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1Center for Molecular and Behavioral Neuroscience, Rutgers University; and 2Department of Mathematical Sciences, New Jersey Institute of Technology and Department of Biological Sciences, Rutgers University, Newark, New Jersey
Submitted 31 January 2005; accepted in final form 20 June 2005
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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). Although recent studies have proposed a variety of roles for short-term depression (Abbott et al. 1997; Chance et al. 1998; Cook et al. 2003; Galarreta and Hestrin 1998; Manor et al. 2003; Nadim et al. 2003; Reyes et al. 1998; Rose and Fortune 1999), the functional significance of this form of synaptic plasticity is still not well understood. Interestingly, synapses made by a single presynaptic neuron onto different types of target neurons can show short-term depression with different dynamics (Hunter and Milton 2001; Markram et al. 1998; Reyes et al. 1998; Watanabe et al. 2005). This differential control of short-term synaptic depression may provide a mechanism for the presynaptic neuron to selectively control the activity of its postsynaptic targets (Markram et al. 1998). However, so far no detailed study has investigated whether the differences in the short-term dynamics observed between synapses made by a single presynaptic neuron to different targets are of true functional importance.
We used the rhythmically active pyloric circuit of the spiny lobster, Panulirus interruptus, to explore the possible functional significance of the distinct dynamics of short-term depression in two synapses efferent from a single presynaptic neuron. In this circuit, the lateral pyloric (LP) neuron is presynaptic to multiple targets, including the pyloric dilator (PD) and pyloric constrictor (PY) neurons (Selverston et al. 1976). Both the LP-to-PD synapse and the LP-to-PY synapse are known to show short-term synaptic depression (Mamiya et al. 2003; Manor et al. 1997). Although their dynamics have not been compared in the same preparations, parameters that describe short-term depression of these synapses are very different (Mamiya et al. 2003; Manor et al. 1997). Because the PD neurons together with the anterior burster (AB) neuron are members of the pacemaker ensemble of the pyloric network whereas PY neurons are followers, the functions of these two synapses may also be different. The LP-to-PD synapse provides the sole chemical synaptic feedback to the pyloric pacemaker group from the follower neurons and has been shown to be important for controlling the period of the pyloric rhythm (Mamiya and Nadim 2004; Nadim et al. 1999; Weaver and Hooper 2003a). In contrast, the LP-to-PY synapse has been proposed to be important for controlling the burst phase of the postsynaptic PY neuron (Mamiya et al. 2003).
In this study, we characterized and directly compared the short-term synaptic dynamics of the LP-to-PD and the LP-to-PY synapses. We then tested the functional roles of these synapses by functionally removing them from the network and observing the effect on the period of the pyloric rhythm and the burst phase of the PY neurons. Finally, we developed a computational model of the pyloric circuit, incorporating the dynamics of the two LP neuron efferent synapses, and tested the hypothesis that the difference in the short-term dynamics of these two synapses are important for the function of each synapse. Using the model, we show that when the short-term dynamics of the LP-to-PD and the LP-to-PY synapses are replaced with the dynamics of the other synapse they fail to function normally.
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METHODS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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All experiments were performed on adult spiny lobsters P. interruptus (Don Tomlinson Fisheries, San Diego, CA). The stomatogastric nervous system (STNS) was isolated following standard procedures (Harris-Warrick 1992; Selverston et al. 1976). The isolated STNS was pinned down on a silicone elastomer (Sylgard)-coated petri dish and superfused throughout each experiment with chilled (16°C) physiological saline containing (in mM) 479.0 NaCl, 12.9 KCl, 13.7 CaCl2 · 2H2O, 10.0 MgSO4 · 7H2O, 3.9 NaSO4 · 10 H2O, 11.2 Trizma base, and 5.1 maleic acid, pH = 7.45.
Pyloric neurons were identified according to their stereotypical axonal projections in identified nerves using conventional techniques (Harris-Warrick 1992; Selverston et al. 1976). The pyloric activity was monitored extracellularly with stainless steel wire electrodes from identified nerves. Extracellular signals were amplified by a differential AC amplifier model 1700 (A-M Systems, Carlsborg, WA). Intracellular recordings were made by impaling the somata with glass microelectrodes filled with 0.6 M K2SO4 +20 mM KCl (for identification of neurons and intracellular recordings; resistance: 30–35 M
) or 3 M KCl (for current injection only; resistance: 8–12 M). All intracellular recordings were done with Axoclamp 2B amplifiers (Axon Instruments, Union City, CA).
Comparison of the short-term dynamics of the LP-to-PD and the LP-to-PY synapses
To compare the short-term dynamics of the LP-to-PD and the LP-to-PY synapses, we activated these synapses (see following text) and recorded the postsynaptic potentials simultaneously from both the PD and PY neurons. For better control of the membrane voltage, synaptic potentials were measured after abolishing the pyloric rhythm. Bath application of 0.1 µM tetrodotoxin (TTX; Biotium, CA) abolished this activity by blocking descending inputs to the stomatogastric ganglion. This also blocked action potential-mediated synaptic transmission in the ganglion. The current study focuses on graded synaptic transmission, which has been shown to be important and sufficient for generating the pyloric rhythm (Hartline and Graubard 1992; Manor et al. 1997; Raper 1979).
To activate the LP-to-PD and the LP-to-PY synapses simultaneously, the presynaptic LP neuron was voltage clamped (with 2 electrodes) and depolarized with 40-mV voltage steps. Postsynaptic potentials (PSPs) were recorded simultaneously from the PD neuron and the PY neuron in current-clamp mode. To study the short-term dynamics of the synapse, the voltage step was repeated five times. The duration of the voltage step was fixed at 400 ms, and each activation set was composed of five voltage steps separated by the inter-pulse interval (IPI) of 400, 800, 2,000, 4,000, or 8,000 ms. For each IPI, the activation set was repeated five times. There was a 30-s interval between every two runs to allow for the complete recovery of the synapse. The LP neuron was held at a holding potential of –60 mV, which is close to its resting potential. The resting potentials of the PD neurons and the PY neurons did not change during the experiment and were in a range of –55 ± 5 mV in all experiments.
The LP-to-PY synapse has both an electrical and a chemical component (Mamiya et al. 2003). Because a specific blocker for the electrical coupling is not known in this system, it was not possible to measure the chemical component directly by blocking the electrical coupling. Instead, the chemical component was estimated by subtracting the electrical coupling component from the postsynaptic potentials recorded in control conditions. For measurement of the electrical coupling component, the chemical synapse was blocked by bath application of 10 µM picrotoxin (PTX) (Marder and Paupardin-Tritsch 1978).
Effect of the LP-to-PD synapse on the pyloric rhythm period
The rhythm period was manipulated by injecting various amounts of current (–12 to +4 nA) into one of the pacemaker neurons (AB/PD) in a step-wise manner. At each step, the LP neuron was hyperpolarized (–10-nA current injection) to remove the LP-to-PD synapse. The rhythm period in the presence (PeriodwithLP) or absence (PeriodwithoutLP) of the LP-to-PD synapse was measured for 30 cycles immediately before hyperpolarizing the LP neuron or 30 cycles during LP hyperpolarization. To avoid any transient effects, cycles within the first 10 s after hyperpolarization of the LP neuron were not used for the calculation of period. To examine the overall effect of the LP-to-PD synapse, we calculated the average difference between PeriodwithLP and PeriodwithoutLP (
Period = PeriodwithLP – PeriodwithoutLP) for each current injection to the pacemaker group in each experiment. The effect of a given synapse in the pyloric circuit is known to vary from preparation to preparation (Weaver and Hooper 2003b). Therefore statistical analysis was done on an experiment-by-experiment basis. Within each experiment, for each value of injected current, there was cycle-to-cycle variability in the period in both the presence and absence of the LP-to-PD synapse. Due to this variability, PeriodwithLP and PeriodwithoutLP cannot be paired without ambiguity. Thus we did our statistical analysis using the general linear model and analysis of covariance by following the method introduced by Weaver and Hooper (2003a). With this method, all measured values of PeriodwithLP and PeriodwithoutLP are plotted against PeriodwithLP as follows: for each value of current injection into the pacemaker neurons, PeriodwithoutLP was matched in ascending order with PeriodwithLP in descending order. Thus the longest PeriodwithoutLP was plotted versus the shortest PeriodwithLP, the second longest PeriodwithoutLP versus the second shortest PeriodwithLP, etc. PeriodwithLP was also plotted against itself using the same matching method. This procedure makes it less likely that the null hypothesis that the LP-to-PD synapse has no effect on the rhythm period is rejected and therefore results in a conservative estimate of the effect of the synapse on the rhythm period. A detailed description of this procedure is given by Weaver and Hooper (2003a).
Effect of the LP-to-PY synapse on the PY burst delay
The aim of this experiment was to study the effect of the LP-to-PY synapse on the delay between the burst of the PD neuron and the burst of the PY neuron (PY burst delay) at different rhythm periods. To remove the LP-to-PY synapse, the LP neuron was hyperpolarized (–10-nA current injection). This hyperpolarization also removes the LP-to-PD synapse and affects the period of the pyloric rhythm. Because the PY burst delay is known to change according to the period of the pyloric rhythm (Hooper 1997a,b), direct comparison of the PY burst delay with and without the LP-to-PY synapse cannot distinguish whether any effect seen is due to the removal of the synapse or simply due to the change in cycle period. To separate these two factors, it was necessary to manipulate the rhythm period and compare the PY burst delay with and without the LP-to-PY synapse for cycles that had the same period.
For manipulation of the rhythm period, a slowly changing ramp current was injected into one of the PD neurons. The current was changed from 0 to –12 nA at a rate of –0.1 nA/s, then from –12 to +4 nA at a rate of 0.1 nA/s, and finally from +4 nA back to 0 nA at a rate of –0.1 nA/s. This ramp current was injected both in the presence of the LP-to-PY synapse and when it was removed by hyperpolarizing the LP neuron.
To examine the overall effect of the LP-to-PY synapse, we generated a summary plot that shows average changes in the PY burst delay caused by the LP-to-PY synapse at each rhythm period. For this summary plot, the PY burst delay was grouped according to the period of the cycle using 10-ms bins in each experiment. Due to the fact that the hyperpolarization of the LP neuron affects the rhythm period, the range of rhythm periods observed in response to the current injection was different with and without the LP hyperpolarization. Only the bins that had more than five cycles in both cases were used to calculate the average change in the PY burst delay.
As in the measurement of PeriodwithLP and PeriodwithoutLP, all statistical analysis on the effect of the LP-to-PY synapse was done on an experiment-by-experiment basis. Both in the presence and the absence of the LP-to-PY synapse, the PY burst delay was measured for all cycles and was plotted against the cycle period. The general linear model was used to detect significant interactions between the effect of the LP-to-PY synapse and the effect of the cycle period on the PY burst delay. When there was no significant interaction, analysis of covariance was used to test whether the LP-to-PY synapse had significant effect on the PY burst delay.
Recording, analysis, and statistics
All intracellular recordings were digitized at 4 kHz and stored on a PC using a PCI-6070-E board (National Instruments, Austin, TX) with custom-made recording software Scope (available for download at http://stg.rutgers.edu/software) developed in the LabWindows/CVI software environment (National Instruments, Austin, TX). All analysis, such as detection of the peak amplitude of the postsynaptic response, averaging of the synaptic response, calculation of the ratios, digital subtraction of the traces, curve fitting, and calculation of the period and burst delay were done by custom-made programs written in Matlab (MathWorks, Natick, MA). Statistical tests were done using a SAS package (SAS Institute, Cary, NC). We used an overall alpha level of 0.05, but because of the multiple comparisons involved with an experiment-by-experiment analysis, when needed, we corrected the alpha value using the Dunn-Sidak (D-S) method. In all cases where multiple comparisons are involved, this value is given as D-S = corrected alpha value.
Model of the pyloric circuit
All neurons, with the exception of the LP neuron, were modeled as conductance-based Hodgkin and Huxley (1952)-type neurons. Each neuron was modeled with two compartments representing the axon (A) and the rest of the neuron (S/N: soma, primary and secondary neurites). This spatial arrangement was chosen to isolate the spike-generation zone (axon) from the site of synaptic inputs and slower intrinsic ionic currents (Soto-Treviño et al. 2005). All synapses connected the S/N compartments of the neurons. Our choice not to use a biophysically realistic model of the LP neuron was intentional so that we could remove any confounding effects of the AB, PD, and PY synapses back to the LP neuron from our model results and focus on the significance of the LP-to-PD and -PY synaptic dynamics. The LP neuron was instead modeled using a library of waveforms as follows. Recordings of the LP neuron membrane potential waveform were low-pass filtered at 10 Hz, normalized in amplitude, and divided into individual cycles or unitary waveforms (Mamiya and Nadim 2004). These unitary waveforms were sampled at 1,000 points each (with the 1st and last points corresponding to 2 consecutive burst onsets of the PD neuron), categorized according to their cycle period and averaged in 10-ms bins to build a library of LP neuron waveforms, indexed by the waveform period. The membrane potential of the model LP neuron was produced by playing back the appropriate prerecorded waveform from the library, beginning with each burst of the PD neuron. The LP waveform chosen for each cycle was the one with a period that matched the last cycle period of the PD neuron. The model LP neuron membrane potential was scaled to oscillate between –60 and –30 mV. Because the voltage of the model LP neuron was predetermined, the model LP neuron did not receive any synaptic input. There was, however, a synapse from the LP neuron to both the PD and the PY neurons. There was also a synapse from the AB neuron to the PY neuron.
All simulations were performed using Network, a home-developed software running on the Linux platform, with a fourth-order Runge-Kutta integration method and dt = 0.05 ms.
Equations
In each segment of the model neurons, the membrane potential, V, was obtained by numerical integration of the differential equation
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with an addition of a low-threshold calcium current in the PD neuron. The parameter values for the low-threshold calcium current were: gCaLo = 0.02 nS, p = 2, q = 1, m
(Vm) = 1/{1+exp[–(Vm + 60)/2]}, 
m = 25 ms, h(Vm) = 1/(1+exp[(Vm + 67)/2)), h = 100 + 500 h(Vm) ms. The parameter values for the ionic and leak currents in the PY neuron are given in Table 1.
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; Manor et al. 2003). The variables a and d were also governed by Eq. 1, with x representing a or d. All the synapses connected the S/N compartments of the model neurons. The parameter values for the synaptic currents are given in Table 2.
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RESULTS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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As a first step in understanding the relationship between the short-term dynamics of a synapse and the function of that synapse, we compared the short-term dynamics of two synapses from the same neuron to different targets. Our hypothesis was that if the short-term synaptic dynamics are important for the function of the synapse, these two functionally distinct synapses should have different dynamics despite the fact that they originate from the same presynaptic neuron.
To study the dynamics of the LP-to-PD and the LP-to-PY synapses, we voltage clamped the LP neuron and activated the synapses with a train of five voltage pulses (amplitude: 40 mV, duration: 400 ms) with different interpulse intervals (IPIs: 400, 800 2,000, 4,000, and 8,000 ms). Figure 2 A shows an example of voltage traces from the LP, PD, and PY neurons when these synapses were activated with an IPI of 400 ms. The PSPs in the PD and PY neurons showed very different dynamics (Fig. 2A, 2nd and 3rd traces). In the PD neuron, the amplitude of the PSP depressed 
40% from the first pulse to the second pulse. Most of the depression took place between the first and the second pulse, and the response stabilized as a hyperpolarizing response. On the other hand, the simultaneously recorded PSPs in the PY neuron switched from hyperpolarizing to depolarizing in the middle of the first pulse. The PSP in response to the second pulse was completely depolarizing, and the response stabilized as a depolarizing response.
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). Because there is no known specific blocker for electrical coupling in this system, we approximated the amplitude of the chemical component by blocking the chemical component (by bath application of 10–5 M PTX) and subtracting the remaining (purely electrical) PSP (Fig. 2A; PYptx) from the control trace (Fig. 2A; PYctl). After subtracting the electrical coupling component, we found a highly depressing chemical synapse (Fig. 2A; PYctl-ptx). The amplitude of the chemical synapse depressed >90% by the second pulse.
To compare the extent of depression and the rate of recovery of the LP-to-PD and the LP-to-PY (chemical component) synapses, we used the conventional paired-pulse recovery paradigm. For each synapse, the paired-pulse recovery ratio was calculated for each IPI by taking the ratio of the peak amplitude in response to the second pulse (A2) to that in response to the first pulse (A1; see Fig. 2B, inset). This is a value between 0 and 1, showing how much the synapse has recovered during the IPI (1 = complete recovery). Figure 2B shows the average paired-pulse recovery ratios of the LP-to-PD and the LP-to-PY synapses for five different IPIs (means ± SD, n = 5). As seen in the figure, the LP-to-PD synapse had a greater recovery ratio than the LP-to-PY synapse for all IPIs, but the difference between the two recovery ratios was larger when the interval was short. To quantify the extent of synaptic depression and the time course of the recovery, we fit the relationship between the paired-pulse recovery ratio and the IPI with a single-exponential decay function 1 –Dmax exp (–IPI/rec), where rec is the time constant of recovery and Dmax is the amount of depression when the IPI tends to zero. The y- intercept of this exponential function (R0 = 1 –Dmax, indicated by arrows in Fig. 2B) shows the extent of recovery as the IPI tends to 0. For the example shown in Fig. 2B, the LP-to-PD synapse had smaller rec and Dmax than the LP-to-PY synapse (rec = 2.80 s compared with 4.38 s, Dmax = 0.456 compared with 0.916), reflecting the fact that the LP-to-PD synapse depressed less and recovered faster than the LP-to-PY synapse.
A scatter plot of rec versus Dmax for eight paired recordings of LP-to-PD and LP-to-PY synapses (Fig. 2C) shows two clearly separated clusters, corresponding to two synapses. In all cases, the LP-to-PD synapse had significantly smaller rec and Dmax values than the simultaneously recorded LP-to-PY synapse (Student's t-test, P < 0.05 and P < 0.001 for rec and Dmax respectively, n = 8). These results indicate that the LP-to-PD synapse always depressed less and recovered faster than the LP-to-PY synapse. Moreover, a comparison between the amplitude of the chemical synapses in response to the first pulse (A1) showed that A1 was significantly larger in the LP-to-PD synapse than in the LP-to-PY synapse [–8.80 ± 6.44 (SD) mV compared with –2.12 ± 0.55 mV; Student's t-test, P = 0.00014, n = 8; data not shown].
Quantifying the effect of the LP-to-PD synapse on the period of the pyloric rhythm and the effect of the LP-to-PY synapse on the PY burst delay
To examine the relationship between the short-term dynamics and the function of the synapses, we contrasted and quantified the previously proposed functions of the LP synapses to the PD and PY neurons. For the LP-to-PD synapse, we investigated its effect on the period of the pyloric rhythm (Mamiya and Nadim 2004; Weaver and Hooper 2003a,b). For the LP-to-PY synapse, we investigated its effect on the PY burst delay (Mamiya et al. 2003). Both effects were studied while manipulating the rhythm period to quantify how the change in the rhythm period affects the function of each synapse.
Effect of the LP-to-PD synapse on the period of the pyloric rhythm
To investigate the effect of the LP-to-PD synapse on the period of the pyloric rhythm, we removed this synapse during the ongoing rhythm (see METHODS) and compared the PD neuron cycle period in the presence (PeriodwithLP) and absence (PeriodwithoutLP) of this synapse (Fig. 3A). In a previous study, we proposed the hypothesis that the LP-to-PD synapse acts to increase the rhythm period when the period is short and to decrease it when it is long (Mamiya and Nadim 2004). To test this hypothesis, we manipulated the rhythm period (see METHODS) and investigated the effect of removing the LP-to-PD synapse at different rhythm periods. Figure 3B shows the average change in the rhythm period caused by the LP-to-PD synapse (Period = PeriodwithLP – PeriodwithoutLP) at different values of PeriodwithLP (the control cycle period) for different preparations. The figure shows that, although the effect of the LP-to-PD synapse varies greatly from preparation to preparation, in most cases, the synapse acts to increase the rhythm period.
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). In 10 of 12 experiments, the general linear model showed that the difference in the slopes of the regression line for the PeriodwithLP and the PeriodwithoutLP were not significantly different (P > 0.05; D-S = 4.26 x10–3), suggesting that contrary to our previous hypothesis in these preparations, the effect of the LP-to-PD synapse was independent of the rhythm period. Analysis of covariance showed that in 7 of these 10 preparations, the LP-to-PD synapse significantly delayed the rhythm period (P < 0.05; D-S = 5.12 x10–3). Figure 3C shows an example of such an experiment. In this experiment, the LP-to-PD synapse delayed the rhythm period by 87.5 ms (P < 0.0001 for the significance of the effect of the LP-to-PD synapse on the rhythm period; this experiment corresponds to Fig. 3B, 7). In 2 of 12 experiments, the slopes of the regression line for PeriodwithLP and PeriodwithoutLP were significantly different (P < 0.05; D-S = 4.26 x10–3). Consistent with our previous hypothesis, in these two cases, the LP-to-PD synapse acted to increase the period more when the rhythm period was short and did not increase the period (or slightly decreased it) when the rhythm period was long. Figure 3D is an example of such an experiment (P < 0.0001 for the significance of the interaction between the effect of the LP-to-PD synapse and the rhythm period; this experiment corresponds to Fig. 3B, 12).
A previous study has shown that the hyperpolarization of the LP neuron changes the activity of another neuron (the ventral dilator VD) in some but not all preparations, presumably through the removal of the inhibitory LP-to-VD synapse (Weaver and Hooper 2003b). It is also known that the VD neuron affects the rhythm period through a rectifying electrical coupling to the PD neurons (Weaver and Hooper 2003a). Thus, we suspected that hyperpolarization of the LP neuron may also have an indirect effect on the rhythm period through its effect on the activity of the VD neuron and that this effect may vary across preparations. To test whether this indirect effect was the cause of the variability seen in the effect of the LP-to-PD synapse on the rhythm period, we repeated the preceding experiment in a subset of preparations (n = 4 of 12) before and after hyperpolarizing the VD neuron, and compared the relationship between the PeriodwithLP and the PeriodwithoutLP in the two cases (data not shown). Hyperpolarization of the VD neuron should remove its effect on the pyloric rhythm period by removing the positive current flow from the VD neuron to the PD neuron. Statistical analysis was performed as in the case without the hyperpolarization of the VD neuron. In one of the four experiments, the difference in the slopes of regression lines for the PeriodwithLP and PeriodwithoutLP was not significantly different before the hyperpolarization of the VD neuron but became different after the hyperpolarization (P < 0.05; D-S = 1.27 x 10–2). However, in another experiment, the difference in the slopes was significant before the hyperpolarization but became nonsignificant after the hyperpolarization. In the remaining two experiments, the slopes were not statistically different before or after the hyperpolarization of the VD neuron. These results indicate that although the VD neuron does seem to affect how the LP-to-PD synapse changes rhythm period, this effect itself also varies across preparations and the difference in the effect of the LP-to-PD synapse on the rhythm period in different preparations cannot be attributed solely to the indirect effect through the VD neuron.
Effect of the LP-to-PY synapse on the burst delay of the PY neuron
In a previous study, we suggested that the LP-to-PY synapse may help maintain the burst phase (burst delay/period) of the PY neuron constant over a wide range of rhythm frequencies by delaying the PY burst more when the rhythm period becomes longer (Mamiya et al. 2003). To examine the effect of the LP-to-PY synapse on the burst delay of the PY neuron (time difference between the PD neuron burst onset and the PY neuron burst onset), we removed the LP-to-PY synapse during the ongoing rhythm (see METHODS) and compared the burst delay in the presence and absence of the synapse (DelaywithLP and DelaywithoutLP; Fig. 4A).
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PY burst delay) for all 12 experiments are plotted in Fig. 4B. The plot shows that the effect of the LP-to-PY synapse is highly variable but it mainly acts to delay the onset of the PY burst. Moreover, the synapses can be grouped roughly into two categories: those that have a near-constant, small effect on the PY burst delay throughout the range of rhythm periods tested and those in which the PY burst delay increases as the rhythm period becomes longer. Because the effect of the LP-to-PY synapse varied greatly from experiment to experiment, all statistical analysis was performed on an experiment-by-experiment basis. For statistical analysis of the effect of the LP-to-PY synapse, we first used a general linear model to check if the regression lines for DelaywithLP and DelaywithoutLP against the rhythm period had the same slope and, when they did, performed analysis of covariance to check if the LP-to-PY synapse had any effect on the PY burst delay. In 8 of 12 experiments, we found that the slopes of the regression lines for DelaywithLP and the DelaywithoutLP were significantly different (P < 0.05; D-S = 4.26 x 10–3), suggesting that the effect of the LP-to-PY synapse was different for different rhythm periods. Consistent with our previous hypothesis, in seven of these eight experiments, the LP-to-PY synapse delayed the PY burst more when the rhythm period was longer and thus helped the PY neuron burst at a more constant phase. Figure 4C shows a scatter plot of DelaywithLP and DelaywithoutLP against the rhythm period from one such experiment (corresponding to Fig. 4B, 8). In this experiment, the LP-to-PY synapse acts to delay the PY burst (69.8 ms at the mean period of 677 ms), and the difference between DelaywithLP and DelaywithoutLP becomes larger as the rhythm period becomes longer (P < 0.0001). In only one case, the LP-to-PY synapse delayed the PY burst less when the rhythm period was longer, but, in this experiment, the effect of the LP-to-PY synapse was very small (8.9 ms at the mean period of 765 ms). In 4 of 12 experiments, the difference in the slopes of the regression lines for DelaywithLP and DelaywithoutLP was not statistically significantly, suggesting that the effect of the LP-to-PY synapse was the same at different rhythm periods (P > 0.05; D-S = 4.26 x 10–3). Analysis of covariance showed that in two of these four experiments the LP-to-PY synapse significantly delayed the PY burst onset (P < 0.05; D-S = 1.27 x 10–2). Figure 4D shows a scatter plot of the DelaywithLP and DelaywithoutLP against the rhythm period from one such experiment (corresponding to Fig. 4B, 4). In this experiment, the LP-to-PY synapse worked to delay the PY burst for a constant amount (17.2 ms) throughout the range of periods tested (P < 0.0001).
Computational model of the LP-to-PD and LP-to-PY synaptic dynamics
To investigate the function of the short-term dynamics observed in the LP-to-PD and LP-to-PY synapses, we used a computational model of the pyloric network and incorporated the experimentally measured synaptic dynamics. The computational model included a pacemaker group consisting of AB and PD neurons coupled electrically to oscillate in phase (Soto-Treviño et al. 2005). The AB neuron had an inhibitory synapse to the follower PY neuron, causing the PY neuron to oscillate out of phase with the AB and PD neurons (Fig. 5B). The intention of this computational study was not to produce the correct phasing of the LP neuron but rather to see the effect of the efferent LP synapses on the PD and PY neurons. Thus, instead of using a biophysically realistic model of the LP neuron, we used an extensive library of LP neuron waveforms (Mamiya and Nadim 2004) to model the membrane potential oscillation of the LP neuron (see METHODS). The LP-to-PD and LP-to-PY synapses were computed using these membrane potential oscillations as the presynaptic input. By using the prerecorded library of LP neurons, we were able to activate the LP-to-PD and LP-to-PY synapses at the correct phase of oscillation, depending on the oscillation period, and thus we not only removed a degree of complexity from the model but also retained relatively accurate presynaptic membrane potentials for the synapses of interest.
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). Figure 5A shows the postsynaptic potentials in the model PD and PY neurons in response to a train of 40-mV voltage pulses applied to the voltage clamped model LP neuron. Also shown are the PSPs in the PY neuron without the chemical component (PYptx) or the electrical component (PYctl-ptx) for comparison with the biological traces shown in Fig. 2A. Effect of the LP-to-PD synapse on the oscillation period in the computational model
To examine the effect of the LP neuron on the period of the AB and PD neurons, we changed the model cycle period by current injection into the AB neuron and measured the influence of the LP-to-PD synapse on the period by setting the maximal synaptic conductance to 0 and thus eliminating the synapse (Fig. 6A). We then compared the difference between the periods with and without the LP-to-PD synapse (Period = PeriodwithLP –PeriodwithoutLP) at different baseline periods (PeriodwithLP). Consistent with the experimental results presented in Fig. 3, at most of the oscillation periods tested, the LP-to-PD synapse acted to slow down the rhythm by a relatively constant amount, whereas at a slower extreme of the oscillation periods, it sped up the rhythm (Fig. 6B, control: 
). Although these results were not quantitatively the same as the experimental results, they do match qualitatively with most aspects of the experimental results. By changing the various ionic conductances in the model PD and AB neurons, we found that the effect of the LP-to-PD synapse of speeding a slow oscillation period was mainly due to the influence of the synapse on a low-threshold Ca2+ current. At slower cycle periods, the LP-to-PD inhibition became larger in amplitude due to recovery from depression. This larger inhibition of the PD neuron allowed more recovery from inactivation of the low-threshold Ca2+ current, causing the PD neuron to burst earlier. In contrast, there was little change in the hyperpolarization-activated inward current Ih, possibly because its activation kinetics was too slow to have different effects at different cycle periods. However, incorporating an additional low-threshold potassium (A) current in the AB or PD model neurons also counteracted the ability of the LP-to-PD synapse to speed up the rhythm when it was slow (data not shown).
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). Although the effect of the LP-to-PD synapse on the rhythm period varied from preparation to preparation, we never observed a biological LP-to-PD synapse that showed this type of effect on the rhythm period. Similarly, when the maximal conductance of the surrogate synapse was tuned to match the oscillation with the control synapse at the longest period, it acted only to speed up the rhythm at high periods but would disrupt the rhythm at low periods (data not shown). In our experimental measurements, we have never observed disruption of the rhythm as a result of manipulating the LP-to-PD synapse. Effect of the LP-to-PY synapse on the burst delay of the PY neuron in the computational model
The experiments described in Fig. 4 show that the LP-to-PY synapse acts to delay the time of the PY neuron activity at all oscillation periods and, in most cases, it delays the activity more when the oscillation periods are longer. We tested this effect in the computational model by comparing the burst delay of the PY neuron (with respect to the PD neuron burst onset) in control conditions and when the LP-to-PY maximal synaptic conductance was set to 0 (Fig. 7A). These results are summarized in Fig. 7B, which show that the model synapse delayed the burst time of the PY neuron by 100–137 ms at different cycle periods. Although these results do not quantitatively match the experiments, they do qualitatively (compare with Fig. 4, C and D).
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; Reyes et al. 1998). Thus we examined the possible functional significance of the differential control of short-term synaptic depression of separate synapses efferent from the same presynaptic neuron. By comparing two functionally different synapses in the lobster pyloric circuit, we first showed that these synapses exhibit short-term depression with different dynamics and second that this difference in dynamics may be important for the proper operation and function of each synapse. LP-to-PD synapse depresses less and recovers faster than the LP-to-PY synapse
Previous studies on short-term depression of the LP-to-PD synapse (Manor et al. 1997) and the LP-to-PY synapse (Mamiya et al. 2003) have indicated that these synapses might have different dynamics. However, because the protocols for the activation of the synapses were different in each of these previous studies, a direct comparison of the dynamics was not feasible. In the present study, we directly compared these two synapses in the same preparations and showed that they have different strengths and dynamics. In particular, the LP-to-PD synapse was stronger, depressed less and recovered faster than the LP-to-PY synapse (Fig. 2C).
Although there was a clear difference between the dynamics of the short-term depression of the LP-to-PD and the LP-to-PY synapses, there was also some variability in dynamics even within the same type of synapse. In a previous study, we showed that the variability in the short-term depression of the LP-to-PY synapse was correlated with the burst phase of the PY neuron (Mamiya et al. 2003). Therefore the variability in the short-term depression of the LP-to-PY synapse observed in this study probably reflected the differences in the firing phase of the six to eight postsynaptic PY neurons. However, no previous study has examined the variability in the short-term depression of the LP-to-PD synapse. Because the LP-to-PD synapse had been proposed to play an important role in controlling the period of the pyloric rhythm, we examined the possible correlations between the parameters that describe the short-term depression of the LP-to-PD synapse (maximum depression and time constant of recovery) and the period of the ongoing pyloric rhythm. However, we saw no correlations between these parameters (data not shown). Thus the reasons for the variability in the parameters of short-term depression of the LP-to-PD synapse remain unknown.
Effect of the LP-to-PD synapse on the period of the pyloric rhythm
There have been conflicting reports on the effect of the LP-to-PD synapse on the period of the pyloric rhythm (Mamiya and Nadim 2004; Weaver and Hooper 2003a). Despite using similar experimental protocols, one study concluded that the LP-to-PD synapse increases the period of the pyloric rhythm by a constant amount regardless of the rhythm period (Weaver and Hooper 2003a), whereas the other study (from our laboratory) suggested that the effect of the LP-to-PD synapse on the period of the rhythm changes with the rhythm period (Mamiya and Nadim 2004). The results from this study show that the effect of the LP-to-PD synapse varies greatly from preparation to preparation. This is consistent with a previous study showing that an effect of a given synapse in a pyloric circuit varies greatly from preparation to preparation (Weaver and Hooper 2003b). In most cases, the LP-to-PD synapse worked to increase the period of the pyloric rhythm by a constant amount regardless of the rhythm period. However, in a few cases, it worked to increase the period when the rhythm was fast but had no effect or worked to decrease the period when the rhythm was slow. There were also some cases where the effect of the synapse on period depended on the rhythm period, but the change was too small to be statistically significant. It is worth noting that although the effect of the LP-to-PD synapse varied greatly, we never observed the biological LP-to-PD synapse to produce a larger increase in cycle period when the rhythm became slower. This is interesting because the strength of the depressing LP-to-PD synapse increases as the rhythm period becomes longer, and a stronger inhibitory synapse onto the PD neuron occurring at the same phase should increase the rhythm period more. The likely explanation is that the phase of the LP-to-PD synapse is changing as proposed by our previous study (Mamiya and Nadim 2004) and that this mechanism is compensating for the increase in the synaptic strength.
Effect of the LP-to-PY synapse on the burst delay of the PY neuron
The LP-to-PY synapse consistently delayed the burst time of the PY neuron. This may seem surprising because the activation of the synapse with a train of voltage pulses showed that after the first pulse, the postsynaptic potential is mostly depolarizing (see Fig. 2) (see also Mamiya et al. 2003). How could a depolarizing synapse delay the burst onset of the postsynaptic neuron? The reason for this paradoxical effect of the LP-to-PY synapse seems to be that the PSPs were measured when the pyloric activity was blocked, and the PY neurons were quiescent at their resting potential of around –55 mV. However, during an ongoing pyloric rhythm, the PY neurons oscillate at much more depolarized potentials (see Fig. 1B for example). When the PY neuron is at a more depolarized potential, the driving force for the chemical inhibition component of the synapse increases while the driving force for the (rectifying) electrical coupling component decreases. Moreover, in a previous study, we showed that the LP-to-PY synapse depresses less when the synapse is activated with a realistic presynaptic waveform (Mamiya et al. 2003). Thus, during an ongoing rhythm, the LP-to-PY synapse may in fact act to hyperpolarize the PY neuron and thus delay the onset of its burst. This is in fact exactly what happens in our computational model of the pyloric circuit in which the total LP-to-PY synaptic current remains outward during the ongoing rhythm (not shown).
Our results on the effect on the LP-to-PY synapse are in apparent conflict with the report of Weaver and Hooper (2003b) that the LP neuron had no significant effect on the activity phase of the PY neuron. This difference is most likely attributed to two factors: the large variability in the effect of the LP-to-PY synapse and the small number (n = 3) used in the data of Weaver and Hooper.
In the pyloric circuit, the tri-phasic pattern of activity composed of bursting by the AB/PD neurons, the LP neuron, and the PY neurons is maintained relatively constant over a wide range of frequencies (around 0.5 to 2.5 Hz) (Hooper 1997a,b). Both the intrinsic properties (Hooper 1998) and synaptic properties (Manor et al. 2003; Nadim et al. 2003) of the pyloric neurons have been proposed to play a role in this phase maintenance. If the short-term depression of the LP-to-PY synapse is helping the PY neuron to burst at a constant phase, the synapse should delay the PY burst time more when the period of the pyloric rhythm is longer. The results from the present study show that in most cases, the LP-to-PY synapse did show this type of increase in the delaying effect, whereas in some cases, it did not. The burst time of the PY neuron is known to be influenced by factors other than the LP-to-PY synapse, including synaptic inputs from the pacemaker neurons (Eisen and Marder 1984) and intrinsic properties of the PY neurons (Hartline 1979; Hooper 1998). It is possible that the variability in the effect of the LP-to-PY synapse on the relationship between the PY burst time and the rhythm period is due to the preparation-dependent interaction of this synapse with these other factors. Further experiments are needed to explore the possible role of the LP-to-PY synapse in maintaining the burst phase of the postsynaptic PY neurons.
Target-specific control of the short-term synaptic depression to suit the function of the synapse
We used computational modeling to demonstrate expressly that target-specific regulation of short-term synaptic depression contributes to the differential control of the target neurons by the LP neuron. Thus we assayed the effect of the efferent synapses of the LP neuron and their dynamics on the synaptic targets. To this end, we used a detailed biophysical model of the pyloric pacemaker AB and PD neurons (Soto-Treviño et al. 2005) to examine the effect of the LP-to-PD synapse on the pyloric rhythm period, and we used a simplified model of the PY neurons that produced activity at the correct phase of the pyloric cycle and fit the dynamics of the LP-to-PD and LP-to-PY synapses to our experimental data. We represented the LP neuron in the model with a library of prerecorded LP neuron waveforms that were indexed by their period (Mamiya and Nadim 2004): each model pyloric cycle used the LP neuron waveform indexed by the previous cycle period. Our choice not to use a biophysically realistic model of the LP neuron was intentional so that we could remove any confounding effects of the AB, PD, and PY synapses back to the LP neuron from our model results and focus on the significance of the LP-to-PD and PY synaptic dynamics. Thus our network model is by no means intended as an accurate representation of the pyloric network and is only intended to examine the consequences of the LP neuron synaptic dynamics.
When the dynamics of short-term depression for the LP-to-PD synapse were replaced with those for the LP-to-PY synapse in the model and the strength of the "surrogate" synapse was increased to produce the appropriate effect at the fastest period (550 ms), the LP-to-PD synapse failed to perform its proper function. This was mainly due to the fact that the LP-to-PY synapse showed much more depression and thus, when the maximal conductance of the surrogate synapse was made large enough to produce the appropriate effect (Period >0) at short cycle periods (when the synapse was most depressed), then at long cycle periods (when the synapse recovered from depression), it became too strong to produce the appropriate effect and Period became larger.
Similarly, the LP-to-PY model synapse also failed to perform its proper function when its dynamics were replaced with those for the LP-to-PD synapse. In this case, the surrogate synapse was too limited in its range of efficacy to allow the PY neuron to produce action potentials at all cycle periods (note the range of synaptic efficacies as a function of the interpulse interval in Fig. 2B). When the maximal conductance of the model surrogate synapse was tuned to match the correct PY neuron burst time at any single period, the PY neuron failed to produce action potentials at other periods. In the biological pyloric network, changing the rhythm period in the range tested never suppressed the firing of the PY neuron. Note that because the PY neuron is also a motor neuron, its failure to produce action potentials would interfere with the proper pyloric motor function.
We conclude, therefore, that it is unlikely that the difference in the dynamics of short-term depression in these two synapses is just a secondary effect of other synaptic properties. Rather these modeling results suggest that the short-term depression of each synapse is differentially controlled to precisely match the function of the synapse.
Conclusion
Controlling the dynamics of synapses efferent from the same presynaptic neuron to different types of targets may be one way of achieving flexible control in networks where each neuron synapses onto multiple targets (Markram et al. 1998; Reyes et al. 1998). However, network activity is the result of the interaction between synaptic and intrinsic membrane properties of all network elements (Clemens and Katz 2001; Katz and Frost 1996; Marder and Calabrese 1996; Nässel 2000; Ramirez and Richter 1996). An accurate comprehension of how outputs of distributed networks are generated would require not only an understanding of the dynamics of the constituent neurons and synapses but also an adequate matching of the synaptic dynamics to their specific targets.
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ACKNOWLEDGMENTS |
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Present address of A. Mamiya: Cold Spring Harbor Laboratory, Cold Spring Harbor, NY 11742.
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Address for reprint requests and other correspondence: F. Nadim, Dept. of Biological Sciences, Rutgers University, 101 Warren St., Newark, NJ 07102 (E-mail: farzan{at}njit.edu)
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REFERENCES |
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Bose A, Manor Y, and Nadim F. Bistable oscillations arising from synaptic depression. SIAM J App Math 62: 706–727, 2001.
, the recovery of each synapse as the IPI tends to 0 (R0). C: the recovery time constant 
