Department of Physiology and Biophysics, School of Medicine, University of Washington, Seattle, Washington 98195
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ABSTRACT |
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Powers, Randall K. and Marc D. Binder. Summation of Effective Synaptic Currents and Firing Rate Modulation in Cat Spinal Motoneurons. J. Neurophysiol. 83: 483-500, 2000. The aim of this study was to examine how cat spinal motoneurons integrate the synaptic currents generated by the concurrent activation of large groups of presynaptic neurons. We obtained intracellular recordings from cat triceps surae motoneurons and measured the effects of repetitive activity in different sets of presynaptic neurons produced by electrical stimulation of descending fibers or peripheral nerves and by longitudinal vibration of the triceps surae muscles (to activate primary muscle spindle Ia afferent fibers). We combined synaptic activation with subthreshold injected currents to obtain estimates of effective synaptic currents at the resting potential (INrest) and at the threshold for repetitive discharge (INthresh). We then superimposed synaptic activation on suprathreshold injected current steps to measure the synaptically evoked change in firing rate. We studied eight different pairs of synaptic inputs. When any two synaptic inputs were activated concurrently, both the effective synaptic currents (INrest) and the synaptically evoked changes in firing rate generally were equal to or slightly less than the linear sum of the effects produced by activating each input alone. However, there were several instances in which the summation was substantially less than linear. In some motoneurons, we induced a partial blockade of potassium channels by adding tetraethylammonium (TEA) or cesium to the electrolyte solution in the intracellular pipette. In these cells, persistent inward currents were evoked by depolarization that led to instances of substantially greater-than linear summation of injected and synaptic currents. Overall our results indicate that the spatial distribution of synaptic boutons on motoneurons acts to minimize electrical interactions between synaptic sites permitting near linear summation of synaptic currents. However, modulation of voltage-gated conductances on the soma and dendrites of the motoneuron can lead to marked nonlinearities in synaptic integration.
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INTRODUCTION |
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The activity of a neuron is influenced by
transmitter release from thousands of presynaptic inhibitory and
excitatory contacts distributed throughout its dendritic tree. The net
effect of synaptic activity on the postsynaptic cell can be quantified
in terms of the total synaptic current reaching the soma [variously
referred to as "effective somatic current" (Redman
1976), "effective synaptic current" (Heckman and
Binder 1988
), and Isoma
(Bernander et al. 1994
)]. The amount of synaptic
current transferred to the soma from a given set of activated synapses
will be affected by concurrent transmitter release from other synapses
as a consequence of changes in the driving force for current flow at
the original synaptic sites and increases in membrane conductance at
the sites of the concurrently activated synapses. Both of these effects
are likely to lead to less-than-linear summation of the currents
produced by two separate sets of synapses (Jack et al.
1975
; Rall 1964
, 1967
). However, the
amount of synaptic current transferred to the soma also may be affected
by the presence of voltage-gated dendritic conductances
(Bernander et al. 1994
; Clements et al. 1986
) that can amplify synaptic currents (Schwindt and
Crill 1995
), possibly leading to greater-than-linear summation.
The widespread distribution of synaptic terminals on the dendritic tree
may help isolate synapses from one another, minimizing the occurrence
of nonlinear interactions. Indeed, measurements of summation of
monosynaptic Ia excitatory postsynaptic potentials (PSPs) in mammalian
motoneurons indicate that linear summation often is observed and
departures from linearity are relatively small (i.e., generally <10%)
(Burke 1967). Significant departures from linearity are
more common when excitatory and inhibitory PSPs are evoked concurrently
(Burke et al. 1971
; Rall et al. 1967
). In
these instances, the timing of the activation of the two inputs is
critical with the largest departure from linearity occurring when the
voltage change produced by the excitatory input encounters the
conductance change underlying the inhibitory input (Burke et al.
1971
; Rall et al. 1967
; Segev and Parnas
1983
).
The magnitude of the deviation from linear summation is likely to
depend both on the relative proximity of the two sets of synapses
(e.g., Rall 1964, 1967
; Rall et al. 1967
)
and on the extent to which the transfer of synaptic current to the soma
is modified by voltage-sensitive dendritic conductances
(Bernander et al. 1994
; Clements et al.
1986
). These two effects may compound the extent of nonlinear
summation or counteract one another. For example, a recent study of
summation of glutamate-evoked PSPs in cultured hippocampal neurons
reported linear summation that was independent of the relative spatial
location of the two inputs (Cash and Yuste 1998
). In
this case, linear summation resulted from the balanced activation of
voltage-sensitive dendritic conductances carrying inward and outward
currents in keeping with recent theoretical work (Bernander et
al. 1994
).
Most of the previous experimental work on synaptic input summation has
been restricted to measurements of PSPs produced by the transient
activation of two inputs. However, physiological activation of neurons
generally is achieved by repetitive discharge in presynaptic fibers.
Fortunately, repetitive activation of presynaptic afferents also
affords a more straightforward method of quantifying synaptic inputs
and their effects on the discharge of the postsynaptic cell (reviewed
in Binder et al. 1996). The steady-state synaptic current reaching the soma (IN) can be
measured with a modified voltage-clamp technique (cf. Heckman
and Binder 1988
; Lindsay and Binder 1991
;
Powers et al. 1992
), and synaptically evoked changes in
firing rate can be predicted from the product of this effective
synaptic current and the slope of the motoneuron's steady-state, firing frequency-current relation (f-I) (Powers
and Binder 1995
; Powers et al. 1992
).
The goal of the present study was to measure the effective synaptic
currents and the changes in motoneuron firing rate evoked by the
separate and concurrent activation of two distinct groups of
presynaptic neurons. We obtained intracellular recordings from cat
triceps surae motoneurons and measured the effects of repetitive activity in different sets of presynaptic neurons produced by electrical stimulation of descending fibers or peripheral nerves and by
longitudinal vibration of the triceps surae muscles (to activate
primary muscle spindle (Ia) afferent fibers) (Heckman and Binder
1988). We combined synaptic activation with subthreshold injected currents to obtain estimates of effective synaptic currents at
the resting potential (INrest) and at the
threshold for repetitive discharge
(INthresh). We then superimposed synaptic
activation on suprathreshold injected current steps to measure the
synaptically evoked change in firing rate. In some motoneurons, we
induced a partial blockade of potassium channels by adding
tetraethylammonium (TEA) or cesium to the electrolyte solution in the
intracellular pipette.
We studied eight different pairs of synaptic inputs. When any two
inputs were activated concurrently, both the effective synaptic currents (INrest) and the synaptically
evoked changes in firing rate were generally equal to or slightly less
than the linear sum of the effects produced by activating each input
alone. However, with partial blockade of potassium channels, persistent
inward currents were evoked by depolarization that led to instances of substantially greater-than linear summation of injected and synaptic currents. Portions of this work have been presented previously in
abstract form (Powers and Binder 1998; Powers et
al. 1991
) and in a symposium proceedings (Binder and
Powers 1999
).
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METHODS |
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Experimental preparation
The data presented here were obtained from experiments on 21 adult cats of either sex, weighing between 2.5 and 3.5 kg. Twelve of
these experiments were designed primarily to measure descending inputs
from the pyramidal tract (4 experiments), Deiters' nucleus (5 experiments), and the red nucleus (3 experiments) on triceps surae
motoneurons, and some of the results from these experiments have been
included in other, recent publications (Binder et al. 1998; Powers et al. 1993
; Westcott et al.
1995
). Details of the location and stimulation of these
descending fibers can be found in these publications, as well as
descriptions of our animal maintenance and surgical procedures (see
also, Heckman and Binder 1988
; Powers and Binder
1995
).
Animals were anesthetized with an intraperitoneal injection of
pentobarbital sodium (40 mg/kg), and supplemental intravenous doses
were administered throughout the surgical and experimental procedures
to maintain a deep level of anesthesia as judged by the absence of
withdrawal reflexes, a mean blood pressure below 140 mmHg and minimal
levels of synaptic noise during intracellular recordings. The
lumbosacral enlargement was exposed by a standard laminectomy from
L5 to S1, and the nerve to
the left medial gastrocnemius (MG) and the combined nerve to the
lateral gastrocnemius and soleus muscles (LGS) were exposed and left in
continuity with their respective muscles. In many of the experiments,
we also prepared the common peroneal (CP) or the sural (SN) nerves for
electrical stimulation by cutting the nerves distally and dissecting
them free for a length of ~1 cm. After these surgical procedures, the
animals were transferred to a rigid "Goteborg-type" frame, from
which they were suspended by clamps on the T4,
L4, and S2 vertebrae. The
left hindlimb was clamped at the knee and ankle in a position that
allowed a natural line of stretch of the triceps surae muscles via a
low compliance Dacron line between the Achilles tendon and our muscle
puller (Heckman and Binder 1988; Powers and
Binder 1985
). In the experiments in which descending pathways
were stimulated, we performed a craniotomy to allow placement of
bipolar stimulating electrodes in the contralateral pyramidal tract
(PT) (cf. Binder et al. 1998
), the ipsilateral Deiters'
nucleus (DN) (cf. Westcott et al. 1995
), or the
contralateral red nucleus (RN) (cf. Powers et al. 1993
).
Before initiating the intracellular recordings, the animals were
paralyzed with gallamine triethiodide and mechanically respired at a
rate adjusted to maintain end tidal CO2 between 3 and 5%. A bilateral pneumothorax was performed to increase recording stability. At the conclusion of the experiments, the animals were killed by administering a lethal dose of pentobarbital. Stimulation sites in the brain stem were confirmed by postmortem histological analysis as previously described (Binder et al. 1998
;
Powers et al. 1992
, 1993
; Westcott et al.
1995
).
Measurement and stimulation techniques
In 16 of the 21 experiments, we used glass capillary
microelectrodes filled with either 0.6 M potassium sulfate or 2 M
potassium citrate to obtain intracellular recordings from MG and LGS
motoneurons (identified by antidromic activation from their muscle
nerves). The tips of the electrodes were broken to obtain in situ
resistances of from 2 to 14 M. Only motoneurons with resting
potentials greater than
55 mV and antidromic action potentials with
positive overshoots were accepted for study. We measured the effects of
stimulating a number of different peripheral and descending inputs,
individually and in combination, on the motoneurons. Selective
activation of Ia afferent fibers was achieved by high-frequency,
low-amplitude (200 Hz, 150 µm peak to peak) longitudinal vibration of
the triceps surae muscles (Heckman and Binder 1988
;
Powers and Binder 1985
). The remaining inputs were
activated by 200-Hz bipolar electrical stimulation (0.1-ms pulse
width). The strength of stimulation of descending inputs was adjusted
to be supramaximal for the descending volley recorded at
L5. The SN was stimulated at five times the threshold for the appearance of a dorsal root volley, and the CP nerve
was stimulated at 5-10 times threshold.
In the other five experiments, we filled our electrodes with 100 mM of
the lidocaine derivative QX-314 to block voltage-gated sodium
channels and either 0.5 1 M tetraethylammonium (TEA) or 3 M
cesium chloride to block voltage-gated potassium channels. Our intent
was to observe how the activation of persistent inward currents
(Lee and Heckman 1996
, 1998a
,b
; Schwindt and
Crill 1977
, 1980a
-c
) and plateau potentials
(Hounsgaard and Kiehn 1985
, 1993
; Hounsgaard
et al. 1984
, 1988
) in the motoneurons would affect synaptic
integration. In these experiments, we combined steady-state Ia input
with simulated inhibitory or excitatory synaptic inputs produced by
injecting 1-s current steps through the recording microelectrode
(Poliakov et al. 1996
, 1997
; Powers and Binder 1996
; Reyes and Fetz 1993
). To simulate a
synaptic input as a change in conductance rather than a fixed-amplitude
current pulse, we operated the intracellular amplifier (Axoclamp 2B) in
the discontinuous current-clamp configuration with a switching rate of
7 kHz. This provided a record of motoneuron membrane potential that was
less subject to the effects of electrode capacitance and changing
electrode resistance than a continuous current-clamp recording in
bridge mode. The sampled membrane potential was sent to a separate
amplifier that multiplied the amplitude of the injected current pulse
by the difference between the membrane potential and a specified synaptic equilibrium potential [
80 mV for inhibitory PSPs (IPSPs) and 0 mV for excitatory PSPs (EPSPs)]. The output of this amplifier then was sent to the external current command input of the Axoclamp. Thus the amplitude of the simulated synaptic current varied with membrane potential just as a current produced by an actual change in
synaptic conductance does. (This procedure is identical to the reactive
current-clamp technique described in Hutcheon et al.
1996
.)
Membrane potential, injected current, the dorsal root and descending volleys, and a muscle length signal were all stored on VCR tape via a pulse code modulated digitizing unit. Membrane potential and injected current were digitized at 10 kHz using a MacAdios II data-acquisition board (GWI Instruments) for off-line analysis.
Experimental protocol
After a motoneuron was identified and judged acceptable by
measurement of the antidromic action potential and resting potential, we determined its rheobase by adjusting the magnitude of depolarizing, 50-ms injected current steps to be just threshold for action potential initiation (cf. Zengel et al. 1985). We then used our
modified voltage-clamp technique (Binder et al. 1998
;
Heckman and Binder 1988
; Lindsay and Binder
1991
; Powers et al. 1993
; Westcott et al.
1995
) to measure the effective steady-state synaptic current (IN) generated in the motoneuron by
two sources of synaptic input, both activated individually and in
combination. The basic protocol combined 1-s steps of injected current
with 1-s periods of high-frequency activation of synaptic inputs and is
illustrated in Fig. 1, A and
D. The onset of synaptic current occurred 500 ms later than the onset of injected current, so that there were three consecutive 500-ms epochs consisting of injected current alone, injected plus synaptic current, and synaptic current alone. Each combination of
injected and synaptic current was repeated four times to obtain an
average response. We measured the mean membrane voltage over the last
300 ms of epochs 1 and 2 (indicated in Fig. 1A) to obtain estimates of the voltage response to injected current alone
(Vi) and that to the combination of
injected and synaptic current (Vi+s), respectively. The steady-state synaptic potential
(
Vs) was taken as the difference
between these two estimates (Vi+s
Vi). We attempted to obtain average
responses to two different synaptic inputs acting alone and in
combination using several different subthreshold levels of injected
current. After these subthreshold measurements, we increased the level
of depolarizing current steps to produce steady repetitive discharge in
the motoneuron (e.g., Fig. 4). (This portion of the protocol could not
be done on those cells recorded with electrodes containing QX-314). Two
trials with injected current alone were alternated with two trials of injected plus synaptic current. In each trial, we calculated the steady-state firing rate as the mean rate over the last 300 ms of the
current step. The change in firing rate (
F) produced by the synaptic input was taken as the difference between the mean steady-state rate in response to synaptic plus injected current and the
mean steady-state rate for the four bracketing control (injected
current alone) trials. As in the case of subthreshold measurements, we
attempted to obtain the firing rate responses to two different synaptic
inputs individually and in combination using a number of different
levels of injected current to produce different background
("control") firing rates.
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Data analysis
We used the experimental measurements described above to derive
three additional parameters describing the effects of a synaptic input
on the motoneuron: the steady-state effective synaptic current measured
at rest (INrest), the effective input
resistance of the cell during the activation of a synaptic input
(RNsyn), and the effective synaptic
current at the threshold for repetitive discharge (INthresh).
INrest is taken to be equal in
magnitude and opposite in sign to the value of injected current
required to "clamp" the membrane potential at its resting value
during the combined application of injected and synaptic current
(Heckman and Binder 1988; Lindsay and Binder
1991
). This value was estimated by calculating a linear regression between Vi+s for a
particular synaptic input and injected current magnitude (Fig. 1,
B and E). INrest
is estimated as
1 times the zero-voltage intercept of this relation.
The slope of this relation represents the steady-state input resistance of the cell during synaptic activation
(RNsyn) and can be compared with the
slope of the relation between Vi and
injected current (Fig. 1, B and E, black lines
and black circles), that represents the steady-state input resistance
of the cell in the absence of synaptic activation
(RNss). Because the driving force for
synaptic current flow will be altered during repetitive discharge, we
also estimated the effective synaptic current at the threshold for repetitive discharge (INthresh) (cf.
Binder et al. 1998
; Powers and Binder
1995
; Powers et al. 1993
; Westcott et al.
1995
). In cases in which the steady-state synaptic potential
(
Vs) was depolarizing at rest and
showed no dependence on membrane potential (e.g., Fig. 1C),
we assumed a reversal potential of 0 mV and calculated INthresh as the product of
INrest and the ratio of the synaptic driving force during repetitive discharge to that at rest:
INthresh = INrest *
Vthresh/Vrest,
where Vrest is the resting membrane potential and Vthresh is the mean
membrane potential during repetitive discharge. As previously described
(cf. Powers and Binder 1995
), this latter quantity was
estimated by adding the product of the threshold current for repetitive
discharge (INthresh = 1.5 * rheobase) (cf. Kernell 1965
), and the cell's input
resistance during synaptic activation
(RNsyn) to the resting potential (i.e.,
Vthresh = Vrest + [Ithresh
* RNsyn]). Alternatively, in cases in which
Vs exhibited a significant dependence on
membrane potential (e.g., Fig. 1F), this dependence was
used to extrapolate the value of
Vs at
Vthresh. INthresh
was then estimated from Ohm's law as the ratio of
Vs and the input resistance during
synaptic current flow: INthresh =
Vs/RNsyn.
We compared the results obtained during concurrent activation of two different synaptic input systems to those expected based on simple linear summation of their individual effects, and we expressed any differences as a percentage of the expected result. We also tested for significant departures from linear summation of synaptic effects using paired t-tests. The measured effects of activating two synaptic inputs served as one variable and the linear sum of their individual effects as the other.
Potential sources of error
We restricted our analyses to motoneuron recordings that met the
following criteria: minimal drift of the resting potential (<5 mV)
over the course of the voltage-clamp measurements, minimal electrode
polarization during 1-s injected current steps, repeatable responses to
a given synaptic input, and in cases in which synaptically evoked
changes in firing rate were measured, regular repetitive discharge in
response to 1-s injected current steps. The last three criteria are
somewhat qualitative and involved selecting the best recordings in our
sample without regard to the degree to which the combined effects of
two inputs departed from the linear sum of their individual effects. We
corrected some of our records for electrode artifacts off-line by
measuring the difference in the voltage values before and after the
capacitative artifacts and subtracting this difference from the
digitized records. We have estimated previously that drifts in resting
potential and variability in synaptic responses are likely to be
associated with about a 15% uncertainty in our estimates of
INrest and that the additional
assumptions used to estimate INthresh
should be associated with an even larger degree of uncertainty
(Powers and Binder 1995). Measurements of synaptically
evoked changes in firing rate will be affected by slow changes in the
cell's repetitive firing capability. We attempted to minimize the
impact of these changes by bracketing the responses to injected and
synaptic current with control trials (i.e., responses to injected
current alone). Nonetheless significant changes in the cells repetitive
firing properties between the application of the different synaptic
inputs will contribute to the degree to which the combined effects of two inputs differ from the linear sum of their individual effects. These various sources of error could easily cause departures from linearity on the order of ±15-30% in individual cases but should not
have caused systematic deviations from linearity across the entire sample.
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RESULTS |
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We measured the effects of activating two different synaptic inputs in 28 triceps surae motoneurons (21 MG and 7 LGS). From this sample, we obtained a total of 28 comparisons of the effective synaptic currents produced by concurrent and separate activation of different input systems and 18 comparisons of synaptically evoked changes in firing rate. We typically combined Ia afferent input produced by triceps surae vibration with the activation of one of the descending systems [contralateral PT (n = 6), ipsilateral DN (n = 3), or contralateral RN (n = 2)] or with one of the other peripheral inputs [afferent fibers in the CP (n = 12) or SN (n = 2) ]. In three cases, we combined stimulation of a descending input with one of the other peripheral inputs (DN + CP, DN + SN, and RN + CP). The results in these cases were similar to those obtained with combinations of Ia afferents and other inputs.
In another 12 triceps motoneurons, we measured the effects of combining Ia afferent input produced by triceps surae vibration with depolarizing or hyperpolarizing "conductance steps" injected into the motoneuron to mimic steady-state EPSPs and IPSPs, respectively. In these cells, the microelectrode electrodes were filled with a solution containing 100 mM QX-314 to block voltage-gated sodium channels and with varying amounts of tetraethylammonium (TEA) or cesium (Cs) salts substituted for potassium to block potassium channels: (1 M K acetate and 1 M TEA acetate: 6 cells; 0.5 M TEA Cl and 2.5 M KCl: 2 cells, 3 M CsCl: 4 cells).
The results obtained without potassium channel blockers will be presented first followed by a description of the effects of the blockers.
Summation of effective synaptic currents
Figure 1 illustrates how we measured and evaluated the effective
synaptic currents (IN) generated by
two different input systems in the same triceps motoneuron. Figure 1,
left, shows the effects of activating Ia afferents alone
(green trace), pyramidal tract fibers alone (blue trace), and the two
inputs concurrently (red trace). Figure 1A shows the
averaged voltage responses to the different inputs, together with a
6.2-nA hyperpolarizing current step. The mean voltages calculated over
the last 300 ms of the period of combined injected and synaptic current
(Vi+s, marked by line 2 in the figure)
are plotted as a function of injected current magnitude in Fig.
1B. The responses to injected current alone
(Vi) are represented by the black
circles. As described in METHODS, the slopes of the
best-fit linear regression lines to the
Vi+s versus I relations
represent the effective input resistance in the presence of synaptic
input (RNsyn), whereas the fit to the
Vi versus I relation
represents the steady-state input resistance in the absence of synaptic
input (RNss). The values of
RNsyn were 96, 90, and 84% of
RNss for the Ia, PT, and Ia + PT
inputs, respectively, indicating that even when the two inputs were
activated concurrently a relatively modest change in input resistance
occurred. The magnitudes of the effective synaptic currents
(INrest), calculated as 1 times the
zero-voltage intercept of the fit to the
Vi+s versus I relations
(see METHODS) were 4.4 nA for the Ia input, 8.2 nA for the
PT input, and 11.0 nA for the combined inputs. In this case,
INrest measured for the combined
inputs was 87% of the sum of their individual effects, indicating
near-linear summation. Figure 1C shows the relation between
the magnitude of the steady-state synaptic potentials (
Vs, see METHODS) and
the background membrane potential
(Vi). Although the inputs were not
constant, they did not show a clear dependence on somatic membrane
potential. The synaptic currents flowing at threshold
(INthresh) therefore were estimated by
assuming a synaptic reversal potential of 0 mV and correcting for the
change in driving force from the resting potential to the mean membrane potential at threshold (see METHODS). The estimates of
INthresh were 3.9, 7.2, and 9.8 nA for
the Ia, PT, and Ia + PT inputs, respectively. Because the same
correction factor was applied in all three cases, the small departure
from linearity was the same as for the
INrest values.
As mentioned in the INTRODUCTION, less-than-linear
summation of effective synaptic currents could result from changes in
the driving force for current flow at the synapses, increases in the conductance of the membrane between the synapses and the soma or a
combination of the two factors. Thus departures from linearity might be
expected to be more prominent in cases in which one or both of the
synaptic inputs causes a large decrease in effective input resistance.
Figure 1, right, shows the effects of activating Ia
afferents alone (green), CP afferents alone (blue), and the two inputs
together (red) in a different motoneuron. Figure 1D shows
that the response to the combination of Ia and CP input is quite
similar to the response to the CP input alone. The CP input acting
alone and in combination with the Ia input causes a large reduction in
input resistance as can be seen from the Vi+s versus I relations
illustrated in Fig. 1E. The slope of this relation for the
Ia input (green line) is nearly parallel to that for
Vi versus I (black line),
as was the case in Fig. 1B. However, the slopes are
significantly lower for the CP (blue) and Ia + CP (red) inputs,
indicating decreases in input resistance of 30 and 42%, respectively.
The estimate of INrest for the Ia + CP
input is 5.6 nA, which is nearly identical to the value of
INrest for the CP input, and markedly different
from the expected linear sum of the Ia and CP effective synaptic
currents (
2.1 nA). The steady-state synaptic potentials produced by
the CP and Ia + CP inputs showed a strong linear dependence on membrane
potential (Fig. 1F), and this dependence was used to predict
the values of INthresh for these
inputs (see METHODS). The
INthresh value for the combined Ia + CP inputs (
13.1 nA) was close to the predicted linear sum of the
estimates for the individual inputs (2.8
13.1 =
12.0
nA), largely because the predicted Ia current was small.
Figure 2 illustrates the relations
between the estimates of effective synaptic current during combined
activation of two inputs versus the predicted linear sum of the
currents produced by each input alone. Each of the eight different
combinations of inputs we studied is denoted by a different symbol. The
filled symbols indicate cases in which the combined inputs caused a
decrease in steady-state input resistance <20%, whereas the open
symbols are cases in which a decrease 20% occurred. Figure
2A shows that the observed values of
INrest produced by combined activation of any two of these inputs are generally slightly below the predicted linear sum of their individual effects (The bold diagonal line is the
line of identity.) For the entire sample, the observed value was 76%
of the predicted linear sum (mean difference =
1.1 nA, paired
t = 3.16, P < 0.01). The mean
difference between observed and predicted effective synaptic currents
was similar for cases in which the combined inputs produced a >20%
decrease in input resistance and those in which the inputs produced a
smaller change in input resistance (
1.1 nA in both groups). However,
there was a weak but significant correlation between the percentage
resistance change (
RN) produced by
synaptic activation and the magnitude of the difference between the
measured and predicted effective synaptic currents
(INrest
INrestpr =
0.57 + 0.023 *
RN, r = 0.374, P < 0.05).
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The magnitude of the effective synaptic current at the threshold for repetitive discharge (INthresh) was estimated either by correcting INrest for the estimated change in synaptic driving force or from the measured voltage dependence of the steady-state synaptic potentials (see METHODS). Figure 2B illustrates the relation between the measured value of INthresh (i.e., that estimated from measurements taken during concurrent activation of 2 inputs) and the value predicted from the linear sum of the values estimated when each input was activated separately. The observed values of INthresh were, on average, 93% of those predicted from the linear sum of their individual values. There was no significant difference even when the sample was restricted to cases in which a large synaptically evoked change in input resistance occurred. It is possible that the increased measurement error associated with our estimates of INthresh (see METHODS) may have obscured a trend toward less-than-linear summation.
Contribution of presynaptic factors to less-than-linear summation
There are two types of presynaptic factors that can contribute to less-than-linear summation of concurrent synaptic inputs. If two polysynaptic pathways use some common interneurons, their concurrent activation may result in less-than-linear summation through occlusion. In the simplest example, if each pathway activated >50% of the common interneurons, then concurrent activation would produce a smaller effect on the target neuron than the linear sum of the individual inputs. Interneuronal occlusion was unlikely to have made a significant contribution to the pattern of results obtained here because monosynaptic Ia excitation was one of the inputs in all of the cases in which synaptically evoked changes in firing rate were measured and in all but three of the cases in which effective synaptic currents were measured.
The most likely presynaptic factor contributing to less-than-linear
summation is presynaptic inhibition of transmitter release. The most
common combination of synaptic input systems we used was activation of
Ia afferents from the triceps surae and afferents from the CP nerve (12 cases). The CP nerve includes afferent fibers that innervate the flexor
muscles tibialis anterior and extensor digitorum longus, and group I
afferents from flexor muscles often have been used to induce
presynaptic inhibition of Ia afferents from the triceps surae muscles
(Rudomin 1990).
To determine whether or not presynaptic inhibition might have contributed to the less-than-linear summation we observed during concurrent Ia and CP activation, we measured the composite Ia EPSP produced in a MG motoneuron by stimulating the synergist LGS nerve with and without a preceding conditioning train of three shocks (at 200 Hz) to the CP nerve at 10 times threshold. Figure 3A illustrates the synaptic potentials measured in the MG cell in response to stimulation of the CP nerve alone (gray trace), the LGS nerve alone (thin black trace), and the LGS nerve when preceded by stimulation of the CP nerve 45 ms earlier (thick black trace). The CP stimulation produces a large IPSP, and when the LGS stimulation is applied 45 ms later, the "area" (i.e., charge) of the "conditioned" monosynaptic EPSP was 30% less than that its "control" value. The difference can be seen more clearly in Fig. 3C, which shows the control EPSP (thin trace) and the conditioned EPSP (thick trace) after subtracting the CP response. However, virtually all of this 30% decrease in the EPSP area can be attributed to the conductance change associated with CP stimulation. Figure 3, B and D, shows the effect of CP stimulation on the amplitude and time course of the voltage response to a 1-ms injected current pulse. The CP stimulus produced a 30% reduction in the area of the response to the current pulse, suggesting that the reduction in the LGS EPSP produced by the preceding CP stimulus should be attributed to changes in the conductance of the postsynaptic cell. In the same motoneuron, the effective synaptic current added by the Ia input was reduced by 28% of its control value when the CP input was applied. These results suggest that presynaptic inhibition did not make a significant contribution to the nonlinearity in the summation of effective synaptic currents from Ia and CP inputs. Further, in the five trials in which stimulation of the contralateral PT produced mixed excitation and inhibition, its summation with Ia afferent input was also significantly less than linear. All of these results suggest that postsynaptic factors were primarily responsible for the observed less-than-linear summation of effective synaptic currents.
|
Differences in the summation of effective synaptic currents and steady-state PSPs
The deviations from linear summation we found for effective
synaptic currents from CP and Ia afferents were smaller than those for
the accompanying EPSPs and IPSPs. Activation of low- and high-threshold afferents in the CP nerve generally produced a PSP containing both
excitatory and inhibitory components with inhibition predominating. The
steady-state PSPs resulting from CP stimulation all exhibited a strong
dependence on somatic membrane potential with reversal potentials
ranging from +1.8 to 23.6 mV relative to the resting potential
(
5.9 ± 6.8 mV; mean ± SD). The somatic
depolarization produced by the Ia excitatory input (mean 4.1 ± 2.4 mV; range: 0.8-7.7 mV) thus would be expected to significantly
increase the driving force for inhibitory synaptic current flow. As a
result, the net depolarization added by a Ia EPSP should be reduced
significantly when it is superimposed on a CP IPSP. In contrast, when
the somatic membrane potential is clamped at the resting potential,
current flow through inhibitory synapses located on or electrotonically close to the soma should be unaffected by concurrent excitatory input.
The difference between summation of synaptic potentials and
effective synaptic currents can be seen in Fig.
4, A and B.
The amplitudes of the steady-state PSPs recorded during membrane
hyperpolarization (Fig. 4A) for the Ia, CP, and Ia + CP inputs were 4.6, 0.5, and 1.5 mV, respectively. The additional
depolarization produced by the Ia input when superimposed on the CP
input was 2.0 mV; equal to 43% of the depolarization it produced when
applied alone. The effective synaptic currents produced by the three
inputs were +4.3 nA for the Ia input,
2.5 nA for the CP input, and
0.2 for the combined input. The additional depolarizing current
supplied by the Ia input when it was concurrently activated with the CP input was 2.3 nA, which represents 54% of the current it supplies when
applied alone. A similar pattern was observed in the other 11 cases of
combined Ia and CP input. When activated at the resting potential
(i.e., in the absence of injected current), Ia activation applied in
combination with CP input produced an average additional depolarization
that was 32% of the depolarization it produced when activated alone.
In contrast, the effective synaptic current added by the Ia input
during CP activation was on average 56% of the amount produced during
Ia activation alone, representing significantly less deviation from
linear summation than that observed for the respective synaptic
potentials (paired t = 2.25, P < 0.05). Overall, during activation of other inputs, the Ia input
added 76% of the synaptic current it produced when activated alone
(vs. 58% of the depolarization it produced when activated alone).
|
Summation of synaptically evoked changes in firing rate
Measurement of the changes in discharge rate produced by synaptic
activity should reflect the effective synaptic current flowing at
threshold (INthresh) more accurately
than estimates based on INrest
(Powers and Binder 1995; Powers et al.
1992
) and also provides a more functionally relevant test of
the linearity of synaptic input summation. We measured both the
effective synaptic currents and synaptically evoked changes in firing
rate produced by separate and combined activation of two inputs in 16 motoneurons. Figure 4 illustrates the effects of repetitive activation
of Ia afferents (green traces), high-threshold afferents in the CP
(blue traces), and combined activation of the two inputs (red traces)
during the injection of subthreshold (A and B)
and suprathreshold (C and D) current steps. As
illustrated previously (Fig. 1, D and E), the CP
input, whether activated alone or in combination with Ia afferent
input, significantly decreased the measured input resistance. In
addition, the effective synaptic current
(INrest) produced by combined Ia and
CP input was less than their linear sum (Ia: 4.3 nA; CP
2.5 nA; Ia + CP
0.2 nA).
After collecting the subthreshold data (Fig. 4, A and
B), we repeated the synaptic activation during injection of
current steps of different magnitude. The black trace in Fig.
4C illustrates a 1-s epoch of repetitive discharge produced
by a 19.3-nA injected current step. On subsequent trials, we
superimposed Ia afferent input (green trace), CP input (blue trace), or
Ia + CP activation (red trace), starting 0.5 s after the onset of
current injection. Each synaptic input was applied twice at each level
of injected current and bracketed by control trials (injected current
alone). The synaptically evoked change in firing rate was calculated as the difference between the mean firing rate over the last 300 ms of the
injected current step during the synaptic activation trials and the
mean rate measured over the same portion of control trials. Figure
4D illustrates the time course of instantaneous discharge
rate during the synaptic activation trials after subtracting the mean
steady-state rate measured during bracketing control trials. The Ia
input produced an increase in discharge rate of 11.4 imp/s, the CP
input decreased the rate by 17.2 imp/s, and the combined input produced
a decrease in rate of 15 imp/s. Thus as was the case for summation of
effective synaptic currents (Fig. 4B), the synaptically
evoked change in firing rate produced by combined activation of these
two inputs was significantly less than the predicted linear sum of
their individual effects (15 vs.
5.8 imp/s).
As mentioned in the preceding text, the less-than-linear summation
observed during concurrent activation of the Ia and CP inputs may have
resulted in part from the fact the depolarization produced by the
monosynaptic Ia excitatory input increased the driving force for
synaptic current flow through the inhibitory synapses activated by CP
stimulation. Our voltage-clamp protocol should minimize these changes
in driving force for somatic synapses but would have less effect on
electrotonically remote synapses. Increased membrane depolarization
during repetitive discharge also should produce an increase in the
driving force for CP synaptic currents. Because the threshold for spike
initiation and the mean level of membrane depolarization increase with
increasing firing rate (Schwindt and Crill 1982), the
effects of CP stimulation might be expected to increase with the
background discharge rate of the motoneuron. Figure
5 shows one example in which the decrease in firing rate produced by CP stimulation increased with the background discharge rate of the motoneuron. When the background discharge rate of
the motoneuron was 20.7 imp/s (Fig. 5A), the CP input produced a decrease in firing rate of
7.1 imp/s (gray lines), whereas
the same input decreased firing rate by
9.0 imp/s when the background
firing rate was 27.2 imp/s (Fig. 5B). The effects of Ia
input on firing rate (dashed lines) were the same at the two different
background discharge rates (6.9 and 6.7 imp/s). At both background
discharge rates, the effects of combined Ia and CP input (thick solid
lines) was less than the expected linear sum of the effects of the
individual inputs (at 20.7 imp/s, observed changed of
2.7 imp/s vs.
predicted change of
0.2 imp/s; at 27.2 imp/s observed change of
4.1
imp/s vs. predicted change of
2.3 imp/s).
|
The example presented in Fig. 5 suggests that even though the decrease in firing rate produced by an inhibitory synaptic input may vary with the background discharge rate of the motoneuron, less-than-linear summation occurs at different background discharge rates. Although we generally only tested input summation at one or two different background discharge rates, in six motoneurons we were able to examine summation at three or more different firing rates. Figure 6 illustrates one such case, in which the effects of Ia and CP synaptic inputs were examined over a wide range of background discharge rates (~10-80 imp/s). The decrease in firing rate produced by the CP input (filled triangles vs. control, open circles) tended to be largest at the highest background discharge rates. As a result, the slope of the frequency-current relation in the presence of the CP input was lower than that of the control frequency-current relation (1.41 vs. 1.75 imp/s), although this difference did not reach statistical significance (t = 1.83, df = 81, P > 0.05). Nonetheless, regardless of the background firing rate, combined activation of the Ia and CP inputs (asterisks) produced a change in firing rate close to that produced by the CP input alone and less than that expected from the linear sum of the Ia and CP effects.
|
Figure 7 illustrates the relation between
the observed changes in firing rate during concurrent activation of two
inputs and the predicted linear sum of the effects of each input alone
(n = 18). Less-than-linear summation of synaptically
evoked changes in firing rate was observed commonly (14 of 18 points
fell below the line of identity). The observed change in firing rate
during concurrent activation of two inputs was on average 77% of the predicted linear sum (observed predicted =
2.6 imp/s,
paired t =
3.43, P < 0.01).
Less-than-linear summation was observed both in the cases in which the
combined input caused a relatively small change in input resistance
(filled symbols: observed
predicted =
2.1 imp/s) and
those in which it caused a large change in input resistance (open
symbols; observed
predicted =
2.7 imp/s), although the
deviation from linearity failed to reach statistical significance in
the subdivided data sets. As was observed for the summation of
effective synaptic currents at rest, the magnitude of the difference
between the observed and predicted changes in firing rate was
correlated with the change in input resistance (
RN) produced by the synaptic
activation (
F
Fpr = 0.69 + 0.073 *
RN, r = 0.633, P < 0.01).
|
Summation of synaptically evoked changes in firing rate also should be
more linear than would be expected from PSP summation. During
repetitive discharge, the spike-generating conductances are much larger
than the synaptic conductances, which exert only minimal effects on the
trajectory of the somatic membrane potential (Schwindt and
Calvin 1973). Thus the presence of repetitive firing reduces
the change in the mean somatic membrane potential that otherwise would
be produced by excitatory inputs (Koch et al. 1995
;
Schwindt and Crill 1982
). This means that inhibitory
current flow through synapses located on or close to the soma will be relatively unaffected by activation of excitatory synapses as discussed
above. This view is supported by our finding that the average increase
in firing rate produced with Ia input was applied in combination with
CP input was 64% of that produced when Ia input was applied alone,
which is twice that predicted from PSP summation (32%).
Voltage-dependent amplification of effective synaptic currents after partial blockade of potassium channels
Although the less-than-linear summation described in the preceding
text is consistent with the nonlinear interactions expected in passive
membranes, these results do not rule out the presence of active
conductances that, under certain conditions, may lead to
greater-than-linear summation. Voltage-dependent amplification of
synaptic current is seen in motoneurons recorded in decerebrate cats
due to the activation of a persistent inward current (Bennett et
al. 1998; Lee and Heckman 1996
, 1998b
). This
effect may depend on the suppression of certain potassium conductances
because pharmacological blockade of potassium channels with internal
TEA can lead to amplification of synaptic inputs (Clements and
Redman 1986
). In 12 cells, we measured the interaction of
injected current and effective synaptic currents produced by repetitive
activation of Ia afferents in the presence of internal TEA or cesium.
Voltage-dependent amplification of Ia input occurred in 10 of these
cells, resulting in a clear increase in the amplitude of the
steady-state Ia synaptic potential once a critical level of
depolarization was reached.
Figure 8 illustrates an example of this
voltage-dependent amplification in an LGS motoneuron impaled with an
electrode containing QX-314 and TEA. Figure 8A illustrates
the averaged voltage responses (top) to muscle vibration in
combination with 6, +6, and +9.5 nA of injected current
(bottom). The amplitude of the steady-state Ia synaptic
potential (
Vs) clearly is increased
when muscle vibration is superimposed on the depolarization produced by
the +6-nA injected current step (middle). The initial
response to muscle vibration (right horizontal arrow) is similar in
amplitude to that seen at the hyperpolarized membrane potential. This
is followed by an increase in depolarization over the next 30 ms (see
inset, bottom) leading to a steady-state synaptic potential
amplitude that is nearly twice that obtained at the hyperpolarized
membrane potential. A further increase in the magnitude of depolarizing injected current leads to amplification before the onset of muscle vibration (left horizontal arrow). The additional depolarization produced by muscle vibration is quite small in this case. The membrane
potential thus appears to be "clamped" at a more depolarized level
as previously reported for plateau potentials obtained in the
decerebrate cat preparation (Hounsgaard et al. 1984
,
1988
).
|
Figure 8B illustrates the relation between the amplitude of
the injected current and the change in voltage produced by injected current alone (Vi; circles) and
injected plus synaptic current (Vi+s;
squares) for a set of responses obtained from 11 to 16 min after
impalement. For hyperpolaring currents, the slopes of the linear fits
between injected current and Vi+s and Vi are nearly identical (2.27 and 2.30 M, respectively), indicating that over this range of membrane
potentials the activation of Ia afferents does not produce a detectable
change in steady-state input resistance. Similar findings were obtained
in the other 11 cells recorded with TEA- or Cs-containing electrodes:
the average value of RNsyn was
2.37 ± 1.68 M
, which was not significantly different from that
of RNss (2.20 ± 1.39 M
;
paired t value = 1.35, P = 0.203). In
contrast, under control conditions, Ia input caused a slight but
statistically significant increase in input resistance
(RNsyn = 1.15 ± 0.62 M
,
RNss = 1.00 ± 0.53 M
,
n = 25, paired t =4.35, P < 0.01). In the presence of potassium channel blockers, both the average
RNsyn and
RNss values were significantly higher
than comparable values for the control sample (t values of
3.25, P < 0.01 and 3.82, P <0.01). These
findings suggest that internal TEA or Cs leads to a decrease in a
resting potassium conductance (see also Campbell and Rose
1997
). The presence of QX-314 also may have contributed to the
increase in steady-state input resistance of blocking
Ih (Perkins and Wong
1995
). Simulations based on a cable model of the motoneuron
with the conductance mediating Ih
present on both the soma and dendrites (Powers and Binder
1998
) suggest that the presence of
Ih leads to a decrease in
RNss and to a value of
RNsyn that is greater than
RNss.
The steady-state amplitude of the Ia synaptic potential exhibited a
steep dependence on membrane potential, first increasing as the
membrane was depolarized from the resting potential and then decreasing
sharply once a critical level of depolarization was reached. Figure
8C illustrates this relation for the same LGS cell. The
filled circles represent synaptic potentials recorded from 11 to 16 min
after impalement when the resting membrane potential remained fairly
stable (61.2 to
60.7 mV). The peak amplitude of the steady-state
synaptic depolarization was 10.6 mV, which was 2.8 times greater than
the mean amplitude recorded at hyperpolarized membrane potentials. For
the 10 cells in which voltage-dependent amplification occurred, the
maximum amplitude of the steady-state synaptic potential ranged from
1.6 to 7.3 (mean = 2.8 ± 1.8) times greater than the
amplitude recorded at membrane potentials equal to or less than the
resting potential. The synaptic current flowing during maximum
amplification could be calculated by dividing the steady-state synaptic
potential amplitude by RNsyn (see
METHODS). This estimated value ranged from 0.6 to 5.1 (mean = 2.3 ± 1.5) times greater than the synaptic current
estimated at the resting potential.
The development of distinct plateau potentials generally occurred
within 5 min after impalement and did not require long depolarizing current pulses. The same relation between membrane potential and the
amplitude of the synaptic potential generally was seen during the
entire time course of the recording, as illustrated by the different
symbols in Fig. 8C, which show responses obtained before (upward triangles) and after (inverted triangles) the data presented in
Fig. 8, A and B. However, the membrane potential
generally depolarized during the course of the recording period, and in the cell of Fig. 8, the resting membrane potential varied from 66.5
mV at the beginning of the recording period to
56.4 mV at the end. If
the resting potential is assumed to depend on the relative magnitudes
of currents flowing through a resting potassium conductance with a
reversal potential of
80 mV and through a nonspecific,
impalement-induced shunt conductance with a reversal potential of 0 mV,
then this progressive depolarization may reflect an increasing block of
the resting conductance, an increasing impalement leak, or a
combination of the two effects (cf. Campbell and Rose
1997
). However, if a progressive block of the resting conductance was the predominant factor, then an increase in
RNss would be expected, whereas an
increased shunt conductance would lead to a decrease in the value of
RNss. In five cells in which the
membrane potential exhibited
5 mV of depolarization over the
recording period, the input resistance tended to increase on average
(15 ± 23%; range
8 to +51%), suggesting that an increasing block of the resting leak conductance predominated over changes in
shunt conductance. A progressive block of the conductance mediating Ih also would be expected to increase
the input resistance.
The time-dependent changes in resting potential and input resistance probably reflect an increasing block of dendritic channels as TEA (or Cs) and QX-314 diffuse from the presumed somatic site of impalement. This increasing block was associated with a lower voltage-threshold for the onset of the plateau as well as a slower decay of the amplified response to the synaptic and/or injected current input. Figure 9 illustrates examples of this time-dependent change in responsiveness in two different motoneurons. The thin black trace in Fig. 9A is the response to the combination of a 7.7-nA step of injected current combined with muscle vibration, obtained ~6.5 min after the cell was impaled with an electrode containing 0.1 M QX-314 and 1 M TEA. The initial depolarization represents the response to the injected current alone and exhibits no sign of voltage-dependent amplification. However, within 10 ms of the onset of muscle vibration, the membrane potential quickly depolarizes to a level that is 11.4 mV above the steady-state depolarization produced by injected current alone, so that the steady-state synaptic potential amplitude is over twice that obtained at more hyperpolarized membrane potentials. At the end of the injected current step, the response to muscle vibration alone is initially greater than that obtained at hyperpolarized membrane potentials but decays over the next 500 ms so that the membrane potential reaches the "control" level just before the offset of vibration. The green trace is the next response to the identical set of stimuli, obtained ~5 s later. The time course of depolarization produced by current alone and vibration plus current is nearly identical to that in the previous response, but there is less decay of the membrane potential after the offset of the current step. In the following response (blue trace), the injected current alone produces a plateau potential, so that the addition of muscle vibration produces very little additional depolarization. The sustained response to muscle vibration alone (last 300 ms) is larger than the previous two responses and also decays more slowly back to the resting potential after the offset of muscle vibration. The thick black and red traces are two consecutive responses to the combination of muscle vibration and a slightly smaller (7.4 nA) injected current step, obtained ~1.5 min later. The resting membrane potential depolarized by ~3 mV and the decay of the depolarization after the offset of muscle vibration is slower.
|
Plateau potentials generally decayed within a few hundred milliseconds
after the end of stimulation except in a few cases in cells impaled
with electrodes containing 3 M Cs. Figure 9B shows examples
of plateaus evoked by a 2.5-s, 8.9-nA current step 33-42 min after
impalement with a Cs-containing electrode. The initial voltage response
to the current step (green trace) declined back to the resting
potential within ~0.5 s after the offset of the current. Six minutes
later the voltage response to the same injected current step (blue
trace) remained at a depolarized level for 15 s after the offset of
the current step, and the subsequent response (red trace) exhibited a
voltage plateau lasting 30 s after current offset. The black trace on
the right is a response to the same stimulus obtained 2.5 min later,
and in this case, the voltage plateau could be terminated only by
applying a hyperpolarizing current step. This stable plateau state
indicates that potassium currents have been blocked sufficiently to
lead to a region of net inward current in the cell's steady-state
current-voltage (I-V) relation (cf. Schwindt and
Crill 1980c).
Time-dependent variations in the degree of channel block made it
difficult to determine the voltage threshold for the plateau onset. The
insets in Figs. 8A and 9A show the
plateau onset in response to either the injected current alone or the
combination of injected and synaptic current. In the example presented
in Fig. 8A, the plateau threshold for the response to
injected current alone (solid line) is ~2 mV higher than for the
response to injected plus synaptic current (dashed line). For the set
of responses illustrated in Fig. 9A, the plateau thresholds
(marked by arrows in the inset) of the responses to injected
plus synaptic currents exhibited about a 2.5-mV range that included the
voltage threshold for the plateau onset in response to injected current
alone. It was not always possible to obtain reliable estimates of the
voltage thresholds for plateaus evoked in response to both injected
current alone and injected plus synaptic current. For five cells in
which both measurements could be obtained, their values did not differ significantly (paired t = 0.240, P = 0.82). For the entire sample of cells, the mean threshold values for
activating the plateau potentials were similar for injected current
alone and injected plus synaptic current [49.0 ± 4.2 mV
(n = 6) and
48.2 ± 5.4 mV (n = 9), respectively]. The development of block of sodium channels by
QX-314 also exhibited considerable variation between cells. In eight
cells, we were able to estimate the voltage threshold for spike
initiation during the initial measurement of rheobase before the action
potential was significantly attenuated. The onset of the spike was
determined as the voltage at which its first derivative first exceeded
10 mV/ms (cf. Brownstone et al. 1992
). The mean voltage
threshold for spike initiation was slightly more depolarized
(
45.9 ± 2.7 mV) than the plateau thresholds, but paired
comparisons of threshold values revealed no significant differences
between the spike threshold and the plateau threshold in response to
either injected current alone or injected plus synaptic current.
The similarity of the voltage thresholds for plateau initiation in
response to injected current alone and injected plus synaptic current
suggests that a significant proportion of the channels contributing to
voltage-dependent amplification are located close to the somatic
recording site. However, inferences about the precise spatial
distribution of the channels are limited by the potential errors in the
estimates of plateau thresholds. An alternative approach is to compare
amplification of steady-state Ia synaptic potentials with that of
potentials produced by a simulated, somatic excitatory conductance.
Because Ia afferent terminals are distributed widely over the dendritic
tree (Burke and Glenn 1996), dendritic channels
contributing to amplification would be expected to have a more marked
effect on Ia synaptic potentials than on potentials produced by a
somatic conductance change. We compared amplification of Ia input with
that of a simulated somatic excitatory conductance (see
METHODS) in three cells impaled with TEA-containing
electrodes. Figure 10A
illustrates results from one of these cells. In this case, the
steady-state amplitudes of the synaptic potentials produced by a
simulated excitatory conductance (blue traces) and by muscle vibration
(green traces) were similar both at the original resting potential
(bottom traces) and after subsequent depolarization (top traces). At the depolarized potential, both responses
are amplified and are followed by a slow decline of membrane potential after the offset of the synaptic input. In one of the other cells, the
response to the Ia input appeared to be amplified to a greater degree
than the response to the somatic conductance and in the remaining cell,
neither response was amplified. A more systematic comparison of the
amplification the two types of responses is warranted because computer
simulations (Powers and Binder 1998
) suggest that the
relative degree of amplification of dendritic and somatic inputs can
help distinguish between different spatial distributions of the
responsible channels.
|
The pattern of voltage-dependent amplification observed after partial
block of potassium channels suggests that summation of synaptic
potentials can range from sublinear to supralinear depending on the
background membrane voltage. For example, the dependence of Ia
steady-state synaptic potential amplitude on membrane voltage
illustrated in Fig. 8C suggests that the combined depolarization produced by two excitatory synaptic potentials might be
near the linear sum of their individual effects at hyperpolarized membrane potentials, greater-than-linear at slightly more depolarized potentials and less-than-linear at potentials more depolarized than
about 50 mV. Voltage-dependent changes in the pattern of summation
also were observed when a simulated somatic inhibitory conductance was
combined with Ia input. Figure 10B illustrates responses of
a motoneuron to a 3.3-nA depolarizing current step in combination with
muscle vibration (green), a somatic inhibitory conductance (blue), or
concurrent activation of both inputs (red). The additional
depolarization produced when the Ia input is superimposed on the
inhibitory input is 2.8 mV, which is only 26% of the depolarization it
produces at this background membrane potential in the absence of the
inhibitory conductance. This marked degree of sublinear summation
results from the fact that the hyperpolarization produced by the
inhibitory input brings the membrane potential out of the region over
which amplification of the excitatory input can occur. In contrast, the
inhibitory input can have the opposite effect at more depolarized
membrane potentials. Figure 10C shows that under these
conditions, the Ia input alone produces very little additional
depolarization (0.7 mV), whereas in the presence of the inhibitory
input the Ia input adds 5.2 mV of depolarization, which is close to the
depolarization that the Ia input produces when it is applied alone at
the resting potential (5.8 mV). Figure 10D shows the
dependence of synaptic potential amplitude
(
Vs) on membrane potential
(relative to the resting potential) for the Ia input alone (green), the
inhibitory conductance (blue), and their combination (red). When the Ia
input is applied alone, the synaptic potential amplitude exhibits the
typical dependence on membrane potential (cf. Fig. 8C). In
contrast, when it is superimposed on an inhibitory conductance, the
additional depolarization it produces is relatively independent of the
background membrane potential.
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DISCUSSION |
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The present results indicate that when two sources of synaptic input are activated concurrently in the absence of potassium channel blockade, their combined postsynaptic effects on cat spinal motoneurons are generally slightly less than those predicted from the linear sum of their individual effects. This was true for measurements of both effective synaptic currents and for synaptically evoked changes in motoneuron firing rate. In contrast, when channel blockers were included in the intracellular electrodes, greater-than-linear summation occurred. Our discussion of these findings will be divided into four parts. First, we will compare our findings to those reported in previous studies of synaptic input summation. Next, we will compare the voltage-dependent amplification seen in the presence of internal channel blockers with that associated with high endogenous or exogenous levels of serotonin, noradrenalin and their agonists. We subsequently will consider the implications of these findings for the utility of measurements of effective synaptic currents and changes in motoneuron firing rate. Finally, we will review briefly the possible dendritic mechanisms contributing to synaptic integration.
Previous studies of synaptic input summation
Much of the previous work on summation of synaptic inputs in
motoneurons has focused on the interaction of PSPs evoked by single
volleys in different sets of presynaptic fibers. EPSPs produced by
combined stimulation of different sets of Ia afferents are generally
within 10% of the expected linear sum of the effects of each set
(Burke 1967). This result is consistent with the fact that Ia boutons are distributed widely across a very large dendritic tree and account for a relatively small percentage of the total input
to motoneurons (Burke and Glenn 1996
; Lev-Tov et
al. 1983
; Segev et al. 1990
). Although there has
been less systematic study of the interaction between Ia EPSPs and
IPSPs produced by different sets of afferents, summation is often close
to linear and large departures from linearity are relatively rare
(Burke et al. 1971
; Rall et al. 1967
).
In the present study, the steady-state depolarization produced in a
motoneuron by repetitive activation of Ia afferents in the presence of
concurrent activation of CP afferents was on average 32% of that
produced during activation of Ia afferents alone. The greater departure
from linearity observed under our experimental conditions can be
attributed to the different effects of transient versus steady-state
synaptic inputs. The low-pass filtering properties of dendrites
(Jack et al. 1975) cause the transient depolarization produced by an excitatory dendritic input to decay rapidly with distance. Thus transient EPSPs will only affect the driving forces operating at concurrently activated synapses if they are in close proximity to the source of the EPSP. In addition, the increase in
membrane conductance produced by transient activation of one set of
synapses will only reduce the transfer of synaptic current from another
set of synapses if the current passes by the "active patch" of
dendritic membrane during the brief conductance change (Burke et
al. 1971
; Rall et al. 1967
; Segev and
Parnas 1983
). Because both of these restrictive conditions are
relaxed by repetitive synaptic activity, greater departures from linear
summation are to be expected.
Comparisons of the effects of neuromodulators and internal channel blockers on synaptic integration
A number of recent studies suggest that active conductances in
motoneuron dendrites can affect the transfer of synaptic current to the
soma and that these conductances are under neuromodulatory control. The
amplitude of somatically recorded current produced by glutamate
iontophoresis onto the dendrites of turtle motoneurons is altered by
the extracellular application of channel blockers and neuromodulators
(Skydsgaard and Hounsgaard 1994, 1996
). The evidence for
the presence of active dendritic conductances in mammalian motoneurons
is less direct but compelling nonetheless. After the intrathecal
administration of a noradrenergic
-1 agonist, the synaptic current
evoked by repetitive activation of Ia afferents is smaller at the
resting potential than when the somatic voltage is clamped at a
depolarized level (Lee and Heckman 1996
). Under current-clamp conditions in decerebrate cat preparations with a high
level of endogenous neuromodulators, the activation of a persistent
inward current produces a depolarizing plateau (Hounsgaard et
al. 1988
), and the somatic voltage threshold for this plateau is reduced during tonic activation of Ia afferents (Bennett et al. 1998
), again supporting a dendritic location for the
responsible channels.
The dendritic conductances supplying inward current normally may be
counteracted by voltage- and/or calcium-activated dendritic potassium
conductances. Monoaminergic neuromodulators have been shown to reduce
calcium-activated potassium conductances, a resting potassium leak
conductance, and a hyperpolarization-activated mixed-cation conductance
in a variety of types of motoneurons (reviewed in Binder et al.
1996). Serotonergic terminals also have been shown recently to
be localized primarily on motoneuron dendrites (Alvarez et al.
1998
). Thus the effects of neuromodulators may be mediated
largely by their action on dendritic potassium and mixed-cation
conductances. For this reason, it is not surprising that the effects of
internally applied potassium channel blockers on motoneuron behavior
seen here are qualitatively similar to those of neuromodulators. In
both cases, there is voltage-dependent amplification of synaptic input
starting at voltages slightly depolarized to the resting potential.
Quantitative differences may arise due to the different spatial
distributions of the modulation of channel behavior: potassium channel
blockers diffusing from the somatic site of electrode impalement should
have the most marked effect on proximally located channels, whereas the
widespread distribution of serotonergic terminals (Alvarez et
al. 1998
) suggests that exogenous neuromodulators may exert
more spatially uniform effects on dendritic channels. Further
differences could arise if neuromodulators modify the behavior of the
channels carrying the persistent inward current.
Predictions based on measurements of effective synaptic currents and firing rates
In the absence of channel blockers, we found that the summation of both effective synaptic currents and synaptically evoked changes in firing rate exhibit smaller departures from linearity than would be expected based on the summation of synaptic potentials. This result is a consequence of our restricting the membrane potential of the soma to a fairly narrow range of values both during measurements of effective synaptic current and during repetitive discharge. This procedure ensured that changes in the driving force for synapses that are located on or near the soma were quite small. During concurrent activation of two sets of synaptic inputs, both the effective synaptic currents and evoked changes in firing rate are correlated with the expected linear sum of the effects of each input. Although there are systematic departures from linearity, the differences between the observed and expected results are relatively small; the effective synaptic current produced by two inputs is on average 1.1 nA or 26% less than predicted and the evoked change in firing rate is 2.6 imp/s or 23% less than predicted.
An alternative measure of the degree of nonlinearity can be obtained by
comparing the amount of effective synaptic current or the increase in
firing rate produced by activating Ia afferents alone and in
combination with one of the other inputs. The effective synaptic
current added by Ia afferent activation in the presence of another
input was on average 76% of that produced when Ia afferents were
activated alone, and the comparable figure for the synaptically-evoked change in firing rate was 78%. These findings suggest that predictions of motoneuron pool output based on the assumption of linear summation of inputs (e.g., Heckman and Binder 1991) will be
reasonably accurate when synaptic inputs with magnitudes comparable
with those previously characterized are considered (i.e., effective
synaptic currents of ±10 nA) (rev. in Binder et al. 1996
,
1998
). However, synaptic inputs required to produce maximum
output of the motoneuron pool are likely to be up to an order of
magnitude larger than those studied to date so that nonlinear summation
is likely to play a more significant role when large force outputs are considered.
Both the summation of synaptic currents and their effects on motoneuron
firing rate are likely to depend on the state of active dendritic
conductances. However, the presence of these conductances does not
necessarily invalidate our simple model of the effects of synaptic
inputs on firing rate. Our prediction of the effects of synaptic
current on firing rate is based on an estimate of the effective
synaptic current flowing during repetitive discharge (INthresh). In dendrites with
significant voltage-activated inward currents,
INthresh will be greater than the
current measured at the resting potential
(INrest). Nonetheless the predicted
change in firing rate (F) produced by this amplified
current is still the product of
INthresh and the f-I slope,
and this prediction has been shown recently to hold for neocortical
pyramidal cells even though persistent inward currents on the dendrites
amplify the effective synaptic current in a voltage-dependent manner
(Schwindt and Crill 1996
).
The effects of amplification of synaptic currents may depend both on
the strength of the synaptic input and on the voltage range over which
the persistent, inward dendritic currents are activated
(Lipowsky et al. 1996). If the dendritic voltages
reached during combined synaptic activation and repetitive discharge
already lead to near maximal activation of these inward currents, then further changes in depolarization associated with increasing firing rates may not lead to any further amplification. In contrast, if
individual excitatory synaptic inputs produce a level of dendritic depolarization that is subthreshold for activation of a persistent inward current but in combination produce a suprathreshold
depolarization, then their combined effective synaptic current and
effects on firing rate will be greater than the linear sum of their
individual effects.
Dendritic mechanisms contributing to synaptic integration
We have initiated computer simulations of our experimental
observations on the effects of internal channel blockers on synaptic integration (Powers and Binder 1998). Our modeling
results are consistent with a broad distribution of synaptic boutons
and voltage-activated conductances on motoneuron dendrites. However,
the experimental results do not tightly constrain either the
distribution of synaptic inputs or the magnitude and distribution of
active dendritic conductances. Previous experimental work suggests that
the density of the leak conductance may be lower on the dendrites than
on the soma (Clements and Redman 1989
; Fleshman
et al. 1988
). However, the data are consistent with either a
step increase in specific membrane resistance from the soma to the
dendrites (i.e., a step decrease in the leak conductance) or a
monotonic increase in resistivity from the soma to the distal dendritic
branches. Assuming that part of the effects of the internal potassium
channel blockers are on a potassium leak conductance, the relatively
rapid effects of the blockers that we observed here are consistent with
the idea that a significant proportion of the blocked channels must be
close to the presumed somatic recording site. However, both direct
dendritic recordings and combined experimental and simulation studies
in other types of neurons suggest that there is a distally increasing
density of both leak (Redman et al. 1987
; Stuart
and Spruston 1998
) and voltage-activated channels
(Hoffmann et al. 1997
; Stuart and Spruston 1998
) in these cell types.
An accurate description of the spatial distribution of dendritic
conductances in motoneurons will probably have to await
immunocytochemical localization of identified channel subtypes. (e.g.,
Westenbroek et al. 1998). However, our preliminary
simulations (Powers and Binder 1998
) suggest that a
systematic comparison of the voltage-dependent amplification of Ia
input with that of a simulated somatic conductance may help distinguish
between different spatial distributions of the conductance mediating
the persistent inward current.
The functional role of these dendritic conductances is unclear at present. Their effects on motoneuron behavior will no doubt depend on their spatial distribution, voltage sensitivity, and response to neuromodulators. In the absence of channel blockers, we found that the summation of effective synaptic currents is qualitatively similar to the summation of synaptically evoked changes in firing rate. This suggests that under these experimental conditions, the contribution of voltage-sensitive dendritic conductances to the transmission of synaptic currents to the soma is similar under subthreshold and suprathreshold conditions. It remains to be determined whether or not this similarity holds under experimental conditions in which the state of dendritic channels favors voltage-dependent amplification.
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ACKNOWLEDGMENTS |
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We thank M. A. Konodi, F. R. Robinson, A. Sawczuk, and S. L. Westcott for assistance in generating the data presented here. We also thank an anonymous reviewer for helpful comments on the manuscript.
This work was supported by Grants NS-26840 and NS-31925 from the National Institute of Neurological Disorders and Stroke.
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FOOTNOTES |
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Address for reprint requests: R. K. Powers, Dept. of Physiology and Biophysics, School of Medicine, University of Washington, Box 357290, Seattle, WA 98195.
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
Received 1 March 1999; accepted in final form 21 September 1999.
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REFERENCES |
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