The Effect of Limb Amputation On Locomotion in the Cockroach Periplaneta Americana

Amputation of legs has long been a popular technique to apply to the study of co-ordination of leg movements during locomotion in insects (see reviews by Roeder, 1953, and Wilson, 1966). The observation that the gait of insects with several legs missing is quite different from that of intact animals, made on different species (stick insects, von Buddenbrock, 1921; grasshoppers, ten Cate, 1936; cockroaches, Hughes, 1957), was considered to be of major importance, suggesting that reflexes play an important role in co-ordination. However, because of the qualitative nature of most of these reports, no firm conclusions can be drawn from them about how, in detail, co-ordination might be achieved.

The purpose of the present paper is to provide a detailed, quantitative description of walking in cockroaches lacking several legs which, when combined with a similar description of walking in intact cockroaches (Delcomyn, 1971), may provide a firm foundation on which to build models of the locomotory system. The results show that removal of the tibia of one or two legs causes only slight disturbance to the gait, while complete amputation of several legs induces dramatic changes in locomotor pattern, depending upon the combination of legs removed.

All subjects used in this study were adult cockroaches, Periplaneta americana. Limb amputations were generally carried out under light carbon dioxide anaesthesia, and the animals were photographed within 1 h of the operation. Two types of amputations were performed: (1) tibial amputations, in which the tibia was cut just distal to the femoro-tibial joint of the left middle leg alone (L2 tibial amputee), or of both middle legs (R2, L2 tibial amputee); (2) femoral amputations, in which the femur was cut just distal to the coxo-femoral joint of either the two middle legs (R2, L2 femoral amputee), or of the right front and left middle legs (Ri, L2 femoral amputee). The freely moving animals were photographed with a high-speed motion-picture camera at 200 frames/s, and the films were analysed frame by frame, as described previously (Delcomyn, 1971).

Amputation of the tibia appears to interfere very little with normal movement of the remainder of the leg during locomotion. In most cases, however, there is a distinct delay between the end of the leg’s forward movement (protraction) and the time at which the tibial stump touches the ground. (This delay was not treated as part of the protraction time in data analysis.) There was not usually any corresponding delay between lift-off and the beginning of forward movement.

The pattern of locomotion of cockroaches with one or two tibiae amputated did not appear substantially different from that of intact animals (Delcomyn, 1971—all statements in the present paper about the locomotion of normal, intact cockroaches are based on this work). Both L2 and R2, L2 amputees used the alternating triangle gait over the observed range of speeds of locomotion (Figs. 1, 2), but the range of variation in the parameters of leg movement and timing was wider than normal (e.g. Fig. 2). The analysis of these parameters is discussed in detail in the following sections.

The duration of both the forward (protraction) and rearward (retraction) movements of each leg decreased as the frequency of leg movement (a measure of the animal’s speed of forward progression) increased, as shown in Figs, 1 and 2. However, retraction decreased more rapidly, so that the ratio of protraction to retraction (p/r) increased as stepping frequency increased (Fig. 3). Correlation and regression statistics for the distribution of p/r vs. frequency of leg movement in L2 and R2, L2 tibial amputees are shown in Tables 1 and 2 respectively. Significant differences between the parameters of the p/r distribution for one leg and those for another are found in the parameters measuring the slope and vertical displacement of the regression lines for some legs.

Before considering these differences in detail it should be stressed that they represent differences in the behaviour of the legs. The slope of the distribution is determined by the average rate at which protraction changes in relation to retraction, as the frequency of leg movement increases. Thus, if the slope of the p/r distribution of leg A were lower than that for leg B, and the mean p/r values about the same, protraction would be relatively longer at lower frequencies of leg movement for A than for B (e.g. Fig. 3). The vertical position of the whole p/r distribution, best estimated by the mean p/r, is determined by the relative magnitudes of protraction and retraction over the whole distribution. Thus, if the mean p/r of leg B were lower than that of leg C, protraction for B would be longer, on the average, at any given frequency of leg movement than it would be for C (e.g. Fig. 7). The use of the mean p/r to estimate vertical differences between distributions is valid only if the frequencies of leg movement corresponding to each mean are equal, or nearly equal. Since this condition is not always satisfied in the present case because of comparisons of entirely different groups of animals, the value of the p/r ratio corresponding to a frequency of leg movement of 13 Hz was calculated from the regression equation for each distribution and used as the basis of comparison.

In each of the legs from which a tibia had been removed the slope of the p/r regression line appeared to be lower than in the intact legs, although in no case was the reduction extensive enough to reach statistical significance. This effect, if it is not simply due to variability in the system, may be an artifact of the operation. At low speeds of walking, the leg stump may continue moving forward as the femur is depressed, thus incorporating into protraction some of the delay between the end of protraction and the time the tibial stump strikes the ground. (This would not be detectable as such in the films.) The effect would be to increase the p/r ratio at low walking speeds and thus lower the slope of the p/r distribution.

In the L2 tibial amputees the p/r slopes of legs L3 and R3 were also affected by the operation. While these slopes did not differ from each other, each was significantly greater than any for the remaining four legs (P < 0·05). In addition, they were greater than the slopes for the homologous legs from R2, L2 tibial amputee (P < 0·005; see Fig. 3) and normal animals (P < 0·025). This is a rather puzzling result, especially since the p/r of the rear legs of the R2, L2 tibial amputee did not show such an increase of slope. It may be due to some effect of the asymmetry of the operation. There were no other significant differences between slopes for any homologous legs in L 2 amputee, normal, or R2, L2 amputee animals.

In intact animals the vertical position of the regression line for each of the two middle legs is significantly lower than that for each of the other legs. Similar differences between the positions of regression lines were found within each of the two groups of tibial amputees. In each group the regression lines for the middle legs were somewhat depressed compared to those for their ipsilateral neighbours, but the difference was only statistically significant for R2 compared to R1 and R3 in the L2 tibial amputees. In the case of leg L2 from the L2 amputees and legs R2 and L2 from the R2, L2 amputees, each of which lacked the tibia and tarsus, the artifact probably introduced into the p/r figures by the operation itself was apparently sufficient to mask the differences one would have expected on the basis of data from intact animals. There was no significant difference in p/r at 13 Hz between homologous legs in L2 amputee, normal, or R2, L2 amputee insects.

As is true for intact animals, insects with one or two tibiae missing show a remarkable consistency of phase relationships between legs, resulting in a constant gait over the entire range of observed speeds of locomotion. This can be seen in the tables of regression and other statistics for both the L2 tibial amputees (Table 3) and the R2, L2 tibial amputees (Table 4). Phase relationships of contralateral leg pairs are constant, being about 0·5 at all speeds of locomotion, even when the stump of an amputated leg is a member of the pair. This means that leg L2, for example, begins its forward movement when leg R2 is about half-way through its cycle of movement. The phase of ipsilateral leg pairs is also independent of frequency of leg movement, with one exception. The exception is the phase of a front leg on an ipsilateral middle leg which lacks the tibia (Fig. 4). In such cases, the phase at low speeds of walking tends to be higher than normal, such that there is a negative correlation of phase with frequency of leg movement overall (see Tables 3, 4). (In normal animals, phase tends to fall at very low speeds of walking.) However, when leg movements above 6–10 Hz only are considered, the correlation between phase and frequency of leg movement disappears, supporting the belief that the phase values generated at low frequencies are responsible for the correlation. Behaviourally, the front legs tend to move somewhat later than they do normally, compared to the movement of ipsilateral injured middle legs, but it should be pointed out that the shift in timing is so subtle that it is not detectable by eye in the films of the walking insects. The phase of the legs at very low speeds of locomotion (at frequencies of leg movement of less than 3 Hz) were unfortunately not obtained, since no tibial amputee could be induced to move so slowly.

Amputation of the leg of a cockroach at the trochantero-femoral joint leaves the insect totally without support at the point of amputation, although other legs alter their positions to take up some of the load (Hughes, 1957). When the animal walks, the coxa and trochanteral stump move, but are not able to contribute to the propulsion or support of the body. It is not surprising, therefore, that femoral amputation of two legs results in a rather dramatic shift in locomotor pattern, such that gait is a function of speed of locomotion at all speeds.

Samples of the gaits of R2, L2 and R1, L2 femoral amputees are shown in the diagrams of stepping patterns in Figs. 5 and 6. Gaits in the R2, L2 amputee vary from those in which the front and rear legs on one side step in close synchrony, as they do normally (Fig. 5B), through those in which they alternate, but step in synchrony with contralateral legs (Fig. 5 A), to those in which each leg steps by itself (Fig. 6 A). Gait in R1, L2 amputees also tends to vary, although not so dramatically (Fig. 6B).

Before going on to a consideration of the effect of femoral amputation on the parameters of leg movement and timing in the undamaged legs, a limitation of the stepping diagrams should be pointed out. These show forward and rearward leg movements without indicating when, or even whether, a leg is actually lifted from the substrate. The locomotion of femoral amputees is quite erratic, in the sense that the animals have a rather difficult time steering a straight course, especially at relatively high speeds of locomotion. The insects might well be said to be careening down the running path. The result of this is that occasionally an insect is tipped toward the left when both left legs are about to move forward. The legs do move, but the forces generated by the tilt of the animal’s body keep them on the ground, acting as supports even as they move forward. This did not appear to have any significant effect on the movements of the legs, and was therefore ignored in subsequent analysis.

In view of the extent of the changes induced in the pattern of stepping for femoral as compared to tibial amputees, it is perhaps surprising that there is less disturbance of individual leg movements in the former than the latter. Yet, the p/r distribution for the unamputated legs is quite unremarkable (Fig. 7). There are no significant differences between the slopes of the regression lines of the p/r data for any leg of the femoral amputees (Table 5). Nor are there any differences between the slopes for homologous legs in either intact or tibial amputee insects, except for legs L3 and R3 in the L2 tibial amputee, the slopes of whose p/r regression lines are greater than those for the same legs in the femoral amputees.

In contrast to the slopes, the position of the regression line measured at 13 Hz was quite sensitive to femoral amputations in many of the legs. In the R1, L2 amputee the average p/r at 13 Hz for the unamputated front and middle legs, L1 and R2, were significantly lower than those for the homologous legs in either of the tibial amputees, or in intact insects. The rear legs were not affected (see Fig. 7). In the R2, L2 amputee average p/r values were significantly lower for the right front and both the rear legs than for the homologous legs in any other animals, normal or tibial amputee. Average p/r in leg L1 was lower than normal, but not significantly so. Most of the differences between p/r values were of a high order of significance (P < 0·005). Interestingly, those legs whose protraction durations were not significantly reduced from normal were those with the greatest number of undisturbed neighbouring legs.

Thus, leg R2 of the R1, L2 femoral amputee, whose protractions were shorter than normal, lacks one of its nearest ipsilateral neighbours (R1), as well as its nearest contralateral one (L2), while leg R3, whose protraction durations are not different from normal, lacks none of its nearest neighbours. Similarly, two legs near leg L1 are missing, while L 3 lacks only one. In the R2, L2 amputee the nearest ipsilateral neighbour of each of the uninjured legs is missing, and the position of the p/r regression of each is significantly depressed, for all the legs except L1.

The different gaits seen in femoral amputees at different speeds of locomotion are reflected in changes in phase for most ipsilateral leg pairs as the frequency of leg movement changes (Table 6). These changes are most striking in the R2, L2 amputees (Fig. 8), in which the changes in gait are also largest. Here there is a strong positive correlation between the phase of a front on a rear leg and frequency of leg movement, a correlation which cannot be eradicated by deleting phase values for low speeds of walking. In the R1, L2 amputee there is also a significant positive correlation between the phase of L1 on L3 and frequency of leg movement, but the slope of the regression line is not as great; i.e. phase does not change as rapidly (Fig. 9, Table 6). Both types of amputees are missing leg L2, yet the range of the Li1, L3 phase is 0·5–1·06 in the R2, L2 amputee, and 0·29–0·64 in the other, over approximately the same range of walking speeds. In addition, the phase of R 2 on R 3 is not significantly changed as a function of the frequency of leg movement (Fig. 9). Thus, the extent to which gait varies with speed of walking in femoral amputees depends on the exact combination of legs which is amputated (see also Discussion).

While phase for most ipsilateral leg pairs varies with speed of walking, phase for contralateral ones does not (Fig. 8, Table 6). This means that each leg begins protracting about half-way through the full cycle of movement of the other leg in that body segment. This difference in phase between contralateral and ipsilateral leg pairs suggests that co-ordinating mechanisms might be different in the two cases.

One purpose of the experiments described in this paper has been to obtain data which might provide clues to possible mechanisms of control and co-ordination of leg movements during walking in cockroaches. The phrase ‘control and co-ordination’ used in this way suggests that control and co-ordination are two aspects of a single phenomenon. However, control of movements is not synonymous with control of co-ordination, since in principle it is not necessary that the movements of two or more appendages have any systematic temporal relationships to one another. It might be useful, therefore, to treat separately questions of the control of the actual movements of each leg and those of the control of the timing of those movements relative to other legs, and I shall do so here.

The experiments described above have demonstrated that the locomotion of Periplaneta is little disturbed by the amputation of one or two tibia, but is strongly affected by the removal of both femur and tibia. These results are substantially similar to those previously reported for other insects. Von Buddenbrock (1921), for example, showed that the gait of stick insects whose middle legs had been amputated would revert to near-normal if the stumps of the amputated legs were allowed to contact a small platform suspended under the animal, and ten Cate (1936) showed that grasshoppers whose femoral stumps were allowed to touch the ground used normal rather than amputee gaits. These experiments have generally been interpreted as evidence for an important role of sensory information from the legs in determining leg phasing (e.g. Hughes, 1957). An alternative suggestion that perhaps a centrally generated pattern might be involved was made by Wilson (1966) on the basis of similarities between the gaits of amputees and slowly moving intact insects. Thus, the gait of the R2, L2 femoral amputees at low walking speeds (Fig. 6 A) is similar to that reported for very slowly moving cockroaches (Blatta) by Hughes (1952): R3, R2, Ri, L3, L2, LI, etc. This argument loses some of its force in Periplaneta, which uses the alternating tripod gait at nearly all speeds of locomotion, and very rarely if ever even approaches these low-speed gaits seen in other insects (Delcomyn, 1971). Thus, the contrast between the consistency of walking pattern in intact cockroaches and the variable gaits observed in femoral amputees can perhaps be better explained in terms of proprioceptive signals from the legs than in terms of central mechanisms.

There are several interesting features in the results described above besides the basic difference in locomotion of tibial and femoral amputees. In tibial amputees the phase of a foreleg on an ipsilateral femoral stump tends to rise at low walking speeds, and it is at low walking speeds that protractions of the stump become longer than usual. Behaviourally, the front leg begins its forward movement later than normal when protraction in the leg behind it is extended beyond normal lengths. This, of course, is suggestive of some sort of link between the two events. Also, it may be observed that phasing between legs in a single body segment is constant (on the average) at all speeds of walking, even if adjacent legs have been amputated, while such is not the case for two ipsilateral legs. It may be that the coupling mechanism is different in the two cases, or that coupling is simply much stronger or more rigidly controlled between contralateral legs. The coupling may be influenced by reflexes even in the latter case, since it is possible to change normal phase relationships in all three contralateral leg pairs by severing one connective between meso- and metathoracic ganglia (Delcomyn, 1969). It also seems that contralateral leg coupling may be weaker in other insects, since Hughes (1957) and D. Graham (personal communication) report shifts in phase between contralateral legs in Blatta orientalis and Carausius morosus, respectively.

The results reported and discussed above, combined with specific studies on leg reflexes and their effects on locomotion (Pringle, 1940; Wilson, 1965; Runion à Usherwood, 1968; Delcomyn, 1969; M. D. Burns, personal communication), present a strong case for an important role of reflexes in co-ordination between legs during walking. Nevertheless, much of this evidence is indirect, and there are reports of central patterning of output to leg muscles in cockroaches independent of sensory signals (Pearson & Isles, 1970). Thus, as Wilson (1966) stated, ‘There is likely to be rather wide agreement now that, even though reflexes conspicuously affect insect walking, some degree of autonomous central nervous organization underlies the reflex superstructure.’

The individual stepping movements of each leg are remarkably stable under all of the experimental conditions imposed in this study. Both protraction and retraction decrease as the frequency of leg movement increases, but at different rates, such that the p/r ratio increases. Not only does this relationship hold for each of the legs in both tibial and femoral amputees, but even the rate of change of p/r against leg movement, with perhaps two real exceptions, is the same in each leg. The only significant effect of amputation is a general reduction in protraction (and concomitant increase in retraction) at all speeds of walking in those legs adjacent to the amputated ones. These results can be accounted for by a simple model, represented in Fig. 10.

The figure depicts three separate functional units, A, B and C, and the main communication channels entering and leaving each. These units have been deliberately represented as simple boxes to avoid suggestions of actual neural elements, which seems premature at this stage. The element A converts a signal of steady frequency (the central command, or on-signal) to one which varies sinusoidally. The period of the sinusoidal wave, and the average frequency of impulses within each cycle, are inverse and direct functions, respectively, of the frequency of the central command. The sinusoidal signal from element A impinges upon B, whose threshold of activation is within the range of excitation delivered from A. Thus, B first becomes active, then shuts off, repetitively, as the signal it receives alternately rises and falls in frequency. Element C, which is activated by the on-signal, is in turn periodically inhibited by the inhibitory input from B, and thus delivers a pattern of bursts which alternates with the pattern delivered by B. The bursts from B and C represent the activation of the leg muscles responsible for protraction and retraction, respectively.

One such control system would be responsible for regulating the movements of each leg. The intensity of the central command, i.e. its frequency, determines the insect’s speed of locomotion by setting the burst period; the higher the command frequency, the shorter the burst period, and thus the higher the frequency of leg movement. The period of activation of individual leg muscles need not necessarily last for the full duration of the output bursts of unit B or C since these bursts only represent the total period during which any of the functional extensor or flexor muscles in the leg are active. This leaves considerable scope for variation in the relative timing of motoneurone bursts to the various muscles while maintaining the necessary alternation of flexion and extension of the leg. Local reflex loops could thus affect the former without influencing the latter.

The postulation of sinusoidal waves of activity in this model has several advantages. Firstly, it allows a very close simulation of observed phenomena. The threshold of B may be visualized as a line cutting the sine curve described by the frequency of the output of A. Then the p/r ratio is represented by the ratio of the time during which the sine curve is above the line (i.e. the frequency is above threshold) to the time during which the curve is below it. The average frequency of impulses within each cycle of activity may be represented by the vertical displacement of the sine curve relative to the threshold line. As the intensity of the input on-signal increases, the vertical displacement increases, but the period of the sine function decreases. Thus, the period of the output bursts goes down (i.e. frequency of leg movement rises), and the p/r rises, since the signal from A is now above the threshold of B for greater periods of time. The increase in p/r is approximately linear for the range of ratios from 0·2 to 1·2. This is the usual range seen in the living animal. Since a similar mechanism would presumably serve each leg, the relationship between p/r and frequency of leg movement would be expected to be the same in each case, as it is. In addition, no sensory signals are required in the basic system, so no change in the slope of p/r would be expected after leg amputations, and there is indeed none, except after some tibial amputations (see below).

However, the mean p/r for any given frequency of leg movement is affected by amputations. This can be accounted for by additionally postulating that there is a general excitatory effect of sensory input from other legs on the average frequency within each cycle, but without an effect on the period of the cycle. The sensory signals are shown impinging on unit A, but the same result could be obtained if they entered unit B. Removal of a significant portion of this input through amputation of adjacent legs would result in a reduction in average frequency within the cyclic signal going from A to B. This would have the effect of reducing the time during which the sinusoidal signal is above the threshold of B (since its overall frequency has been reduced), thus depressing the whole distribution of p/r, but without any effect on its slope. The change in slope in some legs as a result of the L2 tibial amputation is not so easily accounted for unless one accepts an additional exictatory influence upon A from the stimuli generated during walking as a result of the asymmetric operation. In such an event p/r would be elevated rather than depressed. The average slope would then increase because above p/r values of about 1·3–1·4 the curve for p/r vs. frequency of sine signal becomes noticeably non-linear, rising increasingly more steeply.

Additional advantages of employing sinusoidal patterns of activity stem from the ease with which such patterns may be treated mathematically. For example, a complete quantitative description of the behaviour of the present model can be prepared, including transfer functions for the three functional units. Such a description could be extremely useful to investigators searching for neural elements capable of performing the functions described in the model. In addition, although the flexion and extension movements of the legs of a cockroach during walking are not sinusoidal, a sinusoidal function can be used to approximate them, and thus also to approximate some of the sensory signals which arise from them. Since the addition of two or more sinusoidal functions is a simple mathematical procedure, quantitative descriptions of the theoretical implications of interactions between the centrally generated command and sensory feedback become possible.

This model was first described elsewhere (Delcomyn, 1969). Recently, an extremely similar model has been proposed independently by Pearson & Isles (1970) to account for alternating patterns of bursts observed in metathoracic extensors and flexors in the coxa of Periplaneta. Their model employs bursts rather than sinusoidal activity, and suggests inhibition of element C by A rather than B. Also, it lacks the sensory input channel to A, while inserting a bias on C. Except for these relatively minor differences, however, the models are essentially the same. This convergence of physiological and behavioural data on a single type of model acts as an additional element of support for it.

This work was supported by a U.S. Public Health Service Physiology Training Grant to the University of Oregon, N.S.F. grant GB-7413 to Dr G. Hoyle and an S.R.C. grant to Dr P. N. R. Usherwood. I wish to thank Dr T. D. M. Roberts, Institute of Physiology, University of Glasgow for the use of computing equipment, and Drs Hoyle, Usherwood and C. Walther for helpful criticisms of this paper.