The central pattern generator responsible for the gill ventilation rhythm in the shore crab Carcinus maenas can produce a functional motor pattern over a large (eightfold) range of cycle frequencies. One way to continue to generate a functional motor pattern over such a large frequency range would be to maintain the relative timing (phase) of the motor pattern as cycle frequency changes. This hypothesis was tested by measuring the phase of eight events in the motor pattern from extracellular recordings at different rhythm frequencies. The motor pattern was found to maintain relatively constant phase relationships among the various motor bursts in this rhythm over a large (sevenfold) range of cycle frequencies, although two phase-maintaining subgroups could be distinguished. Underlying this phase maintenance is a corresponding change in the time delay between events in the motor pattern ranging from 470 to 1800 ms over a sevenfold (300–2100 ms) change in cycle period. Intracellular recordings from ventilatory neurons indicate that there is very little change in the membrane potential oscillation in the motor neurons with changes in cycle frequency. However, recordings from nonspiking interneurons in the ventilatory central pattern generator reveal that the rate of change of the membrane potential oscillation of these neurons varies in proportion to changes in cycle frequency. The strict biomechanical requirements for efficient pumping by the gill bailer, and the fact that work is performed in all phases of the motor pattern, may require that this motor pattern maintain phase at all rhythm frequencies.

In order to maintain functional motor outputs across a wide range of speeds, the relative timing (phase) of the individual movements that constitute the output must be appropriately regulated. Systems that maintain constant time delays between events in the motor pattern will produce motor outputs in which phase relationships vary with motor pattern duration, whereas systems that maintain phase relationships must increase or decrease the timing between events as the duration of the motor pattern is altered. This issue has been most extensively studied in rhythmic motor patterns, and systems maintaining both constant delay and constant phase have been observed. For example, in terrestrial locomotion, one portion of the motor pattern (swing phase) is maintained at a relatively constant duration over the entire range of walking frequency, while the phase and duration of the opposing (stance) motor burst vary as appropriate for a given locomotor frequency (Grillner, 1981). This relationship, in which return stroke duration is constant and power stroke duration varies, has also been observed in insect walking (Pearson and Iles, 1970), crayfish swimmeret beating (Davis, 1969), insect ventilation (Miller, 1966) and rhythmic uropod movements in the sand crab Emerita analoga (Paul, 1971). In other systems such as Tritonia diomedea swimming (Hume et al. 1982) and the pyloric rhythm of the lobster stomatogastric system (Hooper, 1993, 1997a,b), motor pattern phasing is relatively constant as cycle frequency changes. Relatively constant intersegmental phase relationships are also observed in motor patterns generated by coupled oscillators such as that for swimming in the lamprey (Williams, 1992) and leech (Friesen and Pearce, 1993).

Gill ventilation in decapod crustaceans is produced by the rhythmic dorsoventral movements of the scaphognathite (SG) or gill bailer of the second maxilla, which pumps water through the branchial chamber and over the gills. In vivo, the gill bailer is capable of pumping water at rates from 40 to over 300 cycles min−1 or over an eightfold (0.66–5 Hz) frequency range (Wilkens, 1976; Mercier and Wilkens, 1984).

In the shore crab Carcinus maenas, the ventilatory motor pattern is produced by a central pattern generator (CPG; Delcomyn, 1980) consisting of eight nonspiking interneurons and 27 motor neurons (DiCaprio and Fourtner, 1984; DiCaprio, 1989) that drive the five levator and five depressor muscles of the gill bailer. The levator and depressor groups are divided into two functional subgroups, Lev1 and Lev2, Dep1 and Dep2, and the normal recruitment sequence of these muscle groups during forward ventilation is Lev1–Lev2− Dep1–Dep2 (Young, 1975).

One conclusion of Young’s study of the ventilatory system was that the motor pattern was essentially phase-constant on the basis of an analysis of the correlation between cycle period and time delays in the pattern. However, such correlations are not a sufficient basis on which to conclude that phase remains constant in a motor pattern (see Discussion). In addition, Young’s data were obtained from semi-intact preparations that preserved the sensory input from the gill bailer and the range of cycle periods observed was not stated.

In vitro, the frequency of the motor pattern produced by isolated ganglion preparations could be varied over a sevenfold range from 0.47 to 3.3 Hz. This large frequency range (cycle period 2100–300 ms) would require correspondingly large adjustment of inter-neuronal time delays (up to 1800 ms) to maintain motor pattern phase. We report here that changes of this magnitude are, in fact, observed when cycle frequency varies throughout this range and that the gill ventilation CPG is capable of producing a relatively phase-constant output over a sevenfold frequency range.

Preparation

Male and female green shore crabs, Carcinus maenas (L.), were used in all experiments. The animals were maintained for 2–10 weeks in artificial seawater aquaria at 10 °C until use. The isolated ganglion preparation used in this study has been described in detail elsewhere (Simmers and Bush, 1983; DiCaprio and Fourtner, 1984). Briefly, the walking legs and chelae were autotomized and the dorsal carapace, viscera and brain were removed. The thorax was pinned down in a Sylgard-lined dish containing oxygenated crab saline (Ripley et al. 1968). The sternal artery was immediately cannulated and the thoracic ganglion perfused with oxygenated saline at a rate of 2–3 ml min−1. The nerves to both scaphognathites (SGs) were dissected from the SG musculature and all remaining nerves from the thoracic ganglion were severed. The thoracic ganglion was removed from the thorax and pinned dorsal-surface-up on the Sylgard base. All experiments were performed at room temperature (21–22 °C). In experiments where intracellular recordings were made from ventilatory neurons, the ganglion was desheathed with fine forceps. The isolated ganglion preparation used in this study spontaneously expresses the motor pattern corresponding to forward ventilation for periods of 6–8 h, with a typical intrinsic frequency of 0.75–1.0 Hz. Pauses in the ventilatory motor output and spontaneous bouts of reverse ventilation occurred infrequently in all experiments.

Recording procedures

Extracellular recordings of the ventilatory motor pattern were made using polyethlyene suction electrodes placed on the cut ends of the SG levator (LEV), depressor (DEP) and depressor muscle D2a motor nerves from either the left or right side of the ganglion (Fig. 1). A suction electrode was also placed on the intact circumesophageal connective ipsilateral to the site of extracellular recording to permit stimulation of descending fibers that alter the rate of the ventilatory rhythm (Wilkens et al. 1974). Stimulation of the connective was made with continuous pulse trains (200 μs duration pulses) at frequencies of 30–100 Hz. Stimulus amplitude was adjusted to elicit the maximum change in cycle frequency at the lowest stimulus frequency and was then held constant as stimulus frequency was increased to produce a range of ventilatory cycle frequencies during each experiment. Intracellular recordings were obtained from neuropilar processes of ventilatory neurons using glass microelectrodes filled with 2 mol l−1 potassium acetate with resistances in the range 25–30 MΩ. Intracellular voltages were amplified using a bridge electrometer (WPI 767). All signals were recorded on an eight-channel instrumentation tape recorder (HP 3968A) for later analysis and reproduced on an AstroMed MT8800 chart recorder.

Fig. 1.

Measurement of events in the ventilatory motor pattern. Eight points in the ventilatory motor pattern can be accurately measured from extracellular recordings of the motor pattern. With respect to the four motor neuron groups active during forward ventilation, only the time of the start of the levator group 2 motor burst could not be determined from these recordings. The events that can be unambiguously identified are the start of the entire depressor (DEP) and levator (LEV) motor group bursts (Dep Start = Dep1 group start; Lev Start = Lev1 group start), the end point of the depressor group 1 and levator group 1 bursts (Dep1 End and Lev1 End), the end of the entire depressor and levator bursts (Lev End = Lev2 End; Dep End = Dep2 end), the start and end of the D2a motor burst (D2a Start and D2a End) and the start of the depressor group 2 burst (Dep2 Start = D2a Start).

Fig. 1.

Measurement of events in the ventilatory motor pattern. Eight points in the ventilatory motor pattern can be accurately measured from extracellular recordings of the motor pattern. With respect to the four motor neuron groups active during forward ventilation, only the time of the start of the levator group 2 motor burst could not be determined from these recordings. The events that can be unambiguously identified are the start of the entire depressor (DEP) and levator (LEV) motor group bursts (Dep Start = Dep1 group start; Lev Start = Lev1 group start), the end point of the depressor group 1 and levator group 1 bursts (Dep1 End and Lev1 End), the end of the entire depressor and levator bursts (Lev End = Lev2 End; Dep End = Dep2 end), the start and end of the D2a motor burst (D2a Start and D2a End) and the start of the depressor group 2 burst (Dep2 Start = D2a Start).

Data analysis

The ventilatory motor pattern consists of alternating bursts of activity in the motor neurons that innervate the gill bailer. Levator and depressor activity can each be divided into two subgroups, levator one and two (Lev1 and Lev2) and depressor one and two (Dep1 and Dep2), thereby forming a four-phase motor pattern (Young, 1975). The muscles of the two subgroups, and hence the motor neurons that drive them, are activated more or less concurrently during ventilation (Young, 1975), and thus it is impossible to distinguish the activity of most individual neurons from the four subgroups. However, the activity of one of the neurons driving a Dep2 group muscle (D2a) is easily recorded in isolation from a branch of the SG levator nerve, and this single motor neuron burst was therefore included in this study.

There are eight points in the ventilatory motor pattern that can be accurately measured from extracellular recordings of the motor pattern (Fig. 1). The start of the depressor burst (Dep Start) was taken as the reference, or zero phase point, in the cycle and also marks the start of the depressor group one burst. The next event in the pattern is the start of depressor group two, indicated by the firing of the D2a motor neuron (D2a Start). There are two muscles in the depressor two group, D2a and D2b, and Young’s (1975) electromyographic data demonstrate that D2a is the first muscle activated in this group. The onset of D2a motor neuron activity can therefore be used to determine the Dep2 group start time (Dep2 Start=Dep2a Start). This is followed by the end of the depressor group one burst (Dep1 End), the end of the D2a motor neuron burst (D2a End) and then the end of the D2b motor neuron activity, which also marks the end of the total depressor burst (Dep End=Dep2 End=Dep2b End). The start of levator group one activity (Lev Start=Lev1 group start) occurs just before the end of the depressor burst and is followed by the end of the levator group one activity (Lev1 End) and the end of the entire levator burst (Lev End=Lev2 End). Thus, only the time of the start of the levator group 2 motor burst could not be determined from extracellular recordings. Measurements of individual events were always made on the polarity (positive or negative) of the extracellular recording that provided the most distinct determination of the transition between bursts. In initial experiments, measurements were made independently by two individuals, and no statistical differences were found between the two data sets.

In each experiment, the slowest cycle frequency occurred in unstimulated preparations and was in the range 0.75–1.0 Hz. The circumesophageal connective was stimulated in order to elicit higher frequencies of the ventilatory motor pattern, and intervals of relatively constant motor pattern cycle frequency (variation less than ±5 % of the mean) were selected for analysis. Time points were measured during these constant-frequency intervals from chart recorder recordings (chart speed 100 mm s−1), using a digital micrometer, for five consecutive cycles of the ventilatory pattern. These data were entered into an Excel spreadsheet (Version 4.0, Microsoft, Inc.) for calculation of motor pattern phase, average phase and time delay and for regression analysis. The reference point for all phase measurements was arbitrarily taken as the start of the depressor burst, and the phase of other points in the motor pattern was calculated using the relationship, phase=tev/Tcyc, where tev is the time from the start of the depressor burst to the point of interest and Tcyc is the cycle period of the ventilatory motor output. Data were then transferred to plotting software (Grapher Version 1.5, Golden Software) for presentation.

Twenty-three experiments were performed and data were selected for detailed analysis from seven preparations in which (1) the ventilatory cycle frequency could be varied over at least a fivefold range, (2) the cycle frequency was relatively stable during periods of connective stimulation, and (3) all motor pattern timing points could be clearly identified in the extracellular recordings.

Phase relationships

Fig. 2 shows a comparison of the ventilatory motor pattern running at an intrinsic rate of 0.66 Hz (40 cycles min−1) and at 2.36 Hz (142 cycles min−1), or approximately 3.5-fold faster, during stimulation of the circumesophageal connective (note the different time scales in the two records). It is apparent from visual inspection of these two records that the basic structure and phase relationships of the ventilatory motor pattern are maintained as the ventilatory rhythm frequency increases. To confirm this apparent phase constancy, the phase of identifiable points in the ventilatory motor pattern was plotted using data from a single preparation (Fig. 3). In this experiment, the intrinsic (slowest) frequency of the motor pattern was 0.65 Hz and connective stimulation produced a maximum 4.3-fold increase of the cycle frequency to 2.8 Hz.

Fig. 2.

The ventilatory motor pattern is maintained at different cycle frequencies. In experiments performed on intact shore crabs (Wilkens, 1976), the ventilation frequencies ranged from 40 beats min−1 (frequency 0.6 Hz, period 1.7 s) to 330 beats min−1 (frequency 5 Hz, period 0.20 s), an eightfold range. The recordings show the ventilatory motor output from a typical preparation at its slowest intrinsic frequency of 40 beats min−1 (0.66 Hz, period 1.5 s) and at a higher frequency of 142 beats min−1 (2.36 Hz, period 0.42 s) evoked by connective stimulation. When the time base is scaled proportionally to the change in frequency (note the different time bars), the motor patterns appear to be very similar.

Fig. 2.

The ventilatory motor pattern is maintained at different cycle frequencies. In experiments performed on intact shore crabs (Wilkens, 1976), the ventilation frequencies ranged from 40 beats min−1 (frequency 0.6 Hz, period 1.7 s) to 330 beats min−1 (frequency 5 Hz, period 0.20 s), an eightfold range. The recordings show the ventilatory motor output from a typical preparation at its slowest intrinsic frequency of 40 beats min−1 (0.66 Hz, period 1.5 s) and at a higher frequency of 142 beats min−1 (2.36 Hz, period 0.42 s) evoked by connective stimulation. When the time base is scaled proportionally to the change in frequency (note the different time bars), the motor patterns appear to be very similar.

Fig. 3.

The ventilatory motor pattern maintains phase constancy over a large range of cycle frequencies. The phase of each motor pattern element is plotted against ventilatory motor pattern frequency. Phase is calculated by dividing the time delay from the reference point (the start of the depressor burst) by the cycle period: phase=tev/Tcyc (see Materials and methods). These data are from a single experiment and each point is the mean ± S.D. for five cycles of the motor output; solid lines are the linear regressions for the data. The end of the levator burst (Lev End) and the start of the D2a burst (D2a Start) keep almost perfect phase over a 4.3-fold change in frequency, while the phase for the remaining points in the motor pattern shows a slight overcompensation as motor pattern frequency increases. The dashed line is the calculated phase of D2a Start if the time delay were to remain constant; that is, without phase compensation.

Fig. 3.

The ventilatory motor pattern maintains phase constancy over a large range of cycle frequencies. The phase of each motor pattern element is plotted against ventilatory motor pattern frequency. Phase is calculated by dividing the time delay from the reference point (the start of the depressor burst) by the cycle period: phase=tev/Tcyc (see Materials and methods). These data are from a single experiment and each point is the mean ± S.D. for five cycles of the motor output; solid lines are the linear regressions for the data. The end of the levator burst (Lev End) and the start of the D2a burst (D2a Start) keep almost perfect phase over a 4.3-fold change in frequency, while the phase for the remaining points in the motor pattern shows a slight overcompensation as motor pattern frequency increases. The dashed line is the calculated phase of D2a Start if the time delay were to remain constant; that is, without phase compensation.

Events in the motor pattern that maintained perfect phase constancy over this frequency range would produce a horizontal line (zero slope) with a value equal to the phase measured at the lowest cycle frequency. The phase of events that do not compensate for frequency changes, that is, where the time delay remains constant, would double as frequency doubles, and hence result in a line with a positive slope. This is illustrated by the dashed line in Fig. 3, which is a prediction of the expected phase for D2a Start if this event were to occur at a constant time delay after the start of the depressor burst. The slope of this line is tD2a Start/Tcyc, where the delay and cycle times are measured at the slowest rate of 0.65 Hz. Similar predictions would result for the other events in the ventilatory rhythm, except that the slope of each line would increase in proportion to the (increasing) initial time delays of the other events in the pattern. The slope of these lines would, therefore, be greater than that of the line shown for the D2a burst start time. Note that, for all of these pattern elements, in the absence of phase compensation, phases greater than 1 (and hence loss of 1:1 cycling with respect to the depressor start) would occur over the physiologically observed frequency range.

The phase of the levator burst end (Lev End) and the start of the D2a burst (D2a Start) exhibit the smallest decrease with cycle frequency (slopes of −0.007 Hz−1 and −0.012 Hz−1 respectively), which result in phase changes of −0.015 and −0.025 over the 4.3-fold frequency range. The slopes for the regressions of these data are not significantly different from zero (P>0.35), indicating that the phase of these events is constant over this frequency range. All of the other events in the ventilatory pattern exhibit phase overcompensation as frequency increases. That is, instead of remaining constant, as would be expected with perfect phase compensation, or increasing, as would be expected without compensation, their phase decreases as rhythm frequency increases. These events all have a modest phase decrease over the frequency range, with slopes ranging from −0.024 Hz−1 to −0.054 Hz−1, and all slopes are significantly different from zero at P<0.04 or better. The phase of the end of the depressor group 1 motor burst (Dep1 End) has the largest absolute change in phase (−0.13) over the tested frequency range. In an experiment where intracellular recordings were obtained from a Lev2 group motor neuron (data not shown), the phase of the Lev2 Start decreased at approximately the same rate as the Lev Start phase.

Phase versus cycle frequency data from seven preparations are presented in Fig. 4, which covers a sevenfold increase in ventilatory cycle frequencies from 0.5 to 3.4 Hz. These data illustrate two additional features of phase regulation in the crab ventilatory system. First, phase for all of the events is maintained to the same degree in all preparations; that is, the trends observed in the single experiment presented in Fig. 3 are preserved in the pooled data. For example, the levator burst ending phase (Lev End) and the depressor D2a motor neuron starting phase (D2a Start) remain relatively constant (slope −0.0021 Hz−1 and −0.0091 Hz−1 respectively) over the frequency range, and these slopes are not significantly different from zero (P>0.57 and P>0.32 respectively). The remaining events again show a significant and consistent decrease in phase as the frequency of the motor pattern increases (range of slopes −0.048 Hz−1 to −0.068 Hz−1; P<0.0l for all), indicating a phase overcompensation as frequency increases. The largest phase shift was again seen for the Dep1 motor burst ending (Dep1 End), with a total phase change of −0.12 over the entire frequency range. Second, the low scatter of the experimental points around the regression lines demonstrates that, at any given frequency, the phase of all events is very similar from preparation to preparation. This system thus not only maintains phase in a consistent manner from animal to animal, but the timing of the motor pattern is the same for all animals.

Fig. 4.

Phase constancy is maintained in all preparations. Data from seven preparations show that the trends observed in an individual experiment (Fig. 3) are also seen across different experiments. Each phase point is an average of five cycles of the motor output selected for intervals of relatively constant cycle frequency; standard deviation bars have been omitted for clarity. Phase for the levator burst end (Lev End) and D2a burst start (D2a Start) is almost constant over a sevenfold frequency range (0.5–3.4 Hz), whereas overcompensation is observed for the remaining events in the motor pattern; that is, phase decreases with increasing frequency. Note that there is very little difference in the absolute phase value for any of the events from preparation to preparation.

Fig. 4.

Phase constancy is maintained in all preparations. Data from seven preparations show that the trends observed in an individual experiment (Fig. 3) are also seen across different experiments. Each phase point is an average of five cycles of the motor output selected for intervals of relatively constant cycle frequency; standard deviation bars have been omitted for clarity. Phase for the levator burst end (Lev End) and D2a burst start (D2a Start) is almost constant over a sevenfold frequency range (0.5–3.4 Hz), whereas overcompensation is observed for the remaining events in the motor pattern; that is, phase decreases with increasing frequency. Note that there is very little difference in the absolute phase value for any of the events from preparation to preparation.

Burst durations and duty cycle

The phase measurements also provide a description of the relative burst durations (duty cycle) for each motor neuron group in the ventilatory pattern. If the regression lines for the starting and ending phases of any given motor burst are parallel, duty cycle (burst duration/cycle period) would remain constant; that is, the burst would occupy a constant percentage of the cycle period at any cycle frequency. For example, the starting and ending phases of the levator group one burst (Lev1) both decrease at similar rates (slopes −0.048 Hz−1 and −0.052 Hz−1) as frequency increases, and therefore the Lev1 burst duration maintains a relatively constant duty cycle. Motor neuron bursts whose starting and ending phase lines are not parallel do not maintain a constant duty cycle; divergence of these lines indicates an increasing duty cycle with increasing frequency, while converging lines indicate a decreasing duty cycle as frequency increases. The regression lines for the start (D2a Start) and end (Dep End) of the Dep2 burst in Fig. 4, for example, converge as frequency increases (slope −0.009 Hz−1 and −0.056 Hz−1 respectively), and hence the duty cycle of the Dep2 group decreases as cycle frequency increases. In contrast, the regression lines for the start (Lev Start) and end (Lev End) of the total levator burst diverge (slopes of −0.047 Hz−1 and −0.002 Hz−1 respectively), indicating an increase in duty cycle with increasing frequency.

The duty cycles for the five motor bursts that can be distinguished in extracellular recordings are shown in Fig. 5 as a function of cycle frequency. The duty cycle for each of the depressor groups and the overall depressor burst (Dep Start to Dep End) decreases as frequency increases. As already noted, the Lev1 group maintains a constant duty cycle, although the overall duty cycle of total levator activity (Lev Start to Lev End) increases as frequency increases. It was not possible to determine the duty cycle for the Lev2 burst, as the Lev2 start time cannot be determined accurately from extracellular recordings. At low cycle frequencies, the depressor burst occupies a larger percentage of the ventilatory cycle than the levator burst (70 % versus 35 %) with an overlap of approximately 5 % of the cycle period. The decrease in depressor burst duty cycle and concurrent increase in levator burst duty cycle with increasing frequency result in the duty cycle of the levator and depressor bursts both approaching 0.55 at the highest cycle frequency.

Fig. 5.

Changes in the duty cycle of the motor bursts with cycle frequency. At the lowest cycle frequency that the ventilatory central pattern generator will generate, the complete depressor burst has a duty cycle of approximately 0.73 while the levator burst has a duty cycle of approximately 0.37. With increasing frequency, the duty cycles of the depressor burst (Dep) and the two subsets for the depressor activity, the depressor group 1 bursts (Dep1) and the depressor group 2 bursts (Dep2), all decrease, with slopes of −0.059 Hz−1 for Dep, −0.068 Hz−1 for Dep1 and −0.047 Hz−1 for Dep2. The duty cycle for the levator group 1 burst (Lev1) remains constant (slope −0.00094 Hz−1; P>0.9) at all cycle frequencies, while the duty cycle of the total levator burst (Lev) increases with increasing frequency with a slope of 0.046 Hz−1.

Fig. 5.

Changes in the duty cycle of the motor bursts with cycle frequency. At the lowest cycle frequency that the ventilatory central pattern generator will generate, the complete depressor burst has a duty cycle of approximately 0.73 while the levator burst has a duty cycle of approximately 0.37. With increasing frequency, the duty cycles of the depressor burst (Dep) and the two subsets for the depressor activity, the depressor group 1 bursts (Dep1) and the depressor group 2 bursts (Dep2), all decrease, with slopes of −0.059 Hz−1 for Dep, −0.068 Hz−1 for Dep1 and −0.047 Hz−1 for Dep2. The duty cycle for the levator group 1 burst (Lev1) remains constant (slope −0.00094 Hz−1; P>0.9) at all cycle frequencies, while the duty cycle of the total levator burst (Lev) increases with increasing frequency with a slope of 0.046 Hz−1.

Time delays in the motor pattern

To appreciate fully the task that the ventilatory CPG must perform to maintain phase constancy, it is useful to consider a hypothetical example (Fig. 6). In the three-phase motor pattern shown here (Fig. 6A), neuron A defines the cycle period and is assumed to be a pacemaker cell that keeps a constant duty cycle as the period of the rhythm is altered. Neurons B and C fire in bursts after neuron A, but with different initial time delays after the start of the burst in neuron A. When the period of this rhythm is decreased to half of its initial value (a doubling of cycle frequency), to maintain phase constancy, the time delay from the reference point in the motor pattern (the start of the burst in A) must also decrease by half. This constraint also results in a proportional decrease in the duration of each burst period in the pattern as the cycle period decreases and, therefore, in a constant duty cycle for the motor bursts. Note that changing cycle period without phase compensation would disrupt the motor pattern. For instance, a decrease in the cycle period without concurrent changes in time delay would place the beginning of the burst in neuron B much later in the cycle, and the beginning of the burst in neuron C would fall outside the cycle period (the uncompensated positions for the start of these bursts are indicated by the arrowheads). The time delay, tev, required for perfect phase constancy for each neuron in the pattern is given by tev=(t0/T0)T, where t0 and T0 are the time delay and cycle period at the lowest (intrinsic) cycle frequency, respectively, and T is the new cycle period. Note that the slope (t0/T0) of this relationship is different for each neuron in the pattern, with the slope increasing as the initial time delay (and hence initial phase) from the reference point increases, but the y-intercept is zero in all cases (Fig. 6B). The slope of this relationship for an event that does not maintain perfect phase will not equal t0/T0, and the y-intercept will not be equal to zero; a slope of less than t0/T0 and a positive intercept denote an event that increases in phase as period decreases, while a slope greater than t0/T0 and a negative intercept indicate that the phase decreases with decreasing cycle period. The unfilled bursts for neuron B in Fig. 6A are examples of an instance where this neuron does not keep perfect phase, although the time delay does decrease with decreasing cycle period and there is a strong correlation between burst delay and cycle period (broken line, Fig. 6B).

Fig. 6.

Phase constancy requires proportional changes in the time delay as cycle period changes. (A) In order to maintain phase constancy in the three-phase motor pattern shown here, the time delay from the reference point (beginning of the burst in neuron A) must decrease in proportion to the decrease in cycle period. The arrowheads denote the expected time of occurrence of the bursts in neurons B and C if the time delays did not change as cycle period changed. Perfect phase constancy will result when the time delay to the event of interest (e.g. the beginning of the burst in neuron B) changes to t=(t0/T0)T, where t is the calculated delay required for perfect phase, t0 and T0 are the time delay and cycle period at the slowest rate, respectively, and T is the new cycle period. The unfilled bursts in the record for neuron B indicate an instance where the time delay for this neuron decreases with the decrease in cycle period, but by an amount less than that required for perfect phase maintenance. (B) The broken line on the graph is the relationship between time delay and period that results in this particular case. The solid lines are for the case where there is perfect phase maintenance. Note that the slope (t0/T0) of the perfect phase line is determined by the time delay at the longest cycle period, and therefore the slope of the perfect phase line for neuron C is greater than the slope of the perfect phase line for neuron B.

Fig. 6.

Phase constancy requires proportional changes in the time delay as cycle period changes. (A) In order to maintain phase constancy in the three-phase motor pattern shown here, the time delay from the reference point (beginning of the burst in neuron A) must decrease in proportion to the decrease in cycle period. The arrowheads denote the expected time of occurrence of the bursts in neurons B and C if the time delays did not change as cycle period changed. Perfect phase constancy will result when the time delay to the event of interest (e.g. the beginning of the burst in neuron B) changes to t=(t0/T0)T, where t is the calculated delay required for perfect phase, t0 and T0 are the time delay and cycle period at the slowest rate, respectively, and T is the new cycle period. The unfilled bursts in the record for neuron B indicate an instance where the time delay for this neuron decreases with the decrease in cycle period, but by an amount less than that required for perfect phase maintenance. (B) The broken line on the graph is the relationship between time delay and period that results in this particular case. The solid lines are for the case where there is perfect phase maintenance. Note that the slope (t0/T0) of the perfect phase line is determined by the time delay at the longest cycle period, and therefore the slope of the perfect phase line for neuron C is greater than the slope of the perfect phase line for neuron B.

The relatively constant phase versus cycle frequency relationships observed in the ventilatory system therefore indicate that large proportional changes in the time delays of each event occur as cycle period changes. Fig. 7 shows these time delays in the motor pattern as the ventilatory cycle period changes in a single experiment (these data are from the preparation shown in Fig. 3). Cycle period and time delay are highly correlated for all of the measured events in the ventilatory motor pattern. The correlation coefficients of the linear regressions (solid lines) to the data are all greater than 0.99 except for the D2a start delay, where r=0.945, and all slopes are significantly different from zero at P<0.04 or better. More importantly with respect to phase maintenance, the differences between the slope of the regression and the slope of the line calculated for perfect phase maintenance (dashed lines) are extremely small. This close agreement between experimental and predicted results is expected given the modest changes in phase for each event seen in Fig. 3. The smallest time delay change is seen in the D2a burst start time, which decreases by 240 ms, whereas perfect phase maintenance would require a decrease of 225 ms. The time delay to the end of the levator burst decreases by the largest amount, 1220 ms, as this event has the longest initial delay from the start of the depressor burst, while a decrease of 1225 ms would be required in order to maintain perfect phase. The difference between ideal and measured time delays is very small for these two events, as they maintain the most constant phase (see Fig. 4). Note that, even for the event that has the largest deviation from constant phase (Dep1 End), the difference between the ideal time delay for constant phase at the smallest cycle period (182 ms) and the actual time delay (136 ms) is still rather small and is only 7 % of the total (ideal) change in time delay required for this event.

Fig. 7.

Large changes in time delays are required to maintain phase constancy in the ventilatory motor pattern. Time delays for each of the readily identifiable points in the ventilatory motor pattern are plotted with respect to cycle period. Data from a single experimental preparation (same as that shown in Fig. 3) that produced a fourfold increase in cycle frequency. Linear regressions (solid lines) for the data show that the measured changes in time delay are close to the ideal time delay required for maintenance of perfect phase. The ideal slopes were calculated from the average time delay and period during five cycles of the slowest (unstimulated) ventilatory rhythm. Note that the smallest change in time delay is for the D2a burst start time (D2a Start), which decreases by 240 ms, while the delay to the levator burst end (Lev End) decreases by 1220 ms over the range of cycle periods (365–1570 ms) observed in this preparation. The dashed lines indicate the calculated change in time delay required for each event in order to maintain a constant phase as cycle period changes.

Fig. 7.

Large changes in time delays are required to maintain phase constancy in the ventilatory motor pattern. Time delays for each of the readily identifiable points in the ventilatory motor pattern are plotted with respect to cycle period. Data from a single experimental preparation (same as that shown in Fig. 3) that produced a fourfold increase in cycle frequency. Linear regressions (solid lines) for the data show that the measured changes in time delay are close to the ideal time delay required for maintenance of perfect phase. The ideal slopes were calculated from the average time delay and period during five cycles of the slowest (unstimulated) ventilatory rhythm. Note that the smallest change in time delay is for the D2a burst start time (D2a Start), which decreases by 240 ms, while the delay to the levator burst end (Lev End) decreases by 1220 ms over the range of cycle periods (365–1570 ms) observed in this preparation. The dashed lines indicate the calculated change in time delay required for each event in order to maintain a constant phase as cycle period changes.

Pooled data from the same seven experiments shown in Fig. 4 are presented in Fig. 8. Again, the slopes of the time delay versus cycle period relationships are significantly different from zero (P<0.001) and highly correlated: all the correlation coefficients are greater than 0.99 except for the D2a start delay, where r=0.93. Over the larger range of cycle periods shown for the pooled data (300–2100 ms), the magnitudes of the time delay changes required for phase maintenance are also increased. The delay for the D2a start time decreases by 470 ms from the longest to the shortest period observed, while the delay to the end of the levator burst decreases by approximately 1800 ms over the same range of cycle periods.

Fig. 8.

Time delays for pooled experimental data from seven experiments spanning a sevenfold range of cycle frequency. The time delay changes observed in the single experiment presented in Fig. 7 are maintained when data from multiple preparations are combined. The variation in time delay is highly correlated with cycle period (r>0.93 for all) over the range 300–1200 ms. The time delay to D2a Start requires the smallest change with cycle period (470 ms) as this is the first event after the start of the depressor burst which was used as the motor pattern reference point. The largest change in time delay (1800 ms) occurs for the time to the end of the levator burst, Lev End.

Fig. 8.

Time delays for pooled experimental data from seven experiments spanning a sevenfold range of cycle frequency. The time delay changes observed in the single experiment presented in Fig. 7 are maintained when data from multiple preparations are combined. The variation in time delay is highly correlated with cycle period (r>0.93 for all) over the range 300–1200 ms. The time delay to D2a Start requires the smallest change with cycle period (470 ms) as this is the first event after the start of the depressor burst which was used as the motor pattern reference point. The largest change in time delay (1800 ms) occurs for the time to the end of the levator burst, Lev End.

Intracellular correlates of phase maintenance

The mechanisms that maintain phase relationships in the ventilatory CPG output must reside in the network interactions of the CPG and/or the intrinsic membrane properties of the neurons that constitute this CPG. Unfortunately, we do not possess a detailed circuit for the ventilatory CPG or sufficient data regarding the membrane properties of most of the ventilatory neurons to allow a definitive determination of the mechanisms that underlie phase maintenance in this system. However, inspection of intracellular recordings from ventilatory motor neurons and interneurons does give some insight into the possible location of these mechanisms. Fig. 9 presents intracellular recordings from two motor neurons and two nonspiking interneurons in the ventilatory CPG at different cycle frequencies. The motor neurons that drive the ventilatory muscle have been found to exhibit plateau properties when the CPG is active (DiCaprio, 1993). Fig. 9A is an intracellular recording from a Dep1 group motor neuron at four different cycle periods (0.9, 0.76, 0.54 and 0.44 s) with the traces aligned at the beginning of the burst. There is no difference in the initial slope of the depolarizing phase of the membrane potential oscillation in this neuron, although there is a slight, but significant, change in slope (P<0.03) during the hyperpolarizing phase, with the slope decreasing as cycle period increases. The underlying membrane potential oscillation of a Lev1 motor neuron (Fig. 9B) at four different cycle periods (1.5, 1.25, 1.16 and 0.88 s) is also essentially constant as the period of the rhythm decreases. In both cases, the voltage threshold for spike initiation in the neurons remains constant during changes in cycle period. These recordings indicate that the motor neurons function as bistable elements in that the kinetics of their plateau potential transitions are constant as cycle frequency changes and, hence, changes in their membrane properties are unlikely to play a major role in motor pattern phase maintenance.

Fig. 9.

Intracellular recordings from ventilatory motor neurons and interneurons as ventilatory cycle period changes. A Dep1 group motor neuron (A) is shown at four different cycle periods (0.9, 0.76, 0.54 and 0.44 s) and a Lev1 motor neuron (B) at four different cycle periods (1.5, 1.25, 1.16 and 0.88 s). The membrane potential oscillations of these motor neurons exhibit very little variability as cycle period decreases. Note, however, that the slope of the repolarizing phase of the Dep1 motor neuron decreases as cycle period increases. Intracellular recordings from nonspiking interneurons CPGi6 (C) at cycle periods of 1.65, 1.25, 1.05 and 0.96 s are aligned on the hyperpolarizing phase of the membrane potential oscillation. Interneuron CPGi8 (D) is shown at three cycle periods 1.56, 1.0 and 0.64 s, again aligned on the hyperpolarizing phase of the membrane potential oscillation. Both interneurons have almost uniform membrane potential trajectories during the hyperpolarizing phase of their oscillation, but the slope of the depolarizing phase decreases in proportion to the increase in cycle period. The scaling of membrane potential trajectory with cycle period is demonstrated to the right of each record, where a recording at the shortest cycle period is superimposed on a recording at the longest cycle period after it had been graphically stretched (1.7× for CPGi6 and 2.4× for CPGi8) to fit the longer cycle period. The numbers adjacent to the record of CPGi6 refer to the three different rates of change in the membrane potential observed as this neuron depolarizes.

Fig. 9.

Intracellular recordings from ventilatory motor neurons and interneurons as ventilatory cycle period changes. A Dep1 group motor neuron (A) is shown at four different cycle periods (0.9, 0.76, 0.54 and 0.44 s) and a Lev1 motor neuron (B) at four different cycle periods (1.5, 1.25, 1.16 and 0.88 s). The membrane potential oscillations of these motor neurons exhibit very little variability as cycle period decreases. Note, however, that the slope of the repolarizing phase of the Dep1 motor neuron decreases as cycle period increases. Intracellular recordings from nonspiking interneurons CPGi6 (C) at cycle periods of 1.65, 1.25, 1.05 and 0.96 s are aligned on the hyperpolarizing phase of the membrane potential oscillation. Interneuron CPGi8 (D) is shown at three cycle periods 1.56, 1.0 and 0.64 s, again aligned on the hyperpolarizing phase of the membrane potential oscillation. Both interneurons have almost uniform membrane potential trajectories during the hyperpolarizing phase of their oscillation, but the slope of the depolarizing phase decreases in proportion to the increase in cycle period. The scaling of membrane potential trajectory with cycle period is demonstrated to the right of each record, where a recording at the shortest cycle period is superimposed on a recording at the longest cycle period after it had been graphically stretched (1.7× for CPGi6 and 2.4× for CPGi8) to fit the longer cycle period. The numbers adjacent to the record of CPGi6 refer to the three different rates of change in the membrane potential observed as this neuron depolarizes.

The ventilatory interneurons, however, exhibit much larger changes in their membrane potential trajectories as cycle frequency changes. Fig. 9C,D presents intracellular recordings from interneuron CPGi6 at four different cycle periods (1.65, 1.25, 1.05 and 0.96 s) and interneuron CPGi8 at three cycle periods (1.56, 1.0 and 0.64 s) that are aligned on the hyperpolarizing phase of their membrane potential oscillation.

Both interneurons have almost uniform membrane potential trajectories during the hyperpolarizing phase of their oscillation, but the slope of the depolarizing phase increases in proportion to the increase in cycle frequency. The depolarizing phase of the membrane potential oscillation in interneuron CPGi6 has several inflection points before the neuron reaches its maximum depolarized level. The slopes of the first two depolarizations (Fig. 9C, regions 1 and 2) are correlated (r>0.9) with cycle frequency and the change in slope is significant (P<0.05), while the slopes of the final depolarizing phase (Fig. 9C, region 3) are not significantly different (P>0.63). The depolarizing phase of the membrane potential oscillation of CPGi8 also has at least two inflection points, but these are rather difficult to discern as the cycle frequency increases. If the slope of the depolarization is measured from the point where the cell starts to depolarize to the point of maximum depolarization, the slopes are correlated (r=0.99) with cycle frequency and the change in slope is significant (P<0.01). As has been noted previously with respect to changes in time delay, the mere correlation between these slopes and cycle frequency does not provide evidence that these parameters are changing in exact proportion to the change in cycle frequency.

To determine whether the membrane potential oscillation of the interneurons is scaled with respect to cycle frequency, the membrane potential waveforms are compared at two different cycle frequencies after adjusting the time scale of the higher-frequency oscillation (right-hand panels of Fig. 9C,D). One oscillation cycle at the highest cycle frequency has been superimposed over one cycle at the lowest frequency after the high-frequency record has been graphically stretched (1.7× for CPGi6 and 2.4× for CPGi8) to match the cycle period at the lower frequency. The membrane potential oscillations and their amplitudes are extremely similar when scaled to the same time base. It would therefore appear that the membrane potential trajectory of these interneurons changes in almost exact proportion to the change in cycle frequency, which is consistent with the hypothesis that the changes in motor pattern timing occur at the level of the interneurons.

In Young’s (1975) comprehensive description of the ventilatory musculature and motor pattern in Carcinus maenas, he stated that the motor pattern was phase-constant. This conclusion was based on the observed strong positive correlation of both burst latency (time delay) and burst duration with ventilatory cycle period. However, a correlation between time delay and cycle period does not provide sufficient data to conclude that phase is constant in a motor pattern. Such phase constancy requires that time delays change in exact proportion to the change in cycle period rather than simply correlate with period. For example, if the cycle period (T0) of a motor pattern decreases to half of its initial value (0.5T0), and all of the time delays (t0) decrease by the same factor (0.5 t0), then:
formula
phase = t0/T0 = 0.5t0/0.5T0, (1) will remain constant. If, however, latencies change by a different factor (e.g. 0.7), the slope of the time delay versus cycle period relationship:
formula
will be different from the value required for perfect phase maintenance (slope = t0/T0 = initial phase at the longest cycle period, T0) and the y-intercept will not be equal to zero. The time delays for such events will still be perfectly correlated with cycle period, but the phase of each event in the pattern will vary as period changes (see Fig. 6). Likewise, a perfect correlation between burst duration and cycle period will exist when a motor pattern is phase-constant, but such a correlation does not, in and of itself, denote phase constancy. For example, if cycle period changes by a factor of 0.5, but the time delay for the starting time of a burst changes by a different factor, burst duration will still correlate with cycle period, but the (starting) phase of the burst will shift with the change in period. Young’s analysis only used correlation, rather than the direct determination of phase that is required in order to demonstrate phase constancy and, as such, does not demonstrate that the ventilatory motor pattern is phase-constant.

The data presented here demonstrate that the isolated ventilatory CPG of the shore crab maintains a high degree of phase constancy over a large range of cycle frequencies. Phase measurements using pooled experimental data show that the phase of two of the events in the pattern, Lev End and D2a Start, remains constant over a sevenfold increase in cycle frequency, with changes of only −0.0021 Hz−1 and −0.0091 Hz−1, respectively, and these slopes are not significantly different from zero. The remaining five points in the motor pattern that were examined exhibit a decrease in phase (slopes range from −0.052 Hz−1 to −0.068 Hz−1; P<0.01) over the same frequency range and are therefore overcompensated for changes in cycle frequency. These results are consistent from preparation to preparation, as shown by the relatively small scatter of the points around the regression line. Furthermore, the phase of any of the measured events at any given cycle frequency is approximately the same in all experiments. This motor pattern is therefore extremely similar in all animals; that is, there is very little animal-specific variation in phase, in contrast to the data obtained in other systems (Hooper, 1997a,b).

Two subgroups can be distinguished within the motor pattern with respect to phase maintenance. First, Dep1 Start, Lev End and D2a Start phases remain essentially constant with respect to each other as cycle frequency increases. These three events therefore constitute a phase-maintaining subgroup within the ventilatory motor pattern. Second, the phase of the remaining events, Lev Start, Lev1 End, Dep End, Dep1 End and D2a End, all decrease with respect to the Dep Start reference as cycle frequency increases. Given the similar slopes of the phase versus frequency relationship for these five events (range −0.068 Hz−1 to −0.048 Hz−1), they therefore constitute another phase-maintaining subgroup. Limited intracellular recordings from Lev2 group motor neurons indicate that the start of this burst may also maintain phase within the second subgroup.

Time delay, duty cycle and motor pattern

The relatively constant phase relationships observed in the ventilatory motor pattern result from a change in the time delay of each of the events in the motor pattern as the cycle period of the rhythm varies. As expected, the time delay change for each measured event is very close to the value needed for perfect phase maintenance (Figs 7, 8). Given the sevenfold range of cycle period (300–2100 ms) observed in these experiments, the maximum changes in time delay are quite large, ranging from 470 ms for the D2a start time to 1800 ms for the levator burst end time. Although the deviations from the changes in time delay required for perfect phase maintenance are small in the context of the large changes that are observed, the effect of this difference becomes more pronounced with respect to motor pattern phase as the deviation from ideal delay becomes a larger percentage of the cycle period as frequency increases.

The segregation of the start and end times of the various motor bursts into different phase-maintaining subgroups results in the duty cycle of all but the levator group 1 burst varying with cycle frequency. At low cycle frequencies (approximately 0.6 Hz) the total depressor burst occupies approximately 75 % of the cycle period while the total levator burst lasts for approximately 35 % of the cycle, with a 5 % overlap. As cycle frequency increases, levator duty cycle increases and depressor duty cycle decreases while the overlap remains relatively constant, resulting in approximately equal duty cycles for the levators and depressors at high cycle frequencies (approximately 3.5 Hz). The significance of these changes in duty cycle are impossible to assess without a more thorough understanding of the biomechanics and hydrodynamics of the ventilatory pump.

Changes in relative timing in a motor pattern may be caused by changes in the strength of synaptic excitation or inhibition to neurons in a CPG or by changes in the intrinsic membrane properties of the neurons in the network. For example, Eisen and Marder (1984) demonstrated in the pyloric motor pattern of the lobster stomatogastric system, that PY motor neuron firing could be phase-advanced or phase-retarded by changes in the burst amplitude of the presynaptic PD neurons, which provide chemically mediated synaptic inhibition of the PY neuron. Changes in phase relationships can also be caused by altering the strength of electrical synaptic coupling between pairs of neurons (Sharp et al. 1992) or, in a model system with both electrical and chemical synaptic interactions, by varying the relative strength of the two synapses (Mulloney et al. 1981).

Alternatively, intrinsic membrane properties such as post-inhibitory rebound and plateau potentials can also cause changes in time delays in rhythmic motor patterns. Hooper (1993, 1994) has shown that changing either the amplitude or the temporal characteristics of rhythmic hyperpolarizing current injections can alter rebound firing delays in neurons of the pyloric system. Neuromodulators can also effect phase changes by modifying intrinsic membrane properties. Dopamine, for example, causes an increase in the rate of post-inhibitory rebound, and therefore a phase advance of the PY neuron in the pyloric motor pattern, by decreasing the amplitude of the transient potassium current IA (Harris-Warrick et al. 1995a). In this system, dopamine can also phase-advance the LP neuron by reducing IA and by shifting the voltage-dependence of the hyperpolarization-activated inward current Ih (Harris-Warrick et al. 1995b).

Intracellular correlates of phase maintenance

It is difficult to speculate on the mechanisms that underlie the changes in time delays and the resultant phase compensation observed in this system, because of a lack of detailed information about the intrinsic cellular and/or synaptic properties of the neurons in the ventilatory CPG. However, it does not appear that the plateau properties (DiCaprio, 1993) of the motor neurons play a large role in these changes, as the transition time between their hyperpolarized and depolarized states does not change with cycle frequency. The timing of the motor neuron bursts is presumably determined instead by the timing of the excitatory and inhibitory inputs that they receive from the nonspiking interneurons in the CPG.

In contrast, the rate of change of membrane potential in these interneurons does change with cycle frequency, and these changes are proportional to the change in frequency. Although similar data are not available for all eight CPG interneurons, especially over the large frequency range used in this study, the limited data are consistent with the hypothesis that the interneurons are the principal determinants of phase compensation in this system. These changes are presumably due to the kinetics of the intrinsic membrane properties of these neurons, but insufficient information about the conductances present in these neurons is available to allow speculation about the role of these properties in phase regulation.

Given that the interneurons in the ventilatory CPG are all nonspiking (DiCaprio, 1989), it is difficult to determine the phase of these cells in the motor pattern without a knowledge of transmitter release thresholds for each neuron. In fact, the depolarizing phase of the membrane potential oscillation of these neurons typically overlaps the start and end times of different events, or different groups, in the motor pattern and therefore cannot be simply associated with discrete motor bursts. For example, the depolarized phase of interneuron CPGi6 (Fig. 9C) occurs near the end of the depressor burst and continues until the end of the Lev1 group burst; CPGi8 remains relatively depolarized during the entire levator burst.

However, the frequency-dependent change in slope of the membrane potential trajectories results in an increase in the amount of time that these interneurons spend in transition from their minimum to maximum membrane potentials. As the typical maximum hyperpolarized level of the nonspiking interneurons is in the range −60 to −50 mV, with peak-to-peak amplitude ranging from 15 to 45 mV, the interneurons may be subthreshold for transmitter release for a longer time as cycle period increases. Effective synaptic input to other interneurons will, therefore, be delayed in addition to the delay of any inputs that trigger or terminate the plateau-potential-mediated bursts in the motor neurons. In the event that these interneurons are continuously releasing transmitter or interact via electrical synapses, the change in the slope of the membrane potential of these neurons could still serve to alter the timing of the interactions between neurons in the CPG on the basis of their graded interactions.

Necessity for phase compensation in gill ventilation

Maintenance of motor pattern phase during changes in the ventilatory cycle period is required to preserve the relative timing of motor activity and to ensure that individual components of the pattern are expressed during each cycle. The ventilatory motor pattern not only satisfies this minimum requirement, but the phase of the two events is essentially constant as cycle period changes. In addition, although the phase of the remaining events in the pattern does change (decrease) with cycle period, these changes reflect an overcompensation for the change in cycle period. In contrast to various locomotor systems where the return stroke phase in the motor pattern remains relatively constant, the ventilatory CPG does work during both the levation and depression portions of the cycle. Phase constancy may therefore be a functional requirement of the crab ventilatory system because of the biomechanical constraints of the SG pumping action. The anterior and posterior tips of the SG spend most of the ventilatory cycle in their maximum levated or depressed position, with fast coordinated antiphase transitions between the two extremes of movement (Young, 1975). The transition period for each of these movements lasts for approximately 10 % of the total ventilatory cycle, and the transitions occur at the Lev End to Dep Start phase and the Dep End to Lev Start phase. Note that the relative phase of the Lev End to Dep Start transition is constant with increasing cycle frequency, and the relative phase between Dep End and Lev Start only varies slightly as frequency increases over a sevenfold range (Fig. 4). In the time between these transitions, the blade of the SG sweeps across the pumping chamber, simultaneously expelling water through the exhalant channel and drawing water into the branchial chamber. The SG thus pumps water during both half-cycles of the motor pattern, generating two negative pressure pulses per cycle (Hughes et al. 1969). The inhalant and exhalant channels are open simultaneously during the rapid transitions of the blade tips for approximately 10 % of the cycle period in each half-cycle. The brief opening of both channels ensures that the negative pressure in the branchial chamber does not drop markedly during the ventilatory cycle and hence minimizes possible back-flow through the system.

The strict phase relationships in the ventilatory motor pattern may therefore serve two purposes. First, the tight phasing of the motor pattern at the time of the blade-tip transitions causes one tip to start its transition immediately after the opposite tip has reached its maximum levated or depressed position, which will maximize the expelled volume of fluid and minimize the time that both tips are in the same (levated or depressed) position. Second, the maintenance of phase during the remainder of the motor pattern may serve to produce a smooth, coordinated movement of the blade as it pumps water through the system. Any discontinuity in SG movement might disrupt the flow of water through the pumping chamber, thereby decreasing the efficiency of the pump. It is also interesting to note that ventilation volume and branchial pressure gradient both increase in exact proportion to the increase in ventilation frequency, while SG stroke volume remains constant as cycle frequency increases (Mercier and Wilkens, 1984). In addition, the efficiency of the ventilatory pump remains constant at approximately 85 % over a wide range of ventilatory cycle frequencies (Wilkens et al. 1984). It is possible that the relationship between these ventilatory parameters and ventilation frequency may be dependent on constant motor pattern phase.

We would like to thank Dr Scott Hooper for his extremely valuable advice and discussions throughout the course of this work, Dr Joffre Mercier for clarification of the ventilatory mechanics in Carcinus maenas and Dr Eve Marder for calling our bluff regarding phase regulation in this system. This work was supported by a grant from the Whitehall Foundation (R.A.D.), the Ohio University College of Osteopathic Medicine and a College of Osteopathic Medicine Summer Research Fellowship to G.J. and T.H.

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