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3 Ginsburg, H., and L. Sachs, Virology, 13, 380 (1961); Ginsburg, H., and L. Sachs, J. Natl.Cancer Inst., 27, 1153 (1961); ibid., 28, 1391 (1962).

4Osato, T., E. A. Mirand, and J. T. Grace, Jr., Nature, 201, 52 (1964).6 Prigozhina, E. L., and A. A. Stravovskaya, Acta Virol., 8, 277 (1964).6 Sinkovics, J. G., and C. D. Howe, J. Infect. Diseases, 114, 359 (1964).7Peries, J., J. P. Levy, M. Boiron, and J. Bernard, Nature, 203, 672 (1964).8Rowe, W. P., Science, 141, 40 (1963).9 Sarma, P. S., H. C. Turner, and R. J. Huebner, Virology, 23, 313 (1964).10 Rauscher, F. J., J. Natl. Cancer Inst., 29, 515 (1962).11 Friend, C., J. Exptl. Med., 105, 307 (1957).12 Moloney, J. B., J. Natl. Cancer Inst., 24, 933 (1960).13 Pope, J. H., Austral. J. Exptl. Biol., 39, 521 (1961); ibid., 40, 263 (1962).14 Gross, L., Proc. Soc. Exptl. Biol. Med., 76, 27 (1951).15 Huebner, R. J., W. P. Rowe, H. C. Turner, and W. T. Lane, these PROCEEDINGS, 50, 379

(1963).16 Ward, T. WV., personal communication.17 Pope, J. H., Austral. J. Exptl. Biol., 41, 349 (1963).18 Kilham, L., and L. J. Olivier, Virology, 7, 428 (1959).19 Moore, A. E., Acta, Unio Intern. Contra Cancrum, 19, 273 (1963).

THEORY OF THE FLOW OF ACTION CURRENTS IN ISOLATEDMYELINATED NERVE FIBERS, I*

BY R. LORENTE DE NO AND V. HONRUBIAtTHE ROCKEFELLER INSTITUTE

Communicated March 24, 1965

The systematic presentation of the already outlined theory of the isolated nervefiber' is begun in this communication.Technique.-To the details already given' the following should be added.The dc amplifier (Bioelectric Instruments, Inc.) that has been used includes a device to com-

pensate for the input capacity. Under the conditions of the experiments, however, the inputcapacity could never be fully compensated, and therefore the amplifier always acted as a shunt forthe action currents. From the results of placing various ohmic shunts across the amplifier it maybe estimated that for the action currents the effective input resistance of the amplifier never washigher than 20-30 megohm, and that it often must have been considerably smaller. The presenceof the amplifier, therefore, always modified the mode of propagation of the nerve impulse. Afterthis role of the amplifier had been understood, it became apparent that the most powerful methodof analysis consists precisely of modifying the mode of propagation of the impulse by means ofvarious sets of shunts placed between the Ringer pools. Several of the situations that have beenencountered will be discussed below in reference to the diagrams in Figure 3.Diagrams I to V (Fig. 1) indicate the five manners in which the amplifier has been connected to

the preparation to record the action currents of impulses which are propagating themselves fromright to left. Since in the Ringer pools the flows of action currents do not establish measurablepotential differences, the amplifier can and does measure only the potential differences created bythe flow of action currents in the external longitudinal conductors of those segments of the isolatedfiber which are present in the vaseline gaps. Ordinarily, the external longitudinal resistances werepractically equal in the two gaps. Thus, except in those rare instances in which a short brokensegment of another fiber was present in one of the gaps, the external longitudinal resistances in thetwo gaps may be taken as having had a uniform value r, per unit length.The symbols given in Figure 1, I and IV, have the following meaning. The isolated fiber itself

is taken as the x-axis: xI to X4 are the end points of the two gaps, and i1(x,t) and i2(x,t) are the

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I Am Cal. II

i2(0~)X3 X

iI(xXt)X G.2C.P

G. 1Pi

-Ve(x41t)X V0 _'/e___,t)l

IV VV(c)[We(

550, 270,FL 550MFIG. 1.-Diagrams indicating the five manners in which the amplifier, Amp., has been con-

nected to the isolated fiber. In all instances a calibrating unit, Cal. (Bioelectric Instruments),is placed between ground and the preparation as is indicated in diagram I. With the amplifierin position IV, the two lateral pools are connected by a zero-resistance shunt. With the amplifierin position V, two equal resistances 1 are used (see also legend of Fig. 1 in ref. 1).

external longitudinal currents flowing in the two gaps. The proximal and the distal pools are atthe same external potentials (- V,) as the corresponding end points of the gaps, - V,(x1,t) and- Ve(x4,t), and the central pool is at a potential - V,(c) = - Ve(x2,t) = - Ve(xs,t). And, since atthe center of the symmetrical shunt (Fig. 1, IV and V) connecting the two lateral pools the poten-tial is - Vo = -1/2 [Ve(xi,t) + V6(x4,t)], the quantities measured by the amplifier in positions I, II,III, and IV or V are given, respectively, by the following equations, in which the first term hasbeen provided with an awkward minus sign because in electrophysiology it is customary to plotthe negative of the measured quantities:

-[Ve(Xit) - Ve(X2,t)] = Jfx2eri(xt)dx (1)

- [Ve(X3,t) - Ve(X4,t)] = jX4 rei2(X,t)dX (2)

-[Ve(Xjt) - Ve(X4,t)] = fx'rei,(xt)dx + fX rei2(x,t)dx (3)

1(cx' x-Vo- [-Ve(C)] = 2 -Jei,(Xt)dx-J rei2(xt)dx. (4)

22X

In work with normal nerve fibers, equations (1) to (4) can be brought into much simpler forms.Since the width of the central pool, or rather electrode, and the lengths of the recording gaps canbe made very small in relation to the wavelength of the action potential, those dimensions maybe regarded as being infinitesimal and consequently, the integral signs can be removed fromequations (1) to (4). In their differential form, equations (1) to (4) have simple interpretations.In positions I or II the amplifier measures a quantity proportional to the longitudinal actioncurrent in the corresponding gap; the same quantity is measured, although less accurately, bythe amplifier in position III. In positions IV or V, according to the differential form of equation(4), the amplifier measures a quantity which is proportional to the density of the membrane actioncurrent at the point of the fiber which is in contact with or is nearest to the central electrode.Making use of this circumstance, Cole and Curtis2 inaugurated a valuable method for the measure-ment of the membrane action current of the giant fiber of the squid, which we have used extensivelyin the analysis of the membrane action current of single, undissected nerve fibers.The main ar gument in support of the nodal hypothesis, according to which the action potential

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is produced solely by the nodes, was obtained by the use of equations (1), (2), and (4) in their dif-ferential forms (cf. ref. 3, p. 49). However, during the research that is being reported here, it hasappeared that in work with isolated fibers the use of the differential forms of equations (1) to (4) isabsolutely forbidden by two facts. In the first place, owing to the small electrical resistance thatthe myelin has in isolated fibers,1' 4a the longitudinal electrotonic decrement of the action currentsis very rapid, and therefore, when forward propagation of the impulse occurs, the wavelength of theaction potential is so short that an important part of it may be included within one of the recordinggaps. On the other hand, short or long jumps of the impulse (Fig. 3 in ref. 1; see also below) result,in every experiment, in that for shorter or longer periods of time longitudinal currents are flowingin opposite directions within one or even within both gaps and consequently the longitudinal cur-rents i1(x,t) and i2(x,t) have different values and even different signs at different points of therecording gaps.A Reproducible Experiment.-In records 1 to 4 (Fig. 2), the first part of the spike

displays two upward peaks separated by a sharp downward peak. Such poliphasicspikes are always recorded across the first vaseline gap when node N, has beenplaced anywhere between the centers of the two vaseline gaps, even though themagnitude of the early downward peak may vary between wide limits. The genesesof the three early peaks will be explained below. Also noteworthy are the large,

FIG. 2.-Action currents resulting from the propagation of an impulse in the isolated segment ofthe:nerve fiber. Node N, was located slightly to the right of, but practically at the center of, thesecond vaseline gap. All records were taken at two sweep speeds, which were in the ratio 1 to 2.All calibrating signals are 0.5 msec long. Their heights in my are indicated on the records. Thecalibrating signal in 11 also applies to 13 and 16. The Roman numerals on the upper left cornersof the records indicate the positions of the amplifier (see Fig. 1, IV). Underneath are given, inmegohm, the resistances of the shunts placed across the frtC)or the second gap (s) or theamplifier (a). For example, 1 and 2 were obtained with theamlfe in position' I in the absenceof any other -shunt; 7 and 8 were obtained with the amplifier inposition II in the presence of azero shunt across the first, and of a 1O-megohm, shunt across the second gap, and 11 and 12 wereobtained with the amplifier in position IV in the presence of a 1-megohm shunt across the amplifier.Record 13 was obtained approximately 30 sec after the introduction of 20 mM xylocaine in- thecentral pool.

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terminal downward phases in records 1 to 4. Downward phases of large magnitudealways have the same explanation,' the impulse has executed a jump over a segmentof internode, part of which thereafter fails to become active, and by retaining itsresting emf, remains able to supply a large flow of action current into the active zoneahead of it.

Records 5 to 8 (Fig. 2) present spikes resembling those which in the literaturewere called "binodal" because they were supposed to have been produced by succes-sive activation of two nodes. In point of fact, as will appear in detail in later com-munications, the impulse executed a jump from a zone of internode, f, into anotherzone of internode, g (Fig. 3, V), and thereafter zone f propagated itself decrementallyforward.The most prominent feature of records 9 to 12 (Fig. 2) is that they include a large

downward phase. The belief that with the amplifier in position IV a large down-ward phase can be recorded only when a node is present in the central pool wasregarded as the crucial and definitive proof of the nodal hypothesis.3 5 As a matterof fact, however, no experiment has ever been reported in the literature in which,the amplifier being in position IV, a node had been placed in one of the recordinggaps. In the numerous experiments that we have done, large downward phasessuch as those which appear in Figure 2, 9 to 12, have always been recorded whennode N, had been placed in the central pool as well as when node N, had been placedat the center of either the first or the second gap.

Anticipating the discussion to be made in a future communication, the followingmay be said here. The large downward phases in records 9 to 12 were producedby a jump of the impulse from the proximal pool into. the Pd segment of Int. 1,which was located in the central pool. Activity of this segment of internodecaused the appearance of large flows of longitudinal currents in the two gaps, fromright to left in the first and from left to right in the second, and consequently, as ispredicted by equation (4), a large downward phase appeared in the records. Directproof that the large downward phase was referable to activity of the segment ofinternode present in the central pool was readily obtained. Introduction of ananesthetic (20 mM xylocaine) into the central pool rapidly removed the largedownward phase, leaving only two successive upward peaks (Fig. 2, 13 to 16).

Decremental Conduction.-In normal nerve fibers conduction of impulses usuallytakes place without decrement, even though decremental conduction can readilybe created.8 In work with isolated fibers, instances of decremental conduction areobserved in every experiment.A necessary condition for the appearance of decremental conduction is the

absence of an all-or-nothing relationship between the nerve impulse and the stim-ulus, an outward flow of membrane current, which initiates it. This condition isalways fulfilled in isolated fibers, since up to a certain maximal value the magnitudeof the impulse increases with the magnitude of the stimulus. The other necessarycondition is that the magnitude of the impulse at a given point of the fiber be in-sufficient to initiate an impulse of the same magnitude at the following point.

In isolated fibers conduction with decrement always takes place when the im-pulse is traveling from points of low into points of high threshold (Fig. 3, in ref. 1).For example, in a P, segment the nerve impulse may have maximal magnitude,but during the following forward advance the progressive increase in the stimulation

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942 PHYSIOLOGY: LORENTE DE N6 AND HONRUBIA PROC. N. A. 8.

t Amp.

Ii

C I s ' 4 ' A' =0-______j L.___J L_________.

1~~~~~~~. -~---. r ____

II~~ ~~~' l , X

. -, cIJI~~~~~~~~~~~I__________JL__-__ L ._____

t t~~~~~Air I ' 1 ~~II ' t I-1I;

IV

-------~ - ----J--a

Int. 2 i Int.

g55O! 270pIc 55 'deD.F? G.2 C. G._PP

FIG. 3.-Diagrams explaining the modifications of the flow of action currents which result fromthe presence of the amplifier and/or other shunts across the recording gaps. The flow of actioncurrents indicated in diagram IV also applies to the situation which arises when the amplifier isplaced across the second, and a shunt is placed across the first gap. In diagram V, the curvedarrows indicate jumps of the impulse (see also legend of Fig. 3 in ref. 1).

threshold results in a progressive decrease of the magnitude of the impulse. Sucha situation already appears in the fibers of desheathed nerve,4b but while in thefibers of deshcathed nerve the impulse usually reaches the center of the internode,in isolated fibers often the magnitude of the impulse decreases so far that activationof points of the central part of the internode becomes impossible. In such casespropagation may cease before the center of the internode has been reached by the

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impulse, or further propagation may take place by means of a jump of the impulseover the nonresponding central part of the internode (arrow 3 in Fig. 3 of ref. 1).

For the reason that in isolated fibers the longitudinal decrement of the electro-tonic spread of action currents is very rapid, when the impulse jumps from a P,into a Pd segment, the newly created active zone must be located in the proximalpart of the Pd segment, and in it the impulse (i.e., the action or alteration emf, cf.ref. 4b) must have a small magnitude; but since ahead of the active zone points oflow threshold are located (Fig. 3 in ref. 1), the impulse propagates itself forwardwith increment and soon it regains a large magnitude. Decremental conductionoccurs again when the impulse advances forward into the high threshold Jd segmentand a block of propagation may be established.

Effects of External Shunts upon the Mode of Propagation of the Nerve Impulse.-Diagrams I to III of Figure 3 will serve to explain the geneses of the two upwardpeaks, separated by a sharp downward peak, which appear in records 1 to 4 (Fig. 2).At the instant considered in diagram I (Fig. 3), an active zone a has appeared

in the proximal part of the P, segment of Int. 1. In the absence of the amplifieracross the first vaseline gap, the newly created active zone would have rapidlyinvaded the entire Pp segment, but in the presence of the amplifier a different situa-tion arises.Diagram I shows that the amplifier acting as a shunt for the action currents

enables the active zone a to establish an outward flow of membrane current in thesegment of fiber located within and near to the central pool. This outward flowhas a dual effect. In the first place it constitutes a stimulus for the initiation of anaction emf within or near to the central pool. On the other hand, since the actioncurrent flowing through the amplifier is delivered to the active zone a, the electro-tonic spread of action currents ahead of this zone is reduced, and therefore forwardpropagation of this zone, instead of taking place with increment, takes place withdecrement, which at times may be strong enough to cause a propagation block (seebelow). Ordinarily, however, the forward advance of zone a is only reduced.This fact is indicated by the short length of active zone b in Figure 3, II. As a rule,at the same time that zone b is established, an active zone c appears at or near theproximal margin of the central pool, i.e., in the proximal part of the Pd segment ofInt. 1 (Fig. 3, II). In other words, by virtue of the summated effects of the flowof action current mediated by the amplifier and of the purely electrotonic spreadin the first gap ahead of zone a, the impulse executes an early jump from a to c.As long as only zone a existed, the amplifier had to record an upward deflection,although one of reduced magnitude, because in the first gap part of the longitudinalcurrent was flowing from right to left (Fig. 3, I), but as soon as active zone c ap-peared, the amplifier had to begin to record a downward deflection, because an impor-tant flow of longitudinal current from right to left was established in the first gap(Fig. 3, II).The creation of active zone c had another important effect. Since acting through

the amplifier zone c was drawing outward membrane current from the segment offiber ahead of zone b (Fig. 3, II), a relatively large, active zone d appeared at themargin of the proximal pool at the same time that widening of zone c resulted inthe creation of zone c' (Fig. 3, III). The appearance of zone d, by causing an in-

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944 PHYSIOLOGY: LORENTE DE N6 AND HONRUBIA PROC. N. A. S.

crease in the flow of longitudinal current from left to right in the first gap, had toreveal itself in the form of a second upward peak in the spike.The sequence of events just described readily explains the presence of two upward

peaks separated by a sharp downward peak in records 1 to 4 of Figure 2. More-over, proof can readily be obtained that the early jump of the impulse from a to c(Fig. 3, I and II) was mediated by the amplifier. In the first place, if the amplifieris placed in position III (Fig. 1), no sign of the early downward peak appears.On the other hand, with the amplifier across the first gap the early jump of theimpulse can be prevented by placing an additional zero resistance shunt across thesecond gap. As is shown in diagram IV, owing to the presence of this shunt, thesegment of fiber within and near the distal pool becomes able to supply actioncurrent to active zone a and, since thereby the flow of outward membrane currentin the segment of fiber within and near the central pool is reduced, the impulsefails to execute the early jump from a to c.7 To be sure, the flow of action currentsthrough the shunt and through the amplifier tend to oppose the forward advanceof zone a, but, unless a propagation block is established (see below), zone a ad-vances, ultimately to approach the margin of the proximal pool (Fig. 3, V, e);therefore, the amplifier records a high and single-peaked upward phase, which isreplaced by a large downward phase when the impulse jumps from e to f. There-after, the impulse executes the jump from f to g. Further analysis of those situa-tions which were already outlined in reference 1 will be made in later communica-tions.

Distribution of Stimnulation Threshold in the Internodes.-With slight modificationsto be introduced in a following communication, the diagrams in Figure 3 also explainthe jumps that the impulse executes when node N1 is in other positions. There are,however, phenomena which are quite different depending upon the position ofnode N1, because this position determines the location of the zones of internodehaving low and high threshold (Fig. 3 in ref. 1).When node N1 is located anywhere within the central pool, the following results

are obtained when the amplifier, without shunt across it, is placed across the secondgap, and shunts of progressively decreasing resistance are placed across the firstgap (after a slight modification, diagram IV in Fig. 3 also applies to this situation).If the resistance of the shunt is high, the recorded spikes are similar to those inFigure 2, 5 and 6, in which the rising phase has only a slight discontinuity, butwhen the resistance of the shunt is decreased, the rising phase of the spike becomesfractionated into two distinct parts, much as it happened in the case of records7 and 8 of Figure 2 (in this case the fractionation was effected by placing a 10-megohm shunt across the second gap). If the resistance of the shunt across thefirst gap is further reduced, the second part of the upward deflection appears aftera greater delay, and ultimately, when a certain low resistance is reached, propagationof the impulse is prevented. The second part of the rising phase fails to appearand there remains a small monophasic spike, referable solely to electrotonic spreadof action currents.With node N1 in the central pool, a zero-resistance shunt placed across the first

gap has always produced a propagation block, while, except in one,8 in the numerousexperiments in which the node N1 was located at or near the center of one of thevaseline gaps, a zero-resistance shunt across the first gap has never prevented prop-

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agation of the impulse. For example, in the case of Figure 2, 5 and 6, the zero-resistance shunt across the first gap caused only a slight delay in the start of thesecond part of the rising phase of the spike.The mechanism of establishment of the block is readily understandable. When

the resistance of the shunt across the first gap is decreased, the flow of outwardmembrane current mediated by the shunt is increased, but that which results frompurely electrotonic spread in the first vaseline gap is reduced. If the points ofinternodes having low threshold are present in the central pool, the flow throughthe zero-resistance shunt is by itself almost or entirely sufficient to mediate prop-agation; but if only high-threshold points are present in the central pool, the reduc-tion of the electrotonic flow prevents propagation of the impulse.

Thus, from the experimental results mentioned above, it follows that the jux-tanodal segments of the internodes have a high stimulation threshold and that thepoints of lowest threshold are located in the paranodal segments at some 300-400 ,ufrom the node (Fig. 3, ref. 1). That the stimulation threshold of the central partof the internodes is higher than that of the paranodal segments follows from thisfact. If nodes N1 and N2 are placed in the lateral Ringer pools, relatively high-resistance shunts across the first gap are often sufficient to reduce or even blockforward propagation of the impulse into the central part of Int. 2.The very fact that with node N1 located anywhere within the 270-Es-wide central

pool a zero-resistance shunt across the first gap always blocks propagation of theimpulse is, by itself, conclusive evidence that in the isolated fiber the impulse doesnot advance by jumps from node to node, because, if such were the case, a zero-resistance shunt placed across the first gap would create optimal conditions for theimpulse to jump into node N1. In this connection it should be noted that if thecentral pool is 700 u wide or wider, a zero-resistance shunt across the first gap cannever prevent propagation because low-threshold paranodal segments are alwayspresent in the central pool.The discussion of the theory of the isolated fiber will be continued in following

communications.* This work has been supported in part by a grant (NB 02650) from the USPHS.t Present address: Department of Otolaryngology, Vanderbilt University, Nashville, Ten-

nessee.1 Lorente de N6, R, and V. Honrubia, these PROCEEDINGS, 53, 757 (1965).2 Cole, K. S., and H. J. Curtis, J. Gen. Physiol., 24, 551 (1941).3Hodgkin, A. L., The Conduction of the Nervous Impulse (Springfield, Illinois: Charles C

Thomas, 1964).4 (a) Lorente de N6, R., and V. Honrubia, these PROCEEDINGS, 52, 1142 (1964); (b) ibid., p.

1318.5 Tasaki, I., in Handbook of Physiology (Washington, D.C.: American Physiological Society,

1959), vol. 1, p. 75.6 Lorente de N6, R., and G. A. Condouris, these PROCEEDINGS, 45, 592 (1959).7 The same explanation applies to the fact that when the ,amplifieriwas placed in' position IV,

the initial upward phase was not fractionated into two parts (Fig. 2, 9-12).8 The results of this experiment will be discussed in a later communication.

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