8

Local Signaling: Passive ElectricalProperties of the Neuron

Input Resistance Determines theChanges in Membrane Potential

Magnitud

Membrane Capacitance Prolongs the TIme Courseof Electrical Signals

Membrane and Axoplasmic Resistance Affect the Efficiencyof Signal Conduction

Large Axons Are More Easily Excited Than Small Axonsby Extracellular Current Stimuli

Passive Membrane Properties and Axon Diameter Affectthe Velocity of Action Potential Propagation

An Overall View

W HILE ALL CELLS OF THE body have a membranepotential, only neurons (and muscle cells)generate electrical signals that can be con-

ducted rapidly over long distances. In the last chapterwe saw how these electrical signals are generated by theflux of ions across the cell membrane through special-ized ion channels, and how to calculate the expectedmembrane potential for any set of ionic concentrationgradients and membrane permeabilities using theGoldman equation.

This description does not, however, provide any in-formation about changes in the membrane potential inresponse to a stimulus, since the Goldman equation ap-plies only to the steady state when the voltage does notchange. During signaling, when the neuron generatesaction potentials, synaptic potentials, or sensory genera-tor potentials in response to a stimulus, the membranevoltage changes constantly. What determines the rate

ectrical

of change in potential? Will a brief synaptic current al-ways produce a similar potential change, regardless ofthe size of the postsynaptic cell? What determineswhether a stimulus will or will not produce an action

potential?Here we consider how a neuron's passive electrical

properties and geometry, which are relatively constant,affect the cell's electrical signaling. In the next chapterwe shall consider how the properties of the ion channelsthat generate the active ionic currents also help deter-mine changes in membrane potential.

Neurons have three passive electrical propertiesthat are important to electrical signaling: the restingmembrane resistance, the membrane capacitance, andthe intracellular axial resistance along axons anddendrites. Because these elements provide the returnpathway to complete the electrical circuit when activecurrents flow into or out of the cell, they determine thetime course and amplitude of the synaptic potentialchange generated by the synaptic current. They also de-termine whether a synaptic potential generated in adendrite will result in a suprathreshold depolarizationat the trigger zone on the axon hillock. Still further, thepassive properties influence the speed at which an ac-tion potential is conducted.

Input Resistance Determines the Magnitudeof Passive Changes in Membrane Potential

The difference between the effects of passive and activeproperties of neurons can be demonstrated by injecting

of change in potential? Will a brief synaptic current al-ways produce a similar potential change, regardless ofthe size of the postsynaptic cell? What determineswhether a stimulus will or will not produce an action

e of Passive

lure 8-1 Current-voltage relationships. By passing sub-°eshold, graded, inward and outward current pulses into aII, one can determine the relationship between current in-:ted into the cell and the resulting changes in membrane po-

1tial, VmoIncreases in outward or inward current pulses (A,) produce:>portional and symmetrical changes in Vm (Az). Note that the>tential changes more slowly than the step current pulses.

IITeI\t pulses into the cell body (see Box 7-1). Injectingnegative charge through an electrode increases theaarge separation across the membrane, making the.embrane potential more negative, or hyperpolarized.:\e larger the negative current, the greater is the hyper->larization. In most neurons there is a linear relationrtween the size of the negative current and the steady-ate hyperpolarization (Figure 8-1). The relation be-~een current and voltage defines a resistance, RiJv the~n's input resistance.

Likewise, when a positive charge is injected into the!ll, producing depolarization, the neuron behaves as ample resistor, but only over a limited voltage range. Arge enough positive current will produce a depolar-ation that exceeds threshold, at which point the neu-In generates an action potential. When this happensIe neuron no longer behaves as a simple resistor be-lUBe of the special properties of its voltage-gated chan-~ls considered in Chapter 9. Still, much of a neuron'siliavior in the hyperpolarizing and subthreshold de-[)larizing range of voltages can be explained by simpleIUivalent circuits made up of resistors, capacitors, anditteries.

The input resistance of the cell determines howluch the cell will depolarize in response to a steady.llTeI\t. The magnitude of the depolarization, ~ V, isiven by Ohm's law:

4 V = I X Rm.

141Chapter 8 / Local Signaling: Passive Electrical Properties of the Neuron

B~t"E~0

Vm (mV)

"E

1

l - Hyperpolarization Depolerizetion-

B. An I-V curve is obtained by plotting the steady state voltageagainst the injected current. The slope of the I-V curve definesthe input resistance of the neuron. The I-Vcurve shown here islinear; Vm changes by 10 mV for every 1 nA change in current,yielding a resistance of 10 mV/1 nA, or 10 x 108 a (10 MO).

Thus, of two neurons receiving identical synaptic cur-rent inputs, the cell with the higher input resistancewill show a greater change in membrane voltage. Foran idealized spherical neuron with no processes, theinput resistance depends on both the density of theresting ion channels in the membrane (that is, the num-ber of channels per unit area of membrane) and thesize of the cell. The larger the neuron, the greater willbe its membrane surface area and the lower the inputresistance, since there will be more resting channels toconduct ions.

To compare the membrane properties of neurons ofdiffering sizes, electrophysiologists often use the resis-tance of a unit area of membrane, the spedfic membraneresistance, Rrrv measured in units of fi.cm2. The specificmembrane resistance depends only on the density of theresting ion channels (the number of channels per squarecentimeter) and their conductance.

To obtain the total input resistance of the cell we di-vide the specific membrane resistance by the membranearea of the cell because the greater the area of a cell, thelower its resistance. For the spherical neuron we obtain

Rtn = Rm/ 411'~,

where a is the radius of the neuron. Thus, for a sphericalcell the input resistance is inversely proportional to thesquare of the radius. For a real neuron with extensivedendrites and axons, the input resistance also depends

'42 Part n / Cell and Molecular Biology of the Neuron

on the membrane resistance of its processes as well ason the intracellular cytoplasmic resistance between thecell body and those processes (discussed below).

Membrane Capacitance Prolongs the TimeCourse of Electrical Signals

In Figure 8-1 the magnitude of the steady state changesin the cell's voltage in response to subthreshold currentresembles the behavior of a simple resistor, but the timecourse of the changes does not. A true resistor respondsto a step change in current with a similar step change involtage, but the cell in Figure 8-1 shows a voltage re-sponse that rises and decays more slowly than the stepchange in current. This property of the membrane is dueto its capacitllnce.

To understand how the capacitance slows down thevoltage response we need to recall that the voltageacross a capacitor is proportional to the charge stored onthe capacitor.

v = Q/C,

where Q is the charge in coulombs and C is the capaci-tance in farads. To alter the voltage, charge must eitherbe added or removed from the capacitor:

J1V = J1Q/c.

The change in charge (~Q) is the result of the flow ofcurrent across the capacitor (Ie)' Since current is the flowof charge per unit time (Ie = ~Q/~t), we can calculatethe change in voltage across a capacitor as a function ofcurrent and the time that the current flows (~t):

tJ.V = Ic.tJ.t/C. (8-1)

The magnitude of the change in voltage across a capaci-tor in response to a current pulse depends on the dura-tion of the current, as time is required to deposit and re-move charge on the plates of the capacitor.

Capacitance is directly PrOportional to the area ofthe plates of the capacitor. The larger the area of a ca-pacitor, the more charge it will store for a given poten-tial difference. The value of the capacitance also de-pends on the insulation medium and the distancebetween the two plates of the capacitor. Since all biolog-ical membranes are composed of lipid bilayers withsimilar insulating properties that provide a similar sep-aration between the two plates (4 nm), the specific ca-pacitance per unit area of all biological membranes, Cnvhas the same value, approximately 1 ,...F / cm2 of mem-brane. The total input capacitance of a spherical cell, Cint

is therefore given by the capacitance per unit area multi-plied by the area of the cell:

Cin = Cm(41r~).

Because capacitance increases with the size of the cell,more charge, and therefore current, is required to pro-duce the same change in membrane potential in a largerneuron than in a smaller one.

According to Equation 8-1 the voltage across a ca-pacitor continues to increase with time as long as a cur-rent pulse is applied. But in neurons the voltage levels offafter some time (Figure 8-1) because the membrane of aneuron acts as a resistor (owing to its ion-conductingchannels) and a capacitor (owing to the phospholipid bi-layer) in parallel.

In the equivalent circuit developed in Chapter 7 tomodel current flow in the neuron, we placed the resis-tance and capacitance in parallel, since current crossingthe membrane can flow either through ion channels (theresistive pathway) or across the capacitor (Figure 8-2).The resistive current carried by ions flowing across themembrane through ion channels--for example, Na +

ions moving through Na+ channels from outside to in-side the cell-is called the ionic membrane current. Thecurrent carried by ions that change the net charge storedon the membrane is called the capacitive membrane cur-rent. An outward capacitive current, for example, addspositive charges to the inside of the membrane and re-

Figure 8-2 A simplified electrical equivalent circuit is usedto examine the effects of membrane capacitance (e'n) onthe rate of change of membrane potential in response tocurrent flow. All resting ion channels are lumped into a singleelement (R;n), Batteries representing the electromotive forcesgenerated by ion diffusion are not included because they affectonly the absolute value of membrane potential, not the rate ofchange. This equivalent circuit represents the experimentalsetup shown in Box 7-1 (Figure 7-2CI, in which pairs of elec-trodes are connected to the current generator and the mem-brane potential monitor.

noves an equal number of positive charges from the)utside of the membrane. The total current crossing thenembrane, Irrv is given by the sum of the ionic currentIi) and the capacitive current:

1m = II + Ie- (8-2)

The capacitance of the membrane has the effect of-educing the rate at which the membrane potential:hanges in response to a current pulse. H the membrane1ad only resistive properties, a step pulse of outward:urrent passed across it would change the membranex>tential instantaneously. On the other hand, if thenembrane had only capacitive properties, the mem-)rane potential would change linearly with time in re-lponse to the same step pulse of current. Because thenembrane has both capacitive and resistive propertiesn parallel, the actual change in membrane potential:ombines features of the two pure responses. The initialslope of the relation between V m and time reflects a:>urely capacitive element, whereas the final slope andunplitude reflect a purely resistive element (Figure 8-3).

It is now easy to explain why a step change in cur--ent produces the slowly rising voltage waveform seenn Figure 8-3. Since the resistance and capacitance of thenembrane are in parallel, the voltage across each ele-nent must always be the same and equal to the mem-)rane potential. Assume that the membrane potentialstarts off at 0 m V and that at time t = 0 a depolarizing

:urrent step is applied from a current generator withnagnitude 1m. Initially the voltage across the resistormd capacitor are both equal to 0 m V. Since the ionic:urrent through the resistor is given by Ohm's law (Ii =i/fRin), initially no current will flow through the resistor.since V starts off at 0 m V) and all the current will flowhrough the capacitor (ie, Ie = 1m). As a result of the largenitial capacitive current, the potential across the capaci-or, and hence the membrane potential, will rapidly be-:ome more positive.

As V m increases, the voltage difference across thenembrane begins to drive current across the membrane'e5istance. As the voltage across the membrane becomesnore positive, more current flows through the resistormd less flows across the capacitor, since Ie plus Ii is con-.tant (and equal to 1m), As a result, the membrane po-ential begins to rise more slowly. Eventually, the mem-)rane potential reaches a value where all the membrane:urrent flows through the resistor (Ii = 1m). From Ohm'saw this voltage is given by V m = 1m' Rin' At this point

he capacitative current is zero and, following EquationH, the membrane potential no longer changes. Oncehe step of current is turned off, the total membrane cur--ent 1m equals zero, SO that the positive ionic currentlowing through the resistor must flow back into the cell

Chapter 8 / Local Signaling: Passive Electrical Properties of the Neuron 143

Out

~

In

Figure 8-3 The rate of change in the membrane potential isslowed by the membrane capacitance. The response of themembrane potential (A Vm) to a step current pulse is shown inthe upper plot. The actual shape of the response (red line c)combines the properties of a purely resistive element (dashedline a) and a purely capacitive element (dashed line b). Thelower plot shows the total membrane current (1m) and its ionicWand capacitive (Ie) components (1m = " + 'e) in relation to thecurrent pulse. The time taken to reach 63% of the final voltagedefines the membrane time constant, T. The time constants ofdifferent neurons typically range from 20 to 60 ms.

as an equal and opposite capacitive current, ie, Ii = - Ic.

With no applied current, the charge on the capacitor dis-sipates by flowing in a loop around the circuit throughthe resistive pathway, and the membrane potential re-turns to zero.

The rising phase of the potential change can be de-scribed by the following equation:

AVm(t) = ImRin(1 - e-t/"), (8-3)

where e, which has a value of around 2.72, is the base ofthe system of natural logarithms, and T is the membranetime constant, the product of the input resistance and ca-pacitance of the membrane (RInCIn)' The time constantcan be measured experimentally (Figure 8-3). It is thetime it takes the membrane potential to rise to (1 - 1/ e),about 63% of its steady state value. We shall return tothe time constant when we consider the temporal sum-mation of synaptic inputs in a cell in Chapter 12.

Membrane and Axoplasmic Resistance Affectthe Efficiency of Signal Conduction

So far we have considered the effects of the passiveproperties of neurons on signaling only within the cellbody. Because the neuron's soma can be approximated

144 Part II / Cell and Molecular Biology of the Neuron

Figure 8-4 A neuronal process can be repre-sented by 8n electrical equivalent circuit. Theprocess is divided into unit lengths. Each unitlength of the process is a circuit with its ownmembrane resistance (rm> and capacitance (c",).All the circuits are connected by resistors (rJ.which represent the axial resistance of seg-ments of cytoplasm. and a short circuit, whichrepresents the extracellular fluid.

as a simple sphere, the effect of distance on the propaga-tion of a signal does not matter. However, in electricalsignaling along dendrites, axons, and muscle fibers, asubthreshold voltage signal decreases in amplitudewith distance from its site of initiation. To understandhow this attenuation occurs we will again have need ofan equivalent circuit, one that shows how the geometryof a neuron influences the distribution of current flow.

Synaptic potentials that originate in dendrites areconducted along the dendrite toward the cell body andthe trigger zone. The cytoplasmic core of a dendrite of-fers significant resistance to the longitudinal flow of cur-rent, because it has a relatively small cross-sectionalarea, and ions flowing down the dendrite collide withother molecules. The greater the length of the cytoplas-mic core, the greater the resistance, since the ionsexperience more collisions the further they travel. Con-versely, the larger the diameter of the cytoplasmic core,the lower will be the resistance in a given length, sincethe number of charge carriers at any cross section ofdendrite increases with the diameter of the core.

To represent the incremental increase in resistancealong the length of the dendritic core, the dendrite canbe divided into unit lengths, each of which is a circuitwith its own measurable membrane resistance and ca-pacitance as well as an axial resistance within the cyto-plasmic core. Because of its large volume, the extracellu-lar fluid has only negligible resistance and therefore canbe ignored. The equivalent circuit for this simplifiedmodel is shown in Figure 8-4.

If current is injected into the dendrite at one point,how will the membrane potential change with distancealong the dendrite? For simplicity, consider the variationof membrane potential with distance after a constant-amplitude current pulse has been on for some time (t ~T). Under these conditions the membrane potential willhave reached a steady value, so capacitive current will bezero. When Ie: = 0, all of the membrane current is ionic (Im= II)' The variation of the potential with distance thus de-pends solely on the relative values of the membrane resis-

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lance"m (units of {}.em), and the axial resistance,'. (unitsof Of em), per unit length of dendrite.

The injected current flows out through several par-allel pathways across successive membrane cylindersalong the length of the process (Figure 8-5). Each ofthese current pathways is made up of two resistive com-ponents in series: the total axial resistance, 'XI and themembrane resistance, , D\f of the unit membrane cylin-der. For each outflow pathway the total axial resistanceis the resistance between the site of current injection andthe site of the outflow pathway. Since resistors in seriesare added, 'x = ,.x, where x is the distance along thedendrite from the site of current injection. The mem-brane resistance, , D\f has the same value at each outflowpathway along the cell process.

More current flows across a membrane cylindernear the site of injection than at more distant regions be-cause current always tends to follow the path of least re-sistance, and the total axial resistance, 'XI increases withdistance from the site of injection (Figure 8-5). BecauseV m = Im'D\f the change in membrane potential producedby the current across a membrane cylinder at position x,11 V m(x), becomes smaller with distance down the den-drite away from the current electrode. This decay withdistance is exponential (Figure 8-5) and expressed by

.:1V(x) = .:1Voe-xl).,

where A is the membrane length constant, x is the dis-tance from the site of current injection, and dVo is thechange in membrane potential produced by the currentflow at the site of injection (x = 0). The length constant Xis defined as the distance along the dendrite to the sitewhere d V m has decayed to 1/ t, or 37% of its initialvalue (Fi~ 8-5), and it is determined as follows:

x = V(rm/r.).

The better the insulation of the membrane (that is, thegreater r m) and the better the conducting properties ofthe inner core (the lower r.), the greater the length con-stant of the dendrite. That is, current is able to spread

l

It

farther along the inner conductive core of the dendritebefore leaking across the membrane.

To consider how neuronal geometry affects signal-ing, it will be helpful first to consider how the diameterof a process affects Tm and T. . Both Tm and Ta are mea-sures of resistance that apply to a 1 em segment of an in-dividual neuronal process with a certain radius a. Theaxial resistance of a neuronal process depends on the in-trinsic resistive properties of the cytoplasm, expressedas the specific resistance, p, of a 1 em3 cube of cytoplasm(in units of fi.em), and the cross-sectional area of theprocess, which determines the total volume in a unitlength of the process and hence the number of chargecarriers. Thus, T a is given by

ra = p/Tra2, (8-4)

and r. has the required units of a/em. The diameter ofthe process also affects r m since the total number ofchannels in a unit length of membrane is directly pro-portional to both the channel density (number of chan-nels per unit area) and the membrane area. Since r m isinversely related to the total number of channels in aunit length of membrane and the area in a unit length ofcylinder depends on the circumference, r m is given by

r m = Rm/2'1ra, (8-51

where Rm is the specific resistance of a unit area of mem-brane (units of O.em2) and rm has the units of O-em.

Neuronal processes vary greatly in diameter, fromas much as 1 rom for the giant axon of the squid down to1 ~ for fine dendritic branches in the mammalianbrain. These variations in diameter control the efficiencyof neuronal signaling because the diameter determinesthe length constant. For processes with similar intrinsicproperties (that is with similar values of Rm and p), thelarger the diameter of the process (dendrite or axon), thelonger the length constant, because rm/ra is directly re-lated to the radius (Equations 8-4 and 8-5). Thus, thelength constant is expressed in terms of the intrinsic(size invariant) properties Rm and p as follows:

A = JR;.;.That is, the length constant is proportional to the squareroot of the radius (or diameter) of a process. Thus,thicker axons and dendrites will have longer length con-stants than do narrower processes and hence will trans-mit electrotonic signals for greater distances. Typicalvalues for neuronal length constants range from 0.1 to1.0mm.

The length constant is a measure of the efficiency ofthe passive spread of voltage changes along the neuron,or electrotonic conduction. The efficiency of electrotonic

Chapter 8 / Local Signaling: Passive Electrical Properties of the Neuron 145

A

B

Figure 8.5 The voltage response in a passive neuronalprocess decays with distance due to electronic conduction.Current injected into a neuronal process by a microelectrodefollows the path of least resistance to the return electrode inthe extracellular fluid (A). The thickness of the arrows repre-sents membrane current density at any point along theprocess. Under these conditions the change in Vm decays ex-ponentially with distance from the site of current injection (8).The distance at which .1 Vm has decayed to 37% of its value atthe point of current injection defines the length constant, ~.

conduction has two important effects on neuronal func-tion. First, it influences spatial summation, the process bywhich synaptic potentials generated in different regionsof the neuron are added together at the trigger zone, thedecision-making component of the neuron (see Chapter12).

Second, electrotonic conduction is a factor in thepropagation of the action potential. Once the membraneat any point along an axon has been depolarized be-yond threshold, an action potential is generated in thatregion in response to the opening of voltage-gated Na +

channels (see Chapter 9). This local depolarizationspreads electrotonically down the axon, causing the ad-jacent region of the membrane to reach the threshold forgenerating an action potential (Figure 8-6). Thus the de-polarization spreads along the length of the axon by"local-circuit" current flow resulting from the potentialdifference between active and inactive regions of theaxon membrane. In cells with longer length constantsthe local-circuit current has a greater spread and there-fore the action potential propagates more rapidly.

146 Part n / Cell and Molecular Biology of the Neuron

A+50my

[Vm 0 mY

~mYFigure 8-6 Passive conduction of depolarizationalong the axon contributes to propagation ofthe action potential.A. The waveform of an action potential propagat-

Ijng from right to left. The difference in potentialalong the length of the axon creates a local-circuit,t.current flow that causes the depolarization tospread passively from the active region (2) to theinactive region sh88d of the action potential (1). aswell as to the area behind the action potential (3).However, because there is also an increase in 9K Bin the wake of the action potential (see Chapter 9). +50 mY

Ithe buildup of positive charge along the inner side

of the membrane in area 3 is more than balanced

by the local efflux of K+. allowing this region of vm 0 mYmembrane to repolarize.B. A short time later the voltage waveform and thecurrent distributions have shifted down the axon ~ mYand the process is repeated.

t

Large Axons Are More Easily Excited ThanSmall Axons by Extracellular Current Stimuli

In examination of a neurological patient for diseases ofperipheral nerves the nerve often is stimulated by pass-ing current between a pair of extracellular electrodesplaced over the nerve, and the population of resultingaction potentials (the compound action potentilll) isrecorded farther along the nerve by a second pair ofvoltage-recording electrodes. In this situation the totalnumber of axons that generate action potentials varieswith the amplitude of the current pulse.

To drive a cell to threshold, the current must passthrough the cell membrane. In the vicinity of the positiveelectrode, current flows across the membrane into theaxon. It then flows along the axoplasmic core, eventuallyflowing out through more distant regions of axonal mem-

146

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brane to the second (negative) electrode in the extracellu-lar fluid. For any given axon, most of the stimulating cur-rent bypasses the fiber, moving instead through other ax-ons or through the low-resistance pathway provided bythe extracellular fluid. The axons into which current canenter most easily are the most excitable.

In general, axons with the largest diameter have thelowest threshold for extracellular current. The larger thediameter of the axon, the lower the axial resistance tothe flow of longitudinal current because of the greaternumber of intracellular charge carriers (ions) per unitlength of the axon. Therefore a greater fraction of totalcurrent enters the larger axon, so it is depolarized moreefficiently than a smaller axon. For these reasons, largeraxons are recruited at low values of current; smaUer-diameter axON are recruited only at relatively greatercurrent strengths.

li

A

Figure 8-7 Axial resistance and membrane capacitancelimit the rate of spread of depolarization during the actionpotential.A. The electrical equivalent circuit represents two adjacent seg-ments of the resting membrane of an axon connected by asegment of axoplasm (r.).

Passive Membrane Properties and AxonDiameter Affect the Velocity of ActionPotential Propagation

The passive spread of depolarization during conductionof the action potential is not instantaneous. In fact, theelectrotonic conduction is a rate-limiting factor in thepropagation of the action potential. We can understandthis limitation by considering a simplified equivalentcircuit of two adjacent membrane segments connectedby a segment of axoplasm (Figure 8-7). As describedabove, an action potential generated in one segment ofmembrane supplies depolarizing current to the adjacentmembrane, causing it to depolarize gradually towardthreshold. According to Ohm's law, the larger the axo-plasmic resistance, the smaller the current flow aroundthe loop (1 = VIR) and the longer it takes to change thecharge on the membrane of the adjacent segment.

Recall that since ~ V = ~Q/C, the membrane poten-tial changes slowly if the current is small because ~Qchanges slowly. Similarly, the larger the membranecapacitance, the more charge must be deposited 01\ themembrane to change the potential across the mem-brane, so the current must flow for a lon~~r time to pro-duce a given depolarization. Therefore, the time it takesfor depolarization to spread along the axon is deter-mined by both the axial resistance, r a' and the capaci-tance per unit length of the axon Cm (units F / em). Therate of passive spread varies inversely with the product

Chapter 8/ Local Signaling: Passive Electrical Properties of the Neuron 147

B

B. An action potential is spreading from the membrane seg-ment on the left to the segment on the right. Purple lines indi-cate pathways of current flow.

'.Cm. H this product is reduced, the rate of passivespread increases and the action potential propagatesfaster.

Rapid propagation of the action potential is func-tionally important, and two distinct mechanisms haveevolved to increase it. One adaptive strategy is to in-crease conduction velocity by increasing the diameter ofthe axon core. Because,. decreases in proportion to thesquare of axon diameter, while Cm increases in directproportion to diameter, the net effect of an increase indiameter is a decrease in '.Cm. This adaptation has beencarried to an extreme in the giant axon of the squid,which can reach a diameter of 1 mm. No larger axonshave evolved, presumably because of the opposingneed to keep neuronal size small so that many cells canbe packed into a limited space.

A second mechanism for increasing conduction ve-locity is myelination of the axon, the wrapping of glialcell membranes around an axon (see Chapter 4). Thisprocess is functionally equivalent to increasing the thick-ness of the axonal membrane by as much as 100 times.Because the capacitance of a parallel-plate capacitor suchas the membrane is inversely proportional to the thick-ness of the insulation material, myelination decreases Cmand thus '.Cm. Myelination results in a proportionatelymuch greater decrease in '.Cm than does the same in-crease in the diameter of the axon core. For this reason,conduction in myelinated axons is typically faster thanin nonmye1inated axons of the same diameter.

148 Part n / CeO and Molecular Biology of the Neuron

In a neuron with a myelinated axon the action p0-tential is triggered at the nonmyelinated segment ofmembrane at the axon hillock. The inward current thatflows through this region of membrane is then availableto discharge the capacitance of the myelinated axonahead of it. Even though the thickness of myelin makesthe capacitance of the axon quite small, the amount ofcurrent flowing down the core of the axon from the trig-ger zone is not enough to discharge the capacitancealong the entire length of the myelinated axon.

To prevent the action potential from dying out, themyelin sheath is interrupted every 1-2 rom by barepatches of axon membrane about 2 Vom in length, thenodes of Ranvier (see Chapter 4). Although the area ofmembrane at each node is quite small, the nodal mem-brane is rich in voltage-gated Na + channels and thuscan generate an intense depolarizing inward Na + cur-

rent in response to the passive spread of depolarizationdown the axon. These regularly distributed nodes thusboost the amplitude of the action potential periodically,preventing it from dying out,

The action potential, which spreads quite rapidlyalong the internode because of the low capacitance ofthe myelin sheath, slows down as it crosses the high-capacitance region of each bare node. Consequently, asthe action potential moves down the axon it jumpsquickly from node to node (Figure 8-8A). For this rea-son, the action potential in a myelinated axon is said tomove by saltatory conduction (from the Latin saltare, tojump). Because ionic membrane current flows only atthe nodes in myelinated fibers, saltatory conduction isalso favorable from a metabolic standpoint. Less energymust be expended by the Na + -K+ pump in restoring theNa + and K+ concentration gradients, which tend to run

down as a result of action-potential activity.Various diseases of the nervous system, such as

multiple sclerosis and Guillain-Barre syndrome, causedemyelination (see Box 4-1). Because the lack of myelinslows down the conduction of the action potential, thesediseases can have devastating effects on behavior(Chapter 35). As an action potential goes from a my-elinated region to a bare stretch of axon, it encounters aregion of relatively high Cm and low r m' The inward cur-rent generated at the node just before the demyelinatedsegment may be too small to provide the capacitive cur-rent required to depolarize the demyelinated membraneto threshold. In addition, this local-circuit current doesnot spread as far as it normally would because it is flow-ing into a segment of axon that, because of its low r mthas a short length constant (Figure 8-8B). These two fac- ,-tors can combine to slow, and in some cases actually'block, the conduction of action potentials.

148

A

B

Demyelinltecl region

Figure 8-8 Action potentials in myelinated nerves are re-generated at the nodes of Ranvier.A. In the axon capacitive and ionic membrane current densities(membrane current per unit area of membrane) are muchhigher at the nodes of Ranvier than in the internodal regions.The density of membrane current at any point along the axon isrepresented by the thickness of the arr0W8. Because of thehigher capacitance of the axon membrane at the unmyelinatednodes, the action potential slows down as it approaches eachnode and thus appears to skip rapidly from node to node.B. In regions of the axon that have lost their myelin, the spreadof the action potential is slowed down or blocked. The locak:ir-cuit currents must charge 8 larger membrane capacitance and.because of the low r"" they do not spread well down the axon.

An Overall View

Two competing needs determine the functional designof neurons. First, to maximize the computing power ofthe nervous system, neurons must be small so that largenumbers of them can fit into the brain and spinal cord.Second, to maximize the ability of the animal to respondto changes in its environment, neurons must conductsigJiWs rapidly. These two design objectives are con-strained by the materials from which neurons are made.

Because the nerve cell membrane is very thin and issurrounded by a conducting medium, it has a very highcapacitance, which slows down the conduction of volt-

age signals. In addition, the currents that change thecharge on the membrane capacitance must flow througha relatively poor conductor-a thin column of cyto-plasm. The ion channels that give rise to the restingpotential also degrade the signaling function of the neu-ron. They make the cell leaky and, together with thehigh membrane capacitance, they limit the distance thata signal can travel passively.

As we shall see in the next chapter, neurons usevoltage-gated channels to compensate for these physicalconstraints when generating all-or-none action poten-tials, which are continually regenerated and conductedwithout attenuation. For pathways in which rapid sig-naling is particularly important, the conduction velocityof the action potential is enhanced either by myelinationor by an increase in axon diameter, or by both.

John KoesterSteven A. Siegelbaum

Selected Readings

Hodgkin AL. 1964. Chapter 4. In: The Conduction of the Ner-vous Impulse, pp. 47-55. Springfield, IL: Thomas.

Jack]JB, Noble 0, Tsien RW. 1975. Chapters 1, 5, 7, and 9. In:Electric Current Flow in Excitable Cells, pp. 1-4, ~97,131-224,276-277. Oxford: Clarendon.

Johnston 0, Wu M-S. 1995. Functional properties of den-drites. In: Foundations of Celluwr Neurophysiology, pp.55-120. Cambridge: MIT Press.

Koch C. 1999. Biophysics of Computation, pp. 25-48. New York:Oxford University Press.

149Chapter 8 / Local Signaling: Passive Electrical Properties of the Neuron

Moore }W, Joyner RW, Brill MH, Waxman SO, Najar-Joa M.1978. Simulations of conduction in uniform myelinatedfibers: relative sensitivity to changes in nodal and inter-nodal parameters. Biophys J 21:147-160.

Rall W. 1977. Core conductor theory and cable properties ofneurons. In: ER Kandel (ed). Handbook of Physiology: ACriHcal, Comprehensive Presentation of Physiological Knowl-edge and Concepts, Sect. 1, The Nervous System. Vol. 1, Cellu-lar Biology of Neurons, Part 1, pp. 39-97. Bethesda, MD:American Physiological Society.

References

Hodgkin AL, Rushton W AH. 1946. The electrical constants ofa crustacean nerve fibre. Proc R Soc Lond Ser B.133:444-479.

Huxley AF, Stampfli R. 1949. Evidence for saltatory conduc-tion in peripheral myelinated nerve fibres. J Physiol108:315-339.