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Previous Article | Next Article
Volume 17, Number 14, Issue of July 15, 1997 pp. 5610-5621
Copyright ©1997 Society for NeuroscienceTemporal Dynamics of Graded Synaptic Transmission in the Lobster Stomatogastric Ganglion
Yair Manor, Farzan Nadim, L. F. Abbott, and Eve Marder Volen Center and Biology Department, Brandeis University, Waltham, Massachusetts 02254
ABSTRACT
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
Key words: graded synaptic transmission; pyloric network; central pattern generation; oscillations; synaptic depression; inhibition50 to
INTRODUCTION
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
The chemical synaptic connections between STG neurons are inhibitory (Maynard, 1972
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
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
Microelectrodes were pulled on a Flaming-Brown horizontal puller and were filled with 2 M KCl. The electrode resistances were 8-12 M . All neurons were identified by their stereotypical axonal projections in identified nerves using conventional techniques (Selverston et al., 1976
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
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). 
Fig. 1. Presynaptic stimulation with realistic waveforms. The membrane potential oscillations of an LP neuron were recorded in normal saline. A unitary waveform was created by dividing the trace into single cycles and by averaging the cycles and low-pass filtering to eliminate the action potentials. The waveform was stored in the computer. This procedure was repeated for different LP neurons to capture different duty cycles (the ratio of time that the waveform was above its mean value). The resulting unitary waveforms, scaled to various amplitudes and frequencies, were used to voltage clamp LP neurons periodically (in TTX) in subsequent experiments.
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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
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).
RESULTS
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. 2A). To study graded transmission from the LP neuron to the PD neurons, we voltage clamped the LP neuron with two electrodes (Fig. 2B), monitored the membrane potential of the PD neurons in current clamp, and placed the preparation in TTX to block all action potentials. Figure 2C shows the gIPSPs evoked in the two PD neurons in response to a step depolarization of the LP neuron from
Fig. 2. Inhibitory synaptic connections from the LP neuron to the PD neurons. A, In normal saline, the LP and the two PD neurons bursting in alternation. The most hyperpolarized point was
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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 
Fig. 3. Persistent and transient components of the gIPSP. A, The LP neuron was held at
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Figure 3B shows the peak amplitude (open circles) and the amplitude of the gIPSP at 1.75 sec (filled circles) of the traces in Figure 3A 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 3C (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: where S is the saturation level of the sigmoid, V is the independent variable, Vmid is the half-maximum voltage, and 1/k describes the slope of the sigmoid at Vmid. The values of Vmid and k for the I/O curves were (in mV, mean ± SEM; n = 15): Vmid =
(1) 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
Fig. 4. Depression of the gIPSP in response to trains of square pulses. A, Synaptic responses to trains of 500 msec pulses with intervals of 2 sec (left) and 250 msec (middle) and to a single long pulse (right). The PD neuron initial membrane potential was
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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
Figure 5A 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 
Fig. 5. Comparison of I/O curves for square and realistic waveforms. A, A comparison of the responses to 1.75 sec square pulses (left) and to 1 Hz LP waveforms (right). The holding potential of the square pulses and the average of the LP waveforms was
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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. 6A). 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 6B 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 6B to their respective maximums to obtain the normalized I/O curves (Fig. 6C) 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): Vmid = 
Fig. 6. Synaptic depression does not affect the normalized I/O curve. A, Synaptic response to 1 Hz LP waveforms at different amplitudes. The responses to the first cycle (left) and the average of the last four cycles (right, defined as the steady state) of a 20 sec LP waveform are shown. The initial membrane potential of the PD neuron was 0 mV. Vertical bar, 4 mV (PD) and 40 mV (LP). B, Amplitudes of the responses to the first cycle (filled circles) and the steady state (open circles) of the 1 Hz LP waveform. C, The normalized I/O curves (mean ± SEM; n = 7) for the first cycle and the steady state of the LP waveform. The curves are not different (two-way ANOVA, p = 0.996).
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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 Figure 7, 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 (
Fig. 7. Dependence of the amplitude of the gIPSP on duty cycle. A, Comparison of the synaptic response to 1.5 Hz LP waveforms with duty cycles of 35/65 (thick traces) and 55/45 (thin traces). For both duty cycles, the presynaptic voltage is between
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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 8A 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 (Aref). 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 =
Fig. 8. Effect of frequency on the gIPSP amplitude. A, Peak amplitude of the gIPSP in response to trains of square pulses at different frequencies (mean ± SEM; n = 5). Data are normalized with respect to Aref, the amplitude of the response at 0.1 Hz. The response to the first pulse (filled circles) was identical at all frequencies. The steady state response (open circles) decayed linearly with increasing frequencies (dashed line, slope =
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With realistic waveforms, the dependence of first and steady state gIPSP amplitudes on frequency was more complex. Figure 8B1 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 Aref 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 × Aref (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 × Aref but decayed linearly at frequencies above 0.3 Hz (slope = 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 Figure 9A, 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 definet as the difference between the peak gIPSP (Fig. 9A, upper traces) and the peak of the LP waveform (Fig. 9A, lower trace). At 0.2 Hz, the gIPSP peak was advanced (
Fig. 9. The effect of frequency on the phase of the steady state gIPSP. The phase of the gIPSP is defined as the time lag (
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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.
Fig. 10. The ratio of integrals for different duty cycles. A, An example of the integrals calculated for the presynaptic LP waveforms and the gIPSP in PD neurons (shaded areas). Vertical bar, 5 mV (PD) and 50 mV (LP). B, The ratios of integrals for duty cycles of 55/45 and 35/65 for the LP waveforms (open triangles) and the PD responses (filled squares) are shown.
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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. 11A) is defined as a rectangle of length tequiv (a measure of the waveform duration) and height Vavg (a measure of the average amplitude of the waveform). To calculate tequiv, 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 tequiv. Vavg is calculated in each cycle by dividing the integral of the waveform by tequiv. Therefore the area represented by the product of tequiv and Vavg is equal to the integral, but this area is now expressed such that it weights appropriately the average amplitude and duration of the waveform. 
Fig. 11. Representation of LP waveforms and PD gIPSPs with equivalent rectangles. The equivalent rectangle of a waveform is defined as a rectangle of length tequiv (a measure of the waveform length) and height Vavg (a measure of the average amplitude of the waveform), in which tequiv is twice the time that divides the waveform in two parts with equal integrals, and Vavg is the ratio of the integral of the waveform in one period to tequiv. The area of the equivalent rectangle is therefore equal to the integral of the waveform during one cycle. A, Equivalent rectangles superimposed on one cycle of a 0.2 Hz LP waveform (bottom) and the PD response (top). The integral of the LP waveform is measured from its minimum, and the integral of the PD response is measured from its baseline (
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Figure 11B 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 Vavg values of postsynaptic equivalent rectangles to the Vavg of the 0.1 Hz waveform with the duty cycle of 55/45 (the Aref). At all four frequencies, the Vavg 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 Vavg 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, tequiv 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 tequiv values of the presynaptic waveforms and the postsynaptic responses.
These results are maintained across the whole range of frequencies tested. In Figure 11C, Vavg is plotted as a function of frequency for the two duty cycles. At all frequencies, Vavg of the 35/65 (filled circles) duty cycle was larger than Vavg of the 55/45 (open circles) duty cycle (two-way ANOVA, p < 0.05; n = 14). For both duty cycles, Vavg reached a maximum at 0.8 Hz. Figure 11D shows the plot of the ratio of tequiv to period (defined here as the "normalized tequiv") as a function of frequency. At all frequencies, the tequiv generated 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 tequiv for the presynaptic waveforms. As frequency increased, the normalized tequiv of the postsynaptic gIPSP approached the normalized tequiv of the presynaptic waveform. For the 35/65 duty cycle waveform, the postsynaptic normalized tequiv 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 Figure 12A, 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).
Fig. 12. Effect of simulated spike-mediated IPSPs. A, IPSPs in response to 1 Hz LP waveforms with the spikes filtered out (smooth trace) and with the spikes not filtered (jagged trace). The nonfiltered waveform elicited an IPSP that was larger in amplitude than that of the filtered waveform and was jagged. The jaggedness corresponded one-to-one to IPSPs elicited by the simulated spikes. The jagged trace was also faster to rise. Vertical bar, 10 mV (PD) and 50 mV (LP). B, The gIPSPs in response to the filtered LP waveforms from A compared with the response to the same waveform (bottom LP trace), amplified to the average of the nonfiltered waveform in A (middle LP trace), and amplified to the outer envelope (maximum) of the nonfiltered waveform in A (top LP trace). The larger waveforms elicited gIPSPs that were larger in amplitude and faster to rise. The large amplitude and fast rise of the response to the nonfiltered waveform in A was accounted for by the response to the average of that waveform (middle LP trace). The membrane potential of the PD neuron was
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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 same maximum or the same average amplitude as the nonfiltered waveform, and we compared the result with the injection with the original "envelope" filtered waveform (Fig. 12B). The increase in the amplitude of the IPSP was fully compensated for by the larger average input waveform (Fig. 12B, 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. 12A, jagged PD trace) and to the filtered waveform without spikes but with the same average amplitude (Fig. 12B, middle PD trace) were approximately equal, both in amplitude and in rise time. The filtered waveform with the same maximum (Fig. 12B, top LP trace) produced a disproportionately larger IPSP than the nonfiltered waveform.
DISCUSSION
Graded synaptic transmission is a common feature of many invertebrate sensory and motor networks (Pearson and Fourtner, 1975
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
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 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. 11B) allowed us to decompose the postsynaptic response into an average voltage, Vavg, and an equivalent duration, tequiv. As expected, when the duty cycle increases, the postsynaptic tequiv also increases, but again, nonintuitively, the postsynaptic Vavg 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 (tequiv) or amplitude (Vavg) of the synaptic potential is more important. Specifically, the trajectory of the recovery from the gIPSP will interact with currents such as Ih, IA, 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 Vavg) 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 tequiv). 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. 11B).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
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, tequiv, and Vavg make 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
It is a truism that network dynamics depend on the interaction of synaptic and intrinsic membrane properties (Marder and Calabrese, 1996
FOOTNOTES
Received March 5, 1997; revised April 29, 1997; accepted April 30, 1997.
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.
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