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The Journal of Neuroscience, July 15, 1999, 19(14):5875-5888
Supralinear Summation of Synaptic Inputs by an Invertebrate
Neuron: Dendritic Gain Is Mediated by an "Inward Rectifier"
K+ Current
Ralf
Wessel1,
William
B.
Kristan Jr2, and
David
Kleinfeld1
Departments of 1 Physics and 2 Biology,
University of California at San Diego, La Jolla, California 92093
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ABSTRACT |
Dendritic processing of glutamatergic synaptic inputs was
investigated in the anterior pagoda cell of leech. We observed
that below spike threshold, the amplitude of individual EPSPs decreased with hyperpolarization and that simultaneous stimulation of pairs of
synaptic inputs leads to the supralinear summation of EPSPs. Voltage-clamp measurements revealed a hyperpolarization-activated, Ba2+-sensitive, fast, noninactivating
K+ conductance that depends on the external
[K+]. These features are those of an "inward
rectifier," Kir. Microsurgery experiments, in combination with
electrophysiological measurements, revealed an inhomogeneous spatial
distribution of the Kir conductance. Furthermore, on surgical removal
of the neurites that contain the Kir conductance, the amplitude of
EPSPs from the remaining synaptic inputs increased with
hyperpolarization. A model cell, with the Kir conductance as the sole
voltage-dependent conductance, reproduced qualitatively the observed
voltage dependence of individual EPSPs as well as the supralinear
summation of EPSP pairs.
Key words:
dendritic processing; leech; inward rectifier; supralinear summation; model; synaptic inputs
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INTRODUCTION |
Most neuronal dendrites have various
voltage-gated channels (for review, see Midtgaard, 1994
; Johnston et
al., 1996; Yuste and Tank, 1996; Magee et al., 1998) along with
ligand-gated channels that are activated by synaptic inputs from many
presynaptic neurons. Understanding the interaction of membrane and
synaptic properties is essential for the study of information
processing in nervous systems (for review, see Borst and Egelhaaf,
1994; Mel, 1994; Koch, 1999).
When two neighboring regions of a passive dendrite receive simultaneous
synaptic inputs of the same type, the resulting postsynaptic potential
is less than the linear sum of the potentials generated by each synapse
alone. Such sublinear summation is caused by the increase in the
membrane conductance attributable to the synaptic conductance, and by
the corresponding drop in synaptic driving force by each PSP on the
other synapse. Sublinear summation has been demonstrated experimentally
(Burke, 1967; Kuno and Miyahara, 1969; Haag et al., 1992, 1995).
However, linear summation (Burke, 1967; Langmoen and Andersen, 1983;
Skydsgaard and Hounsgaard, 1994; Grabauskas and Bradley, 1996; Cash and
Yuste, 1998) and supralinear summation (Margulis and Tang, 1998) have
been observed as well, suggesting that the dendrites have voltage-gated
channels that counteract the sources of sublinear summation.
EPSP amplification has been shown in different neurons to be
mediated by various mechanisms: activation of voltage-gated
Na+ channels (Hirsch and Gilbert, 1991; Schwindt and
Crill, 1995; Stuart and Sakmann, 1995; Haag and Borst, 1996; Lipowsky
et al., 1996; Margulis and Tang, 1998), activation of voltage-gated
Ca2+ channels (Deisz et al., 1991; Gillessen and
Alzheimer, 1997; Seamans, 1997), and deactivation of the "inward
rectifier" potassium channel Kir, (Kandel and Tauc, 1966; Kawaguchi
et al., 1989).
We examine dendritic integration in the nervous system of the medicinal
leech (Muller et al., 1981). Specifically we have studied inputs from
the pressure-sensitive sensory cells (P cell) onto the anterior pagoda
(AP) cell (Stewart et al., 1989; Gu, 1991; Wolszon et al., 1995;
Melinek and Muller, 1996; Osborn and Zipser, 1996) (Fig.
1). The P cells make monosynaptic
excitatory inputs onto the AP cell at specific locations in their
neurites (Gu, 1991). A spike triggered in a P cell by a short
current-pulse injection induces an EPSP in the AP cell (Gu, 1991).
There are two P cells on each side, with similar morphology within the
central neuropil (Muller and McMahan, 1976). P cells are mirror
symmetric across the midline to their contralateral partner. In the
intact leech the P cells respond to pressure on the skin and have
receptive fields on the dorsal (Pd) and ventral
(Pv) ipsilateral side of the skin (Nicholls and
Baylor, 1968).
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Figure 1.
Morphology of the AP cell and the contralateral
dorsal P cell. A, Light microscopic image of the AP cell
(yellow/green, fluorescein-filled)
and one of the two contralateral P cells, the dorsal P cell
(orange/red, rhodamine-filled). Note the
extensive overlap of the AP and P cell neurites contralateral to the AP
cell soma. All four P cells have similar morphology and are mirror
symmetric across the midline to the P cells on the opposite side. The
dim somata result from autofluorescence and serve to show the outline
of the ganglion. Anterior is up. Scale bar, 100 µm. B,
Schematic of the P-to-AP cell circuit.
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In the present study we ask the following questions. (1) What are the
characteristics of individual P cell inputs to the AP cell? (2) What is
the nature of the interaction among simultaneous P cell inputs? (3) How
is such interaction mediated by synaptic or cellular properties?
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MATERIALS AND METHODS |
Preparation, dissection, and solutions. Leeches
(Hirudo medicinalis) were obtained from a commercial
supplier (Leeches USA, Westbury, NY) and maintained in artificial pond
water at 15°C. Animals were anesthetized in ice-cold saline, and
individual ganglia were dissected using surgical methods similar to
those described previously (Muller et al., 1981). Ganglia were pinned
ventral side up in Sylgard (Dow-Corning, Midland, MI)-lined Petri
dishes (bath volume, 10 ml), and the connective tissue sheath over the neuronal somata was removed with fine scissors. For the
hemisectioning experiments, the ganglia were cut at the desired
location with a scalpel blade, and the AP cell was hyperpolarized below
60 mV with current injection for 30 min. Ganglia were superfused (3 ml/min) with normal leech saline containing (in mM): NaCl
115, KCl 4, CaCl2 1.8, MgCl2 1.5, glucose 10, Tris-maleate 4.6, Tris-base 5.4, pH 7.4. Equimolar amounts of
N-methyl-D-glucamine replaced Na+ in 0 Na+ salines. Equimolar
amounts of Co2+ replaced Ca2+ in
0 Ca2+ salines. In solutions with increased
Ca2+ or K+ concentration, the
Na+ concentration was reduced by equal amounts to
maintain osmolarity. Experiments were performed at room temperature
(20-23°C).
Electrophysiology. Intracellular recordings were made with
sharp borosilicate microelectrodes (1 mm outer diameter, 0.75 mm inner
diameter, A-M Systems, Carlsborg, WA) pulled on a micropipette puller
(P-80, Sutter Instruments, Novato, CA) filled with 3 M K-acetate with resistances of 40-80 mOhm. An Axoprobe 1A (Axon Instruments, Foster City, CA) was used for current-clamp measurements, and an Axoclamp 2B (Axon Instruments) was used for either current-clamp (bridge mode) or two-electrode voltage-clamp (TEVC-mode) measurements. Analog data were low pass-filtered (four-pole Butterworth) at 1 kHz,
digitized at 2 kHz, stored, and analyzed on a personal computer
equipped with AT-MIO-16E-1 (National Instruments, Austin, TX) and
Labview (National Instruments).
The AP cell was impaled with two microelectrodes, one for passing
current and one for measuring voltage. P cell somata were impaled and a
spike was triggered with a +3 nA, 10 msec current pulse, which in turn
produced an EPSP in the AP cell. This EPSP was constant in size and
shape for >2 hr when allowing for a 3 min recovery period between
trials. For shorter recovery periods, the EPSP peak amplitude
decreased. In normal leech saline the EPSP displayed multiple
components, indicating the activation of polysynaptic inputs in
addition to the monosynaptic input. All polysynaptic inputs were
abolished in saline with [Ca2+]o
raised from 1.8 to 10 mM, which raises spike threshold,
thereby reducing the efficacy of polysynaptic pathways (Nicholls and
Purves, 1970; Cohen et al., 1978; Getting, 1981). Raising both
[Mg2+]o and
[Ca2+]o also abolished polysynaptic
pathways, but in addition led to reduced monosynaptic EPSP peak
amplitudes (Nicholls and Purves, 1970); therefore this combination was
not used. All experiments involving synaptic stimulation were performed
in leech saline with [Ca2+]o = 10 mM, similar to previous studies of synaptic interaction in
leech (Nicholls and Purves, 1970).
Data are expressed in the text and figures as mean ± SEM.
Histology. To observe pairs of P and AP cells in light
microscopy, an AP cell was iontophoretically injected with Fluorescein dextran [5% in H2O, 3000 molecular weight (MW), Molecular
Probes, Eugene, OR], and the P cell was injected with
tetramethylrhodamine dextran (5% in H2O, 3000 MW,
Molecular Probes) using sharp electrodes of 10-30 M
resistance and
pulsed current (5 ± 2 nA, 10 Hz, 30 min). The ganglia were
fixed in 2% paraformaldehyde in 0.1 M phosphate buffer for
2-12 hr, rinsed in PBS, and mounted in a solution of 20% PBS and 80%
glycerin. Digital images were taken at 20× magnification with a
confocal microscope (Bio-Rad, MRC1024, Hercules, CA) equipped with a
krypton/argon laser using the 488 and 563 nm lines for excitation, and
the emission filters 540/30 for fluorescein and 585LP for
tetramethylrhodamine. Images were adjusted with respect to brightness
and contrast using Adobe Photoshop (Adobe Systems, Mountain View, CA).
Numerical simulations. Simulations were programmed in
LabVIEW (National Instruments) using the forward Euler method with an integration time-step of 0.01 msec. The capacitance was
C = 0.5 nF. For simplicity, synaptic input was modeled
as a pulsed change in conductance from 0 to Gsyn
during a period of 200 msec. Synapses had a reversal potential,
Esyn, of 0 mV. The model included a voltage-independent leak conductance, GL,
and a voltage-dependent inward rectifier conductance,
GKir, with reversal potentials of EL = 45 mV and
EK = 80 mV, respectively. The Kir-channel
model was of the form:
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(1)
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Because the inward rectifier acts so quickly, it is permissible
to neglect any time dependence. To insure consistency with the EPSP
measurements, all parameter values were taken from I-V curves measured with voltage-clamp in saline with
[Ca2+]o raised to 10 mM.
The parameter values for the conductances were
GL = 24 nS,
Gmax = 28 nS,
V1/2 = 67 mV, and 
= 8 mV. The one-compartment model was of the form:
|
(2)
|
with V the membrane potential and
Iinj the injected current. The variable 
takes the value 1 during the time of synaptic stimulation and is 0 otherwise, and the variable 
specifies the number of synaptic
inputs. The difference between the membrane potential before and at the
end of the synaptic input was taken as the EPSP peak amplitude.
In the two-compartment model the synaptic conductance, the inward
rectifier conductance Gmax2, and a leak
conductance, GL2, were placed in the
"neurite" compartment that was connected through an axial
conductance, Gax, with the "soma"
compartment that contained the leak conductance and the injected
current. In this model, the measured leak conductance
GL is the result of the combined leak
conductances from both compartments. Assuming for simplicity the same
leak conductance GL2 in each compartment,
Kirchoff's law yields the relation between the measured leak
conductance GL and the leak conductance
GL2 in each compartment:
GL = GL2 (GL2 + 2Gax)/(GL2 + Gax). Similarly, because the Kir
conductance was placed in the "neurite" compartment but not in the
soma compartment, Kirchoff's law yields the relation between the
measured Kir conductance Gmax and the Kir
conductance Gmax2 in the "neurite"
compartment: Gmax2 = (Gax
Gmax)/(Gax Gmax). For the considered axial
conductance of 40 nS, the relations yield
GL2 = 14 nS and
Gmax2 = 93 nS. The two-compartment model
was of the form:
|
(3)
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for the "soma" compartment and
|
(4)
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for the "neurite" compartment, with
VS and VN the membrane
potentials in the "soma" and "neurite" compartments,
respectively, and GKir2(V)
given by Equation 1 with parameters Gmax2 = 93 nS, V1/2 = 67 mV, = 11 mV,
and Gsyn = 9 nS.
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RESULTS |
AMPA receptors mediating EPSPs
We characterized the P-to-AP monosynaptic inputs under conditions
that blocked polysynaptic pathways (see Materials and Methods) and
found a major contribution to the EPSP from AMPA receptors and a much
smaller fraction from an electrical coupling. When we blocked the
presynaptic neurotransmitter release with saline that had its
Ca2+ replaced by the Ca2+ channel
blocker Co2+ (Simon et al., 1992), the EPSPs were
reduced by 87 ± 1% (mean ± SEM, n = 3 cells) (Fig. 2A),
suggesting that chemical transmission was the dominant source of the
EPSP, with the residue caused by an electrical coupling.
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Figure 2.
Contribution of AMPA receptors to P-to-AP EPSPs.
A, Unitary average EPSPs (average of 4 trials) in
response to contralateral Pd stimulation at an initial
membrane potential of 65 mV in leech saline (10 mM
Ca2+) and in saline with 0 mM
Ca2+ and 1.8 mM Co2+,
as indicated. B, Unitary average EPSPs (average of 4 trials) in response to contralateral Pd stimulation at an
initial membrane potential of 65 mV in leech saline (10 mM Ca2+) and in the presence of 50 µM APV, as indicated. C, Unitary average
EPSPs (average of 4 trials) in response to contralateral Pd
stimulation at an initial membrane potential of 65 mV in leech saline
(10 mM Ca2+), in the presence of 50 µM CNQX, and in the presence of of 50 µM
CNQX and 50 µM APV, as indicated.
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The effect of APV was tested at holding potentials of 65 mV, i.e.,
below the threshold for spiking. The amplitude and time course of the
average evoked EPSP were unaffected by the addition of 50 µM APV to the extracellular solution (n = 9 cells) (Fig. 2B). Assuming that APV blocks
invertebrate NMDA receptors, this result suggests that NMDA receptors
either are absent from the P-to-AP synapses or blocked by extracellular
Mg2+ in the subthreshold range of membrane
potentials. This observation is consistent with previous studies of
other leech synapses that also failed to reveal APV-sensitive
transmission (Thorogood and Brodfuehrer, 1995).
The EPSP was reduced by 75 ± 2% (n = 12 cells)
after addition of 50 µM CNQX to the extracellular
solution (Fig. 2C), which suggests that the EPSPs are
largely mediated by AMPA receptors. The remaining EPSP was not affected
by further addition of 50 µM APV to the extracellular
solution (n = 3 cells). Furthermore, this remaining
EPSP did not depress in response to a train of 10 spikes at 5 Hz
(n = 5 cells; data not shown), thus strengthening the
hypothesis that the residue is caused by an electrical coupling as
suggested above (Fig. 2A). At a membrane potential of
120 mV the EPSP was reduced by 73 ± 5% (n = 3 cells) after addition of 50 µM CNQX to the extracellular
solution (data not shown), which suggests that at this membrane
potential the response maintains a chemical component.
Voltage dependence of EPSPs
The amplitude and time course of the P-to-AP EPSPs displayed a
voltage dependence that is anomalous for an AMPA response (Fig. 3A). Below the threshold for
spiking (approximately 50 mV in 10 mM
Ca2+ saline), the EPSP peak amplitude (Fig.
3B, thick trace) (n = 9 cells)
and duration (Fig. 3C) (n = 9 cells)
decreased with hyperpolarization and did not reverse, even at soma
membrane potentials well below the potassium equilibrium potential
EK. The voltage response to a constant current
pulse (2000 msec, +0.2 nA) (Fig. 3B, inset) injected into the soma also decreased with hyperpolarization (Fig. 3B, thin trace) (n = 10 cells).
This voltage dependence is similar to the one of the EPSP peak
amplitude, which suggests that the EPSP voltage dependence is caused by
a postsynaptic membrane current rather than synaptic properties. The
difference between the two voltage dependencies above 80 mV occurs
because in the case of the current injection the amplitude of the
current is constant, whereas in the case of synaptic stimulation the
synaptic current decreases with depolarization attributable to the
accompanying reduction in driving force.
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Figure 3.
Dendritic gain in AP cells decreases with
hyperpolarization in the subthreshold range. A, Response
of a representative AP cell to synaptic stimulation via the
contralateral dorsal P cell at different membrane potentials in saline
with [Ca2+]o elevated to 10 mM. The amplitude and width of the EPSP decrease with
hyperpolarization but do not reverse even at soma membrane potentials well below the potassium
equilibrium potential. The arrow indicates the timing of
the stimulus. B, Plots showing how the EPSP amplitude
and the voltage response varied with initial membrane potential.
Left axis, EPSP peak amplitude versus initial membrane
potential for nine AP cells tested. Right axis, Average
steady-state voltage responses to +0.2 nA, 2000 msec current pulses
versus initial membrane potential (n = 10 AP
cells). Inset, Voltage responses to +0.2 nA, 2000 msec
current pulses at different initial membrane potentials.
C, EPSP half-width versus initial membrane potential for
nine AP cells.
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Supralinear summation of synaptic inputs
To investigate synaptic interactions in the AP cell, we stimulated
two P cells from the same side of the ganglion, first separately and
then simultaneously, and compared the algebraic sum of the separate
EPSPs with the EPSP elicited by simultaneous stimulation. Supralinear
summation was observed when the initial membrane potential was between
110 and 70 mV (Fig.
4A) (average of eight
trials). The two bottom traces are the responses from separate ventral (Pv) and dorsal (Pd)
contralateral P cell inputs. The gray trace indicates the algebraic sum
of the two EPSPs, and the top trace is the response obtained from
simultaneous stimulation of both P cells; it is significantly higher
than the gray trace. We define a measure of linearity as:
|
(5)
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with Vin the initial membrane potential,
VPdPv the peak membrane potential after
simultaneous activation of Pd and Pv,
and VPd or VPv the peak
membrane potential after separate activation of Pd or
Pv, respectively. The EPSP peak amplitude for
simultaneous stimulation was 122 ± 5% of the algebraic sum of
the separate stimulation. For simultaneous stimulation of contralateral
(contra/contra; 21 cells) or ipsilateral (ipsi/ipsi; six cells) P
cells, we found supralinear summation in the range of initial membrane
potential between 110 and 70 mV (average % linearity = 117 ± 2 and 117 ± 5% for contra/contra and ipsi/ipsi,
respectively) (Fig. 4B). The EPSP peak amplitude for
simultaneous stimulation decreased with hyperpolarization and covered a
range between 2 and 16 mV (Fig. 4B,
inset). Because EPSPs from ipsilateral stimulation were smaller in general than those from contralateral stimulation, we chose
contra/contra stimulation for most experiments. Because of the small
size of the EPSPs, we did not explore summation for ipsi/ipsi
stimulation below a membrane potential of 90 mV. Synaptic inputs
from opposite sides (ipsi/contra, n = 9 cells)
summed in a linear manner (average % linearity = 102 ± 2%), suggesting that synaptic inputs from opposite sides are
electrically remote from each other. This observation is consistent
with the anatomical observation that the processes of a P cell remain
largely on the same side as the soma (Fig. 1).
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Figure 4.
Supralinear summation of synaptic inputs from two
sources. A, Averaged results from a representative AP
cell (8 trials). The preparation was in a saline with high
Ca2+ concentration to avoid polysynaptic pathways.
The two bottom traces are the responses from individual
ventral and dorsal P cell stimulation. The somata of both P cells were
contralateral to the AP cell soma. In this case, the EPSP from
Pv is smaller than from Pd, although the
relative sizes varied in different preparations. The gray
trace indicates the algebraic sum of the two EPSPs. The
top trace is the response to simultaneous stimulation of
both P cells; its peak is 122% of the algebraic sum of individual
stimulation. B, Peak EPSP from simultaneous stimulation
of contralateral dorsal and ventral ( , 21 cells) or ipsilateral
dorsal and ventral ( , 6 cells) P cells expressed as % of algebraic
sum at different membrane potentials (mean ± SEM; 5-10 trials).
The arrow indicates the zero-current membrane potential
Vo. Inset, EPSP peak
amplitude from simultaneous stimulation of dorsal and ventral P cells
for the data points shown in the main figure, showing that the EPSP
amplitudes decrease with hyperpolarization, as in Figure
3B.
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Cellular properties: the inward rectifier Kir
To test the possibility that the voltage dependence and
supralinear summation of EPSPs is caused by postsynaptic membrane properties, we used a two-electrode voltage clamp to measure the I-V characteristics of AP cells. We note that the voltage
clamp is only assumed to be effective in the AP cell soma. When the cell membrane potential was stepped to test voltages between 120 and
30 mV from a holding potential of 70 mV with the ganglion in normal
leech saline, the resulting current showed a strong inward
rectification. Furthermore, the current activated in <1 msec, and for
test voltages below 50 mV it did not inactivate during the 3 sec
voltage steps used in these experiments (Fig. 5A). The steady-state
I-V curve measured from the current at the end of the 3 sec
voltage step was strongly nonlinear (Fig. 5B, thick
trace) (n = 8 cells). In 0 Na+,
0 Ca2+, 1.8 mM Co2+
saline, chosen to isolate K+ and
Cl
currents, the I-V curve was only
marginally changed (Fig. 5B, dotted line)
(n = 7 cells). The shift of the zero-current potential to a more hyperpolarized level is presumably attributable to the absence of the Na+ and Ca2+ leak
currents. In contrast, an increase of
[K+]o to 15 and 45 mM led
to a significant increase of the inward current (Fig. 5B,
thin lines) (n = 6 cells), strongly
suggesting that K+ is the dominant current
carrier.
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Figure 5.
Evidence for an inward rectifier, Kir.
A, Current-response (average of 9 trials) to voltage
steps from a holding potential of 70 mV to various test membrane
potentials between 120 and 30 mV. B, The current at
the end of the 3 sec voltage step plotted versus the test membrane
potential in (1) normal leech saline
([K+]o = 4 mM)
(average of 8 cells), (2) 0 Na+, 0 Ca2+, 1.8 mM Co2+
saline (average of 7 cells), (3) saline with
[K+]o elevated to 15 (average of 6 cells), and (4) saline with [K+]o
elevated to 45 mM (average of 5 cells). C,
Measured current, IM, in normal
saline ([K+]o = 4 mM)
minus the non-K+ leak current,
IL = GL(V EL). The value of the equilibrium
leak potential, EL, was assumed to be
50 mV, and the non-K+ leak conductance was
estimated for each cell from the measured current,
IM,EK, at the assumed
EK value of 80 mV:
GL = IM,EK/(EK EL). The inset
shows the measured current and the estimated non-K+
leak current for one representative cell. D, Potassium
chord conductance, G = (IM IL)/(V EK). The continuous curve is a
least-squares fit of the Boltzmann equation to the data points. The
fitting parameters are Gmax = 40 nS,
V1/2 = 76 mV, and = 12 mV.
For comparison the average non-K+ leak conductance,
GL = 28 ± 2 nS, is indicated by
the horizontal arrow. The inset shows the
potassium chord conductance for
[K+]o = 15 and 45 mM,
estimated as described in the text. For comparison the chord
conductance for [K+]o = 4 mM (i.e., the data shown in the graph) is
replotted in the inset.
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In an attempt to separate the K+ current from the
measured current IM, we assumed that the
measured current is the sum of the K+ current
IK = GK(V EK), and a non-K+ leak
current IL = GL(V EL) (Hagiwara and Yoshii, 1979),
with a voltage-independent conductance,
GL, and a reversal potential, EL = 50 mV, a value assumed close to the
zero-current membrane potential that was used previously in modeling
studies of leech neurons (Calabrese et al., 1995). At the equilibrium
potential for potassium, EK, the
K+ current vanishes and thus at V = EK the measured current
IM,EK is equal to the non-K+
leak current, i.e., IM,EK = IL,EK = GL(EK EL). We estimated the
non-K+ leak conductance for each cell using the
relation GL = IM,EK/(EK EL).
The value of EK for leech neurons has been
estimated by various methods: extrapolation from the change of membrane
potential with [K+]o
(EK = 83 mV) (Nicholls and Kuffler,
1964), flame photometry (EK = 86 mV)
(Nicholls and Kuffler, 1965), and ion exchanger microelectrodes
(EK = 80 mV) (Deitmer and Schlue, 1981;
Schlue and Deitmer, 1984). A value of EK = 80 mV has been used previously in modeling studies in the leech
(Calabrese et al., 1995). We took EK = 80
mV for our data analysis.
With these assumptions in mind, subtracting for each cell the estimated
non-K+ leak current IL = GL(V EL) from the measured current
IM reveals the potassium current
IK = IM IL for that cell. For illustration, the measured
current IM and the estimated
non-K+ leak current IL are
shown for one representative AP cell in Figure 5C
(inset). Because the leak current varies between cells, we performed this procedure on each cell rather than on the mean to
minimize the variation in the estimated potassium current between cells. The average potassium current thus derived from eight cells is shown in Figure 5C. The shape of the potassium
I-V curve with a local minimum at 50 mV suggests that
there is only a minor contribution of a potassium leak current to
this I-V curve. An upper bound of the potassium leak
current is a straight line that crosses the data point at
EK = 80 mV and the data point at the local minimum at 50 mV, yielding a potassium leak conductance of
<2.7 nS. Above 50 mV, additional potassium conductances that are
activated with depolarization contribute to the current. Thus data
points above 50 mV were excluded from the subsequent analysis of the
potassium chord conductance.
From the average potassium I-V curve
IK = IM IL, we obtained the potassium chord
conductance:
|
(6)
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(Fig. 5D, black dots). The continuous curve
is a least-squares fit of a Boltzmann factor:
|
(7)
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to the calculated data points. The fitting parameters are
the maximal conductance, Gmax = 40 nS, the
membrane potential at which the conductance is half-activated,
V1/2 = 76 mV, and the slope factor,
= 12 mV. Because = kT/ze, where
kT is the thermal energy (25 meV at T = 297 K), e is the elementary electric charge, and z is
the number of effective charges of the gating particle, the value of
= 12 mV yields approximately z = 2.
The observed features of this potassium conductance, i.e., (1) opening
with hyperpolarization, (2) activation in <1 msec, and (3) no
inactivation, are consistent with the previously described inward
rectifier Kir (Hagiwara and Jaffe, 1979; Hagiwara, 1983; Doupnik et
al., 1995; Fakler and Ruppersberg, 1996; Isomoto et al., 1997; Nichols
and Lopatin, 1997).
In our experiments the chord conductance was best fitted to a Boltzmann
expression with a slope factor of = 12 mV, corresponding to an
effective gating charge of z = 2. Interestingly, the
estimated effective gating charge is consistent with the
Mg2+ block that controls, in part, rectification for
Kir channels (Vandenberg, 1987). Inward rectification has previously
been fitted to a Boltzman expression with a similar steepness for the
voltage dependence: = 7 (Hagiwara and Takahashi, 1974);
= 12-14 (Stanfield et al., 1985); = 6-15 (Williams
et al., 1988); = 10-15 (Lopatin et al., 1994); = 12 (Dong and Werblin, 1995); = 10 (Aleksandrov et al., 1996).
This Kir conductance has been shown previously to be sensitive to
external Ba2+ (Hagiwara et al., 1978; Constanti and
Galvan, 1983; Tachibana, 1983; Shingai and Christensen, 1986; Williams
et al., 1988; Uchimura et al., 1989; Kass et al., 1990; Golard et al.,
1992; Kubo et al., 1993; Dong and Werblin, 1995; Holt and Eatock, 1995;
Aleksandrov et al., 1996; Döring et al., 1998; Mermelstein et
al., 1998; Töpert et al., 1998). For the AP cell, the current,
measured in voltage-clamp at a test potential of 120 mV in 15 mM Ba2+, was reduced down to 56 ± 5% (mean ± SEM, n = 4 cells) compared with the
value from control measurements in 0 Na+, 0 Ca2+, 1.8 mM Co2+
saline. The Ba2+-sensitive current was similar in
its voltage dependence (n = 2 cells; data not shown) to
the estimated potassium current (Fig. 5C). Thus this aspect
of the conductance is also consistent with the description of the
inward rectifier.
[K+]o-dependent gating
It has been noted previously that the gating of the Kir
conductance changes with external [K+]: with
increased [K+]o, the chord
conductance shifts to more depolarized levels and the maximal chord
conductance increases (Hagiwara and Takahashi, 1974; Hagiwara et al.,
1976; Hagiwara and Yoshii, 1979; Leech and Stanfield, 1981; Stanfield
et al., 1985; Williams et al., 1988; Uchimura et al., 1989; Dong and
Werblin, 1995; Holt and Eatock, 1995; Aleksandrov et al., 1996; Lopatin
and Nichols, 1996a,b). To test whether the conductance under
investigation displays this property, we measured the I-V
curve in saline with [K+]o = 4, 15, and 45 mM (Fig. 5B). According to the Nernst
equation and assuming that [K+]i = 96 mM (a value consistent with
[K+]o = 4 mM and
EK = 80 mV) is independent of
[K+]o, the potassium
equilibrium potential EK would be 47, and 19 mV for [K+]o = 15 and 45 mM, respectively. Assuming for simplicity that EL and GL remain
constant, we obtained the chord conductance as described above for
[K+]o = 15 and 45 mM
(Fig. 5D, inset) (n = 6 cells).
For comparison, the chord conductance for
[K+]o = 4 mM is
replotted in the inset. The observed shift to more depolarized levels and the increase of the chord conductance
with increasing [K+]o is consistent
with the description of the Kir conductance.
Spatial distribution of the Kir channels
Microsurgery experiments, similar to those performed on
hippocampal neurons (Benardo et al., 1982), in combination with slope resistance measurements revealed an inhomogeneous spatial distribution of the Kir conductance. Because of the activation of the Kir
conductance with hyperpolarization, the observed voltage response to a
constant-current pulse (+0.2 nA, 2000 msec) decreased with
hyperpolarization in the intact ganglion (Fig.
6A, intact,
B, gray curve) (n = 10 cells). When the ganglion was cut (see Materials and Methods) between the
ipsilateral lateral and the medial packet (Fig. 6A,
cut), we observed that the voltage response to a
constant-current pulse no longer decreased with hyperpolarization (Fig.
6A, cut; Fig. 6B,
black curve) (n = 11 cells). This
observation indicates that the Kir channels are expressed contralateral
but not ipsilateral to the cut, i.e., the border between the
ipsilateral lateral and medial packet. Cutting the ganglion down the
midline (data not shown) did not separate the soma from the Kir
channels.
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Figure 6.
Inhomogeneous spatial distribution of the Kir
channels. A, Top, Schematic diagram of
the AP cell in an intact (left) and surgically cut
(right) ganglion. The location of the cut is indicated
by the rectangle. Bottom, Voltage
responses to +0.2 nA, 2000 msec current pulses at different initial
membrane potentials for the intact (left) and cut
(right) AP cell in normal saline. B,
Average steady-state voltage responses to +0.2 nA, 2000 msec current
pulses versus initial membrane potential for intact
(gray, 10 cells) and cut (black,
11 cells) AP cells. The voltage response does not increase with depolarization in the cut cell,
indicating a lack of Kir channels ipsilateral to the cut.
C, Inset, EPSPs in response to
stimulation of the synaptic input remaining after the cut (average of 8 trials alternating between a membrane potential of 65 and 95 mV).
The presynaptic ipsilateral P cells were stimulated with +4 nA, 500 msec current pulses initiating an average of 20 spikes.
C, Comparison of the voltage dependence of the EPSP peak
amplitude in intact (gray, 9 cells) (Fig.
2B; 10 mM Ca saline) and cut
(black, 6 cells, 10 mM Ca saline) AP cells.
In cut AP cells the EPSP peak amplitude decreases with depolarization.
In all cases tested the EPSP peak amplitude at 65 mV was smaller than
at 95 mV. On average the EPSP peak amplitude at 65 mV was 55 ± 4% of the amplitude at 95 mV.
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Although most synaptic inputs were severed by the cut described above,
a few synaptic inputs were still present on the neurites proximal to
the soma. Stimulation of the ipsilateral P cells with a +4 nA, 500 msec
current pulse triggered on average 20 spikes, which evoked measurable
EPSPs in the AP cell. In the cut cell the amplitude of the EPSP
increased with hyperpolarization (Fig. 6C, inset
and black curve) (n = 6 cells), consistent
with a passive dendrite, rather than decreased, as was observed in the
intact cell (Fig. 6C, gray curve)
(n = 9 cells). In all cases tested the EPSP peak
amplitude at 65 mV was smaller than at 95 mV. The average EPSP peak
amplitude at 65 mV was 55 ± 4% of the amplitude at 95 mV.
Thus, when neurites containing the dominant fraction of the Kir
conductance had been surgically removed, the EPSP peak amplitude
increased with hyperpolarization in a manner consistent with a passive
dendrite and a synaptic reversal potential that was more positive than
65 mV.
Despite the drastic surgical procedure, the AP cell soma and proximal
neurite under investigation appeared to be healthy. The following
observations are taken as evidence of normal functioning of the cut AP
cell. (1) The voltage response to a constant-current pulse at a
membrane potential of 65 mV is slightly larger than in the intact
cell, i.e., the slope resistance increased in the cut cell, indicating
that the cut ends sealed rather than remained open; (2) the voltage
response to a constant-current pulse decreased with depolarization
above 65 mV, indicating that voltage-gated conductances remained
active (in the intact cell it was not possible to explore this range of
membrane potential because of the occurrence of spikes triggered at the
contralateral spike initiating zone); and (3) the cut cell still
received synaptic inputs.
Model calculations
We have used numerical simulations to illustrate how the opposing
effects of the reduced synaptic driving force and the deactivation of
the inward rectifier with depolarization interact to produce the
observed voltage dependence of (1) the EPSP peak amplitude and (2) the
summation of pairs of synaptic inputs in the AP cell. The
one-compartment model (Fig.
7A, inset)
contained a leak conductance, GL, the
inward rectifier conductance, GKir, two
synaptic conductances, Gsyn, and an
injected current, Iinj. Because all EPSP
measurements were taken in saline with
[Ca2+]o raised to 10 mM,
the parameter values for GL and
GKir were taken from I-V
measurements in saline with this ion composition (see Materials and
Methods for details). To prevent confusion with the effects of the
inward rectifier, additional conductances that might be activated, in
particular above a membrane potential of 50 mV, were excluded from
these simulations. For simplicity the synaptic input was modeled as a
chemical synapse, ignoring the electrical component that contributes
~25% to the EPSP.
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Figure 7.
Model of interactions of
GKir with GL and
Gsyn. A, I-V
curve, I = GKir(V EK) + GL(V EL), with the inward rectifier
conductance, GKir = Gmax/(1 + exp(V V1/2)/)), the leak conductance,
GL = 24 nS, the leak reversal
potential, EL = 45 mV, the potassium
equilibrium potential, EK = 80 mV,
and the parameters of the inward rectifier conductance,
Gmax = 28 nS,
V1/2 = 67 mV, = 8 mV (all
parameters from measurements from AP cells in 10 mM
Ca2+ saline). The I-V curve for the
model without the inward rectifier is indicated by the dotted
line. Inset, Schematic diagram of the model.
B, Response characteristics of the model cell.
Left axis, Voltage response,  V, of the model cell to
a +0.2 nA, 200 msec current pulse. Right axis, Slope
resistance, dV/dI, of the I-V
curve in A. The slope resistance for the model without
the inward rectifier is indicated by the dotted line.
C, Voltage dependence of the EPSP peak amplitude. The
synaptic input is modeled by a 200-msec-long pulsed conductance change
of different magnitudes: Gsyn = 2, 5, and 8 nS, Esyn = 0 mV. The result for
the model without the inward rectifier
(GKir = 0, Gsyn = 5 nS) is shown for comparison
(dotted line). The data points from Figure
3B are replotted for comparison (gray
squares). D, Voltage dependence of summing two
synaptic inputs of equal conductance change
(Gsyn = 2, 5, and 8 nS;
Esyn = 0 mV). The result for the model
without the inward rectifier (GKir = 0;
Gsyn = 5 nS) is shown for comparison
(dotted line). The result for the model with increased
Kir conductance (GKir = 50 nS;
Gsyn = 5 nS) is shown by the
dashed trace. The result for the two-compartment model
(see Materials and Methods for details) is shown by the gray
trace. The data points from Figure 4B are
replotted for comparison (gray squares).
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The combined effect of the leak current and the inward rectifier
current:
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(8)
|
with the inward rectifier conductance:
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(9)
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leads to an I-V curve with a strong nonlinearity in
the subthreshold range of membrane potential (Fig. 7A,
thick curve). The leak current alone is shown by the dotted
line for comparison. From the monotonously growing I-V
curve we derive the slope resistance:
|
(10)
|
The slope resistance is a measure of the voltage response to an
infinitesimal small current pulse and is thus a useful measure to
discuss the cell's response to a synaptic current.
The nonlinear I-V curve yields a slope resistance with a
steep voltage dependence in the subthreshold range of membrane
potential (Fig. 7B, thick trace). At extremely
negative membrane potentials (i.e., below 120 mV), the inward
rectifier is fully activated. The slope resistance is
1/(GL + Gmax) and
independent of the membrane potential. With less hyperpolarization the
Kir conductance is partially deactivated, and the slope resistance
increases. Because of the potassium outward current above
EK = 80 mV, the slope resistance
overshoots the leak resistance 1/GL (Fig.
7B, dotted line), reaches a peak (61 mOhm at 54
mV), and approaches asymptotically 1/GL from
above with further depolarization. The shape of the slope resistance is
caused by the interplay of the Kir conductance and the value of
EK, which results in an outward potassium
current with a peak in the subthreshold range of membrane potential.
Although the slope resistance represents the voltage response to an
infinitesimally small current pulse, we find that it is still a good
approximation of the steady-state voltage response of the model cell
(see Materials and Methods) to a +0.2 nA current pulse (Fig.
7B, thin trace), a level of current expected in
the case of synaptic stimulation. This will allow us to discuss the
voltage dependence of the EPSP peak amplitude and the summation of
synaptic inputs in terms of the interplay between the slope
resistance and the synaptic driving force.
First, we consider the voltage response of the model cell (Fig.
7A, inset) to a synaptic conductance change (see
Materials and Methods). The voltage dependence of the model cell
responses to excitatory synaptic inputs follows the slope resistance;
however, it is modulated by the counteracting change in the synaptic
driving force (Fig. 7C). In particular, in the limit of an
infinitesimally small synaptic conductance change, the model cell's
voltage response is determined by a constant slope resistance and
driving force: V 
(dV/dI)
Gsyn (V Esyn). For larger synaptic conductance changes, however, both the slope resistance and the driving force change dynamically. Starting at a membrane potential of 130 mV, the
inward rectifier is fully activated, and the slope resistance is
independent of voltage. The EPSP peak amplitude decreases with depolarization, as is expected because of the reduced driving force. At less hyperpolarized levels the inward rectifier conductance decreases (compare with Fig. 5D), and the slope resistance
increases sharply with increasing depolarization (compare with Fig.
7B). The resulting increase of EPSP amplitudes is stronger
than the decrease caused by the reduced driving force, which leads to a net increase of EPSP amplitudes with depolarization in the range of
membrane potential between approximately 90 and 60 mV (Fig. 7C; also compare with Fig. 3B). Because of the
reduction of the inward rectifier outward current with depolarization
above 70 mV, the slope resistance is larger than the leak resistance
and reaches a peak of 61 mOhm at 54 mV (Fig. 7B). As a
result the EPSP amplitude reaches values larger than in the case
without the inward rectifier (Fig. 7C)
(Gsyn = 5 nS). Beyond the peak the slope
resistance decreases with depolarization, asymptotically reaching the
value of the leak resistance. Now the EPSP peak amplitude decreases
with depolarization caused by both the reduced slope resistance and the
reduced driving force.
Second, we consider the summation of pairs of synaptic inputs. We
observe that when two synaptic inputs are stimulated simultaneously and
the resulting membrane potential at the peak of the EPSP is in the
range where the slope resistance (Fig. 7B) increases with depolarization, the resulting EPSP peak amplitude is larger than the
algebraic sum of the EPSPs from individual stimulation, i.e., supralinear summation (Fig. 7D). The membrane potential at
the peak of the EPSP is larger than the initial membrane potential. The
difference increases with increasing synaptic conductance. Thus the
voltage dependence of the supralinearity, expressed as "%
linearity" versus initial membrane potential, shifts with the synaptic conductance.
The model explained qualitatively how the Kir conductance can lead to
the supralinear summation of synaptic inputs in the considered range of
membrane potential. The amplitude and width of the measured % linearity versus membrane potential relation is less well explained by
this simple model. However, larger values of supralinearity, similar to
those measured, are reproduced in a model with an increased Kir
conductance (Gmax = 50 nS,
Gsyn = 5 nS) (Fig. 7C,
dashed trace).
Because of the spatial extent of the neuron, the control of the
membrane potential at the sites of electrically remote synaptic inputs
and Kir conductances is limited. Therefore the sites of synaptic inputs
and Kir conductances are sampled over a smaller range of membrane
potential around the local resting membrane potential than the somatic
recording site is. It is expected that this sampling error leads to a
broadening of the % linearity versus membrane potential relation. Such
broadening, caused by the limited control of the membrane potential in
the neurites, is illustrated using a two-compartment model (Fig.
7D, gray trace). In this model the synaptic
conductance, the inward rectifier conductance, and a leak conductance
were placed in the neurite compartment, which was connected through an
axial conductance with the soma compartment that contained the leak
conductance and the injected current (see Materials and Methods for details).
Some insight into the numerical results for the summation of synaptic
inputs may be found by considering the equation for the one-compartment
model in the particular limit of a small synaptic conductance, and with
the membrane conductance dominated by
GKir(V), i.e.,
GS 
GL
GKir(V). In terms of the % linearity measure, defined in Equation 5, we find (see Appendix):
|
(11)
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This equation shows that the relation between the synaptic
reversal potential and the synaptic conductance is not solely multiplicative; in particular, the supralinearity increases with increasing Esyn. At levels of
Vin significantly hyperpolarized to
V1/2, i.e., Vin
(V1/2 ), the term in square
parentheses becomes negative, yielding sublinear summation. However, at
levels of Vin closer to
V1/2 the term turns positive, yielding
supralinear summation. At levels of Vin
depolarized to V1/2, the Kir conductance GKir(V) is no longer the
dominating membrane conductance and the above approximate relation (Eq. 11) no longer holds. For a more general relation, see Appendix.
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DISCUSSION |
Inward rectification is responsible for nonlinear subthreshold
summation of synaptic inputs
The major findings of the present experiments are as follows: (1)
AP cell neurites express an inhomogeneous spatial distribution of the
Kir conductance, (2) activation of the Kir conductance by
hyperpolarization decreases the EPSP peak amplitude and half width, and
(3) deactivation of the Kir conductance with EPSPs causes supralinear
summation of paired excitatory synaptic inputs.
The observed voltage dependence of the EPSP peak amplitude was reversed
when the neurites expressing the Kir channel were surgically removed.
Both the observed voltage dependence of EPSPs as well as the
supralinear summation were reproduced qualitatively in a model with the
inward rectifier as the sole voltage-dependent conductance.
The physiological significance of the Kir conductance could be
demonstrated experimentally only in the subthreshold range of membrane
potential, as a result of the lack of a Na+ channel
blocker for leech to abolish spikes (Kleinhaus and Angstadt, 1995).
However, the extension of the tail end of the activation curve for the
Kir conductance into the range of membrane potential above threshold
suggests that the physiological significance extends into this range,
as demonstrated in the modeling study (Fig. 7). In particular, because
the Kir conductances are located in the neurites remote from the soma
(Fig. 6), the activation curve, as measured in the soma, represents
only a lower estimate of the Kir conductance located in the neurite.
Therefore, the Kir conductance in the neurite is likely to be larger
than the somatic measurement revealed and thus is expected to
contribute significantly to the neurite conductance at zero-current potential.
Comparison with other amplifying mechanisms
The activation of voltage-gated Na+
conductances (Hirsch and Gilbert, 1991; Schwindt and Crill, 1995;
Stuart and Sakmann, 1995; Haag and Borst, 1996; Lipowsky et al., 1996;
Margulis and Tang, 1998) or Ca2+ conductances (Deisz
et al., 1991; Gillessen and Alzheimer, 1997; Seamans, 1997) by EPSPs
amplifies the magnitude of the EPSPs en route to other areas of the
neuron. Na+ conductances mediate supralinear
temporal summation in cultured rat hippocampal neurons (Margulis and
Tang, 1998). The presence of the hyperpolarization-activated current
Ih in pyramidal cell dendrites (Stuart and
Spruston, 1998) decreases EPSP amplitude and duration (Magee,
1998).
The experimental evidence suggests that the Na+ and
Ca2+ currents, as well as the mixed
Na+/K+ H-current, play a minor,
if any, role for the observed voltage dependence of the EPSP peak
amplitude and supralinear summation in the AP cell in the subthreshold
range of membrane potential (less than 55 mV) under investigation.
(1) The AP cell I-V curve is only marginally changed in 0 Na+, 0 Ca2+, 1.8 mM
Co2+ saline (Fig. 5B) but changes
significantly with changes in [K+]o.
These observations suggest that the slope resistance (Fig. 7B) is dominated by the voltage-dependent potassium
conductance. (2) The slope of the voltage dependence of the EPSP
peak amplitude as a function of membrane potential was reversed when
the neurites expressing the Kir conductance were surgically removed
(Fig. 6C). (3) The observed voltage dependence of EPSPs as
well as the supralinear summation were reproduced qualitatively in a
model with the inward rectifier as the sole voltage-dependent
conductance (Fig. 7C,D).
Two kinds of postsynaptic receptors
NMDA or conductance-decrease
receptorscould cause, in principle, the observed EPSP voltage dependence. We consider both possibilities unlikely. (1) In the AP
cell, the EPSP was not affected by 50 µM APV, a NMDA
receptor blocker in vertebrates, whereas most of the EPSP mediated by
chemical transmission was blocked by 50 µM CNQX, a
blocker of AMPA-type glutamate receptors. (2) If the observed EPSPs
were caused by a potassium conductance-decrease EPSP (Kobayashi
and Libet, 1968; Weight and Votava, 1970; Krnjevic et al., 1971; Kuba
and Koketsu, 1976; Ross, 1989), the binding of a neurotransmitter could
lead to a decrease in membrane conductance. Such an EPSP would reverse around EK = 80 mV, and the EPSP
half-width is likely be of the order of seconds. Neither of these
features were observed in the P-to-AP EPSP (Fig. 3).
The logical possibility that the CNQX-sensitive glutamate receptor
channels are themselves voltage dependent is excluded by the
observation that in the truncated preparation without the Kir
conductance, the EPSP peak amplitude decreases with depolarization (Fig. 6C), consistent with voltage-independent glutamate
receptor channels and a decrease in driving force with depolarization. We were unable to measure the reversal potential of the P-to-AP synapse, because depolarizing the AP cells caused spikes and large decreases of the input resistance. However, previous studies of L-glutamate excitation in leech Retzius cells have shown
that glutamate causes a conductance increase in both sodium and
potassium ions (James and Walker, 1979). Extrapolation of the change of the voltage response to glutamate excitation with the membrane potential indicated a reversal potential around 10 mV (Mat Jais et
al., 1983), close to the value of 0 mV for mammalian AMPA receptors (Johnston and Wu, 1995).
Generalization to other systems
Kir channels are expressed in various invertebrate (Kandel and
Tauc, 1966; Benson and Levitan, 1983) and vertebrate neurons (Constanti
and Galvan, 1983; Gaehwiler and Brown, 1985; Stanfield et al., 1985;
Faber and Korn, 1986; Lasater, 1986; Shingai and Christensen, 1986;
Williams et al., 1988; Kawaguchi et al., 1989; Uchimura et al., 1989;
Ueda et al., 1992; Dong and Werblin, 1995; Holt and Eatock, 1995;
Krapivinsky et al., 1998; Mermelstein et al., 1998; Töpert et
al., 1998<
TOP
ABSTRACT
INTRODUCTION
