Burst Reset and Frequency Control of the Neuronal Oscillators in the Cardiac Ganglion of the Crab, Portunus Sanguinolentus

It has been widely assumed that the rhythmic activity of bursting pacemaker neurones is controlled by an underlying membrane potential oscillation, and that the burst of action potentials which occurs during maximum depolarization is secondary to the underlying oscillation. Tazaki & Cooke (19796) have recently shown that burst generation in the cardiac ganglion of Portunus, in the form of a slow depolarizing driver potential and the burst of action potentials generated during this depolarization, can occur independently of the pacemaker mechanism. This paper examines the effects of altering driver potential duration and of evoking driver potentials during the interburst interval. The observations suggest that the driver potential and associated burst of action potentials have an important role in the control of pacemaker activity in the cardiac ganglion.

In the neurogenic hearts of decapod Crustacea, the pacemaker is localized in the cardiac ganglion which can be isolated and still continue its rhythmic activity (Welsh & Maynard, 1951). In crabs and lobsters the cardiac ganglion consists of nine closely coupled neurons which will produce cyclic output in an isolated ganglion. Five large cells are motoneurones which control heart contraction, and the four small posterior neurones are the endogenous oscillators which drive the network as a whole (e.g. Maynard, 1955; Otani & Bullock, 1959a, b;Mayeri, 1973).

In Portunus all the cardiac neurones are electrotonically coupled (Tazaki & Cooke, 1979a). The small cells also provide input to the large cells via excitatory chemical synapses. The sites of action potential initiation are distant from the cell somata so that full-sized action potentials are recorded from the axons but not the cell bodies within the ganglion. Electrototonic coupling among the five large neurones is sufficiently strong to produce complete synchrony of the membrane potential oscillation and driver potentials under normal experimental conditions. Among the large cells, EPSP’s together with the action potentials are also always synchronous. Driver potentials have been elicited in large neurone somata isolated by ligature from small neurone input (Cooke & Tazaki, 1979).

It will be shown in this paper that the cardiac oscillator normally resets in an all-or-none fashion following a driver potential, and that when a driver potential is elicited by intracellular current injection, the pacemaker resets immediately causing a phase shift in all subsequent cycles. Partial resetting can be produced by altering the duration of a spontaneous driver potential or by eliciting driver potentials of abnormal duration. This effect is discussed in relation to the ionic mechanism for driver potential activity proposed by Tazaki & Cooke (1979c). Phase and pulse duration response curves derived from the resetting effects of depolarizing and hyperpolarizing pulses can predict entrainment of the cardiac oscillator by periodic current injection. Treatment with high concentrations of octopamine sometimes inhibits anontaneous burst activity in the large neurones, so that the action of feedback from activity in the large neurones on to the small pacemaker neurones can be observed. These experiments suggest that driver potentials in the large cells contribute to the control of small cell pacemaker frequency, but that feedback is not necessary for regenerative pacemaker activity in small cells.

Semi-isolated cardiac ganglion preparations were made from 100–200 g specimens of male and female Portunus sanguinolentas (Herbst). The crabs were collected locally and maintained in a circulating sea-water system prior to experimentation. The carapace was cut away from the dorsal surface of the crab, the heart removed, and its ventral wall dissected away. This exposed the interior surface of the dorsal heart muscles which were then teased away from the ganglion trunk. Muscle blocks containing the anterior and posterior bifurcations and their branches were cut free, and this preparation was transferred to a Sylgard recording chamber and pinned out. Experiments were conducted at room temperature (23 °C).

An extracellular 50 μm platinum-wire electrode was hooked around the ganglionic trunk and isolated with petroleum jelly. One or more large neurones were impaled with 15–60 MΩ, 3 M-KCl-filled, ‘Omega’ glass microelectrodes (1·1 mm). One intracellular recording channel was equipped with a constant current-injection bridge circuit (WP Instruments M4) for simultaneous recording and current injection through a single electrode. The recording chamber was grounded by a virtual ground (WP Instruments, model 180) which was used to monitor injected current. Records were made using a Brush 280 pen-writer, a kymograph camera (Grass, model C4) on a multibeam oscilloscope (Tektronix, model RM565), and a 7-channel FM Ampex FR1300 tape-recorder, with frequency response to 10 kHz. Intracellular records were unattenuated by both the pen-writer and the tape-recorder.

The physiological saline (pH 7·6) was a modification of Pantin’s saline for Cancer pagurus. It contained the following in mM/1: Na, 486; K, 14; Ca, 13; Mg, 26; SO₄, 23; Cl, 532; Hepes buffer, 3.

Tazaki & Cooke (1979 a) provide a detailed account of the electrical activity recorded from the semi-isolated cardiac ganglion of Portunus. The features which are of importance in the present study are illustrated in Fig. 1, which shows the activity recorded from the ganglionic trunk and from two large neuronal somata, one anterior and one posterior. In the extracellular recording, the action potentials originating in small cell axons are of small amplitude, and precede, accompany and follow the burst of compound action potentials resulting from the synchronized activity in large cell axons. Bursts in small cells were always longer and may drive those in the large cells. The intracellular recordings illustrated show the characteristic slow depolarization of the pacemaker potential between square-shaped driver potentials surmounted by attenuated action potentials. The sites of both driver and action potential initiation further from the soma in posterior than in anterior cells, so that the burst amplitude is smaller in the recording from a posterior cell body. The EPSP’s seen in the intracellular recordings coincide with small cell action potentials recorded extracellularly.

Carefully dissected ganglia showed considerable regularity in burst length and interburst interval and hence in frequency. For example, 27 cycles of spontaneous activity of above-average regularity from the ganglion used to obtain the data illustrated in Fig. 7(b) showed an average burst length of 324 ms with a standard deviation of 30 ms, and an average interburst interval of 1233 ms with a standard deviation of 22 ms (see Fig. 1 for parameter definitions).

In all ganglia from which measurements were made, the interburst interval showed a strong positive correlation with the duration of the preceding burst, but only a weak negative correlation with the duration of the following burst. The ganglion providing the data illustrated in Fig. 4(a) had an average burst length of 304 ± 119 ms and an average period of 1895 ± 218 ms, for 47 cycles. Fig. 2(a) shows a series of measurements of spontaneous burst lengths from this ganglion plotted against the duration of the following interburst interval. There is a significant positive correlation between the two variables (correlation coefficient, r = 0 · 802). When burst length is plotted against total period (i.e. burst length + interburst interval) (Fig. 26), the correlation is improved, as expected, and becomes highly significant (r = 0 · 953). These observations suggest that burst length might be involved in frequency control in the spontaneously active ganglion.

In contrast, when burst length is plotted against the previous interburst interval (Fig. 2c) there is only a weak negative correlation which becomes less significant while burst length is plotted against total period of the preceding cycle. (Fig. 2 d).

By injecting prolonged depolarizing and hyperpolarizing currents it was possible to obtain a wider range of burst and interburst interval durations than occurs spon-taneously (Tazaki & Cooke, 1979a). During depolarization, burst frequency increased, and burst length and interburst interval were shorter. During the initial stage of hyperpolarization, there was a decrease in frequency with an increased burst length and interburst interval. After the first few bursts during hyperpolarization, accommodation occurred, and frequency returned towards normal. These observations (from a different ganglion) are illustrated in Fig. 3, where burst length is plotted against interburst interval for depolarized, control and hyperpolarized preparations. The points in Fig. 3 derived from the prolonged hyperpolarization show the effects of accommodation. As before, there is a strong positive correlation between burst length and the following interburst interval (r = 0 · 834), so that as bursts increase in length, frequency decreases.

Harmonic oscillators produce a sinusoidal output much like the membrane potential oscillation in some TTX-treated molluscan bursters (Mathieu & Roberge, 1971). They tend to respond to perturbations with phase advances or delays depending on the phase at which the perturbation occurs, and with transient cycles before a new steady state is achieved (cf. fig. 8, Pinsker, 1977 a). Relaxation oscillators on the other hand, reset partially or completely to the same phase point, producing phase shifts all of the same sign and without transient cycles (Wever, 1965). The perturbation experiments described in this section show that the cardiac oscillator behaves like a relaxation oscillator which is reset to a maximally hyperpolarized potential by the occurrence of a driver potential and the associated burst of action potentials. It will also be shown that changes observed in the interburst interval following experimentally shortened bursts are consistent with the relation between interburst interval and duration of the preceding burst in the spontaneously active ganglion.

In perturbation experiments, three parameters can be varied: phase of application, duration, and intensity of stimulus. In the present experiments, there was a fourth parameter - current could be depolarizing or hyperpolarizing. The following sections present the results of experiments in which these various parameters were systematically varied.

Fig. 4 shows examples from experiments in which hyperpolarizing pulses of various intensities and durations were applied at different phases in the burst cycle. In Fig. 4(a) hyperpolarizing pulses of 50 ms duration were applied during the interburst interval. These pulses produced small phase advances of between 0 · 1 and o in many preparations as long as they occurred during the interburst interval itself. A consider’ able range of pulse duration and intensities was tested, all with similar results. When a pulse extended close to or beyond the projected time of burst initiation, the burst was delayed until the end of the pulse (Fig. 4a, record v). The following interburst interval was always within the normal range of variation, so that the new steady-state oscillation was phase delayed.

However, when hyperpolarizing pulses were applied beginning within a burst so that the driver potential was prematurely terminated, the following burst and all succeeding cycles of the oscillator were advanced (Fig. 4b). The sooner in the burst the termination occurred, the greater the phase advance. These phase advances were composed of three components. First, there was an advance in subsequent cycles due simply to the fact that the pulse terminated a burst so that the new pacemaker depolarization began sooner than projected. Secondly, there was a delaying component due to the hyperpolarizing pulse itself preventing the onset of slow depolarization, and thirdly, there was a decrease in the interburst interval due to reduction in burst length. The existence of this third effect is suggested by the relation already described between burst length and interburst interval in spontaneously active ganglia, and is of considerable interest in relation to the ionic basis of the ganglionic activity.

The effect of shortened burst length on the duration of the interburst interval is shown in more detail in Fig. 5. The interburst interval was defined as the interval between the beginning of the hyperpolarizing pulse and the phase reference of the next driver potential (usually the third EPSP). This means that short pulses (50 ms) were required in order that very little inaccuracy be introduced due to inclusion of pulse length as part of the interburst interval. Fig. 5 (a) shows four records in which the points of hyperpolarizing pulse initiation are aligned so that the progressive decreases in interburst interval as bursts are shortened can be seen. In Fig. 5 (b) three sets of points are plotted. Unperturbed spontaneous cycles (⦶) are clustered with burst lengths ranging from about 250 to 350 ms and interburst intervals of 16001800 ms. Data from cycles in which hyperpolarizing pulses were applied during the interburst interval have burst lengths in the normal range but show a somewhat decreased range of interburst intervals (◯), thus accounting for the small phase advances caused by such pulses. However, for bursts which are prematurely terminated by brief hyperpolarizing pulses, the interburst interval is greatly reduced. Furthermore, the degree of reduction in interval increased in proportion to the decrease in burst length (•). This observation will be related to the ionic basis of the driver potential and the potassium currents which mediate the postburst hyperpolarization (Tazaki & Cooke, 1979 c).

The results of such perturbation experiments can be presented in the form of phase-response curves, in which the phase advance or phase delay is plotted against the phase of the oscillator cycle at which the pulse was applied. By expressing phase shifts in terms of a fraction of a cycle, preparations with different spontaneous frequencies can be compared.

Three typical phase-response curves for hyperpolarizing pulses applied to a different ganglion are illustrated in Fig. 6. The abscissa represents a single cycle of the neuronal oscillation beginning at the phase reference point (in this case, the base of the thus EPSP at the beginning of a burst). The burst of action potentials occupies approximately the initial 0 · 18 of a cycle with maximum hyperpolarization occurring soon after. The points represent the phase at which each pulse was initiated, as measured along the abscissa, and the phase shift, as a fraction of the preceding spontaneous period, along the ordinate. All phase-response curves for hyperpolarizing pulses have a form similar to those illustrated, with three main features:

(i) Pulses initiated within a burst and of a sufficient magnitude to terminate the burst were followed by a shorter than normal interburst interval which, combined with earlier initiation of the slow depolarizing potential, resulted in a phase advance. The magnitude of the advance increased as the phase of pulse initiation approached the beginning of the burst (i.e. towards the left on the abscissa).

(ii) When pulses were applied during the interburst interval, slow depolarization was interrupted, but overall only slight phase advances occurred.

(iii) Towards the end of a cycle (on the right along the abscissa), when pulses began to approach and overlap the projected time of occurrence of the next burst, a delay resulted which was related to the duration of the pulse and its phase of application. As soon as the membrane depolarized following such a pulse, the next driver potential occurred.

When depolarizing current pulses of sufficient intensity were injected into large cell somata, a burst of action potentials was evoked. These action potentials were usually confined to the duration of the depolarizing pulse at high current intensities. However, at lower current, full driver potentials with superimposed action potentials were evoked. In such cases, of course, the burst was much longer than the stimulating pulse. If the pulse was applied during the spontaneous burst, it usually caused premature termination of the burst at the end of the pulse. The details of these effects and the resulting phase-shifts are described in this section. Evoked driver potentials completely reset the oscillator and partial reset could be produced by evoking short bursts of action potentials with strong depolarizing current pulses. When the membrane potential shifted out of the recorder range, due to bridge imbalance, the occurrence and frequency of evoked action potentials could be determined by examining the extracellular trace.

Several examples of the effects of 150 ms depolarizing pulses at different phases of the pacemaker cycle are illustrated in Fig. 7(a). At a current intensity of 0 · 75 nA, pulses early in the cycle caused a displacement of the membrane potential but did not induce action potentials or a driver potential, while those later in the cycle evoked a driver potential. The neurone hyperpolarized following such bursts and the pacemaker cycle reset, with the slow depolarization and subsequent burst forming an interburst interval within normal duration range. In some large cell intracellular records the slow depolarization during the interburst interval was not seen. It is not clear whether the slow depolarization observed in most large cell recordings is a property of large cells or is electrotonically conducted from small cells.

Fig. 7(b) shows examples from a series of experiments in which pulses of the same duration (50 ms) but different intensities were applied at similar phases, at about the middle of the interburst interval. These pulses are illustrated in order of increasing current intensity, and it can be seen that driver potentials were evoked only at current levels above a certain threshold. As before, when a driver potential occurred the pacemaker reset, and the evoked activity was followed by cycles of normal period, so that all subsequent cycles were phase delayed.

The pulses in Fig. 7(a) and (b) were all applied during interburst depolarizing pacemaker potential. In Fig. 7(c) three examples are given of depolarizing pulses applied during spontaneous bursts. In some cases, as in the first record, the length of the burst was virtually unaltered and the length of the following interburst interval was within the normal range of variation. When stimulus intensity was greater (Fig. 7 c, records (ii) and (iii)) and action potential frequency was increased, the burst often terminated prematurely at the end of the pulse. This resulted in phase advances of subsequent cycles, with two components. First, the interburst interval was initiated earlier in the cycle, and, secondly, the truncated bursts were followed by shorter interburst intervals. As before, this is to be expected if the relation between burst length and interburst interval shown in Fig. 2(a) can be applied to bursts shortened by depolarizing pulses. A possible ionic mechanism for truncation due to increased depolarization during a driver potential is discussed below. Lengths of three bursts altered by strong depolarizing pulses are plotted against the duration of the following interburst interval in Fig. 2(a) (open circles, ◯). They are close to the regression slope for spontaneous activity in the same ganglion.

Fig. 8 shows four typical phase-response curves for depolarizing current pulses slotted as described above for hyperpolarizing pulses. These are presented in ascending order of current intensity, and, as with the phase-response curves for hyperpolarizing pulses, they are characterized by a common general form. When pulses were applied during the spontaneous burst (far left on the abscissa), phase-shifts in the subsequent cycles were zero or small advances when the cessation of the depolarizing current terminated the spontaneous burst prematurely. Pulses applied during the slow depolarizing phase of the interburst interval, providing that they elicited a burst, caused phase delays approximately equal in magnitude to the phase angle at which they were applied. This means that the oscillator was reset to the beginning of its cycle and the next spontaneous burst occurred after a normal interburst interval. The slope of the phase-response curve is therefore close to +1, for points representing the effects of elicited bursts.

However, at the lowest stimulus intensity (Fig. 8 a, 0·75 nA) only pulses applied just prior to the projected time of the next spontaneous burst, when the slowly depolarizing membrane potential was close to the threshold for spontaneous activity, could evoke driver potentials and so phase delay the next spontaneous burst. Pulses of the same intensity applied earlier in the cycle had no phase-shifting effect (cf. Fig. 7a). The slope of the phase-response curve region containing these points is o. As current was increased (Fig. 8 b, 3 nA) driver potentials were evoked earlier in the interburst interval, until the injected current was sufficient to evoke a driver potential close to the maximum hyperpolarization of the pacemaker cycle, as well as throughout the remainder of the interburst interval (Fig. 8c, 6 nA).

The phase-response curve in Fig. 8(d) is for depolarizing pulses of relatively high current intensity (15 nA) which did not evoke normal duration driver potentials but which produced high-frequency action-potential activity during the course of the depolarization. Hyperpolarization and initiation of the slow membrane potential depolarization took place immediately following the end of the pulse. Since the pulse length (100 ms) was less than the average burst length for this experiment (250 ms) the measured phase delay was decreased by about 0·1 ([350–100]/normal period). Thus the data points are parallel to and below the theoretical + 1 line, and not through the origin.

The depolarizing pulse experiments described so far indicate that activity must be evoked in the large neurones before a phase delay due to resetting can occur. It has been shown that for 100 ms pulses there is a current threshold above which bursts are evoked, and that this threshold decreases during the interburst slow depolarizing pacemaker potential. The following data demonstrate that there is also a threshold of pulse duration for burst induction. These experiments also emphasize the distinction between evoking action potentials, which occurred during depolarizing pulses of any duration of sufficient current intensity, and the induction of a driver potential and associated action potentials.

To test the influence of pulse length, a series of pulses at various current strengths and durations ranging from 10 msec to 500 msec was applied at a fixed phase of the oscillation. For the ganglion used to obtain the data illustrated in Figs. 9 and 10, the average period was approximately 1600 ms, and the pulses began 1000 ms after the phase reference point (in this case, the third EPSP of the burst). In fractional terms, the phase point of pulse initiation was 0·625.

Some examples of pulses of different lengths but identical intensities (5 nA) are given in Fig. 9. In record (i) a pulse of 30 ms duration produced a change in membrane potential but evoked no more than one action potential and no driver potential. A longer pulse (60 ms), shown in record (ii) induced a driver potential that was followed by a normal interburst interval. Current injection lasting 100 ms (record iii) evoked action potentials during the depolarization (observed in the extracellular record - not shown) and briefly afterwards, but did not cause a driver potential. The interval from the hyperpolarization following this pulse to the next driver potential was shorter than a normal interburst interval. Finally, in record (iv) a 400 ms pulse was applied evoking action potentials during its course. After its termination, hyperpolarization was followed by a slow depolarizing pacemaker potential of approximately normal duration. As usual, when no driver potential and few or no action potentials occurred, no phase delay occurred. In the case of full driver potential production, the oscillator reset and a normal duration slow depolarizing potential led up to a phase-delayed spontaneous driver potential. At the low current intensity used here, action potential activity lasting for a time shorter in length than a normal driver potential caused a partial reset. A long pulse could produce a phase delay comparable with that following an induced driver potential. The effects of short pulses at higher intensities will be considered below.

Pulse-duration response curves, representing examples from a series of these experiments, are given in Fig. 10. The pulse length in milliseconds is plotted along the abscissa, and the time of the first post-pulse spontaneous burst is plotted against the ordinate, o ms on the ordinate is the phase reference point at the beginning of the prepulse burst, projected time for control bursts is 1600 ms, and time of pulse initiation is 1000 ms. The termination times of the pulses are represented by the diagonal line. For pulses of the lowest current (1 nA), plotted in Fig. 10a, driver potentials were evoked by pulses of 250 ms duration or more, but only towards the end of the 250 ms of depolarization. Nevertheless, full driver potentials were evoked and complete resetting occurred so that the next spontaneous bursts occurred about 1600 ms after the driver potentials were initiated. It is important to note that this means that the depolarizing current per se was not responsible for the reset - new bursts occurred 1850 ms after pulse onset. No action potentials occurred during the pulses prior to driver potential induction (cf. Fig. 7 a, record iii). For pulses shorter than 250 ms no driver potential or action potentials occurred and there was no phaseshift in the following spontaneous bursts.

Fig. 10(b) and (c) are pulse duration response curves for pulses of 3 and 6 nA respectively. In these cases, where driver potentials were evoked, they began close to the time of pulse initiation (cf. Fig. 9, record ii), and they were evoked by pulses progressively more brief; 100 ms in the case of 3 nA, and 60 ms for 6 nA. Finally, in Fig. 10(d), for a current of 15 nA, driver potentials could be evoked by pulses as short as 40 ms. In the particular example presented in Fig. 10(d) pulses of 80 and 100 ms did not evoke full driver potentials, although action potentials occurred during the pulses and for a short time afterwards (cf. Fig. 9, record iii). These pulses caused only partial resetting, and were followed by shorter than normal interburst intervals producing abnormally small phase delays.

Where pulses were longer than average driver potentials (250–300 ms), action potentials occurred throughout the course of the depolarization. The resulting phase delays were larger than those caused by evoked driver potentials. This was due in part to a small increase in the interburst interval, such as is predicted qualitatively from the dependence of this interval on burst length, but the main contributing factor was that the reset point occurred at the end of the depolarization, and it was from this point that the slow pacemaker depolarization began.

The depolarizing current pulse experiments so far described show that there was a threshold for evoking driver potentials, in relation to both intensity and duration of pulses, which decreased during the course of the slow depolarizing pacemaker potential. When a pulse above this threshold in both current strength and duration was applied, a driver potential and associated burst of action potentials was evoked and the neuronal oscillator was reset to the beginning of its slow pacemaker potential depolarization. It has also been shown that when the current pulse and driver potential did not coincide (Fig. 10a), it was the driver potential termination that controlled resetting.

The final set of single depolarizing pulse experiments to be described was designed to test systematically whether evoked action potential activity of duration much shorter than a normal driver potential would produce complete or partial resetting of the oscillatory system. These experiments arise from the observation that very short pulses (40 ms), even of relatively high intensity, did not evoke driver potentials of normal duration.

Some examples of the results of these experiments are summarized in Fig. 11, which shows phase-response curves for depolarizing current pulses of high intensity Jio and 15 nA) but short duration (20 and 30 ms). The diagonal dashed line represents the phase shifts predicted for complete reset following an induced full-length driver potential. Complete reset following a comparatively brief current pulse should produce a phase-response curve of slope + 1 intersecting y = o at between 0·20 (the phase of average burst termination) and 0·275 (the phase of maximum post-burst hyperpolarization), i.e. phase delays of similar magnitude to those due to evoked driver potentials, but minus the duration of the driver potential itself. The points plotted in Fig. 11 parallel the +1 curve but meet y = o at between approximately 0·40 and 0·45, with the longer and more intense pulses tending to intersect slightly closer to the origin. These results show that brief current pulses of relatively high intensity, which evoked high-frequency action potential activity during their course, produce an incomplete reset. Pulses applied at phases of less than 0·2 usually caused premature termination of the spontaneous driver potential and thus phase advances, as described above.

In general, the requirement for a reset of the oscillator was the occurrence of a driver potential or a depolarization with evoked action potentials. Partial resetting occurred and the following interburst interval was shorter than normal if the driver potential was incomplete or abnormally short, or if a short low intensity depolarizing pulse was applied. It was possible to produce more complete resetting either by extending the pulse duration and/or increasing the frequency of action potentials occurring during the depolarization.

When a self-sustaining non-linear oscillator is subjected to a periodic stimulus, if certain conditions are met, it may change its frequency and become synchronized with or entrained by the external input. For this to happen, the external input has to produce a phase-shift in the oscillator, and this phase-shift must vary with the phase of application of the stimulus (Enright, 1965). As has been shown, these conditions are fulfilled by the cardiac ganglion neurones as an oscillator, and injected current as the external stimulus. In this case, and for relaxation oscillators in general, entrainment can be thought of as a process of repeated discrete phase shifts, each phase-shift correcting the discrepancy between the periods of the entrained and driver oscillators. This means that not only will the frequencies of the two oscillators be identical, but for any particular combination of entrained and driving oscillators, the phase-angle difference between the two will be the same. This is because the external stimuli (train of current pulses) comprising the driving oscillator must always perturb the driven oscillator (cardiac burst cycle) at the phase producing the appropriate phase shift. The phase-angle difference can thus be obtained from the phase-response curve for the particular pulse under consideration. For stable, one-for-one entrainment to occur, the difference between the periods of the spontaneously active oscillator and the periodic input cannot be more than the maximum phase delay for the pulse when driver frequency is lower, and it cannot be more than the maximum advance when the driver is of higher frequency than the spontaneously active oscillator. This means that the limits of entrainment are given by the positive and negative pages of the phase-response curve. If a perturbation causes complete resetting, entrainment is immediate, with only a single transient cycle, unlike in harmonia oscillators, where typically many cycles of transients occur before steady-state entrainment is achieved (Wever, 1965). In the cardiac ganglion, hyperpolarizing pulses did not produce resetting, but any depolarizing pulse inducing a driver potential, or too msec or more of high-frequency action potentials, did cause complete resetting. Transients can therefore be expected during entrainment by hyperpolarizing pulses and short and/or low-intensity depolarizing pulses, but there should be only a single transient cycle during entrainment to evoked driver potentials and long and/or high-intensity depolarizing pulses. Similar reasoning indicates that a single pulse, if it produces complete resetting, can synchronize a population of endogenous oscillators of similar frequency. This has been shown experimentally for cells L3 and L5 in Aplysia (Pinsker, 1977b). The observations reported below show that the Portunus cardiac ganglion is a relaxation oscillator and predictions made on this basis are sustained by the experimental results.

For hyperpolarizing current pulses, only small phase advances and delays were obtained (Fig. 6a, b, c). Advances occurred when the pulse was applied during the burst, and delays were caused by pulses applied towards the end of the interburst interval. Fig. 12(a) shows two examples of the action of periodic hyperpolarizing pulses on the frequency of the cardiac oscillator. In record (i) the spontaneous period of the oscillator was 2450 ms and a driving train of hyperpolarizing pulses (50 ms, 5 nA) with a period of 2150 ms was applied. After two transient cycles the cardiac oscillator became entrained, its period changing to that of the driving input (i.e. a period change of 300 ms, equivalent to a phase advance of 0·14). The phase-angle difference between the two was 0·12. Referring to the appropriate phase-response curve (Fig. 6c), it can be seen that a pulse applied at phase 0·12 gives a positive phase shift of about 0·14.

In Fig. 12 a, record (ii), the spontaneous period of the cardiac oscillator was 2050 ms, and a driving train of pulses (parameters as for record (i)) was applied with a period of 2800 ms, representing a repeated phase delay of 0·30. The phase-angle difference after four cycles of transients was 0·93, for which the phase-response curve indicates a phase delay of 0·30. These values cannot be established precisely because the dynamic phase-response curve must differ to some extent from the static one derived from single pulse experiments (Wever, 1972; Kuhnke, 1975; Benson, 1976). During the course of this experiment, the ganglion spontaneously produced a double driver potential which immediately threw the cardiac oscillator into an inappropriate phase-angle relation with the driving pulse train. Re-entrainment followed after two transient cycles (Fig. 12 a, record (ii)).

A systematic check for a range of entrainment of particular hyperpolarizing pulse trains was not carried out, but trains of frequency outside the range predicted from the phase-response curve failed to cause steady-state entrainment.

Two general points can be noted from these experiments. First, transients occurred before steady-state entrainment was achieved. This is because hyperpolarizing pulses did not reset the cardiac oscillator, so that driven and driver oscillations often had to move through several unstable phase-angle differences before the ‘correcting’ phase shift equalled the difference in periods. Secondly, once steady-state entrainment occurred, for entrainment to lower-frequency oscillatory input, the length of the driver potentials was substantially increased (Fig. 12 a, record (ii)), and for the case of a small decrease in period during entrainment, there was a slight decrease in burst length during the steady-state cycles (Fig. 12(a), record (i)). Again the correlation between burst length and interburst interval was preserved.

The phase-response curves shown in Fig. 8 for 100 ms depolarizing pulses are characteristic of relatively high-intensity current and pulses of too ms or longer and they fall close to the line with slope +1 and passing through the origin. According to the theory outlined above, entrainment to trains of such pulses should always occur when the phase-angle difference between the entraining oscillation and the cardiac oscillation is equal to the difference between their spontaneous periods. Furthermore, no entrainment can occur to driving oscillations with periods of more than marginally less than the spontaneous period of the cardiac oscillation, nor to those with twice or more the spontaneous period. This was verified experimentally, and some examples of applied pulse trains are shown in Fig. 12(b). In records (i) and (ii), 150 ms pulses (10 nA) were applied with periods of approximately 1·5 and 1·75 times the spontaneous cardiac period. As predicted, entrainment was immediate, and the phase-angle differences between forcing and driven oscillation were 0·5 and 0·75 respectively. In record (iii) the period of the forcing oscillation was 2·3 times that of the cardiac oscillator, which is outside the predicted range of entrainment (1·0–2·0 × ). As shown, steady-state entrainment did not occur. Finally, in record (iv), brief, low-intensity pulses were applied with a period 1·25 times spontaneous cardiac period. The phase-response curves in Fig. 11 show that resetting was incomplete following pulses with parameters in this range, and they indicate that a phase delay of 0·25 would occur following pulse application at about 0·6. The experimental record shows a phase-angle difference of 0·58, and, as expected during entrainment to stimuli that produce incomplete resetting, there were several cycles of transients before steadystate entrainment occurred.

A high concentration (10⁻⁵M) of octopamine in the bathing medium produced marked effects on the spontaneous activity of the ganglion. The concentration of octopamine used in these experiments was probably above the physiological range and no conclusions are drawn here about the action of octopamine at lower concentrations. This has been examined in vitro and will be described elsewhere (Benson & Cooke, in prep.). However, the use of 10⁻⁵M octopamine provided a tool for investigating further the role of driver potentials in frequency control in the ganglion. It provided a method to inhibit driver potential production in the large neurones while allowing burst production to continue in the small cells. The octopamine effect was completely reversed after 10 min washing in normal medium (Fig. 13).

In 10⁻⁵ M octopamine the following changes were observed in intracellular activity recorded from a large neurone cell body (Fig. 13) and in the extracellular recording from the ganglion trunk.

(1) Membrane potential increased by 4 mV.

(2) Burst frequency decreased and burst duration increased.

(3) Driver potentials were evoked after increasingly larger numbers of EPSP’s from the small cells.

(4) EPSP input sometimes failed to evoke a driver potential.

(5) Small cell burst length (measured from EPSP’s and the extracellular record was much longer when a driver potential occurred in the large neurones than when a driver potential was not evoked

(6) The interburst interval was much shorter (about the same as in normal medium) if a driver potential did not occur.

In view of the relation between burst length and interburst interval, and the resetting action of a driver potential experimentally evoked in the large neurones, a possible interpretation of the octopamine effects is as follows. Octopamine, by hyperpolarizing the neurone or by other means, increased the driver potential threshold. Therefore greater numbers of EPSP’s were required to evoke a driver potential, and the driver potential was delayed in relation to the beginning of the small cell burst. If a driver potential was evoked, this depolarization fed back on to the small cells, holding them depolarized and increasing the length of their burst. A driver potential (and longer small cell burst) produced a long interburst interval. An ionic basis for this is suggested in the discussion. If a driver potential was not evoked, the small cell burst terminated rapidly, and the following interburst interval was short. This interpretation implies that the driver potential may have a similar role in frequency control in the untreated ganglion.

On the basis of ion substitution experiments, Tazaki & Cooke (1979b, c) have proposed the following model as the ionic basis of driver potential and slow pacemaker potential activity in the Portunus cardiac ganglion. In the spontaneously active ganglion, the small neurones are pacemakers which drive the large neurones towards driver potential threshold by an electrotonic spread of depolarizing current reinforced by synaptic potentials produced by the small cell burst of action potentials. The driver potential depolarization is suggested to be produced by a voltage-dependent Ca conductance, and the driver potential is terminated by voltage and probably Ca-dependent K+ currents. The driver potential serves as the source of depolarizing current initiating the burst of action potentials recorded from the large neurones. The hyperpolarizing after-potentials of two time courses, seen in TTX-treated ganglia, are attributed to a large voltage-dependent K⁺ current, and a smaller Ca-sensitive K+ current that declines more slowly and contributes to the slow pacemaker depolarization in the interburst interval. The main pacemaker current may be a continuous leak-and-pump current. Tazaki & Cooke (1979 c) emphasize the autonomous nature of the driver potential and the dependence of the slow pacemaker depolarization on the preceding driver potential rather than on an underlying membrane potential oscillation. The observations reported in the present paper support this hypothesis.

The first set of observations showed that in the spontaneously active ganglion and during prolonged depolarizing and hyperpolarizing current injection, the duration of the interburst interval increased with increase in the length of the preceding driver potential. The interburst interval is the amount of time taken for the membrane potential to depolarize from the post-burst hyperpolarization to the driver potential threshold. According to the ionic model, a slow inactivating of a K+ conductance contributes to this slow interburst depolarization. The length of the driver potential could exert control over the interburst interval via the proposed calcium-sensitive K+ current. A longer burst would allow greater calcium entry, consequent activation of K⁺ channels and hence increased hyperpolarization and longer decay time.

The control exerted by burst length is, of course, even greater over the frequency of oscillation, since this is a function of the period which includes the burst length as well as the interburst interval. A very strong correlation was seen between burst length and period.

There was a slight negative correlation between burst length and the duration of the preceding interburst interval. A similar dependence has been reported by Mayeri (1973) for the lobster cardiac ganglion, and by Hartline, Gassie & Sirchia (in preparation) for the lobster stomatogastric ganglion.

Hyperpolarizing pulses injected part way through driver potentials truncated the bursts and produced phase advances in subsequent activity. These advances were due to the advance in initiation of the slow depolarizing potential, together with a decrease in the interburst interval. This decrease in interburst interval following prematurely terminated driver potentials increased markedly in proportion to the imposed decrease in the length of the driver potential. This suggests that a Ca-dependent K+ current may contribute more to the post-burst hyperpolarization and control of the slow pacemaker depolarization than a slowly activated voltage-de pendent K⁺ current. A shorter driver potential would mean less Ca entry and a smaller residual K+ current opposing the inward leak current. This is in contrast to a voltage-dependent K+ current that might simply inactivate when the neurone was artificially hyperpolarized, thus prematurely resetting the oscillator but not altering the interburst interval.

Hyperpolarizing pulses applied during the interburst interval produced small decreases in interval duration resulting in small phase advances which decreased in magnitude towards the end of the interburst interval. These pulses were followed by small and slow depolarizations of the membrane potential beyond the projected level. This resulted in a more rapid approach to the driver potential threshold and hence a phase advance.

Similar pulses applied towards the end of the interburst interval, so that they extended into the projected onset of the spontaneous driver potential, caused phase delays. By holding the membrane potential below threshold for driver potential initiation, the bursts were delayed in proportion to the pulse duration and phase of pulse application.

Simple but tedious extensions of the arguments presented above account in terms of the model for the observed behaviour of the cardiac oscillator during prolonged injection of small depolarizing and hyperpolarizing currents.

Hartline, Gassie & Sirchia (in preparation) have reported identical responses to hyperpolarizing pulses applied at different phases of a neuronal oscillation in the stomatogastric ganglion of the lobster. Comparison with the observations of Pinsker (1977 a) on the bursting neurones in the parieto-visceral ganglion of Aplysia are difficult, firstly, because no information is given on changes in interburst interval following truncation of bursts, and, secondly, because the postsynaptic hyperpolarizations with which the neuronal cycle was perturbed were of considerable duration and hence made a significant contribution to the resulting phase-shift. However, in those published records where the stimulus was short and greatly reduced the burst length, the interburst interval was reduced. Hyperpolarizing synaptic input during the interburst interval in the Aplysia system appeared to reset the oscillator in much the same way as a depolarizing pulse applied to the cardiac ganglion. The ionic model for the cardiac ganglion is similar to proposals for the ionic basis of activity in molluscan bursting neurones (Smith, Barker & Gainer, 1975), so it is not surprising that similar effects of burst truncation have been seen in both.

The effects of depolarizing current pulses on the cardiac neuronal oscillation in Portunus can be divided into three categories :

• At low current intensities (e.g. 0·75 nA) the depolarizing current pulses produced a change in membrane potential for the duration of the pulse without inducing any regenerative activity.

• At medium current intensities (e.g. 3 nA) the depolarizing pulses induced normal-sized driver potentials.

• At high current intensities (e.g. 15 nA) action potentials occurred at high frequency (i.e. greater than the frequency of action potentials occurring during a normal driver potential) during the course of the pulse. No normal duration driver potentials were evoked and activity ceased at the end of the pulse.

These responses depended not only on current, as indicated, but also on pulse duration and phase of application. In other words, the responses were separated by thresholds that decreased during the course of the slow pacemaker depolarization, and the thresholds were for both current strength and pulse duration.

A pulse applied near the beginning of the interburst interval might fail to evoke regenerative activity, while an identical pulse later in the cycle could induce a driver potential. Similarly, a pulse that evoked a driver potential near the phase of maximum hyperpolarization could produce action potentials but no normal duration driver potential if repeated at a later phase in another cycle.

Increasing the current strength and/or duration of a pulse repeated at any particular phase of the oscillation similarly changed the response through the three categories, from membrane potential displacement, through driver potential induction, to high-frequency action potential production.

This change in threshold with phase may be due to a number of factors. Membrane resistance increases during the interburst interval (Tazaki & Cooke, 1978 a) thus increasing the effectiveness of the injected current; residual outward currents are postulated to be greater immediately after a burst, and the membrane potential is further from the thresholds earlier in the cycle.

The observations described above can be generalized further. Any depolarizing current pulse that evoked regenerative activity caused a phase shift (usually a delay) in the cycles of the oscillation following the stimulus. This made it possible to present, in the form of phase and pulse duration response curves, the results of experiments in which a wide range of durations and intensities were tested at all phases of the pacemaker oscillation. These response curves demonstrate that following an evoked driver potential or action potentials, the cardiac oscillator was reset partially or completely. Resetting the oscillator is defined as driving it to the phase of its cycle from which the slow depolarizing pacemaker potential was initiated. In a normal cycle, this is the maximum post-burst hyperpolarization. Complete reset means that the interburst interval following reset was of a duration within the normal range of variation for an interburst interval during spontaneous activity. After partial reset there was an interburst interval of abnormally short duration.

Depolarizing pulses which did not induce regenerative activity, when applied during the interburst interval, did not cause significant phase shifts. This is consistent with the suggestion that the slow depolarizing pacemaker potential is partly due to a voltage-insensitive leak current.

When depolarizing pulses evoked driver potentials or action potential activity for more than 150 ms, there was always complete reset of the oscillator. In the former case the current pulse might hold the membrane potential above threshold sufficiently long for the activation of the voltage-dependent depolarizing current (Ca) to produce a driver potential that was terminated and which controlled the following interburst interval as suggested above for spontaneous driver potentials. In the case of evoked action potentials in the absence of a normal duration driver potential there may be (a) increased Ca conductance during greater than normal depolarization and/or action potential frequency, consequently followed by Ca sensitive K+ current activation, and (b) more rapid activation of a voltage-dependent K+ conductance, again due to greater than normal depolarization. These currents could produce repolarization at the end of the current pulse.

This interpretation is further supported by the data from partial resets that occurred following the few cases in which incomplete driver potentials were evoked, and the experiments involving high intensity but very short duration (10–30 ms) current pulses. In both these cases there may have been a smaller than normal influx of Ca resulting in a smaller K⁺ conductance increase and therefore a shorter subsequent interburst interval. The K+ conductance would have to be sufficient to repolarize the neurone, and in fact partial resetting observed in these circumstances always produced interburst intervals of about 75% or more of normal. Shorter interburst intervals were seen only when the driver potential was terminated by a hyperpolarizing pulse.

The application of very long depolarizing pulses (up to 500 ms) did not significantly extend the interburst interval, although phase delay increased because the depolarizing pacemaker potential was not initiated until the end of the pulse. This is consistent with a Ca-sensitive mechanism that saturates at close to the duration of a normal driver potential (250–300 ms).

Phase-response curves for many depolarizing pulses showed small phase advances for pulses applied during the bursts, especially early in the bursts. Depolarizing pulses applied during driver potentials usually terminated them at the end of the pulse. As with hyperpolarizing pulses, the resulting phase advances were composed of two components: an advance due to earlier initiation of the slow pacemaker potential depolarization and a further advance contributed by a small decrease in the interburst interval (e.g. Fig. 7c). Again, a shortening of the burst resulted in a shorter interburst interval, but of smaller magnitude than the decrease following premature termination by hyperpolarizing pulses. This observation can be interpreted as being due to less Ca entry because the driver potential was shorter than normal but with some additional influx during the imposed depolarization and associated high-frequency action potentials. Reduction in interburst interval was observed to be less following termination by depolarizing pulses than by hyperpolarizing pulses of similar duration applied at the same phase.

An outline has been given in the Results of the theory of entrainment for relaxation oscillators. Predictions from the phase-response curves were confirmed experimentally, indicating that the cardiac ganglion is appropriately described as a relaxation oscillator. It responds to depolarizations that evoke driver potentials with complete reset, and to hyperpolarizations with smaller phase-shifts. The conditions for entrainment of an oscillator to be possible are phase-shifts, in response to external stimuli, which vary in magnitude with the phase of application of the stimulus. The cardiac ganglion meets these criteria in its responses to injected current. It proved possible to predict quantitatively, from the phase-response curves, the ranges of entrainment and the phase-angle difference that would be adopted between the cardiac and entraining oscillators. Similar findings have been reported for synaptic input to neuronal oscillators in the parietovisceral ganglion of Aplysia (Pinsker, 1977b), and the pyloric system of the lobster (Ayers & Selverston, 1979). Entrainment by synaptic input (i.e. depolarizing or hyperpolarizing current) is likely to be the mechanism of synchronization of cardiac activity with other rhythmic behaviours.

Finally, it has been shown that by the use of octopamine some further information bean be obtained on the role of large neurone driver potentials in frequency control in the cardiac ganglion. At micromolar concentrations and less, octopamine decreases spontaneous frequency of the Portunus cardiac ganglion (Benson & Cooke, in prep.) and at higher concentrations, driver potentials sometimes failed to be evoked in the large neurones. When there was no driver potential, the next burst of EPSP’s, reflecting small cell activity, occurred much sooner than was the case when a driver potential did occur. This is consistent with the interpretation of ganglionic responses described above. If the interburst interval depends partly on the magnitude of the influx of calcium that occurs during the driver potential (Tazaki & Cooke, 1979b), then in the absence of large cell driver potentials the interburst interval should be smaller. In normal medium the large neurone driver potentials probably feedback on to the small neurones and hold them depolarized. In the absence of large neurone driver potentials the small neurones repolarize faster, permitting a smaller influx of Ca and thus a smaller post-burst hyperpolarization, so that the interburst interval was shorter and the burst frequency higher.

This electrotonic feedback mechanism from large neurones to small may also play a role in intraganglionic coordination. Tazaki & Cooke (1979 a, r) showed that perfusion of the ganglion with salines whose common property was the inhibition of driver potentials resulted in the disintegration of rhythmic bursting.

Tazaki & Cooke (1979b, c) have shown that the driver potential may represent an endogenous neural mechanism, independent of those giving rise to pacemaker functions or action potential generation, by which a burst of impulses can be generated. Evidence has been presented here to suggest that the occurrence and duration of the regenerative driver potential recorded in large neurone somata exerts considerable control over the duration of the following interburst interval. It is now unnecessary to hypothesize an autonomous, underlying pacemaker oscillation to account for the rhythmic activity of the nine cardiac neurones. The K+ conductances proposed by Tazaki & Cooke (1979 c) for the termination of the driver potential are influenced by the duration and magnitude of the preceding driver potential, so that they may represent the process by which the driver potential controls the following interburst interval and thus the frequency of the cardiac rhythm.

The author thanks Professor I. M. Cooke for practical help during the course of the experimental work, and for critical comments on previous drafts of this paper.

This study was supported in part by National Institutes of Health Grant NS1 1808 to Professor Cooke, a National Institutes of Health Biomedical Sciences Support Grant to the University of Hawaii, and by grants from the University of Hawaii Foundation to the Békésy Laboratory of Neurobiology.