The coordination of force oscillations and of leg movement in a walking insect (Carausius morosus)

As in the preceding paper stick insects walk on a treadwheel and different legs are put on platforms fixed relative to the insect's body. The movement of the walking legs is recorded in addition to the force oscillations of the standing legs. The coordination between the different legs depends upon the number and arrangement of the walking legs and the legs standing on platforms. In most experimental situations one finds a coordination which is different from that of a normal walking animal.Supported by DFG (Cr 58/1)     

The effect of amputation and leg restraint on the free walking coordination of the stick insectCarausius morosus

Summary The stepping patterns of intact, amputated and leg restrained first instar stick insects were examined by analysing video tape records of their free walking behaviour. Amputation produced changes in the relative timing of protraction movements both along and across the body axis. Restraint of individual front or rear legs produced walking behaviour similar to that of the amputee animal but restraint of middle legs caused a breakdown in the coordination of front and rear legs. The changes in behaviour produced by leg autotomy and restraint were used to test certain assumptions of a model for generating the step pattern of these insects and to investigate how the tonic influence of proprioceptive input might be incorporated into the model.I would like to thank Professor P.N.R. Usherwood and Drs. M.D. Burns and W.J.P. Barnes for their comments and ideas on this work. A special acknowledgement goes to Dr. F. Delcomyn whose Fortran step analysis programs assisted greatly in the data reduction. I wish to thank S.R.C. for a returning scientist award and the support and equipment provided by grant B/SR/9774 to Professor Usherwood. A preliminary survey of some of the amputees was carried out at the Biology Department, Case Western Reserve University and I would like to acknowledge the support provided by a P.H.S. grant NB-06054 to Professor R.K. Josephson.     

Analysis of a distributed model of leg coordination

Using tools from discrete dynamical systems theory, we begin a systematic analysis of a distributed model of leg coordination with both biological and robotic applications. In this paper, we clarify the role of individual coordination mechanisms by studying a system of two leg oscillators coupled in one direction by each of the three major mechanisms that have been described for the stick insect Carausius morosus. For each mechanism, we derive analytical return maps, and analyze the behavior of these return maps under iteration in order to determine the asymptotic phase relationship between the two legs. We also derive asymptotic relative phase densities for each mechanism and compare these densities to those obtained from numerical simulations of the model. Our analysis demonstrates that, although each of these mechanisms can individually compress a range of initial conditions into a narrow band of relative phase, this asymptotic relative phase relationship is, in general, only neutrally stable. We also show that the nonlinear dependence of relative phase on walking speed along the body in the full hexapod model can be explained by our analysis. Finally, we provide detailed parameter charts of the range of behavior that each mechanism can produce as coupling strength and walking speed are varied. Received: 22 June 1999 / Accepted in revised form: 7 September 1999     

The influence of load and leg amputation upon coordination in walking crustaceans: A model calculation

The following results were obtained by earlier authors when investigating the leg coordination of walking crustaceans (Decepoda): 1) After a leg is amputated, its stump moves in anti-phase with the next posterior intact leg. This corresponds to the coordination of intact animals. The stump, however, moves in-phase with the next anterior intact leg which contrasts with the coordination of intact animals (Clarac and Chasserat, 1979; Clarac, 1981). 2) Different results have been reported for the relation between the return stroke duration and step period: some authors found a significant dependency (e.g. MacMillan, 1975), others found none (e.g. Ayers and Davis, 1977). The calculation presented here shows, that these results can be described by a model incorporating the following assumptions: A) The forces developed by both, return stroke and power stroke muscles depend upon the load under which the leg walks. B) The influences which produce the coordinating effects found by Clarac and Chasserat for amputees also exist in intact animals and their strength depends upon the intensity of the motor output of the controlling leg. Within the model the selection of protraction or retraction is made at a “central unit” which calculates a value corresponding to the sum of graded inputs from several sources. The resulting fluctuation in this value might be considered analogous to graded oscillations recorded from central non-spiking interneurons. Qualitatively the model describes similar results obtained from insects.     

Convergence of load and movement information onto leg motoneurons in insects

The interaction of two feedback loops was investigated: one regulating cuticular stress in the stick insect's leg and the other controlling leg posture. Exclusive stimulation of either of the two relevant sense organs, the load-sensitive trochantero-femoral campaniform sensilla (CS) or the position-/movement-sensitive ventral coxal hairplate (cxHPv), elicits resistance reflex responses in the retractor and the protractor coxae motoneuron pools. Concurrent application of both stimulus modalities reveals that the strength of the postural feedback response is dependent on sign and amplitude of the load feedback response and vice versa. This superposition of the two reflex responses appears to be non-linear. The results indicate that the CS information is underlying a force control function in this six-legged animal. It is hypothesized that the force control of each single leg could help to optimize the force distribution of the six-legged system, even - due to the mechanical coupling - without explicit neuronal pathways. On the level of the single leg control it was studied whether the different information provided by the two feedback transducers converge on the level of retractor coxae motoneurons or whether this information is fully preprocessed at the level of premotor interneurons. It is shown here that the hairplate afferents make direct, excitatory connections with the retractor motoneurons. Studies of the motoneurons' membrane conductances during exclusive CS stimulation reveal that both, excitatory as well as inhibitory synaptic drive is delivered onto the retractor motoneurons. Thus, the motoneuronal membrane is shown to be an important stage for the sensor fusion of the two modalities.     

Stick insects walking on a wheel: Perturbations induced by obstruction of leg protraction

Summary Stick insects (Carausius morosus) walking on a wheel were perturbed by restricting the forward protraction of individual legs. A barrier placed before a single middle or rear leg prevented that leg from reaching its normal protraction endpoint but allowed it unimpeded retraction. Upon striking the barrier, the protracting leg attempted to get past it and thereby prolonged protraction. This prolongation increased with the extent to which the obstruction infringed upon the leg's normal step range. Barriers placed near the midpoint of this range elicited large perturbations: the blocked leg often continued its protraction throughout many step cycles of the other legs (Fig. 1 E, F). For the most part walking was irregular and smooth forward progression was disrupted. Nevertheless, the infrequent steps by the affected leg usually were coordinated with those of the adjacent ipsilateral legs.More rostral barrier positions elicited smaller perturbations: the blocked leg usually made one step in each step cycle of the other legs (Fig. 1 B, C, D, G). Measurements for these regular step sequences showed quantitatively that protraction duration increased in proportion to the severity of the infringement on normal leg movement (Figs. 3, 4). The fraction of the step period occupied by protraction increased from ca. 10% for normal walking to ca. 50% for caudal barrier positions. This proportionality is interpreted to show the importance of spatial components of the walking program.When one leg was obstructed, its extended protraction influenced the stepping of the three adjacent legs as follows. First, the ipsilateral rostral leg showed the largest change: its protraction onset was regularly delayed for the duration of the extended protraction (Figs. 4, 7, 8), demonstrating a strong, centrally mediated inhibition. The presence of a further delay of up to 100 to 140 ms suggests that peripheral input from the protracting leg may be important for releasing this inhibition. Second, steps by an adjacent caudal leg were not measurably affected. However, the method may not have sufficed to reveal such effects because during regular walking middle leg protractions rarely lasted long enough to conflict with subsequent steps by the ipsilateral rear leg. Third, contralateral effects differed between middle and rear leg obstructions. If the obstructed leg was a middle leg, its extended protraction had little effect upon stepping by the contralateral middle leg: the latter leg frequently protracted while the blocked leg continued its protraction and there was no consistent change in the phase relation of these two legs (Table 1). In contrast, if the obstructed leg was a rear leg, protractions by the contralateral rear leg tended to be delayed (Table 1).     

A self-organizing model of walking patterns of insects

Insects generate walking patterns which depend upon external conditions. For example, when an insect is exposed to an additional load parallel to the direction in which it is walking, the walking pattern changes according to the magnitude of the load. Furthermore, even after some of its legs have been amputated, an insect will produce walking patterns with its remaining legs. These adaptations in insect walking could not previously be explained by a mathematical model, since the mathemati cal models were based upon the hypothesis that the relationship between walking velocity and walking patterns is fixed under all conditions. We have produced a mathematical model which describes self-organizing insect walking patterns in real-time by using feedback information regarding muscle load (Kimura et al. 1993). As part of this model, we introduced a new rule to coordinate leg movement, in which the information is circulated to optimize the efficiency of the energy transduction of each effector orga n. We describe this mechanism as ‘the least dissatisfaction for the greatest number of elements’. In this paper, we introduce the following aspects of this model, which reflect adaptability to changing circumstances: (1) after one leg is exposed to a transient perturbation, the walking pattern recovers swiftly; (2) when the external load parallel to the walking direction is continuously increased or decreased, the pattern transition point is shifted according to the magnitude of the load increme nt or decrement. This model generates a walking pattern which optimizes energy consumption at a given walking velocity even under these conditions; and (3) when some of the legs are amputated, the model generates walking patterns which are consistent with experimental results. We also discuss the ability of a hierarchical self-organizing model to describe a swift and flexible information processing system. Received: 8 February 1993/Accepted in revised form: 12 November 1993     

A self-organizing model of walking patterns of insects

It is well known that the motor systems of animals are controlled by a hierarchy consisting of a brain, central pattern generator, and effector organs. An animal's walking patterns change depending on its walking velocities, even when it has been decerebrated, which indicates that the walking patterns may, in fact, be generated in the subregions of the neural systems of the central pattern generator and the effector organs. In order to explain the self-organization of the walking pattern in response to changing circumstances, our model incorporates the following ideas: (1) the brain sends only a few commands to the central pattern generator (CPG) which act as constraints to self-organize the walking patterns in the CPG; (2) the neural network of the CPG is composed of oscillating elements such as the KYS oscillator, which has been shown to simulate effectively the diversity of the neural activities; and (3) we have introduced a rule to coordinate leg movement, in which the excitatory and inhibitory interactions among the neurons act to optimize the efficiency of the energy transduction of the effector organs. We describe this mechanism as the least dissatisfaction for the greatest number of elements, which is a self-organization rule in the generation of walking patterns. By this rule, each leg tends to share the load as efficiently as possible under any circumstances. Using this self-organizing model, we discuss the control mechanism of walking patterns.     

The contributions of diverse sense organs to the control of leg movement by a walking insect

Summary During locomotion, stick insectsCarausius morosus, place the tarsus of the rear leg near the tarsus of the ipsilateral middle leg, whatever the position of the latter. This adjustment by the hind leg requires that it receive information on the actual position of the middle leg tarsus. It is shown by ablation experiments that such information is contributed by the following proprioceptors of the middle leg: the ventral and dorsal coxal hairplates, the coxal hair rows, the trochanteral hairplate and the femoral chordotonal organ. Additional information comes from other, as yet unidentified, sense organs. Several alternatives are considered to explain how the signals from the diverse sense organs of the subcoxal joint might be combined in computing the target position for the protracting hind leg. The experimental results support the hypothesis that the signals are added nonlinearly and that a signal deviating from the majority pattern is weighted less.Abbreviations cxHPu ventral coxal hairplate - cxHPd dorsal coxal hairplate - trHP trochanteral hairplate - HR hair row - feCO femoral chordotonal organ - AEP anterior extreme position     

Sensory influences on the coordination of two leg joints during searching movements of stick insects

Animals (Cuniculina impigra) possessing only one foreleg with restrained coxa perform very stereotyped searching movements during which the movements of the femur-tibia and coxa-trochanter joints are well coordinated. After ablation of either hairfield BF1 (measuring the position of the coxa-trochanter joint) or the apodeme of the femoral chordotonal organ (measuring the position of the femur-tibia joint) each joint can still be moved but the coordination changes and becomes very labile. The consequences for the ideas about the construction principles of the pattern generator for searching movements are discussed.     

A new model describing the coordination pattern of the legs of a walking stick insect

A computer (Fortran) model is proposed that describes the temporal and spatial coordination pattern of straight walking stick insects (Carausius morosus) for a broad speed range. It provides a stable pattern independent of the different starting positions. The model is based on six relaxation oscillators. The leading oscillator corresponds to a frontleg. Therefore the information flow runs from front to rear in contrast to earlier models (Graham, 1972; Wendler, 1968).Supported by DFG     

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.     

A model of coordination of sperm flagella movement

The periodicity of bulls and humans' spermatozoa motion is investigated. The period of their motion is divisible by 24 and 15 turns of spermatozoa heads respectively. The interrelation of the observed periodicity with the ultrastructure of gamete tails is pre-supposed. A model of mitochondrial coordination of sperm flagella movement is proposed.     

Comparison of forces developed by the leg of the rock lobster when walking free or on a treadmill

Summary In the free walking rock lobster the forces developed by legs 4 and 5 were investigated during the power stroke. Two orthogonal force components lying in the horizontal plane were measured. Based on these results the diffent tasks of the two legs during walking are discussed. The forces developed by leg 4 were compared when the animal walked freely and on a treadmill. In these two situations the results differ qualitatively as in driven walking the forces are nearly identical in a long series of consecutive steps whereas in free walking the forces can vary greatly from step to step. However, similar mean values of force were measured with those on the treadmill being somewhat higher. This shows that, although the treadmill is driven by a motor, the animal does perform active walking movements. In the treadmill situation the forces increase as the speed of treadmill motor is decreased.Supported by DAAD and DFG (Cr 58) for H. Cruse and by ATP (80 119.112) INSERM for F. Clarac     

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

The kinematic model presented in a separate report is used here to investigate several questions concerning the nature of the coordinating mechanisms. First, one or more mechanisms are inactivated in order to compare the relative efficiencies of the different coordinating mechanisms in maintaining proper coordination. Second, the most efficient mechanism, the position-dependent influence, is varied in order to illustrate the consequences for coordination. Third, the strength of the contralateral coupling is varied in order to make predictions about how contralateral legs establish alternation when started from symmetric positions. The consequences of adding reciprocal contralateral inhibition during swing is tested in the same context.     

Electrophysiological properties of pyridine receptors in the crayfish walking leg

Summary Responses of pyridine sensitive units on walking legs of the crayfishOrconectes limosus have been studied using extracellular recording techniques.Post-stimulus-time histograms were established and the mean values of the maximal frequencies were plotted in dose-response curves. The curves can be separated into two groups having a slope of 0.3 and 1 in double logarithmic plots and a sensitivity range of 4 and 2 decades, respectively. This implies two different types of pyridine receptors.Abbreviation vH van Harreveld solution     

Timing and shaping influences on the motor output for walking in stick insects

An examination of the literature on walking stick insects shows: sensory influences on the transition from stance to swing phase (timing influences) also influence the shape of the stance phase motor output, as far as this was tested. Therefore, the distinction between timing and shaping influences seems to be artificial in this case. The results suggest that the walking pattern generator is a relaxation oscillator.     

Muscle coordination of mediolateral balance in normal walking

The aim of this study was to describe and explain how individual muscles control mediolateral balance during normal walking. Biomechanical modeling and experimental gait data were used to quantify individual muscle contributions to the mediolateral acceleration of the center of mass during the stance phase. We tested the hypothesis that the hip, knee, and ankle extensors, which act primarily in the sagittal plane and contribute significantly to vertical support and forward progression, also accelerate the center of mass in the mediolateral direction. Kinematic, force plate, and muscle EMG data were recorded simultaneously for five healthy subjects who walked at their preferred speeds. The body was modeled as a 10-segment, 23 degree-of-freedom skeleton, actuated by 54 muscles. Joint moments obtained from inverse dynamics were decomposed into muscle forces by solving an optimization problem that minimized the sum of the squares of the muscle activations. Muscles contributed significantly to the mediolateral acceleration of the center of mass throughout stance. Muscles that generated both support and forward progression (vasti, soleus, and gastrocnemius) also accelerated the center of mass laterally, in concert with the hip adductors and the plantarflexor everters. Gravity accelerated the center of mass laterally for most of the stance phase. The hip abductors, anterior and posterior gluteus medius, and, to a much lesser extent, the plantarflexor inverters, actively controlled balance by accelerating the center of mass medially.