Download Passive cable properties of hippocampal CA3 pyramidal neurons

Cellular and Molecular Neurobiology, Vol. I, No. 1, 1981
Passive Cable Properties of Hippocampal CA3
Pyramidal Neurons
Daniel Johnston I
Received June 30, 1980; accepted July 30, 1980
The passive electrical cable properties o f CA3 pyramidal neurons from guinea pig hippocampal slices were
investigated by applying current steps and recording the voltage transients from 25 CA3 neurons, using a
single intracellular microelectrode and a 3-kHz time-share system. Two independent methods were used
for estimating the equivalent electrotonic length of the dendrites, L, and the dendritic to somatic
conductance ratio, p. The first method is similar to that used by Gorman and Mirolli (1972) and gave an
average L o f 0.96; the average p was 2.44. The second method is derived here for the first time and assumes
a finite-length cable with lumped soma. It is an exact solution for L and p, using the slopes and intercepts
of the first two peeled exponentials. The average L was 0.94; the average O was 1.51. The results, using
both methods, are in close agreement. The average membrane time constant for all 25 CA3 neurons was
23.6 ms, suggesting a large (23,600 ~2cm2) average membrane resistivity. It is concluded that CA3 neurons
are electronically short.
KEY WORDS: hippocampus; cable theory; CA3 pyramidal neurons; passive membrane properties.
INTRODUCTION
Hippocampal pyramidal neurons are among the most studied mammalian cortical
neurons. The early work of Spencer and Kandel (1961a,b), Kandel and Spencer
(1961a,b) and Kandel et al. (1961) characterized some of their basic firing behavior,
synaptic inputs, and active membrane responses. With the advent of the in vitro
hippocampal slice, our knowledge of the basic electrophysiology of hippocampal
neurons has increased rapidly (Andersen, 1975; Schwartzkroin, 1975, 1977; Brown et
al., 1979; Wong et al., 1979; Johnston et al., 1980; Johnston and Brown, 1981).
The hippocampus is of particular interest because of its relatively simple and
highly organized structure. It has one of the lowest seizure thresholds in the brain
This work was supported by Grants NS 11535 and NS 15772 from the National Institute of Neurological
and Communicative Disorders and Stroke, National Institutes of Health, U.S. Public Health Service.
1 Program in Neuroscience, Section of Neurophysiology, Department of Neurology, Baylor College of
Medicine, Houston, Texas 77030.
41
0272-4340/81/0300-0041503.00/0
© 1981 Plenum Publishing Corporation
42
Johnston
(Green, 1964) and can be induced to seizure with relatively simple stimulus paradigms
(Kandel and Spencer, 1961 a). Moreover, the hippocampus has long been suspected of
playing a role in some forms of learning and memory (Green, 1964; Isaacson, 1974),
Most of the synapses in the hippocampus display a remarkable degree of usedependent changes in efficacy following brief periods of activation (Bliss and LCmo,
1973). Many feel that this phenomenon (called long-term potentiation) may be a
cellular correlate of learning and memory (Bliss, 1979).
Despite a growing literature on the electrophysiology of hippocampal neurons,
little attention has been focused on their passive cable properties, i.e., their electrotonic structure. This gap in the literature is particularly noteworthy, since some of the
theories proposed for learning and memory involve changes in the electrotonic
structure of the postsynaptic neuron (Rall, 1962; Diamond et al., 1970). Furthermore,
although the active properties of dendrites have been studied intensively (Fujita and
Iwasa, 1977; Wong et al., 1979), their electrotonic properties have not been explored
adequately.
In this study, an attempt is made to define some of the passive cable properties of
hippocampal CA3 pyramidal neurons. CA3 neurons were chosen because of an
interest in their endogenous burst characteristics, and the desire to apply voltageclamp techniques to study some of their active membrane responses (Johnston et al.,
1980; Johnston and Brown, 1981). Also, the proximity of mossy-fiber synapses to the
soma may make CA3 cells an adequate preparation for a study of the biophysical
properties of these synapses. This paper addresses the following questions. (1) What is
the membrane time constant for CA3 neurons when the electrotonic structure of the
cell is accounted for, and how does this time constant compare to that measured in
other mammalian neurons? (2) Since it has been suggested that CA1 pyramidal cells
are electrotonically short (Traub and Llinas, 1978), is this true for CA3 neurons, and
can this suggestion be put into more quantitative terms? (3) If a voltage-clamp is
applied to the soma and a step change in potential made, what is the theoretical
prediction (in time) for the passive spread of current into nonisopotential regions of
the cell? That is, how long will it take to reach a steady potential in unclamped areas
of the cell? In addition to these specific questions, it is hoped that the data will allow
construction of an accurate electrotonic model of these cells and subsequently provide
additional insight into their basic physiology through model simulations.
The results indicate that the membrane time constant for CA3 neurons is about
24 ms. The total electrotonic length of the dendrites is just under one space constant,
and the dendritic to somatic conductance ratio is between 1.5 and 2.4. The theoretical
time constant for the decay of current following a step change in potential at the soma,
using the average electrotonic structure for CA3 neurons, would be 6.3 ms. A
preliminary report of these results has appeared as an abstract (Johnston, 1979).
METHODS
Adult guinea pigs were decapitated, and the whole brain was removed quickly
and placed in cool saline at 15°C. The hippocampus was dissected from the brain and
sliced transverse to the longitudinal axis with a McIlwain tissue chopper set for
Cable Properties of HippocampalNeurons
43
400-500 #m sections. The slices were transferred with a small brush or a broken
Pasteur pipette to a perfusion chamber. The chamber was similar in design to that of
Schwartzkroin's (1975). In approximately half the experiments, the slices were
perfused continuously with Ringer's solution at 1.0 ml/min; in the remainder, the
bathing medium was stationary and merely replenished, via a syringe, at approximately half-hour intervals. Both methods yielded healthy slices, from which cells
meeting the criteria given below could be maintained for up to 6 hr. The slices were
oxygenated with 95% 02/5% COz; temperature was maintained at 34-36°C. The
Ringer's solution used throughout these experiments had the following ionic composition: 125 mM NaC1, 5 mM KC1, 1.25 mM NaH2PO4, 2 mM MgSO4, 2 mM CaCI2, 26
mM NaHCO3, and 10 mM dextrose.
Data were taken only from cells that had, throughout the time course of the
measurements, at least a - 5 5 mV resting membrane potential and an overshooting
action potential with an amplitude of at least 65 inV. After impaling a cell, dc
hyperpolarizing current was passed until the amplitude of the resting membrane
potential and action potential had stabilized. After the dc current was removed, the
amplitude of the action potential was determined; the resting membrane potential was
measured when backing out of the cell.
Electrodes were pulled on a Narashigi vertical puller from thin-walled, 1.5
mm-diam tubing containing a small bundle of glass fibers. Electrodes were filled with
either 3 M KC1 or 4 M KAc, and had tip resistances of 30-50 Mf~, measured in saline.
No differences in the measured neuron parameters were observed between cells
recorded from using KC1 or KAc filled electrodes. Electrodes were tested carefully
before use for their ability to pass up to 5 nA without developing tip potentials. KC1
filled electrodes were somewhat better in this regard than KAc filled electrodes.
Impalement of neurons with these relatively low resistance micropipettes was facilitated by briefly activating the voltage-clamp when the electrode was just outside a
cell. The resulting 3-kHz square wave of hyperpolarizing current usually forced the
electrode into the cell with a minimum of damage. The entire experiment was
recorded on a Brush chart recorder and a 4-channel FM tape recorder at 15 ips
(frequency response of 5 kHz).
The current-clamp apparatus (hereafter called single-electrode clamp, SEC)
utilized for these studies is based on the circuit of Wilson and Goldner (1975). A block
diagram of the apparatus is shown in Fig. 1. Amplifier A2 supplies 3-kHz current
pulses at 40% duty cycle. The amplitude of these pulses is determined by the output of
amplifier A 6 when in current-clamp or by the output of amplifier A~ when in
voltage-clamp. During the quiescent period, the voltage developed across Re decays
through the low input capacity of A1, and the voltage across Cmis sampled just before
the beginning of the next current pulse. The output of the sample-and-hold module
can be used as the input to a standard voltage-clamp circuit (As) or as the membrane
potential when in current-clamp. The switching sequence controlling the analog
switch and the sample-and-hold modules is shown to the right of the diagram. The
voltage developed across the microelectrode due to the 3-kHz current pulses is
monitored continuously during an experiment to ensure its complete decay before
voltage sampling occurs (see Fig. 1B). A theoretical requirement for the operation of
the SEC is that the membrane time constant must be much larger than the electrode
44
Johnston
A
T cornmond$
Analog
swit©h
VaL
-
-
t
--"q
~
....
I
i
Switching Sequence
sample
v
Anolo~
__
D
_N
twitch
~
fl
B
open
.......................
sample
s..__rl
I1
................. ..,.. ............
I
. . . . . . . . . . . . . . . . •. . . . . . . . . . . . . . . . . . . . . .
... .................... .,. ................
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I
SINGLE ELECTRODE CURRENT AND VOLTAGE CLAMP
Fig. 1. Single-electrodecurrent- and voltage-clamp (SEC). Block diagram of the SEC is shown on the left.
See text for explanation. (A) Upper trace is the voltage recorded across the electrode and cell membrane
(output of A4) in response to a 1-nA, 40-ms current step (middle trace). Bottom trace is the membrane
potential recorded from the output of V-S&H at a higher gain than in the upper trace. (B) Same as in (A)
except at much higher sweep speed. Only the first few cycles are captured. The steps in the middle trace
represent the output of I-S&H, while the notches in the bottom trace represent the sampling times of
V-S&H. Note that in the upper trace the electrode potential (across Re) completely decays before voltage
sampling occurs. Calibrations: 200 mV, upper trace of (A); 3 nA, middle traces of (A) and (B); 20 mV,
bottom traces of (A) and (B); 100 mV, upper trace in (B); 20 ms in (A); 200 ~s in (13).
time constant. This allows for the voltage developed across the electrode to decay
completely with little decay of the m e m b r a n e potential between cycles (see Fig. 1B).
Data Analysis
Thc nomenclature follows that given in Rall (1969, 1977) for an equivalent cable
model of a neuron with finite-length dendrites and lumped soma. The neuron
parametcrs are designated rm, p, and L. Tm is the m e m b r a n e time constant, p is the
stcady-state dendritic to somatic conductance ratio, and L is the equivalent electrotonic length of thc dendrites ( L = I / X , wherc l is thc length of thc equivalent cable and
~, is the space constant).
The voltage transient in response to a current step applied to the soma can be
represented by an infinite sum of exponentials (Rall, 1969):
V, = Co e-t/*" + C]e -'/~' + • • • + C,,e t/qo
(1)
where 1I, is the m e m b r a n e transient potential due to the current step, t is time, r ] . . . ~',
are the equalizing time constants, and Co. • • C, are constants. In principle, one should
be able to determine several of these exponential terms by plotting logVt versus t and
"peeling" exponentials (Rall, 1969). If the dendritic cable length is finite, and the end
terminates in an open circuit, the latter part of the voltage transient will decay
exponentially, with time constant z,, representing the m e m b r a n e time constant.
For the measurements on hippocampal neurons, it was found that r~ << rm (this
implies a small L; see Fig. 1 of Rall, 1969) and C~ < Co; therefore, plots of l o g d V / d t
versus t were used to enhance the higher-order exponential terms. The slope of the
latter portion of the curve defines ~'m, and by peeling exponentials, r~ also was
Cable Properties of Hippocampal Neurons
45
determined. Another method for measuring % that involves plotting log(~/t dV/dt)
proved of little use because of the short electrotonic length of these neurons (Jack et
al., 1975).
The first method used for estimating p is similar to that used by Gorman and
Mirolli (1972). If p is between 0 and 10, it can be calculated with sufficient accuracy
by finding the time at which the function log(,/T dV/dt) is a maximum during the
voltage transient, where T = t/%. A theoretical plot of p versus Tm~x(see Gorman and
Mirolli, 1972) can be obtained by substituting different values of p, equating to zero,
and calculating Tmaxfrom the expression
d
exp(-p2r)
dtlOg(,/TdV/dt) = 1 / ( 2 T ) + p 2 _ 1 - (zcT)l/2erfc(ox/T)
(2)
The experimental p can be obtained from this curve after calculating Tma~from the
voltage transient. L can be determined from the expression (Rall, 1969)
[ p/(p +
1) ]U2
(3)
L --- ((727;5 -- 1l
or by solving the following transcendental equation for L (Rail, 1969):
P
-o~cot(aL)
coth(L)
(4)
where a = [ ( r m / ' r l ) - 1] 1/2. The method described above for determining p assumes a
semi-infinite cable with lumped soma. However, when p is small (<5), the Tm,xvalues
used in determining o are only about 5-25% less for a finite-length cable of L = 1 than
for the semi-infinite cable (L = ~), the difference decreasing the smaller the 0 (cf.
Figs. 7.17 and 7.18 of Jack et al., 1975, for p = 2; and W. Rall, unpublished
calculations). Since o was found to be about 2 in these neurons, and given the
difficulty in determining the exact Tm,x when p is small and L is short (cf. Figs. 7.17
and 7.18 of Jack et al., 1975), it was felt that this was a reasonably accurate method
for calculating p for a finite-length cable. It should be noted that Tm,xfor a short cable
is slightly less than Tmaxfor a long cable for a given small p; hence, the resulting p and
L using this method are overestimates.
A second method for determining L and o can be derived from the solution of the
cable equation for a finite cylinder with lumped soma (Eq. 4.17 of Rall, 1977):
V(X, T) = V(X, ~) - ~-" B . c o s [ a . ( L - X ) ] • e x p [ - ( 1
+ a.Z)T]
(5)
n~0
where X and T are normalized distance and time (X = x/X, T = t/To), the coefficients, B.'s, are defined below, and a. = [(ro/r.) - 1] 1/2. The derivative of Eq. (5),
using only the first two terms of the series and letting X = 0 and % = r0, is
dV(O, T)
dt
Bo
r m
exp(-
t/%) +
B,cos(aL)
exp( --
l/'rl)
(6)
7" 1
where c~ = c~, = [(rm/~'l)- 1] 1/2.
Plotting logdV/dt versus t and peeling exponentials should yield slopes (% and
46
Johnston
r~) and intercepts (Bo/'r m and B1cos(aL)/'cl) of the two exponential terms in Eq. (6).
The coefficients (B.) are given in Rall (1977):
B.cos(a.L) =
2Bo ~'./ro
1 + (a.L)2/(K 2 + K)
(7)
where K = - o~Lcot(oLL).
The intercepts (designated a 0 and am) from the l o g d V / d t versus t plot are ao =
ao/'C,, and al = Blcos(aL)/'rv Substituting into Eq. (7),
2a0
a~ = 1 + ( ~ L ) 2 / ( K 2 + K )
(8)
Since ( a L ) 2 = K2/[cot(oLL)] 2, substituting this into Eq. (8) yields
2 ao
a~ = 1 + {K/[cot(aL)] 2 ( K + 1)}
(9)
Substituting the expression K = -o~Lcot(aL) into (9) and rearranging reduces the
expression to
cot(aL )[cot(aL ) - 1 / ( a L )] = a J ( 2ao - a l )
(10)
Given a0, al, and a, Eq. (10) can be solved numerically for L. Since Eq. (10) has an
infinite number of roots, a prior estimate of L must be used for the first iteration of
(10). If p is large (e.g., >1), an initial estimate of L can be obtained from L =
• "/[(r,~/rl)-1] 1/2 (Rall, 1969). If p _< 1, then an alternative method should be used
first to estimate L. Given L from Eq. (10), p can then be determined from Eq. (4).
For illustrative purposes, the first two exponential terms of the series in Eq. (5)
were used to derive Eq. (10), because in practice these are the only terms that can
usually be obtained from the charging transients. However, a similar equation can be
derived for any two terms of the series. Equation (10) is therefore an exact solution for
L based on the first two coefficients. The inability to resolve the higher-order terms
will not bias the solution of Eq. (10) unless the value obtained graphically for a~ is
influenced by these higher-order terms.
The term d V / d t was determined graphically from the voltage transients in a
manner similar to that of Lux et al. (1970). The voltage transients analyzed from any
one cell were selected on the basis of an absence of detectable synaptic input and any
slow changes in membrane resistance. Because of the tedious method of determining
d V / d t , ~'m, and Zl, usually only one transient per cell was analyzed. In a few cases,
however, several transients were analyzed from the same cell and compared for
consistency~
RESULTS
In some CA3 neurons, large hyperpolarizing current pulses cause a "droop" in
the vokage-transient response after approximately 50-100 ms. This "droop" was first
described by Purpura et al. (1968) and is a form of anomalous rectification, i.e., an
increase in conductance in the hyperpolarizing direction. Although the membrane
Cable Properties of Hippocampal Neurons
47
events underlying this anomalous rectification are unknown, it reflects a time- and
voltage-dependent increase in inward current during step hyperpolarizing voltageclamp commands (D. Johnston and J. Hablitz, unpublished observations). In order to
determine with accuracy the passive cable properties of these neurons, the current
pulses must not alter membrane properties. In these experiments, not all cells
exhibited anomalous rectification; those that did, showed it at somewhat different
membrane potentials. This variation between cells could have been a function of the
variation in resting membrane potentials between cells or some other parameter, but
no systematic analysis of the data in this regard was attempted. To avoid voltagedependent changes in conductance, either low-amplitude, 100-ms hyperpolarizing
pulses or short pulses (approximately 20 ms) were used, and voltage transients
displaying any "droop" were not analyzed. The voltage transient was always measured
following the end of the current pulse in order to avoid measurements during current
flow through the microelectrode. The values of ~'m,P, and L, calculated from cells when
short current pulses were used, fell within the ranges that were measured using longer
current steps.
In Fig. 2, voltage transients measured with a standard microelectrode preampli-
A
i
in
A
2
-
>
mS
"D
0.5
i
,
•
~
,-
=2.6
0.2
4
mS
12
:l'O
mS
TIME
40 mS
40~S
20~S
Fig. 2. Current-clamp voltage transients. (A) Recorded with a standard intracellular preamplifier
and bridge circuit. The solid line is the zero-current reference, and the step of current is illustrated.
The voltage record begins with a 10-mV, 10-msec calibration pulse, followed by the hyperpolarizing
voltage transient. (B) Recorded from a different cell using the SEC; current is at top, voltage at
bottom. (C) The end of the current step from (B), on an expanded time scale. (D) Plot of logdV/dt
vs. t for a similar transient as that shown in (C), but from a different cell (No. 2-08-78-1). The time
constants peeled from the curve are illustrated. Calibrations: (A) 20 mV, 0.5 nA, 40 ms; (B), 10 mV,
1 hA, 40 ms; (C), 5 mV, 0.5 hA, 20 ms.
48
Johnston
y
~
20mY
20 m$
2.0
Current-clamp control. A parallel 20M9 resistor and 10-9-F capacitor were used as a
model "cell." The top half of the figure shows
the end of a hyperpolarizing 2-nA current step
(top trace) applied across the model "cell," and
voltage transient (bottom trace) recorded
through a 35-M9 electrode, using the SEC.
LogdV/dtvs. t of this transient is shown at the
bottom. Curve can be fit by a single exponential
with a time constant of 21.3 ms.
Fig. 3.
"~
1.0
>
0.8
0.6
0.4
;
,'2
I'6
TIME
2'o
tier and bridge network (Fig. 2A) are compared with those measured with the SEC in
current-clamp (Fig. 2B,C). Similar transients are obtained with both techniques,
although the SEC is much easier to use because there is no troublesome bridge to keep
in balance. A plot of logdV/dt versus t, illustrating the determination of two time
constants, is shown in Fig. 2D. It was not possible to compare voltage transients
directly in the same cell, using the SEC and a standard preamplifier. The two time
constants calculated from voltage transients recorded with a standard preamplifier
and bridge network from six cells fell within the range of values for all cells recorded
with the SEC. As a further test to determine if the SEC circuitry was introducing
artifactual time constants into the voltage transients, the following control was
performed. A 35-M9 electrode, identical to those used for intracellular recordings,
was placed in a saline bath. A parallel network of a resistor and capacitor (20 Mg,
1 x 10 -9 F) was put in series with the bath ground to simulate a passive cell
membrane. The end of a voltage transient, following the passage of a 100-ms current
pulse through this model "cell," is shown at the top of Fig. 3. A plot of logdV/dt versus
t from one of these transients is shown at the bottom of Fig. 3. Only one time constant
results, identical to the time constant of the model "cell." No fast time constant is
evident, indicating that the SEC system faithfully reproduces the actual voltage
transient across the circuit.
Data from one CA3 pyramidal neuron are shown in Fig. 4. At the top of the
figure, logVversus t is plotted. The membrane potential of this cell very nearly follows
a single exponential time course in response to a current step. Without further analysis
or assumptions regarding geometry, this result suggests that these cells behave as a
large, nearly isopotential compartment, consisting of a parallel resistor and capacitor.
Cable Properties of Hippocampal Neurons
49
e
>
10
08
06
0.4
02
10C
80
6O
40
o
"o
O8
Fig. 4. Plots of data from current-clamp transients. At the top of the figure, logV/Vo vs. t is
plotted for a voltage transient from cell No.
4-20-78-5. V is the membrane potential; V0 is
the membrane potential at t - 0 (the end of the
current step). A single exponential fits the data
points reasonably well except for early time
intervals. A plot of logdV/dt vs. t for the same
voltage transient is shown at the bottom. The
exponential term with the smaller time constant
is enhanced by this method of plotting, and the
two time constants are peeled easily, as shown.
06
04
0.2
01
1
0
4
~
8
I
12
I
16
I
20
mS
TIME
If dV/dt is calculated from the transient, and the logdV/dt is plotted as shown at the
bottom of Fig. 4, the faster time constant can be determined as discussed in Methods.
In Fig. 5, similar plots of logVand logdV/dt versus t are made from another cell, but
at three different current intensities. Similar time constants result, indicating that
voltage dependent changes in membrane conductance can be avoided when taking
measurements.
The membrane time constant, ~,~, and the first equalizing time constant, rl, were
obtained from 25 CA3 neurons from graphs such as those shown in Figs. 4 and 5. The
average rm was 23.6 ms. Plots of log(~/TdV/dt), such as that shown in Fig. 6, were
made for each cell to determine the peak or Tm,x values as discussed in Methods. Using
Eqs. (2) and (4), above, the average L was 0.96, and the average p was 2.44. Using
Eqs. (10) and (4) for data collected from 13 neurons, the average L was 0.94 and the
average p was 1.51 (see Table I).
50
Johnston
1.0
08
o06
>
>04
Oi
ool.
3.eO~i.
i,s
I
e- 725 mV
mV
96.3
mY
•-
03
0.1
• - 88.5
t
0
;
lJO
Fig. 5. Voltage independence of r,,. Similar plots as in
Fig. 4 are shown, except that the transients were
recorded at three different current intensities, producing three different steady-state membrane potentials
during the current step (cell No. 3-23-78). At the top,
log V/V o vs. t is plotted, and a single exponential fits the
data points reasonably well. At the bottom, logdV/dt
vs. t is plotted (to enhance the higher-order terms) for
the three transients, and a straight line, representing rm,
is fitted to the data points at long time intervals. The
r,,'s were 25.9, 26.7, and 26.4 ms for the circles,
triangles, and squares, respectively. The r,,'s would be
expected to decrease with hyperpolarization if a timeand voltage-dependent increase in conductance in the
hyperpolarizing direction were significantly influencing
the data.
~
1;
2'0
TIME
2'5
mS
DISCUSSION
T h e c a l c u l a t e d values for the c a b l e properties of C A 3 n e u r o n s are q u i t e different
from those o b t a i n e d from spinal m o t o n e u r o n s , a m a m m a l i a n n e u r o n for w h i c h
extensive d a t a a r e a v a i l a b l e (r,, ~ 5 - 7 ms, L = 1.5, p > 5; s u m m a r i z e d in Rall, 1977)
a n d for cortical n e u r o n s (rm ~- 8.5 ms, L = 0o [ a s s u m e d ] , p ~ 6.5, L u x a n d Pollen,
1966). C A 3 n e u r o n s t h e r e f o r e have c o m p a r a t i v e l y long m e m b r a n e t i m e c o n s t a n t s a n d
electrically short d e n d r i t i c lengths, a n d t h e total i n p u t c o n d u c t a n c e of the d e n d r i t e s is
only a b o u t twice t h a t of the soma.
S i m i l a r v a l u e s for rm, L, a n d p have b e e n r e p o r t e d in C A 3 n e u r o n s b y F r i c k e et al.
(1979), u s i n g the s a m e a n d different m e t h o d s of analysis. W o n g et al. (1979) r e p o r t e d
~.00.90.60.74
0.6~ o.sb
~ o.4~
o.3-
o12
oi,
T
o16
06
,~
Fig. 6. Plot of Iog(x/T dV/dt) vs. T is shown for cell
No. 12-21-78-2. The Tmaxvalue was estimated to be
0.17, yielding a p of about 3. From Eq. (4), L was
calculated to be 1.3.
51
Cable Properties of Hippocampal Neurons
Table I.
Cable Properties of CA3 Neurons as derived from Voltage Transients
Cell no.
~-,,(ms)
rl (ms)
L
1-17-78-1
2-08-78-1
2-10-78-1
3-23-78-1
4-10-78-1
4-20-78-5
5-17-78-1
8-31-78-1
9-12-78-1
9-12-78-4
10-19-78-1
10-26-78-1
12-20-78-1
12-21-78-1
12-21-78-2
12-28-78-4
12-28-78-5
12-28-78-7
12-28-78-8
12-28-78-9
12-28-78-10
1-04-79-2
1-04-79-3
1-16-79-1
1-16-79-3
Mean (_+ SD)
38.5
30.8
14.7
25.9
17.1
17.2
51.9
17.8
17.7
22.7
30.1
35.1
14.5
13.1
24.4
29.4
15.3
17.4
18.5
25.4
13.0
20.0
30.1
15.6
33.5
23.6 + 9.5
3.6
2.6
2.6
1.6
2.2
2.0
7.4
2.6
1.4
5.9
3.9
4.6
2.1
2.9
4.7
2.3
1.1
2.4
3.7
3.1
1.2
5.1
7.0
2.9
2.3
3.3 + 1.7
0.9
0.8 (0.7) a
1.3 (1.0)
0.5 (0.8)
1.0
0.8 (0.8)
0.8 (0.8)
0.8 (0.9)
0.5 (0.6)
1.1 (1.1)
1.0
0.9 (1.0)
1.1
1.4 (1.4)
1.3
0.5 (0.6)
0.6
1.0
1.2 (1.4)
1.0
0.8
1.6
1.4
1.1 (1.1)
0.7
0.96 (0.94)
4.5
3.0 (3.0) ~
4.5 (1.3)
0.5 (2.0)
4.5
1.5 (1.3)
0.5 (0.7)
0.5 (0.9)
0.5 (1.1)
0.5 (0.4)
3.0
2.0 (3.0)
4.5
3.5 (2.0)
3.0
0.5 (0.9)
1.5
2.0
2.0 (2.5)
5.5
3.0
3.0
2.0
1.5 (0.5)
3.5
2.44 (1.51)
aNumbers in parentheses represent calculations using Eqs. (4) and (10) in the text and the intercepts of the
peeled exponentials (see text for explanation).
an average membrane time constant for eight CA3 neurons of 31.8 ms. However, it is
unclear how rm was determined in that report, or if the large average rm would be
typical if a larger population of neurons were sampled. The membrane time constant
for CA1 pyramidal neurons from guinea pigs has been reported to be 9.8 ms by
Schwartzkroin (1977). In that study, rm was determined by measuring the time for the
voltage transient to reach 1 - 1/e of its steady-state value. Rall (1957) pointed out
how this method can lead to large underestimates of ~'m.
In Table I (values in parentheses), L and # were calculated by using Eqs. (4) and
(10) and the intercepts of the peeled exponentials from the logdV/dt versus t plots. As
mentioned above, the equations could be applied only to about half the cells, and the
values derived for L and o were somewhat smaller than those calculated by the
alternative method. It seems reasonable that this method for determining L and p is
least accurate when the denominator of the right-hand side of Eq. (10) is small. In
some cells, the data points may yield values for a~ that are influenced by the
coefficients of the higher-order terms, thus reducing the denominator in Eq. (10). In
the 12 cells for which this method was not used, a~ >_ 2ao.
The nonohmic behavior of the membrane in the hyperpolarized region should
have played a relatively minor role in these measurements. Care was taken to avoid
transients in which noticeable "droop" was present. Moreover, low-amplitude current
pulses or brief current pulses were used in most of the cells from which the data in
52
Johnston
Table I were tabulated. Johnston et al. (1980) reported a persistent inward current in
CA3 neurons that is activated at about - 4 5 mV. This voltage-dependent conductance
should not be significant, however, at membrane potentials more negative than about
- 5 5 mV, where all of the measurements were made.
Spontaneous synaptic input should not have significantly affected the results,
since data were not taken in the presence of noticeable synaptic input. Synaptic input
to the dendrites would tend to increase p. The p's calculated were smaller than those
found previously for spinal motoneurons (Rall, 1977) or neocortical neurons (Lux and
Pollen, 1966), and the possibility exists that measurements from neurons in intact
animals yield a larger p due to synaptic contamination. It is doubtful that slicing
shortens the dendrites of the pyramidal neurons, since they are oriented in the plane of
the slice, and all of our recordings were made from cells toward the center of the slices.
However, this possibility cannot be ruled out.
The electrode resistances used in this study were somewhat smaller than those
used by other workers (Schwartzkroin, 1975). The larger tip diameter may select for
the larger CA3 neurons. Certainly, it is likely that the neurons meeting the criteria for
acceptable data were the larger cells. Although it is possible that neurons with larger
cell bodies would yield smaller L and p values, no significant difference in electrotonic
structure between small and large motoneurons has been found (Burke and Ten
Bruggencate, 1971). In any event, our average L and p may have been biased toward
the larger cells.
Significance
For spinal motoneurons, L is between 1 and 2, and p is generally >5 (Rall, 1977).
From the results presented in this report, it can be concluded that CA3 neurons in
vitro are electrotonically shorter than spinal motoneurons. Without any assumptions
concerning neuron geometry, this can bc concluded by noting that the logV versus t
plots in Figs. 4 and 5 suggest a nearly single exponential decay and that the ratio of
rm/rl for most cclls is large. Therefore, most of the current injected into thc soma of a
CA3 ncuron flows across membrane that is electrically closc to the soma.
To obtain an appreciation for the comparison of electrotonic length between CA3
and spinal motoneurons, some simple calculations can be made for the prcdictcd
steady-statc voltage attenuation from the soma to thc tip of the dendrites in each typc
of neuron. For CA3 neurons, an electrotonic length of 0.95 implies that a 10-mV
signal at the soma would attenuatc to 6.7 mV at the tip of the dendrites ( H = coshL,
where H is the attenuation factor; see Jack et al. (1975, p. 73), and Pcrkcl and
Mulloncy, (1978)). For a spinal motoncuron with L = 1.5, a 10-mV signal would
attentuate to 4.2 mV at the tip of the dendrites. A seemingly small difference in
electrotonic length thcrcforc corresponds to a large difference in voltage attenuation.
The average membrane time constant of 23.6 ms for CA3 neurons suggests also
that the specific membrane resistivity is high. Assuming a membrane capacity of 1 ×
10 -6 F / c m 2, a valuc that has been dctcrmined for all biological membranes where
accurate measurements have been madc (Cole, 1968; Jack, 1979; Brown et al., 1981),
Cable Propertiesof HippocampalNeurons
53
the average specific membrane resistivity would be approximately 24,000 f~cm2, some
five times larger than that estimated for spinal motoneurons (Rall, 1977).
The small L and o for CA3 neurons implies that there may be little decrement in
synaptic charge from distal areas of the dendrites to the cell body. With this
suggestion in mind, it is interesting to speculate that dendritic spikes, which are
reputed to be prevalent in the hippocampal neurons (Fujita and Iwasa, 1977; Wong et
al., 1979), may play an integrative role or be involved with intrinsic firing behavior
instead of merely amplifying incoming synaptic inputs. The short L indicates also that
events occurring anatomically near the soma should be under good spatial control of
voltage during a clamp of the soma. For example, a cable of 5 #m diameter (probably
a low estimate for the main shaft of a CA3 apical dendrite; see Wong et al., 1979),
with R m 24,000 f~cm2 and internal resistivity of 70 f~cm (Rall, 1977), would have a
dc space constant of 2.1 mm (Xo = [(Rm/Ri)(d/4)] ~/2, Rail, 1977). The ac space
constant calculated at 100 Hz from the following equation (Steinbach and Stevens,
1976, p. 83),
=
2
]1/2
~'f= X° 1 + [1 + (27rfrm)2] ll2]
would be approximately 0.75 mm. In addition to the large length constants, the large
rm also makes it feasible to use the SEC system in these neurons (Johnston et al., 1980;
Johnston and Brown, 1981), since the membrane time constant is many times larger
than the time constant of a 30-M~2 electrode.
Rail (1969) derived equations for calculating the decay of current for a
voltage-clamp applied to a soma and finite cylinder. Using Eq. (32) of Rail (1969), the
average membrane time constant of 23.6 ms, and the average L of 0.95 for CA3
neurons, a time constant of 6.3 ms would be predicted for the passive current decay
following a step change in potential at the soma. For spinal motoneurons, a similar
analysis yields a predicted time constant for current decay of 3-4 ms. Although L is
larger for spinal motoneurons, rm is smaller. Therefore, in CA3 neurons, more of the
dendritic tree may be under voltage-clamp control than in spinal motoneurons, but the
passive decay of current following a step change in potential at the soma will take
about twice as long.
SUMMARY
1. The passive electrical cable properties of CA3 pyramidal neurons from guinea
pig hippocampal slices were investigated. Three neuron parameters were determined:
the membrane time constant, rm; the equivalent length of the dendrites, L;
and the dendritic to somatic conductance ratio, p.
2. Current steps were applied and the voltage transients recorded from 25 CA3
neurons, using a single intracellular microelectrode and a 3-kHz time-share system.
Two independent methods were used for estimating L and p. Both methods require
peeling two time constants from the logdV/dt versus t plots of the voltage transients.
3. The first method is similar to that used by Gorman and Mirolli (1972). It
Johnston
54
assumes a semi-infinite cable with lumped soma and uses the peak of log(~/T dV/dt)
as a function of T = t/~mto estimate p. L can then be calculated from a transcendental
equation given by Rall (1969), using the estimated P- When p is less than 5, this
method is reasonably accurate, although it yields an overestimate of p and L. The
average L was 0.96; the average p was 2.44.
4. The second method assumes a finite-length cable with lumped soma and is
derived for the first time in this paper. It is an exact solution for L and p, using the
slopes and intercepts of the first two peeled exponentials. This method could be used
on only 13 neurons, for reasons discussed in the text. The average L was 0.94; the
average p was 1.51. The results, using both methods, are in close agreement.
5. The average membrane time constant for all 25 CA3 neurons was 23.6 ms,
suggesting a large (23,600 ~cm 2) average specific membrane resistivity.
6. It is concluded that CA3 neurons are electrotonically short, especially when
compared to spinal motoneurons. The significance of these results is discussed with
respect to synaptic integration and to the application of voltage-clamp techniques to
the somata of these neurons.
ACKNOWLEDGMENTS
I thank Dr. W. Rall for many helpful suggestions after reading an early draft of
this manuscript, Dr. T. H. Brown for critical reading of the final version, Dr. W. A.
Wilson for help with the SEC, and Dr. J. J. Hablitz for assisting with some of the
experiments. I also thank Ms. Jan Bravo for technical assistance, Mrs. M. Ekeroot for
editing the manuscript, and Ms. Carol Shull for typing it.
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