1. The dynamic properties of the intrasegmental swimmeret reflexes of the lobster Homarus americanas were studied by recording the discharge of the motor neurones while the swimmeret was moved sinusoidally in its natural arc over a wide range of frequencies.

  2. The reflex responses of the excitor neurones of both powerstroke (retractor) and returnstroke (protractor) muscles display hysteresis. In both cases the efferent response corresponding to a given limb position is usually greater during imposed retraction than during protraction.

  3. The cyclic efferent reflex response follows the sinusoidal movement stimulus at movement frequencies up to and beyond those which occur naturally during swimmeret beating, with no change in the position of maximum reflex activity in the cycle. The reflexes are therefore capable of influencing the motor output on a cycle-by-cycle basis.

  4. The strength of the reflex response is maximum between 1 and 3 Hz. of imposed movement, and declines to either side of this range. The dynamic properties of the reflexes are therefore adjusted so that the maximum amplification of the rhythmic central motor command occurs at the natural frequency of swimmeret beating.

The intrasegmental reflexes in the swimmeret system of the lobster were described in the preceding paper (Davis, 1969 b). It was shown that these reflexes are incapable of directly initiating and/or sustaining the cyclic pattern of neuronal discharge which underlies swimmeret beating, and that, instead, the reflexes act to strengthen several features of the motor output pattern which are already programmed into the central nervous motor score. On this basis it was argued that the intrasegmental reflexes act as simple ‘amplifiers’ for mechanisms which are endogenous to the CNS.

If the swimmeret reflexes are to play their postulated role as amplifiers, the time constant of the reflex response must be small compared to the duration of a normal cycle of movement. Some locomotory reflexes are indeed organized in this fashion (e.g. Wilson, 1965). In the flight system of the locust, on the other hand, stretch receptors located in the wings provide rhythmic feedback in phase with the rapid wing movements, but the reflex initiated by this feedback responds with a relatively slow time constant of one or two seconds. Thus, the phasic information contained in the feedback is lost in the conversion to the motor output. The reflex effect is instead distributed over many wing-beat cycles to regulate the average frequency and amplitude of the wing movements (Wilson & Gettrup, 1963 ; Wilson & Wyman, 1965).

The present paper describes the dynamic responses of the intrasegmental swimmeret reflexes to sinusoidal movements of the limb. It is shown that the reflex response can follow limb movements as rapid as those which normally occur during swimmeret beating in the intact lobster, i.e. one to three Hz., and that the dynamic properties of the reflexes are in fact finely ‘tuned’ to the natural movement frequency of the appendage.

The general methods are described in the preceding paper (Davis, 1969 b). In the present work, several parameters of the reflex response to a sinusoidal stimulus were computed and are described in the appropriate sections of the results. All computations were performed with an IBM/360 digital computer, which was additionally programmed to print the resulting graphs and histograms. The computer programme, written in E level Fortran IV by Dr F. Delcomyn, can be obtained through the SHARE contributed programme library maintained by IBM (Delcomyn & Davis, 1969).

A typical experiment consisted of several records, each showing the reflex response of the swimmeret motor neurones to a different frequency of imposed sinusoidal movement of the swimmeret (Fig. 1). Records which were analysed contained from 4 to 42 cycles of imposed movement, depending upon the movement frequency.

Fig. 1.

A series of records showing the response of the excitor neurones which innervate the main powerstroke muscle (muscle 4−8 ; Davis, 1968 b, 1969 b) during imposed sinusoidal movement of the swimmeret in its natural arc. Upward deflexion of the movement trace corresponds to retraction of the swimmeret. Time scale, one second for (a) and (b), 500 msec, for (c), (d) and (e).

Fig. 1.

A series of records showing the response of the excitor neurones which innervate the main powerstroke muscle (muscle 4−8 ; Davis, 1968 b, 1969 b) during imposed sinusoidal movement of the swimmeret in its natural arc. Upward deflexion of the movement trace corresponds to retraction of the swimmeret. Time scale, one second for (a) and (b), 500 msec, for (c), (d) and (e).

Position of reflex discharge in the movement cycle

In several experiments the mean phase position of efferent impulses in the movement cycle was computed for each record. The records comprising each experiment represented a wide spectrum of imposed movement frequencies, 0·1−1·0 Hz. The means of the spike phase positions for several such experiments are summarized in the histograms of Fig. 2. As expected from the reflex responses to stepwise movements of the swimmeret (Davis, 1969 b), the means are grouped around the position of maximum retraction of the swimmeret.

Fig. 2.

Mean value per record of phase positions of spikes in the imposed sinusoidal movement cycle (deg.)

Histograms of the mean phase positions of spikes in the sinusoidal movement cycle. Each observation is the mean value computed from a single record in which the movement frequency was held constant (average record length, approx. 125 spikes). A wide spectrum of movement frequencies is represented. 0°−180° corresponds to protraction of the swimmeret, 180°−360° to retraction, (a) the response of excitor neurones which innervate the main powerstroke muscle; (b) the response of returnstroke excitor neurones.

Fig. 2.

Mean value per record of phase positions of spikes in the imposed sinusoidal movement cycle (deg.)

Histograms of the mean phase positions of spikes in the sinusoidal movement cycle. Each observation is the mean value computed from a single record in which the movement frequency was held constant (average record length, approx. 125 spikes). A wide spectrum of movement frequencies is represented. 0°−180° corresponds to protraction of the swimmeret, 180°−360° to retraction, (a) the response of excitor neurones which innervate the main powerstroke muscle; (b) the response of returnstroke excitor neurones.

In order to see whether the position of maximum reflex discharge was related to the frequency of the imposed movement, several experiments on both powerstroke and returnstroke motor neurones were analysed by preparing graphs of the mean spikephase position in each record against the movement frequency during the record. The reflex activity of both powerstroke and returnstroke excitor neurones occasionally showed a weak advance or a progressive lag as the movement frequency was increased, but opposite effects were sometimes obtained in consecutive experiments. Moreover, within individual experiments there was usually no consistent relation between mean spike phase position and the movement frequency. A similar independence between the phase position of the reflex discharge and the frequency of the imposed movement has been described for the walking legs of cockroaches (Wilson, 1965).

Reflex hysteresis

During sinusoidal movement of the swimmeret the most intense discharge within each cycle occurred at the position of maximum retraction of the limb. Reflex activity in both powerstroke and returnstroke motor neurones was usually distributed over a large segment of the movement cycle, however. The reflex discharge typically commenced at the mid-point of the retraction phase, and ended at the mid-point of protraction (e.g. Fig. 1). The intensity of the discharge associated with a given limb position was greater, however, when the position was approached by retraction rather than by protraction. That is, the reflex response of the swimmeret motor neurones to sinusoidal limb movement displayed hysteresis. This hysteresis is reflected in the asymmetry of the histograms of the mean spike phase positions (Fig. 2). More values fall between 180 °and 360 ° (the retraction phase) than between o° and 180 ° (the protraction phase). The hysteresis appeared in the reflex response of both powerstroke and returnstroke motor neurones (Figs. 2, 3, 4) and was usually present over the full range of movement frequencies in which grouped efferent impulses could be elicited.

Fig. 3.

(a) graph of the duration of interspike intervals within a single record against the phase position of the mid-point of the interval in the movement cycle. The data are from powerstroke excitor neurones and were taken from 12 consecutive cycles of movement. A segment of the record analysed is shown in Fig. 1 (b). 0°−180° corresponds to protraction of the swimmeret, 180°−360° to retraction, n = the number of observations, low = the phase position of the low point on a sine curve fitted to the data and corresponds to the average position of the most intense reflex discharge in the movement cycle, and r = the correlation coefficient between the value of the duration of each inter-spike interval and the corresponding value on the sine curve fitted to the data. The magnitude of r is a measure of the strength of the grouping of efferent impulses within the movement cycle (see text). Congruent points are shown as one point, (b), histogram of the phase positions of efferent impulses in the movement cycle for the same data as in (a). The asymmetry of the histogram is caused by the hysteresis in the reflex response (see text).

Fig. 3.

(a) graph of the duration of interspike intervals within a single record against the phase position of the mid-point of the interval in the movement cycle. The data are from powerstroke excitor neurones and were taken from 12 consecutive cycles of movement. A segment of the record analysed is shown in Fig. 1 (b). 0°−180° corresponds to protraction of the swimmeret, 180°−360° to retraction, n = the number of observations, low = the phase position of the low point on a sine curve fitted to the data and corresponds to the average position of the most intense reflex discharge in the movement cycle, and r = the correlation coefficient between the value of the duration of each inter-spike interval and the corresponding value on the sine curve fitted to the data. The magnitude of r is a measure of the strength of the grouping of efferent impulses within the movement cycle (see text). Congruent points are shown as one point, (b), histogram of the phase positions of efferent impulses in the movement cycle for the same data as in (a). The asymmetry of the histogram is caused by the hysteresis in the reflex response (see text).

Fig. 4.

Graph and histogram similar to those in Fig. 3, for data from the excitor neurons which innervate the main returnstroke muscle (muscle 1−3; Davis, 1968b).

Fig. 4.

Graph and histogram similar to those in Fig. 3, for data from the excitor neurons which innervate the main returnstroke muscle (muscle 1−3; Davis, 1968b).

Reflex strength

In several experiments various indices of reflex strength were computed for a wide range of sinusoidal movement frequencies. These indices were plotted against the frequency of the imposed movement for a quantitative description of the dynamic properties of the swimmeret reflexes. Three measures of reflex strength during a sinusoidal input have been used: (1) the average number of efferent impulses per cycle of imposed movement; (2) the average frequency of the impulses; and (3) the degree to which the impulses were non-randomly grouped within the movement cycle. The degree of impulse grouping was determined by first plotting the duration of the interval between efferent impulses against the phase position of the mid-point of the interval in the sinusoidal input cycle. Graphs of this kind are shown in Figs. 3 a, 4a. A sine curve of the form
was then fitted to the data, using the method of least squares to optimize the fit. Finally, the product moment correlation coefficient was computed between the real duration of each inter-spike interval and the corresponding value on the fitted sine curve. If the efferent spikes were positioned at random in the input cycle, then the amplitude of the fitted sine curve approached zero, i.e. the curve approximated a straight line with zero slope. In this case the correlation coefficient between real points and the corresponding points on the fitted curve approached zero. If, on the other hand, the distribution of efferent spikes was strongly related to the sinusoidal input, then the amplitude of the fitted sine curve was large and the resulting correlation coefficient approached its maximum possible value, + 1·00. Thus, the computational method yielded correlation coefficients between zero and +1·00, whose magnitude was a sensitive index of the grouping of efferent impulses in the sinusoidal input cycle.

The three parameters described above were computed for several experiments on both powerstroke and returnstroke motor neurone reflexes. The results of these experiments were nearly identical and are illustrated by the typical case shown in Figs. 5−7 

Fig. 5.

Semi-log plots of the mean number of efferent impulses per movement cycle against the frequency of the imposed sinusoidal movement of the swimmeret. Each point represents the mean value calculated from a single record in which the frequency of the imposed limb movement was held constant. The number adjacent to each point shows the number of spikes used in deriving the mean. The eight individual records used in making this graph were taken in a random sequence from one preparation in a period of a few minutes.

Fig. 5.

Semi-log plots of the mean number of efferent impulses per movement cycle against the frequency of the imposed sinusoidal movement of the swimmeret. Each point represents the mean value calculated from a single record in which the frequency of the imposed limb movement was held constant. The number adjacent to each point shows the number of spikes used in deriving the mean. The eight individual records used in making this graph were taken in a random sequence from one preparation in a period of a few minutes.

As the frequency of imposed sinusoidal movement of the swimmeret was increased, the number of efferent impulses per movement cycle decreased monotonically (Fig. 5), while the average impulse frequency increased (Fig. 6). The curve relating the strength of the grouping of efferent impulses in the movement cycle to the frequency of imposed movement, however, was approximately bell-shaped, with the maximum value between 1 and 3 Hz. of imposed movement. Thus, the grouping of reflex motor impulses was strongest at that frequency of imposed movement which corresponds to the most commonly encountered frequency of swimmeret beating in the intact lobster (Davis, 1968a).

Fig. 6.

Semi-log plot of the mean interspike interval per record against the frequency of the imposed sinusoidal movement of the swimmeret. The data were taken from the same records as in Fig. 5. Each point again represents the mean value calculated from a single record in which the frequency of the imposed movement was held constant. The number beside each point shows the number of inter-spike intervals in the record.

Fig. 6.

Semi-log plot of the mean interspike interval per record against the frequency of the imposed sinusoidal movement of the swimmeret. The data were taken from the same records as in Fig. 5. Each point again represents the mean value calculated from a single record in which the frequency of the imposed movement was held constant. The number beside each point shows the number of inter-spike intervals in the record.

The proprioceptors which probably provide the sensory inputs for the swimmeret reflexes insert next to the insertions of some of the muscles which cause the swimmeret movements (Davis, 1968b, 1969b). In the intact lobster the sensory feedback from these receptors may therefore contain information about both limb position and muscle contraction. In the present experiments, however, the tension response of the muscles usually deteriorated long before the reflex activity of the motor neurones. Many of the experiments were therefore performed in the complete absence of muscular contraction. Even when the tension response was strong, the normal sequence of muscular contraction did not occur, since the central oscillators were inactive. Furthermore, in the intact lobster the amplitude and velocity of the powerstroke both increase as the frequency of swimmeret beating increases (Davis, 1968a). In the present experiments, however, the amplitude of the limb movement was the same for all frequencies of imposed movement. These considerations must be taken into account in extrapolating the present results to the operation of the reflexes in the intact lobster. Their effects, however, are probably simply to accentuate the reflex hysteresis described here, to strengthen the reflexes, and to shift the frequency response curves (i.e. Figs. 5−7) somewhat toward the high end of the frequency spectrum.

Fig. 7.

Semi-log plot of the correlation coefficient which expresses the strength of impulse grouping in the movement cycle (see text), against the frequency of imposed sinusoidal movement of the swimmeret. The data were taken from the same records as in Fig. 5. Each point again represents the value calculated from a single record in which the movement frequency was held constant. The number next to each point represents the number of interspike intervals used to derive the correlation coefficient.

Fig. 7.

Semi-log plot of the correlation coefficient which expresses the strength of impulse grouping in the movement cycle (see text), against the frequency of imposed sinusoidal movement of the swimmeret. The data were taken from the same records as in Fig. 5. Each point again represents the value calculated from a single record in which the movement frequency was held constant. The number next to each point represents the number of interspike intervals used to derive the correlation coefficient.

Reflex position

As described in the preceding paper (Davis, 1969b), stepwise retraction of the swimmeret initiates excitatory discharge to both powerstroke and returnstroke muscles, even though these muscles are functional antagonists. In spite of this reflex excitation from a common source, separation into antagonistic reflex activities could occur if the corresponding reflex pathways of powerstroke and returnstroke displayed opposite frequency-phase characteristics. Such a mechanism is apparently not used, however, since the mean of the phase positions of efferent impulses in the imposed movement cycle was not systematically related to the frequency of imposed movement of the swimmeret. Consequently, reflex antagonism between powerstroke and returnstroke excitor neurones must depend entirely upon a source of sensory feedback different from that which initiates the retraction responses. The sensory setae which fringe the rami of the swimmeret are sufficient for the purpose, since their stimulation has opposite effects on the powerstroke and returnstroke excitor neurones (Davis, 1969b).

Reflex hysteresis

During imposed movement of the swimmeret the reflex discharge of powerstroke excitor neurones occurs during late retraction and early protraction. It therefore appears that in the intact lobster, powerstroke excitor neurones receive excitatory input during the initial portion of the returnstroke. This possible inefficiency is minimized by hysteresis in the powerstroke reflex; the efferent reflex discharge is more intense during the late stages of imposed retraction than during the early stages of protraction. The similar hysteresis in the returnstroke reflex is probably not manifest in the intact lobster, owing to the powerful reflex inhibition of returnstroke excitors during the powerstroke (Davis, 1969b). Moreover, the central motor score exerts the dominant control over the swimmeret motor neurones. Thus, even in the absence of reflex inhibition, the returnstroke excitor neurones are quite unresponsive during the powerstroke (Davis, 1969b).

The source of the hysteresis in the swimmeret reflexes is unknown, but it may reside in the afferent responses of the sensory receptors. Accommodation in the afferent response could account for the hysteresis, as could a preponderance of afferent input from unidirectional movement fibres which respond only during retraction of the limb. Both phenomena have been found in crustacean proprioceptors (e.g. Bush, 1965 ; Hartman & Boettiger, 1967; Mendelson, 1963 ; Taylor, 1967; Wiersma & Boettiger, 1959; Wyse & Maynard, 1965).

Reflex strength

The strength of a reflex in response to a sinusoidal stimulus is most directly expressed by the peak-to-peak amplitude of the cyclic tension which results. The absolute amplitude of this tension fluctuation is in turn presumably some fairly simple function of the three parameters of reflex strength which have been studied here, i.e. the number of impulses per cycle of imposed movement, the average frequency of the impulses and the strength of the grouping of the impulses in the input cycle. At high frequencies of imposed sinusoidal movement of the swimmeret (> 3 Hz.), the average frequency of impulses within each movement cycle is usually high, but the number of impulses per cycle is few compared to the number of efferent impulses per movement cycle during swimmeret beating in the intact lobster (Davis, 1968b, 1969) and the impulses are distributed at random within the cycle. At low frequencies of imposed movement (< 1 Hz.), many efferent impulses are produced during each movement cycle, but their frequency is low compared to the discharge frequency during swimmeret beating (Davis, 1968b, 1969) and the impulses are also relatively ungrouped in the cycle. In the range between 1 and 3 Hz. of imposed movement, however, which corresponds to the usual frequency of swimmeret beating in the intact lobster, several high-frequency impulses are produced during each cycle of movement. Moreover, it is in this range of movement frequencies that the non-random grouping of efferent impulses in the movement cycle is the strongest. The intrasegmental reflexes are therefore organized so that their strength is greatest at the natural frequency of swimmeret beating, and declines to either side of this value. The reflexes are thus capable of providing cycle-by-cycle amplification of the cyclic motor output patterns which are generated in the CNS, in accord with the interpretations offered in the preceding paper (Davis, 1969b). Furthermore, the present study has shown that this amplification is most effective in the natural frequency range of swimmeret beating.

This work was supported by NIH postdoctoral fellowship NB 24, 882 to the author and by NIH grant 5 Ro1 NB 01624 to Dr Melvin J. Cohen. I am grateful to Dr D. Kennedy, Dr D. M. Wilson, Dr P. Stein, Dr A. Selverston and Dr D. Hartline for discussion and criticism of the manuscript.

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