INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Synchronized oscillations in neuronal ensembles are a topic of considerable interest in neurobiology not least because of their importance in the normal and pathological operation of brain circuits (Gray 1994; Steriade et al. 1993; von Krosigk et al. 1993). Within the last decade, computational and analytical studies have uncovered a synchronizing effect of mutual synaptic inhibition (van Vreeswijk et al. 1994; Wang and Rinzel 1992). As is well known, reciprocal inhibition between pairs of neurons (a half-center organization) (Brown 1911) underlies alternating (antiphasic) patterns of spiking or bursting provided that synaptic time constants are shorter than the duration of the presynaptic signals (Friesen 1994; Marder and Calabrese 1996; Perkel and Mulloney 1974; Skinner et al. 1994; Wang and Rinzel 1992). However, with slow inhibitory kinetics (long time constants), pairs of model neurons have the ability to synchronize (oscillate in-phase) (Terman et al. 1998; van Vreeswijk et al. 1994; Wang and Rinzel 1992, 1993; White et al. 1998). Note that the time constant(s) considered here are those governing postsynaptic responses, not those controlling presynaptic transmitter release. At biological synapses, differences in receptor type, ion channel coupling, and gating, etc., permit different speeds of postsynaptic response to the same neurotransmitter independent of the kinetics of release. Using model neurons, Wang and Rinzel (1993) lengthened the inhibitory time constant progressively and observed a sudden transition from antiphase to in-phase oscillations. Inhibitory synchronization has also been found in simulations of much larger neural assemblies (thalamic and hippocampal networks in vertebrate brain) (Destexhe et al. 1994a; Jefferys et al. 1996; Traub et al. 1996; Wang and Buzsáki 1996; Whittington et al. 1995).

Experimental evidence for this type of synchronization in spiking neurons comes from studies of hippocampal slices, where inhibitory interneurons continue to oscillate in synchrony (firing 1 or 2 spikes per cycle) after phasic, excitatory synapses are blocked. The frequency of these synchronized oscillations varies with the rate of decay of the inhibitory postsynaptic currents (IPSCs) (Traub et al. 1996; Whittington et al. 1995). Although pharmacological manipulations of large, intricate networks warrant some caution of interpretation, these findings nevertheless provide strong evidence for spiking synchronization.

Empirical evidence for inhibitory synchronization of bursting is much less complete. Cellular burst generation is an important component of oscillatory activity in neural circuits of both vertebrates and invertebrates (Llinas 1988; Marder and Calabrese 1996; Smith et al. 1991; Steriade et al. 1993). The dynamics of bursting are more complex than those of tonic spiking because processes slower than those of individual spikes alternately shift the neuron between states of repetitive firing and quiescence (Wang and Rinzel 1995). "Burst synchronization" implies that mutually inhibitory neurons will generate bursts with little or no difference in onset time and duration. Potentially this is a more difficult task because each postsynaptic neuron must generate its burst at the same time that it receives inhibition from its antagonist.

We set out to study this general problem by varying the time constant of inhibition in artificial half-center circuits constructed from biological bursters. Working with biological neurons is important because real neurons inevitably have richer biophysical properties than even sophisticated models (although one's ability to dissect mechanisms is more constrained). The crustacean stomatogastric ganglion (STG) contains a well-characterized set of neurons with bursting membrane properties (Harris-Warrick et al. 1992). Using established methods, one can disconnect oscillating neurons from their natural synaptic interactions (Bal et al. 1988; Miller and Selverston 1982). One can then use the dynamic clamp (Sharp et al. 1993) to insert simulated synapses whose parameters can be varied at will. With this technique, Sharp et al. (1996) simulated reciprocal inhibition between a pair of gastric mill neurons in the crab STG. When the IPSCs happened to rise slowly, the spikes of the connected neurons could synchronize (Marder 1998; Sharp et al. 1996). This was an important result but it suffers two limitations. First, the uncoupled neurons showed no oscillatory behavior more complex than tonic firing and postinhibitory rebound. Second, to obtain synchrony, the neurons had to spend almost all their time more depolarized than the (simulated) synaptic release threshold. Thus it remains uncertain whether inhibitory synchronization can occur between repetitive bursters and by activating synaptic transmission only during presynaptic bursts (a more likely condition in biological circuits).

In this study, we construct the half-center circuits using STG neurons with cellular burst-generating properties. These identified neurons are components of the pyloric network of the lobster STG (Harris-Warrick et al. 1992; Miller 1987). Normally, they interact via a stereotyped array of chemical and electrical synapses, the chemical connections operating by a combination of graded and spike-mediated transmission (Graubard et al. 1983; Hartline and Graubard 1992). When uncoupled from their normal synaptic partners (by synaptic blockade and cell photoinactivation), pyloric neurons can continue to burst repetitively in either pacemaker-like or irregular patterns (as long as the STG continues to receive modulatory input) (Bal et al. 1988; Eisen and Marder 1982; Elson et al. 1998, 1999; Marder and Eisen 1984; Miller and Selverston 1982). We use the dynamic clamp to reconnect these bursters by reciprocal inhibition in "test-bed" circuits. We report the effects of varying the time constant (_syn) of IPSCs on the frequency, phase synchrony, and stability of coordinated burst patterns.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Preparation, dynamic clamp and synaptic circuits

Adult spiny lobsters, Panulirus interruptus, were caught locally and kept in running seawater until use. The stomatogastric nervous system (Harris-Warrick et al. 1992), consisting of the STG and anterior (commissural and esophageal) ganglia and their connecting and motor nerves, was removed from the foregut (Mulloney and Selverston 1974) and pinned out in a silicone elastomer (Sylgard)-lined dish, filled with normal Panulirus saline [which contained (in mM) 479 NaCl, 13 KCl, 14 CaCl₂, 6 MgSO₄, 4 Na₂SO₄, 5 HEPES, and 5 TES; pH 7.4] (n = 9 preparations). The STG was surrounded by a petroleum jelly (Vaseline) chamber for separate superfusion. Both the STG and the rest of the nervous system were continuously superfused by continuous flows of chilled saline (14-17°C; temperature was kept within 1°C during each recording session). When drugs were applied, they were introduced to the STG superfusion only. The ganglion was desheathed and the somata of pyloric neurons impaled by microelectrodes (filled with 3 M-KCl; resistance, 10-20 M) connected to conventional intracellular electrometers (Neuroprobe 1600: A-M Systems; Axoclamp 2B: Axon Instruments). Neurons were identified by their characteristic phase of bursting and by the correlation of their spikes with impulses monitored extracellularly in output motor nerves. During dynamic current-clamp experiments, we used separate microelectrodes for voltage recording and current injection. Dual impalement was used for the soma of the single lateral pyloric (LP) neuron. The two pyloric dilator (PD) neurons are electrically coupled. In some preparations, we inserted both the voltage and the current electrode in one PD; alternatively, we placed the voltage-recording electrode in one PD while injecting current into the other (thus "spreading" the simulated conductance through the neuropilar pathway between the 2 somata). Similar results were obtained with either configuration. Dynamic clamp methods (for details, see following text) were implemented using a Digidata 1200A interface (Axon Instruments) and either commercial software (DCLAMP2.0: Dyna-Quest Technologies, Sudbury, MA) or custom-built programs (DYNCLAMP4) (Pinto et al. 2001).

In the intact STG, the neurons of the pyloric central pattern generator (CPG) are connected to each other by a known set of chemical and electrical synapses (Harris-Warrick et al. 1992; Miller 1987), shown in simplified form in Fig. 1A1. Established techniques were used to disable natural connections and then to insert simulated synapses between the LP and PD neurons, producing two types of "test circuit" (Fig. 1A, 2 and 3).

View larger version (40K): [in this window] [in a new window]   Fig. 1. Methodology: synaptic test circuits, dynamic clamp inhibitory postsynaptic currents (IPSCs), and burst analysis. A: test circuits. For symbols, see key: electrical coupling is either nonrectifying (resistor symbol) or rectifying (diode symbol) (cf. Johnson et al. 1993). Connections with two other classes of pyloric neuron are omitted: those remaining after PTX blockade are weak. B: postsynaptic current (Ipost) generated by dynamic clamp in response to presynaptic voltage signal from a bursting pyloric dilator (PD) neuron (Vpre) at 3 different time-constant values (syn), for 2 values of presynaptic threshold voltage (Vth). [Postsynaptic membrane potential (Vpost) held constant at 50 mV. Right: the release slope voltage, Vslope, was decreased slightly to make the burst-evoked IPSCs comparable in amplitude to those in the left panel]. For further explanation of parameters, see METHODS. Calibration bars: 20 mV; 2.2 nA; 500 ms. C: measurement of burst statistics. Top: spike density functions (SDFs), corresponding to the voltage signals from bursting neurons [lateral pyloric (LP and PD, respectively), bottom]. Burst phase was estimated as dLP,PD/pLP, where dLP,PD is the delay between the peak SDFs for LP and PD, and pLP is burst cycle period measured from the interval between successive SDF peaks for LP. Measurements of burst duration, duty cycle, and time differences were computed from the beginning times (LPb, PDb) and end times (LPe, PDe) of the bursts (see METHODS). Calibration bars: 10 mV; 20 spikes/s; 500 ms.

Test circuit 1 was produced by pharmacological blockade of chemical synapses (Fig. 1A2; n = 6 preparations). For this, we used 10 µM picrotoxin (PTX) to block glutamatergic inhibition [evoked by all the pyloric neurons except the PDs and the ventricular dilator (VD) neuron] and 0.6-2 mM tetraethylamonium chloride (TEA) to block slower cholinergic inhibition (evoked by PD and VD) (Eisen and Marder 1982; Marder and Eisen 1984). In test circuit 1, the two PDs remain coupled electrically to each other, to VD, and to the anterior burster (AB) neuron, forming a pacemaker ensemble (Miller 1987).

Test circuit 2 resulted from additional photoinactivation of VD and AB (Miller and Selverston 1979; Selverston and Miller 1980) (Fig. 1A3; n = 3 preparations). In this circuit, the PDs remained electrically coupled to each other, but otherwise they and the LP neuron were now isolated from strong synaptic interactions with other pyloric neurons. In all cases, the STG continued to receive descending modulatory inputs from the anterior ganglia, which sustains cellular burst-generating processes in these cells (cf. Bal et al. 1988; Miller and Selverston 1982). At the concentrations used, TEA also enhanced burst generation, increasing the amplitude and regularity of slow voltage oscillations, the peak spike frequency, and the duration of individual spikes (Gola and Selverston 1981; Harris-Warrick and Flamm 1987; Elson, unpublished observations).

Synaptic simulation, threshold and kinetics: application to bursting neurons

A chemical synaptic connection between two neurons was simulated using a simple scheme proposed by several authors (Abbott and Marder 1998; Destexhe et al. 1994b; Nadim et al. 1999; Sharp et al. 1993). The current, I_post, injected into a postsynaptic neuron is simulated by

(1)

where g_syn is the maximal synaptic conductance, and V_rev is the synaptic reversal potential. V_post, S, and h describe, respectively, the instantaneous postsynaptic membrane potential, the synaptic activation, and the synaptic "inactivation," which was used to approximate depression.

The activation term, S, models the release of neurotransmitter as a function of the membrane potential of the presynaptic neuron (V_pre). The kinetics of S simulate the time course of the release of the transmitter and its action at the postsynaptic membrane. S is described through the differential equation

(2)

where _syn is a voltage-independent time constant that plays the central role in our studies. In this formulation, _syn describes the effective kinetics of the postsynaptic conductance change. By choosing different values of _syn while keeping other synaptic parameters constant, we aim to simulate different rates of activation and deactivation of postsynaptic ion channels. (In real synapses, these different rates could result from differences in receptor identity, coupling pathways, ion channel structure, etc.).

We represent S as

(3)

where V_thresh is a threshold voltage, and V_slope controls the slope of the function.

We used parameter ranges 45 mV  V_slope  40 mV, 10 mV  V_slope  15 mV, and 40 nS  g_syn  80 nS. V_rev was held fixed at 80 mV. These parameter values produce synaptic input-output behavior approximating that of natural pyloric synapses, where transmitter can be released as a graded response to presynaptic depolarizations subthreshold to spike generation (Graubard et al. 1983; Hartline and Graubard 1992).

Generally h =1, meaning no inactivation/depression. In one experiment (see Fig. 2), h was allowed to vary with first-order kinetics

(4)

with _h = 100 ms and

(5)

It is clear from Eq. 2 that S approaches S at a rate 1/[_syn (1 - S)] (cf. Abbott and Marder 1998). A presynaptic depolarization will cause S to increase, whereas an equivalent hyperpolarization will cause a decrease. However, the voltage dependence of the rate factor ensures that S will rise faster than it falls. The time constant, _syn, is voltage independent and scales both processes. If the presynaptic signal dips below V_thresh, S will decay as 1/_syn.

View larger version (54K): [in this window] [in a new window]   Fig. 2. Transition between alternating and synchronous bursting produced by varying the time-constant of reciprocal inhibition (syn) in test circuit 2. A, 1-4: sample recordings of membrane potential of LP and a PD neuron with no dynamic clamp connection (A1, free-running) and with simulated reciprocal inhibition (schematized as arrow-circle symbols at left) at 3 different time constants (syn). In A, 2-4, we also monitor 1 of the Ipost signals: iPD, the current injected into PD to simulate the LP-to-PD connection. Dashed lines indicate 45 mV (Vthresh) for voltage traces, 0 nA for current trace. B: time series of burst phase during free-running activity. C: time series of burst phase during reciprocal inhibition at syn = 5 ms (filled squares) and at syn = 500 ms (open squares). D: phase (mean ± SD) over a range of syn values. E: burst cycle period (mean ± SD; filled squares) for a range of syn. Also shown are the values for free-running neurons (open circles). In D and E, each point represents statistics from 30 cycles. At syn = 250 ms and syn = 300 ms, episodes of alternating (phase ~0.5) and synchronous (phase ~0) bursting occurred within the same time series (cf. A3). In those cases, phase and cycle period values are plotted for the pattern adopted by the majority of cycles. Calibrations: 10 mV; 0.8 nA; 2 s. Parameter settings: Vthresh = 45 mV, Vslope = 10 mV; gsyn = 60 nS (LP-to-PD), 40 nS (PD-to-LP). In this experiment, h (Eq. 2) was allowed to vary to simulate synaptic depression (see METHODS for details). In this and Fig. 5, phase and cycle period were measured as described in Fig. 1 and METHODS.

The detailed time course of S therefore depends on the value of _syn and the setting of V_thresh relative to the variations in V_pre. In bursting neurons, such as those of the pyloric circuit, V_pre undergoes slow oscillations crowned by bursts of fast spikes. To check the kinetics of S in this case, we recorded I_post (with V_post held constant and h = 1; cf. Eq. 1) while V_pre was supplied by the membrane potential of a bursting pyloric neuron. When V_thresh was less negative than the peak of the slow voltage oscillation, "release" occurred only in response to the presynaptic spikes (Fig. 1B, right: V_thresh = 36 mV). In this case, lengthening _syn increased the temporal summation of the discrete synaptic currents evoked by individual spikes. At any given _syn, the overall postsynaptic response to the presynaptic burst rose faster than it fell (as expected). Increasing _syn caused a decrease in the rate of both rise and fall. When V_thresh was set more negative than the peak slow oscillation (Fig. 1B, left: where V_thresh = 45 mV), graded as well as spike-mediated "release" could occur (as in the natural synapses) (Graubard et al. 1983; Hartline and Graubard 1992). Nevertheless, the effect of varying _syn on the rates of rise and decay of the overall postsynaptic response was similar to the previous case. The main difference occurred at the shortest _syn, 5 ms, where temporal summation of spike-mediated currents was minimal and graded release contributed an additional, smooth component. In both cases, long _syn values prevented the postsynaptic current from decaying completely between bursts, resulting in a small offset (e.g., Fig. 1B, _syn = 500 ms).

Burst pattern analysis

To derive a general measure of relative burst phase, we used the maxima of spike density functions (SDFs) (cf. Szücs 1998; Szücs et al. 2001) (Fig. 1C). For a given neuron, a SDF was generated by first detecting the sequence of spike times in the recording of membrane potential and then convolving the time of each spike with a Gaussian function using the analysis software, Orbital Spike 2 (Szücs 1998, 2001). The half-width of the Gaussian kernel was 0.3-0.4 s and the sampling resolution, 4 ms. For phase analysis, we measured the burst cycle period for LP (p_LP) from the interval between successive maxima in that neuron's SDF. Phase was defined by measuring the temporal distance d_LP,PD between a given peak SDF in LP and the "neighboring" peak in the SDF of PD (Fig. 1C), and then evaluating phase = d_LP,PD/p_LP.

By these definitions, burst times indicated by maxima in the SDF are called synchronized when phase = 0. Strict out-of-phase behavior is indicated by phase = 0.5 (PD following LP). If, during a time series, the burst of PD shifted to precede that of LP, phase was assigned a negative value. If the phase grew more negative than 0.2, the corresponding PD burst was omitted from the analysis, the calculation being reset to the next PD burst. In each experimental condition, period and phase values were measured for 30-40 consecutive cycles and plotted as time series or reported as means ± SD.

For more detailed analysis (Fig. 3), we used Orbital Spike 2 to discriminate, from the sequence of spike times, the precise times of burst beginning (LP_b, PD_b) and burst ending (LP_e, PD_e; see Fig. 2C). From these series of values, we calculated burst beginning time difference = (PD_b,i - LP_b,j), and burst ending time difference = (PD_e,i - LP_e,j), where i and j represent "neighboring" bursts as explained in the preceding text. The same measurements yielded, for each burst i of (e.g.,) LP, a value for burst duration = (LP_e,i - LP_b,i) and burst duty cycle = (LP_e,i - LP_b,i)/(LP_b,i+1 - LP_b,i), with corresponding calculations being made for PD. As before, these statistics are reported as means + SD (see Fig. 3). SDF peak detection, statistical calculations, and plotting of graphs were performed in Origin 6.0 (Microcal Software, Northampton, MA).

View larger version (26K): [in this window] [in a new window]   Fig. 3. Burst timing statistics as a function of syn for test circuit 2 (same data as those illustrated in Fig. 2). A: burst durations. B: burst duty cycles. C: differences between the burst beginning times in LP and PD, and between the burst ending times of the same neurons. Values for free-running neurons are labeled free; double-headed arrows indicate ranges of syn for which the sole or dominant coordination pattern is antiphase or in-phase, respectively (cf. Fig. 2D). Points show means; error bars show SD. For further details of statistics, see METHODS.

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Using the dynamic clamp to change the time constant, _syn, of reciprocal inhibition between the bursting pyloric neurons, LP and PD, produced changes in burst duration, burst period and relative burst phase. In both types of half-center circuit (see Fig. 1A and METHODS), increasing _syn resulted in a transition from out-of-phase oscillations to in-phase bursting. However, the slope of the transition differed in the two test circuits.

Synchronization between cellular bursters (test circuit 2)

First, we describe the behavior of test circuit 2. This is the simpler half-center circuit, in which the LP and PD neurons were isolated from strong synaptic interactions with each other and with other neurons of the pyloric network (Fig. 1A3). Figure 2 illustrates results from one of three preparations with this configuration. With no dynamic clamp connections, LP and PD each generated slow oscillations of membrane potential, surmounted by bursts of fast spikes (attenuated in soma recordings; Fig. 2A1; see METHODS) (cf. Bal et al. 1988, Miller and Selverston 1982). The phase of bursts in PD, measured relative to those in LP, drifted, indicating little or no residual synaptic interaction (Fig. 2B). During this "free-running" activity, both LP and PD produced bursts of varying duration and cycle period (Fig. 2A1); however, their average cycle periods were similar (Fig. 2E, "LP free" and "PD free").

We then used the dynamic clamp to insert reciprocal inhibitory synapses between LP and PD and varied the time constant (_syn) governing the rate of activation and deactivation of the postsynaptic conductance. (For the effect of _syn on IPSC time course, see Fig. 1B and METHODS. Other synaptic parameters were left unchanged).

With fast (_syn = 5 ms) synapses, bursts immediately began to alternate (Fig. 2A2; phase = 0.5-0.6: Fig. 2C, filled squares). Initially, increasing _syn caused little change in burst phase (Fig. 2D), although the cycle period rose (Fig. 2E, filled squares). However, when _syn  250 ms, the coordination switched to in-phase synchronized bursting (Fig. 2A4), maintaining phase ~0 (Fig. 2C, open squares). The sudden change in phase was accompanied by a shortening of the cycle period (Fig. 2E). Further increases in the synaptic time constant produced only small additional changes of phase, while cycle period tended to lengthen once more (Fig. 2, D and E). In the vicinity of the phase transition (_syn = 250-300 ms), brief bouts of antiphasic activity interrupted the sequence of synchronized bursting, the circuit switching rapidly and spontaneously between the two coordination states (e.g., Fig. 2A3). We found similar effects on the timing and phase of bursting in the two other preparations where test circuit 2 was studied.

To examine effects on burst activity in more detail, we performed a further quantitative analysis of the experiment illustrated in Fig. 2 (see Fig. 3). The burst durations of neurons on both sides of the half-center shortened when the coordination switched from antiphase to in-phase (Fig. 3A). Burst duty cycles showed less change (Fig. 3B), suggesting that the decrease in cycle period (cf. Fig. 2E) was produced mostly by shortening the burst durations. The neuron with the longer free-running burst duration (LP) shortened its bursts to approach the duration of those in the other cell (PD). Although the durations of in-phase bursts were not identical (Fig. 3A), they were positively correlated (P < 0.001, except for _syn = 400 ms, where P < 0.05); in contrast, the neighboring bursts of antiphase rhythms showed no significant correlation (data not illustrated). A plot of absolute time differences (Fig. 3C) showed that in-phase bursts began at, or near, to the same time, the difference in burst duration appearing as a small difference in end times; the variance in both burst beginning and ending time differences was much smaller in the in-phase, compared with the antiphase patterns (Fig. 3C). Inspection of time series suggested that similar changes of burst duration and timing occurred in the other experiments (although the slope of transition differed between test circuits, see following text).

Details of spike activity, slow voltage oscillations. and synaptic currents

These are illustrated in Fig. 4 (from the experiment shown in Figs. 2 and 3). The synaptic threshold voltage, V_thresh, was set more negative than the peaks of the slow depolarizations so as to simulate natural stomatogastric connections (Graubard et al. 1983). Thus the IPSC evoked by a presynaptic burst was a sum of spike-mediated and graded components as can be seen at the short time constant (Fig. 4A). At this value of _syn, bursting occurred in antiphase, and the IPSC evoked by the presynaptic burst arrived during the interburst interval of the postsynaptic cell (Fig. 4A; see also Fig. 2A2). At long _syn, during in-phase rhythms, the IPSC rose and fell more slowly, reaching a peak as the postsynaptic burst was occurring, and then slowly declining during the inter-burst interval (Fig. 4B; cf. Fig. 2A4). A small, steady background current could build up as a result of incomplete deactivation of the IPSC; however, this was not essential for synchronization (data not shown). The time course of the synaptic currents reflected the kinetics of the synaptic activation function (see METHODS and Fig. 1B) together with the variations in postsynaptic membrane potential (which affects driving force). During slow activation and deactivation of the postsynaptic conductance, rapid changes of membrane potential in the postsynaptic cell produced corresponding fluctuations in the postsynaptic current. Thus the spiky components appearing in the synaptic currents in Fig. 4B resulted from the occurrence of spikes in the postsynaptic not the presynaptic, neuron. When the antagonistic neurons produced bursts in phase, individual spikes were not synchronized (Fig. 4B).

View larger version (18K): [in this window] [in a new window]   Fig. 4. Details of spike timing and synaptic currents during antiphase (A) and in-phase (B) bursting (test circuit 2; extracts of data used in Figs. 2 and 3). Intracellular recordings of membrane potential for LP and PD neurons and simultaneous monitors of simulated synaptic currents injected into LP (iLP) and PD (iPD), respectively. · · · , voltage and current traces for PD. - - -, 0 current level. (In A, phasic IPSPs, correlated with spike-mediated IPSCs, are not visible in the PD because the synaptic current was injected into the electrically coupled partner neuron; the depression of the IPSC during the presynaptic burst reflects the inclusion of an inactivation term in the equation simulating the synaptic currents, see METHODS). Calibrations: 20 mV, 1.5 nA (iPD), 0.75 nA (iLP); 500 ms.

Coordination between an individual burster and a pacemaker group (test circuit 1)

Slow, reciprocal inhibition also synchronized bursting between the LP and PDs when the latter remained coupled by electrical synapses to the AB and VD neurons, as part of the pyloric pacemaker group (test circuit 1, Fig. 1A2; n = 6 preparations). However, as _syn was increased, the phase transition from alternating to synchronized bursting occurred more gradually, with no large jumps in period. Typical behavior is shown in Fig. 5.

View larger version (44K): [in this window] [in a new window]   Fig. 5. Changes in burst phase produced by varying syn in test circuit 1. A, 1-5: sample recordings of LP and a PD, and the current injected into them (iLP and iPD, respectively); before (A1, free-running) and after inserting dynamic clamp connections at different syn (A, 2-5). - - -, Vthresh = 40 mV (voltage traces), 0-nA level (as in A1; current traces). Calibrations: 12 mV; 1.7 nA (iLP); 1 nA (iPD); 500 ms. B: time series of phase values: , free-running; , syn = 5 ms; , syn = 700 ms. C: phase (mean ± SD) vs. syn. D: cycle period (mean ± SD) vs. syn. Conventions for C and D are as in Fig. 2. Parameters: Vthresh = 40 mV; Vslope = 10 mV; gsyn = 40 nS (LP-to-PD) and 80 nS (PD-to-LP).

In the free-running condition with chemical synaptic interactions blocked, the pacemaker group containing the PDs generated a robust, periodic pattern of bursts primarily because of the presence of the AB neuron (Bal et al. 1988; Szücs et al. 2001). The phase of the pacemaker bursts, relative to those of LP, drifted continuously (Fig. 5, A1 and B, filled squares).

Fast reciprocal inhibition (_syn = 5 ms) enforced an out-of-phase pattern (Fig. 5, A2 and B, open squares). As the time constant was increased, the alternating pattern was initially maintained (Fig. 5A3); however, with further increase of _syn, the bursts began to overlap (Fig. 5A4). Full overlapping ("synchronization") of bursts was achieved at _syn = 700 ms in this example (Fig. 5, A5 and B, triangles). At intermediate values of _syn, we observed that bursts could synchronize for a few cycles but then adopt a larger phase-lag with only partial overlapping (see Fig. 5A4). The extent of overlap increased with _syn. This graded phase-shift dominated the plot of mean phase values (Fig. 5C). Once consistent synchronization had been achieved, further increases of _syn produced no substantial phase shift (data not shown). The time course and phase of burst-evoked IPSCs (i_LP and i_PD) varied in a way similar to that of test circuit 2 (cf. Figs. 2 and 4).

The variation in cycle period duration is shown in Fig. 5D. Initially, inserting fast inhibition (_syn = 5 ms) produced a rhythm with a cycle period longer than that of the free-running bursters. In this and most other examples, the synchronized rhythms had cycle periods shorter than those of the alternating patterns (compare Fig. 5A, 2 and 5). However, during gradual phase-shifting it was difficult to discern a trend in cycle period (Fig. 5D). Similar quantitative behavior was seen in two other analyzed preparations.

Burst synchronization could also occur when the burst duration and cycle period of the free-running neurons clearly differed as illustrated in Fig. 6. In this example, the bursting of the PDs, as part of the pacemaker group, was periodic and regular (as expected), while the LP generated bursts of greater and irregular duration, with an average cycle period ~25% longer than that of PD (Fig. 6A). Nevertheless the neurons synchronized when coupled by slow inhibition (Fig. 6B). When free-running tempos differed further, slow inhibition could induce 1:2 phase-locking, the faster neuron generating one burst in synchrony and one in alternation with the bursts of the slower cell (data not shown).

View larger version (42K): [in this window] [in a new window]   Fig. 6. Synchronizing regular and irregular bursters (PD and LP, respectively), in test circuit 1. A: free-running neurons. B: reciprocal inhibitory synapses, syn = 600 ms. Most negative membrane potentials (mV): LP, 52 and 54, A and B, respectively; PD, 54 and 56, A and B, respectively. Parameters: Vthresh = 40 mV, Vslope = 15 mV, gsyn = 60 nS (LP-to-PD) and 40 nS (PD-to-LP).

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Using the dynamic clamp technique, we examined the effects of selectively changing the kinetics of reciprocal inhibition between biological neurons with cellular bursting properties. Lengthening the time constant of synaptic activation and deactivation caused a transition from out-of-phase to synchronized in-phase burst patterns. This is, to our knowledge, the first experimental demonstration of such an effect among biological bursters. In our approach, pyloric neurons of the lobster STG were isolated from their normal synaptic interactions and then re-connected in artificial "test circuits." Rather than focusing on particular aspects of the natural synapses (cf. Manor et al. 1997; Nadim et al. 1999), we chose to study a general problem of synaptic coordination in bursting circuits. Nevertheless, the findings do raise some issues for the function of biological CPGs (see following text).

Mechanisms of bursting and synchronization

Before considering mechanistic aspects of synchronization, we should first recall the general picture of bursting in pyloric neurons as it has emerged from experimental and modeling studies (Gola and Selverston 1981; Harris-Warrick and Flamm 1987; Hartline and Graubard 1992; Hermann and Wadepuhl 1987; Turrigiano et al. 1995).

CELLULAR BURSTING. Repetitive burst activity of synaptically isolated neurons is conditional on modulatory input. The fast spikes are produced by conventional voltage-dependent sodium and potassium currents located in the axon(s). Slow burst-generating voltage oscillations arise from currents located in neurites within the STG neuropil, where synaptic interactions also occur. The depolarized phase, which drives repetitive spiking, is a plateau (or "driver") potential produced by an unstable equilibrium of inward (sodium and calcium) and outward (potassium) currents (Hartline and Graubard 1992; Russell and Hartline 1982). The plateau may terminate spontaneously (e.g., due to the growth, during the burst, of calcium-dependent potassium currents) or in response to inhibitory input. Burst termination is a voltage-dependent repolarizing process and is followed by a hyperpolarized (interburst) phase. This is initially dominated by the increased potassium conductance. Deactivation of these currents, together with the action of persistent inward currents, causes a gradual, "pacemaker" depolarization, which eventually reaches a threshold for the voltage-dependent initiation of another plateau. In general terms, this mechanism of bursting is qualitatively similar to that seen in many neurons of both vertebrates and invertebrates (cf. "square-wave" bursting in Rinzel and Ermentrout 1989; Wang and Rinzel 1995). [The TEA that was used to block cholinergic inhibition (cf. Marder and Eisen 1984) also blocks some of the voltage- and calcium-dependent potassium currents involved in spike and burst generation. This increases the amplitude, shortens the duration, and regularizes the pattern of the slow voltage oscillation underlying the bursts (cf. Gola and Selverston 1981, Hartline and Graubard 1992, Hermann and Wadepuhl 1987; Elson, unpublished observations). Nevertheless the general mode of bursting is probably not qualitatively changed].

SYNAPTIC COORDINATION. Not surprisingly, fast reciprocal inhibition enforced alternating burst patterns, which seemed to operate mainly by a "release" mechanism (Wang and Rinzel 1992). Slow inhibition produced a synchronized (in-phase) pattern of bursting whose tempo matched the time course of IPSC growth and decay. Synchronized overlapping bursting was achieved when the synaptic time constant approached the duration of burst (or interburst) periods in the uncoupled neurons. When the synaptic currents change slowly, it becomes difficult to say whether the bursting occurs in "release" or "escape" mode or some combination of both (cf. Sharp et al. 1996).

Additional aspects of mechanisms

Spike and burst synchronization also differ in some respects. Whereas fast spikes may be considerably shorter than the IPSPs they evoke, bursts elicit a summed IPSP that grows as the burst continues. Synchronized neurons inhibit each other throughout their burst phase. It is not surprising, therefore that we could observe shortening of burst and/or cycle period durations on synchronization. This occurred in the neuron(s) with the (intrinsically) longer bursts or period.

Coincident growth of slow IPSCs may encourage the interacting neurons to end their bursts at similar times. Burst termination resets the membrane potential of the postsynaptic neuron to a hyperpolarized state, beginning the interburst recovery phase. These effects are probably redundant when the uncoupled neurons generate bursts of similar and stereotyped duration: in this case, the bursts resemble slow "spikes," and inhibitory synchronization is relatively straightforward (Terman et al. 1998; Wang and Rinzel 1992, 1993). If, however, the uncoupled neurons burst with differing or fluctuating durations, inhibitory control of burst termination and interburst recovery is likely to be critical for stable synchronization. Neural simulations have examined the influence of heterogeneity and noise on spiking synchrony (Wang and Buzsáki 1996; White et al. 1998); similar effects deserve examination in models of burst synchronization as well.

Finally, note that we used a combination of graded, as well as spike-mediated, transmission, so as to simulate natural STG synapses (Graubard et al. 1983; Hartline and Graubard 1992). However, this detail need not limit the generality of the results. Temporal summation of spike-mediated components smoothes the postsynaptic response to a presynaptic burst, blurring distinctions between graded and spike-evoked IPSCs at all but the shortest time constants (cf. Fig. 1B). The same smoothing can account for the lack of synchronization of spikes within the bursts of pre- and postsynaptic neurons.

Phase shifting in synaptic circuits

We observed phase and cycle period transitions similar to those of some simple, biophysical and dynamical models (Terman et al. 1998; Wang and Rinzel 1992, 1993). Spontaneous "flipping" between alternating and synchronized patterns (e.g., Fig. 2A3) may result from noise carrying the system between two coexisting attractors (cf. Wang and Rinzel 1992); such intermittent activity is typical of the behavior of a dynamical system near a bifurcation boundary.

Test circuit 1 differed from circuit 2 in showing a gradual, rather than sudden, phase transition as the time constant was changed. The presence of the coupled AB neuron, whose cellular burst patterns are periodic and robust (cf. Szücs et al. 2001), may account for this difference. Thus while some burst cycles of test circuit 1 could jump to the synchronized state as the time constant was lengthened, the averaged response was a graded phase-shift resembling well-known resetting behavior (cf. Ayers and Selverston 1979) (similar actions can account for influences on cycle period duration).

Synchronization of bursting in motor circuits and other networks

Mutual inhibition between bursting neurons is an almost ubiquitous motif in CPGsthose circuits that control rhythmical movements (Arshavsky et al. 1993; Friesen 1994; Getting 1989; Marder and Calabrese 1996; Perkel and Mulloney 1974). Our results indicate that bursts (or slow spikes or graded potentials) of oscillating neurons can become locked in-phase if postsynaptic inhibition is sufficiently slow. Chemical synapses in CPGs do exhibit time constants ranging from tens to hundreds of milliseconds (Eisen and Marder 1982, 1984; Elson and Selverston 1995; Getting 1981) [in some cases, differences in time course are known to result from the expression of metabotropic or ionotropic responses to the same neurotransmitter (cf. Clemens and Katz 2001)]. However, in all CPGs studied, the inhibitory synapses important for phase coordination show kinetics faster than the burst tempo, so that alternating rhythms result (Friesen 1994; Marder and Calabrese 1996; Skinner et al. 1994). Where mutually inhibitory neurons produce bursts that overlap, one finds that the inhibition is fast and controls the timing of individual spikes, while the bursts are synchronized by common excitation or parallel, electrical coupling (Evans et al. 1999; Mulloney and Selverston 1974; Nagy et al. 1988).

Where inhibitory synchronization may be important is in interneuronal networks of vertebrate brain (particularly in cortex and hippocampus) (Gray 1994; Jefferys et al. 1996; Steriade et al. 1993). Theoretical and empirical studies suggest that gamma frequency (20-80 Hz) spiking of interneuronal networks can be synchronized via GABA_A-ergic inhibition (_syn ~ 10 ms) (Traub et al. 1996; Wang and Buzsáki 1996; Whittington et al. 1995). Synchronized bursting occurs in thalamic and cortical neurons during sleep and in some pathological states such as epilepsy (Steriade et al. 1993; von Krosigk et al. 1993). These circuits incorporate both fast, GABA_A-ergic and slower GABA_B-ergic inhibition (_syn ~ 100-200 ms) (Destexhe et al. 1994a, 1996). When the GABA_A responses are blocked, thalamocortical and reticulothalamic neurons generate an intense low-frequency (3-4 Hz) rhythm of bursts with enhanced local synchrony (resembling one type of epileptic state: von Krosigk et al. 1993). In modeling studies, a dynamic interaction between neuronal burst properties and slow, GABA_B-ergic inhibition contributes to both cycle period and synchronization (Destexhe et al. 1994a, 1996; Golomb et al. 1994) (other, excitatory synapses are probably important as well). The ratio of cycle period to time constant in the thalamic models approximates the values at which synchronization occurred among the pyloric neurons in this study. Nevertheless, slow inhibition is not the only synaptic mechanism for synchronizing bursting in brain networks: others include electrical coupling (e.g., Skinner at al. 1999; Zhang et al. 1998) and mutual excitation (e.g., Butera et al. 1999). We have explored the dynamics of synchronization occurring via both of these mechanisms in pairs of biological and model neurons (Abarbanel et al. 1996; Elson et al. 1998; Pinto et al. 2000; Varona et al. 2001).

Maintenance and stability of phase-relationships

We found phase shifts and instability as the ratio of inhibitory time constant to cycle period changed. In a given biological CPG (or other oscillatory circuit), one expects postsynaptic kinetics to remain relatively constant (being determined by the type of neurotransmitter receptor, ion channel, coupling mechanism, etc.), whereas the circuit's cycle period may vary significantly. This still implies changes in the ratio of cycle period to synaptic time constant. However, real CPGs maintain stable phase relationships over a wide frequency range (e.g., Hooper 1997). The apparent paradox can be resolved if one recalls that synaptic dynamics can be modified. In fact, synaptic time course is influenced by both pre- and postsynaptic processes. At a given connection, the time constant governing the activation of postsynaptic ion channels may remain constant, while frequency-dependent changes occur in presynaptic processes such as calcium currents and transmitter release. These changes will alter the effective time constant governing the synapse as a whole and may introduce additional dynamics (e.g., depression or facilitation). Such short-term plasticity may help maintain phase constancy (Hooper 1997; Manor et al. 1997; Nadim and Manor 2000).