 ) showed that sodium inactivation is faster in rabbit compared with frog nerve fibers. Furthermore, these authors found that the action potential duration in frog and rabbit is similar. They explained

fig. 13-3. Action potential and membrane currents recorded from the same fiber isolated from a human ulnar nerve. Left, Action potential elicited with a 0.5 millisecond depolarizing current stimulus. Right, Membrane currents recorded upon depolarizing potential steps from a holding potential of −80 mV to membrane potentials between −20 and +100 mV in steps of 20 mV. Each depolarization was preceded by a 50 millisecond hyperpolarization to −120 mV. Leakage and capacity currents were not subtracted. (From Schwarz et al., 1993 .)

(p. 260 )

fig. 13-4. Membrane currents induced by a 50 mV depolarizing potential step in a single myelinated rat nerve fiber at 20°C following a 50 mV hyperpolarizing potential of 50 milliseconds. Top, Pulse protocol. A, Membrane current in normal Ringer’s solution. B, Same protocol as in A, except that 300 nM TTX was added to the Ringer’s solution. C, TTX-sensitive current obtained by subtracting the membrane current shown in B from that in A. One data point is plotted every 50 μs during the first 1.5 milliseconds, and thereafter every 0.5 millisecond. The continuous line was calculated assuming two time constants for sodium inactivation.

the similarity of the action potential duration by the faster sodium conductance inactivation in rabbit compared to frog nerve, which could compensate for the lack of delayed potassium conductance activation for repolarization of the action potential. However, these findings contrast with the experiments of Neumcke et al. ( 1987 ), which show that sodium inactivation kinetics are even slower in rat compared with that of the frog. This corresponds to the observation that the action potential of rat nerve fibers has a longer duration compared to that in frog nerve (compare Figure 13-1 and Figure 13-18 ).

To describe sodium and potassium currents in the node of Ranvier, a better approximation often is obtained when permeabilities instead of conductances are calculated with the Goldman equation (Frankenhaeuser, 1960, 1963 ). A complete analysis of sodium permeability activation and inactivation in rat nerve fibers has been made by Schwarz and Eikhof ( 1987 ) and Neumcke et al. ( 1987 ). An analysis of potassium conductance in rat nerve fibers based on that done in the frog (Dubois, 1981 ) can be found in the paper by Röper and Schwarz ( 1989 ).

### Temperature Dependence.

In vivo, action potentials in mammalian myelinated nerve fibers are generated and propagated at 37°C. Figure 13-1B shows that the duration of an action potential recorded at 37°C is about 0.3 milliseconds, in contrast to 1.5 milliseconds at 20°C (Schwarz and Eikhof, 1987 ). The temperature coefficient, Q 10, for action potential duration is dependent on temperature, decreasing from 3.7 between 0° and 10°C to 2.2 between 20° and 40°C (Schwarz, 1986 ). In addition to the change in duration, the action potential recorded at 37°C has a smaller amplitude than that recorded at 20°C. This difference is due to the larger leakage conductance and the lower sodium equilibrium potential measured at 37°C. Both changes could be due to experimental artifacts, which occur more easily at 37° than at 20°C. The smaller action potential amplitude also could be explained by differences in the Q10 of the rate constants for sodium activation and inactivation. Indeed, in amphibian nerve fibers, Frankenhaeuser and Moore ( 1963 ) found that the Q 10 for sodium inactivation rate constants α h and β h are 2.8 and 2.9, respectively, for a temperature range between 5° and 20°C. The rate constants for sodium activation, α m and β m , were less temperature dependent, the Q 10 being 1.8 and 1.7, respectively. This difference in Q 10 also was found in rat (Schwarz and Eikhof, 1987 ) and squid (Kimura and Meves, 1979 ) axons.

## Single-Channel Sodium Currents

Numerous experiments during several decades have suggested that there exist different membrane channels selective for Na+, K+, and Cl ions and less specific leakage channels. With the introduction of the patch-clamp technique by Neher and Sakmann ( 1976 ), these channels could be visualized directly and their kinetics studied. Additionally, membrane patches can be excised from the axonal membrane in two different modes. Either the external side (outside-out configuration) or the cytoplasmic side (inside-out) of the membrane faces the bath solution (Hamill et al., 1981 ). Inside-out patches allow the investigator to change the solution facing the inner side of the membrane. The tip of the recording pipette carrying the cell-free membrane patch including the channels under investigation can be directed with (p. 261 ) the help of a micromanipulator into other solutions (Koh and Vogel, 1993 ; Yellen, 1982 ). Thus the effects of different substances and toxins, of different ions (including H+) or adenosine triphosphate (ATP), or of nucleotides now can be investigated easily when they are applied to the cytoplasmic side of the channels, permitting observations that in the intact axon had been difficult and unsatisfactory (Koppenhöfer and Vogel, 1969 ).

Single-channel recording from peripheral myelinated axonal membrane was impeded in early studies by the myelin sheath covering the membrane, but it finally was achieved by mechanically pulling the myelin away from its axoglial junctions or, even more effectively, by enzymatic demyelination using the proteolytic enzymes collagenase and protease (Jonas et al., 1989 ). Thus, demyelinated and clean nodal and paranodal parts of amphibian (Figure 13-5 ), mammalian, and even human axons have been obtained in a condition that is ready to form a tight seal with a glass pipette. In order to ensure that the axonal membrane, rather than the glial membrane, formed the patch, Lucifer Yellow dye was allowed to diffuse from the pipette after breaking the membrane by suction (Wilson and Chiu, 1990 ). In more than 50 control experiments on demyelinated Xenopus fibers, always axoplasmic structures and never external myelin fragments were stained. No remnants of myelin were left, as also could be shown in other staining experiments with Gal C, a specific marker of myelin membranes (Koh et al., 1994 ).

Recordings and current-voltage data of single axonal sodium channels from human nerve have been obtained by Scholz et al. ( 1993 ) and are shown in Figure 13-6 . At the beginning of weak depolarizations, inwardly directed single-channel events appear that vanish after some time. Averages of single-channel currents from amphibian nerve (Jonas et al., 1989 ) show the characteristic kinetics of voltage-gated sodium channels. They rise quickly to a peak and then decline more slowly, like macroscopic sodium currents reflecting activation and inactivation. The single-channel events can be suppressed in the presence of external TTX, and their open time is prolonged by external Anemonia sulcata toxin II. They are found preferentially in the constricted area of the demyelinated axon (presumably in the nodal part of the axon membrane), specifically around its central part, which sometimes is marked by a ring of dark spots (Koh et al., 1994 ). The single-channel conductance of human and amphibian sodium channels is found to be 13 and 11 pS, respectively. The slight differences only reflect some differences in experimental conditions such as Na+ ion concentration and temperature. The extrapolated reversal potential (Figure 13-6B ) is close to the Nernst potential of Na+ ions calculated for these experimental conditions. This indicates that the channels are selective for Na+ ions. Between single sodium channels from human and amphibian nerve, no major differences have been seen in electrophysiological and pharmacological characteristics studied so far (Jonas et al., 1989 ; Scholz et al., 1993 ) (see Table 13-1 p. 266).

Dividing the peak sodium current amplitude of 25 nA in the macroscopic current measurement of Figure 13-3 by the corresponding single-channel current amplitude of 1 pA (cf. Figure 13-6 ; Table 13-1 ) leads to an estimated sodium channel number of 25,000 per node. Assuming a nodal area of 25 μm2 (Berthold and Rydmark, 1983 ) yields a minimum channel density of about 1000 sodium channels per μm2 of mammalian nodal membrane. This is similar to the densities arrived at by other methods (see Chapter 4 ).

fig. 13-5. Demyelinated axon from Xenopus laevis sciatic nerve. Enzymatic treatment with collagenase and protease led to disruption of the axoglial connections and retraction of the myelin from the node, which appears as a constricted area. Scale bar = 20 μm. (Courtesy of D.-S. Koh.)

(p. 262 )

fig. 13-6. Single sodium channels recorded from a demyelinated human axon and i-E curve. A, Traces of individual responses from an outside-out patch that contained at least three sodium channels. Holding potential, −90 mV; 50 millisecond prepulses to −130 mV; 24°C. Ordinates at left give current levels of open channels. B, Sodium current-voltage relationship obtained from seven outside-out patches (mean values ±SEM, n = 5 to 20). Based on the steepness of the i-E curve, the single-channel conductance is 13 pS. Extrapolated linear regression line indicates a reversal potential of +61 mV. (From Scholz et al., 1993 .)

# POTASSIUM CURRENTS

## Macroscopic Potassium Currents

Figure 13-2 shows that large outward-rectifying potassium currents can be elicited in frog nerve fibers. These potassium currents first were described quantitatively by Frankenhaeuser ( 1963 ) using the Hodgkin-Huxley equations. The probability that a potassium channel will be in an open state is expressed by the product r a k, where n denotes the potassium current activation and k the potassium current inactivation parameter. Analogous to the sodium current and assuming a homogeneous population of potassium channels, the macroscopic potassium current (I K) can be described by the equations $Display mathematics$ and $Display mathematics$ where N is the number of potassium channels, which vary with membrane potential and time, and with a single-channel conductance γK. A value greater than unity is necessary for the exponent a of the potassium current activation parameter n to take account of the sigmoidal activation of the potassium current during a depolarizing potential step. The value of a varies between 2 for nodes of Ranvier of Xenopus laevis (Frankenhaeuser, 1963 ) and 4 for Rana fibers (Dodge, 1963 ; Hille, 1968 ; Koppenhöfer, 1967 ). At the end of depolarizations lasting several seconds, potassium currents are inactivated. The potassium inactivation parameter k decreases exponentially with time for macroscopic potassium currents (Frankenhaeuser, 1963 ) and is the sum of two exponential components, k 1 and k 2, the earliest indication of more than one component of potassium conductance (Schwarz and Vogel, 1971 ).

### Fast Potassium Currents.

A depolarization to +60 mV in the frog node of Ranvier in normal Ringer’s solution elicits a large outward-rectifying potassium current, which in turn induces a large potassium tail current upon repolarization to the holding potential (Figure 13-7 ). To avoid potassium accumulation outside the nodal membrane, the same experiment was repeated in isotonic KC1. After a depolarization to 0 mV, the potassium equilibrium potential in isotonic KCl, a large inward potassium tail current occurs on repolarization consisting of a fast and a slow tail current component, the former being selectively blocked by 4-aminopyridine (4-AP) in frog (Dubois, 1981 ) and rat (Röper and Schwarz, 1989 ) nerve fibers. Plotting the amplitudes of the instantaneous fast potassium tail currents recorded after a conditioning depolarization of various amplitudes (p. 263 )

fig. 13-7. Delayed-rectifier potassium currents of toad node of Ranvier. Top, Pulse protocols. A, Outward potassium current in Ringer’s solution. B, Potassium tail currents in isotonic KCl solution following a 100 millisecond conditioning pulse to E = 0 mV. The dashed lines indicate zero current; capacity and leakage currents have been subtracted. (Modified from Bräu et al., 1990 .)

showed a systematic bend in the curve near −30 mV (Figure 13-8 ). These and other observations led Dubois ( 1981 ) to the conclusion that two types of fast potassium channels can be distinguished in the frog node of Ranvier. In addition, the slow tail current component indicates the presence of a slow potassium channel population.

The existence of three different voltage-dependent potassium channel types recently has been confirmed with the patch-clamp technique (I, F, and S channels; see section on single-channel potassium currents later in this chapter). The two fast potassium tail current components, f1 and f2, can be separated pharmacologically in frog nerve fibers. The f2 component can be blocked selectively with capsaicin (Dubois, 1982 ) and the f1 component with dendrotoxin (DTX) or mast cell degranulating peptide (MCDP; Bräu et al., 1990 ). Capsaicin and DTX were not found to be as selective in rat as in frog nerve fibers (Corrette et al., 1991 ; Röper and Schwarz, 1989 ). Figure 13-8 also shows that the relative contribution of f1 channels is larger in motor than in sensory fibers in frog peripheral nerve (Dubois, 1981 ).

fig. 13-8. Total fast potassium conductance (circles) in toad peripheral nerve as calculated from the amplitude of fast potassium tail currents recorded at the holding potential of E = −90 mV after 100 millisecond conditioning depolarizations of various amplitudes. The values of the f1 conductance (squares) were calculated from the values obtained using a holding potential of 0 mV. The difference between total potassium conductance and f1 conductance yields the f2 conductance. Note that the relative amplitudes of the f1 and f2 conductances are different in motor and sensory fibers. (From Dubois, 1981 .)

### Slow Potassium Current.

At large depolarizations of an intact rat node of Ranvier, a slowly increasing potassium current of small amplitude is apparent (Figure 13-2 ). The amplitude of this slow potassium current can be increased by increasing the KCl concentration in the external solution. On depolarizing potential steps, potassium currents exhibiting slow activation kinetics can be recorded. Hyperpolarizing potential steps induce slowly deactivating potassium currents. Further analysis shows that about 50% of this slow potassium conductance is activated at −60 mV (Figure 13-9C ). The activation curve is flat; therefore, a considerable amount of the slow potassium conductance already is activated at the resting potential of about −80 mV (Brismar and Schwarz, 1985 ). The slow potassium conductance can be blocked with TEA (Figure 13-9Ab ). Because of the absence of fast potassium channels in rat and human nodal membranes, that part of the slow potassium conductance already activated at the resting potential assists, together with the leakage conductance, in repolarizing the action potential. As shown in our laboratories and by Kocsis et al. ( 1987 ), activation of additional slow potassium conductance is involved in action potential frequency adaptation (see Figure 13-21 ).

A small potassium current is activated on large negative pulses and superimposed on the deactivating slow potassium current (Figure 13-9Aa ). This small current could be due to an inward-rectifying potassium current. This assumption is supported by reports about the presence of an inward-rectifying potassium current in dorsal root fibers (Baker et al., 1987 ; Birch et al., 1991 ), optic nerve (Eng et al., 1990 ), and sciatic nerve (Gordon et al., 1991 ) of the rat. The predominant location of the inward-rectifying potassium channels has been assigned to the internode.

### Distribution of Potassium Channels in Mammalian Myelinated Nerve Fibers.

Whereas only small outward potassium currents and potassium tail currents can be elicited in intact mammalian nerve fibers, large outward potassium currents emerge after paranodal demyelination. Early attempts to induce acute demyelination were made by using osmotic shock or mechanical stretch (Chiu et al., 1979 ). A more reliable method is the superfusion of the node with 0.2% pronase or 0.2% lysolecithin (Figure 13-10 ). Kinetic and pharmacological analysis of potassium tail currents recorded in rat nerve fibers after paranodal demyelination suggest the existence of two fast and one slow potassium channel populations, very (p. 264 )

fig. 13-9. Potassium currents in rat peripheral myelinated axon recorded during 80 millisecond depolarizing and hyperpolarizing pulses of increasing amplitude. The positive pulses were from −45 to 0 mV in steps of 15 mV and one pulse to +25 mV; the negative pulses were from −105 to −150 mV in steps of 15 mV. A, measurements were made in the presence of 300 nM TTX. Aa: measurements in isotonic KCl; Ab: measurements after addition of 10 mM TEA to the isotonic KCl solution; Ac: pulse protocol. Leakage and capacity currents were not subtracted. B, Current-voltage relation of the steady-state currents in Aa (open circles) and Ab (solid circles). The straight line denotes the leakage current as measured in the same fiber in Ringer’s solution. The potassium current (I K) was determined from the difference between the steady-state currents and the leakage current. C, The normalized slow potassium conductance (g K,s) was calculated from the equation g K = I K/(EE K), and plotted against membrane potential. The curve was calculated from the fitted parameters of a Boltzmann equation (g K,s = 1/[1 + exp ((Es E)/k)]) with the inflection point at E s = −59.6 mV and the slope factor k = 18.2 mV. The holding potential (E H) was −75 mV. (From Röper and Schwarz, 1989 .)

fig. 13-10. Potassium currents (upper traces) recorded during depolarizing pulses of increasing amplitude before and after paranodal demyelination of rat peripheral myelinated axon with 0.2% lysolecithin for 15 minutes. Pulse potentials were between −55 and +80 mV in steps of 22.5 mV. Capacity and leakage currents (lower traces) were elicited by a potential step to −150 mV. External solution: Ringer’s solution +300 nM TTX; holding potential: −77 mV. (From Röper and Schwarz, 1989 .)

similar to those first described by Dubois ( 1981 ) in the nodal membrane of the frog. The increase in the capacity current following demyelination allows calculation of the density of each potassium current component and hints at their distribution within the node of Ranvier (Chiu and Ritchie, 1981 ). The presence of ionic channels in the internodal axolemma can be demonstrated after internodal demyelination (Bostock and Sears, 1978 ). Grissmer ( 1986 ) showed that the frog internode contained a very low density of sodium and potassium channels compared with the density of both channel types in the nodal membrane. This also has been shown for sodium channels in voltage-clamp experiments in the rabbit internode (Chiu and Schwarz, 1987 ). In the rat, the density of the different ionic current components changes within the nodal, paranodal, and internodal part of the axolemma. Fast potassium channels are concentrated in the paranode, and their density decreases to 1/6 in the nodal and internodal membrane. This distinct distribution recently has been confirmed by immunocytochemistry using antibodies against the Kv 1.1 and Kv 1.2 channel (Wang et al., (p. 265 ) 1993 ; O. Pongs, personal communication). Slow potassium channels are confined mostly to the nodal membrane, and their density decreases to 1/30 in the internode (Röper and Schwarz, 1989 ).

## Single-Channel Potassium Currents

Single-channel measurements have provided unequivocal evidence for the existence of different potassium channel types. Their main electrophysiological and pharmacological characteristics are listed in Table 13-1 . There are voltage-dependent potassium channels that can be distinguished by their intermediate, fast, and slow time course of deactivation; they are termed I, F, and S, respectively. The activity of another voltage-gated potassium channel additionally depends on the internal calcium concentration, and it is called the KCa channel. Furthermore, three less voltage-sensitive background potassium channels have been observed, an ATP-sensitive, a flicker, and a sodium-activated potassium channel. It will be shown that the potassium current components f1, f2, and s closely resemble the potassium channel types I, F, and S, respectively, in their electrophysiological and pharmacological properties.

### I Channel.

In Figure 13-11 , recordings from potassium channel types I, F, and S are shown. Their different kinetic behavior is evident during the deactivation process. A depolarizing pulse to E = 0 had opened the channels, but no potassium current flows at the reversal potential in high-potassium internal and external solution. At the beginning of repolarization (see arrows at top recordings of Figure 13-11A and B), instantaneous potassium currents flow and closing of channels starts. In the channel type that is presented in the left-hand column, deactivation occurs within some tens of milliseconds. Because of the time constant of deactivation, this channel is called the intermediate (I) channel, as compared to a faster (F, right-hand column) and a slower (S, lower recording in left-hand column) channel. The current-voltage relation of the single I channel amplitudes (circles in Figure 13-11C ) reveals a conductance of 23 pS (−120 mV < E < −40 mV, high-potassium external solution, 13° to 15°C), It is the I channel type that is observed most frequently in frog nerve fibers in nodal as well as in paranodal regions, whereas, in mammalian nerve fibers, I channels are located predominantly in the paranodal region (see section on distribution of potassium channels in mammalian myelinated nerve fibers). The I channel is selectively permeable to K+ ions. With sustained depolarization, I channels inactivate slowly, in about 1 minute at −60 mV. Activation proceeds steeply in a potential range between −60 and −40 mV (Jonas et al., 1989 ).

The delayed rectifier is well known for its sensitivity to TEA (Hille, 1967 ; Koppenhöfer and Vogel, 1969 ). TEA reduced the amplitude of unitary I currents to a 50% value at a concentration of 0.6 mM (IC50; D.-S. Koh, B. Safronov, and W. Vogel, unpublished results). A Hill coefficient of 1 revealed binding of one blocker molecule to one channel. The reduction of the single-channel current amplitude by TEA, as seen also with other potassium channel types (see sections on the calcium-activated potassium channel, sodium-activated potassium channel, and flicker potassium channel; see also Figure 13-15 ), suggests a fast blocking mode (Hille, 1992 ). The TEA block of the I channel did not depend on either membrane potential or direction of ionic current in the physiological potential range between −80 and +40 mV. However, the macroscopic I currents were suppressed selectively by much lower concentrations of DTX and MCDP. These blockers reduced the macroscopic current amplitude but did not change the time course of the current. The unitary I current amplitudes also were not affected by these blockers. A half-maximal reduction of macroscopic I current was observed at IC50 = 7 nM for DTX and at 42 nM for MCDP, which also compares well with earlier voltage-clamp data for component f 1 of delayed rectifier currents in peripheral nerve obtained by Bräu et al. ( 1990 ).

Barium at millimolar concentrations suppressed I currents by reducing the unitary amplitudes. This block depended weakly on membrane potential. In contrast, the blocking effect of cesium was strongly dependent on membrane potential. At negative potentials, the amplitudes of inwardly directed unitary I currents were reduced considerably in the presence of external cesium, whereas the block was much weaker for outward currents at positive potentials. Externally applied 4-AP at a concentration of 1 mM was effective in suppressing I channel activity at negative membrane potentials, producing a flicker-type block of inward currents. However, only a weak effect of 4-AP was observed at positive potentials. Capsaicin has been described as a specific blocker of the f2 component (corresponding closely to potassium channels of the F type; see section on the F channel later in this chapter) of macroscopic potassium current (Dubois, 1982 ). However, the same concentration (10 μM) of the blocker suppressed I as well as F currents at positive membrane potentials. A specific blocker of some calcium-activated potassium channel types, charybdotoxin (500 nM), suppressed I currents in a manner similar to that of DTX. Glibenclamide, known as a specific blocker of ATP-sensitive potassium channels, failed to block I channels at concentrations up to 1 μM. A more complete characterization of I channels in amphibian axons is in preparation (D.-S. Koh, B. Safronov, and W. Vogel).

I channels in rat and in human fibers have been described (p. 266 )

table 13-1. Ionic channels in peripheral myelinated nerve a

Conductance [pS]

Density

Blocker b IC50 [M]

Channel type

Ri

High-K o

Paranodal

Nodal

Deactivation τ [ms]

Activation E50 [mV]

Inactivation τ [ms]

TEA

Other

Function b

References c

Na

7–11

1000/u.m2

−37

4n TTX

AP rising phase

1, 8, 10

Rat

9–13

8 μ Bup

Human

13

2–4 h

LA

KI

8

23

++++

++++

10–200

−75 (KCl)

10 s (−40 mV)

0.6 m

7 n DTX, 4-AP

AP repolarization

1, 4, 6–8, 11

Rat

11

33

30/μm2

5/μm2

(−120 to −70 mV)

−58 (Ri)

24 s (+40 mV)

MCDP, Ba, Cs, Phlor, CTX

2nd phase

Human

34

+++

++

(cf. component f1)

KF

30

+++

+

5

1 m

4-AP: (KF & KI similar)

AP repolarization

1, 6–8, 11

Rat

19

55

12/μm2

2/μm2

1 r

140 r

10–100 μ(−60 mV)

1st phase;

Human

++

+

3–10 m (+40 mV)

(cf. component f2)

KS

7

+

+

>10 s

3–9 m

No Cs

Neuromodulation, resting potential

1, 8, 11

Rat

10

110/μm2

130 r

−76 r

Human

7–9

+

+

KS2

Human

18

+

>100

>−100

8

KCa

75

132

++

<5

Ca;>10−6 M

No

0.2 m

No CTX

AP repolarization, neuromodulation?

2, 4, 8, 11

Rat

249

(−90 mV)

E>−50

Human

200

100 μM Phlor

KATP

44

+

Run-down

4.2 m

35 μ ATP, Glib, Ba, no 4-AP

Links metab. to excitability protection of MP

2, 5, 11

Rat

63

KNa

34

90

++

KD = 33 mM

No

21 m

Ba, Cs

Posttetanic hyper- polarization

9

Na i (a = 2.9)

Kflicker

19

49

+++

Thin > thick fiber

No

No

No

23 m

160 n Bup, Cs, Ba, Zn, LA

Resting potential in thin fibers?

3, 10

Cl

28 (−80 mV)

++

Slow

−80 to +20

No

Zn, ATP, Mg

Stabilizer of resting potential

5

100 (+4 mV)

(a) Data from sciatic nerve or Xenopus measured at 15 ± 2°C in Ringer (Ri) or high-potassium solution (high-K o ), mammalian channels measured at 22°C; r and h correspond to data of rat and human channels.

(b) Abbreviations: AP, action potential; 4-AP, 4-aminopyridine; Bup, bupivacaine; CTX, charybdotoxin; DTX, dendrotoxin; Glib, glibenclamide; LA, local anesthetics; MCDP, mast cell degranulating peptide; MP, membrane potential; Phlor, phloretin; TTX, tetrodotoxin.

(c) References: 1, Jonas et al. ( 1989 ); 2, Jonas et al. ( 1991 ); 3, Koh et al. ( 1992 ); 4, Koh et al. ( 1993 ); 5, Koh (unpublished); 6, Dubois ( 1981 ); 7, Bräu et al. ( 1990 ); 8, Scholz et al. ( 1993 ); 9, Koh et al. ( 1994 ); 10, Nau et al. ( 1993 ); 11, Safronov et al. ( 1993 ).

(p. 267 )

fig. 13-11. Discrimination of delayed-rectifier potassium channels I, F, and S by deactivation in Xenopus nerve in high-potassium solution at 15°C. Upper line gives pulse programs: From a holding potential of E = −80 mV to E = 0 (to activate the channels), repolarization (at which deactivation proceeds) was made to −70, −105, and −120 mV (from top to bottom recording) in A and to −65, −105, and −115 mV in B. Duration of the first pulse was 100 milliseconds in A and 5 milliseconds in B. Three current recordings show deactivation of single-channel events of I channels in A, including an S channel event at −120 mV, and F channels in B. Dashed lines give zero current level. High-potassium solution (105 mM) in pipette and in bath. C, Amplitude (i) of single-channel currents plotted versus membrane potential for I channels (circles), F channels (diamonds), and S channels (squares). Solid symbols, external solution containing DTX to block I channels. Each point represents the mean current amplitude of 3 to 100 events. (From Jonas et al., 1989 .)

recently on the single-channel level (Safronov et al., 1993 ; Scholz et al., 1993 ). In contrast to the differences in channel distribution (see section on distribution of potassium channels in mammalian myelinated nerve fibers), the electrophysiological and pharmacological properties of rat and human I channels are close to those described above for amphibian I channels (see Table 13-1 ), suggesting small evolutionary changes.

### F Channel.

A second potassium channel type can be seen in the right-hand column of Figure 13-11 . It deactivates within a few milliseconds at potentials between −120 and −65 mV. This comparatively fast-deactivating potassium channel is called the F channel (Jonas et al., 1989 ). Its conductance in high-potassium solution is 30 pS. F channels activate less steeply than I channels and at more positive potentials, between −40 and +40 mV. During sustained depolarization, F channels inactivate within seconds. They are less sensitive to blockage by DTX. F channels are not seen as regularly as I channels; normally, they are observed together with other delayed-rectifier potassium channels. They become visible if the bulk of I channels are blocked by DTX. Recordings in Ringer’s solution are shown in Figure 13-12 . F channels can be recognized from their larger single-channel current amplitude and a more stable open state. F channels have been described in Xenopus fibers (Jonas et al., 1989 ) and in rat fibers (Safronov et al., 1993 ).

### S Channel.

The third type of voltage-gated potassium channel can be seen in the bottom recording of Figure 13-11A as small events. It was observed in about 20% of the patches and had a conductance of 7 pS, which is clearly lower than that of either the I or F channel (Jonas et al., 1989 ). Its deactivation proceeded very slowly, hence the name S channel. The potential dependence of the S channel is very flat, and the channel already is active at potentials around −70 mV (i.e., at about the resting potential). Its TEA sensitivity is in the millimolar range (see Table 13-1 ).

From the peak S current of nearly 2.5 nA in Figure 13-9B and the corresponding single-channel current of 1 pA (see Figure 13-11C ), a density of 2500 S channels per node may be estimated. Assuming a nodal area of 25 μm2 (Berthold and Rydmark, 1983 ), there may be around 100 S channels per square μm2 in the nodal membrane (see Safronov et al., 1993 ).

The functional role of the voltage-gated potassium channel types I, F, and S may be repolarization of the membrane potential during the falling phase of the action potential in amphibian fibers. The lower potassium current density in rat and human fibers, as mentioned in the previous section, reduces this function in these preparations. Together with other potassium-selective channels (see sections on the sodium-activated potassium channel, flicker potassium channel, and functional aspects of channel distribution), the S channels contribute to the resting potential.

### Calcium-Activated Potassium Channel.

This channel type is gated not only by potential but also by micromolar (p. 268 )

fig. 13-12. Activity of F and I channels in rat nerve in Ringer’s solution at 21° to 23°C. A, Single-channel recordings of the F and I channels activated by long-lasting voltage steps from a holding potential of −90 mV to +20 mV and 0 mV. Capacity and leakage currents were not subtracted. Bath solution contained 8 nM DTX to reduce the number of active I channels. B, i-E data for the F (open symbols) and I (solid symbols) channels fitted by straight lines corresponding to 19 pS (F channels) and 11 pS (I channels). Each point is based on 3 to 33 measurements from three out-side-out patches. (From Safronov et al., 1993 .)

concentrations of internal Ca2+ ions (Jonas et al., 1991 ). A recording of KCa channels in a Xenopus axon is shown in Figure 13-13A . The single-channel conductance is 132 pS with 105 mM potassium solution on both sides of the membrane and 75 pS with normal Ringer’s solution on the outside. The extrapolated reversal potential is negative to −50 mV in Ringer’s solution and 0 in symmetrical high-potassium solution, indicating that this channel is selective for K+ over Na+ ions. It is activated on exposing the intracellular membrane surface to Ca2+ ions; this effect is readily reversible (Figure 13-13A ). Open probability is increased not only by raising the internal calcium concentration, but also by depolarization (Figure 13-13C ). Interestingly, this channel is activated strongly by phloretin (Koh et al., 1993 ). The KCa channel is not blocked by charybdotoxin, but it is most sensitive to external TEA (IC50 = 0.19 mM; see Table 13-1 ), which produces a reduction of the single-channel current amplitude and an increase in open-channel noise at 1 kHz bandwidth (see Hille, 1992 ). In conclusion, this channel has many features in common with the calcium-activated potassium channels of large conductance found in a variety of preparations (Latorre et al., 1989 ; Marty, 1981 ).

KCa channels have been identified in about one third of all membrane patches. The maximum number of channels ever observed in one patch (40 MΩ pipette resistance) was 17, which means that they are clearly less frequent than the most prominent potassium channel of peripheral amphibian nerve fiber, the I channel.

Activation of KCa channels is likely to have effects on the time course of the action potential and on the recovery process following impulse conduction, but, in a healthy resting myelinated nerve fiber, the internal concentration of calcium is probably too low to allow significant activity. However, in critical situations such as hypoxia or hypoglycemia, a pronounced increase in internal calcium concentration could occur. A more detailed description of this KCa channel is given elsewhere (Jonas et al., 1991 ).

### ATP-Sensitive Potassium Channel.

Openings of this channel typically occur in bursts. With 105 mM potassium solution on both sides of the membrane, its single-channel (p. 269 )

fig. 13-13. Calcium-activated potassium channels in Xenopus nerve at 15°C. A, Recording from an inside-out patch during change of bath solution from high-K+ i + 3 mM EGTA to high-K+ i + 10 μM Ca2+ i and back to high-K+ i + EGTA. The patch contained 12 calcium-activated potassium channels; pipette solution, 105 mM K+ o ; E = +40 mV. B, i-E data with 105 mM K+ o (open circles, five outside-out patches) and Ringer-TTX (solid circles, one outside-out patch) in the bath and high-K+ i + 1 μM [Ca2+ i in the pipette. C, Open probability as a function of membrane potential; Popen was calculated from the maximum number of simultaneously open channels observed in a patch. Bath: high-K+ i + EGTA (circles), high-K+ i containing 10−5 M calcium (triangles), 10−4 M calcium (diamonds), and 10−3 M calcium (inverted triangles); pipette: 105 mM Ko. The curves represent the function Popen (E) = 1/[1 + exp((E midE)/k)], with E mid = 40.4, 21.7, and 3.2 mV and k = 14.3 mV. (Modified from Jonas et al., 1991 .)

fig. 13-14. ATP-sensitive potassium channel in Xenopus nerve at 15°C. A, Consecutive recordings from inside-out patch with different bath solutions: high-K+ i + EGTA (control; upper), high-K+ i + EGTA containing 96 μM ATP (middle), and control again (lower trace); E = −80 mV. B, Fractional block versus ATP concentration, 11 measurements on four patches. Block estimated as the relative reduction of open probability. The curve represents the fractional block f(c) = 1/[1 + (IC50/c) a ], with half-maximal inhibitory concentration (IC50) = 35 μM and Hill coefficient (a) = 1.5 as obtained by least-squares fit. (Modified from Jonas et al., 1991 .)

conductance is 44 pS for inward currents. The reversal potential varies with external potassium concentration, indicating that this channel is also selective for K+ ions. Most important, it is blocked by internal ATP (Figure 13-14 ); the block develops immediately on switching from control to ATP solution and is reversible. ATP reduces the open probability of the channel (IC50 = 35 μM), whereas the amplitude of the single-channel events remains unchanged. This feature is unlikely to be caused by phosphorylation because the presence of Mg2+ ions is not required for the block. The Hill coefficient of 1.5 suggests binding of more than one ATP molecule per channel (Figure 13-14 ). Variable run-down of channel activity is observed, occurring within tens of minutes in axon-attached patches and slightly faster in excised patches. Pharmacologically, the single-channel current is reduced by external TEA, but, compared to the KCa channel, it is less sensitive to this blocker (IC50 = 4.2 mM). The axonal ATP-sensitive potassium channel resembles the ones described in cardiac muscle (Noma, 1983 ), skeletal muscle (Spruce et al., 1985 ), and pancreatic beta cells (Cook and Hales, 1984 ). It is clearly different from a potassium channel observed in rat cultured central neurons (Ashford et al., 1988 ), which is suppressed only partly by 1 mM ATP and has a higher single-channel conductance (53 pS in 5 mM K+ o , 140 mM K+ i ).

KATP channels occur nearly as frequently as KCa channels, and they also may have effects on the time course of the action potential and on the recovery process following (p. 270 ) impulse conduction. In situations with low energy supply or after high activity of signal conduction, the function of both the KCa and the KATP channels might consist in counteracting failure of the Na K pump, thus protecting the axon from progressive depolarization and paroxysmal discharge. A more detailed description of the KATP channel has been given elsewhere (Jonas et al., 1991 ).

### Sodium-Activated Potassium Channel.

The single channel conductance of the KNa channel is 88 pS in symmetrical high-potassium solution and 34 pS with Ringer’s solution on the outer side of the membrane. The reversal potential was shifted from 0 to −75 mV when the external high-potassium solution was exchanged for 2.5-mM potassium Ringer’s solution, suggesting a high selectivity of this channel for K+ over Na+ ions. The open probability of the channel only weakly depends on membrane potential. It is 0.37 at E = −90 mV and 0.59 at E = +40 mV, with intracellular Na+ (Na+ i ) equal to 100 mM.

Channel activity was studied at different internal sodium concentrations with inside-out patches. At 2 mM Na+ i , the channel openings seldom could be observed. At 20 mM Na+ i , channel openings were long enough to measure the apparent single-channel conductance and frequent substates could be observed. The activity of the channel saturated at internal sodium concentrations higher than 50 mM. A least-squares fit of the activation curve based on the open probability of the KNa channel gave a half-maximal axoplasmic sodium concentration of 3.3 mM Na+ i and a Hill coefficient of 2.9, suggesting that the channel has more than two binding sites for Na+ ions. Replacement of sodium by lithium could not activate the axonal KNa channels. One prominent gating property of the KNa channel is the frequent occurrence of substates; at least nine and a main open state could be identified.

TEA reduced only the apparent single-channel conductance but not the open probability of the channels. Compared to other potassium channels in this preparation (except the flicker channel; see later in this chapter), the KNa channel is relatively insensitive to this blocker, the IC50 being 21 mM TEA. The channel is more sensitive to external cesium (10 mM) at negative membrane potentials. Barium at a concentration of 1 mM profoundly reduced the open probability without any significant reduction of the single-channel current amplitude, and the blocking effect occurred only at negative potentials.

The relative density of KNa channels in the nodal as compared to the paranodal membrane is demonstrated by experiments in which many patches were obtained from a single axon. The highest number of simultaneously open channels recorded with 20 MΩ pipettes was four within the nodal area, and the probability of finding a channel was 0.8. Because the patch area corresponds to approximately 1 to 4 μm2 (Sakmann and Neher, 1983 ), the minimum density of this channel at the node of Ranvier could be estimated at about 0.25 to 1 KNa channel per μm2. The patches made within paranodal regions revealed a density of KNa channels at least 10 times lower.

Cytoplasmic sodium concentration is increased during repetitive activity (Bergman, 1970 ) and may reach the range of about 30 mM where KNa channels change their activity steeply. This gives a hint as to the functional role of these potassium channels. During periods of high sodium channel activity and depending on activities of the Na K pumps, sodium-activated potassium channels may contribute to the nodal membrane potential. A detailed description of the sodium-activated potassium channel is given elsewhere (Koh et al., 1994 ).

### Flicker Potassium Channel.

A potential-independent (“leakage”) potassium conductance that cannot be blocked by the classical potassium channel blocker TEA has been suggested to generate the resting potential in sympathetic ganglia (Jones, 1989 ), in invertebrate axons (Chang, 1986 ), and in vertebrate myelinated axons (Schmidt and Stämpfli, 1966 ). All potassium channels described so far except the S channel and the KNa channel have a low open probability around the resting potential under physiological conditions. Moreover, they are all blocked by less than 10 mM external TEA. Therefore, these channels are not likely to provide a major contribution to the resting potential of the peripheral myelinated axon, which is almost completely TEA resistant (Schmidt and Stämpfli, 1966 ).

Recordings of potassium channels often are disturbed by background activity of voltage-insensitive potassium channels. The activity of the so-called flicker channel is shown in Figure 13-15A with symmetrical potassium concentrations on both sides of the membrane (105 mM). Flickering dominates the gating of this potassium channel type. The apparent single-channel conductance is 49 pS in high-potassium solution. The iE curve with Ringer’s solution on the outer side of the membrane shows a single-channel conductance of 17 pS for outward currents. The reversal potential was E rev = −70 mV in 2.5 mM K+ o as opposed to 0 mV in external high-K o solutions, indicating that the channel is fairly selective for K+ ions. In addition, the flicker channel is weakly potential dependent.

The effect of external TEA at negative membrane potential is illustrated in Figure 13-15B . High concentrations of TEA (50 mM) reduce the mean current during bursts without noticeably changing the channel activity. The IC50 is 19 mM TEA. Compared to other potassium channels in this preparation, the flicker channel (p. 271 )

fig. 13-15. TEA block of flicker potassium channel. A, Outside-out patch recordings with 105 mM K+ o (control) and with 105 mM K+ o containing 50 mM TEA in the bath and wash pipette; 105 mM K+ i , E = −90 mV, low-pass filtered at 1 kHz (−3 dB, four-pole Bessel). B, Fractional block of mean current during bursts versus concentration of TEA at E = −90 mV; three outside-out patches. IC50 = 19.0 mM and Hill coefficient a = 1.0 as obtained by least-squares fit (see Figure 13-14 ). (From Koh et al., 1992 .)

and the KNa channel are very insensitive to this blocker. In contrast, the flicker channel is sensitive to external cesium, barium, and zinc. Figure 13-16 shows that bupivacaine, an uncharged local anesthetic applied to the outer side of the membrane, barely affects the single-channel conductance but reversibly reduces the probability of bursting by causing long closings. The plot of fractional block against bupivacaine concentration shown in Figure 13-16B demonstrates that bupivacaine is the most potent blocker of the flicker K channel so far tested, with an IC50 value of 0.165 μm. In order to characterize the binding of local anesthetics at the flicker K channel in peripheral nerve membrane, the blocking effects of bupivacaine, ropivacaine, etidocaine, mepivacaine, and lidocaine have been studied when applied to either side of the membrane. The respective half-maximal effects (IC50) were 0.16, 3.5, 7.4, 55, and 218 μm with external application and 2.2, 6.6, 16, 223, and 1200 μm when the drugs were applied to the axoplasmic side of the membrane (Nau et al., 1993 ). The log (IC50)-values linearly depend on the logarithm of their octanol:buffer distribution coefficients with two regression lines for the piperidine derivatives and the standard amino-amides indicating an inherently higher potency of the cyclic piperidine series (M. E. Bräu, C. Nau, G. Hempelmann, and W. Vogel, in preparation).

The functional role of the flicker channel was investigated by recording ionic currents from “macropatches” containing several channels under voltage-clamp conditions in the range of possible resting membrane potentials. At Em = −90 mV, an inward current with 105 mM K+ o was observed (Figure 13-17A ), which at higher time resolution shows the rapid kinetics typical for the flicker channel (not shown). This current could not be blocked by 10 mM TEA, but was inhibited by barium and cesium. Its pharmacological features are thus similar to (p. 272 )

fig. 13-16. Bupivacaine block of flicker potassium channel. A, Outside-out patch recordings with 105 mM K+ o (control) and with 105 mM K+ o containing 1 μM bupivacaine in the bath and wash pipette; 105 mM K+ i , Em = −100 mV. Three channels were open at most times in the control recordings. B, Fractional block of mean total current versus concentration of bupivacaine at the same potential; six outside-out patches. IC50 = 0.165 μM and a = 1.0, obtained as in Figure 13-14 . (From Koh et al., 1992 .)

those of the flicker channel, suggesting dominance of this channel type at rest and, at least under certain conditions, its contribution to the resting conductance of vertebrate axons.

The flicker channel has been observed in high density in nodal, paranodal, and internodal regions of the axonal membrane of thin myelinated nerve fibers. It has been suggested that paranodal and internodal potassium channels contribute to the resting potential (Chiu and Ritchie, 1984 ), and therefore it is likely that not only the nodal but also the paranodal and internodal flicker channels contribute to the resting potential of the myelinated nerve fiber. A more detailed description of this channel is given elsewhere (Koh et al., 1992 ).

### Other Channel Types.

In rat and human demyelinated axons, a chloride channel has been observed with a conductance of 33 to 65 pS (high symmetrical CsCl solutions, 22°C). Its selectivity for sodium and cesium is P Na/P Cs/P Cl = 0.1/0.2/1 (Strupp and Grafe, 1991 ). Chloride channels were observed much more often in patches from nodal regions than in those from paranodal regions.

Calcium channels, although obviously present in the soma membrane and at the presynaptic terminal of the peripheral neuron, have not been found so far in the nodal or paranodal demyelinated membrane (C. Nau, personal communication).

There are nonspecific leakage currents of considerable amplitude in macroscopic voltage-clamp measurements from the node of Ranvier, especially from mammalian nerve fibers, as mentioned above. In the patch-clamp recordings, however, leakage current is minimal or absent. This supports the hypothesis of Barrett and Barrett ( 1982 ) that the leakage current originates from the internodal membrane segments and reenters the external (p. 273 )

fig. 13-17. Pharmacological blockade of currents recorded at E = −90 mV (A) and E = −60 mV (B). Currents from an outside-out macropatch with 105 mM K+ i in the pipette were recorded in different external solutions: 105 mM K+ o (control), 105 mM K+ o + 10 mM TEA (TEA), 105 mMK+ o + 1 mM barium + 10 mM TEA (Ba + TEA), and 105 mM K+ o + 10 mM cesium + 10 mM TEA (Cs + TEA). Record at −60 mV was obtained more than 1 minute after the voltage step to this potential, when the current was stationary. Pipette resistance: 18 MΩ. (From Koh et al., 1992 .)

nodal gap via the axoglial junctions. Therefore, to explain and calculate action potentials, allowance for a nonspecific leakage current must be made, although corresponding ionic “leakage” channels may not exist.

# MOTOR AND SENSORY NERVE FIBERS

As early as 1938, Erlanger and Blair found that motor nerve fibers accommodate faster than sensory nerve fibers, which exhibit repetitive activity. Subsequent current- and voltage-clamp experiments performed in single myelinated frog nerve fibers confirmed that both fiber types have distinctly different properties (Neumcke, 1981 ). Motor nerve fibers have a larger resting potassium conductance than sensory fibers (Stämpfli, 1959 ). After blockage with TEA, the membrane of motor fibers is depolarized by 5 to 10 mV, whereas in sensory fibers only a slight depolarization of 1 to 2 mV occurs (Stämpfli and Hille, 1976 ). Furthermore, it has been shown that the maximum potassium conductance is larger in sensory than in motor fibers, and that potassium conductance activation is faster in sensory than in motor fibers (Palti et al., 1980 ). More potassium channels are opened during a small depolarization in motor fibers than in sensory fibers. This difference is explained by a shift of the steady-state activation curve, n (E), to more depolarized potentials in sensory compared to motor fibers (Bretag and Stämpfli, 1975 ). From noise measurements, it was inferred that the single-channel conductance of potassium channels is larger in sensory than in motor fibers (Neumcke et al., 1980 ). These differences in single-channel conductance are in agreement with the finding that the relative contribution of the two fast potassium current components is different in both fiber types. Dubois ( 1981 ) found that, in the frog, the f1 component has a mean contribution of 60% to the total fast potassium conductance in motor fibers, in contrast to 35% in sensory fibers (Figure 13-8 ). These differences recently have been confirmed in toad nerve by Bräu et al. ( 1990 ). The results of the fluctuation measurements by Neumcke et al. ( 1980 ) now can be interpreted on the basis of single-channel conductance (Jonas et al., 1989 ), if the macroscopic f1 component is assumed to be produced mainly by the microscopic I channel (single-channel conductance of 11 pS) and the f2 component by the F channel (single-channel conductance of 19 pS) (see Table 13-1 ).

Sodium inactivation differs in frog motor and sensory fibers. If the sodium current decay is described with two exponentials, then the relative contribution of the slower sodium inactivation component in motor nerve fibers is about 30% throughout a large potential range, whereas in sensory nerve fibers the amount of slower sodium (p. 274 ) inactivation is smaller and vanishes at higher depolarizations (Schwarz et al., 1983 ). Similar differences in sodium inactivation have been found when comparing rat dorsal and ventral root fibers (Mitrovic et al., 1993 ).

The different sodium inactivation kinetics can explain the characteristic action potential shapes of frog motor and sensory fibers. The motor fiber action potential at 20°C is longer in duration than that of a sensory nerve fiber and exhibits a typical “shoulder” during repolarization that is not seen in sensory fibers (Figure 13-18 ). These differences are exaggerated after blocking the potassium conductance with TEA (Figure 13-19 ). TEA increases the duration of the motor nerve action potential by a factor of 3 to 5, whereas in sensory nerve fibers this factor is about 2 (Schmidt and Stämpfli, 1966 ). The clear differences in action potential shape between frog motor and sensory fibers are usually smaller or absent in mammalian nerve fibers, although Bowe et al. ( 1985 ) have demonstrated different effects of 4-AP in rat ventral root, compared to dorsal root, myelinated axons.

# CALCULATION OF ACTION POTENTIALS

The depolarizing upstroke of the action potential is due to the steep voltage-dependent sodium conductance activation, whereas repolarization is induced by sodium conductance inactivation and the delayed potassium conductance activation. In mammalian myelinated nerve fibers, outward current necessary for repolarization of the action potential is provided by potassium current through those slow potassium channels, which are open at the resting membrane potential, and by leakage current.

Dodge ( 1963 ) and Frankenhaeuser and Huxley ( 1964 ) were the first to compute action potentials from data derived from voltage-clamp experiments in the amphibian node of Ranvier. Their results showed that the ionic currents underlying the generation of the action potential in the amphibian myelinated nerve fiber are basically similar to those in the squid giant axon (Hodgkin and Huxley, 1952 ). Mathematical modeling also could be extended successfully to calculations of repetitive activity (Bromm and Frankenhaeuser, 1972 ) and of the characteristic action potential shape of a particular nerve fiber (Bromm et al., 1981 ; Dodge, 1963 ; Spielmann et al., 1983 ).

fig. 13-18. Superimposed action potentials of a motor (wider action potential) and a sensory (narrower action potential) nerve fiber from the same frog (R. esculenta) recorded at the same temperature (20°C). (From Stämpfli and Hille, 1976 .)

fig. 13-19. Action potentials and membrane currents of a motor (A and B) and a sensory (C and D) frog nerve fiber in Ringer’s solution with 10 mM TEA added. Action potentials were elicited with a 0.1 millisecond depolarizing current. Membrane currents were elicited with depolarizing pulses to potentials between −70 and +50 mV in steps of 10 mV. The depolarizing pulses were preceded by a 50 millisecond hyperpolarizing pulse to −115 mV. Leakage and capacity currents were subtracted. (From Schwarz et al., 1983 .)

The action potentials shown in Figure 13-20 have been calculated with the data given by Schwarz and Eikhof ( 1987 ). There is a close resemblance between the shape of the computed action potential and the action potential recorded from a single rat node of Ranvier at 20°C (see Figure 13-1 ). Figure 13-20 also shows that the sodium activation and inactivation kinetics based on the first-order kinetics of the Hodgkin-Huxley model suffices to calculate an action potential. Incorporation of the small fast potassium conductance has only a minor influence on the time course of repolarization (Figure 13-20 , dashed line). An action potential also can be calculated with data measured at 37°C (Figure 13-20 ). This action potential is similar to that recorded in a rat nerve fiber at the same temperature (see Figure 13-1 ).

Using their voltage-clamp data recorded in squid axons, Hodgkin and Huxley ( 1952 ) calculated permeabilities of Na+ and K+ ions during an action potential. de Haas and Vogel ( 1989 ) subjected the nodal membrane of a Xenopus fiber to the voltage-clamp command of an action potential that previously had been measured in the same fiber. Based on the resultant membrane (p. 275 )

fig. 13-20. Action potentials computed with data given by Schwarz and Eikhof ( 1987 ) for rat nerve fibers at 20° and 37°C. Dashed lines represent action potentials with incorporation of fast potassium conductance. (Modified from Schwarz and Eikhof, 1987 .)

currents, they calculated the permeability changes during this action potential, which were in good agreement with the corresponding calculations of Frankenhaeuser and Huxley ( 1964 ).

With the detection of differences in the composition and distribution of ionic currents in amphibian and mammalian nerve fibers, it became evident that the organization of ionic channels of myelinated nerve fibers is much more complex than previously assumed. Two new results had to be taken into account. First, the distribution of ionic channels is different in amphibian and mammalian myelinated nerve fibers. Sodium channels and slow potassium channels are concentrated in the mammalian nodal membrane, whereas predominantly fast potassium channels are located in the paranodal axolemma. Second, previous modeling of action potentials assumed that the myelinated nerve fiber consists of an “active” nodal membrane equipped with the ionic mechanisms to generate action potentials and a “passive” element comprised of the paranodal and internodal parts of the fiber, which are devoid of ionic channels and surrounded by an insulating myelin sheath. The much more complex structural and functional organization of the node of Ranvier is reflected in newer models that take into account the flow of current through the paranodal and internodal parts of the axolemma (Baker et al., 1987 ; Barrett and Barrett, 1982 ).

Attempts have been made to incorporate the new findings about the complex sodium inactivation kinetics, the distribution of ionic channels, and additional ionic channel populations into calculations of action potentials. Inactivation of sodium currents is a multiexponential process (Ulbricht, 1989 ). This has been described in frog (Chiu, 1977 ; Kniffki et al., 1981 ) and also has been observed in rat (Neumcke and Stämpfli, 1982 ; Neumcke et al., 1987 ) nerve fibers. To account for the multiexponential time course of sodium inactivation, Ochs et al. ( 1981 ) introduced a three-state model for sodium inactivation. A long-lasting plateau of the action potential could be calculated with this model, which is very similar to that recorded in frog motor nerve fibers after blocking potassium conductance with TEA. The action potential calculated with the Hodgkin-Huxley equations does not produce a long-lasting plateau phase after omitting the outward potassium current. Attempts also have been made to account for the complex compartmentalization of the nodal, paranodal, and internodal parts of the myelinated nerve fiber (Halter and Clark, 1991 ). Other calculations incorporated the additional potassium conductances, which have been separated experimentally (Awiszus, 1990a, b ). Figure 13-2A shows repetitive activity recorded from a single human ulnar nerve fiber. A long-lasting depolarizing current elicits an action potential followed by three additional discharges with increasing interspike intervals. The Hodgkin-Huxley equations, which take into account only sodium, fast potassium, and leakage conductances, predict ongoing repetitive activity with a constant interspike interval (Figure 13-21B ). Incorporation of slow potassium conductance kinetics yields repetitive activity exhibiting accommodation similar to that actually recorded (Figure 13-21C, D ). The functional importance of the slow potassium conductance for accommodation first was suggested by Krylov and Makovsky ( 1978 ).

# FUNCTIONAL ASPECTS OF IONIC CHANNEL DISTRIBUTION

The voltage-clamp data from amphibian and mammalian myelinated nerve fibers reviewed here, together with intra-axonal recordings and immunoultrastructural information (see Chapter 11 ), show that the node of Ranvier has a complex distribution of a number of different ionic channels. Earlier work on the amphibian node of Ranvier (Frankenhauser and Huxley, 1964 ; Stämpfli and Hille, 1976 ) assumed the existence of homogeneous populations of sodium and potassium channels of a type similar to those described by Hodgkin and Huxley ( 1952 ) in the squid giant axon. Further analysis of macroscopic nodal currents and the introduction of the patch-clamp technique led to the discovery of a multiplicity of ionic channels. At present, one type of sodium channel, one type of chloride channel, and several types of potassium channels have been described. Among the potassium channels, three types that are gated primarily by voltage (I, F, and S type), one voltage- and calcium-dependent (KCa), and three background (KATP, KNa, and flicker) channels have been identified in axons (Table 13-1 ; Figure 13-22 ). These (p. 276 )

fig. 13-21. A, Repetitive activity elicited in a single human nerve fiber with a 100 millisecond depolarizing current. B, Repetitive activity as calculated from the data given by Schwarz and Eikhof ( 1987 ) for a rat nerve fiber at 20°C. C, Same computation as in B except that the kinetics of the slow potassium conductance is added. Steady-state parameters and time constants of slow potassium conductance were taken from Dubois ( 1981 ). D, Time course of slow potassium conductance underlying action potential adaptation in C. (Modified from Reid et al., 1993 .)

fig. 13-22. Schematic diagram of the distribution and function of ion channels in nodal and paranodal membrane. Channel types that are found mostly in the nodal membrane of amphibians [Na and K(Na)J and of mammals (S) are shown in the nodal cleft together with active pumps. Other voltage-gated ion channels [I, F, K (Ca)] and K (ATP) and flicker channels, which are less specifically located, are shown in the paranodal region. (Modified from Koh, 1992 .)

(p. 277 ) channels and their complex distribution in the node and paranode have led to a new concept of myelinated nerve excitation and impulse propagation.

An action potential in the rat node of Ranvier is brought about by inward current through sodium channels. The high safety factor for impulse propagation is due to the high nodal density of sodium channels of about 1000/μm2 (single-channel data; see section entitled “Single-Channel Sodium Currents”) or 1500/μm2 (noise measurements; Neumcke and Stämpfli, 1982 ). The density of sodium channels in the nodal membrane is much higher than in the axolemma of most mammalian nonmyelinated axons that have been studied (approximately 100 to 200/μm2; Pellegrino et al., 1984 ). Electrophysiological experiments (Chiu and Schwarz, 1987 ; Grissmer, 1986 ; Shrager, 1987 ), immunocytochemical staining of sodium channels (Black et al., 1989 ), and saxitoxin-binding studies (Ritchie and Rogart, 1977 ) demonstrate that only a very low density of sodium channels is present in the paranodal and internodal axolemma. The mechanisms that confine sodium channels to the nodal part of the axon membrane are discussed by Waxman (see Chapter 11 ).

In the mammalian node of Ranvier, repolarization is mainly due to sodium inactivation kinetics (Chiu et al., 1979 ; Schwarz and Eikhof, 1987 ), whereas activation of delayed-rectifying potassium channels contributes to action potential repolarization in amphibian myelinated nerve fibers. However, mammalian nerve fibers also contain various types of potassium channels that fulfill different functions. Fast voltage-dependent potassium channels (F and I type) are located predominantly in the paranodal axolemma. Anatomically, this region is characterized by “axoglial junctions” that form relatively tight contacts between the Schwann cell loops and the axolemma. The specialized structure of the axonal and glial membranes at these junctions may be responsible for the high density of fast potassium channels in the paranodal region (Meves, 1992 ; see also Chapter 21 ). After disruption of this close contact following chronic demyelination, the distinct distribution of ionic channels vanishes and a homogeneous distribution is observed (Schwarz et al., 1991 ). The main function of these paranodally located fast potassium channels seems to be to prevent reexcitation of the nodal membrane by the long-lasting afterdepolarization of the internode following the nodal action potential (Chiu and Ritchie, 1981 ; Kocsis et al., 1982 ). This notion is supported by intracellular recordings from myelinated axons that demonstrate the existence of a depolarizing afterpotential with a peak amplitude of 5 to 20 mV and a half-time of 100 to 200 milliseconds (Barrett and Barrett, 1982 ). This afterpotential is interpreted as being due to a passive discharge of the axolemmal capacitance via a low-resistance leakage pathway (Barrett and Barrett, 1982 ; Funch and Faber, 1984 ).

Although the mammalian nodal membrane is almost devoid of fast potassium channels, it contains a relatively high density of voltage-dependent slow potassium channels. The nodal density of slow potassium channels (about 100/μm2; Safronov et al., 1993 ) decreases in the paranodal and internodal axolemma to 1/30 (Röper and Schwarz, 1989 ). Because 20% to 40% of the total slow potassium conductance already is activated at the normal resting potential, it can serve several functions. First, current through these open slow potassium channels could provide outward current necessary to repolarize the action potential. This function is the same as that of the leakage current. However, because of its slow kinetics, additional activation of slow potassium channels does not contribute to the time course of repolarization of the action potential in mammalian nerve fibers. Second, the slow potassium conductance present in the internodal axolemma may contribute to maintaining the resting potential, together with TEA-insensitive sodium-activated potassium channels (KNa), leakage channels, and flicker channels. This function of internodal potassium channels has been suggested by Chiu and Ritchie ( 1984 ). A further important function of slow potassium channels is to contribute to frequency adaptation (Kocsis et al., 1987 ; Krylov and Makovsky, 1978 ). On long-lasting depolarizations, additional slow potassium channels are activated, inducing accommodation and slow changes of the threshold potential (see Figure 13-21 ). Block of slow potassium channels with TEA induces repetitive activity (Baker et al., 1987 ; Kocsis et al., 1987 ).

In addition to voltage-dependent potassium channels, amphibian and mammalian myelinated axons contain potassium channels that are modulated by intracellular calcium, ATP, or sodium. This shows that the axonal properties are regulated not only by membrane potential but also by axoplasmic factors. At present, we do not know the physiological function of the channels that are modulated by calcium and ATP. In pathological states such as hypoxia, however, the ATP concentration may be reduced and the calcium concentration increased to levels at which these channels would be opened. This opening may lead to hyperpolarization and restoration of cell function.

Possible functions for KNa channels are easier to conceive. These channels occur at a density that is about 10 times higher in the nodal membrane than in the internodal membrane, and they are co-localized with sodium channels and with Na,K pump molecules at the node of Ranvier. KNa channels are activated by axoplasmic sodium concentrations above 10 to 20 mM. Such concentrations of sodium can occur after long-lasting trains of action potentials and then may activate KNa channels, contributing to the afterhyperpolarization. The afterhyperpolarization previously was thought to be solely due to an increase in the Na,K pump activity (p. 278 ) (Schöpfle, 1976 ). The presence of a diffusion barrier under the membrane at the node, as suggested by Bergman ( 1970 ), also would favor a local increase in axoplasmic sodium concentration; there is, in fact, some evidence for such a barrier in myocardial cells (Lederer et al., 1990 ).

There is some evidence that the flicker channel helps set the resting potential in peripheral nerve. Its reversal potential is close to the resting potential; it is insensitive to TEA (Figure 13-17 ), as is the resting potential (Schmidt and Stämpfli, 1966 ); and the flicker channel has a substantial open probability around the resting potential (Koh et al., 1992 ). Other channels also may contribute to the resting potential, such as S channels, KNa channels, KATP channels, chloride channels, and certainly also active pumps. Single-channel recording almost certainly will provide additional data that will help to elucidate further the mechanisms that generate the resting potential, as well as the action potential, in peripheral nerve.

We would like to acknowledge the criticism of the manuscript by Drs. D. Siemen (Regensburg) and W. Ulbricht (Kiel), and the continued support we obtained from the members of our groups in Hamburg and Giessen.

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