Published July 1, 1962
Interpretation of the Repetitive
Firing of Nerve Cells
M. G. F. F U O R T E S and F R A N C O I S E M A N T E G A Z Z I N I
From the Ophthalmology Branch, National Institute of Neurological Diseases and Blindness,
National Institutes of Health, Bethesda, Maryland, and the Istituto Neurologico, Milan,
Italy
D u b o i s - R e y m o n d (1848) i n t r o d u c e d the view t h a t m o t o r nerves respond
(evoking contraction of the a t t a c h e d muscle) to change of current, b u t n o t
to presence of constant current. This notion has been generaUy accepted a n d
r a p i d a c c o m m o d a t i o n to constant stimuli has often been considered to be a
typical p r o p e r t y of all nervous structures. However, such a generalization
does n o t a p p e a r to be correct, since it is n o w clear t h a t several structures,
including m y e l i n a t e d peripheral nerves, m a y discharge repetitive impulses
in response to a constant depolarizing stimulus.
Repetitive Firing of Sensory Cells I n sensory ceils, it has long been k n o w n
t h a t sustained n a t u r a l stimuli usually evoke sustained repetitive firing (Adrian,
1928). K a t z (1950) d e m o n s t r a t e d t h a t in the stretch receptor terminals of
~I63
The Journal of General Physiology
Downloaded from on June 16, 2017
ABSTRACT Eccentric cells of Limulus respond with repetitive firing to sustained depolarizing currents. Following stimulation with a step of current,
latency is shorter than first interval and later intervals increase progressively.
A shock of intensity twice threshold can evoke firing 25 msec. after an impulse.
But in the same cell, a current step twice rheobase evokes a second impulse more
than 50 msec. after the first, and current intensity must be raised to over five
times rheobase to obtain a first interval of about 25 msec. Repetitive faring was
evoked by means of trains of shocks. With stimuli of moderate intensity, firing
was evoked by only some of the shocks and intervals between successive impulses
increased with time. This is ascribed to accumulation of refractoriness with
successive impulses. Higher frequencies of firing are obtained with shocks of
intensity n X threshold than with constant currents of intensity n X rheobase.
It is concluded that prolonged currents depress the processes leading to excitation and that (in the cells studied) repetitive firing is controlled both by the
after-effects of firing (refractoriness) and by the depressant effects of sustained
stimuli (accommodation). Development of subthreshold "graded activity" is
an important process leading to excitation of eccentric cells, but is not the principal factor determining frequency of firing in response to constant currents.
Published July 1, 1962
~64
THE
JOURNAL
OF
GENERAL
PHYSIOLOGY
• VOLUME
45
"
I96~
Sustained Firing in Peripheral Nerves Several authors (Katz, 1936;
Skoglund, 1949; Granit and Skoglund, 1943) have described responses
obtained in vertebrate medullated nerves following stimulation with constant current, but more detailed studies have been performed on non-medullated nerves of crabs (Fessard, 1936; Arvanitaki, 1938; Hodgkin, 1948;
Wright and Adelman, 1954; Adelman, Pautler, and Epstein, 1960). In
disagreement with the requirement that latency be shorter than intervals these
authors found that in Carcinus nerves stimulated by steps of depolarizing
current, the latency for the first impulse is approximately equal to the interval
between the first and second impulses. Hodgkin (1948) also measured the
course of recovery from firing of one impulse and pointed out that frequency
of firing is m u c h slower than refractoriness would justify. He deduced from
these results that rhythmical firing of crab's nerves is primarily controlled by
the time required to displace membrane potential to threshold value.
It should be noted that in these structures, threshold voltage displacement is not
reached as an IR drop evoked by the stimulating current across the membrane resistance so that frequency of firing is not controlled by the time constant of the membrane
(as implied by Tasaki, 1959, p. 117, in a recent review). Hodgkin's records show that
Downloaded from on June 16, 2017
frogs, tension elicits depolarization of the nerve membrane and considered
this depolarization as the cause of the repetitive firing. This conclusion was
strengthened by Edwards' (1955) study of the effects of currents on the discharges produced by tension. Similar findings were obtained later on visual
sensory cells, (Hartline, Wagner, and MacNichol, 1952; MacNichol, 1956;
Fuortes 1958, 1959 a) where it could also be shown that depolarization evoked
by electrical currents elicited repetitive firing similar to that induced by the
natural stimuli (Hartline, Coulter, and Wagner, 1959; MacNichol, 1956;
Fuortes, 1958, 1959 b).
To interpret the mechanisms leading to repetitive firing of sensory cells,
Adrian (1928, p. 62 and Fig. 10) suggested that these structures possess
negligible accommodation and that frequency of impulse discharge elicited
by a constant stimulus is controlled by the course of refractoriness. According
to this view, a prolonged stimulus will produce an impulse at the onset and
a second impulse will be fired as soon as the cell has recovered sufficiently
from the refractoriness left over from the first impulse. The process is then
repeated and since the course of recovery is supposed to be the same after
each impulse, all intervals in a train evoked by a constant stimulus will be
equal (Fig. 1 A). With stronger stimuli, refractoriness can be overcome earlier
and frequency of firing will be higher.
This interpretation requires that (with a stimulus in the form of a step
function) latency for the discharge of the first impulse be shorter than the
intervals between the following impulses.
Published July 1, 1962
FUORTES AND MAz'~r~oAzzmi RepetitiveFiring of Nerve Cells
II6 5
after the current has displaced m e m b r a n e potential to an almost final value, a "graded
response" (recognized by a change of curvature in the potential-time record) occurs
which brings m e m b r a n e potential to threshold. T h e graded response (called also
"local response" or "subthreshold activity") develops to threshold level within a time
controlled by the intensity of the stimulating current (Fig. 1 C).
H o d g k i n ' s results a n d i n t e r p r e t a t i o n a r e r e p r e s e n t e d in t h e d i a g r a m of
Fig. 1 B a n d C, w h e r e it is seen t h a t t h e course of refractoriness is faster t h a n
d e v e l o p m e n t of d e p o l a r i z a t i o n , so t h a t it c a n n o t interfere w i t h t h e response
until f r e q u e n c y of firing is high. H o d g k i n ' s conclusions b e a r s o m e similarity
\
\
\
/I/"
L
Vth
Vgr
/
¢
/
v,h
............................_./__
FIGURE 1. Mechanisms proposed to explain repetitive firing. A, first impulse is discharged when the membrane is depolarized to level V,~. The stimulus can depolarize the
resting membrane to a level higher than Vth, but during refractoriness the even higher
level (indicated by the dotted line) is needed. Alternatively it can be assumed that,
during the refractory state, the stimulus cannot evoke depolarization to Vth level because
the membrane is hypopolarized or has low resistance. B, the stimulus depolarizes the
membrane to a level (indicated by the thin dashed fine) lower than Vjh, but higher
than Vat. At Vg~ a graded response develops and brings the depolarization up to Vth.
Recovery (indicated by the dotted line) is rapid and does not appreciably change the
course of the graded response. C, detail of B to show development of graded responses
for stimuli of different intensities. Dotted lines indicate the potential change which
steps of current of four different intensities would elicit if the membrane remained passive. The divergence between dotted and solid lines is due to development of graded responses. All-or-none firing initiates at Vth.
Downloaded from on June 16, 2017
vth
Published July 1, 1962
~66
THE
JOURNAL
OF
GENERAL
PHYSIOLOGY
• VOLUME
45
"
1962
to previous conclusions by Eccles and Sherrington (1931), who stated that
slow development of "central excitatory state" rather than refractoriness
controls frequency of the reflex firing of spinal cord motoneurons.
Repetitive Firing of Spinal Motoneurons It has been thought for some time
that spinal motoneurons accommodate rapidly to depolarizing influences, so
that they can be excited only by quickly changing stimuli. (See, however,
contrary evidence in Frank and Fuortes, 1960.) In order to reconcile this
postulation of rapid accommodation with the classical finding that constant
sensory stimulation can evoke repetitive firing of motoneurons, it has been
suggested that the afferent trains of impulses are transformed in the central
nervous system in a succession of volleys. This reorganization has often been
supposed to be the outcome of "reverberating activity" in chains of interneurons.
W h e n Barron and Matthews (1938) reported that repetitive firing of
motoneurons can be evoked by constant currents it was suggested (Eccles,
1939, p. 371) that the constant currents did not of themselves evoke firing
b u t "merely lowered the threshold of the motoneurones to the detonator
action of impulses." T h e view that spinal motoneurons can be excited only
by rapid changes has been criticized on several occasions (e.g. Fuortes, 1954;
Frank and Fuortes, 1960, 1961), but is apparently still held by some authors
(e.g. Lloyd, 1957; Eccles, 1957, p. 65, 1961).
Relations between Stimulus and Response In most of the cases mentioned
above, frequency of firing decreased gradually during constant stimulation.
O n occasions, however, (Hodgkin, 1948) a moderate increase of frequency
("warming u p " ) was observed to occur shortly after the beginning of the
stimulation. Measuring frequency some time after the onset of the stimulus,
it was found in m a n y instances that the rate of firing was linearly related to
current intensity over a considerable range. This linear relation was first
explicitly described by MacNichol (1956) for visual cells of Limulus, b u t it
Downloaded from on June 16, 2017
This general view is derived from Lorente de N6's work (1938) on midbrain motoneurons, but it should be noted that Lorente de N6 ascribed to activity of interneuronal chains the prolongation of a short lasting sensory input, without postulating
rapid accommodation of motoneurons. He suggested that the interneuronal impulses
evoked by sensory stimulation would reach the motoneurons in the form of a continuous bombardment, and not in the form of separate volleys. Further, it should be
noted that rhythmical reflex firing can be readily evoked without activating excitatory interneurons by stimulation of receptors whose fibers reach the motoneurons
directly. In these cases, it is difficult to see how the sensory bombardment upon motoneurons can be organized other than in the form of a more or less continuous action
(Alvord and Fuortes, 1953; Fuortes, 1954).
Published July 1, 1962
FUORTES AND MANTEOAZZINI-Repetitive Firing of Nerve Cells
II6 7
can be seen that it holds also for the crab axon, from the records published
by Hodgkin (1948). It was also found in spinal cord motoneurons of cats
(Frank and Fuortes, unpublished) where slopes between 0.4 and 1.6 imp/see.
per nA (lnA = 10 -9 A) were determined for stimulation with intracellular
electrodes. In frog's sensory terminals (Katz, 1950) as well as in Limulus eccentric
cells (MacNichol, 1956; Fuortes, 1958), firing was induced by natural stimulation and frequency of firing was plotted as a function of the depolarization
recorded during the "resting" intervals between impulses. This relation
between voltage and frequency was also found tO be linear.
The present article describes the features of the firing elicited in eccentric
cells of Limulus by stimulation with long lasting depolarizing current, and an
attempt will be m a d e to identify the factors which influence the response to
prolonged stimuli.
Intracellular stimulation and recording were used in these experiments, employing
the techniques already described in a previous article (Fuortes, 1959 a). Additional
details of the methods used have been described by Frank and Fuortes (1955, 1956).
RESULTS
Responses of Eccentric Cells of Limulus to Depolarizing Currents Some features
of the responses elicited in eccentric cells of Limulus by long lasting depolarizing currents have been described in previous work (Hartline, Coulter, and
Wagner, 1952; MacNichol, 1956; Fuortes, 1958, 1959). Typical responses
are again shown in Fig. 2. Data taken from records such as those illustrated
are plotted in Fig. 3 where the horizontal sequences of points indicate the
times at which impulses occurred, and the elevation of each row of points
indicates the current intensity used. It is seen that latency is always shorter
than any of the successive intervals, even for moderate currents producing
slow frequency firing. Intervals increase gradually and moderately with
time. T h e reciprocals of first and last interval (for stimulating current of 1
see.) are plotted as a function of current intensity in Fig. 4. In agreement
with previous reports (both on Limulus cells and on other structures), it is
seen that when late intervals are measured, the relation fits closely a straight
line. T h e relation holding for early intervals was found to be more complex
and varied somewhat in different cells.
In some responses from Limulus, it was observed that frequency increases slightly a
little after the beginning of the discharge, a phenomenon similar to what Hodgkin
(1948) called warming up in crab's peripheral nerves. This phenomenon might be
due to leakage of potassium in a small space around the cell, occurring as a conse-
Downloaded from on June 16, 2017
METHODS
Published July 1, 1962
i~68
THE
JOURNAL
OF
GENERAL
PHYSIOLOGY
• VOLUME
45
"
x962
Downloaded from on June 16, 2017
FIGURE 2. Responsesto steps of current. Upper traces, current intensity through intracellular microelectrode (depolarizing currents give downward deflection); lower traces,
potentials recorded by means of the same microelectrode. A bridge circuit (described
by Frank and Fuortes, 1956, and Fuortes, 1959) was used in order to prevent recording
of the potential drop elicited by the applied currents across the high resistance of the
microelectrode. Bridge was balanced so that no potential drop occurred as long as currents were subliminal. This and all following illustrations are from same unit.
quence of firing. Some similar process might perhaps explain the observation illustrated in Fig. 2, where it is seen that the difference between early and late intervals
decreases as frequency of firing is increased.
Refractoriness in Eccentric Cells
T h e course of r e c o v e r y after firing of one
impulse (evoked b y a brief electric shock) in the same cell w h i c h gave the
responses illustrated in the p r e c e d i n g figure is s h o w n in Fig. 5. R e c o v e r y is
quite slow as c o m p a r e d to t h a t of m e d u l l a t e d or n o n - m e d u l l a t e d axons (see
for instance E r l a n g e r a n d Gasser, 1937; H o d g k i n , 1948) b u t it is n o t slow
Published July 1, 1962
FUORTES AND MANTEOAZZml Repetitive Firing of Nerve Cells
I
I
I
l
I
I
~
~z69
I
I
I
I
6
5
4.
nA
3
2
I
0
0
I
I
I
I
I
1
I
I
I
I
o
o.I
0.2
0.3
0.4
0.5
0,6
0.7
0.8
0.9
I
I sec.
I
I
I
I
I
I
40
/
30
imp
SeC.
20
/
I0
0
0
I
I
I
I
l
I
I
2
3
4
5
6
7
nA
FIouP~ 4. Initial and "steady state" frequencies of discharges evoked by current steps.
Circles and dots measure respectively the reciprocals of first and last intervals in wains
evoked by current steps of 1 sec. duration and different intensities. Crosses are measurements of first intervals taken from another experiment.
Downloaded from on June 16, 2017
FtGtnu~ 3. Trains of impulses elicited by depolarizing currents. Measurements from
experiments such as those of Fig. 2. Circles represent impulses discharged following current steps starting at time zero. Horizontal lines join impulses evoked by same stimulus.
Ordinate shows intensity of the stimuli used. Slanted lines join first, s e c o n d . . . , etc. impulse in each train.
Published July 1, 1962
I~7o
THE
JOURNAL
OF
GENERAL
PHYSIOLOGY
" VOLUME
45
" I962
enough to justify the length of the intervals between impulses in trains evoked
by direct currents. In the case illustrated, it was sufficient to increase the
stimulating pulse to a value twice threshold in order to obtain a second impulse 25 msec. after the first. But when long steps of current were used, stimulus strength had to be increased to over five times rheobase in order to obtain
a first interval of about 25 msec. (see Fig. 3).
I
I
I
I
I
I
I
0.1
I
0.2
I
0.3
I
0.4
I
0.5
I
0.6
I
0.7
I
nA
2
I --
0
0
f
0.8 see.
FIGUm~.5. Courseof recovery after one impulse. Ordinate measures intensity i of a current pulse of 7 msec. duration, required to evoke an impulse at different delays t after
firing of a preceding impulse. Solid line is a graph of the relation: i,h/i --- I - e-tl~,
where i,h is threshold intensity of the pulse and r is 55 msec.
Discharges Elicited by Trains of Pulses in Eccentric Cells T h e results just
quoted show that the 'refractoriness left over by the first impulse is not sufficient to explain the duration of the first interval in a train evoked by a current
step. However, in order to assess the possible role of refractoriness at later
stages of the discharge, it is important to determine whether the course of
refractoriness changes after firing of several impulses. To do this, it would be
desirable to elicit trains of two, three, or more impulses at different frequencies, and to test excitability in the conventional m a n n e r at different times after
the last impulse. But, since this method would be very laborious and timeconsuming, the less accurate method described below was employed.
Trains of identical stimuli at different frequencies were delivered to the
impaled cell, and for each frequency used, the experiment was repeated using
different intensities of the stimuli. Fig. 6 illustrates responses obtained with
Downloaded from on June 16, 2017
I
Published July 1, 1962
FUORTES AND MANTEGAZZINI Repetitive Firing o/Nerve Cells
ii7i
this type of experiment. As long as frequency is low (e.g. 1/sec.) a shock just
threshold for the first impulse can evoke also the later impulses. W i t h higher
frequencies, a threshold (or just above threshold) shock elicits an i n t e r m i t t e n t
discharge. In these conditions, a progressive lengthening of the intervals,
Downloaded from on June 16, 2017
FlouRE 6. Responsesto trains of shocks. Upper traces, depolarizing current pulses (of
7 msec. duration) through intracellular microelectrode. Lower traces, potentials recorded
as in Fig. 2. Stimulation at 5/sec. in A; 10.5/sec. in B; 21/sec. in C, and 40/sec. in D.
Note potential deflections of different amplitude following stimuli which do not evoke
all-or-none impulses, especially for higher frequencies of stimulation.
similar to t h a t occurring with current steps, m a y be observed (as for instance,
in the records of rows 2 a n d 3 of Fig. 6). Stimulus strength has to be increased
in order to obtain the response to the second shock a n d still m o r e to obtain
three or m o r e consecutive spikes, until a complete train of responses is elicited.
Results obtained by changing intensity of trains of stimuli of constant freq u e n c y are illustrated in greater detail in Fig. 7.
O n e m a y conclude from these findings t h a t some form of depression accumulates with time also w h e n responses are evoked by trains of shocks.
Published July 1, 1962
ii72
THE
JOURNAL
OF
GENERAL
PHYSIOLOGY
- VOLUME
45
"
1962
It is seen in Fig. 7 (F to H) that the n u m b e r of consecutive impulses discharged in
response to trains of shocks at constant frequency increases with increasing shock intensity. T h e relation between strength of the stimuli and n u m b e r of consecutive impulses discharged is shown (for various frequencies of stimulation) in Fig. 8. T h e experimental points fitted roughly a set of straight lines, showing that (for a certain
frequency of stimulation) the current intensity required to produce an impulse increases more or less proportionally to the logarithm of the n u m b e r of consecutive impulses previously discharged.
Downloaded from on June 16, 2017
FIGURE 7. Responses to trains of shocks of constant frequency. Same as Fig. 8 but
shocks here are of 3 msec. duration and sweep speed is greater. Frequency of stimulation
50/sec. Observe progressive depolarization before impulse firing in A, responses of different amplitude following stimuli which do not evoke all-or-none impulses, and inflection
in rising phase of some of the spikes evoked by strong shocks during refractoriness.
Published July 1, 1962
FUORTES AND MANTEOAZZINI Repetitive Firing of Nerve Cells
T~73
F o r frequencies a b o v e 20/see., it is often seen t h a t w e a k shocks a r e m o r e
effective s o m e t i m e a f t e r the start, t h a n at t h e b e g i n n i n g of t h e t r a i n of stimuli,
so t h a t o n e or m o r e impulses m a y be elicited b y a t r a i n of i d e n t i c a l stimuli
e v e n if c u r r e n t intensity is s u b t h r e s h o l d for a single stimulus (or for t h e first
stimulus of t h e train). T h i s p h e n o m e n o n should p r o b a b l y b e c o r r e l a t e d to
the o b s e r v a t i o n t h a t shocks w h i c h d o n o t elicit a full spike m a y e v o k e a small
g r a d e d response, such as is seen in the records of Figs. 6 or 7.
i
I
l
I
i
I I tl
l
I
[
[
I
[ I
7-
6-
50
I00
FmuRE 8. Increase of refractoriness with successive impulses. Data from experiments
such as illustrated in Fig. 7. Abscissa shows number of consecutive impulses obtained
with trains of pulses delivered at the frequencies indicated. Ordinate measures intensity
of stimulating current pulses. Intensity of the stimuli required to elicit n impulses at a
frequency f can be considered as a measure of "excitability" at the time 1/f after discharge of the (n - 1)th impulse.
I t can also be noted in these records that some of the spikes elicited by strong
stimuli during the refractory period present a rising phase inflection suggestive of the
A and B components of spinal motoneuron spikes (Fuortes, Frank, and Becket, 1957).
Presence of these two components had not been observed in previous work on Limulus
(Fuortes, 1958, p. 213). According to the interpretations offered for motoneurons, this
division of the spike in two components indicates that two different regions of the
m e m b r a n e are invaded in close succession. But the similarity of the features of spike
production in sensory ceils of Limulus and in central cells of vertebrates opens in fact
a problem because some interpretations proposed to explain these features or to justify
their functional role in central cells would probably not apply to the sensory cells of
Limulus.
Downloaded from on June 16, 2017
5
I0
NUMBER OF CONSECUTIVE IMPULSES
Published July 1, 1962
THE JOURNAL
i i74
OF G E N E R A L
PHYSIOLOGY
• VOLUME 45
" I962
Comparison of Responses Obtained with Trains of Shocks or with Steps of Currents
I t a p p e a r s f r o m t h e a b o v e results t h a t s o m e of the features c h a r a c teristic of responses to p r o l o n g e d c u r r e n t s c a n b e r e p r o d u c e d also using
40
/t
f
•
30
im._.~p
sec.
]+
20
•
40
v,,/ : ®
/ / _/ "
imip
sec.
4 X",,"
30
ok__~
0
I
2
3
4
5
6
/
/
/
i
,
,V
AI
I
[
2
3
20
:"
/
0
w
i
•4¢
' 0
i
9
I0
0
/
4
5
6
7
nA
Fmum~ 9, Relations between stimulus intensity and discharge frequency, for constant
currents and for wains of shocks. Curve A, steps of current of 1 sec. duration. Abscissa
measures current intensity and ordinate indicates average frequency of the discharge.
Curve B, trains of pulses of 7 msec. duration at 40/see. frequency. Ordinate and abscissa
as in curve A. Curve G, trains of pulses of 7 msec. duration and different frequencies, as
shown on ordinate. Abscissa measures current intensity required to give a complete
train of responses. The different symbols in curves B (v,+) and C (i,o) refer to two sets
of measurements, taken at different times. Inset, curves A and B replotted measuring
current intensity in units of rheobase for current steps and in units of threshold for the
trains of impulses.
trains of pulses, as c a n b e seen b y c o m p a r i n g Fig. 2, d i s p l a y i n g responses to
c u r r e n t steps, to Figs. 6 a n d 7 illustrating responses to trains of shocks. I t
b e c o m e s t h e n r e l e v a n t to ask w h e t h e r the a c c u m u l a t i n g depression o c c u r r i n g
w i t h r e p e t i t i v e s h o c k s t i m u l a t i o n is all t h a t is n e e d e d to e x p l a i n the essential
f e a t u r e s of r e p e t i t i v e discharges elicited b y c o n s t a n t currents. T o a n s w e r
this question, t h e relations b e t w e e n c u r r e n t intensity a n d f r e q u e n c y w e r e
examined.
Downloaded from on June 16, 2017
A
I/I o
Published July 1, 1962
FUORTES AND MANTEOAZZlNI
Repetitive Firing of Nerve Cells
II75
A typical plot relating to discharges evoked by trains of shocks is shown in
Fig. 9. Curve B in this figure is a plot of the data presented in Fig. 6 D and
measures average frequency of the responses elicited by trains of shocks of
constant frequency (40/sec.) and of different intensities. T o construct curve
C, trains of shocks of different frequencies were used and, for each frequency,
intensity of the stimuli was increased until a complete train of responses was
obtained. T h e trains of shocks at 40/sec. were more effective in eliciting the
slower frequencies, partly (perhaps) because of more effective summation of
graded responses, partly due to limitations of the method, as explained below.
Fig. 9 includes also (curve A) a plot of the average frequency of responses
evoked (in the same cell) by steps of depolarizing current of 1 sec. duration
(see Figs. 2 and 3). With the constant currents less intensity is required to
evoke a given frequency of response than with pulses, up to response frequencies of about 35 imp/sec. Above this limit, the curves cross, indicating that
the pulses are now more effective than the constant currents. But in comparing responses to prolonged and to short lasting stimuli in these cells, one
should take into account results of the type illustrated in Fig. 3, which show
that if a current is to evoke firing within 7 msec., its intensity must be about
twice rheobase. If the conditions responsible for this persist after the first
impulse, then comparison of responses to prolonged currents and to trains
ot shocks should be m a d e measuring current intensity in units of rheobase for
current steps and in units of threshold for shocks. T h e inset of Fig. 9 shows the
results obtained w h e n this scaling is done. It appears from this figure that,
for a given proportional increase of current intensity, frequency of firing
increases less with constant currents t h a n it does with trains of shocks. Thus,
it m a y be legitimate to conclude that sustained currents exert a depressant
effect (accommodation) which reduces frequency of firing to values lower
than those imposed by accumulating refractoriness.
.DISCUSSION
Interpretation of the responses evoked by prolonged stimuli requires consideration of (a) the normal excitation processes and (b) the changes in m e m brane properties occurring with time. A distinction is usually m a d e between
these changes: those which result from impulse firing are generally called
Downloaded from on June 16, 2017
Suppose that a cell is stimulated with pulses of intensity i, first at 50/sec. and again
at 10/sec. If i is sufficient to elicit firing 35 msec. after a preceding spike, an impulse
will be elicited in the first case by the second shock after the spike, giving an interval
of 40 msec.; but in the latter case, a shock is applied only 100 msec. after the spike
and this interval will be measured. Thus, for a given intensity of the stimuli, lower
firing rates will occur when frequency of stimulation is lower.
Published July 1, 1962
~76
THE
JOURNAL
OF
GENERAL
PHYSIOLOGY
• VOLUME
45
"
~962
Downloaded from on June 16, 2017
"refractoriness," while those brought about by persistence of the stimulus
are called "accommodation" or "adaptation."
Normally, all that is required in order to produce all-or-none exckation of
a nerve cell is to depolarize its membrane to a certain threshold voltage
V,h. Thus, study of the process normally leading to exckation amounts simply
to determining in what manner depolarization develops for a given stimulus.
In m a n y structures, with stimuli in the form of current steps, membrane
depolarization develops essentially along an exponential course of short time
constant, so that the time required to reach threshold depolarization (and
therefore latency for the first impulse) decreases rapidly with increasing
intensity of the stimulating current. If a membrane is depolarized by the
stimulus to a level Vgr, less than F,h, a graded response may develop, which
increases the depolarization and may bring it up to the F,h level (see Fig.
1. C). If V0, and Vth have significantly different values, and ff the graded
response develops slowly while the stimulus is maintained, then it can become
important in controlling the time of firing of impulses evoked by a sustained
current step. This is what happens in Carcinus axons of Glass I (Hodgkin, 1948)
where, in addition, the normal excitation process is not appreciably modified
by firing of impulses (because of the rapid course of refractoriness) or due to
the persistance of the stimulus (because of negligible accommodation).
Therefore, following a step of depolarizing current, latency and intervals
will have the same duration within a considerable range of intensities of the
stimulus. This same type of graded activity occurs probably also in eccentric
cells of Limulus as part of their normal excitation process. For stimulation with
current steps, the graded activity takes the form of an inflection in the curve
of the potential between spikes; for stimulation with short pulses it appears
as sharp depolarizing transients of different amplitudes. But in Limulus (as
also in motoneurons, Frank and Fuortes, unpublished; see also Fig. 7 in
Fuortes, 1959 b), latency was found to be shorter than first interval, and later
intervals increased progressively during stimulation with a step of current.
This shows that the normal process of excitation (including the development
of graded activity) is not the only important factor determining the features
of responses to constant currents. Rather, it must be concluded that the processes leading to excitation change in time, due either to impulse firing or to
persistence of the stimulus or to a combination of both processes.
To distinguish between changes due to refractoriness and to accommodation
respectively, the same firing was evoked using either long lasting currents or
series of short pulses. As one can readily derive from the plot of Fig. 9, the
quantity of electricity required to elicit a certain frequency of firing was
always considerably greater for the steady currents than for the trains of
pulses. Thus, essentially identical responses could be evoked by means of
greatly different stimuli. With equal firing, refractoriness should be the same
Published July 1, 1962
FuoRzes
AND
MANTEGAZZINI
Repetitive Firing of Nerve Cells
~77
Thanks are due to Dr. W. J. Adelman, Dr. R. FitzHugh, Dr. P. G. Nelson and Dr. W. Rall for
reading this manuscript and for offering useful suggestions.
Most of the results described in this article were obtained by one of us (M. G. F. F.) during work
performed between 1957 and 1960. The data were analyzed for the major part by the other author
Downloaded from on June 16, 2017
while accommodation should exert a greater effect when the stimulus is
stronger unless accommodation is altogether negligible.
Comparison of the stimulus-response relations for discharges evoked by
continuous or by interrupted currents showed that larger proportional increases of current intensity are required to elicit given increases of frequency
with prolonged current steps than with short pulses. This observation can be
reasonably correlated to the fact that steps carry a greater amount of charge,
and leads to the conclusion that frequency of the firing evoked by prolonged
currents is limited not only by refractoriness but also by accommodation. It
is not easy, however, to reach any safe conclusion on the role of accommodation in responses elicited by trains of shocks. In the first approximation, it
may be acceptable to assume that, in these responses, refractoriness was a
predominant action, determining frequency of firing (for stimulus intensities
resulting in intermittent discharges).
It would be desirable to specify what is meant by refractoriness and by
accommodation besides stating that the first is an unknown process brought
about by firing and the second is an equally unknown process due to the
stimulus. Hodgkin and Huxley (1952 a) have suggested that both accommodation and refractoriness occur as a consequence of depolarization of the membrane; in the first case a depolarization brought about by the stimulus, in the
second by impulse firing. Depolarization evokes a delayed increase of potassium conductance and (after a brief increase of conductance for sodium) a
delayed "inactivation" of the membrane's ability to conduct sodium ions.
These two processes are precisely specified in Hodgkin and Huxley's (1952 b)
formulation and it is possible to calculate how they would affect responses to
sustained constant currents. This calculation has been recently performed by
FitzHugh (1961) who found that the constant currents would produce trains
of impt~lses of infinite duration. Latency of the first impulse would be shorter
than intervals and all intervals would have equal duration. Frequency of
firing would be linearly related to the logarithm of current intensity. Comparison of these results on the mathematical model with those obtained in
real nerve cells seems, therefore, to indicate that Hodgkin and Huxley's
equations do not include some slow process which is important in determining
the features of the responses of nerve cells to prolonged depolarizing currents.
Changes of ionic concentration and diffusion are among the first possibilities
that come to mind. Whatever the case may be, it appears that identification
of this slow process (or processes) will be required for a more precise interpretation of the results described above.
Published July 1, 1962
It78
THE
JOURNAL
OF
GENERAL
PHYSIOLOGY
* VOLUME
45 • I962
(F. M.) in 1961. Control experiments were performed together during this period and the article
in collaboration.
Recdvedfor publication, January 25, 1962.
was prepared
Downloaded from on June 16, 2017
BIBLIOGRAPHY
l. ADELMAN,W. J., PAUTLER, E., and EPSTmN, S., Analysis of repetitive transient
response of lobster motor axons, Am. J. Physiol., 1960, 199,367.
2. ADRIAN, E. D., The Basis of Sensation, London, Christophers, 1928.
3. ALVORD, E. C., and FUORTES, M. G. F., Reflex activity of extensor motor units
following muscular afferent excitation, J. Physiol., 1953, 122, 302.
4. ARVANITAKI,A., Propridt6s rythmiques de la matiSre vivante. Variations gradu6es
de la polarisation et rythmicitds, Paris, Hermann et Cie, 1938.
5. BARRON,D. H., and MATTrmWS, B. H. C., The interpretation of potential changes
in the spinal cord, or. Physiol., 1938, 92, 276.
6. DuBols-R~YgOND, E., Untersuchungen fiber thierische Elektricit/it, Berlin,
Reimer, 1848.
7. Eec~s, J. C., The spinal cord and reflex action, Ann. Rev. Physiol., 1939, 1, 363.
8. Ecc~s, J. C., The Physiology of Nerve Cells, Baltimore, The Johns Hopkins
Press, 1957.
9. Ecc~s, J. C., Discussion on p. 27 in The Nature of Sleep, Ciba Foundation
Symposium, (G. E. W. Wolstenholme and M. O'Connor, editors), London,
Churchill, 1961.
10. ECCLES, J. C., and SHERRINOTON,C. S., Studies on the flexor reflex. Part IV.
Afterdischarge, Proc. Roy. Soc. London, Series 13, 1931, 107, 586.
11. EDWARDS, C., Changes in the discharge from a muscle spindle produced by
electrotonus in the sensory nerve, or. Physiol., 1955, 127, 636.
12. ERLANOER,J., and GASSER, H. S., Electrical signs of nervous activity, Philadelphia, University of Pennsylvania Press, 1937.
13. FESSARD,A., Propri~t6s rythmique de la mati~re vivante. Nerves non-my6linis6s.
II, Paris, Hermann et Cie, 1936.
14. FITZHUOH, R., Impulses and physiological states in theoretical models of nerve
membrane, Biophysic. J., 1961, 1, 445.
15. FRANK,K., and FUORTES,M. G. F., Potentials recorded from the spinal cord with
microelectrodes, J. Physiol., 1955, 130, 625.
16. FRANK, K., and FUORTES, M. G. F., Stimulation of spinal motoneurones with
intracellular electrodes, or. Physiol., 1956, 134, 451.
17. FRANK, K., and FOORTES, M. G. F., Accommodation of spinal motoneurones of
cats, Arch. ital. biol., 1960, 98, 165.
[8. FRANK,K., and FUORTES,M. G. F., Excitation and conduction, Ann. Rev. Physiol.,
1961, 23,357.
19. FUORaXS, M. G. F., Direct current stimulation of motoneurones, J. Physiol.,
1954, 126, 494.
20. FUORTES,M. G. F., Electric activity of cells in the eye of Limulus, Am. Jr. Ophth.,
1958, 46, 210.
21. Fuoga~s, M. G. F., Initiation of impulses in visual cells of Limulus, J. Physiol.,
1959 a, 148, 14.
Published July 1, 1962
FUORTES AND M.~TEQAZZn~I RepetitiveFiring of Nerve Cells
II79
Downloaded from on June 16, 2017
22. FUORT~S,M. G. F., Integrative mechanisms in the nervous system, Am. Naturalist,
1959 b, 93, 213.
23. FUORTES, M. G. F., FRA~I~, K., and BECKER, M. C. Steps in the production of
motoneuron spikes, J. Gen. Physiol., 1957, 40, 735.
24. GRAmT, R., and SKOGLUND,C. R., Accommodation of autorhythrnic mechanism
in single sensory fibres, J. Neurophysiol., 1943, 6, 337.
25. HARTLmE, H. K., COUT.TER, N. A., JR., and WAGNER, H. G., Effects of electric
current on responses of single photoreceptor units in the eye of Limulus, Fed.
Proc., 1952, 11, 65.
26. HARTLmF., H. K., WAGNER, H. G., and MACNIcI-IOL, E. F., JR., The peripheral
origin of nervous activity in the visual system, Cold Spring Harbor Symp. Quant.
Biol., 1952, 17, 125.
27. HODOKn~, A. L., The local electric changes associated with repetitive action in a
non-medullated axon, J. Physiol., 1948, 107, 165.
28. HODGKIN,A. L., and HUXLEY,A. F., The dual effect of membrane potential on
sodium conductance in the giant axon of Lollgo, J. Physiol., 1952 a, 116, 497.
29. HOD~XIN, A. L., and HuxLEY, A. F., A quantitative description of membrane
current and its application to conduction and excitation in nerve, J. Physiol.,
1952 b, 117,500.
30. KATZ, B., Multiple response to constant current in frog's medullated nerve, jr.
Physiol., 1936, 88,239.
31. KATZ, B., Depolarization of sensory terminals and the initiations of impulses in
the muscle-spindle, J. Physiol., 1950, 111, 261.
32. LLOYD, D. P. C., Monosynaptic reflex response of individual motoneurons as a
function of frequency, J. Gen. Physiol., 1957, 40, 345.
33. LORENTEDE N6, R., Synaptic stimulation of motoneurones as a local process, J.
Neurophysiol., 1938, 1, 195.
34. MAcNICnOL, E. F., JR., Visual receptors as biological transducers, in Molecular
Structure and Function Activity of Nerve Cells, (R. G. Grenell and L. J.
Mullins, editors), Washington, American Institute of Biological Sciences, 1956.
35. SKOGLUND, C. R., The response to linearly increasing currents in mammalian
motor and sensory nerves, Acta Physiol. Scan&, 1942, 4, suppl. 12, 1.
36. TASAKI, I., Conduction of the nerve impulse, in Handbook of Physiology-Neurophysiology. I, (J. Field, H. W. Magoun, and B. E. Hall, editors), Washington,
American Physiological Society, 1959.
37. WRIGHT, E. B., and ADELMAN, W. J., Accommodation in three single motor
axons of the crayfish claw, J. Cell. and Comp. Physiol., 1954, 43, 119.