Synaptic transmission between neurons in the stomatogastric ganglion of the lobster Panulirus interruptus is a graded function of membrane potential, with a threshold for transmitter release in the range of −50 to −60 mV. We studied the dynamics of graded transmission between the lateral pyloric (LP) neuron and the pyloric dilator (PD) neurons after blocking action potential-mediated transmission with 0.1 μm tetrodotoxin. We compared the graded IPSPs (gIPSPs) from LP to PD neurons evoked by square pulse presynaptic depolarizations with those potentials evoked by realistic presynaptic waveforms of variable frequency, amplitude, and duty cycle. The gIPSP shows frequency-dependent synaptic depression. The recovery from depression is slow, and as a result, the gIPSP is depressed at normal pyloric network frequencies. Changes in the duration of the presynaptic depolarization produce nonintuitive changes in the amplitude and time course of the postsynaptic responses, which are again frequency-dependent. Taken together, these data demonstrate that the measurements of synaptic efficacy that are used to understand neural network function are best made using presynaptic waveforms and patterns of activity that mimic those in the functional network.
- graded synaptic transmission
- pyloric network
- central pattern generation
- synaptic depression
Most rhythmic movements are produced by central pattern-generating circuits (Marder and Calabrese, 1996). In many cases, the rhythmic movements are produced over a significant frequency range without appreciable alteration of the fundamental phase relationships or the character of the movement; e.g., an animal is allowed to breathe or to walk at different rates, slowly or quickly. Because circuit dynamics depend on both synaptic and intrinsic properties, it is interesting to ask how these dynamics are affected by changes in network frequency. In this paper we present the effects of frequency on the graded synaptic transmission between neurons of the pyloric circuit of the spiny lobster Panulirus interruptus.
The pyloric network of the stomatogastric ganglion (STG) of P. interruptus is one of the best understood pattern-generating circuits. The connectivity among these neurons and their intrinsic membrane properties have been determined (Selverston and Miller, 1980;Eisen and Marder, 1982; Miller and Selverston, 1982a,b). Both in vivo and in vitro studies in a variety of crustacean species have shown that the triphasic pyloric rhythm operates over a frequency range from ∼0.1 to ∼2.5 Hz (Ayers and Selverston, 1979;Rezer and Moulins, 1983; Eisen and Marder, 1984; Turrigiano and Heinzel, 1992; Hooper, 1997a,b). One of the essential puzzles is how the pyloric rhythm can produce approximately the same motor pattern over such a wide frequency range. One possibility is that time-dependent changes in functional synaptic strength, such as facilitation and depression, play a critical role in maintaining network phase relationships as the frequency changes. This theory prompted us to examine the dynamics of graded synaptic transmission at one of the synaptic connections that is important for frequency regulation of the pyloric rhythm.
The chemical synaptic connections between STG neurons are inhibitory (Maynard, 1972; Mulloney and Selverston, 1974a,b). The threshold for transmitter release is close to the resting potential, and synaptic release is both spike-mediated and graded (Maynard and Walton, 1975;Graubard, 1978; Graubard et al., 1980, 1983; Johnson and Harris-Warrick, 1990; Johnson et al., 1995). At some synapses the graded component of transmitter release is significantly larger than that evoked by action potentials and is the major contributor to network dynamics (Raper, 1979; Graubard et al., 1983; Hartline et al., 1988). When spike-mediated transmission is blocked by tetrodotoxin (TTX), an alternating pattern of slow wave oscillation characteristic of the pyloric rhythm can be generated by applying various activating modulatory substances (Raper, 1979; Anderson and Barker, 1981).
Graded synaptic transmission between pyloric neurons has been extensively studied in a “static” context in which the time dependence of the transmission was ignored (Graubard, 1978; Graubard et al., 1980, 1983; Johnson and Harris-Warrick, 1990; Johnson et al., 1995). However, graded synaptic transmission between pyloric neurons shows depression and depends on the amplitude, frequency, and shape of the depolarization of the presynaptic neuron (Graubard et al., 1989;Hartline and Graubard, 1992). Here we give, for the first time, a detailed characterization of the dynamics of graded inhibitory transmission from the lateral pyloric (LP) neuron to the two pyloric dilator (PD) neurons. These synapses are the sole feedback from the pyloric constrictors to the pyloric pacemaker group [consisting of the anterior burster (AB) neuron and the two PD neurons]. This analysis provides some counterintuitive results that may help us to understand how frequency and duty cycle-dependent changes in synaptic strength participate in maintaining a constant pyloric rhythm over a wide frequency range.
MATERIALS AND METHODS
All experiments were performed on the spiny lobster P. interruptus. The experiments reported in this paper used 17 animals, both male and female. Animals weighed between 400 and 800 gm. Animals were obtained from Don Tomlinson (San Diego, CA) and were maintained in artificial seawater tanks at 12–15°C up to several weeks before use.
Standard procedures (Selverston et al., 1976; Harris-Warrick et al., 1992) were used to isolate the complete stomatogastric nervous system (the STG attached to the esophageal and paired commissural ganglia). The preparations were superfused during the dissection with cool, 13–15°C, pH 7.4–7.5, normal saline containing (in mm): 479 NaCl, 13.7 KCl, 3.9 NaSO4, 10 MgSO4, 2 glucose, and 5.1 Trizma base acid.
Microelectrodes were pulled on a Flaming–Brown horizontal puller and were filled with 2 m KCl. The electrode resistances were 8–12 MΩ. All neurons were identified by their stereotypical axonal projections in identified nerves using conventional techniques (Selverston et al., 1976; Harris-Warrick et al., 1992).
The presynaptic (LP) cell was impaled with two electrodes, and each postsynaptic (PD) cell was impaled with one electrode. After identification of these neurons, the preparation was superfused with 0.1 μm TTX to block action potentials and to eliminate pyloric slow wave oscillation. The preparation was then kept at room temperature (21°C) to increase the amplitude of the graded IPSP (gIPSP) (Johnson et al., 1991). This temperature is within the normal range of water temperatures in these animals’ natural habitat. The presynaptic cell was voltage-clamped with an Axoclamp 2A amplifier (Axon Instruments) in the two-electrode voltage-clamp mode. Postsynaptic cells were recorded in current-clamp mode. The postsynaptic membrane potential was depolarized by current injection (see the legends of individual figures) to keep this potential far from the reversal potential of the synapse (approximately −70 mV), thus ensuring that the gIPSPs were large in amplitude. An AT-MIO-16E-2 board was used both for data acquisition and for current injection with LabWindows/CVI software (National Instruments) on a PC clone.
The LP neuron was stimulated in voltage clamp both with square pulses and with realistic waveforms. Figure 1 illustrates the procedure that we used to stimulate the LP neuron using realistic waveforms. The trajectories of the rhythmic membrane potential waveforms of several LP neurons were recorded in normal saline. Each recorded trace was divided into single cycles. Because we were interested in studying the graded component of synaptic transmission, these cycles were averaged and filtered to eliminate the action potentials, and the resulting “unitary” waveform was stored in the computer. The unitary waveform, scaled to various amplitudes and frequencies and reproduced in a periodic manner, was then used to voltage clamp the LP neuron (in TTX).
When the presynaptic cell is voltage-clamped at the soma, it may not be completely space-clamped because of cable properties. The cable problems will be most significant for the case of waveforms with sharp transitions, such as action potentials or square waves. As the rise time of the command signal decreases, these problems become less significant. The potential artifacts attributable to the presynaptic cable effects are therefore minimized when realistic waveforms are used, because these waveforms have a smooth shape and are injected at relatively low frequencies. Furthermore, the synaptic IPSPs in response to simulated action potentials injected from the soma were fast and comparable in amplitude to individual IPSPs observed under normal biological conditions (Eisen and Marder, 1982), suggesting that even the most rapid rise time waveforms used in this paper were only minimally attenuated by the cable properties of the neuron. To compensate for attenuation of the waveform from the injection site to the synaptic release site, and to obtain easily measurable IPSPs in the PD cells, we used LP waveforms with amplitudes of 40 mV, except when measuring the input/output (I/O) relationships when the amplitude was varied.
Data acquired with the computer were stored in individual files in binary and in ASCII formats on CD-ROMs and were analyzed on a Linux platform. All of the analysis programs, such as peak detection, averaging, curve fitting, and low-pass filtering, were written in C, gawk, and Unix shell scripts. Statistical tests were done with SigmaStat software (Jandel Corporation).
The I/O curve of the LP to the PD neurons in response to square pulses
During the normal pyloric rhythm, the PD and LP neurons fire bursts of action potentials in alternation. In control saline, each LP neuron action potential evokes a unitary IPSP in the PD neurons, superimposed on a summed synaptic envelope (Fig.2 A). To study graded transmission from the LP neuron to the PD neurons, we voltage clamped the LP neuron with two electrodes (Fig. 2 B), monitored the membrane potential of the PD neurons in current clamp, and placed the preparation in TTX to block all action potentials. Figure 2 Cshows the gIPSPs evoked in the two PD neurons in response to a step depolarization of the LP neuron from −50 to −10 mV. The gIPSP shows a large early component that decays to a lower persistent value. After the depolarizing pulse in the LP neuron, the PD neurons show a small amount of postinhibitory rebound.
We studied the effect of the amplitude of the LP neuron depolarization on the amplitude of the early and persistent components of the gIPSP. The presynaptic LP neuron was held at −50 mV, and a sequence of 1.75 sec voltage steps, to voltages ranging from −45 to 0 mV, was applied (Fig. 3 A). Changing the holding potential from −50 to −80 mV had a negligible effect on the amplitude of the gIPSP (data not shown).
Figure 3 B shows the peak amplitude (open circles) and the amplitude of the gIPSP at 1.75 sec (filled circles) of the traces in Figure3 A plotted against the presynaptic potential. The I/O curves for the persistent (filled circles, 1.75 sec) and transient (open triangles, peak minus persistent) components of the gIPSPs of 13 cells are shown in Figure 3 C(mean ± SEM). In each experiment, the gIPSPs were normalized with respect to the peak amplitude of the gIPSP in response to a step of the LP neuron to +10 mV. The transient and persistent components of the gIPSP had a sigmoidal dependence on the presynaptic potential. As the presynaptic potential was increased, the amplitude of the persistent component increased more gradually than that of the transient component. We fit the I/O curves for each experiment with sigmoidal functions of the form: Equation 1where S is the saturation level of the sigmoid,V is the independent variable, V midis the half-maximum voltage, and 1/k describes the slope of the sigmoid at V mid. The values ofV mid and k for the I/O curves were (in mV, mean ± SEM; n = 15):V mid = −32.15 ± 0.68 andk = 5.86 ± 0.31 for the transient component andV mid = −26.96 ± 1.45 andk = 9.25 ± 0.73 for the persistent component. The I/O curves of the transient and persistent components were different (two-way ANOVA, p < 0.01); the transient I/O curve rose at a lower potential and was steeper than the curve of the persistent component.
Depression and recovery of the gIPSP in response to square pulses
We next injected a train of 500 msec, 40 mV voltage pulses (from a baseline of −50 mV) into the LP neuron and varied the duration of the interval between pulses (Fig. 4). With shorter intervals, the synapse showed depression; the amplitude of the gIPSP for the second and subsequent pulses was smaller than that of the first gIPSP. The degree of recovery from depression depended on the interval between the pulses. Figure 4 A shows the postsynaptic responses to trains of pulses with intervals of 2 sec (left) and 250 msec (middle) and to a single long pulse (right). Figure 4 B shows the depression of the gIPSP amplitude in response to trains of pulses at different intervals plotted against time. This depression is represented as the ratio of each peak amplitude to the amplitude of the first peak. This ratio was independent of the duration of the pulse used and depended only on the intervals between pulses. The decay of the gIPSP in response to a single long pulse (normalized with respect to the peak) is also shown. To quantify the time of recovery from synaptic depression, we compared the amplitudes of the first gIPSP peaks with those of the second gIPSP peaks. Figure 4 C shows the ratio of these amplitudes plotted against the interval between the pulses (mean ± SEM; n = 10). A recovery of >90% required intervals of 4 sec or longer. Such intervals exceed the characteristic period of length of 0.5–1 sec when the pyloric rhythm is strongly active.
The I/O curve of the LP to the PD neurons in response to realistic LP waveforms
Unlike spike-mediated synapses, there is no stereotyped waveform to use in studying graded synaptic transmission. Square pulses are the easiest waveforms to generate but are not necessarily the best to characterize the temporal dynamics of graded synapses (Olsen and Calabrese, 1996). During normal oscillations, the membrane potential of pyloric neurons shows smooth envelopes of slow wave depolarizations on which action potentials are superimposed (Fig. 2 A). The synaptic response to a natural waveform may be different from the response to a square pulse. This motivated us to use realistic waveforms (see Materials and Methods) to voltage clamp the presynaptic cell.
Figure 5 A presents a comparison of the responses to 1.75 sec square pulses and to 1 Hz realistic waveforms at various amplitudes. The average voltage of the realistic waveforms injected was −50 mV, the same as the holding potential for the pulses. The peak potential was used as the presynaptic voltage in the experiments shown in Figure 5, B and C. The amplitude of the gIPSP response to the realistic LP waveform increased gradually to a saturated level with the presynaptic amplitude. Figure5 B shows the gIPSP amplitudes in one experiment in response to realistic 1 Hz LP waveforms and to 1.75 sec square pulses plotted against the presynaptic potential. Note that the peak amplitude of the gIPSP in response to the LP waveform is only slightly less than that of the peak gIPSP resulting from a pulse and is considerably larger than the persistent value at the same level of presynaptic depolarization. We normalized the amplitudes (see Fig. 5 B) to their respective maximums to obtain the normalized I/O curve for LP waveforms and square pulses (Fig. 5 C). The normalized I/O curves for the LP waveforms of each experiment were fit with sigmoidal functions given by Equation 1. The values of V mid andk obtained were (in mV, mean ± SEM; n= 8): V mid = −32.18 ± 1.19 andk = 5.15 ± 0.31. The I/O curve of the LP waveform was different from both the transient and the persistent I/O curves for pulses (two-way ANOVA, p < 0.01).
For trains of pulses in response to periodic stimulation using the LP waveform, the synapse showed depression over time. The peak amplitude of the gIPSP decayed from its value during the first cycle to a constant steady state value (Fig. 6 A). Note that the steady state gIPSP defined here is not the same as the persistent component of the gIPSP measured at the end of a long pulse. In each experiment, we averaged the last four cycles to measure the amplitude of the steady state gIPSP. Figure 6 B shows the average amplitudes of the first (filled circles) and the steady state (open circles) gIPSPs in response to a 1 Hz LP waveform plotted against the maximum presynaptic potential (n = 7). We normalized the amplitudes shown in Figure 6 B to their respective maximums to obtain the normalized I/O curves (Fig.6 C) and fit the I/O curves of each experiment with sigmoidal functions given by Equation 1. The values obtained were (in mV, mean ± SEM; n = 7): V mid = −32.18 ± 1.19 and k = 5.15 ± 0.31 for the first peak and V mid = −31.96 ± 1.15 andk = 5.89 ± 0.32 for the steady state. The I/O curves for the first and steady state gIPSP were not significantly different.
The effect of the duty cycle on the amplitude of the gIPSP
The duty cycle of the presynaptic waveform affected the gIPSP amplitude. The duty cycle of an LP waveform was defined as the percentage of the period that the waveform was above/below its mean membrane potential. In the experiments shown in Figure7, the LP neuron was voltage-clamped using two LP waveforms of different duty cycles (55/45 and 35/65). These two duty cycles represent the upper and lower bounds of the LP neuron duty cycles measured in 17 experiments (with inputs from the commissural ganglia remaining attached). The two waveform trajectories spanned the same voltage range (−32 to −72 mV). Figure 7 A shows an example of the response to the two duty cycles at 1.5 Hz. Figure7 B shows the amplitude of the steady state gIPSP as a function of frequency for the duty cycles of 55/45 (open circles) and 35/65 (filled circles). At all frequencies tested, the amplitude of the gIPSP for the 35/65 duty cycle waveform was larger than that for the 55/45 duty cycle waveform (two-way ANOVA, p < 0.001; n= 11).
Frequency dependence of synaptic depression
To illustrate directly the effect of frequency on synaptic depression, we now plot a comparison of the response to a first presynaptic depolarization with the response obtained at steady state. Figure 8 A shows the dependence of the first (filled circles) and steady state (open circles) gIPSP amplitudes on frequency for square pulses. Amplitudes obtained in each experiment are normalized by the value at the reference amplitude 0.1 Hz (A ref). As expected, the response to the first pulse in the train had a constant amplitude, but the response at steady state decayed linearly with frequency (slope = −0.19 ± 0.02 sec, mean ± SEM; n = 5).
With realistic waveforms, the dependence of first and steady state gIPSP amplitudes on frequency was more complex. Figure8 B1 shows the dependence of the first and steady state gIPSP amplitudes on frequency for the LP waveform with a duty cycle of 55/45. Amplitudes obtained in each experiment are normalized by A ref for this waveform. As frequency was increased, the amplitude of the first gIPSP increased, and at frequencies >0.4 Hz, the amplitude stabilized to a constant level of ∼1.4 × A ref (no frequency dependence above 0.4 Hz; Tukey test, p > 0.01; n= 14). The initial increase in the amplitude of the first gIPSP is attributable presumably to the slow rise of the presynaptic waveform at very low frequencies, resulting in the inactivation of presynaptic Ca2+ currents that mediate synaptic transmission. In contrast, as frequency was increased, the steady state gIPSP increased to ∼1.2 × A ref but decayed linearly at frequencies above 0.3 Hz (slope = −0.10 ± 0.02 sec, mean ± SEM; n = 14). Similar results were obtained for an LP waveform with a duty cycle of 35/65 (Fig.8 B2). The first gIPSP amplitude stabilized to a constant level of ∼1.45 × A ref (no frequency dependence above 0.2 Hz; Tukey test, p > 0.01; n = 8); the steady state gIPSP increased to ∼1.3 × A ref but decayed linearly at frequencies >0.3 Hz (slope = −0.16 ± 0.03 sec, mean ± SEM; n = 8).
The effect of frequency on the phase of the peak gIPSP
The frequency of the injected waveform affected not only the amplitude of the gIPSP but also its shape and, in particular, its rise, decay, and time to peak. We analyzed the gIPSP waveform at frequencies from 0.1 to 3.0 Hz for both 55/45 and 35/65 duty cycles. In Figure9 A, we show a sample response to the 35/65 LP waveform at 0.2, 0.8, and 2.4 Hz. To elucidate the difference in the shape of the gIPSP at different frequencies, we rescaled time so that the traces of the LP voltages could be superimposed. We define Δt as the difference between the peak gIPSP (Fig.9 A, upper traces) and the peak of the LP waveform (Fig. 9 A, lower trace). At 0.2 Hz, the gIPSP peak was advanced (Δt < 0) with respect to the peak of the LP waveform; at 2.4 Hz, it was delayed (Δt > 0); at 0.8 Hz, it was approximately aligned (Δt = 0). This dependence of phase (Δt/period) on frequency was affected by the duty cycle of the LP waveform, as shown in Figure 9 B. The phase is plotted for frequencies ranging from 0.1 to 3 Hz for both 35/65 (filled circles) and 55/45 (open circles) LP waveforms. At frequencies <1.5 Hz, the postsynaptic response was more phase-advanced (negative phase) with respect to the LP waveform with the 55/45 duty cycle compared with the 35/65 duty cycle (two-way ANOVA, p < 0.01;n = 10). The zero-phase frequency (the frequency for which Δt = 0, calculated by linear interpolation between the two frequencies immediately above and below the zero phase) was 1.39 ± 0.17 Hz (mean ± SEM) for the 55/45 duty cycle waveform, a value significantly larger than 0.92 ± 0.09 Hz (mean ± SEM), the value for the 35/65 duty cycle waveform (p < 0.002, paired t test;n = 10). In calculating phase, we chose the peak of the LP waveform as a point of reference. Choosing any other point at a fixed phase of the LP waveform would just shift the phase (Δt/period) traces in Figure 9 B by fixed constant values.
The effect of duty cycle and frequency on the shape of the gIPSP
Until this point we have focused on the amplitude of the gIPSP, because this is the usual parameter used to express synaptic strength. However, the duration of the synaptic potential may be critical for determining when the PD neurons can resume firing after LP neuron inhibition. Therefore, it is important to study the effect of frequency on the duration of the gIPSP as well. Given the complex waveforms of the postsynaptic responses, it is not trivial to decide exactly how to measure the duration of the gIPSP or, for that matter, how to express a “synaptic weight over time” that best captures the time and amplitude information together. The simplest strategy is to calculate the integral. In Figure 10, we show the ratio of these integrals for the duty cycles of 55/45 and 35/65. The ratio of the postsynaptic integrals (filled squares) was 20–30% smaller than the ratio of the presynaptic integrals (open triangles) and was fairly independent of frequency. This reduction implies that the synapse acts as a buffer to reduce the difference of integrals from the input to the output at all frequencies.
The integral alone, however, does not distinguish between amplitude and duration of the synaptic potential. Therefore, we have defined “equivalent rectangles” that attempt to capture the time and amplitude dependence of the integrals. The equivalent rectangle of a waveform (Fig. 11 A) is defined as a rectangle of length t equiv (a measure of the waveform duration) and height V avg (a measure of the average amplitude of the waveform). To calculatet equiv, we first calculate the integral of the waveform in each cycle and find the time of the half-integral. This time is then doubled to give t equiv.V avg is calculated in each cycle by dividing the integral of the waveform by t equiv. Therefore the area represented by the product of t equivand V avg is equal to the integral, but this area is now expressed such that it weights appropriately the average amplitude and duration of the waveform.
Figure 11 B shows the equivalent rectangles of the presynaptic waveform (bottom) and the postsynaptic response (top) at frequencies of 0.2, 0.8, 2.0, and 2.8 Hz (mean ± SEM; n = 14) for waveforms with the duty cycles of 35/65 (dark gray) and 55/45 (light gray). To remove variability among experiments, we normalized V avg values of postsynaptic equivalent rectangles to the V avg of the 0.1 Hz waveform with the duty cycle of 55/45 (theA ref). At all four frequencies, theV avg values obtained for LP waveforms with the duty cycle of 35/65 were larger than the corresponding values obtained for the waveforms with the duty cycle of 55/45. As frequency increased, the V avg of response to both the 55/45 and the 35/65 duty cycle waveforms increased to a peak at 0.8 Hz and then decreased. As the frequency increased, t equiv of both the presynaptic waveform and the postsynaptic response decreased. This decrease was more moderate for the postsynaptic responses. The dotted vertical lines indicate the t equiv values of the presynaptic waveforms and the postsynaptic responses.
These results are maintained across the whole range of frequencies tested. In Figure 11 C, V avg is plotted as a function of frequency for the two duty cycles. At all frequencies, V avg of the 35/65 (filled circles) duty cycle was larger thanV avg of the 55/45 (open circles) duty cycle (two-way ANOVA, p < 0.05; n = 14). For both duty cycles,V avg reached a maximum at 0.8 Hz. Figure11 D shows the plot of the ratio oft equiv to period (defined here as the “normalized t equiv”) as a function of frequency. At all frequencies, the t equivgenerated by the 55/45 (open circles) duty cycle LP waveform was larger than that produced by the 35/65 (filled circles) duty cycle LP waveform (two-way ANOVA, p < 0.01). The horizontal dotted lines show the normalized t equiv for the presynaptic waveforms. As frequency increased, the normalizedt equiv of the postsynaptic gIPSP approached the normalized t equiv of the presynaptic waveform. For the 35/65 duty cycle waveform, the postsynaptic normalizedt equiv crossed that of the presynaptic waveform at ∼1.7 Hz.
The effect of spike-mediated IPSPs
Because we were interested in graded transmission, the waveforms that we used to mimic realistic oscillations in the cells were averaged and low-pass filtered so that the action potentials were eliminated. To study the additional effect of presynaptic action potentials on the IPSP, we compared the response to filtered waveforms injected in the LP cell with the response to nonfiltered waveforms. In Figure12 A, we show the response to superimposed nonfiltered and filtered waveforms. Compared with the response to the filtered waveform, the response to the nonfiltered waveform was jagged (corresponding one to one to the injected spikes), was ∼35% larger, and was faster to rise (maximum slope of rise was ∼100% larger).
Was the larger amplitude in the response to the nonfiltered waveform merely caused by the larger average potential of the input waveform, or was this response caused by other factors such as the slope of the LP waveform or the existence of spikes? To answer this question, we injected the LP neuron with filtered waveforms that had the samemaximum or the same average amplitude as the nonfiltered waveform, and we compared the result with the injection with the original “envelope” filtered waveform (Fig.12 B). The increase in the amplitude of the IPSP was fully compensated for by the larger average input waveform (Fig.12 B, middle LP trace). Surprisingly, the filtered waveform with the same average amplitude as the nonfiltered one also produced a sharp initial rise in the IPSP, similar to the response to the nonfiltered waveform. The envelopes of the synaptic response to the nonfiltered waveform with spikes (Fig.12 A, jagged PD trace) and to the filtered waveform without spikes but with the same average amplitude (Fig. 12 B, middle PD trace) were approximately equal, both in amplitude and in rise time. The filtered waveform with the same maximum (Fig.12 B, top LP trace) produced a disproportionately larger IPSP than the nonfiltered waveform.
Graded synaptic transmission is a common feature of many invertebrate sensory and motor networks (Pearson and Fourtner, 1975;Burrows and Siegler, 1978; DiCaprio, 1989; Nadim et al., 1995; Olsen et al., 1995) and of the vertebrate retina (Roberts and Bush, 1981). Synaptic potentials in the stomatogastric nervous system, like those in the leech (Nadim et al., 1995; Olsen et al., 1995), are both graded and spike-mediated. Previous work on graded transmission in the STG suggested that most of the transmitter release was graded with a relatively minor spike-mediated component (Graubard et al., 1980, 1983,1989). Our research provides an excellent opportunity to develop the frameworks needed for a detailed description of the dynamic properties of graded synaptic transmission.
Like spike-mediated synapses, graded synapses exhibit use-dependent changes in efficacy. However, the study of graded synaptic transmission introduces a number of challenging issues that are not confronted in the study of spike-mediated synapses. Transmission at spike-mediated synapses depends primarily on the timing of action potentials arriving at the presynaptic terminal and secondarily on changes in action potential duration and waveform, when they occur. At a graded synapse, both the timing and the waveform of the presynaptic depolarization are always important. Here we extend the discussion and analysis of short-term synaptic plasticity to the richer domain of graded synaptic transmission.
We began by investigating the postsynaptic response to square pulses of presynaptic depolarization. For trains of brief pulses, these synapses showed depression similar to the depression that can be seen at some spike-mediated synapses (Del Castillo and Katz, 1954; Betz, 1970;Charlton et al., 1982; Magleby, 1987; Thomson and Deuchars, 1994;Abbott et al., 1997). However, as the duration of each pulse was extended, depression was seen not only from one pulse to another but within a single extended pulse. As a result, the response to a single extended pulse consists of transient (depressing) and sustained (nondepressing) components. Ninety percent recovery from depression takes ∼4 sec, which means that when the pyloric period is <4–5 sec (most of the time), the synapse is continuously depressed to some degree. The fact that the synapse is neither full strength nor maximally depressed within the natural frequency range (0.1–2.5 Hz) enables it to be strengthened or weakened by variations in frequency, suggesting a functional role.
Almost all of the previously published work studying graded synaptic transmission in the stomatogastric nervous system used single, long, square presynaptic current pulses (Maynard and Walton, 1975; Graubard, 1978; Graubard et al., 1980, 1983; Johnson and Harris-Warrick, 1990;Johnson et al., 1991, 1995). Our study reveals that the amplitude of the postsynaptic response depends on the specific shape of the presynaptic waveform. In particular, the peak amplitude is sensitive to the slope of the rising phase of the presynaptic depolarization. This sensitivity means that square pulses, with their extremely high initial slopes, are inappropriate waveforms. Correlation of presynaptic Ca2+ currents with graded postsynaptic currents in leech heart interneurons (Angstadt and Calabrese, 1991) and subsequent modeling of that network (Nadim et al., 1995) indicated that graded synapses are sensitive to the slope of the presynaptic waveform. This sensitivity was experimentally demonstrated (Olsen and Calabrese, 1996). One message of our work is that it is important to use presynaptic waveforms typical of natural conditions when studying graded synapses. We used prerecorded presynaptic waveforms from rhythmically active preparations that we scaled to generate different amplitudes and frequencies. Our work, summarized below, was based on these “natural” waveforms.
Effect of duty cycle and waveform
A somewhat surprising result was that increasing the duty cycle of the presynaptic neuron decreases the peak amplitude of the evoked gIPSP (Fig. 7). This is presumably because of the increased recovery time between pulses and the more steeply rising slope of the waveform with the shorter duty cycle. The dependence of postsynaptic response on the initial slope of the presynaptic waveform may arise because the Ca2+ currents that are responsible for release of transmitter inactivate during slowly rising depolarizations. The use of the equivalent rectangle representation (Fig. 11 B) allowed us to decompose the postsynaptic response into an average voltage, V avg, and an equivalent duration, t equiv. As expected, when the duty cycle increases, the postsynaptic t equiv also increases, but again, nonintuitively, the postsynapticV avg decreases. It is possible that alterations in the intrinsic properties of the postsynaptic neuron (by modulatory substances or by network dynamics) may influence whether the time course (t equiv) or amplitude (V avg) of the synaptic potential is more important. Specifically, the trajectory of the recovery from the gIPSP will interact with currents such as I h,I A, and low-threshold Ca2+ currents that influence when the postsynaptic cell fires after inhibition.
Effect of frequency
We found that the frequency of the presynaptic waveform affects the amplitude (peak and V avg) of the postsynaptic response in an interesting way. As frequency increases, the amplitude of the gIPSP first increases and then decreases. The initial increase may be caused by less inactivation of presynaptic Ca2+ currents during the rise of the LP waveform at higher frequencies. The shorter recovery period, as frequency increases further, is probably responsible for the subsequent decrease in the gIPSP amplitude. We also found that frequency influences the gIPSP time course (time to peak and t equiv). As the frequency increases, the waveforms of the presynaptic and postsynaptic responses become better aligned (Fig. 11). This means that the time course of the postsynaptic response tracks that of the presynaptic depolarization best at high frequencies (Fig.11 B).
The role of the LP neuron in controlling pyloric frequency
It is natural to ask what effect the synaptic dynamics investigated here has on the operation of the pyloric network of the STG. Although we do not have a definitive answer to this question, a number of features are suggestive. The LP to PD synapse provides the only feedback to the AB and PD pacemaker from other pyloric neurons, so it is well placed to affect the frequency and phase relationships of the three-component rhythm. Under some modulatory conditions, increasing the duty cycle of the LP neuron slows down the pyloric frequency (Weimann et al., 1997), but this is not always the case (Hooper and Marder, 1987). Phase response curves obtained by firing single LP neuron action potentials (Ayers and Selverston, 1979) show a phase advance when the LP neuron fires during or just after the PD neuron burst but shows a phase delay when the LP neuron fires late in the cycle. However, because graded synaptic transmission arising from the slow wave potential of the LP neurons is probably the dominant source of synaptic transmission, it is essential to understand the dynamics of graded transmission and its role in frequency and phase regulation before we can fully appreciate the role of LP neuron to PD neuron feedback in the pyloric network.
The kinetics of depression and its recovery at the synapse studied here are tuned so that synaptic transmission is sensitive to frequency and to duty cycle in the range over which the pyloric network normally operates. When the pyloric rhythm is slow, the LP neuron is either silent or fires only one or two spikes or bursts. Under these conditions, the LP to PD synapse will be relatively constant. As the pyloric frequency increases or when the LP duty cycle increases, the amount of depression also increases. In our paradigms, synaptic depression is almost totally attained within one or two cycles, depending on frequency. This implies that the amplitude of the synapse will follow quickly any rapid changes in frequency produced by synaptic or neuromodulatory inputs. The complex effects of frequency and duty cycle on the gIPSP peak, integral,t equiv, and V avgmake it difficult to predict how different LP waveforms will affect the pyloric period and phasing without more detailed modeling studies. However, the results reported here suggest that the synaptic dynamics we have measured should, in general, have a buffering effect on fluctuations of rhythm and phase within the network.
Previous work has shown that modulatory substances can alter the peak amplitude of the gIPSP evoked by square pulses in the STG (Johnson and Harris-Warrick, 1990; Johnson et al., 1991, 1995). Because, in principle, a modulatory substance could alter the kinetics of depression, it will be interesting to determine how modulatory substances alter graded transmission studied with natural waveforms of different frequencies.
It is a truism that network dynamics depend on the interaction of synaptic and intrinsic membrane properties (Marder and Calabrese, 1996). Many attempts have been made to measure synaptic strength between pattern-generating neurons, with the presumption that these measurements would be useful in constructing models of circuit behavior (Getting, 1989). Unfortunately, measurements of synaptic strength are most easily made in inactive networks and then extrapolated to networks with ongoing activity. Models of networks using spike-mediated and/or graded transmission must be built with synaptic models that incorporate the appropriate time-dependent alterations in synaptic function, or they are unlikely to be adequate for explaining the dynamics of networks.
This research was supported by National Institute of Neurological Diseases and Stroke Grant NS17813 and National Institute of Mental Health Grant MH46742, the Sloan Center for Theoretical Neurobiology, and the W. M. Keck Foundation. The first two authors contributed equally to this work. We thank Dr. Jorge Golowasch for helpful discussions.
Correspondence should be addressed to Dr. Eve Marder, Volen Center, Brandeis University, 415 South Street, Waltham, MA 02254.