Volen Center and Biology Department, Brandeis University, Waltham, Massachusetts 02454-9110
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ABSTRACT |
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Birmingham, J. T., Z. B. Szuts, L. F. Abbott, and Eve Marder. Encoding of Muscle Movement on Two Time Scales by a Sensory Neuron That Switches Between Spiking and Bursting Modes. J. Neurophysiol. 82: 2786-2797, 1999. The gastropyloric receptor (GPR) neurons of the stomatogastric nervous system of the crab Cancer borealis are muscle stretch receptors that can fire in either a spiking or a bursting mode of operation. Our goal is to understand what features of muscle stretch are encoded by these two modes of activity. To this end, we characterized the responses of the GPR neurons in both states to sustained and rapidly varying imposed stretches. The firing rates of spiking GPR neurons in response to rapidly varying stretches were directly related to stretch amplitude. For persistent stretches, spiking-mode firing rates showed marked adaptation indicating a more complex relationship. Interspike intervals of action potentials fired by GPR neurons in the spiking mode were used to construct an accurate estimate of the time-dependent amplitude of stretches in the frequency range of the gastric mill rhythm (0.05-0.2 Hz). Spike trains arising from faster stretches (similar to those of the pyloric rhythm) were decoded using a linear filter to construct an estimate of stretch amplitude. GPR neurons firing in the bursting mode were relatively unaffected by rapidly varying stretches. However, the burst rate was related to the amplitude of long, sustained stretches, and very slowly varying stretches could be reconstructed from burst intervals. In conclusion, the existence of spiking and bursting modes allows a single neuron to encode both rapidly and slowly varying stimuli and thus to report cycle-by-cycle muscle movements as well as average levels of muscle tension.
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INTRODUCTION |
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Sensory neurons use a variety of coding strategies to deal with the wide dynamic range of the stimuli to which they respond. Some sensory neurons respond phasically to a signal, that is, their firing rates are initially affected by rapid changes in the stimulus but subsequently adapt. Other sensory neurons show considerably less or no adaptation and encode sustained stimulus intensities. An advantage of sensory neurons that show adaptation is that they can report changes in stimulus intensity over a very large range, whereas neurons that do not have appreciable adaptation may only be able to report stimulus intensity over a more limited range of values. It is often assumed that information about changes in stimulus intensity and information about sustained stimuli are encoded by different neurons. In this paper we demonstrate that a single muscle stretch receptor neuron can encode information over two different time scales by firing in two modes, spiking and bursting. Information about rapid changes in muscle stretch is encoded by interspike intervals, whereas information about sustained muscle length is encoded by burst intervals.
The gastropyloric receptor (GPR) neurons are two bilateral pairs of
stretch-sensitive neurons that provide sensory input to the
stomatogastric nervous system of the crab Cancer borealis (Katz et al. 1989). The stomatogastric nervous system of
C. borealis is a small, well-studied neural network that
controls stomach movements (Harris-Warrick et al. 1992
).
The 25-26 motor neurons (Kilman and Marder 1996
) in the
C. borealis stomatogastric ganglion (STG) can be divided
roughly into two groups: those innervating the muscles that move three
teeth in the gastric mill (chewing) and those innervating the muscles
that dilate and constrict valves in the pylorus (filtering)
(Maynard and Dando 1974
). The pyloric rhythm has a
period of 0.5-2 s (Harris-Warrick et al. 1992
), whereas the period of the gastric mill rhythm is typically 5-20 s
(Coleman et al. 1995
; Mulloney and Selverston
1974a
,b
). Gastropyloric receptor neuron 2 (GPR2) innervates
both a gastric mill muscle gm9 and a pyloric muscle
cpv3a. Katz et al. (1989)
found that GPR2
fired action potentials in response to either passive stretch or
nerve-evoked contraction of the innervated muscles. In response to two
second duration ramp-and-hold stretches, the GPR2 firing rate showed modest adaptation, and the number of spikes varied linearly with either
the muscle length or tension (Katz et al. 1989
). In some preparations, GPR2 was observed to fire rhythmic bursts of action potentials in the absence of any apparent sensory stimulus (Katz et al. 1989
). In this paper, we study quantitatively the
encoding properties of GPR2 in the two modes that Katz et al.
(1989)
initially described.
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METHODS |
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Animals and solutions
Adult crabs, Cancer borealis were obtained from local seafood suppliers and kept stored in aerated aquaria at 12-15°C. We used physiological saline with the following composition (in mM): 440 NaCl, 11.3 KCl, 13.3 CaCl2, 26.3 MgCl2, 5.2 maleic acid, and 11.0 Trizma base, pH 7.4-7.5.
Physiology
The STG and muscles were dissected according to Hooper et
al. (1986). The stomach was removed from the animal, slit
ventrally from the esophagus to the midgut, and pinned flat in a
dissecting dish. The anterior ganglia, STG, and nerves and muscles
associated with the GPR2 neuron from one side of the animal were
removed and pinned in 20-ml silicone elastomer (Sylgard)-coated (Dow
Corning, Midland, MI) Petri dishes. After confirming the presence of a pyloric rhythm, we cut the dorsal ventricular nerve (dvn),
isolating the GPR2 neuron and muscles from the STG (Fig.
1). During recording sessions, the
preparations were continuously superfused (~10 ml/min) with saline
cooled to 11-13°C. Extracellular measurements of the activity in the
gastropyloric nerve (gpn), which contains the GPR2 axon,
were made using stainless steel bipolar pin electrodes or glass suction
electrodes, amplified by an AM-Systems 1700 differential amplifier
(Carlsborg, WA), and recorded using an Axon Instruments (Foster City,
CA) data interface board. Spike times were extracted from extracellular
recordings using the program Datamaster developed in our laboratory by
W. Miller and C. Howe and were analyzed using routines written in
Matlab (The MathWorks, Natick, MA). All of the motor axons that project
into the dvn bifurcate and then project into both lateral
ventricular nerves (lvns), whereas the GPR axons project up
only in the ipsilateral lvn. To be certain that action potentials measured in the gpn were from GPR2 and not a
motor axon, we often placed another extracellular electrode on the
contralateral lvn and confirmed that the action potentials
were not observed.
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Muscle stretching
For all measurements, we stretched the cpv3a muscle
(Maynard and Dando 1974). The muscle origin was pinned
to the Sylgard-coated dish (Fig. 1). The insertion was attached to a
Grass force-displacement transducer (Model FT03, Quincy, MA) via no. 6 suture thread. The transducer in turn was attached to the lever arm of
a chart recorder pen motor [removed from a defunct Gould 440 (Cleveland, OH)] via another thread. Because the thread between the
muscle insertion and the transducer was taut and much less elastic than
the muscle, in this configuration the transducer measures muscle length
(Fig. 1). The pen motor was driven and hence the muscle stretched using voltage waveforms generated on a Pentium 266 MHz computer using the
data acquisition program LabView (National Instruments). In the
decoding experiments we stretched the muscle with filtered white noise.
The white noise was generated using the computer and was filtered by
passing it through a single pole RC filter. The muscle displacement was
measured using the displacement transducer and calibrated visually to
±0.02 mm using an eyepiece with a reticule. Before each experiment the
transducer was adjusted so that the muscle was completely extended
(relaxed length 2-3 mm) but under no tension. The muscle was then
stretched (<0.1 mm) until a threshold response was observed and then
slightly relaxed.
Decoding techniques
GPR2 fires either in a spiking or bursting mode. We used two
techniques, interspike interval (ISI) decoding and linear filters, to
generate an estimate
Sest(t) of the muscle
stretch waveform S(t) that evoked a given spike
train with spike times ti, i = 1, 2, . . . in a GPR2 preparation in the spiking mode. We found that we
could use an interspike interval code to describe the encoding of
stretch when the stimulus varied slowly compared with the interspike
interval. The interspike interval at spike time ti is the time since the last spike,
ti ti
1. Because increased stretch amplitude results in decreased
interspike interval, it is useful to define a "rate" at each spike
time by inverting the interspike interval,
R(ti) = (ti
ti
1)
1. When stretch increases, this rate increases.
To construct an ISI decoding relationship, we stretched the muscle with
waveform S(t) and calculated
R(ti) for all values of
i. We then plotted S(ti) versus
R(ti) for each of the spike
times and fit a function
(R) to the data
points using the SigmaPlot program (Jandel Scientific, San Rafael, CA.)
The function was of the form
(R) = A + B(1
e
CR), where A, B,
and C are free parameters used in the fit. For small values
of R,
(R) depends linearly on
R. For large values of R,
(R) approaches a constant. To decode
another spike train with spike times tj,
j = 1, 2, . . . we computed
R(tj) and constructed an
estimate of the stretch Sest at time
tj as
[R(tj)].
Between spike times, R(t) was defined by linear interpolation.
We used the technique of linear filters (Rieke et al.
1997) to reconstruct the stretch stimulus from spike times for
spiking GPR2 neurons when the stimulus varied rapidly. From spike times ti, i = 1, 2, . . . N, we constructed an estimate of the stimulus Sest(t) using a linear
kernel K(t) and a constant
S0
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(1) |
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(2) |
When the GPR2 neuron was in the bursting mode, we used a burst interval (BI) decoding scheme to interpret the burst train and to estimate the stretch. The burst interval, BI, is the time from the start of the previous burst to the start of the present burst. The decoding procedure was identical to that used with spiking mode neurons, except in this case ti referred to the start time of the ith burst. The duration of the burst was not used in the decoding.
For each of our estimates of the stimulus
Sest(t), 0 < t < T, constructed using the ISI decoding
method, the BI decoding method, or the linear filter technique, we
calculated a normalized root-mean-square (RMS) error
Enorm
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(3) |
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RESULTS |
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GPR2 neurons show two modes of activity, spiking and bursting
Figure 2A shows the response of a GPR2 neuron to a rapid muscle stretch. The GPR2 response began soon after the start of the stretch. During the first few hundred milliseconds of firing, the instantaneous firing rate (the reciprocal of the interspike interval) adapted rapidly, falling from >20 Hz to ~5 Hz. The rate continued to decrease during the next 6 s before stabilizing near 2.5 Hz. The cell stopped firing when the muscle was released. We define GPR2 neurons with this kind of behavior as being in the spiking mode. In the absence of a stretch stimulus, spiking mode neurons were either quiescent or fired at a slow (<1 Hz) rate. Thirty-seven of 58 GPR2 neurons were in the spiking mode at the start of our recordings.
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Figure 2B illustrates the behavior of GPR2 neurons that we define as being in the bursting mode. During the 4 min preceding the stimulus, the neuron shown in Fig. 2B fired bursts of action potentials with a burst period of 63.1 ± 2.8 (SD) s. We then gave a train of 3-s duration stretches at 30-s intervals. This entrained the bursting to a 30-s period. During the 3 min after the periodic muscle stretch was stopped, the burst period was 65.7 ± 2.1 s. Twenty-one of 58 GPR2 neurons were in the bursting mode at the start of our recordings. The average burst period of unstretched bursting mode preparations ranged from 12 to 101 s. The mean average burst period was 32.7 ± 20.1 s (n = 21) in the absence of stretch.
Response of spiking mode GPR2 neurons to persistent (DC) and time-varying (AC) stretches
We wished to characterize the response of spiking GPR2 neurons to stimuli that varied in amplitude, rise-time, and duration. We used long duration constant stretches to characterize the persistent response (we call this the DC stimulus), and we employed sine waves to characterize the phasic response (we call this the AC stimulus). We chose 3 s as the period of the time-varying stimulus because this is between the periods of the pyloric and gastric mill rhythms.
Figure 3A shows the response of a spiking mode GPR2 neuron when unstretched and in response to persistent stretches of 0.23 and 0.51 mm. Each recording was made after allowing the firing rate to stabilize (~5 s). Figure 3B shows the equilibrium firing rate in response to DC stretches for five spiking preparations. Here, "equilibrium rate" means the average rate after spike rate adaptation has taken place. To calculate the equilibrium firing rate for a given stretch amplitude, we stretched the muscle, waited 15 s, and then counted the number of spikes fired during the next minute. We then released the stretch and waited 2 min before making the next measurement. For each preparation, the equilibrium firing rate increased with amplitude for stretches up to 0.5 mm. Linear fits to the data sets showed that the sensitivity to stretch measured in Hz/mm varied over a factor of three for the five preparations. Analysis of variance (ANOVA, 1-way) of the entire data set showed a statistically significant (P < 0.001) dependence of the firing rate on amplitude. We note that the maximum equilibrium firing rate observed at any amplitude was ~4.5 Hz.
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Figure 4A shows the response of a spiking mode GPR2 neuron to a series of sine wave (3-s period) stretches with the same mean (DC component) value but different AC amplitudes. The amplitude of the DC component of the stretch was 0.3 mm, which prevented the muscle from becoming completely relaxed during the minima of the stretch. As the amplitude increased, the number of spikes fired during each period increased, and the spikes became more tightly clustered, firing at a nearly constant phase with respect to the stimulus.
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To describe the relationship between AC stretch amplitude and GPR2 activity, we computed the instantaneous firing rate for the experiment shown in Fig. 4A. The dependence of the average instantaneous firing rate on the AC amplitude is plotted in Fig. 4B. The average instantaneous firing rate was that calculated from all interspike intervals over a 60-s time period. As the AC amplitude increased, the rate increased dramatically. The average instantaneous firing rates from six preparations and two AC amplitudes are shown in Fig. 4C. The increase in the rate with increased amplitude was highly significant (P < 0.003).
Response of bursting mode GPR2 neurons to persistent (DC) and time-varying (AC) stretches
Figure 2B shows that GPR2 neurons in the bursting mode responded to muscle stretch. We repeated the DC and AC stretch experiments that had been done on spiking mode neurons to determine whether a different aspect of stretch is encoded in the bursting mode. Figure 5A shows the response of a GPR2 neuron to sustained stretch. The response before any stretch was applied is shown in the top trace. The average burst period was 79.3 ± 14.2 s. The second trace shows the response during a 0.2-mm DC stretch, 5 min in duration. The average burst period was 39.1 ± 1.8 s. The third trace shows the response during a 0.35-mm stretch. The average burst period was 29.0 ± 2.2 s. After the release of the muscle from the larger stretch, the bursting stopped for 2 min (missing 1 burst) and then resumed (bottom trace). The average period during the next 5 min was 74.5 ± 13.0 s. Figure 5B is a plot of the burst interval for the two stretches during the time shown in Fig. 5A. It remained relatively constant and did not adapt during the two imposed stretches.
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Because the burst period decreases with increased DC stretch, it is useful to define the equilibrium bursting "rate" to be the inverse of the average burst period. We determined the relationship between the equilibrium bursting rate and the amplitude of DC stretch for seven preparations stretched to a range of DC amplitudes. For each measurement we stretched the muscle from the rest length, held it at a particular length for 5 min, and measured the average burst period. Between stretches we waited 5 min. The average burst period of unstretched preparations varied between 20 and 101 s. For purposes of comparison, we normalized the burst rates of each preparation to the rates when the preparations were unstretched, and we computed the fractional changes in the burst rate. These are plotted in Fig. 5C, where each symbol corresponds to a different preparation. In all cases the burst rate increased with stretch with an approximately linear dependence. The solid line is the best linear fit to the pooled data and has a Y intercept of 0.04 and a slope of 3.47/mm. There was a significant association between the bursting rate and stretch (1-way ANOVA, P < 0.001, F = 70.4).
Figure 6A shows the response of a bursting preparation to sinusoidal stretches (3-s period) with amplitude ranging from 0 to 0.27 mm. When the AC amplitude was increased from 0 to 0.135 mm the average burst period remained almost constant (29.0 vs. 29.7 s), although the timing of the burst onsets was affected. With increased amplitude, the bursts became more likely to be triggered by stretch, and hence individual burst periods tended toward multiples of the 3-s stimulus period. Increasing the AC amplitude to 0.20 mm decreased the average period to 25.6 s. When a 0.27-mm AC stretch was used, the average period decreased slightly to 24.4 s. In between bursts, spikes phase-locked to the stimulus were fired, as shown in the inset. In this case, GPR2 reports information about the fast component of the stimulus in the phase-locked spikes and information about the slow component, that is the DC stretch, in the average burst frequency. It is interesting to note that the bursting mode GPR2 response to the sinusoidal stretch during the interburst interval (Fig. 6A, inset) is much smaller that when it is in the spiking mode (Fig. 4A).
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Figure 6B shows the dependence of normalized burst rate on AC amplitude for five bursting preparations. Again, the rate was normalized to the unstretched rate to facilitate comparison. Each data point was measured from 5 min of stretch. The solid line is the best linear fit to the data and has a Y intercept of 0.01 and a slope of 0.065/mm. There was no significant association between the bursting rate and stretch (1-way ANOVA, P = 0.695, F = 0.157).
GPR2 can switch between the spiking mode and the bursting mode
During stretch experiments, 14 of the 37 preparations originally in the spiking mode switched into the bursting mode. In three cases we observed this to occur suddenly while the cpv3a muscle was being stretched. Figure 7 shows one of these transitions. While the neuron was in the spiking mode, the firing rate increased sharply with incremental stretches of the cpv3a muscle, each time adapting to an equilibrium value after a few seconds, as shown in the left inset. As the stretch was increased beyond 0.3 mm, the equilibrium firing rate became less sensitive to changes in stretch. When the rate was ~4.5 Hz, the cell spontaneously switched into the bursting mode while the stretch was being held constant, as shown in the right inset. Further stretch while in the bursting mode resulted in an increased burst rate. When the muscle was allowed to relax, GPR2 switched back to the spiking mode. An immediate repetition of a large stretch did not result in a return to the bursting mode, and hence the transition into the bursting mode is not triggered simply by stretching the muscle past a threshold length. The sudden transitions into the bursting mode always occurred during a stretch >0.35 mm. However, in two other preparations we were unable to induce the switch from spiking to bursting even when applying a 0.5-mm DC stretch for 30 min.
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Conversely, we observed a preparation initially in the bursting mode switch into the spiking mode. Figure 8 shows five 3-min snapshots taken during 16 h of GPR2 activity in a preparation initially in the bursting mode in the absence of muscle stretch. There was no stretch imposed at any time during the 16 h. The initial burst period was very short, 13 s. One hour later, the preparation was not bursting at all, but rather firing spikes at a rate of 1 Hz. In the traces 6, 11, and 16 h after the first measurement, we see that the neuron returned to the bursting mode. During the experiment, the average burst period, as well as the burst duration and intraburst firing frequency, varied considerably.
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Very slowly varying stretches can be decoded from bursts using a burst interval code
Can the timing of bursts or spikes be used to reconstruct the muscle stretch waveform that generated them? Two observations from the experiments described above suggested that a simple decoding scheme could be used to reconstruct slowly varying stretch waveforms from burst intervals. First, the average burst frequency depended sensitively on stretch amplitude. Second, there was no adaptation of the bursting rate (Fig. 5B), indicating that the bursting rate depended primarily on stretch amplitude but not on its derivative (velocity) or integral (history).
To test the BI decoding hypothesis, we stretched a
cpv3a muscle for 30 min with a slowly varying random
waveform. The waveform consisted of computer-generated white noise
filtered using an RC low-pass filter with a 1,000-s time constant. The
first 15 min of the stretch were used to determine the relationship
between stretch and burst interval. As discussed in
METHODS, it is convenient to define a burst rate
R(ti) = (ti ti
1)
1 for each of the bursts. We
measured the start times ti of the bursts,
and in Fig. 9A we plot the
stretch S(ti) versus the
R(ti) as solid circles. The
solid line is a fit to the data
(R) = [
0.76 + 1.16(1
e
56.7R)]mm, where
R is measured in hertz. At low burst rates, the relationship is close to linear, consistent with the results from Fig.
5C. For the largest stretches, we observed a flattening of
the stretch versus rate curve, indicating that, for the larger
amplitudes, more variability in the burst rate was observed. This
variability may arise from a secondary dependence of the rate on
stretch velocity or another higher order characteristics of the
stretch. We tested the BI decoding scheme using the second 15 min of
the data set. We measured the burst start times and again computed
R(ti). Between bursts, we
linearly interpolated to obtain R(t) for all
times. We predicted the stretch waveform at each time t to
be
[R(t)]. Figure
9B shows the actual waveform (black) and the prediction (red). The Enorm (Eq. 3)
between this prediction and the actual stretch was 0.76.
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As the filter time constant is reduced, we expect that the
ability of the BI decoding scheme to reconstruct the stimulus will decrease. Eventually, when the characteristic time of the stretch waveform is comparable to or smaller than the average burst interval, BI decoding will not work because the burst interval will report only
the mean stretch amplitude. We varied the time constant used to
filter the white noise and found that the decoding scheme could still
be used when
was reduced to 100 s, but that it could not be
used when
was reduced to 10 s or smaller. Figure 9C
shows the response of a bursting mode GPR2 neuron to a white noise
stimulus filtered with
= 10 s (black trace). The dashed
lines mark the start times of the bursts. The red trace shows the
calculated burst rate. Although the burst interval is no longer useful
for BI decoding, bursts still provide some information about a fast stimulus, because the bursts tend to be triggered by large positive slopes or peaks in the stretch waveform. When the waveform is very fast
(
= 0.1 s), even those features are ignored by the bursting mode.
Slowly varying (gastric mill-like) stretch waveforms can be decoded from spikes using an interspike interval code
Can the interspike interval similarly be used to
reconstruct the stimulus from spike times when GPR2 is in the spiking
mode? The spiking mode is a less likely candidate for this than the bursting mode because of adaptation; the firing rate is a function not
only of the stretch amplitude, but also of the recent stretch history
(Fig. 2). We stretched spiking mode GPR2 preparations with white noise
waveforms filtered over a range of time constants to determine whether
and when an ISI decoding scheme would work. In Fig.
10A we show a portion of an
experiment where a spiking mode preparation was stretched with a slow
( = 1,000 s) waveform (black trace). The resulting
instantaneous GPR2 firing rate is plotted in red. When the amplitude
was large for a long period of time, the firing rate adapted
considerably. Figure 10B plots the relationship between
stretch and rate for three 40-s intervals S1-S3 of the
waveform shown in Fig. 10A. Although the stretch extended over different ranges of amplitudes during the three intervals, the
instantaneous firing rate varied over overlapping intervals. Hence a
unique stretch-rate relationship could not be defined, and accurate ISI
decoding was not possible.
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We found that the history dependence of the firing rate seen in Fig.
10, A and B, was not a problem when the waveform
varied over a fast enough time scale ( = 10 s). We
stretched the same preparation for 10 min with white noise filtered
with
= 10 s. Figure 10C shows the relationship
between stretch and firing rate during the first 5 min of the stretch.
The solid circles are data points. The curve is a fit to the data:
(R) = 0.432(1
e
1.239R) mm, where
R is measured in hertz. No systematic variation in the
stretch-rate relationship was observed when different subintervals of
the data set were examined. ISI decoding was used to reconstruct the
waveform from the spike times during the second 5 min of the experiment. A portion of the reconstruction is shown in Fig.
10D. The actual waveform is shown in black and the ISI
decoding prediction is in red. Enorm
for the reconstruction of the entire 5 min was 0.67. The typical period
of the gastric mill rhythm is 10-20 s, and hence the interspike
interval might be useful for decoding spikes generated by muscle
movements generated during this motor pattern.
A linear filter successfully decodes spikes for pyloric frequency stretches
When the characteristic time of the stretch waveform is comparable
to or smaller than the average interspike interval, ISI decoding cannot
capture the details of the stretches between the action potentials. The
GPR2 neuron, as we have seen, fires at average rates of a few hertz in
response to cpv3a stretch, and, as expected, we found that
the decoding method performed poorly when was reduced below 1 s. Using a spiking mode GPR2 preparation, we stretched the
cpv3a muscle for 3 min using filtered white noise with
= 0.3 s. We used the first 90 s of the stretch to
determine the relationship between stretch and instantaneous spiking
rate shown in Fig. 11A. The
data are the solid circles, and the curve is a fit to the data:
(R) = [0.187 + 0.217(1
e
0.280R)] mm, where
R is measured in hertz. The data and fit reflect two
observations. 1) For firing rates below 4 Hz, the clustering of points is almost vertical. A firing rate of 1.5 Hz could result from
a stretch amplitude anywhere between 0.15 and 0.3 mm with almost equal
probability. The fit chooses some average stretch. 2) The
curve is almost completely flat for rates above 4 Hz. We tested the ISI
decoding method on the second 90-s period of data. A 20-s interval is
shown in Fig. 11C. The actual stretch is in black, and the
ISI decoding prediction is in green. ISI decoding picked out the big
peaks but cannot reconstruct the structure away from the peaks. The
Enorm for the reconstruction of the
90-s test interval was 0.90.
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In an effort to improve the reconstruction, we tried the linear filter technique described in METHODS. Using the same 90 s of the stretch waveform that generated the ISI decoding relationship, we determined the best combination of a constant S0 and kernel K(t). The optimum kernel is shown in Fig. 11B. The corresponding best S0 was 0.18 mm. We used Eq. 1 to reconstruct the stimulus from the spike times during the 90-s test interval and obtained an Enorm of 0.73. A 20-s portion of the reconstruction is shown in red in Fig. 11C. The reconstruction is much better than that obtained with ISI decoding. In particular, the amplitude is predicted accurately in response to clusters of spikes. This indicates that the assumption of linearity is justified and that spike rate adaptation does not prohibit reconstruction of a waveform containing these frequencies. The typical period of the pyloric rhythm is 1 s, and hence a linear filter might be useful for decoding spikes generated by such a waveform.
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DISCUSSION |
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It is difficult for a neuron to encode in its spike train a stimulus that sometimes changes extremely slowly (hours), but in other situations fluctuates from second to second. If the firing rate of the neuron is nonadapting, the neuron can report unambiguously about slowly varying stimuli. To describe a rapidly varying stimulus, on the other hand, requires the ability to fire at high frequencies over short durations. This may involve firing frequencies that cannot be maintained over extended periods of time.
We have found that the GPR2 sensory neuron in the crab stomatogastric nervous system can encode accurately muscle movements that vary on times scales of both 1 s and 1,000 s. Two firing modes, spiking and bursting, are used. Faster stimuli are encoded in the spiking mode by interspike intervals. Extremely slow stimuli can be described in the bursting mode, where the stretch is encoded in the burst interval.
GPR2 bursting mode encodes sensory information about slow muscle movements
There is very little in the literature about how sensory neurons
in general, and mechanoreceptors in particular, might use bursts to
encode sensory information. Oscillations have been observed in a number
of mechanosensory systems, including hair cells (Fuchs et al.
1988; Sugihara and Furukawa 1989
) and muscle
spindles (Sokabe et al. 1993
), but these oscillations
are at high frequencies (5-250 Hz), and their encoding significance is
unclear. Another mechanoreceptor that might use bursts to encode
sensory information is the anterior gastric receptor (AGR)
(Combes et al. 1997
; Simmers and Moulins 1988
), also found in the crustacean stomatogastric nervous
system. There are important differences in the ways in which GPR2 and AGR encode stretch using bursts. The increase in the GPR2 bursting rate
resulting from muscle stretch does not adapt, and hence the burst
interval can unambiguously describe the DC stretch amplitude. The
bursting in AGR is much faster than in GPR2 with a typical frequency of
0.5-2 Hz. An AGR burst contains 5-10 spikes and lasts 100-200 ms. In
response to a short (<5-s duration) stretch of gm1, the
muscle innervated by AGR, burst frequency and spike frequency rise,
whereas the burst duration decreases. However, the increases in the
bursting and firing rates begin to reverse immediately after the
stimulus onset and have almost completely adapted after only 4 s.
An AGR burst code thus would be history dependent and only able to
describe rapidly varying stretches.
Two GPR2 modes encode information about movement on two different time scales
We observed spiking and bursting modes of GPR2 activity in
isolated neuromuscular preparations. Previous investigations have shown
that both modes occur in minimally dissected, semi-intact preparations
(Katz et al. 1989), and hence they both appear to be
physiologically relevant. In the bursting mode, GPR2 reports slow DC
movements but ignores faster AC movements. In the spiking mode, GPR2
fires more rapidly in response to AC movements than to DC stretches.
The two GPR2 modes allow the encoding of information about muscle
movements that vary on time scales of both a few seconds and many
minutes. What sensory stimuli on these time scales would GPR2 likely
encounter in vivo? The faster time scale most likely corresponds to
rhythmic muscle movements during an ongoing motor pattern. In this
mode, GPR2 appears to provide feedback to the STG on a cycle-by-cycle
basis. Peripheral feedback from proprioceptors can be used to ensure
precise timing of central pattern-generated movement in response to
changing conditions (Pearson 1993
). Katz et al.
(1989)
found that GPR neurons responded to muscle movements
generated by the gastric mill rhythm, but not the pyloric rhythm, in
semi-intact preparations. We found that ISI decoding was best able to
reconstruct filtered white noise stretches with a characteristic time
of 10 s. Thus an ISI decoding scheme would be well suited for
gastric mill motor movements.
The GPR2 bursting mode is best able to encode stretches that vary with
characteristic times of many minutes rather than stretches with time
courses characteristic of the STG motor patterns. What could cause a
DC-like stretch of the innervated muscles? All of the intrinsic muscles
in the stomatogastric nervous system insert on ossicles attached to the
stomach wall or to the wall itself. When the foregut is filled with
food, these muscles are stretched. The process of the clearing of food
from the foregut takes several hours (Fleischer 1981).
The bursting mode thus might provide the STG with a report of the
clearing of the foregut of food, unaffected by the ongoing motor
program. In this mode, GPR2 would no longer participate in a
cycle-by-cycle feedback loop but would simply provide long-term sensory
and modulatory input to the circuit.
AGR is similar to GPR2 in that it operates in both a spiking and a
bursting mode. AGR differs from GPR2 in that both AGR modes respond
most vigorously to stretch stimuli with a similar characteristic time
scale (~1 s) (Combes et al. 1997). Although it is
possible that a careful study of the two AGR modes might reveal that
different characteristics of the stretch (e.g., amplitude or velocity)
can be encoded better using one of the modes, it is unlikely that the
modes can effectively encode stimuli on two radically different time scales.
Muscle activity triggers the switch into the bursting mode
More than one-third of the preparations initially in the spiking
mode started to burst during the stretch experiments. The transition
into the bursting mode thus seems to be triggered by muscle stretch.
One possibility is that the transition may result from a change in the
neuromodulatory environment, triggered by muscle activity. In the AGR
experiments it was observed that exogenous application of the peptide
TNRNFLRF-NH2 could rapidly and reversibly trigger
a switch from the spiking to the bursting mode (Combes et al.
1997). However, in our experiments, the switch in GPR2 was
obtained without the exogenous application of any neuromodulatory agent, and hence, if the bursting were the result of neuromodulation, the responsible neuromodulator must originate in the preparation itself. GPR2 uses acetylcholine, serotonin, and an allatostatin-like peptide as neurotransmitters (Katz et al. 1989
;
Skiebe and Schneider 1994
). We think it unlikely that
the bursting results from automodulation using one these transmitters,
because we were not able to induce bursting in unstretched spiking
preparations through bath application of high concentrations of
serotonin (5-HT), allatostatin-3, or the muscarinic agonist
pilocarpine. We conclude that the transition either results from the
release by GPR2 of an as yet unidentified neuromodulatory substance or
is due to some process internal to GPR2 that is triggered by muscle stretch.
Spiking and bursting may have different synaptic targets
The use of a spiking and a bursting mode by GPR2 may be correlated
with the dynamics of its release of neurotransmitters. The synaptic
connections of GPR2 in the STG and anterior ganglia are complicated.
The GPR neurons make rapid, cholinergic excitatory synapses onto at
least five STG motor neurons. An examination of the dynamics of these
synapses suggests that spikes and bursts may be differentially
effective in driving different STG neurons. The postsynaptic potentials
in the lateral gastric (LG) neuron resulting from GPR action potentials
show significant depression (Katz and Harris-Warrick
1989), and hence their effect would weaken during a GPR2 burst.
The synapse from the GPR neurons to the dorsal gastric (DG) neuron, on
the other hand, although initially weaker than that to the LG neuron,
shows little short-term depression (Katz and Harris-Warrick
1989
), and hence the DG neuron should respond strongly to a burst.
There is a large body of literature that argues that peptides are
preferentially released by trains of multiple presynaptic action
potentials (Cropper et al. 1990; Peng and Horn
1991
; Peng and Zucker 1993
; Vilim et al.
1996a
,b
; Whim and Lloyd 1989
). Therefore it is
possible that a single or even several GPR2 spikes might liberate only
ACh, and that burstlike discharge is required to release the other
transmitters. Several seconds of high-frequency (20 Hz) stimulation of
GPR has been shown to increase the frequency of an ongoing pyloric
motor pattern (Katz and Harris-Warrick 1990
). Realistic
burstlike GPR stimulation (5-Hz interspike frequency, 4-s burst
duration, 16.7-s burst period) for 1.5-3 min has been shown to start
gastric mill motor activity (Blitz and Nusbaum 1996
).
Many of the effects of GPR stimulation seen in the STG have been
mimicked by bath application of 5-HT (Katz and Harris-Warrick 1989
; Kiehn and Harris-Warrick 1992
). These
results suggest that one functional role for the bursting mode is to
enhance release of the GPR2 cotransmitters.
GPR2 bursts and single spikes likely have different meanings. Careful study of the dynamics of the synapses that GPR2 makes in the STG will give us a better understanding of how the different temporal characteristics of muscle stretch encoded by GPR2 are decoded to affect motor patterns.
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ACKNOWLEDGMENTS |
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This work was supported by National Institutes of Health Grants NS-17813 and MH-46742, Individual National Research Service Award NS10564 to J. T. Birmingham, the Sloan Center for Theoretical Neurobiology at Brandeis University, and the W. M. Keck Foundation.
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FOOTNOTES |
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Address for reprint requests: E. Marder, MS 013, Volen Center, Brandeis University, Waltham, MA 02454-9110.
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 16 April 1999; accepted in final form 3 August 1999.
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REFERENCES |
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