CHAPTER 3

PROPERTIES OF EXCITABLE MEMBRANES: THE SPIKE

n the experiment shown in Figure 3-8, only very small amounts of current were Ipassed through the membrane, and these caused only small changes in . If greater currents are used some new phenomena show up in the recordings. When current is passed through the membrane from outside to inside (the micropipette is the cathode), the voltages shown in Figure 3-15 can be recorded from the immediately adjacent membrane. The membrane responds as a simple passive resistance-capacitance circuit, i.e., the responses are predictable from Ohm’s law. Figure 3-15. Changes in membrane potential caused by inward The membrane potential changes more current flow. Five equal 4-msec steps of inward transmembrane slowly than the applied current as the current, with current magnitude increasing from a to e, resulted in membrane capacitor charges and discharges. five proportional hyperpolarizing changes in membrane potential. Even with the greatest currents the Responses reflect simple electrotonic potentials. membrane still behaves as a simple passive circuit. We speak of the resting membrane depolarization1. Inward currents, therefore, as being polarized (negative inside with hyperpolarize the resting membrane. respect to outside). The terminology applied When current is passed in the other in most textbooks to changes in the direction across the membrane, from inside membrane potential is often confusing and to outside, the membrane at first behaves as inaccurate. For example, many times the a simple resistance-capacitance circuit, membrane potential will be described as approximately symmetrical with its behavior "increasing or decreasing." But is a change that makes the membrane potential more negative inside with respect to outside an increase or a decrease? We will use the term hypopolarization to refer to a change in the membrane potential that makes the membrane less negative inside; a change that makes it more negative than V is called r 1 The term “” is used in an hyperpolarization. A change in the most literature and textbooks for any membrane potential to 0 mV is a hypopolarization. Though this is strictly incorrect, it is customary and widely accepted. Be warned!

3-1 for inward current. Responses in Figure 3- 16 were obtained for the same strength outward currents as were used for the correspondingly lettered responses to inward currents in Figure 3-15. Responses in Figure 3-16 a and b are symmetrical with responses in Figure 3-15 a and b2, but the change in the membrane potential is hypopolarizing instead of hyperpolarizing. Outward currents hypopolarize resting membrane3. Figure 3-16 c is, however, not symmetrical to its counterpart in Figure 3- 15. The response begins like its counterpart, but the response is larger in amplitude and longer in duration. Response d is even more Figure 3-16. Changes in membrane potential due to outward current flow. Five equal 4-msec steps of outward variant; the shape is no longer that expected transmembrane current, with current magnitude increasing for a capacitor being charged. An active from a to e (and the same magnitudes as for similarly lettered process has been initiated by the change in traces in Fig. 3-15), resulted in hypopolarizing electrotonic membrane potential that occurred in c and d; potentials in a and b, electrotonic potentials leading to local it was not initiated by the smaller changes in active responses (region between solid and dashed lines) in c and d, and an electrotonic potential leading to a spike in e. membrane potential in a and b. CFL=critical firing level. When a still stronger current is passed outward through the membrane, the membrane potential begins to change toward zero (the membrane is passively (Fig. 3-16 e); then the active hypopolarized), and it even becomes process begins; and finally the membrane positive inside with respect to outside. The polarization continues to diminish rapidly membrane polarity actually becomes reversed. After the peak of positivity is reached, the membrane rapidly returns to its

2 original polarity and potential and may Note: The amplification illustrated in proceed to a potential more negative than V . Fig. 3-16 is less than that in Fig. 3-15 so the r Finally, the membrane returns to Vr, the traces appear to be smaller. In fact, they whole event lasting 2-3 msec. Actually, the would not be. event, from its start at Vr to peak positivity and back to V (omitting the period when V 3 This should make sense if you recall r m is more negative than V ), requires only 0.5- that current entering a resistor makes that r 1.0 msec, depending upon the . This end of the resistor positive with respect to event is called the or the other end. Thus, current passing inward simply the spike. through the membrane will make the outside more positive with respect to the inside (that's hyperpolarization), whereas current passing outward through the membrane will make the inside more positive with respect to the outside (that's hypopolarization).

3-2 Figure 3-17 shows the action frequently absent. potential on an expanded time scale. The The action potential is initiated when various parts of the spike are labeled. The the membrane is hypopolarized beyond a rapid positive change in membrane potential certain value. This value, termed the is called the upstroke, the rising phase, or critical firing level (CFL), varies from cell the hypopolarization phase. The positive to cell; it is of the order of 10-20 mV, but portion of the spike is the overshoot and the constant for a given cell under its normal return to the resting potential is called the working conditions. The critical firing level falling phase or the repolarization phase. is a highly unstable condition. If the At the end of the falling phase, the membrane is hypopolarized just to but not repolarization (re-establishment of the beyond the critical firing level, it may either resting polarity) slows down and may pass discharge a spike or it may simply return to the resting potential to a value more Vr.

negative than Vr, i.e., the membrane may Actually, a minimum rate of change become hyperpolarized. This is the in membrane potential is required to initiate the spike. If the membrane potential is changed very slowly, the critical firing level can be passed without an action potential being initiated. In Figure 3-18, the responses of an axon to stimuli with five different rates of rise are shown. As the rate is decreased (going from a to e), the apparent critical firing level becomes more positive, going from 21 mV of

hypopolarization from Vr in a to 28 mV in d. In e, no spike is initiated at all, in spite of the fact that the membrane is hypopolarized Figure 3-17. Phases of the action potential. by more than 30 mV. Actually, during any The time course of the spike is shown with maintained hypopolarization that does not hypopolarization (depolarization) and cause a spike to occur, the critical firing repolarization phases, overshoot, and level becomes more positive. This hyperpolarizing and hypopolarizing phenomenon is called accommodation. after-potentials labeled. Also indicated are When the hypopolarization is terminated, levels of the resting membrane potential, Vr, and the critical firing level, CFL. both the membrane potential and the critical Transmembrane voltage is indicated on the firing level return to their original values. ordinate; time is indicated on the abscissa. If, however, the minimum rate of change of membrane potential is exceeded, the spike hyperpolarizing after-potential or after- will be initiated as the membrane potential hyperpolarization. In some cells, there becomes more positive than the critical may also be another phase of firing level. Most neural events are rapid, hypopolarization following this, the and it is doubtful the firing level is ever hypopolarizing after-potential or after- crossed in natural functioning of the healthy hypopolarization (not shown in Fig. 3-17). neuron without a spike occurring. There are This phase is usually small, a few mV, and certain pathological conditions where this

3-3 occurs, e.g., in certain kinds of epileptic when the spike is initiated starting with the seizures where there are extremely large membrane at or near Vr. The amplitude of changes in membrane potentials at synaptic the spike does not depend upon the size of junctions. the stimulus; larger stimuli do not give rise to larger spikes. Longer duration stimuli do not prolong spikes. Therefore, the spike is referred to as an all-or-none (often written all-or-nothing) event. The fixed size results from the fact that the stimulus only triggers events that lead to the spike; once they are triggered their time-course is independent of the stimulus. The consequences of slowly rising stimuli producing accommodation (Fig. 3-18) are an apparent contradiction to this all-or-none property; but, as pointed out above, most naturally-occurring changes in membrane potential occur rapidly at rates higher than 4 mV/msec, at which the spike amplitude is reduced by less than 2%. The voltage clamp. What are the events that lead to the action potential? Obviously, the change in membrane potential of the spike results from a membrane current, and that current must result from an increase in membrane conductance. If membrane conductance were unchanged, there would be no disturbance of the resting membrane equilibrium. Membrane currents can be Figure 3-18. Accommodation of the nerve membrane. measured directly using a device called Upper graph shows a single response and the nature of the the voltage clamp. The circuit of the ramp stimulus. In the lower graph, five superimposed voltage clamp is shown in Figure 3-19. traces show the membrane response to linearly varying The membrane potential of the squid electrical stimuli with rates of rise decreasing from a to e. Note that the critical firing level changes from a 21-mV axon or another cell is measured with a hypopolarization in a to a 28-mV hypopolarization in d, micropipette as in previous figures, using and no spike occurs in e. Note also that the amplitude of the amplifier 1. The output of this amplifier spike falls with decreasing rate of rise (Frankenhaeuser and is compared, by a second amplifier (#2), Vallbo, Acta Physiol Scand 63:1-20, 1965). with a command signal specified by the experimenter. The command signal Once the action potential is initiated, indicates the voltage at which the membrane it goes to completion. The maximum value of the positive overshoot is a constant (usually about +30 mV) for a given neuron

3-4 is to be "clamped," i.e., the clamp voltage. If the membrane potential is not the same as the command signal, a current is generated by the second amplifier that is appropriate in magnitude and direction to bring the membrane potential to the clamp voltage. If, in the neuron, a current is generated that would result in a change in membrane potential, that change is sensed and countered as it occurs by the voltage clamp. In this way, the membrane potential is maintained at the clamp voltage. The current that is generated by the second amplifier, the clamp current, is measured by the ammeter. This current will be equal in magnitude, but opposite in direction to any membrane current. If the voltage clamp is applied to the squid axon and the membrane voltage clamped at -10 mV (55 mV Figure 3-20. Transmembrane currents during a spike. a. The transmembrane potential showing rapid clamp at -10 mV from a resting potential of -65 mV, a 55-mV hypopolarizaton. b. Total membrane current consists of a brief capacitative current, lasting only a few microseconds, a slower net inward current (downward deflection of the trace is inward current by convention) lasting about 1.5 msec, and a prolonged outward current. Total ionic current can be divided into two components: a transient inward current caused by sodium entry (c) and a prolonged outward current caused by potassium efflux (d). (Hodgkin and Huxley, J Physiol (Lond)116:449-472, 1952).

Figure 3-19. Circuit diagram for the voltage clamp. Figure 3-20a. The membrane simply Transmembrane potential is measured between an changes instantaneously from -65 mV (V , intracellular micropipette electrode and an electrode in the r extracellular fluid by amplifier 1 and compared with the in this case) to -10 mV, and stays there. clamp voltage by amplifier 2. A current (downward arrow) Note that this hypopolarization is more than is generated to bring the membrane potential to the clamp enough to start the spike mechanism, but, of voltage, and the current is measured by the ammeter. course, the membrane potential cannot change. At the time when the rapid hypopolarization), a current flow results, as membrane hypopolarization of the spike shown in Figure 3-20b. The effect of the would have occurred, there is a brief clamp on membrane potential is shown in outward current (upward deflection in

3-5 current traces is an outward current), determine which ions are carrying the followed immediately by an inward current currents. First, suppose that the that reaches a peak at about 0.6 msec and concentration of Na+ in the extracellular declines to zero by 1.5 msec. This inward fluid is reduced, and Na+ is replaced by current is followed by a prolonged outward choline, such that εNa+ = -10 mV. Then, current that lasts as long as the membrane is when the membrane potential is clamped at - clamped. The brief outward current at the 10 mV, Vm = εNa+ and beginning of the record represents the discharging of the membrane capacitance. iNa+ = gNa+(Vm - εNa+) = 0. This current is short because the change in membrane potential, as it moves from Vr to Therefore, there will be no current due to the clamp voltage, is so rapid. Recall that ic sodium ions. The resultant voltage-clamp = C dV/dt and dV/dt = 0 except at the time current is shown in Figure 3-20d as a the clamp is initiated. smoothly rising outward current. The There are a number of ways to inward current is eliminated completely, suggesting that it was carried by sodium ions. Another way to show this is to vary the clamp voltage in an axon with normal ion concentrations. The result of doing this is shown in Figure 3-21. When the membrane is clamped at +26 mV, the inward current is reduced but present, and the outward current is larger than that at a clamp voltage of -10 mV. At a clamp voltage of +39 mV, the inward current is still smaller and the outward current still larger, whereas, at +52 mV (approximately

εNa+), the inward current is eliminated completely. This is what would be expected if the inward current is carried by Na+

because at +52 mV, Vm = εNa+ and thus iNa+ = 0. When the membrane potential is Figure 3-21. Effect of membrane potential clamped at +65 or +70 mV, an outward on membrane current. Upper traces show current appears where the inward current five different clamp voltage, +26 to +78 used to be, again as expected. mV, applied to the squid axon. Lower trances show total net current flows for each clamp voltage. As the clamp voltage becomes more positive, the net outward current becomes larger and larger, whereas the net inward current becomes smaller, is zero at 52 mV, and then becomes net outward (Hodgkin, Huxley and Katz, J Physiol (Lond) 116:424-448, 1952).

3-6 K+. (The arrow in the driving force diagram indicates the direction of current flow. A cation will move in that direction; an anion will move in the opposite direction.) If the sodium conductance increases, there will be

an inward iNa+; if gK+ increases, there will be an outward iK+. The magnitudes and directions of the driving forces for both Na+ and K+ are similarly indicated by the lengths and directions of the lines to the +26 and +65 mV clamp voltages. Notice that the driving force for K+ is greater as the clamp voltage becomes more positive, and it is always directed outward. We should, therefore, expect the magnitude of the outward current, if it is carried by potassium ions, to become larger as the membrane potential is clamped at more and more positive values. This is Figure 3-22. Driving force diagram. The left pair seen clearly in Figure 3-21. + + of arrows shows the driving forces of K and Na The driving force for Na+ decreases at a clamp voltage of -10 mV. The center pair shows driving forces+ at a clamp voltage of +26 as the clamp voltage approaches εNa+. When mV, whereas the right pair shows them for a the clamp voltage is more positive than + clamp voltage of +65 mV. Note that all K driving εNa+,the driving force reverses direction from forces are outward; sodium driving forces are toward the inside to toward the outside of inward for -10 and +26 mV, and outward for +65 the membrane. At even more positive mV. values of the clamp voltage, the driving force will increase in magnitude, but its Consider the driving force diagram direction will still be outward. At clamp

of Figure 3-22. In this diagram, Vr, εNa+, and voltages less positive than εNa+, iNa+ will be εK+ are indicated along with the clamp an inward current; at values more positive it voltages -10, +26, and +65 mV. Recall that will be an outward current, again as seen in

the driving force on an ion is Vr - εion. There- Figure 3-21. fore, at a clamp voltage of -10 mV (Vm), the driving force on Na+ is equal to the length of the line (downward arrow) in the driving

force diagram from εNa+ to the -10 mV clamp voltage. Likewise, the driving force on K+

is the length of the line from εK+ to the -10 mV clamp voltage (upward arrow). In both cases, the direction of the arrowhead indicates the direction of the driving force and the direction of the current flow that results from it, inward for Na+, outward for

3-7 Na+ and K+ ions or their conductances. This is probably a good assumption, because, as we shall see, the conductances for the two ions change at different times during the action potential, and the outward and inward currents can be blocked independently. Tetrodotoxin (TTX), a toxic substance that occurs naturally in the puffer fish4, blocks the inward sodium current and, with it, the action potential, without changing the outward potassium current. The lethality of TTX is due to its ability to block sodium action potentials. The behavior of TTX contrasts sharply with that of tetraethylammonium (TEA); TEA ions block the outward K+ current without influencing the sodium current. Having measured both the current flow and the change in membrane potential during the spike, we can compute the changes in membrane conductance from

Figure 3-23. Changes in sodium and Ohm's law, gNa+ = iNa+/(Vm - εNa+). In Figure potassium conductances during the spike in 3-23, the changes in both sodium and the squid axon. Upper trace shows the time potassium conductances (lower graph) course of the spike. Lower traces show the during the spike are shown in relation to the earlier rapid increase in gNa+ from near 0 to 30 mS/cm2 and the slower return to near zero time course of the spike (upper graph). The and the delayed, slower increase in gK+ to sodium conductance increases rapidly at the more than 10 mS/cm2, followed by a slower beginning of the upstroke, reaches a peak return to resting levels (Aidley: The near the peak of the overshoot of the spike, Physiology of Excitable Cells. Cambridge: Cambridge Univ. Press, 1971). and then rapidly declines. The potassium conductance increases more slowly, reaches a peak during the falling phase of the spike, We can show that the outward and gradually declines back to its initial current in Figure 3-20 is a potassium value. current in a similar way. If the extracellular Activation and inactivation. What + K concentration is increased such that εK+ is causes the increase in gNa+ during the action equal to the clamp voltage, there is no outward current, only inward current (shown in Figure 3-20C), the sodium current. The 4 According to fanciers of puffer fish, the sodium current can also be calculated by fish are best when eating them makes the subtracting the potassium current in Figure lips tingle. The sensation must be similar to 3-20d from the total current in Figure 3-20b. that which occurs when novocaine begins to To make this calculation, it is necessary to wear off following a trip to the dentist. assume that there is no interaction between

3-8 potential? The answer is, the initial is altered by hypopolarization, according to hypopolarization! How? Recall that some a popular hypothesis, causing the dipoles to of the membrane proteins act as channels or reorient and open the channel. At any rate, pores through which lipid-insoluble the channel is opened by hypopolarization, substances can pass. Actually, three types allowing Na+ to enter the cell, which it does of channels are recognized. Some channels, because of its concentration gradient. e.g., some K+ channels, are open all the time Sodium entry holds the channel open longer and allow ions to pass through the and causes more channels to open, allowing membrane down their electrochemical more sodium to enter and more channels to gradients. Many K+ channels are open in the open, etc. Opening of the channel is called resting membrane, but few Na+ channels are. activation. Other channels are gated, some electrically Until recently, it has been impossible and some chemically. Chemically gated to study the behavior of ion channels channels are opened by substances called because the currents that flow through them transmitter substances, and they occur in are so small, a few picoamps, that noise in specialized regions of cells where contacts the recording system completely hid the are made with other cells (i.e., at synapses). small signals. However, a new recording We will have more to say about them later. technique, called the patch-clamp, allows The voltage-gated channels are the opening and closing of single channels opened when the membrane is to be studied. Briefly, the patch-clamp hypopolarized. Because the cell membrane technique involves pressing a polished is so thin, the resting potential sets up an micropipette electrode against the cell electric field across the membrane that has a membrane and applying a bit a negative strength of about 100 kV/cm of membrane pressure to the lumen of the pipette. If all thickness. The Na+ channel, and perhaps goes well, the orifice of the pipette seals similarly the K+ channel, is a single glyco- against the membrane with sufficient polypeptide of molecular weight 260,000- strength that no current can pass between the 300,000 (at least, the one in Electrophorus membrane and the pipette edge, and the electricus, an electric fish). The molecule is pipette can be withdrawn and actually rip- estimated to be 29% carbohydrate, and it off the piece of membrane covering the consists of four homologous domains, each orifice. The seal formed ensures that composed of 6 segments. The molecule currents passing through the membrane must be elaborately folded, with some patch will flow into the pipette and be recorded. portions making up the channel itself and others comprising either intra- or extracellular appendages (for a possible structure see Guy and Seetharamulu: Proc Nat Acad Sci 83: 508-512, 1986). The diameter of the channel is estimated at about 0.8 nm. The charged groups within the channel give it a large electric dipole moment, and the dipoles tend to align themselves with the electric field in such a way as to close the channel. Field strength

3-9 patch-clamp technique has also shown that there is a vast array of types of ionic channels in different types of cells. Fortunately, at our level of analysis, we need not concern ourselves with most of them. Once sodium channels are opened, something causes them to close again. This is called inactivation. The channels do not, Figure 3-24. Sample channel activity. Channel is closed with trace is "up," open however, go back to their original closed when trace is "down." From Sigworth, state. The inactivated channel cannot be FJ. Chapter 14 in Sakmann and Neher reopened until the membrane repolarizes Single-channel Recording, New York: and the channel returns to the resting, closed Plenum1985, 309. condition, and Na+ conductance during inactivation is even lower than in the resting Using this technique, we now know membrane. The membrane potential has to that ion channels open and close so quickly remain at a value more negative than the that transitions cannot be resolved, i.e., the critical firing level for a msec or so before current pulses appear to be rectangular. the channel can be opened again. This Channels appear to open in an all-or-none accounts for the phenomenon of fashion, each increasing conductance by accommodation: As the membrane is about 8 x 10-12 siemens, although changes in hypopolarized by a small amount, less than conductance vary from channel to channel5. the critical firing level, some Na+ channels There have been some reports of channels open and then (after a brief time) are with two open states, but most appear to inactivated, but not enough are opened to have only one. In general, increasing the generate a spike. More and more channels amount of hypopolarization or, for are opened as long as the hypopolarization is chemically gated channels the amount of maintained, but the rate of opening is still transmitter substance, does not increase the too low to lead to a spike and no channels size or duration of the currents that flow are allowed to return to the closed, openable when a channel opens, but rather decreases state. Once a channel is inactivated, it the time between openings, i.e., it increases remains inactivated until the membrane the probability of the channel being open. repolarizes. If the rate of hypopolarization Also, the channels appear to open is slow enough, many of the Na+ channels independently, i.e., the opening of one can be inactivated without causing a spike, channel is not influenced by the condition of and the critical firing level will be pushed in other channels in the same membrane. The the positive direction. When most of the channels have been inactivated, no spike can be initiated no matter how positive the membrane potential becomes. 5 A change in conductance of 8 x 10-12 siemens would allow a Vm of 100 mV to drive a current of about 10-12 amperes through a channel. This amount of current would involve a movement of about 6000 Na+ ions.

3-10 Figure 3-26. The result of this regenerative cycle is that the sodium battery is relatively much more important than the potassium battery in determining the membrane

potential, Vm. You can see this if you reduce the sodium resistance in Fig. 3-25. Perhaps recalling the discussion of the circuits in Figure 3-7 will help to understand how the membrane potential can change so drastically with only a change in membrane

Figure 3-25. Membrane equivalent circuit. The circuit of Fig.conductance 3-14 (gNa+). As the sodium battery redrawn to show that conductances (resistances) for sodiummakes and itself felt, the membrane potential potassium are not fixed, but variable. moves rapidly toward εNa+. If nothing changed at this point, gNa+ remained high The ionic mechanism of the action and gK+ remained low, the membrane would potential. How then can we account for the seek a new resting potential predictable action potential? First, we must update from equation 5 and near εNa+. But now, the Figure 3-14 to include the variability of the inactivation begins; Na+ channels close + + Na and K resistances or conductances. In (inactivate) and gNa+ drops. At the same Figure 3-25, the fixed resistors are replaced time, the hypopolarization of the membrane with variable resistors, as indicated by the has increased gK+ by opening voltage-gated arrows through the resistor symbols. With K+ channels. Figure 3-26 shows that this this change, we can understand the process is not a regenerative one–increased mechanism of generation of the action hypopolarization leads to increased gK+, but potential. Initially, before the stimulus is increased gK+ leads to repolarization not applied to the neuron, gK+ is small, but gNa+ hypopolarization. Any change in is much smaller, so Vr is near εK+. The stimulus or, as we shall see, an approaching action potential, provides an outward current that passively discharges the membrane capacitance, causing a hypopolarization of the membrane. As the membrane is hypopolarized, the sodium conductance rises as voltage-gated channels open, allowing some sodium ions to enter the cell down their electrochemical gradient, an inward current. The inward current (this is now active membrane) results in further hypopolarization, further increase in conductance as more voltage-gated channels open, and further entry of Na+ ions. This cycle of hypopolarization and increased conductance is sometimes called the Hodgkin cycle, and it is schematized in

3-11 even if the sodium conductance inactivated and potassium conductance remained at resting levels, but the repolarization would take longer. The purpose of the increased potassium is to accelerate the repolarization and shorten the action potential. The potassium conductance also begins to decrease as the membrane repolarizes, but

gK+/gNa+ is greater than in resting membrane, so the membrane potential passes the resting

level and moves even nearer to εK+ (hyperpolarizing afterpotential). Finally, as

gK+ falls back to resting levels, the Figure 3-26. Effects of increasing membrane membrane potential moves back toward Vr conductance on the membrane potential. Hypopolari- as determined by equation 5. zation leads to increased gNa+, which leads to sodium entry, which reinforces hypopolarization in the Hodgkin cycle (above), whereas hypopolarization leads + to increased gK+, which leads to K efflux, which leads The value of the resting potential to repolarization (below). depends strongly on the potassium equilibrium potential, weakly on the conductance with a change in voltage is a sodium equilibrium potential. The value 6 rectification . The change in gK+ is often of the peak overshoot potential is the called delayed rectification because it reverse.

occurs at a later time than the change in gNa+. As gNa+ decreases and gK+ increases, the potassium battery again becomes relatively Sodium deficiency. We saw more important in determining the previously that the resting membrane membrane potential, and so the potential potential depends upon the concentration

falls back toward εK+. This repolarization gradient for potassium. If the extracellular + further reduces gNa+, and the change in Na concentration is slowly lowered, the potential accelerates. The potassium resting potential hardly changes; usually it conductance does not inactivate as the becomes about 10 mV more negative. sodium conductance does; it simply However, as the extracellular Na+ is decreases with repolarization. This ensures reduced, the peak of the positive overshoot that the repolarization occurs completely. becomes less positive, i.e., the amplitude of Actually, the membrane would repolarize the action potential decreases, and the spike rises more slowly. When the extracellular Na+ concentration is lowered below 20 mM, the neuron becomes totally inexcitable and 6 This use of the term rectification by no spikes can be initiated. This results from biophysicists is quite different from that of a reduction in the Na+ concentration gradient electrical engineers, meaning lower and, therefore, the sodium current. We have resistance to current flow in one direction already seen that the sodium current is an than the other through a circuit element. Do integral part of the mechanism of the spike. not confuse these usages.

3-12 Movements of ions during the spike. the outward current that results in a spike If there is a significant ionic current during can also be generated by a spike occurring the spike, ion concentrations both inside and in an adjacent region of membrane. outside the neuron should change. Actually, the ionic shifts through the membrane during the spike are small in relation to the intracellular and extracellular ion concentrations. Measurements of ion movements show that there is a net influx of about 3.7 x 10-12 moles of Na+ ions/cm2 of membrane and an equal K+ efflux during the spike. In large axons, this is about 1/1,000,000 of the resting concentrations. Even in small , the actual ion movement is only 1/1000 of the resting concentration. There is, therefore, only a small change in ion concentration as a result of ion movement during the spike, a change that would not be measurable using ordinary chemical techniques, at least for large cells. The sodium ions that flow in are expelled by the sodium pump, which works not only to maintain resting ion concentrations, but also to restore these concentrations when they are disturbed. Actually, the sodium pump is not important for the individual spike because thousands of spikes can still be initiated in an axon in which the sodium pump has been poisoned with ouabain, cyanide, or dinitrophenol. It is required for long-term maintenance of excitability.

Propagation of the action potential. Obviously, neurons must be able to generate action potentials without an experimenter passing current through the membrane. We will see later how sensory stimuli and synaptic transmission from other cells can lead to action potentials; it suffices for now to say that both types of stimuli eventually result in generation of a current outward through the membrane and a hypopolarization as described earlier. But,

3-13 3-14 Figure 3-27. Local circuit current flow during propagation of a spike. A. Spike frozen in time in a region of membrane as it was traveling from right to left. B. Magnitudes and directions of total membrane current, Im, capacitative current, ic, and ionic current, ii, along the membrane. As usual, downward deflections indicate inward current. C. The direction and density of membrane currents are indicated by arrowhead orientations and density of red lines. D. Current flow directions and magnitudes in membrane equivalent circuits shown at five points (indicated by vertical dashed lines) along the membrane at which the spike is just beginning, 1; in its upstroke phase, 2; at its peak overshoot, 3; in its downstroke phase, 4; in its hyperpolarizing after potential, 5; and at rest, 6 (Noble, Physiol Rev 46:1-50, 1966; Brinley, Excitation and conduction in nerve fibers, in Mountcastle, Medical Physiology, 13th ed. Vol I, St. Louis: Mosby, 1974).

Because of Kirchhoff's law (current inside of the cell and out through adjacent flows only in complete circuits), the current membrane as shown in Figure 3-27. This that flows into the cell during the upstroke outward current flows through passive of the action potential must flow along the membrane, discharges the capacitance of the

3-15 adjacent membrane, leading to an the capacitative current, ic, and the ionic hypopolarization, an increase in gNa+, and an portion of the current, ii. Obviously, im = ic action potential. Once the inward ionic + ii. The total membrane current is indicated current of the spike is started, an outward schematically through a section of current will be generated through the next membrane in C, where arrowheads indicate segment of membrane7. This process will be the direction of current flow, and the repeated in each adjacent segment of closeness of the lines indicates the membrane throughout the length of the approximate current density. In D, the membrane, that is, the action potential will equivalent circuit is shown with directions be propagated essentially without decrement and approximate magnitudes of the along the membrane. The spike itself is an membrane, capacitative, and ionic currents active process, due to the sodium battery, indicated by arrows. The changes in but propagation results from electrotonic conductances are indicated by changes in (decremental) conduction (a passive the lengths of the Na+ and K+ resistance process) into nearby membrane segments symbol. where a new spike is initiated. Each new Reading from left to right, spike has the same amplitude, so conduction successive segments of membrane are going occurs without decrement. This is equivalent through successive phases of the action to what the booster stations do along the potential at a given instant in time. Thus, at transatlantic telephone cables. the time the spike was "frozen" in this If the action potential is initiated in position, it had not yet begun at site 1, but the middle of a length of axon membrane, it outward current (being driven by the inward will propagate in both directions away from current at site 3 and nearby) has begun to the site of initiation. We shall see later that discharge the membrane capacitance. At conduction does not normally occur in both site 2, the membrane is hypopolarized, directions along an axon, but it can and this increasing gNa+, and, therefore, iNa+. fact is used in stimulation of the dorsal Between sites 1 and 2 the membrane current columns to treat pain (see Chapter 6). is mainly capacitative and outwardly One result of propagation is that the directed, but between sites 2 and 3 the ionic action potential pattern as seen plotted in current becomes larger as the Na+ channels time in Figures 3-17 and 3-23 can just as open (Fig. 3-27B). The increased Na+ well be plotted in length along the conductance is indicated by the shorter membrane as shown in Figure 3-27. The resistance symbol at site 2 than at site 1, and spike, shown in the upper panel, A, has been at site 3 than at site 2 in D. The sodium stopped instantaneously in space as it was conductance has reached its maximum at traveling from right to left. In Figure 3-27 B site 3, and the potassium conductance has are shown the total membrane current, im, increased somewhat (as indicated by the shorter K+ resistance symbol in D) at the peak overshoot potential or the spike. The capacitative current is zero at site 3 because 7 The inward current is carried by sodium dV/dt=0 and thus, i =i . ions as we have just seen, but it is not m i Sodium inactivation is well possible to say what ions carry the outward underway, but potassium conductance is still current. The most likely candidate would be high during the repolarization phase at site K+.

3-16 4. Total membrane current is small and the membrane to the critical firing level, are outwardly directed. Sodium inactivation is not propagated along the axon, but conduct complete (as indicated by the long Na+ decrementally. Events like those in Figure resistance symbol in D), but potassium 3-15 and Figure 3-16a-d will produce no conductance is still higher than normal effect on the membrane of the cell at a causing the membrane potential to approach distance of more than a few millimeters. the equilibrium potential for potassium and The action potential will be of the same generating the hyperpolarizing afterpotential magnitude at the site of initiation and at the at site 5. Both sodium and potassium end of the cell, a meter or even several conductances are normal and the membrane meters away. When it is necessary to is back at the resting potential at site 6. communicate information (neural Thus, the sequence of events occurring information) over distances greater than a along the length of the membrane at an few hundred micrometers, only the action instant in time during conduction is exactly potential will suffice. the same as that occurring in time at a fixed Saltatory conduction. The ionic point on the membrane. current that flows inward through the The velocity of the propagation of membrane results from an active process, the spike increases with the magnitude of the change in sodium conductance. On the + iNa+ or with the amount of the Na influx. other hand, the longitudinal current flow The more current there is available to inside and outside the axon is passive, hypopolarize adjacent, unexcited membrane following the rules of electrotonic after local capacitance is discharged, the conduction. If the electrotonic potentials faster the adjacent membrane will rise faster, i.e., if the time constant of the hypopolarize to critical firing level and the membrane, τ, is decreased, and if they faster it will generate current to decline less with distance, i.e., if the space hypopolarize unexcited membrane next to it, constant, λ, is increased, the conduction and so on. In order to hypopolarize adjacent velocity must increase because more current regions of membrane, the inward iNa+ must will flow through more distant segments of traverse a volume of intracellular fluid. The membrane. The membrane time constant resistance of that fluid is a factor in will decrease if the membrane capacitance is determining how much current actually reduced, and the space constant will increase reaches the adjacent membrane. The if the membrane resistance is increased. resistance to passage of current along the During evolution, animals first inside of the fiber decreases with the square exploited increasing axon diameter as a of the inside fiber diameter; a larger area means of increasing conduction velocity, but contains a larger number of potential current there is a limit to how large neurons can be; pathways. Thus, larger axons will have the problem is simply one of bulk. Few lower values of Ri and therefore have faster giant axons could be accommodated by the conduction velocities than smaller axons. squid's body, unless it were greatly enlarged. It is in propagation, nearly without Fortunately for the squid, it does not need decrement, that the reason for the existence many. The problem becomes even more of the action potential lies. The severe when the nervous system contains subthreshold events, that is, the events that more than 109 rapidly conducting neurons, occur in response to stimuli that do not bring as does the human nervous system. Another

3-17 solution, which uses the principles of Ωcm2, whereas that at the internode is electrotonic conduction, requires the 160,000 Ωcm2. Conversely, the capacitance cooperation between neurons and glia, the of the node is 3 μF/cm2, whereas the Schwann cells in the peripheral nervous internode has a capacitance of 0.0025 system and oligodendrocytes in the central μF/cm2. For a 12-μm axon, the node has an nervous system (CNS). During area of 20 μm2; the internode has an area of development, the Schwann cells and 88 x 103 μm2. Using these areas, the oligodendrocytes wrap themselves around capacitance of a node and internode can be the axons, producing a fatty sheath, calculated (Fig. 3-28C). The calculated composed of layers of membrane and called capacitance of the node is 0.6 pF, that of the myelin. Axons with a myelin sheath are internode 2 pF (recall that the area of the said to be myelinated axons; axons without internode is much larger). At the same time, a myelin sheath are called unmyelinated the measured transverse membrane axons. Each Schwann cell covers (totally resistance at the node is 80 MΩ, that of the surrounds) an area of membrane about 1 mm internode is 200 MΩ, and the internal in length, with a space between adjacent longitudinal resistance, Ri, is only 20 MΩ. Schwann cells, called the or Because the internode's membrane simply the node. The region of myelin resistance is so high, most of the coverage between two nodes is the longitudinal current generated by a spike internode. Figure 3-28A shows a node (with occurring at a node will pass along the two adjacent segments of internode) in the intracellular fluid rather than outward peripheral nervous system (above) and the through the myelin. Although there will still CNS (below). The central node is be some loss of electrotonic potential along apparently more open to extracellular fluid, the internode, the high resistance and low but the peripheral node is also bathed in capacitance ensure that the loss will be less extracellular fluid. The tightly wrapped than in the same length of unmyelinated layers of membrane prevent contact of axon. The result is that most of the current extracellular fluid with the axon membrane will flow out through the nodes adjacent to in the internode, but such contact is the one with the ongoing spike, and the provided at the nodes. Overlapping current density there will be high, Schwann cell membranes in the internode sufficiently high to discharge the membrane act as series resistances and capacitances as capacitance rapidly to the critical firing shown in Figure 3-28B. Because resistances level, initiating a spike. No action potential in series are simply additive, the total can occur in the internode, so the spike resistance across the membrane and myelin jumps from node to node to node. The at any point along the internode will be conduction in myelinated axons is called much higher than at any point along saltatory (from the Latin, to jump). The unmyelinated membrane or in the node. current density at the node is about 20 Because series capacitances add as mA/cm2 (current density in unmyelinated reciprocals, the transverse capacitance per squid axon is seldom greater than 1 mA/cm2 unit area at any point along the internode under the same conditions), and this is 5-7 will be much lower than at any point in the times greater than that required to bring the node. Measurements in the frog axon show membrane to the critical firing level. that the resistance of the node is only 20

3-18 Figure 3-28. Saltatory conduction in myelinated axons. A. Longitudinal section through a small myelinated axon in the peripheral nervous system (above dashed line) and in the central nervous system (below dashed line). Note difference in structure of nodal regions. (Landon and Hall, The myelinated nerve fibre, in Landon, The Peripheral Nerve. London: Chapman and Hall, 1976). B. Equivalent circuit for a region of internode, showing how membrane resistances, Rm, and capacitances, Cm are arranged in series, making resistance very high, capacitance low in the internode. C. Equivalent circuit for two nodes and intervening internode, with values of membrane resistance, membrane capacitance, and internal longitudinal resistance inserted (Aidley, The Physiology of Excitable Cells. Cambridge: Cambridge Univ. Press, 1971).

This safety factor ensures that conduction further down the axon (1 or 2 nodes away) from node to node will occur. In fact, by virtue of the longer space constant. The saltatory conduction probably occurs largest unmyelinated fibers in mammals are between every other node or even every 2 μm in diameter and conduct at 2 m/sec; third node because there is sufficient current the largest myelinated fibers are 22 μm in to bring to the critical firing level even the diameter and conduct at 120 m/sec. second or third node away from that where a Longitudinal, intracellular resistance spike is occurring. decreases as the square of internal diameter Conduction in myelinated axons is in myelinated as in unmyelinated axons, so much faster than in unmyelinated axons conduction velocity in larger myelinated because the spike, at one point on the axons will be higher than in smaller ones. membrane, initiates another spike at a point In peripheral nerves, a rough rule of thumb

3-19 is that conduction velocity of myelinated refractory period. axons in m/sec is six times the axon diameter expressed in μm. This estimate does not work well for axons in the central nervous system. Refractory periods. Note in Figure 3-27 that current flows outward through the membrane both in front of and behind the advancing action potential. What prevents the action potential from turning around and propagating in the reverse direction? The answer lies in the refractory period. After the peak overshoot of the spike, the Na+ conductance begins to be inactivated, and, by the time the membrane repolarizes to the resting potential, sodium conductance is almost entirely inactivated. Recall that the membrane must remain near the resting Figure 3-29. Time course of refractoriness potential for sometime (a millisecond of so) following a spike. Spikes elicited by pairs of before the sodium channels return to their stimuli at a long time interval. The first closed state, ready for activation again. stimulus was applied at the leftmost downward During this time, the sodium conductance arrow. The second stimulus of the first par occurred 2 msec after the first stimulus (second cannot be changed substantially by arrow), of the second pair occurred about 2.8 hypopolarization. Thus, a new spike cannot msec after the first (third arrow), and (as in a) be initiated no matter how large the of the third pair occurred 4 msec after the first hypopolarization. This phase of inexcita- (fourth arrow). Spikes initiated during the bility, called the absolute refractory refractory period are stunted and prolonged. Dashed line on rising phase of each spike period, is shown in Figure 3-29. It has indicates approximate critical firing level. B. about the same duration as the spike itself in Time course of change in critical firing level many cells. through the refractory periods. Approximate The channels do not all convert to durations of absolute and relative refractory the closed, activatable state at the same time. periods are indicated at the bottom of the Therefore, as time passes after the figure (Dudel, in Schmidt RF, Fundamentals of Neurophysiology, 2nd ed. New York: repolarization, more and more channels will Springer-Verlag, 1978). be available until all are available. The excitability increases or, in other words, the threshold falls as a function of time after the The refractory periods, absolute and spike. The fall in the threshold is shown in relative, have two important consequences. Figure 3-29B. Even though a spike can be First, the refractory period is long enough initiated within 2 or 3 msec after another that the electrotonic and ionic voltages spike has occurred, it is only a partial spike behind the spike have declined to below the because not all Na+ channels are available to critical firing level before the refractory the spike generating mechanism. This period is over. Thus, the spike cannot turn period of reduced excitability is the relative around and go the other way. Likewise,

3-20 because two action potentials cannot occupy depress neuron firing at many places in the the same region of membrane at the same central nervous system, yet they do not time, two action potentials approaching each change either resting membrane potentials other along an axon will cancel each other or membrane resistance. Synaptic out; neither action potential will pass the potentials, the potentials that occur as a part point of their meeting. This is called of transmission between cells, are not occlusion. influenced by increasing extracellular Ca++. Another consequence of the Magnesium ions have an influence on axon refractory periods is that there is a maximum excitability similar to that of calcium, but, as rate of discharge for the neuron. This rate is we shall see, magnesium's effect on synaptic limited by the absolute refractory period for transmission is opposite to that of calcium. strong stimulation and by the relative Ok, why does this occur? It could be refractory period for weak stimulation. A that the effect of mild reduction in Ca++ is neuron that fires a 0.5-msec duration spike explained by supposing that Ca++ is a with a 1.0 msec refractory period cannot, voltage sensor–a gating particle that moves under any circumstance, fire at a frequency in the electric field of the membrane. It greater than 1000/sec. If the spike and the binds to a channel component at rest, refractory period are longer, the maximum keeping the pore closed, and it is pulled off frequency decreases. the channel by membrane hypopolarization, Influences of other ions. Other ions, opening the channel. The less calcium there beside Na+ and K+, do not seem to play a is in the medium, the more channels are major role in generation of the action open and the lower the threshold (CFL). At potential, at least in axons like the squid even lower Ca++ levels, the membrane may giant axon. That is not to say that they become excessively leaky to many small cannot affect the action potential, however. molecules, making the cell inexcitable. One Calcium has a complex effect on the action explanation for the effect of increased Ca++ potential threshold. When the extracellular concentrations is that Ca++ is absorbed to the concentration of calcium is lowered, the outer edge of the membrane, creating an axon becomes more sensitive to excitation, electric field inside the membrane which lowering the threshold for intracellular adds to that provided by the resting stimulation and causing the cells to potential. This would be equivalent to a discharge spikes spontaneously. The membrane hypopolarization, so channels influence of calcium seems to be to stabilize would open and stay open. If channels do the membrane. In some cases, muscle not close, they cannot be reopened. Keep in twitches occur when serum calcium levels mind that this is still speculative. are low; they cease when the person drinks Neurons and muscles in mammals some milk. This probably reflects this use sodium and potassium conductance dependence upon calcium. changes to generate action potentials, but At very low concentration of Ca++, these are not the only ions that can serve this less than 1 x 10-5M, the axon becomes function. In fact, in crustacean muscles and inexcitable by any stimulus intensity, in the and, in some cases, somata although excitability can be restored by of neurons in the cerebral cortex, of Purkinje increasing extracellular Ca++ again. Above- cells of the cerebellar cortex, of neurons in normal extracellular calcium concentrations the inferior olivary nucleus, and perhaps of

3-21 spinal motoneurons in mammals, Ca++ takes The existence of sodium spikes in the place of Na+ in carrying inward current. the axon and calcium spikes in the dendrites Calcium conductance is activated by of some cells in the CNS suggests that the hypopolarization, but the kinetics of membrane of a neuron is not the same all activation are slower than those for sodium over, from dendrites, to soma, to axon, to and thus the calcium spike develops more axon terminals. Older concepts of the slowly and it lasts longer. Like the sodium neuron treated the as the receptive conductance, the calcium conductance part of the cell, receiving either sensory inactivates with time and potassium stimuli from the environment or inputs from conductance increases, repolarizing the other cells. The soma was an integrative membrane. The calcium spike is not part of the cell, summing inputs from a blocked by tetrodotoxin as is the sodium variety of sources and generating an output spike. Likewise, procaine, which blocks based on the sum. Axons were simply sodium spikes, is without effect on calcium conducting cables following the output of spikes. Tetraethylammonium ions prolong the soma but not altering it in any way, and increase the amplitude of the calcium whereas the axon terminals transmitted the spike as they do for the sodium spike. The action potentials to other neurons or calcium spike is blocked (by competitive effectors by releasing small amounts of a inhibition) by other divalent ions, Mn++, transmitter substance. More recent concepts Cd++, Ni++, but the sodium spike is not. This of neurons do not delegate such exclusive implies that, although Ca++ can pass through functions to parts of neurons, but allow Na+ channels, it has its own channels in broader overlap in function. Still, the membranes sustaining calcium spikes. differences in properties of parts of a nerve It has been noted that sodium spikes cell membrane suggest that the membrane is are found where rapid conduction of the inhomogeneous. action potential is important. Surely, the We have seen that the axon conduction velocity of the calcium spike membrane contains an abundance of would be slow; a definite speed advantage voltage-gated sodium and potassium would lie with the sodium spike. On the channels, giving it the ability to generate other hand, in primitive, slowly moving action potentials. The density of such animals, there was no particular premium on channels in axons has been estimated at speedy conduction; calcium spikes probably 1000 per μm2. Membranes that do not sufficed. Calcium spikes are found when contain voltage-gated channels do not electrical excitation couples to an effector generate spikes. The soma and dendrites of process, for example, muscle contraction or some neurons have few, if any, voltage- glandular secretion. The role of calcium gated channels, although neurons that spikes in the dendrites of neurons in the support dendritic and somatic sodium or central nervous system is not known. It has calcium spikes may have many. The been suggested that these calcium spikes are receptor sites on membranes, sites sensitive a holdover from more primitive times; yet to sensory stimuli and transmitter there is no compelling evidence for this substances, do not generate spikes, but they conjecture. do support non-propagated, graded potentials that lead to spikes. As we shall Inhomogeneity of the nerve membrane. see, the generation of spikes in such

3-22 membranes would disrupt their ability to At other synapses, the channels open to encode the qualities of the stimulus. create a more selective change in membrane The dendrites and soma have many conductance for potassium and chloride. chemically-gated channels, especially at the Axons themselves contain no chemically- sites of contact with other cells at synapses. gated channels, except at sites of special Some estimates indicate the number of such synaptic contacts, the axoaxonic and nodal channels at synapses is limited only by their synapses. maximum packing density. Chemically- gated channels are of numerous types that can be classified either in terms of the chemical transmitter substance that opens them or in terms of their selectivity for certain ions. Some chemically-gated channels are opened by acetylcholine, others by norepinephrine and others by other substances. (For a further discussion of the topic of transmitter substances, see Chapter Figure 3-30. Accommodation in the soma. 13). Channels are seldom absolutely A-C. Intracellularly recorded responses of a motoneuron to prolonged hypopolarizing selective. Thus, the acetylcholine-gated current at increasing strength. A: 7 x 10-9 channels at the neuromuscular junction, the A, B: 7.7 x 10-9 A; C: 10 x 10-9 A. D. synapse between the motoneuron and the Monitor of current flow; upward muscle, allow both sodium and potassium deflection is on (Granit, Kernell and ions, in fact, nearly all ions to pass through. Shortess, J Physiol (Lond) 168:911-931, 1963). This non-selective change in membrane permeability leads to a hypopolarization of the muscle membrane, the endplate Not only is the density of different potential, a spike, and muscle contraction. kinds of ionic channels different in various parts of the nerve membrane, but the behavior of the sodium channel is different in different parts of the membrane. If a pair of micropipette electrodes is used to penetrate the cell body of a neuron as in Figure 3-8 and a constant current is passed outward through the membrane, a train of action potentials will be initiated, lasting as long as the current is maintained. Figure 3- 30 shows this for three different magnitudes of current through the soma of a motoneuron. In D is shown the monitor of the current which turns on abruptly as the trace deflects upward and off abruptly as the trace deflects downward. At a current magnitude of 7 x 10-9 A, the spike train is a bit irregular, but continues for the duration

3-23 of the current flow (A). At higher currents is indicated in B and the axon's response to (B and C), the trains are regular and the that current step is shown in A. Within frequency of discharge (spikes/sec) within reasonable limits, larger currents will give the trains is proportional to the current only a similar single-spike discharge, magnitude. This kind of behavior is although the spike will occur slightly sooner representative of most somata of after the start of the larger currents. mammalian neurons, though it is debated However, if the current is turned on and off whether it is a property of the soma itself or several times within the same time period, the initial segment of the axon (the transition as indicated by the repeated upward and from soma to axon). For this discussion, we downward deflections of the current monitor will treat the initial segment as part of the in D, the axon discharges a spike each time soma. the current comes back on (C), as long as there is sufficient time after the previous spike for the refractory periods to have ended. This kind of behavior is typical of axons in mammalian nervous systems (but not invertebrate systems). How the sodium channels differ in these two types of membranes is unclear, but there is a clear difference in Figure 3-31. Accommodation in the axon. accommodation. There are different A. Response of an axon to prolonged isoforms of the sodium channel; some are hypopolarizing current as shown in B. C. found in cell bodies, others in axons. Response of the same axon to repeated Perhaps this difference reflects a difference short pulses of hypopolarizing current in the isoform of the local channels. shown in D. Actually, there is no reason for the axon to behave like the soma in response to If the same experiment were done in prolonged outward currents, because axons an axon, each current step would result in a probably never experience such currents. single action potential as the membrane The axon is basically a follower; it follows potential crossed the critical firing level. what the soma (or initial segment) does. Its Trains of spikes are never generated in spikes are caused by the soma spikes by mammalian axons unless the currents are propagation as described earlier. (This is excessively (perhaps pathologically) high. probably what George Bishop (Ann Rev This rapid fall in the firing frequency of the Physiol 27: 1-8, 1965) had in mind when he axon in spite of the constant stimulus is said comically, "The axon doesn't think. It called adaptation and, in the case of the only ax.") The soma spikes generate fast axon, probably results from an extremely current transients that recur with each spike rapid accommodation of the membrane. and repeatedly initiate axon spikes as in Adaptation also occurs in sensory receptors Figure 3-31C. Axons, therefore, always (as we shall see in Chapter 4) where it may generate trains of spikes identical in their have causes other than accommodation. The timing (the spikes occur at the same times adaptation of the axon membrane is relative to each other) to those that occur in illustrated in Figure 3-31. A step of current the soma. The soma, on the other hand, is

3-24 the pacemaking or spike-generating region the channel through which it must pass. of the neuron, responsible for coding Nerve membranes have a high conductance information it receives from other neurons for chloride and potassium ions, but a low (a property the soma shares with sensory conductance for sodium ions. The receptors as we shall see in the next membrane has both resistance and chapter). It experiences prolonged current capacitance, causing electrical signals flows (synaptic currents) and must respond applied to it to be greatly attenuated and to changes in current flow with changes in badly distorted within a few millimeters of frequency of discharge. The soma's the site of application, i.e., it is a poor behavior, like that of the axon, is appropriate conductor of electricity. The time constant to its role in neural function. of the membrane ranges from 0.5-5.0 msec The existence of different kinds of and the space constant is about 2 mm. ionic channels in different densities in The membrane contains no metallic different regions of the neuron's membrane conductors, therefore any currents through re-emphasizes that the fluidity of the lipid the membrane must be carried by ions. Ions membrane is not unlimited. If it were so, are not distributed equally on both the inside then the dendrites would often have and outside of the membrane: sodium, properties of axons, the somata often calcium, and chloride concentrations are properties of dendrites, and so forth. In much higher outside than inside, potassium cases where an element external to the cell concentration is higher inside than outside, is involved, as at synapses, these elements and the intracellular fluid contains some may influence the aggregation of certain large anions that cannot leave the cell. channels near them. Not every case Because of the differing concentrations of involves an external element; in these other ions, there is always a tendency for ions to cases, some internal factor likely aggregates diffuse through the membrane. Differing appropriate channels. concentrations of ions on two sides of a semi-permeable membrane (like the cell Summary. membrane) comprise a concentration cell or The membranes of excitable cells are battery that creates electrical forces to composed of lipids and proteins organized counteract ion diffusion. There will be an into a fluid mosaic. It is the proteins that equilibrium when concentration forces give different membranes their specific balance electrical forces, an electrochemical character. These proteins can sit on the equilibrium. For each ion, electrochemical membrane, they can be embedded in the equilibrium occurs at its equilibrium surface of the membrane, or they can pass potential. For chloride, the equilibrium all the way through the membrane, and they potential is about -66 mV (for nerve, higher can act as structural elements, pumps, for muscle); for potassium, it is about -75 to channels, receptors, and enzymes. -80 mV; and for sodium, it is about +55 to Membranes are permeable to small- and +60 mV, all expressed as voltage inside with medium-sized lipid soluble molecules, but respect to outside. only small lipid insoluble molecules can The resting membrane has a pass through. The ease with which a potential difference across it, called the molecule passes through depends upon its resting membrane potential, that has a value hydration radius and the characteristics of of -50 to -90 mV depending upon the cell.

3-25 This potential occurs because (1) the is produced by both sodium inactivation and membrane is 20-30 times more permeable to a delayed increase in potassium conductance chloride and potassium than to sodium; (2) leading to an outward current and chloride ions are able to redistribute repolarization. A period of themselves with changes in membrane hyperpolarization following the spike is potential and are thus at equilibrium; and (3) produced by a continued, heightened potassium ions cannot freely redistribute potassium conductance but a lower-than- themselves because they must remain inside normal sodium conductance. The spike the cell to balance the electrical charge of does not occur in the absence of the sodium the non-diffusible anions and maintain concentration gradient. electrical neutrality. The value of the The spike, once initiated, travels membrane potential depends upon the ratio down the axon because the inward current of of potassium conductance to sodium the spike upstroke produces an electrotonic conductance. Because this ratio is usually hypopolarization of the membrane in front very high, the membrane potential is usually of the spike. This hypopolarization is near the potassium equilibrium potential. usually sufficient to bring the membrane to Thus, the membrane potential depends the critical firing level, and thus the spike mainly upon the concentration gradient for propagates to the end of the axon. potassium ions. The membrane is leaky, so Conduction velocity increases if the that concentration gradients for sodium and diameter of the axon is increased and if the potassium ions must be maintained by the axon is myelinated. Myelination decreases sodium pump. The pump within a single the membrane time constant and increases neuron can be non-electrogenic, pumping the space constant of the membrane, thereby equal numbers of sodium and potassium increasing the current density at the nodes ions, or it can be electrogenic, generating a and allowing the spike to jump from node to net outward current that may influence the node. value of the membrane potential. The Spike frequency is limited by the pumping rate depends upon the intracellular refractory periods that result from the sodium concentration. sodium inactivation process and the fact that When an excitable membrane is sodium channels are not available for re- strongly stimulated, it generates an active activation for a short time after the response that is not predictable from the membrane returns to the resting potential. simple resistance-capacitance equivalent Ca++ plays a role in stabilizing the circuit. This response, called the action membrane. Thus, as extracellular Ca++ potential, is an initial rapid concentrations drop, the neuron becomes hypopolarization, a period of reversed more excitable, whereas at very low polarization, and a rapid repolarization. The concentrations it becomes completely spike is triggered by hypopolarization of the inexcitable. In some neurons, Ca++ takes the membrane that leads to increased sodium place of Na+ in generating the upstroke of conductance, inward current, and more the action potential. Usually, this occurs in hypopolarization until the sodium dendrites or other places where rapid conductance is inactivated. The period of conduction over long distances is increasing sodium conductance accounts for unnecessary. the upstroke of the spike. The falling phase The membrane is not the same all

3-26 over a cell. Densities of voltage-gated New York, McGraw-Hill, 1966. channels are high in axons but usually lower 10. Llinas R, Hess R: Tetrodotoxin- in the soma and dendrites. Chemically resistant dendritic spikes in avian gated channels are normally absent in axons Purkinje cells. Proc Nat Acad Sci but dense in the soma and dendrites. The 73: 2520-2523, 1976. behavior of channels also varies in different 11. Salzer, JL: Nodes of Ranvier come parts of a cell. In the axon, there is rapid of age. Trends Neurosci 25: 2-5, adaptation, presumably due to 2002. accommodation, whereas in the soma 12. Sigworth FJ: The patch clamp is adaptation is minimal. This difference more useful than anyone had reflects the role of the soma as pacemaker or expected. Fed Proceed 45:2673- spike generator and the axon as a simple 2677, 1986. follower-conductor. 1. Stevens CF: The Neuron. Sci Am 241: 55-65, 1979. 14. Waxman SG: Integrative properties and design principles of axons. Int Rev Neurobiol 18: 1-40, 1975. Suggested Reading

1. Catterall, WA: From ionic currents to molecular mechanisms: The structure and function of voltage-gated sodium channels. Neuron 26: 13-25, 2000. 2. Cooke I, Lipkin M [eds]: Cellular Neurophysiology, New York, Holt, Rinehart, and Winston, 1972. 3. Eccles JC: The Physiology of Nerve Cells. Baltimore, Johns Hopkins Press, 1968. 4. Goldin, AL: Resurgence of sodium channel research. Ann Rev Physiol 63: 871-894, 2001. 5. Guy HR, Seetharamulu P: Molecular model of the action potential sodium channel. Proc Nat Acad Sci 83: 508- 512, 1986. 6. Hagiwara S: Ca spike. Advan Biophys 4: 71-102, 1973. 7. Hodgkin AL: The Conduction of the Nervous Impulse, Springfield IL, Thomas, 1964. 8. Junge D: Nerve and Muscle Excitation, Sunderland MA, Sinauer, 1976. 9. Katz S: Nerve, Muscle, and Synapse,

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