BY B. FRANKENHAEUSER AND B. WALTMAN From the Nobel
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J. Physiol. (I959) I48, 677-682
MEMBRANE RESISTANCE AND CONDUCTION VELOCITY OFLARGE MYELINATED NERVE FIBRES FROM
BY B. FRANKENHAEUSER AND B. WALTMANFrom the Nobel Institute for Neurophysiology, Karolinska Institutet,
Stockholm 60, Sweden
(Received 29 June 1959)
During recent experiments on myelinated nerve fibres of the clawed toad(Xenopus laevis) with the voltage clamp technique (Dodge & Frankenhaeuser,1959; Frankenhaeuser, 1959) it was observed that the nodal membraneresistance was quite appreciable when measured in isotonic KCI solution.Since this contradicts the frequently held view that the membrane resistancebecomes negligibly low in KCI solution, it was considered desirable to investi-gate this point by conventional methods, with whole desheathed nerve.The space constant A (Rushton, 1927, 1934) was therefore measured with thenerve in Ringer's solution and in isotonic KCI solution, and the ratio of nodalresistances in the two solutions was calculated from these measurements. Inaddition, because many fibres ofXenopus laevis are exceptionally large (outsidediameter about 30,u), the opportunity was taken to measure the maximalconduction rate of the nerve.
Peroneal nerves from Xenopuwlaevis were used for the experiments. After the connective-tissuesheath of the whole sciatic trunk had been cut open with scissors and carefully removed, theperoneal branch was gently freed and a uniform length pulled through capillary tubes in a par-titioned cell. One of the capillaries limited the external fluid between the current electrodes andother capillaries were used between the recording electrodes. For measurements of the spaceconstant, the capillary at the recording site was 1F5 cm long and could be moved along the nerve,relative to the fixed polarizing site. The distance between the polarizing site and the recording sitewas measured with the ocular micrometer of a microscope. The nerve was kept fully immersedin solution during the experiment and a constant recording resistance was obtained. When solu-tions were changed, the long sliding capillary was moved to expose the nerve in the recording siteto the new solution.A conventional rectangular pulse stimulator and a d.c. amplifier were used. Photographic records
of the extrapolar current spread and action potentials were optically enlarged and measured.The Ringer's solution had the following composition: (mM) NaCl 112-0; KCI 2-5; CaCl2 2-0;
NaHCO3 2-5. 120 mM-KCl was used as isotonic KCI solution.Most of the experiments were carried out at room temperature (200 C).
B. FRANKENHAEUSER AND B. WALTMAN
Conduction rate. The conduction rate in the fast fibres was calculated fromthe time lag between two records of longitudinal current, measured across twoshort (0.7 mm) capillaries situated 15 mm apart. The conduction rate in fournerves was found to be 64, 68, 73 and 66 m/sec respectively at 200 C, and itincreased with increasing temperature of the surrounding Ringer's solution byabout 2m/sec per degree in the range 10-30 C.
The space constant of nerve in Ringer's solution and in isotonic KCl solution.The space constant of the desheathed nerve was determined by plottingextrapolar current spread against extrapolar distance and finding that distanceat which the current had declined to 1/e. The polarizing pulses were anodal andwere 50% of the amplitude of a threshold cathodal pulse of long duration.The measurements were taken at 7-5 msec after the onset of the pulse. Thespace constant A is defined by
where Rm is membrane resistance for unit length of nerve, Ri and Ro areinternal and external longitudinal resistances per unit length of nerve (e.g.Rushton, 1934). Provided that the internal resistance remains constant andthe external resistance is either constant or negligibly small, it follows that theratio between the membrane resistances in the two solutions is
Rm (Ringer) _ [A (Ringer)]2Rm (KCl) L A (KCl)
Results obtained from this relationship are given in Table 1. It was quiteevident that the membrane resistance of the nerve was lower in KCl than whenthe nerve was in Ringer's solution, but none the less the decrease was only bya factor of four, which hardly produces an effective short-circuit.
If a length of passive nerve fibre is treated as a cable of known properties,the attenuation of an action potential at successive nodes may be readilycalculated. Such an approximate calculation, based on the above measure-ments and a ratio of 1: 3 for internodal resistance to nodal resistance (Dodge &Frankenhaeuser, 1959), was made for the special case that one node (N_1)discharges a full action potential of 120 mV, while the neighbouring node (No)is in isotonic KCl solution and is fully inactivated, and the other nodes(N+1 to N+oo) are in Ringer's solution and have normal resting potential (i.e. ifcurrent spread from the depolarized node is prevented by a backing-off e.m.f.).This calculation indicated that the action potential in N-1 would be attenuatedat N+1 to about 20 mV. Since the threshold of a normal node is about 20 mV,it appeared that an impulse might be conducted through a segment having
NODAL RESISTANCE IN KCl
one node in isotonic KC1 solution. An experiment was made to test thisprediction.A desheathed nerve was pulled through a number of capillaries in a
measuring cell depicted in Fig. 1. This arrangement permitted stimulation ofthe nerve at one end and recording of the action potential at the other, whilebetween these sites was situated the narrow (2-8 mm) pool C separated fromthe side pool B by short capillaries (0.1 mm). Pool C contained either Ringer's
TABLE 1. Ratio of membrane resistance in Ringer's solution to that in isotonic KCI solution,from measurements of space constant
Date Solution A A (Ringer) Rm (Ringer)March (mm) A (KCl) Rm (KCI)195919 Ringer's 2-2 1
Isotonic KCI 1.0 2-1 4-4Ringer's 2-0 f
24 Ringer's 2-1Isotonic KCl 1D0 2-0 4-0Ringer's 1.9
29 Ringer's 2-3Isotonic KCI 11 2-1 4-4Ringer's 2-3
Fig. 1. Arrangement for testing effect of isotonic KCI on conduction. Capillary AB 2-5 mm,capillaries BC 0.1 mm, capillary BD 15 mm; length of pool C 2-8 mm, total length of pool B15 mm. Figure not drawn to scale.
solution or isotonic KCI solution, while A and B contained Ringer's solutionand D contained KCI. An e.m.f. of the order of 70 mV could be applied by atripolar electrode arrangement between the pool C (negative) and the neigh-bouring pool B in order to prevent 'demarcation current' of nodes in KCL fromdepolarizing nodes in Ringer's solution. The dimensions of the measuring cellwere chosen in order to fulfil the following requirements: (a) at least one nodein each fibre should be in the narrow pool (internodal length of the large fibres= 2-3 mm), (b) many large fibres should have not more than one node inpool C, (c) the capillaries in the partitions limiting the narrow pool C, beingshort, ensured that only a few nodes would be in a mixed solution, and beingreasonably tight fitting prevented flow of solution between pools, so that the
B. FRANKENHAEUSER AND B. WALTMAN
concentration gradients in the solution were reasonably sharp and welldefined.
In Fig. 2 are typical photographic records from one such experiment. Stimu-lus strength was maximal for the large fibres. In record 1, pool C was filledwith Ringer's solution and a normal action potential was recorded. In record 3,pool C was filled with isotonic KCI solution and conduction was clearlyblocked in most fibres, the little which remained being probably due to thefew fibres which did not have a node in that pool. In record 4, an e.m.f. of78 mV was applied between the KCl-filled pool C (negative) and the adjacentRinger's-filled pool B; the action potential grew to slightly more than one-third
2 ,4 \
Fig. 2. Maximal action potentials recorded in situation of Fig. 1. In records 1 and 2, Ringer'ssolution in pool C; in 3 and 4, isotonic KCl in pool C. In records 1 and 3, pools B and Cequipotential; in 2 and 4, pool C - 78 mV relative to pool B.
of its size in record 1, indicating that an appreciable number of fibres wereconducting through isotonic KCI solution. The remainder, which were not con-ducting, had not been excited at nodes N+1. As our calculation indicated, anaction potential would be attenuated by a single node in KCI to very close tothreshold; attenuation by two or more nodes in KlC would certainly be toomuch to permit excitation at an adjacent normal node. Hence, all the fibreswith more than one node, and some with only one node, in KCI would beblocked. In record 2 the same backing-off e.m.f. was applied when pool Ccontained Ringer's solution; conduction was effectively blocked, because inthis case nodes No were inactivated by cathodal polarization while the thresholdof nodes N-1 and N+1 was raised by anodal polarization.The approximate calculation, mentioned above, gave a safety factor very
close to one for the experimental situation in Fig. 2, record 4. The experimentwas therefore in full agreement with the findings from measurements of thespacewconstant, but7in disagreement with the commonly held view that themembrane is effectively short-circuited when the fibre is in isotonic KC1solution.
NODAL RESISTANCE IN KCl
The conduction rate in myelinated fibres is linearly proportional to the fibrediameter (Erlanger & Gasser, 1937; Rushton, 1951). The measurements ofTasaki, Ishii & Ito (1943) indicate that a 15,u bull-frog nerve conducts impulseswith a rate of about 32 m/sec at 240 C. Extrapolation of the results for bull-frog nerve would give a value of about 63 m/sec for a hypothetical 30, fibre.The present figures for whole desheathed nerve gave a maximum conductionrate at 200 C of 68 m/sec, and at 240 C of 76 m/sec. Possibly then 30, Xenopusfibres may conduct slightly more rapidly than corresponding (hypothetical)bull-frog fibres, but the difference is too small to be worth emphasizing.The finding that the steady-state resistance of the membrane was not very
low when the node was in isotonic KCI solution may be related to some otherrecent observations. When a node was polarized to about zero membranepotential in voltage clamp experiments, the membrane resistance (i.e. Rm =WV/AI) was clearly much lower than that found here; but when the membrane
was kept for a long time (i.e. several seconds) at a low potential, then themembrane currents decreased and Rm increased (unpublished voltage clampresults). This increase in membrane resistance cannot be accounted for byaccumulation of potassium in a limited space outside the membrane (cf.Frankenhaeuser & Hodgkin, 1956), although such an effect might occur infrog nerve in very low external potassium concentrations (Meves, 1959).These findings indicate that the potassium permeability change is inactivatedjust as the sodium transport mechanism is inactivated, but at a very muchlower rate, actually so slowly that this inactivation can hardly play any partin the permeability changes during an action potential.
Mueller (1958) has recently described exceedingly prolonged 'actionpotentials', which occur when the membrane in isotonic KCI solution is pola-rized with external currents. Under these conditions the potassium equilibriumpotential (EK) would be at about zero membrane potential and the potassiumpermeability-membrane potential curve is expected to have its generalcharacteristics unchanged, although the curve would be shifted along thevoltage axis owing to the change in external calcium concentration (Franken-haeuser & Hodgkin, 1957). This would give, on the basis of the formulation ofHodgkin & Huxley (1952), a region of negative membrane resistance. This hasclearly been demonstrated by Moore (1959) on the squid fibre, and has alsobeen found in voltage clamp experiments on frog fibre (Frankenhaeuser,unpublished observation). The rising phase of these 'action potentials' istherefore, as Moore points out, included in the equations of Hodgkin & Huxley.Inactivation of the potassium carrying mechanism can more readily explainthe falling phase of these 'action potentials' than can concentration changesoutside the membrane, as was tentatively suggested by Moore (1959).
682 B. FRANKENHAEUSER AND B. WALTMANThese phenomena will be discussed in further detail when the voltage clamp
potassium currents have been analysed quantitatively.
1. Experiments were made on desheathed peroneal nerves of Xenopuslaevis.
2. The maximum conduction velocity averaged 68 m/sec at 200 C, with atemperature dependence of 2 m/sec per degree for the range 10-30 C.
3. The space constant of the whole desheathed nerve was found to be about2-0 mm when the nerve was in Ringer's solution, and about 1 0 mm in isotonicKCl solution. This indicated that the nodal membrane resistance in isotonicKCI solution was about one-fourth of that in Ringer's solution.
4. Since the nodal resistance was appreciable in isotonic KCI solution, itwas predicted that a fibre might conduct an impulse through a short segmentof nerve in KCI, provided that spread of demarcation current is prevented.This prediction was experimentally verified.
5. The significance of these findings is discussed in relation to other recentobservations on potassium permeability in nerve membrane.
This investigation was supported by the Rockefeller Foundation and Stiftelsen Therese ochJohan Anderssons Minne.
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