1Howard Hughes Medical Institute, Computational Neurobiology Laboratory, The Salk Institute, La Jolla 92037; and 2Department of Physics, 3Neurobiology Unit, Scripps Institution of Oceanography, 4Department of Neuroscience, and 5Department of Biology, University of California, San Diego, La Jolla, California 92093
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ABSTRACT |
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Moortgat, Katherine T.,
Theodore H. Bullock, and
Terrence J. Sejnowski.
Precision of the Pacemaker Nucleus in a Weakly Electric Fish:
Network Versus Cellular Influences.
J. Neurophysiol. 83: 971-983, 2000.
We investigated the relative
influence of cellular and network properties on the extreme spike
timing precision observed in the medullary pacemaker nucleus (Pn) of
the weakly electric fish Apteronotus leptorhynchus. Of
all known biological rhythms, the electric organ discharge of this and
related species is the most temporally precise, with a coefficient of
variation (CV = standard deviation/mean period) of 2 × 104 and standard deviation (SD) of 0.12-1.0 µs. The
timing of the electric organ discharge is commanded by neurons of the
Pn, individual cells of which we show in an in vitro preparation to
have only a slightly lesser degree of precision. Among the 100-150 Pn
neurons, dye injection into a pacemaker cell resulted in dye coupling
in one to five other pacemaker cells and one to three relay cells, consistent with previous results. Relay cell fills, however, showed profuse dendrites and contacts never seen before: relay cell dendrites dye-coupled to one to seven pacemaker and one to seven relay cells. Moderate (0.1-10 nA) intracellular current injection had no effect on
a neuron's spiking period, and only slightly modulated its spike
amplitude, but could reset the spike phase. In contrast, massive
hyperpolarizing current injections (15-25 nA) could force the cell to
skip spikes. The relative timing of subthreshold and full spikes
suggested that at least some pacemaker cells are likely to be intrinsic
oscillators. The relative amplitudes of the subthreshold and full
spikes gave a lower bound to the gap junctional coupling coefficient of
0.01-0.08. Three drugs, called gap junction blockers for their mode of
action in other preparations, caused immediate and substantial
reduction in frequency, altered the phase lag between pairs of neurons,
and later caused the spike amplitude to drop, without altering the
spike timing precision. Thus we conclude that the high precision of the
normal Pn rhythm does not require maximal gap junction conductances
between neurons that have ordinary cellular precision. Rather, the
spiking precision can be explained as an intrinsic cellular property
while the gap junctions act to frequency- and phase-lock the network oscillations.
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INTRODUCTION |
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The electric organ, whose timing precision was
first quantified decades ago (Bullock 1970;
Bullock et al. 1972
), remains the most precise known
biological pacemaker, but the mechanism of its extreme precision has
yet to be elucidated. The electric organ is commanded by the medullary
pacemaker nucleus (Pn), whose neurons in the in vivo Pn fire
synchronously with a coefficient of variation (CV = SD/mean
period) as low as 6 × 10
4, in turn
driving the electric organ to produce a signal with CV = 2 × 10
4, which gives SDs in the submicrosecond
range (Moortgat et al. 1998b
). Most other pacemaking
systems have CVs in the range of 10
2 to
10
1, with circadian rhythms slightly better
with CVs of 2-5 × 10
3 (see Table
1). We investigated the relative roles of
network electrotonic coupling and intrinsic cell properties in setting the extreme spike timing precision observed in one species of weakly
electric fish, Apteronotus leptorhynchus.
|
The weakly electric fish electrolocates using its electric organ
discharge, detecting its own electric field which is modified by the
surrounding environment, with electroreceptors along its body. The
timing and amplitude of the electric field at the electroreceptors are
the key information the fish has to make electrosensory discriminations (Heiligenberg 1991). The precise timing of the electric
organ is commanded by the Pn. Neurons of the Pn fire in synchrony, with each cell firing every cycle of the 500- to 900-Hz oscillation, even
when its inputs and outputs are cut (Dye 1988
;
Meyer 1984
).
The Pn is a network of 100-160 neurons that develop from the same
rhombomeres as other brain stem pacemakers, including the inferior
olive and VOR circuitry (Bass and Baker 1997). The Pn contains neurons of two types: pacemaker cells (25-30 µm soma diameter), which remain intrinsic to the nucleus, and relay cells (60-70 µm soma diameter) (Dye and Heiligenberg 1987
;
Elekes and Szabo 1985
), whose somata lie in the nucleus
and whose axons project down the spinal cord (Ellis and Szabo
1980
) to the electromotor neurons [electric organ in
Apteronotus (Bennett et al. 1967a
)]. These
two neuron types occur in a ratio of ~4:1, respectively, in adult
fish (Elekes and Szabo 1985
), although the number of pacemaker cells increases linearly with a fish's length without a
corresponding increase in relay cells (Dye and Heiligenberg 1987
). The input impedance of the pacemaker and relay neurons is ~3 and 1-4 M
, respectively (Dye 1991
;
Juranek and Metzner 1998
). The pacemaker cells converge
onto relay cells, which in turn send their axons down the spinal cord
to command the precise firing of the electric organ, with each relay
cell spike corresponding to one cycle of the electric organ discharge.
Evidence for a third neuron type have been reported (Turner and
Moroz 1995
) but was not mentioned in earlier electron
microscopic studies (Elekes and Szabo 1985
; Ellis
and Szabo 1980
). What role this third neuron type could have in
the Pn oscillations remains unclear.
Among Pn neurons of Apteronotus leptorhynchus, the species
studied here, gap junctions are the sole synaptic communication, and
occur at large axosomatic and axoaxonic club endings (Dye and
Heiligenberg 1987; Elekes and Szabo 1985
). Each
neuron appears to contact only a small fraction of the total number of
neurons, similar to the coupling reported in Hypopomus
pinnicaudatus (Dye and Heiligenberg 1987
;
Moortgat and Keller 1995
; Spiro 1997
). Gap junctions are present in abundance throughout the adult gymnotid electrosensory and electromotor pathways (Bennett et al.
1967a
; Yamamoto et al. 1989
) and are thought to
be important in time coding (Carr et al. 1986
) and
synchronization. It has been proposed that gap junctions among Pn
neurons could also play a role in reducing the CV of spike timing below
the intrinsic or natural CV of isolated neurons.
We investigated the network and cellular basis of spike timing precision in the in vitro Pn. We provide evidence that the precision of the pacemaker nucleus (Pn) in an electric fish could derive from cellular rather than network properties, and that the frequency- and phase-locking is modulated by gap junction coupling.
Earlier versions of this work were included in a PhD thesis and a
conference abstract (Moortgat 1999; Moortgat et
al. 1998a
).
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METHODS |
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Male and female Apteronotus leptorhynchus were
obtained under the common name "brown ghost" from a commercial fish
supplier. Fish were kept in aquaria whose water was maintained in
temperature (26.0-28.0°C), pH (7.0-8.0), and resistivity (5-15
k-cm). Fifty-six fish of 11-20 cm body length were used in this study.
The dissection procedure was similar to that of previous studies
(Dye 1988; Meyer 1984
; Spiro
1997
). Each fish was cold anesthetized, and the brain was
rapidly removed into cold artificial cerebral spinal fluid (ACSF; in
mM: 124 NaCl, 2 KCl, 1.25 KH2PO4, 1.1 MgSO4, 1.1 CaCl2, 16 NaHCO3, and 10 D-glucose), which had
been oxygenated and pH adjusted to 7.4. Tissue 1 mm rostral and caudal,
and ~2 mm dorsal to the Pn's ventral surface was cut away with a
scalpel. The remaining tissue block, including the whole Pn, was pinned in a silicone elastomer (Slygard) well and the meninges pulled away.
The tissue was continuously perfused with oxygenated ACSF.
Neural activity was monitored with a combination of sharp intracellular
(9-30 M) and local field potential electrodes (300
500 k
).
Amplified voltage signals were either directly digitized (National
Instruments ATMIO 16E2) at a rate of 20-200 kHz, or passed to a
Schmitt trigger circuit. The Schmitt trigger (Getting Instruments, Iowa
City, IA) has independently adjustable hysteresis center and width to
allow measurement of individual cycle periods within the detection
(±50 ns) of the data acquisition board.
To reveal neuron morphology and dye coupling, some neurons were filled
intracellularly with Neurobiotin (2% in 3 M KCl, Vector Laboratories,
Burlingame, CA). This tracer was injected ionotophoretically with
depolarizing current (0.5-2.0 nA) for 30-120 min. Tissue was then
fixed in 4% paraformaldehyde for 1-3 days and processed as described
elsewhere (Wong 1997).
We aimed to reduce gap junctional conductance with bath application of
gap junction blockers. The three agents used were halothane vapor
(2.5-5.0% in 95% O2-5%
CO2) (Peinado et al. 1993;
Wojtczak 1985
), octanol (1-5 mM, from 1 M stock in
DMSO, Sigma) (Johnston et al. 1980
), and carbenoxolone
(100 µM to 1 mM, Sigma) (Draguhn et al. 1998
).
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RESULTS |
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The spiking precision observed in neurons of the in vitro Pn, an
intact nucleus with all inputs and outputs cut, matched that seen in
neurons in the in vivo preparation. Namely, the distribution of
cycle-by-cycle periods (interspike intervals, Fig.
1A) for single cells tested
was Gaussian (2 tests were
significant) with a minimum half-width of 1.2 µs, corresponding to a
coefficient of variation (CV = standard deviation/mean period) of
7.0 × 10
4, similar to minimum values seen
in vivo (Moortgat et al. 1998b
). CV values, observed
during intracellular recordings, ranged from this minimum to ~25 × 10
4 in 40 neurons from 17 nuclei (Fig.
1B), with no apparent correlation between a cell's CV and
its frequency at room temperature. The pacemaker and relay cells, which
were distinguishable visually (when somata lay on the Pn surface) and
sometimes from spike shapes (see for example, Fig. 4A), did
not appear to differ in the distribution of their mean CV values (Fig.
1B).
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Because the pacemaker cells contact other pacemaker cells and relay cells, simultaneously recorded neurons could have correlations in the cycle-by-cycle variability about the mean period, correlations that could act to increase the CV. If the variability were correlated between cells, we would expect a distinct peak in the covariance. We would also expect that the root sum of the squared CV of two neurons would be greater than the CV of the cycle-by-cycle period difference. In the eight neuron pairs for which cycle-by-cycle periods were simultaneously recorded (Fig. 1C), the CVs were additive, and we found no clear peak in the covariance (Fig. 1D) and thus conclude that the cycle-by-cycle variability is independent between neurons.
Because the precision of Pn cell firing was maintained when all Pn inputs and outputs are cut, the spiking precision must be intrinsic to the Pn; either due to network connections, single cell properties, or a combination of the two. We first characterized the numbers and strengths of electrotonic connections and then modulated their strengths without altering the number of electrotonic connections.
Neuron morphology and dye coupling between neurons
Previous intracellular horseradish peroxidase (HRP) injections
into a number of pacemaker cells and one relay cell revealed their
cellular morphology and the number of axosomatic contacts made
(Dye and Heiligenberg 1987). We have extended these
anatomic studies by intracellularly injecting the tracer Neurobiotin
into multiple pacemaker and relay cells. Neurobiotin, unlike HRP,
crosses gap junctions, thus allowing us to assess not only physical
proximity but also functional gap coupling. The functional gap
junctions permit staining in coupled neurons, which are then readily
recognized and typed, even when coupling occurs between processes.
These latter contacts have been documented as axoaxonic gap junctions in electron microscopy studies (Ellis and Szabo 1980
)
but were not counted in the HRP studies.
Only one cell per Pn was injected with Neurobiotin. Three of six stained pacemaker cells were filled darkly in tissue with low enough background staining to evaluate dye coupling to other pacemaker cells and relay cells (Table 2). The filled pacemaker cells were dye coupled to one to five other pacemaker cells and one to three relay cells.
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The morphology of pacemaker cells stained with Neurobiotin and viewed
as fixed and histologically processed tissue was consistent with
previous studies (Dye and Heiligenberg 1987;
Elekes and Szabo 1985
). A few additional pacemaker cells
were injected with Lucifer yellow, which did not cross gap junctions in
these neurons, and observed in the live tissue under combined infrared
and fluorescent light using DIC optics. A striking observation was the
abundance of large-diameter (~6-9 µm) processes coursing
throughout the Pn [also noticed in electron microscopy (Elekes
and Szabo 1985
)]. These processes were found to be the
pacemaker cells' primary axons and their multiple, equally large
diameter branches. The axon narrowed slightly at branch points, but
within ~5 µm regained its initial diameter in both new branches.
These large pacemaker cell axons appear to take up a large percentage
of the Pn volume.
In five relay cells, dye injection resulted in staining of one to seven
pacemaker and one to seven other relay cells. Unlike previously
observed contacts, none of these contacts appeared to stem from the
filled relay cell's soma or axon but rather from its dendrites, one of
which is shown in Fig. 2A
coming in close proximity to a dye-filled pacemaker axon. This result
was not reported in previous electron microscopic or
electrophysiological studies, but is not contradicted by them. To
confirm that the dye coupling from the relay cell dendrites did not
result from the "shish kebob artifact," in which multiple cells
absorb dye through cell damage along the electrode track (Spray
and Bennett 1985), we injected neurons (1 per Pn) that lay on
the brain surface and were the only cell recorded in that Pn. Still,
dye coupling was observed. In addition, dye was localized to the soma
and axon initial segment of some dye-coupled neurons that were on
opposite sides of the Pn from the directly stained neuron. Thus our
data suggest electrotonic coupling at the relay cell dendrites.
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The morphology of relay cells was found to be more complex, with more
profuse and more finely branching dendrites than previously reported.
The dendrites sometimes tapered, only to increase in diameter again
more distally from the relay soma (Fig. 2A), and the finest
dendrites showed swellings or "beads." The dendrites of two relay
cells, one from a 12.9-cm-long female and one from a 12.4-cm-long male,
were particularly well stained and cover, respectively, ~100% and
68% of the lateral, 100% and 62% of the dorsal-ventral, and 61% and
53% of the rostral-caudal extent of Pn. One of these neurons (the
former) is drawn in Fig. 2B. If we assume that each relay
cell's dendrites are similarly extensive, the branches of different
relay cells are highly overlapping. The overlaps may be crucial to the
prepacemaker nuclei's ability to rapidly and simultaneously modulate
all relay cells' frequency, which is thought to be modulated primarily
at relay cell dendrites (Heiligenberg et al. 1996).
Electrophysiological measures of coupling strength across gap junctions
To unveil the effect of gap junctions on the firing of each neuron, we need to know not only the number of contacts, but also their strengths. The strength of coupling between a pair of neurons can be quantified by the coupling coefficient, defined as the ratio of the voltage deflection in one cell to that in another cell that is injected with a constant current. We hypothesized that the coupling coefficient between pairs of neurons making direct contact would be large because, despite relatively sparse connections (low numbers of contacts), the frequency and phase are tightly locked between all Pn neurons.
Coupling coefficient
Because the contacts are sparse, we expected only a subset of coupling coefficients to be nonzero. We were initially surprised that the coupling coefficients measured between every one of 26 neuron pairs, including both pacemaker and relay cells, were not significantly different from zero. These coupling coefficients were calculated from the deflection of the minimum voltage during 0.5-2.0 s of constant current injections (0.1-1.5 nA). Coupling coefficients were not observed at either long or short time constants. Likewise, current injection in one cell changed the spike amplitude in that cell but not in any simultaneously recorded neuron.
We recorded spike amplitudes to test whether poor space clamping or
membrane voltage fluctuations could explain the lack of measurable
coupling coefficient. A poor space clamp could allow a somatic current
injection to dissipate through leak conductances in the cell membrane,
resulting in a much smaller current at the distant gap junction contact
at the end of the axon. The low spike amplitude, often recorded at the
soma (as confirmed visually during the experiment and in some cases
after Neurobiotin staining), and its unusual decay with increased
membrane potential suggest that the injected current did indeed leak.
First, in the hundreds of intracellular recordings we made, the
recorded spike amplitude had a maximum of ~40 mV, but was more
typically in the range of 15-30 mV. The low spike amplitudes were not
indicative of poor recordings, because they occurred with stable
membrane potentials of approximately 75 to
65 mV in recordings that
lasted from tens of minutes to 7 h. Second, when currents were
injected, the peak voltage of the spike was not fixed (Fig.
3A, ±0.3 nA sine wave). Also,
the spike amplitude (Fig. 3B) decreased with depolarizing current at a lower rate than the minimum membrane potential increased (Fig. 3C) and showed hysteresis with membrane potential.
These results indicate that current was not injected in electrotonic proximity to the spike initiation zone.
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In our recordings, neurons did not have a fixed initial membrane potential, as required for measuring coupling coefficient. Rather, the neurons' active spikes clouded their passive responses to the gap junction drive. An active spike in a presynaptic neuron causes a substantial voltage drive across the gap junction to a phase-lagged postsynaptic neuron (Fig. 4A). The voltage drive is as large as the amplitude of a spike, or ~40 mV. Thus the effect of a small somatic current injection, like those we applied, whose amplitude has decayed along the long axon, may be overwhelmed by the drive of the presynaptic spike and the subsequent postsynaptic spike response.
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Phase shift with moderate current injection
Because measuring electrotonic coupling proved difficult with the
traditional measure, we sought other ways of detecting coupling. We
looked for phase and frequency shifts between a neuron injected with
current and another simultaneously recorded neuron. Normally, any two
neurons in the Pn fired at the same frequency with a fixed phase lag
(Fig. 4A). The phase lag was smaller between cells of the
same type than different types (Fig. 4B) (Dye
1988). If a neuron responds to current injection with either a
change in phase or frequency, then a similar simultaneous shift in the
second neuron would suggest coupling between the two neurons. We found that current injections into one neuron did not alter the phase of the
simultaneously recorded neuron (relative to its original phase) in any
of the 26 pairs we recorded. However, an injected neuron's phase
relative to another neuron (or its own original phase) was linearly
advanced with depolarizing current and delayed with hyperpolarizing
current (Fig. 4C, slope =
0.55%/nA,
r2 = 0.99). These results further
confirm that the current injections in one cell's soma were not
reaching the other recorded cell.
Skipped spikes during massive current injection
A neuron's firing frequency was immune to somatic injection of at
least ±10 nA. Even with this large current injection, a neuron
continued to fire with every cycle of the collective Pn oscillations.
How could large current injections have no effect on pacemaking
frequency when the Pn neurons can be driven to a range of frequencies
by higher-order brain centers, as shown in many previous studies
(Dye 1988; Heiligenberg et al. 1996
;
Spiro 1997
; see Heiligenberg 1991
for
review)? We sought to answer this question by injecting even larger
currents. A strong gap junction drive to each neuron (which could bring
the neuron to threshold and act as a current shunt) combined with the
large electrotonic distance between the gap junctions and the recording
electrode could result in the lack of response to the ±10 nA current
injections. If so, such injections at the soma might not be sufficient
to overcome the combined gap junction inputs at the axon initial segment and at the soma, and larger currents would be required to alter
the firing rate of the neuron in the intact Pn.
Intermediate current injections (10-14 nA) caused an alternation in the voltage amplitude from cycle to cycle. In one example, the spike amplitude was ~20% higher in one cycle than the succeeding cycle, and the time intervals were constant between the oscillations (Fig. 5B). All current injections caused an immediate, substantial drop in membrane voltage, followed by a slower voltage decay with time constant ~0.5 s (Fig. 5C), too large to be the membrane time constant of the single neuron, but possibly the time constant for slowly charging the entire Pn. The alternation in spike amplitudes began sooner, sometimes within the stimulus artifact time. During the time of slower voltage decay, the low-amplitude oscillations were distinguishable from the full amplitude oscillations, but both changed amplitude over 1 s.
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When neurons were instead injected with massive hyperpolarizing step currents of 15-25 nA, not only the spike amplitude but also the spike timing was affected. The full spikes that persisted arrived at roughly integer multiples of the preinjection cycle period, but the neuron no longer spiked with every cycle of the Pn oscillation (Fig. 5A). That is, the hyperpolarized neuron no longer had full amplitude oscillations locked 1:1 with the Pn oscillation, but rather had a full amplitude oscillation followed by a low-amplitude oscillation, usually locked 1:2 with the Pn oscillation. Concomitant with the alternation of amplitudes was an alternation in the peak-to-peak interval times of the oscillations (Fig. 5A). The intervals varied by ±0.05 ms (4%) around the cell's mean spike period before current injection.
Frequency locking between an injected neuron and the rest of the Pn could take on values of 1:1 and 1:2, and also much lower integer ratios that could change in time during the current injection. One neuron receiving 20 nA hyperpolarization, for example, went from normal firing (firing with every network oscillation) to skipping 1 spike in 16 network oscillations (1:16, Fig. 6A3), back to normal spiking, and then to skipping in a ratio of 1:23 (Fig. 6B3). When this neuron, which had a pacemaker cell waveform, skipped a spike, the membrane voltage still oscillated with a mean amplitude of 3.7 mV (range 0.5-7 mV). The ratio of the skipped to full spike amplitude can be taken as an estimate of the coupling coefficient (see discussion). The cycle period varied slightly and took on a new value during the cycle after every subthreshold oscillation (Fig. 6, A2 and B2). The membrane voltage continued to hyperpolarize in the repolarizing phase (trough) after each spike during the 2-s current injection (Fig. 6C).
|
Effects of pharmacological gap junction blockers
We next tested the importance of the observed gap junction
inputs in setting the extremely low CV of spike timing. We compared the
effects of bath application of halothane (1-5% vapor), carbenoxolone (100 µM to 1 mM), and octanol (1-5 mM), three putative gap junction blockers (halothane: Peinado et al. 1993;
Wojtczak 1985
; octanol: Johnston et al.
1980
; carbenoxolone: Draguhn et al. 1998
). Of primary interest were their effects on the CV of interspike periods. We
found that the CV, measured intracellularly, remained at its initial
low value, sometimes decreasing slightly (up to 20%) during application of halothane (Fig.
7A, n = 4) or
carbenoxolone (n = 2) over 30-40 min, or sometimes up
to 100 min, of sustained application of medium or high drug
concentrations. This relative constancy in the CV occurred during
substantial frequency decay elicited by all three drugs. In fact, the
frequency decreased by up to 50% in halothane (Fig. 7A),
20% in carbenoxolone, and 50% in octanol. Application of the blockers
also shifted the phase lag between simultaneously recorded neurons,
sometimes even changing its sign (Fig. 7B1). The phase lag
returned to its original value when the drugs were washed out.
|
After prolonged and continuous application of a high drug concentration, the spike amplitude decreased to a point beyond which no further spikes were elicited (Fig. 7, B2 and B3). As the spike amplitude decreased, the measured CV increased. This CV increase could simply be due to lower ratio of biological signal to electrical noise rather than to major changes in the gap junction strength. The minimum membrane potential (during the repolarization phase after a spike) remained within 5-10 mV of its original in all 11, 6, and 2 trials in, respectively, halothane, carbenoxolone, and octanol.
Spiking frequency decreased, apparently at the same rate in all Pn neurons, reaching a dose-dependent minimum frequency. Continued drug application reduced the spike amplitude such that all neurons appeared to stop firing simultaneously in halothane (Fig. 8A). That is, once one neuron stopped firing in a halothane-treated Pn, all others were also silent. In contrast, neurons in an octanol- or carbenoxolone-treated Pn stopped firing minutes apart. Neurons on the ventral surface of the Pn (which is the ventral surface of the brain stem) stopped firing while about two or three neurons deeper in the Pn continued firing for 1-3 min, although with reduced amplitude and often with 1:2 locking in the spike amplitude (Fig. 8B).
|
We tested whether the frequency decrease could be due to a
decrease in excitatory drive. Namely, halothane, known to depress glutamate transmission in some preparations (MacIver et al.
1996), might be blocking glutamatergic synapses from glia or
from axons arriving from higher order centers onto both cell types
(Dye et al. 1989
; Heiligenberg et al.
1996
). However, 30 min of bath application of
2-amino-5-phosphonovaleric acid (APV; 100 µM) and
6-cyano-7-nitroquinoxaline-2,3-dione (CNQX; 10 µmM), which are
N-methyl-D-aspartate (NMDA) and
-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA)
antagonists, respectively, did not alter the firing frequency or its
CV, and, on addition of halothane, did not alter halothane's ability
to decrease the Pn frequency (Fig. 9).
Therefore halothane does not seem to decrease frequency by modulating
glutamatergic synapses.
|
Other parameters that could affect precision of spike timing
Because pharmacological reduction of network coupling within the
range tested did not alter the firing precision of Pn neurons, the
precision must either have a highly nonlinear dependence on coupling,
or be largely a cellular property. We considered whether other
manipulations known to change cellular spike frequency also alter the
spike timing precision, or CV. Increasing the aquarium water
temperature from 20 to 30°C did not affect the CV of the electric
organ discharge in two A. leptorhynchus (B. Keeley and K. T. Moortgat, unpublished observations), although the frequency changed with a Q10 of 1.5 (Enger and Szabo 1968).
We found no correlation between female fish's body length and the CV
of their electric organ discharge, although body length and number of
pacemaker cells in the Pn are positively correlated (Dye and
Heiligenberg 1987). Two large males who chirped repeatedly had
particularly high CV of the electric organ discharge (CV = 20 × 10
4), even when not chirping.
Although the CV of the fish's electric organ discharge varies
spontaneously, as well as in response to behavioral stimuli (Moortgat et al. 1998b), we found no such CV modulations
in the 10-s intracellular recordings made in the isolated in vitro Pn.
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DISCUSSION |
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We have shown that the A. leptorhynchus Pn retains its extreme precision of firing in vitro. We have quantified the number of functional gap junctions between pacemaker and relay cells, and measured and modulated their strength.
We estimated the number of neurons electrotonically coupled to an
intracellularly dye-filled neuron by the number of dye-coupled neurons,
as done in rat neocortex (Kandler and Katz 1998;
Peinado et al. 1993
). The extent of dye coupling to
pacemaker and relay cells varied widely, due to natural variation in
the number of contacts and total number of Pn neurons, as well as
inconsistent dye uptake and transport. Indeed, dye appeared to travel
more completely into some neurons, sometimes even better in one process or type of process than others of the directly injected neuron. For
example, one relay cell showed a well-stained soma and axon, but only
part of one dendritic process was obviously filled. Dye coupling was
not symmetrical: the number of relay cells dye coupled to a pacemaker
cell was slightly smaller than the number of pacemaker cells dye
coupled to a relay cell. Some of the differences in dye uptake and
transport could result from larger currents for longer durations in
some cells, as well as the difficulty of fully filling with dye the
huge volume, including, for the pacemaker cell, a 30-µm-diam soma and
7- to 10-µm-diam axon of 1 mm length and multiple branches, a volume
that can be even larger for the relay cell. Because many of these
factors act to reduce the number of dye-coupled neurons, we tend to
bias our estimate of the number of contacts toward the higher values.
In a typical adult Pn of 150 neurons, in a ratio of 4:1 pacemaker to
relay cells (Ellis and Szabo 1980), the pacemaker cells contact a maximum of 4% (5/120) of other pacemaker cells and 10% (3/30) of relay cells. The relay cells in turn are in electrotonic contact with 6% (7/120) pacemaker cells and 23% (7/30) other relay cells. This coupling is quite sparse compared with the all-to-all coupling often estimated in models of tightly synchronized oscillatory systems.
We found that relay cell dendrites were intricately branched and could
reach across the full dorsal-ventral and medial-lateral extent, and
~60% of the rostral-caudal extent of the Pn. This dendritic arbor
exceeds estimates from the one relay cell fill previously described
(Dye and Heiligenberg 1987) and may provide multiple
sites of contact with the widely distributed inputs
(Heiligenberg et al. 1996
) from higher centers. These
higher centers may require multiple contact sites to effect their
strong and rapid modulations of the Pn frequency (Dye
1987
; Kawasaki and Heiligenberg 1990
; Keller et al. 1991
; Metzner 1993
),
something that proved difficult to do with somatic current injection
into a single neuron (Fig. 3).
Dendritic gap junctions onto relay cells were previously reported in
other species of electric fish (Sternopygus and
Steatogenys) but were thought to originate only from
pacemaker cell axons (Bennett et al. 1967b).
Electrotonic coupling between relay cells, which was physiologically
supported in these species, was hypothesized to occur indirectly
through pacemaker cell terminals (Bennett et al. 1967b
).
In the species studied here, A. leptorhynchus, axosomatic
and axoaxonic electrotonic coupling had been reported (Elekes
and Szabo 1985
). We provide the first evidence in this species
that an additional site of coupling occurs: axodendritic connections
between pacemaker and relay cells. Additionally we show that relay
cells are directly dye coupled to other relay cells, often through
connections from one relay cell's soma to another's dendrite. Thus
electrotonic spread between relay cells can occur directly. This may
facilitate coordination between relay cells when higher order inputs
bypass the pacemaker cells and send commands directly to the relay
cells (Heiligenberg et al. 1996
; Kawasaki and
Heiligenberg 1989
). Similarly, dendritic gap junctions are
thought to be involved in synchronization of spiking in the inferior
olive (review in DeZeeuw et al. 1998
) and in the developing visual
cortex (Kandler and Katz 1998
).
How can higher order centers drive Pn cells to fire at higher
frequencies while intracellular injection of up to 10 nA has no effect
on firing frequency? The main reason may be that the higher order
centers synaptically modulate many cells simultaneously, while we
inject current into only one or two cells at a time. Also, the location
of the inputs may be crucial. Boutons of chemical synapses, thought to
arise from the higher order centers, cover the dendrites, somata, and
axon hillock (Elekes and Szabo 1985). Even when these
synaptic inputs are silent, our current injections must overcome gap
junction inputs. Gap junctions from one pacemaker cell contact other
pacemaker cells primarily at the axon initial segment, but also on a
short dendrite, and the soma. Likewise, the axon initial segment of the
relay cell receives particularly dense axoaxonic gap junction
innervation, which is considered "the morphological correlate of a
synchronizing function" (Elekes and Szabo 1985
).
Likewise, axoaxonic gap junctions in a model of another system, the
hippocampus, were shown sufficient to synchronize high-frequency
oscillations between pyramidal neurons (Draguhn et al.
1998
; Traub et al. 1999
).
The limited effect of current injections to the pacemaker and relay
cell somata may also arise from a long electrotonic distance to the
action potential initiation zone. Indeed, the small somatic spike
amplitude, particularly in the relay cell, indicates just this.
Similarly small somatic action potentials can be seen in other systems
when the spike initiation zone lays distant from a neuron's soma, such
as in the molluscan photoreceptors (Alkon and Fuortes
1972). Another reason to believe the Pn cells' action potential initiation zones are distant from the soma is the small size
of observed changes in spike amplitude with current injection. In the
example of Fig. 3, the spike amplitude only decreased ~5.8 mV during
a recorded membrane potential shift of ~17 mV. Thus the peak spike
voltage, rather than being a fixed property of the spike, appears
labile to membrane voltage at the electrode. We hypothesize that the
small change in spike amplitude reflects a small membrane voltage
deflection at the site of action potential initiation. The recorded
membrane potential is local to the recording electrode, but does not
indicate the true membrane potential at the axon initial segment. That
is, the neuron is not well space clamped.
Lack of space clamping in a neuron will hinder traditional measures of
coupling coefficient: the voltage deflection of a current-injected neuron will decay down the axon and may not alter the membrane potential of a coupled neuron. Even measuring coupling coefficients between neurons silenced with tetrodotoxin or 4-aminopyridine (Dye 1991; Smith and Zakon 1998
) would
fix membrane potentials of both cells at the recording sites, but still
have a space-clamp problem. A space clamp could best be achieved with
dual patch-clamp recording, in which the prejunctional axon and the
postjunctional soma or axon are simultaneously recorded. The latter
experiments have not yet been conducted for technical reasons.
We can, nevertheless, estimate the coupling coefficient. When massive
current was injected in the soma, a neuron began to skip spikes in
multiples of the Pn oscillation. The ratio of the subthreshold
oscillation to the full spike amplitude can be taken as an estimate of
the total coupling coefficient, the ratio of postsynaptic voltage to
presynaptic voltage, if we assume that the presynaptic voltage has the
amplitude of a full spike. For the data in Fig. 6 (probably a pacemaker
cell recording), the ratio is ~0.08. Dividing by the maximum number
of contacts to a pacemaker cell (Table 1) yields a coupling coefficient
of ~0.01. Similar analysis of the data from a likely relay cell (Fig.
5) yields a post- to presynaptic voltage ratio of ~0.65, giving a coupling coefficient of ~0.05. Thus the larger subthreshold
oscillations in Fig. 5 than in Fig. 6 may reflect larger numbers of gap
junction contacts, higher coupling coefficient, and different cell
types. Certainly the coupling coefficient among Pn neurons is
significantly smaller than the 0.03-0.14 measured in mouse motoneurons
(Rekling and Feldman 1997), or the 0.6-0.9 between
pairs of cultured horizontal cells (Lasater and Dowling
1985
). Our estimate of the coupling coefficients will vary
slightly depending on the strength of injected current. Also, the true
coupling coefficient between pacemaker and relay cells may be
significantly higher if there are fewer contacts, or if presynaptic
voltage is less than the amplitude of a full spike as recorded in the
current-injected cell.
Although the relative amplitudes of the subthreshold oscillations and
the spike peaks provide an estimate of the coupling coefficient, the
relative timing of the two events provides evidence for the cell's
intrinsic firing properties. Certainly we expect to find at least a
subset of Pn neurons that are spontaneously active, because the Pn
oscillates without external drive (Meyer 1984). The
small precession in the pacemaker cell's cycle period around the Pn
oscillation frequency during the massive current injection suggest that
the pacemaker cell has an intrinsic firing frequency that is different
from the Pn frequency (Chay et al. 1995
; Winfree
1987
). The cell's intrinsic frequency may normally be close to
the Pn oscillation frequency, but may have been decreased by the
massive current injection. The electric fish pacemaker neurons need not
have the same firing frequency to synchronize: simulations have
demonstrated synchrony between coupled oscillators of distributed
intrinsic frequencies (Matthews and Strogatz 1990
; Moortgat et al. 2000
).
We next tested the importance of gap junctions in setting the extremely
low CV of spike timing observed intracellularly in Pn cells. Our
investigations mainly focused on decreasing the gap junctional coupling
strengths with pharmacological agents that, in the ideal case,
electrically dissociate neurons. Physical dissociation of the Pn, using
techniques developed by Turner et al. (1995), resulted
in live neurons with phase-bright somata and axon initial segments, but
preliminary experiments yielded neurons that were electrically inactive
(both spontaneously and with step current stimulation). The lack of
electrical activity may reflect damage caused by the dissociation
rather than the true nature of the normal neurons.
All 3 pharmacological gap junction blockers in 19 total trials
decreased the spike frequency, demonstrating that the drugs are having
some effect on the Pn. Still we did not know whether the drugs were
affecting the gap junctions. Evidence that the drugs do indeed act on
gap junctions was the consistency of responses to the three chemically
different drugs: no drug caused an increase in the CV of a neuron's
interspike period while the spikes maintained their full amplitude. Our
preliminary results with high-pH ACSF, known to reduce gap junction
conductance in some systems (Spray and Bennett 1985),
showed reversible frequency and spike amplitude decreases, similar to
those reported here with other gap junction blockers.
Additional evidence that the gap junctions were closing comes with
comparison to a realistic compartmental model of the Pn (Moortgat et al. 2000). The model is consistent with the
biological spike waveform and frequency (Fig. 4A), the phase
distribution observed in the Pn (Fig. 4B), and in a cell's
phase response to current injection. The model predicts shifts in
relative phase lag between neurons, even to the point of switching
polarity, as gap junction coupling is decreased, as observed in the
physiological data (Fig. 7B1). That the phases are still
locked at all suggests that the drug is causing partial but possibly
not full block while the spikes have their full amplitude. Another more
general model also confirms that decreased gap junction conductance
reduces firing frequency in neurons whose spike shape is similar to the Pn neurons (Chow and Kopell 2000
). Other lines of
evidence that the drug was taking its purported action, including a
decreasing coupling coefficient or decreasing number of dye-coupled
neurons, were considered but not pursued for technical reasons.
Although the three gap junction blockers had many consistent effects, they differed in the way their continued application stopped Pn oscillations. Although halothane seemed to stop oscillations in all neurons simultaneously, octanol and carbenoxolone left a few neurons oscillating deep in the nucleus while the surface neurons were silent. The halothane may diffuse more uniformly through the tissue, although this is not due to a lower formula weight (formula weights for halothane, octanol, and carbenoxolone are 197.4, 130.2, and 614.7, respectively). Another difference between the drugs was the reversibility of their effects: washing out halothane returned the Pn to its original synchronized firing state within minutes, with the phase lags returning to prewash values, whereas octanol and carbenoxolone were not entirely reversible, leaving only a subset of neurons firing asynchronously after hours of wash out. The ease of reversibility with halothane, and relatively greater difficulty with octanol, has been similarly observed in other systems (D. Spray, personal communication).
The Pn neurons stopped oscillating when a drug-dependent frequency was
reached. The dependence of the minimum frequency on the drug suggests
that frequency changes may not be mediated by gap junction closure, but
by drug side effects. Halothane, for example, is known to enhance
GABAA-mediated inhibition (Pearce 1996), depress glutamate-mediated excitation (Perouansky
et al. 1995
, 1996
), and inhibit
Ca2+ and Na2+ channels
(Franks and Lieb 1994
), in addition to blocking gap junctions (Peinado et al. 1993
; Wojtczak
1985
). The first of these effects is not relevant to the
A. leptorhynchus Pn, whose inputs are not GABA mediated but
glutamatergic (Dye et al. 1989
; Heiligenberg et
al. 1996
). We found that blocking the glutamatergic synapses did not decrease frequency, nor does it hinder halothane's ability to
reduce Pn frequency. The possibility remains that halothane blocks the
Pn neurons' Ca2+ and Na2+
channels, which is known to reduce the Pn firing frequency (Dye 1991
; Smith and Zakon 1998
). This hypothesis has
not yet been tested experimentally but is supported by our realistic Pn
model (Moortgat et al. 2000
). In contrast, another model
of gap junction-mediated oscillations did achieve ~40% frequency
change with modulated gap junction conductance (Kepler et al.
1990
).
In addition to modulating the strength of contacts between Pn neurons,
we considered reducing their number by removing Pn neurons.
Unfortunately, cutting the Pn in half with a razor or vibratome
irreversibly silenced the Pn. More selective removal, killing one
neuron at a time with Lucifer yellow injection followed by strong
illumination (Miller and Selverston 1979), is feasible, but the data analysis is problematic. Functional removal of single neurons by hyperpolarization was not possible because even
25 nA did
not silence a neuron.
Another way of assessing the importance of the number of Pn cells on
their spike timing precision is to look at developmental changes in the
CV of the electric organ discharge. Hagedorn et al.
(1992) found in a related weakly electric fish,
Eigenmannia, that the CV of the electric organ discharge
decreases with increasing body length up to 1.5-2.0 cm, at which stage
the Pn contains ~60 neurons, differentiated into two classes, as seen
in the adult fish. The A. leptorhynchus Pn continues to
develop more pacemaker cells with increasing body length even at the
adult body lengths of 15-25 cm (Dye 1991
). However, we
did not observe a decrease in the CV of the electric organ discharge
with increasing body length in the fish we studied (11-20 cm). Thus
the spiking precision does not appear to be sensitive to the addition
of neurons beyond a minimum number.
In summary, decreasing the gap junction strength, the number of gap
junction inputs, or the number of Pn neurons did not alter the CV of
the interspike period. Instead of dramatically decreasing CV, the gap
junctions may be most involved in frequency and phase locking. Indeed,
Dye (1991) showed that treatments thought to increase
intracellular calcium broke up the frequency and phase locking between
simultaneously recorded Pn neurons.
Taken with previous studies, our results indicate that the extreme
spike timing precision in the A. leptorhynchus Pn could primarily be an intrinsic property of each neuron and may only minimally depend on the Pn network interactions. That is, the network
may not act to dramatically increase the precision of otherwise sloppy
neurons. The CV commonly reported for individual neurons is
~101 to 10
2 (Table
1). This is the first suggestion that individual neurons could
intrinsically have a CV as low as ~7 × 10
4, equivalent in this example cell to SD = 1.2 µs.
On the other hand, convergence of relay cells onto the electromotor
neurons of the electric organ could explain the relatively small
decrease in CV (increase in precision) between them. The minimum CV of
the electromotor neurons, as measured outside the tail, is ~2 × 104 (Moortgat et al. 1998b
),
3-4 times less than the minimum CV of relay cells. According to the
law of large numbers, such a CV decrease would require a convergence of
9-16 independent relay cells onto each electromotor neuron. This
prediction of convergence is consistent with anatomic data showing that
each relay cell electrotonically innervates most or all the
electromotor neurons (Ellis and Szabo 1980
). We must
assume that the electromotor neurons do not themselves add noise to the
output; they too must be capable of extremely high precision spiking.
The CV of the fish's electric organ discharge varies spontaneously, as
well as in response to behavioral stimuli. These changes may be
mediated by a higher order nucleus, the prepacemaker nucleus (Moortgat et al. 1998b). We found no such CV modulations
in the 10-s recordings made in vitro. However, we did observe that two large males (~20 cm) who repeatedly modulated their electric organ frequency (in a glutamate-driven "chirp") had particularly high CV
of the electric organ discharge (CV = 20 × 10
4). The CV of Pn neurons, and hence of the
electric organ discharge may be increased with active glutamatergic
(AMPA) PPn inputs to their site of contact, the relay cells
(Heiligenberg et al. 1996
). Similarly, the CV of Pn
neurons could be at its lowest with all inputs to the Pn silent. If so,
application of AMPA to specific locations on the relay cell soma and
dendrites would increase the interspike period CV.
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ACKNOWLEDGMENTS |
---|
We thank J. Fellous for assistance with recording data in Fig. 3; J. Dye, J. Fellous, W. Kristan, J. Seamans, and C. Wong for helpful discussions; E. Calloway, G. Kennedy, and D. Needleman for assistance with histology; and W. Kristan and two anonymous reviewers for thoughtful critique of the manuscript.
K. T. Moortgat was supported by National Institute of Mental Health Predoctoral Fellowship MH-10864-03 and by the Sloan Foundation; T. H. Bullock by the National Institute of Neurological Disorders and Stroke; and T. J. Sejnowski by the Howard Hughes Medical Institute.
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FOOTNOTES |
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Present address and address for reprint requests: K. T. Moortgat, Sloan Center, Dept. of Physiology, University of California, San Francisco, Box 0444, 513 Parnassus Ave., San Francisco, CA 94143-0444.
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 19 March 1999; accepted in final form 18 October 1999.
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REFERENCES |
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