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The Journal of Neuroscience, December 15, 2002, 22(24):10580-10592
Bursting in Leech Heart Interneurons: Cell-Autonomous and Network-Based Mechanisms
Gennady S. Cymbalyuk, Quentin Gaudry, Mark A. Masino, and Ronald L. Calabrese Biology Department, Emory University, Atlanta, Georgia 30322
ABSTRACT
TOP
ABSTRACT
INTRODUCTION
Rhythmic activity within the heartbeat pattern generator of the medicinal leech is based on the alternating bursting of mutually inhibitory pairs of oscillator heart interneurons (half-center oscillators). Bicuculline methiodide has been shown to block mutual inhibition between these interneurons and to cause them to spike tonically while recorded intracellularly (Schmidt and Calabrese, 1992
). Using extracellular recording techniques, we show here that oscillator and premotor heart interneurons continue to burst when pharmacologically isolated with bicuculline, although the bursting is not robust in some preparations. We propose that a nonspecific leak current introduced by the intracellular microelectrode suppresses endogenous bursting activity to account for the discrepancy with results using intracellular recording. A two-parameter bifurcation diagram (Eleak vs gleak) of a mathematical model of a single heart interneuron shows a narrow stripe of parameter values where bursting occurs, separating large zones of tonic spiking and silence. A similar analysis performed for a half-center oscillator model outlined a much larger area of bursting. Bursting in the half-center oscillator model is also less sensitive to variation in the maximal conductances of voltage-gated currents than in the single-neuron model. Thus, in addition to ensuring appropriate bursting characteristics such as period, phase, and duty cycles, the half-center configuration enhances oscillation robustness, making them less susceptible to random or imposed changes in membrane parameters. Endogenous bursting, in turn, ensures appropriate bursting if the strength of mutual inhibition is weakened and limits the minimum period of the half-center oscillator to a period near that of the single neuron.
Key words: half-center oscillator; Hirudo medicinalis; bicuculline methiodide; dynamical system; bifurcation analysis; leak current
INTRODUCTION
Oscillatory patterns of neuronal activity underlie the control of motor functions, information processing, memory formation, and sleep (Cohen et al., 1988
We have analyzed the CPG that generates a heartbeat in the leech (Calabrese et al., 1995
Parts of this paper have been published previously in abstract form (Cymbalyuk and Calabrese, 2000
MATERIALS AND METHODS
Leeches (Hirudo medicinalis) were obtained from Leeches USA and maintained in artificial pond water at 15°C. After the animals were anesthetized in ice-cold saline, individual ganglia were dissected and pinned ventral side-up in Petri dishes lined with SYLGARD (Dow Corning, Midland, MI; bath volume, 0.5 ml). The methods for preparing and maintaining leech ganglia and for identifying heart interneurons for electrophysiological recording have been described previously (Olsen and Calabrese, 1996
For intracellular recording, neurons were penetrated with borosilicate microelectrodes (1 mm outer diameter, 0.75 mm inner diameter) filled with 4 M potassium acetate with 20 mM KCl (20-35 M
). Currents were injected using a switching single-electrode current clamp (Axoclamp 2A; Axon Instruments, Foster City, CA). Sample rates ranged between 2.5 and 3 kHz. The electrode potential was monitored on an oscilloscope to ensure that it had settled between current injection cycles. At the end of the experiment, microelectrodes were withdrawn from the cell, and only those preparations in which the electrode was within ±5 mV of the bath potential were accepted for further analysis. Extracellular recordings were obtained as described by Masino and Calabrese (2002)
Integration and bifurcation analysis of the systems of stiff ordinary differential equations describing a single oscillatory heart interneuron and a half-center oscillator (Hill et al., 2001
8 and 10
where
(1) 1 = 0.002 sec; and
SynS to 150 × 10
RESULTS
In the heartbeat pattern generator of the medicinal leech (Fig. 1A), two segmentally repeated pairs of reciprocally inhibitory heart interneurons located in ganglia 3 and 4 form half-center oscillators that pace the rhythm. These oscillator interneurons are coupled by coordinating interneurons whose somata are located in ganglia 1 and 2 to form an eight-cell beat-timing network. Other premotor interneurons located in ganglia 6 and 7, along with the oscillator interneurons, inhibit heart motor neurons, sculpting their activity into rhythmic bursts. Switch interneurons located in ganglion 5 interface between oscillator interneurons and premotor interneurons to produce two alternating motor neuron coordination states: peristaltic and synchronous. Bicuculline methiodide (10
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Figure 1. A, Connectivity diagram of the heartbeat neuronal network. Large open circles represent neurons. The neurons playing similar functional roles in the heartbeat network and with similar input and output connections are lumped together. Numbers identify ganglia where somata are located. Small filled ellipses represent inhibitory chemical synapses. Two pairs of reciprocally inhibitory heart interneurons located in ganglia 3 and 4 form half-center oscillators. These oscillators are coupled by coordinating interneurons whose somata are located in ganglia 1 and 2. Other premotor interneurons located in ganglia 6 and 7, along with the oscillator interneurons, inhibit heart motor neurons. Switch interneurons located in ganglion 5 interface between oscillator interneurons and premotor interneurons to produce two alternating coordination states, peristaltic and synchronous, of the motor neurons. B-D, Pharmacologically isolated oscillator heart interneurons fire tonically when recorded with sharp microelectrodes but burst rhythmically when recorded extracellularly. The left oscillator interneuron from a mutually inhibitory pair is recorded intracellularly, and the right one is recorded extracellularly. B, Under control conditions, the two neurons produce rhythmic alternating bursts. C, Addition of bicuculline results in tonic spiking in the intracellularly recorded cell and continued bursting in the other. D, The effects of bicuculline were reversible with washout. In this and all subsequent figures, voltage traces recorded from heart interneurons are labeled HN and indexed by body side (R, L) and ganglion number.
In contrast to intracellular recordings, extracellular recordings from pharmacologically isolated oscillator heart interneurons reveal endogenous bursting
Previous results, using sharp microelectrode recordings, have shown that when mutually inhibitory oscillator heart interneurons are pharmacologically isolated with bicuculline, they spike tonically (Schmidt and Calabrese, 1992
When pharmacologically isolated, oscillator heart interneurons burst independently
Simultaneous extracellular recordings from both interneurons forming a half-center oscillator in either ganglion 3 or 4 show that these neurons can burst independently when isolated (n = 5 for each of ganglia 3 and 4) (Fig. 2). In normal saline, simultaneous extracellular recordings from the two oscillator interneurons show alternating bursting. With the addition of bicuculline methiodide (1 mM), the oscillator interneurons showed bursting that was regular in most preparations (7 of 10). The burst periods of the two isolated oscillator heart interneurons could be slightly different (Fig. 2B), leading to the bursting activity in the two neurons drifting against each other, which indicates that the inhibition between the two neurons is indeed blocked and that the bursting is independent. If bicuculline exposure is limited to <10 min, rhythmic alternating bursting resumes after washout with normal saline (Fig. 2C). In some preparations (3 of 10), we observed less robust activity in which bursting was interspersed with bouts of tonic spiking (Fig. 3). In these preparations, we observed that when one neuron is spiking tonically, its partner may show bursting activity.
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Figure 2. Oscillator heart interneurons recorded extracellularly burst independently when pharmacologically isolated with bicuculline. A1, Oscillator interneurons burst rhythmically in alternation in normal saline. A2, Instantaneous phase between the activity of the neurons plotted against burst number stays close to 0.5. B1, The oscillator interneurons burst independently in bicuculline methiodide (1 mM). B2, The instantaneous phase drifts gradually from 0 to 1, demonstrating independent bursting with different cycle periods. C1, The oscillator interneurons burst in alternation after washout with normal saline. C2, The instantaneous phase stays near 0.5, although with larger deviations. The instantaneous phase was defined as the delay of the HN(R,3) burst median spike relative to the HN(L,3) burst median spike divided by the current HN(L,3) cycle period.
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Figure 3. In some preparations, pharmacologically isolated oscillator interneurons show bursting interspersed with bouts of tonic spiking. A, Normal pattern of alternating bursting in saline. B, In a solution containing bicuculline methiodide (1 mM), bursting is sporadic. Trains of bursts are interrupted by long intervals of tonic spiking. One heart interneuron can be bursting while the other is spiking tonically. C, The normal alternating bursting pattern was restored after washout with normal saline (exposure to bicuculline <10 min).
In bicuculline, bursting activity of premotor heart interneurons in ganglia 6 and 7 is similar to activity of oscillator heart interneurons
The premotor heart interneurons in ganglia 6 and 7 receive all their inhibitory input from the switch heart interneurons of ganglion 5 (Fig. 1A). Unlike the oscillator interneurons, they do not form mutually inhibitory synapses. When recorded extracellularly (n = 5 for each of ganglia 6 and 7, both heart interneurons recorded in each ganglion) in isolated ganglia, these heart interneurons show rhythmic bursting activity, which can be either independent or in apparent synchrony (data not shown). This bursting can be interrupted by bouts of tonic spiking. When recorded extracellularly and pharmacologically isolated with bicuculline (1 mM), they continue rhythmic bursting, but in most preparations (9 of 10 preparations), the cells start showing long passages of tonic spiking similar to those presented in Figure 3 for the oscillator heart interneurons.
Seizure-like synchronous bursting
In some preparations (3 of 10 preparations), "seizure-like" synchronous bursting occurred sporadically in pairs of oscillator interneurons recorded extracellularly in bicuculline (1 mM) (Fig. 4A). Simultaneous intracellular recordings from other neurons, e.g., Retzius (Fig. 4A) or Leydig (data not shown) neurons, suggest that all cells in a ganglion discharge synchronously during this seizure-like activity. In heart interneurons, these seizures take the form of an extension of ongoing bursts coincident with the seizure discharge so that two or three bursts occur without intervening silent periods. After a "seizure," both heart interneurons sped up their bursting and then monotonically recovered to a baseline period (Fig. 4B). Thus these seizures interrupted regular bursting activity in the oscillator interneurons. Similar seizure-like bursts were observed in heart interneurons from ganglia 6 and 7 (1 of 10 preparations). The seizure-like bursts were qualitatively different from the bouts of tonic spiking observed in heart interneurons in bicuculline in that the seizure bursts were synchronous, perhaps involving the whole ganglion, and were always followed by a transient decrease in the burst period, whereas bouts of tonic spiking were often independent and were not followed by a change in the burst period. The seizure-like bursts occur with very long intervals (hundreds of seconds), and although they reset and modify heart interneuron bursting activity, they do not appear to account for it directly. These seizures may depend on general electrical coupling, whose effects could be potentially enhanced by blockade of inhibitory synapses. Similar synchronized bursts have been observed in all neurons when the nerve cord is exposed to inorganic Ca2+ channels blockers such as Co2+ and Mn2+ (Angstadt and Friesen, 1991
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Figure 4. Seizure-like synchronous bursting observed in oscillator interneurons and other neurons in bicuculline (1 mM). A, Electrical activity of a Retzius cell (top trace) and left and right oscillator interneurons from ganglion 4 (bottom 2 traces) showing a synchronous burst two to three times longer than the asynchronous bursts in the oscillator interneurons. The Retzius cell was recorded with a sharp microelectrode. In bicuculline, the Retzius cell was silent most of time. A strong depolarization underlies the seizure-like burst. B, Graph of the cycle period plotted against time for the heart interneurons HN(L,4) and HN(R,4) (open circles, asterisks, respectively) shows that the burst period shortens right after the synchronous burst occurred and returns to baseline after ~25 sec. The cycle period was defined as the interval between the median spikes of two consecutive bursts.
Activity of coordinating heart interneurons from ganglia 1 and 2 in bicuculline
Because axons of coordinating interneurons from ganglia 1 and 2 initiate spikes and make mutual inhibitory synaptic connections with ipsilateral oscillator interneurons in ganglia 3 and 4 (Fig. 1A), it is conceivable that despite blockade of the synapses between oscillator interneurons by bicuculline, the synapses between oscillator and coordinating interneurons persist in bicuculline, leading to the observed bursting activity. To eliminate this possibility, we performed experiments in which ipsilateral heart interneurons from ganglia 1, 2, or both and 3 or 4 were simultaneously recorded, and bicuculline was applied in preparations consisting of the head brain through ganglion 4. Coordinating interneurons recorded extracellularly in normal saline generate bursting activity, alternating with ipsilateral oscillator interneuron activity and having a duty cycle and spike frequency smaller than those of the oscillator interneurons (Masino and Calabrese, 2002
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Figure 5. Paired extracellular recordings of a coordinating interneuron (ganglion 2) and an ipsilateral oscillator interneuron (ganglion 3). A, In normal saline (Control), the coordinating interneuron and the oscillator interneuron produced alternating bursts. B, In bicuculline (1 mM, after 8 min of exposure), both interneurons burst independently. C, On washout with normal saline, normal alternating bursting returned.
Characterization of bursting activity in heart interneurons in bicuculline
We quantified bursting activity in oscillator interneurons and in premotor interneurons from ganglia 6 and 7 by measuring burst period, duty cycle, average spike frequency within a burst (spike frequency), and number of spikes per bursts. For this analysis, data were taken only during episodes of regular bursting. In preparations showing bouts of tonic spiking, we did not use stretches of the record containing such bouts, and in preparations showing seizures, after each seizure we waited an interval sufficient for recovery to the baseline period (normally ~10 bursts). Only burst trains containing at least 20 bursts and having a coefficient of variation of period <20% were considered. We analyzed the bursting characteristics of the heart interneurons in all preparations (n = 5 for each ganglion) and eliminated those that did not meet these criteria. One preparation of ganglion 3, one of ganglion 6, and two of ganglion 7 had no trains of bursts with a sufficiently small coefficient of variation of the period. One preparation of ganglion 4 did not produce sufficiently long burst trains.
The oscillator interneurons (ganglia 3 and 4) form half-center oscillators with their contralateral homologues, but the premotor interneurons (ganglia 6 and 7) do not (Fig. 1A). On the basis of their similarity in connectivity and apparent similarity in intrinsic properties, data obtained from oscillator interneurons and from premotor interneurons were pooled to obtain sufficient sample numbers for statistical comparison of these two groups. These data are summarized in Table 1. Two-way ANOVA was performed on the two neuron groups (oscillator interneurons and premotor interneurons) under the three treatment conditions (control, bicuculline, and washout). Then post hoc pair-wise multiple comparisons were made with a t test using Bonferroni
-level compensation to determine differences. Significant differences, which were found, are described below.
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Table 1. Characteristics of bursting activity recorded extracellularly from heart interneurons in ganglia 3, 4, 6, and 7 Under control conditions, the two neuron groups differed in period, duty cycle, and spike number per burst (p < 0.05 in each case), possibly reflecting their different connectivity. Bicuculline application produced significant changes in period, duty cycle, spike frequency, and spike number per burst in oscillator heart interneurons (p < 0.05 in each case). In bicuculline, period, spike frequency, and spike number per burst were smaller by ~25, 30, and 35%, respectively, whereas duty cycle was longer by ~25% (p < 0.05). In contrast, bicuculline did not produce changes in period, spike frequency, and spike number per burst (p > 0.05 in each case) in premotor interneurons, although duty cycle did lengthen by ~6% (p < 0.05). In bicuculline, the spike frequency and duty cycle of oscillator interneurons are different from those of premotor interneurons (p < 0.05 in each case). In general, most effects of bicuculline were only partially reversible on washout. The alternation between the bursting activities of the two oscillator heart interneurons was always restored (exposure limited to 10-15 min).
Bursting activity in an oscillator heart interneuron model is sensitive to leak current variation
The results shown in Figure 2 suggest that oscillator interneurons are sensitive to a leak current introduced by sharp microelectrode penetration. We tested this hypothesis with a single-compartment model of an oscillator interneuron. Ionic currents of the oscillator interneurons were determined in voltage-clamp studies, and the kinetic data were incorporated into a thoroughly tested conductance-based model (Nadim et al., 1995
The leak current produced by microelectrode penetration is assumed to be nonselective. Thus penetration modifies original values of E
and g to the measured values Eleak and gleak by the addition of a nonspecific leak current component described by E and g :
Thus variation of the parameters, Eleak and gleak in the model can simulate the additional component of leak current introduced by the intracellular microelectrode. Here we study how changes in the leak current parameters, Eleak, and gleak, affect activity of a single oscillator interneuron.
(2) To study the effects of this microelectrode-induced change in leak current parameters on model activity, we constructed a two-parameter bifurcation diagram (Eleak vs gleak) of model activities (Fig. 6A). Curves indicating the borders between major dynamic regimes of the model, tonic spiking (pink area), bursting (white area), and silence (yellow area, steady state) are plotted. Figure 6A shows a narrow stripe of parameter values in which bursting occurs (white area) that separates large zones of tonic spiking activity and silence. Plotted points (Fig. 6A) correspond to the different examples of the activity of the model illustrated in Figure 7A-E. The model oscillator interneuron spikes tonically for parameters covering a relatively large area with relatively depolarized values of Eleak and small values of gleak (Figs. 6A, plus sign, 7A). The transition from tonic spiking to bursting starts at the border marked by the red curve, where a period-doubling bifurcation occurs (Ermentrout, 1984
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Figure 6. Bifurcation diagram of the single-cell oscillator interneuron model activities (A) and bifurcation diagram of the bursting activity in a half-center oscillator model (B). A, Pink, white, and yellow areas mark the parameter regimes in which tonic spiking, bursting, and silence are stable, respectively. Green areas mark parameter regimes of multistability in which more than one activity is stable. Multistability(A) points to the area where bursting coexists with silence; multistability(B) points to the area where bursting coexists with tonic spiking; multistability(C) points to the area where tonic spiking coexists with silence. The asterisk corresponds to the gleak and Eleak parameter values (g = 0) used in the models illustrated in Figure 9. Plus sign, open circle, filled circle, asterisk, and open diamond correspond to the gleak and Eleak parameter values for oscillator interneuron model activity illustrated in Figure 7 and fall along a line generated when the introduced g changes from 0.35 to 1 nS about model parameters of E
and g (asterisk) as used in Figure 9, A and B. Open triangles mark the parameter values corresponding to Figure 7E1-E3. B, The blue area corresponds to the parameter region where stationary bursting activity was observed, and the white area corresponds to the region where stationary bursting was not observed. The borders separating the major activity regimes of the single-cell model taken from A are plotted for comparison. The pink patch delimits the single-cell model parameter values that produced bursting characteristics within the ranges measured experimentally. The green line was generated by varying g from 0 to 1 nS about model parameters of E and g (asterisk). The marked points in A (except for open triangles) fall along this line. The pink line was generated similarly by varying g from 0 to 1 nS starting with E and g at the lowest point of the experimentally constrained patch. A family of such lines originating in the pink patch defines by their end points the upper delimited area.
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Figure 7. Characteristic activities of the single-oscillator interneuron model. A, Tonic spiking (Fig. 6A, plus sign). B, Two-spike bursting (Fig. 6A, open circle). C, Multispike bursting near the border of bursting and tonic spiking (Fig. 6A, filled circle). D, Multispike bursting near the border of bursting and silence (Fig. 6A, open diamond). E, Three coexisting oscillatory activities of the single oscillator interneuron model at a point (gleak = 12.703 nS; Eleak =
The area of bursting activity also includes areas of multistability, where different oscillatory regimes and a stable stationary point can coexist with each other. Multistability zones marked in Figure 6A (A-C) are areas where the major activities coexist. In area A, bursting activity coexists with silence; in area B, bursting activity coexists with tonic spiking activity; and in area C, tonic spiking activity coexists with silence. A complex example of multistability can be found at the point [gleak = 12.703 nS; Eleak =
The sensitivity of model endogenous bursting to leak current variation can be reduced
In the single-cell model, there are several parameter variations that can considerably expand the region of Eleak and gleak supporting bursting, thus reducing its sensitivity to leak current parameters. Varying maximal conductances of different currents can shift and expand or shrink the region of bursting. Increasing the maximal conductance of inward currents shifts the region of bursting toward larger gleak and more hyperpolarized Eleak. For example, for Eleak =
h by a factor of 2 ( h = 8 nS vs canonical value h = 4 nS) enables the model to support bursting activity for gleak from 9.5 to 11.8 nS, thus enlarging the range appropriate for bursting activity approximately by a factor of 2. Increasing the maximal conductance of outward currents shifts the region toward smaller gleak and more depolarized Eleak. As an example of influence of an outward current, we increased the maximal conductance of a FMRFamide-activated potassium IKF described by Nadim and Calabrese (1997) KF = 0. The model with KF = 20 nS demonstrates bursting for gleak from 7 to 9.42 nS, whereas with KF = 40 nS, it can burst with gleak from 4.5 to 8.17 nS, thus expanding the bursting range by factors of 2 and 3, respectively. This study indicates that the modulatory action of FMRFamide not only speeds the rhythm, for example, but reduces the sensitivity of endogenous bursting activity to the leak current parameter variation. This hypothesis gains additional plausibility in light of experimental data demonstrating that applied FMRFamide decreases the size of spike-mediated IPSCs between oscillator interneurons (Simon et al., 1994 The most dramatic expansion of the region of bursting is observed when the half-activation potential of ICaS is shifted in the negative direction. A shift from V1/2mCaS =
Comparison of bursting characteristics in model and experiment
To compare the model and experimental results, the same burst characteristics were measured for model activity as in our experiments. The model shows a variety of bursting activities depending on the values of gleak and Eleak. Burst period, duty cycle, and spike frequency within a burst versus (gleak, Eleak) are shown in Figure 8A-C, respectively. The burst period (Fig. 8A) and number of spikes per burst (data not shown) grow monotonically as Eleak is hyperpolarized or gleak is decreased; the duty cycle (Fig. 8B) and spike frequency (Fig. 8C) show a more complicated dependence. The minimum and maximum values of corresponding characteristics measured for oscillator heart interneurons recorded extracellularly in bicuculline are marked by pairs of green lines on the axes, except for spike frequency, for which only the lower boundary is marked (Table 1; boundaries were slightly expanded by rounding down the lower boundary and rounding up the upper boundary to the nearest integer). Projection of the surfaces of characteristic values on the plane (gleak, Eleak) describes the stripe of parameters corresponding to the white area on the bifurcation diagram (Fig. 6A) where bursting occurs. It includes the green area that defines the model values conforming to the experimentally measured boundaries (Fig. 8). Comparison of the plots (Fig. 8) shows that the sets of parameter values (gleak, Eleak) conforming to each of the experimentally determined bursting characteristic are not identical. Nevertheless, there exists a subset of parameters (gleak, Eleak) conforming to all the constraints (experimentally constrained patch shown in Fig. 6B, pink). Although the model can demonstrate bursting inside the experimentally imposed regimes, it will require additional parameter changes to match average values of the experimentally derived burst characteristics.
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Figure 8. Major bursting characteristics for the single-oscillator interneuron model: the burst period (A), duty cycle (B), and spike frequency (C) observed in the model when the values of (gleak, Eleak) are varied. The minimal and maximal values experimentally measured for oscillator interneurons are marked by the pairs of green lines on the axes, except for the spike frequency (C), for which the maximum value (upper boundary) was never exceeded by the model; thus only the lower boundary was marked. Projection of the surfaces of characteristics values on the plane (gleak, Eleak) describes the area where bursting occurs. It includes the green area that defines the model values conforming to the experimentally measured boundaries.
According to Equations 2, microelectrode penetration projects the experimentally constrained patch on the bifurcation diagram (Fig. 6B) toward a more depolarized leak reversal potential (Eleak) and larger leak conductance (gleak), making the model heart interneuron tonically spiking instead of bursting. Projecting a 1 nS addition of g
generates an upper patch, which corresponds to experimentally constrained model neurons penetrated with a sharp microelectrode that adds 1 nS of leak conductance. Bursting in a half-center oscillator
A mathematical model of two mutually inhibitory oscillator interneurons (a half-center oscillator) has been developed (Nadim et al., 1995
The point marked by an asterisk was chosen for analysis from the experimentally constrained pink patch so that the difference in the burst duration of the single-cell model and the half-center model would be similar to that observed experimentally for oscillator interneurons (Table 1). The periods of the two models are comparable, but that of the half-center model is slightly longer (by 0.7 sec). Such a period difference was also observed experimentally for oscillator heart interneurons, although the corresponding average period difference is larger (by 2.3 sec). This parameter point is also illustrated in Figure 6A, asterisk, and falls along the projection line defined by the parameter variations of Figure 7A-D. With these gleak and Eleak parameters, the half-center oscillator model behaves qualitatively very similar to the corresponding model tuned to the intracellularly recorded gleak and Eleak parameters (Hill et al., 2001
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Figure 9. Voltage and current traces produced by the single-cell (A) and half-center oscillator (B) models. Parameters Eleak =
Comparison of bursting in the single-cell and half-center configurations
Bursting in the single-cell model appears to be dominated by two time constants. The slow inactivation of the low-threshold Ca2+ current, ICaS, leads to burst termination, thus controlling the duration of the burst phase of the oscillation (Fig. 9A). The slow activation of the hyperpolarization-activated inward current, Ih, leads to burst formation, thus controlling the duration of the hyperpolarized phase of the oscillation. Note that Ih is maximal just at the transition to the burst phase (Fig. 9A). Our previous analysis of the half-center model (Hill et al., 2001
The half-center oscillator model is considerably less sensitive to the variation of the maximal conductances of the voltage-gated currents as it is with leak current parameters. One maximal conductance was varied at a time, whereas all others were set to their canonical values. Table 2 shows the range of maximal conductances of each current that supports bursting activity for both models. The single-neuron model is very sensitive to the variation of gleak and
p, each of which can only be varied in a range of ~1 nS. The single-neuron model is a bit less sensitive to the variation of CaS and h; these conductances can be varied over a range of ~5 and 8 nS, respectively. Other maximal conductances can be varied on the order of tens to hundreds of nanosiemens. In a half-center model, these ranges considerably expand, ranging from factor 1.7 for CaS up to factor of 9.7 for h.
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Table 2. Ranges of the values of the maximal conductances where the bursting state was observed Leak current subtraction via dynamic clamp
To test our hypothesis concerning the crucial role of a leak current introduced by sharp microelectrode penetration, we performed a series of experiments in which the dynamic clamp (Sharp et al., 1993
= 0 and g = =
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Figure 10. Subtraction of a leak current using a dynamic clamp elicits a few bursts in intracellular recordings (sharp microelectrodes) from oscillator heart interneurons isolated pharmacologically with bicuculline (1 mM). A, Leak current subtraction (Eleak = 0 mV; gleak =
Injection of a constant hyperpolarizing current that caused shifts of the membrane potential similar to ones observed in the dynamic clamp experiments did not elicit any bursting (Fig. 10C). Although injection of a hyperpolarizing current is not equivalent to manipulation of leak current parameters, it corresponds approximately to a reduction of Eleak without changing gleak. Thus in parameter space, it is equivalent to moving the system vertically in the bifurcation diagrams of Figure 6. [Note in Fig. 6B that adding nonspecific leak conductance is equivalent to moving the system along steep curves (pink, green lines) up and to the right in the Eleak and gleak parameter plane and that application of a dynamic clamp to subtract nonspecific leak conductance moves the system along such curves down and to the left.) It should therefore be possible to adjust the hyperpolarizing current so that the neuron demonstrates the bursting mode as long as vertical movement of the system in the parameter plane can enter the bursting zone; i.e., gleak is not greater than ~14 nS. In this case, the value of the hyperpolarizing current should fall within a certain range (approximately, smaller currents support tonic spiking, whereas larger currents cause silence). For example, assuming an introduced nonspecific leak conductance of 1 nS with a starting (single-cell) model leak current parameter (*), the range of injected current that supports bursting is only ~0.02 nA wide (between -0.04 and -0.06 nA). This range lessens and ultimately vanishes as the introduced nonspecific leak conductance grows.
DISCUSSION
Here we have demonstrated that oscillator heart interneurons, which make mutually inhibitory synapses and pace the leech heartbeat CPG, burst autonomously when isolated with bicuculline. Such bursting had not been observed before (Schmidt and Calabrese, 1992
An oscillator heart interneuron model displays bursting only within a narrow range of leak current parameters (Fig. 6A); thus bursting is very sensitive to perturbations of these parameters. We estimated the introduced leak conductance in our microelectrode recordings to be in the range of 1-9 nS. In the model, a nonspecific leak conductance as small as 0.3 nS can suppress bursting. In some other neurons (e.g., in geniculate local interneurons in the rat), microelectrode-introduced leak conductance appears to suppress bursting (Pape and McCormick, 1995
Any conclusion that heart interneurons are endogenous bursters must be tempered by the observation that bicuculline methiodide may block a small-conductance calcium-activated potassium current and thus support bursting. In rat neostriatal cholinergic (Bennett et al., 2000
Endogenous bursters in a half-center oscillator
The oscillator heart interneurons appear to be endogenous bursters yoked by strong mutual inhibition into a half-center oscillator. This inhibition stabilizes oscillation within the system to variations in intrinsic membrane properties of the oscillator interneurons. In the model of the heart interneuron half-center oscillator, bursting occurs over a wider range of the maximal conductance of intrinsic membrane currents than in a single-cell model (Table 2). Bursting of the single-cell model is especially sensitive to leak current parameters and the maximal conductance of IP, whereas bursting of the half-center oscillator model is much less sensitive (Table 2; Fig. 6, compare A, B). These predictions of the models are borne out in our experiments. When a nonspecific leak current is introduced by microelectrode penetration, endogenous bursting is suppressed, but the half-center oscillator functions normally. In 30% of preparations, bursting of oscillator heart interneurons isolated in bicuculline was sporadically interrupted by bouts of tonic spiking (Fig. 3). In contrast, in the half-center oscillator configuration, these neurons did not show this intermittency. These results indicate that the half-center oscillator configuration improves the robustness of oscillations in the heartbeat CPG.
Control of burst period, duty cycle, and spike frequency
The burst period, duty cycle, and spike frequency all differ between the half-center and pharmacologically isolated configurations in our extracellular recordings (Table 1). The strong inhibition in the half-center configuration constrains the interburst interval to be approximately equal to the burst duration of the opposite cell, thus lengthening the period (by ~25%) and reducing the duty cycle to ~50%. Analysis of the half-center and single-cell models in the constrained region of Figure 6B corroborates these conclusions, although in the particular example illustrated in Figure 9, the increase in the period is smaller than experimentally observed.
Role of endogenous bursting
The period of endogenous bursting may set the lower and upper limits on the period of the half-center oscillator. In experiments in which single oscillator interneurons (intracellular recording) were driven with rhythmic current pulses and entrainment throughout the network was observed (extracellular recording), Masino and Calabrese (2002)
Endogenous bursting could also ensure os
