Mechanisms of stick insect locomotion in a gap-crossing paradigm

Locomotion of stick insects climbing over gaps of more than twice their step length has proved to be a useful paradigm to investigate how locomotor behaviour is adapted to external conditions. In this study, swing amplitudes and extreme positions of single steps from gap-crossing sequences have been analysed and compared to corresponding parameters of undisturbed walking. We show that adaptations of the basic mechanisms concern movements of single legs as well as the coordination between the legs. Slowing down of stance velocity, searching movements of legs in protraction and the generation of short steps are crucial prerequisites in the gap-crossing task. The rules of leg coordination described for stick insect walking seem to be modified, and load on the supporting legs is assumed to have a major effect on coordination especially in slow walking. Stepping into the gap with a front leg and antennal contact with the far edge of the gap provide information, as both events influence the following leg movements, whereas antennal non-contact seems not to contain information. Integration of these results into the model of the walking controller can improve our understanding of insect locomotion in highly irregular environments.Abbreviations AEP anterior extreme position - fAEP fictive anterior extreme position - PEP posterior extreme position - TOT treading-on-tarsus     

Leg movements of stick insects walking with five legs on a treadwheel and with one leg on a motor-driven belt

Five legs of a fixed stick insect walked on a double treadwheel. The left hindleg (L3) walked on a motor-driven belt. When the belt was slower than the wheels L3 made less steps than the other legs and when the belt was faster than the wheels it made more steps than the other legs. In the case of slowlier stepping of the belt-leg, the motor neurons of the retractor coxae muscle of this leg showed a high activity when the leg was pulled backwards by the belt. This activity was modulated in the step rhythm of the wheel-legs. When all legs showed the same stepping frequency (1:1-coordination) the protraction duration of L3 was almost independent of step-period, as well as the lag between onset of protraction of L3 and that of L2. In some cases only L3 could be made to step on the belt even when all other legs did not walk.     

Dynamics and stability of insect locomotion: a hexapedal model for horizontal plane motions

We develop a simple hexapedal model for the dynamics of insect locomotion in the horizontal plane. Each leg is a linear spring endowed with two inputs, controlling force-free length and hip position, in a stereotypical feedforward pattern. These represent, in a simplified manner, the effects of neurally activated muscles in the animal and are determined from measured foot force and kinematic body data for cockroaches. We solve the three-degree-of-freedom Newtonian equations for coupled translation-yawing motions in response to the inputs and determine branches of periodic gaits over the animals typical speed range. We demonstrate a close quantitative match to experiments and find both stable and unstable motions, depending upon input protocols.Our hexapedal model highlights the importance of stability in evaluating effective locomotor performance and in particular suggests that sprawled-posture runners with large lateral and opposing leg forces can be stable in the horizontal plane over a range of speeds, with minimalsensory feedback from the environment. Fore–aft force patterns characteristic of upright-posture runners can cause instability in the model. We find that stability can constrain fundamental gait parameters: our model is stable only when stride length and frequency match the patterns measured in the animal. Stability is not compromised by large joint moments during running because ground reaction forces tend to align along the leg and be directed toward the center of mass. Legs radiating in all directions and capable of generating large moments may allow very rapid turning and extraordinary maneuvers. Our results further weaken the hypothesis that polypedal, sprawled-posture locomotion with large lateral and opposing leg forces is less effective than upright posture running with fewer legs.     

Systemanalytische Untersuchung eines aufgeschnittenen Regelkreises,der die Beinstellung der Stabheuschrecke Carausius morosus kontrolliert: Kraftmessungen an den Antagonisten Flexor und Extensor tibiae

In the leg of the stick insect Carausius morosus there exists a feedback loop which controls the position of the femur-tibia joint (Bässler, 1965). This feedback mechanism is broken to investigate the open loop system. As output the forces of the two antagonistic muscles flexor tibiae and extensor tibiae are measured separately. As input the feedback transducer of the control mechanism, a chordotonal organ, is stimulated by different kinds of input functions: sine-, step-, delta-, rectangular-and ramp functions. As a qualitative result one can say, that both the flexor-system and the extensor-system have rectifying and high-pass filter properties. However, the comparison between responses to different input functions show that the quantitative properties of this high-pass filter change very strongly with the shape of the input function. Therefore the existence of different nonlinearities has to be assumed.

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Mit Unterstützung der Deutschen Forschungsgemeinschaft (Nr. Ba 578/1)

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Die Arbeit enthält einen Teil der Dissertation von J. Storrer     

Oscillations of force in the standing legs of a walking insect (Carausius morosus)

In the experiments presented here adult stick insects (Carausius morosus) walk on a treadwheel with various legs standing on platforms fixed relative to the body of the insect. These standing legs produce large forees directed towards the rear which are modulated in the rhythm of the walking legs. Neighbouring legs which both stand on a platform often oscillate in phase. Possible reasons for the occurrence of the force oscillations are discussed.Supported by DFG (Cr 58/1)     

A dynamic model of thoracic differentiation for the control of turning in the stick insect

Leg movements of stick insects (Carausius morosus) making turns towards visual targets are examined in detail, and a dynamic model of this behaviour is proposed. Initial results suggest that front legs shape most of the body trajectory, while the middle and hind legs just follow external forces (Rosano H, Webb B, in The control of turning in real and simulated stick insects, vol. 4095, pp 145–156, 2006). However, some limitations of this explanation and dissimilarities in the turning behaviour of the insect and the model were found. A second set of behavioural experiments was made by blocking front tarsi to further investigate the active role of the other legs for the control of turning. The results indicate that it is necessary to have different roles for each pair of legs to replicate insect behaviour. We demonstrate that the rear legs actively rotate the body while the middle legs move sideways tangentially to the hind inner leg. Furthermore, we show that on average the middle inner and hind outer leg contribute to turning while the middle outer leg and hind inner leg oppose body rotation. These behavioural results are incorporated into a 3D dynamic robot simulation. We show that the simulation can now replicate more precisely the turns made by the stick insect. This work was supported by CONACYT México and the European Commission under project FP6-2003-IST2-004690 SPARK.     

The control of walking movements in the leg of the rock lobster

1. Experiments with rock lobsters walking on a treadmill were undertaken to obtain information upon the system controlling the movement of the legs. Results show that the position of the leg is an important parameter affecting the cyclic movement of the walking leg. Stepping can be interrupted when the geometrical conditions for terminating either a return stroke or a power stroke are not fullfilled. 2. The mean value of anterior and posterior extreme positions (AEP and PEP respectively) of the walking legs do not depend on the walking speed (Fig. 1). 3. When one leg is isolated from the other walking legs by placing it on a platform the AEPs and PEPs of the other legs show a broader distribution compared to controls (Figs. 2 and 3). 4. Force measurements (Fig. 4) are in agreement with the hypothesis that the movement of the leg is controlled by a position servomechanism. 5. When one leg stands on a stationary force transducer this leg develops forces which oscillate with the step rhythm of the other legs (Fig. 5). 6. A posteriorly directed influence is found, by which the return stroke of a leg can be started when the anterior leg performs a backward directed movement. 7. Results are compared with those obtained from stick insects. The systems controlling the movement of the individual leg are similar in both, lobster and stick insect but the influences between the legs seem to be considerably different.     

Vom femoralen Chordotonalorgan gesteuerte Reaktionen bei der Stabheuschrecke Carausius morosus: Messung der von der Tibia erzeugten Kraft im aktiven und inaktiven Tier

In the Introduction (A) there is a list of unsolved problems concerning the role of the femoral chordotonal organ. A method to solve these problems by measuring the force at the distal end of the tibia during stimulation of the femoral chordotonal organ is described in (B). The step-response in inactive animals (C) is similar to that of the free-moving tibia. After an active movement caused by touching the abdomen the amplitude of the flexion-force is always higher than before. In (D) a method is described to measure the amplification of the control-system in intact animals. With this method it is verified, that the flexion-force produced by a distinct stimulus is higher after active movements caused by touching the abdomen. But this force is lower after spontaneous active movements caused by darkening the room (Fig. 2). Therefore one must assume, that there are two different types of activity: spontaneous activity and activity after a disturbance. In the frequency-response of the inactive animal (F) (Figs. 4 and 5) the amplitude of the force decreases with increasing frequency at a constant amplitude of stimulus. The phase-shift between reaction and stimulus is much smaller than with the free-moving tibia. Therefore, the large phase-shift as well as the strong decrease of the reaction-amplitude near 1 Hz observed in free-moving tibias (1972b) is mainly due to the mechanical attributes of the system. In Section (F) the receptor-apodeme is sinusoidally moved during active movements of intact and decerebrated animals. As with the free-moving tibia no reaction can be observed during active movements at that phase position for which the response occurs in inactive animals. Instead of this inactive response there is another response, called active with a phase-shift of about 180°. At the end of an active period the active and the inactive response can be observed simultaneously (Figs. 7 and 10). The amplitude of the active response decreases, and the amplitude of the inactive response increases from cycle to cycle. In decerebrated animals there are normally several minutes from the exclusively active response to the exclusively inactive response without a further increase in amplitude. In intact animals this transition takes only a few seconds. Step-stimuli during active movements (G) show, that in active animals stretching the chordotonal organ causes a flexion of the femor-tibia-joint. Releasing the chordotonal organ does not produce any reaction. Moving the receptor-apodeme in active animals influences the contralateral leg significantly only in middle legs (H). These legs tend to move within the same phase position as the stimulated leg. Moving the receptor-apodeme in a middle leg has no influence on the ipsilateral hind leg, but a weak influence on the ipsilateral front leg, which tends to move within the same phase position as the middle leg. In the discussion (I) a hypothesis is presented according to which the active response is a mechanism for adapting the leg movement to a surface which suddenly gives way (I 5). The influence on the contralateral middle leg seems to be a part of this mechanism (I 6). This reaction has nothing to do with the coordination of leg movements in walk (I 7). The feed-back systems which control the distance between the body and the walking surface may be inactive during walking (I 8), but those systems which control the forward movement of the body must be active. Since the feed-back system of the Kniesehnen-reflex controls predominantly the body-ground-distance it seems likely that it is normally inactive during walking.     

A model of leg coordination in the stick insect,Carausius morosus

Mechanisms dependent upon leg position coordinate the alternate stepping of adjacent ipsilateral and contralateral legs in the stick insect. In this insect, swing duration and step amplitude are independent of walking speed. A simple geometrical model of the leg controller is used here to test different mechanisms for compatibility with these two invariant features. Leg position is the state variable of a relaxation oscillator and position thresholds determine the transitions between swing and stance. The coordination mechanisms alter these thresholds. The position-dependent mechanisms considered differ either in the form or the speed-dependence of the function relating the shift in the posterior threshold of the receiving leg to the position of the sending leg. The results identify parameter combinations leading to alternate stepping with symmetric or asymmetric phase distributions, to shifts in the posterior extreme position as a function of speed, to double stepping or to in-phase stepping. An optimal position-dependent excitatory mechanism is described. Finally the consequences of adding either inhibitory influences or time-dependent excitatory influences are analyzed.     

Selection on male size,leg length and condition during mate search in a sexually highly dimorphic orb-weaving spider

Mate search plays a central role in hypotheses for the adaptive significance of extreme female-biased sexual size dimorphism (SSD) in animals. Spiders (Araneae) are the only free-living terrestrial taxon where extreme SSD is common. The gravity hypothesis states that small body size in males is favoured during mate search in species where males have to climb to reach females, because body length is inversely proportional to achievable speed on vertical structures. However, locomotive performance of males may also depend on relative leg length. Here we examine selection on male body size and leg length during mate search in the highly dimorphic orb-weaving spider Argiope aurantia, using a multivariate approach to distinguish selection targeted at different components of size. Further, we investigate the scaling relationships between male size and energy reserves, and the differential loss of reserves. Adult males do not feed while roving, and a size-dependent differential energy storage capacity may thus affect male performance during mate search. Contrary to predictions, large body size was favoured in one of two populations, and this was due to selection for longer legs. Male size was not under selection in the second population, but we detected direct selection for longer third legs. Males lost energy reserves during mate search, but this was independent of male size and storage capacity scaled isometrically with size. Thus, mate search is unlikely to lead to selection for small male size, but the hypothesis that relatively longer legs in male spiders reflect a search-adapted morphology is supported.     

Pattern specification in imaginal discs ofDrosophila melanogaster

Summary l(1)su(f)^mad-ts (mad) is a new temperature-sensitive (ts) lethal mutant ofDrosophila melanogaster which produces duplicated legs after temperature pulse treatment during larval development. The ts-lethality was studied in temperature experiments and genetic mosaics. Temperature pulses given during two distinct TSPs of larval development result in two different types of leg pattern duplication. Total differ from partial duplications with respect to the affected leg compartments and the orientation of the planes of symmetry which are perpendicular to the dorso-ventral and the proximo-distal leg axes in total and partial duplications, respectively. Genetic mosaic studies indicate (i) disc autonomy of leg pattern duplication, (ii) clonal separation of the anlagen of the two pattern copies, and (iii) clonal restriction along the antero-posterior compartment border in the two pattern copies of totally duplicated legs.The results suggest thatmad leg pattern duplication is caused by a change in positional information rather than by cell death and subsequent regeneration. Our data are compatible with the assumption that during normal development the leg disc cells acquire information about their position within the disc with respect to the different leg axes independently and at different times.     

A quantitative model of walking incorporating central and peripheral influences

Using the experimental results of Cruse and Saxler (1980a, b) and other authors (Graham, 1972; Pearson, 1972; Bässler, 1977, 1979) a quantitative model is developed in order to describe the behaviour of the systems controlling the leg movements of a walking insect. The whole model consists of six subsystems each of which controls the movement of an individual leg. The single subsystem (Fig. 1) consists of a central part which can assume two modes (protraction, retraction) the transition between which can be controlled by sensory influence. The central part produces the reference input for a feedback loop which controls the leg position. The reference input is however also determined by influences from other subsystems. Four different types of such connections are assumed to exist between the subsystems. Two of these produce alternating (t1, t3), two others in phase coupling (t2, t4) between the subsystems to be connected. These connections can transfer information originating from the central part as well as from the periphery of other subsystems. The model is capable of describing either quantitatively or qualitatively the experimental results of Cruse and Saxler (1980a, b) (see Figs. 3 and 4). In addition it is capable of describing the results of other authors, e.g. the temporal leg coordination of the free walking animal (Graham, 1972).Supported by DFG (Cr 58/1)     

A mathematical modeling study of inter-segmental coordination during stick insect walking

The biomechanical conditions for walking in the stick insect require a modeling approach that is based on the control of pairs of antagonistic motoneuron (MN) pools for each leg joint by independent central pattern generators (CPGs). Each CPG controls a pair of antagonistic MN pools. Furthermore, specific sensory feedback signals play an important role in the control of single leg movement and in the generation of inter-leg coordination or the interplay between both tasks. Currently, however, no mathematical model exists that provides a theoretical approach to understanding the generation of coordinated locomotion in such a multi-legged locomotor system. In the present study, I created such a theoretical model for the stick insect walking system, which describes the MN activity of a single forward stepping middle leg and helps to explain the neuronal mechanisms underlying coordinating information transfer between ipsilateral legs. In this model, CPGs that belong to the same leg, as well as those belonging to different legs, are connected by specific sensory feedback pathways that convey information about movements and forces generated during locomotion. The model emphasizes the importance of sensory feedback, which is used by the central nervous system to enhance weak excitatory and inhibitory synaptic connections from front to rear between the three thorax-coxa-joint CPGs. Thereby the sensory feedback activates caudal pattern generation networks and helps to coordinate leg movements by generating in-phase and out-of-phase thoracic MN activity.     

Neurosecretory endings associated with striated muscles in three insects (Schistocerca,Carausius, and Phormia) and a frog (Rana)

Summary Neurosecretory nerve-endings are found in association with the ventral longitudinal muscles of the body wall in locust, stick insect and blowfly larva, and with toe muscles in the frog. In the stick insect the endings are less intimately associated with the muscles than in the locust or in the blowfly larva. In the locust and the stick insect and in the frog there are separate neurosecretory and ordinary motor endings but in the blowfly larva the characteristic features of motor and neurosecretory endings are combined in the same axon. The apparent sites of release of neurosecretory material show a characteristically rippled plasma membrane and are covered by only a flimsy layer of connective tissue material (stroma). In all three insects studied most of the neurosecretory material appears to be liberated into the haemolymph. Neurosecretory material appears to be released through the membrane at any point however, including, in the locust and in the blowfly larva, that part applied to the muscle. In the stick insect no endings have been seen as closely associated with the muscle as in the other two species. In the frog, as in the stick insect, the neurosecretory material is not liberated directly on to the muscle but into the connective tissue that lies between muscle fibres.Supported by a grant from the Science Research Council.Commonwealth Foundation Research Scholar.     

Sensory control of leg movement in the stick insect Carausius morosus

Hind legs with crossed receptor-apodemes of the femoral chordotonal organ when making a step during walking often do not release the ground after reaching the extreme posterior position. After putting a clamp on the trochanter (stimulation of the campaniform sensilla) the leg is no longer protracted during walking. However, during searching-movements the same leg is moved very far forwards. The anatomical situation of the campaniform sensilla on the trochanter and the sensory innervation of the trochanter is described. After removal of the hair-rows and continuously stimulating the hair-plate at the thorax-coxa-joint the extreme anterior and posterior positions of the leg in walking are displaced in the posterior direction. Front and middle legs operated in this way sometimes do not release the ground at the end of retraction. In searching-movements the same leg is moved in a normal way. If only one side of a decerebrated animal goes over a step, then on the other side a compensatory effect is observed. The main source of this compensatory information appears to be the BF1-hair-plates. If the animal has to drag a weight the extreme anterior and posterior positions of the middle and hind legs are displaced in the anterior direction. Crossing the receptor-apodeme of the femoral chordotonal organ, when it causes the leg to remain in the protraction phase, displaces the extreme posterior position of the ipsilateral leg in front of the operated one in the posterior direction. Influences of different sources on the extreme posterior position can superimpose. A model is presented which combines both a central programme and peripheral sensory influence. The word programme used here means that it does not only determine the motor output but also determines the reactions to particular afferences. The fact that the reaction to a stimulus depends on the internal state of the CNS is also represented by the model.Supported by Deutsche Forschungsgemeinschaft     

Studies on the neurosecretory system of Iphita limbata Stal.

Summary The present paper gives an account of some experiments upon the insect Iphita limbata Stal. (Hemiptera: Pyrrhocoridae). The experiments were carried out in order to find out whether in the adult animal there is a relationship between the activity of the neurosecretory cells and the water balance. Under varying conditions one group of the neurosecretory cells of the pars intercerebralis of the brain, the so called A-cells, show histological differences. It has been seen that under conditions stimulating hydration there is a marked retention of the stainable colloids in the cytoplasm of A cells. This retention probably indicates a relationship between the secretions of A cells and the water balance of the insect.The author is indebted to Mr. N. R. Prabhoo and Miss Maya Menon of this Department for a critical discussion of the paper.     

Reversal of a reflex to a single motoneuron in the stick insect Çarausius morosus

In inactive stick insects ramp-wise stretching of the femoral chordotonal organ excites the slow extensor tibiae motoneuron. In active animals the same stimulus decreases the firing rate of this motoneuron. The time-course of increased and decreased activity of this motoneuron can be seen with triangular stimulation.Supported by the Deutsche Forschungsgemeinschaft     

Coding proprioceptive information to control movement to a target: Simulation with a simple neural network

When the stick insect walks, the middle and rear legs step to positions immediately behind the tarsus of the adjacent rostral leg. Previous reports have described this movement to a target as a relationship between the tarsus positions of the two legs in a Cartesian coordinate system. However, leg proprioceptors measure the position of the target leg in terms of joint angles and leg muscles bring the tarsus of the moving leg to the proper end-point by establishing appropriate angles at the joints. Representation of this task in Cartesian coordinates requires non-linear coordinate transformations; realizing such a transformation in the nervous system appears to require many neurons. The present simulation using the back-propagation algorithm shows that a simple network of only nine units — 3 sensory input units, 3 motor output units, and 3 hidden units — suffices. The simulation also shows that an analytic coordinate transformation can be replaced by a direct association of joint configurations in the moving leg with those in the target leg.     

Open loop analysis of a feedback mechanism controlling the leg position in the stick insect Carausius morosus: Comparison between experiment and simulation

In the legs of the stick insect Carausius morosus a feedback mechanism exists to control the value of the angle between femur and tibia. It is possible to investigate the open loop system by moving as input experimentally the receptor apodeme of the femoral chordotonal organ, which acts as feedback transducer measuring the angle between femur and tibia (Bässler, 1965). As output the forces are measured separately which are developed by the two antagonistic muscles moving the femur-tibia joint. The response of this system to different step-, sine-, ramp-and -functions are measured. An electronic analog model is constructed to simulate the biological system (Fig. 1). Although a number of different nonlinearities arise in the biological system, as a first-order approximation the model shows a sufficient fit to the experimental results (Figs. 2–9). The main characteristics of the model are as follows. It consists of two independent subsystems, the flexor system and the extensor system. Each subsystem again consists of two parallel branches with high-pass properties of different time constants. In each subsystem one branch is only excitable by input functions of a slope smaller than a certain degree. It is remarkable, that no mutual inhibitory influence between the sub-systems controlling the antagonistic muscles is necessary in the model.Supported by the Deutsche Forschungsgemeinschaft (Nr. Ba 578/1)