From Motor-Output to Connectivity: An In-Depth Study of in-vitro Rhythmic Patterns in the Cockroach Periplaneta americana

The cockroach is an established model in the study of locomotion control. While previous work has offered important insights into the interplay among brain commands, thoracic central pattern generators, and the sensory feedback that shapes their motor output, there remains a need for a detailed description of the central pattern generators' motor output and their underlying connectivity scheme. To this end, we monitored pilocarpine-induced activity of levator and depressor motoneurons in two types of novel in-vitro cockroach preparations: isolated thoracic ganglia and a whole-chain preparation comprising the thoracic ganglia and the subesophageal ganglion. Our data analyses focused on the motoneuron firing patterns and the coordination among motoneuron types in the network. The burstiness and rhythmicity of the motoneurons were monitored, and phase relations, coherence, coupling strength, and frequency-dependent variability were analyzed. These parameters were all measured and compared among network units both within each preparation and among the preparations. Here, we report differences among the isolated ganglia, including asymmetries in phase and coupling strength, which indicate that they are wired to serve different functions. We also describe the intrinsic default gait and a frequency-dependent coordination. The depressor motoneurons showed mostly similar characteristics throughout the network regardless of interganglia connectivity; whereas the characteristics of the levator motoneurons activity were mostly ganglion-dependent, and influenced by the presence of interganglia connectivity. Asymmetries were also found between the anterior and posterior homolog parts of the thoracic network, as well as between ascending and descending connections. Our analyses further discover a frequency-dependent inversion of the interganglia coordination from alternations between ipsilateral homolog oscillators to simultaneous activity. We present a detailed scheme of the network couplings, formulate coupling rules, and review a previously suggested model of connectivity in light of our new findings. Our data support the notion that the inter-hemiganglia coordination derives from the levator networks and their coupling with local depressor interneurons. Our findings also support a dominant role of the metathoracic ganglion and its ascending output in governing the anterior ganglia motor output during locomotion in the behaving animal.

The roles of ascending sensory signals and top-down central control in the entrainment of a locomotor CPG

Previous authors have proposed two basic hypotheses about the factors that form the basis of locomotor rhythms in walking insects: sensory feedback only or sensory feedback together with rhythmic activity of small neural circuits called central pattern generators (CPGs). Here we focus on the latter. Following this concept, to generate functional outputs, locomotor control must feature both rhythm generation by CPGs at the level of individual joints and coordination of their rhythmic activities, so that all muscles are activated in an appropriate pattern. This work provides an in-depth analysis of an aspect of this coordination process based on an existing network model of stick insect locomotion. Specifically, we consider how the control system for a single joint in the stick insect leg may produce rhythmic output when subjected to ascending sensory signals from other joints in the leg. In this work, the core rhythm generating CPG component of the joint under study is represented by a classical half-center oscillator constrained by a basic set of experimental observations. While the dynamical features of this CPG, including phase transitions by escape and release, are well understood, we provide novel insights about how these transition mechanisms yield entrainment to the incoming sensory signal, how entrainment can be lost under variation of signal strength and period or other perturbations, how entrainment can be restored by modulation of tonic top-down drive levels, and how these factors impact the duty cycle of the motor output.

Pectoral fin kinematics and motor patterns are shaped by fin ray mechanosensation during steady swimming in Scarus quoyi

For many fish species, rhythmic movement of the pectoral fins, or forelimbs, drives locomotion. In terrestrial vertebrates, normal limb-based rhythmic gaits require ongoing modulation with limb mechanosensors. Given the complexity of the fluid environment and dexterity of fish swimming through it, we hypothesize that mechanosensory modulation is also critical to normal fin-based swimming. Here, we examined the role of sensory feedback from the pectoral fin rays and membrane on the neuromuscular control and kinematics of pectoral fin-based locomotion. Pectoral fin kinematics and electromyograms of the six major fin muscles of the parrotfish, Scarus quoyi, a high-performance pectoral fin swimmer, were recorded during steady swimming before and after bilateral transection of the sensory nerves extending into the rays and surrounding membrane. Alternating activity of antagonistic muscles was observed and drove the fin in a figure-of-eight fin stroke trajectory before and after nerve transection. After bilateral transections, pectoral fin rhythmicity remained the same or increased. Differences in fin kinematics with the loss of sensory feedback also included fin kinematics with a significantly more inclined stroke plane angle, an increased angular velocity and fin beat frequency, and a transition to the body-caudal fin gait at lower speeds. After transection, muscles were active over a larger proportion of the fin stroke, with overlapping activation of antagonistic muscles rarely observed in the trials of intact fish. The increased overlap of antagonistic muscle activity might stiffen the fin system in order to enhance control and stability in the absence of sensory feedback from the fin rays. These results indicate that fin ray sensation is not necessary to generate the underlying rhythm of fin movement, but contributes to the specification of pectoral fin motor pattern and movement during rhythmic swimming.

Information-based centralization of locomotion in animals and robots

The centralization of locomotor control from weak and local coupling to strong and global is hard to assess outside of particular modeling frameworks. We developed an empirical, model-free measure of centralization that compares information between control signals and both global and local states. A second measure, co-information, quantifies the net redundancy in global and local control. We first validate that our measures predict centralization in simulations of phase-coupled oscillators. We then test how centralization changes with speed in freely running cockroaches. Surprisingly, across all speeds centralization is constant and muscle activity is more informative of the global kinematic state (the averages of all legs) than the local state of that muscle's leg. Finally we use a legged robot to show that mechanical coupling alone can change the centralization of legged locomotion. The results of these systems span a design space of centralization and co-information for biological and robotic systems.

The Metastability of the Double-Tripod Gait in Locust Locomotion

Insect locomotion represents a fundamental example of neuronal oscillating circuits generating different motor patterns or gaits by controlling their phase coordination. Walking gaits are assumed to represent stable states of the system, often modeled as coupled oscillators. This view is challenged, however, by recent experimental observations, in which in vitro locust preparations consistently converged to synchronous rhythms (all legs oscillating as one), a locomotive pattern never seen in vivo. To reconcile this inconsistency, we developed a modeling framework to capture the trade-off between the two competing mechanisms: the endogenous neuronal circuitry, expressed in vitro, and the feedback mechanisms from sensory and descending inputs, active only in vivo. We show that the ubiquitously observed double-tripod walking gait emerges precisely from this balance. The outcome is a short-lived meta-stable double-tripod gait, which transitions and alternates with stable idling, thus recovering the observed intermittent bouts of locomotion, typical of many insects' locomotion behavior.

•

Isolated in vitro locust preparations indicate that idling is a stable fictive gait

•

This is in contrast to the dominant in vivo locomotive pattern (i.e., double tripod)

•

Hence functional locomotion behavior is dependent on descending and sensory inputs

•

The presented model generates intermittent double-tripod bouts as seen empirically

The functional connectivity between the locust leg pattern generators and the subesophageal ganglion higher motor center

Higher motor centers and central pattern generators (CPGs) interact in the control of coordinated leg movements during locomotion throughout the animal kingdom. The subesophageal ganglion (SEG) is one of the insect head ganglia reported to have a role in the control of walking behavior. Here we explored the functional relations between the SEG and the thoracic leg CPGs in the desert locust. Backfill staining revealed about 300 SEG descending interneurons (DINs) altogether. Recordings from an in-vitro isolated chain of thoracic ganglia, with intact or severed connections to the SEG, during pharmacological activation were used to determine how the SEG affects the centrally generated motor output to the legs. The SEG was demonstrated to both activate leg CPGs and synchronize their bilateral activity. The role of the SEG in insect locomotion is discussed in light of these findings.

Signatures of proprioceptive control in Caenorhabditis elegans locomotion

Animal neuromechanics describes the coordinated self-propelled movement of a body, subject to the combined effects of internal neural control and mechanical forces. Here we use a computational model to identify effects of neural and mechanical modulation on undulatory forward locomotion of Caenorhabditis elegans, with a focus on proprioceptively driven neural control. We reveal a fundamental relationship between body elasticity and environmental drag in determining the dynamics of the body and demonstrate the manifestation of this relationship in the context of proprioceptively driven control. By considering characteristics unique to proprioceptive neurons, we predict the signatures of internal gait modulation that contrast with the known signatures of externally or biomechanically modulated gait. We further show that proprioceptive feedback can suppress neuromechanical phase lags during undulatory locomotion, contrasting with well studied advancing phase lags that have long been a signature of centrally generated, feed-forward control.This article is part of a discussion meeting issue 'Connectome to behaviour: modelling C. elegans at cellular resolution'.

The effects of feedback on stability and maneuverability of a phase-reduced model for cockroach locomotion

In previous work, we built a neuromechanical model for insect locomotion in the horizontal plane, containing a central pattern generator, motoneurons, muscles actuating jointed legs, and rudimentary proprioceptive feedback. This was subsequently simplified to a set of 24 phase oscillators describing motoneuronal activation of agonist-antagonist muscle pairs, which facilitates analyses and enables simulations over multi-dimensional parameter spaces. Here we use the phase-reduced model to study dynamics and stability over the typical speed range of the cockroach Blaberus discoidalis, the effects of feedback on response to perturbations, strategies for turning, and a trade-off between stability and maneuverability. We also compare model behavior with experiments on lateral perturbations, changes in body mass and moment of inertia, and climbing dynamics, and we present a simple control strategy for steering using exteroceptive feedback.

The use of MEMRI for monitoring central nervous system activity during intact insect walking

BACKGROUND

Monitoring neuronal activity in the intact behaving animal is most desired in neuroethological research, yet it is rarely straightforward or even feasible. Here we present the use of manganese enhanced magnetic resonance imaging (MEMRI), a technique allowing monitoring the activity of an animal's nervous system during specific behavioral patterns. Using MEMRI we were able to show activity in different ganglia of the central nervous system of intact locusts during walking.

RESULTS

We injected two groups of locusts with manganese, which serves as a magnetic contrast agent. One group was forced to walk on a treadmill for two hours, while the other was immobilized and served as a control. Subsequently, all animals were scanned in a T1 MRI protocol, and the accumulation of manganese in the neuronal tissues that were active during walking was demonstrated by comparing the scans of the two groups. Two neuronal sites showed significantly higher T1 signal in the walking locusts compared to the immobilized ones: the prothoracic ganglion, which locally controls the front legs, and the subesophageal ganglion, a head ganglion which takes part in initiation and maintenance of walking.

CONCLUSION

MEMRI is a potent, non-invasive technique for monitoring neuronal activity in intact locusts, and arthropods in general. Specifically, it provides a promising way for revealing the role of central and high-order neuronal structures in motor behaviors such as walking.

The subesophageal ganglion modulates locust inter-leg sensory-motor interactions via contralateral pathways

The neural control of insect locomotion is distributed among various body segments. Local pattern-generating circuits at the thoracic ganglia interact with incoming sensory signals and central descending commands from the head ganglia. The evidence from different insect preparations suggests that the subesophageal ganglion (SEG) may play an important role in locomotion-related tasks. In a previous study, we demonstrated that the locust SEG modulates the coupling pattern between segmental leg CPGs in the absence of sensory feedback. Here, we investigated its role in processing and transmitting sensory information to the leg motor centers and mapped the major related neural pathways. Specifically, the intra- and inter-segmental transfer of leg-feedback were studied by simultaneously monitoring motor responses and descending signals from the SEG. Our findings reveal a crucial role of the SEG in the transfer of intersegmental, but not intrasegmental, signals. Additional lesion experiments, in which the intersegmental connectives were cut at different locations, together with double nerve staining, indicated that sensory signals are mainly transferred to the SEG via the connective contralateral to the stimulated leg. We therefore suggest that, similar to data reported for vertebrates, insect leg sensory-motor loops comprise contralateral ascending pathways to the head and ipsilateral descending ones.

Six-legged walking in insects: how CPGs, peripheral feedback, and descending signals generate coordinated and adaptive motor rhythms

Walking is a rhythmic locomotor behavior of legged animals, and its underlying mechanisms have been the subject of neurobiological research for more than 100 years. In this article, we review relevant historical aspects and contemporary studies in this field of research with a particular focus on the role of central pattern generating networks (CPGs) and their contribution to the generation of six-legged walking in insects. Aspects of importance are the generation of single-leg stepping, the generation of interleg coordination, and how descending signals influence walking. We first review how CPGs interact with sensory signals from the leg in the generation of leg stepping. Next, we summarize how these interactions are modified in the generation of motor flexibility for forward and backward walking, curve walking, and speed changes. We then review the present state of knowledge with regard to the role of CPGs in intersegmental coordination and how CPGs might be involved in mediating descending influences from the brain for the initiation, maintenance, modification, and cessation of the motor output for walking. Throughout, we aim to specifically address gaps in knowledge, and we describe potential future avenues and approaches, conceptual and methodological, with the latter emphasizing in particular options arising from the advent of neurogenetic approaches to this field of research and its combination with traditional approaches.

Intra- and intersegmental influences among central pattern generating networks in the walking system of the stick insect

To efficiently move around, animals need to coordinate their limbs. Proper, context-dependent coupling among the neural networks underlying leg movement is necessary for generating intersegmental coordination. In the slow-walking stick insect, local sensory information is very important for shaping coordination. However, central coupling mechanisms among segmental central pattern generators (CPGs) may also contribute to this. Here, we analyzed the interactions between contralateral networks that drive the depressor trochanteris muscle of the legs in both isolated and interconnected deafferented thoracic ganglia of the stick insect on application of pilocarpine, a muscarinic acetylcholine receptor agonist. Our results show that depressor CPG activity is only weakly coupled between all segments. Intrasegmental phase relationships differ between the three isolated ganglia, and they are modified and stabilized when ganglia are interconnected. However, the coordination patterns that emerge do not resemble those observed during walking. Our findings are in line with recent studies and highlight the influence of sensory input on coordination in slowly walking insects. Finally, as a direct interaction between depressor CPG networks and contralateral motoneurons could not be observed, we hypothesize that coupling is based on interactions at the level of CPG interneurons.NEW & NOTEWORTHY Maintaining functional interleg coordination is vitally important as animals locomote through changing environments. The relative importance of central mechanisms vs. sensory feedback in this process is not well understood. We analyzed coordination among the neural networks generating leg movements in stick insect preparations lacking phasic sensory feedback. Under these conditions, the networks governing different legs were only weakly coupled. In stick insect, central connections alone are thus insufficient to produce the leg coordination observed behaviorally.

Rigidity and Flexibility: The Central Basis of Inter-Leg Coordination in the Locust

Many motor behaviors, and specifically locomotion, are the product of an intricate interplay between neuronal oscillators known as central pattern generators (CPGs), descending central commands, and sensory feedback loops. The relative contribution of each of these components to the final behavior determines the trade-off between fixed movements and those that are carefully adapted to the environment. Here we sought to decipher the endogenous, default, motor output of the CPG network controlling the locust legs, in the absence of any sensory or descending influences. We induced rhythmic activity in the leg CPGs in isolated nervous system preparations, using different application procedures of the muscarinic agonist pilocarpine. We found that the three thoracic ganglia, each controlling a pair of legs, have different inherent bilateral coupling. Furthermore, we found that the pharmacological activation of one ganglion is sufficient to induce activity in the other, untreated, ganglia. Each ganglion was thus capable to impart its own bilateral inherent pattern onto the other ganglia via a tight synchrony among the ipsilateral CPGs. By cutting a connective and severing the lateral-longitudinal connections, we were able to uncouple the oscillators’ activity. While the bilateral connections demonstrated a high modularity, the ipsilateral CPGs maintained a strict synchronized activity. These findings suggest that the central infrastructure behind locust walking features both rigid elements, which presumably support the generation of stereotypic orchestrated leg movements, and flexible elements, which might provide the central basis for adaptations to the environment and to higher motor commands.

Endogenous rhythm and pattern-generating circuit interactions in cockroach motor centres

Cockroaches are rapid and stable runners whose gaits emerge from the intricate, and not fully resolved, interplay between endogenous oscillatory pattern-generating networks and sensory feedback that shapes their rhythmic output. Here we studied the endogenous motor output of a brainless, deafferented preparation. We monitored the pilocarpine-induced rhythmic activity of levator and depressor motor neurons in the mesothoracic and metathoracic segments in order to reveal the oscillatory networks’ architecture and interactions. Data analyses included phase relations, latencies between and overlaps of rhythmic bursts, spike frequencies, and the dependence of these parameters on cycle frequency. We found that, overall, ipsilateral connections are stronger than contralateral ones. Our findings revealed asymmetries in connectivity among the different ganglia, in which meta-to-mesothoracic ascending coupling is stronger than meso-to-metathoracic descending coupling. Within-ganglion coupling between the metathoracic hemiganglia is stronger than that in the mesothoracic ganglion. We also report differences in the role and mode of operation of homologue network units (manifested by levator and depressor nerve activity). Many observed characteristics are similar to those exhibited by intact animals, suggesting a dominant role for feedforward control in cockroach locomotion. Based on these data we posit a connectivity scheme among components of the locomotion pattern generating system.

Summary: Detailed analysis of fictive motor patterns unveils endogenous characteristics of the cockroach thoracic locomotion control networks and their interrelations and enables an explanatory connectivity model.

Evaluation of the Phase-Dependent Rhythm Control of Human Walking Using Phase Response Curves

Humans and animals control their walking rhythms to maintain motion in a variable environment. The neural mechanism for controlling rhythm has been investigated in many studies using mechanical and electrical stimulation. However, quantitative evaluation of rhythm variation in response to perturbation at various timings has rarely been investigated. Such a characteristic of rhythm is described by the phase response curve (PRC). Dynamical simulations of human skeletal models with changing walking rhythms (phase reset) described a relation between the effective phase reset on stability and PRC, and phase reset around touch-down was shown to improve stability. A PRC of human walking was estimated by pulling the swing leg, but such perturbations hardly influenced the stance leg, so the relation between the PRC and walking events was difficult to discuss. This research thus examines human response to variations in floor velocity. Such perturbation yields another problem, in that the swing leg is indirectly (and weakly) perturbed, so the precision of PRC decreases. To solve this problem, this research adopts the weighted spike-triggered average (WSTA) method. In the WSTA method, a sequential pulsed perturbation is used for stimulation. This is in contrast with the conventional impulse method, which applies an intermittent impulsive perturbation. The WSTA method can be used to analyze responses to a large number of perturbations for each sequence. In the experiment, perturbations are applied to walking subjects by rapidly accelerating and decelerating a treadmill belt, and measured data are analyzed by the WSTA and impulse methods. The PRC obtained by the WSTA method had clear and stable waveforms with a higher temporal resolution than those obtained by the impulse method. By investigation of the rhythm transition for each phase of walking using the obtained PRC, a rhythm change that extends the touch-down and mid-single support phases is found to occur.

Humans and animals tune their walking rhythms when motion is disturbed, such that they hesitate before making the transition from stance to swing phase. The effectiveness of rhythm control for stability has also been shown, and thus the elucidation of rhythm responses is important to understanding human strategies for walking control. In this research, how and when humans change their walking rhythm in response to disturbance is analyzed over the complete walking cycle. Phase response of human walking has previously been estimated by pulling the swing leg. The problem with this perturbation is that it hardly disturbs the stance leg, so here we apply the perturbation by changing floor velocity. However, perturbation from the floor yields another problem in that it weakly influences the swing leg, decreasing the precision of the PRC. The present research tackles this problem by introducing a new method for identifying rhythm characteristics by use of high-frequency perturbation, which allows us to obtain results with clear temporal resolution. We found that the human walking rhythm changes by lengthening the touch-down and mid-single support phases. These phase responses are compared with neural mechanisms for rhythm control, and relevance to the cutaneous and proprioceptive originated responses is shown.

Recovery of locomotion after injury in Drosophila melanogaster depends on proprioception

Locomotion is necessary for survival in most animal species. However, injuries to the appendages mediating locomotion are common. We assess the recovery of walking in Drosophila melanogaster following leg amputation. Whereas flies pre-amputation explore open arenas in a symmetric fashion on average, foreleg amputation induces a strong turning bias away from the side of the amputation. However, we find that unbiased walking behavior returns over time in wild-type flies, while recovery is significantly impaired in proprioceptive mutants. To identify the biomechanical basis of this locomotor impairment and recovery, we then examine individual leg motion (gait) at a fine scale. A minimal mathematical model that links neurodynamics to body mechanics during walking shows that redistributing leg forces between the right and left side enables the observed recovery. Altogether, our study suggests that proprioceptive input from the intact limbs plays a crucial role in the behavioral plasticity associated with locomotor recovery after injury.

Fin ray sensation participates in the generation of normal fin movement in the hovering behavior of the bluegill sunfish (Lepomis macrochirus)

For many fish species, the pectoral fins serve as important propulsors and stabilizers and are precisely controlled. Although it has been shown that mechanosensory feedback from the fin ray afferent nerves provides information on ray bending and position, the effects of this feedback on fin movement are not known. In other taxa, including insects and mammals, sensory feedback from the limbs has been shown to be important for control of limb-based behaviors and we hypothesized that this is also the case for the fishes. In this study, we examined the impact of the loss of sensory feedback from the pectoral fins on movement kinematics during hover behavior. Research was performed with bluegill sunfish (Lepomis macrochirus), a model for understanding the biomechanics of swimming and for bio-inspired design of engineered fins. The bluegill beats its pectoral fins rhythmically, and in coordination with pelvic and median fin movement, to maintain a stationary position while hovering. Bilateral deafferentation of the fin rays results in a splay-finned posture where fins beat regularly but at a higher frequency and without adducting fully against the side of the body. For unilateral transections, more irregular changes in fin movements were recorded. These data indicate that sensory feedback from the fin rays and membrane is important for generating normal hover movements but is not necessary for generating rhythmic fin movement.

Differential control of temporal and spatial aspects of cockroach leg coordination

Ensembles of neuronal networks and sensory pathways participate in controlling the kinematic and dynamic parameters of animal movement necessary to achieve motor coordination. Determining the relative contribution of proprioceptive feedback is essential for understanding how animals sustain stable, coordinated locomotion in complex natural environments. Here, we focus on the role of chordotonal organs (COs), proprioceptors found in insect legs, in the spatial and temporal regulation of walking. We compare gait parameters of intact cockroaches (Periplaneta americana) and sensory-impaired ones, injected with pymetrozine, a chemical previously shown to abolish CO function in locusts. We verify that afferent CO activity in pymetrozine-treated cockroaches is inhibited, and analyze the effect of this sensory deprivation on inter-leg coordination. We find significant changes in tarsi placement and leg path trajectories after pymetrozine treatment. Leg touchdown accuracy, measured from relative tarsi positions of adjacent legs, is reduced in treated animals. Interestingly, despite poorer spatial coordination in both stance and swing, temporal properties of the gait remain largely the same as in the intact preparations, apart from changes in ipsilateral phase differences between front and middle legs. These findings provide insights into the role of COs in insect gait control and establish pymetrozine as a useful tool for further studies of insect locomotion.

Intersegmental coupling and recovery from perturbations in freely running cockroaches

Cockroaches are remarkably stable runners, exhibiting rapid recovery from external perturbations. To uncover the mechanisms behind this important behavioral trait, we recorded leg kinematics of freely running animals in both undisturbed and perturbed trials. Functional coupling underlying inter-leg coordination was monitored before and during localized perturbations, which were applied to single legs via magnetic impulses. The resulting transient effects on all legs and the recovery times to normal pre-perturbation kinematics were studied. We estimated coupling architecture and strength by fitting experimental data to a six-leg-unit phase oscillator model. Using maximum-likelihood techniques, we found that a network with nearest-neighbor inter-leg coupling best fitted the data and that, although coupling strengths vary among preparations, the overall inputs entering each leg are approximately balanced and consistent. Simulations of models with different coupling strengths encountering perturbations suggest that the coupling schemes estimated from our experiments allow animals relatively fast and uniform recoveries from perturbations.

A survey on CPG-inspired control models and system implementation

This paper surveys the developments of the last 20 years in the field of central pattern generator (CPG) inspired locomotion control, with particular emphasis on the fast emerging robotics-related applications. Functioning as a biological neural network, CPGs can be considered as a group of coupled neurons that generate rhythmic signals without sensory feedback; however, sensory feedback is needed to shape the CPG signals. The basic idea in engineering endeavors is to replicate this intrinsic, computationally efficient, distributed control mechanism for multiple articulated joints, or multi-DOF control cases. In terms of various abstraction levels, existing CPG control models and their extensions are reviewed with a focus on the relative advantages and disadvantages of the models, including ease of design and implementation. The main issues arising from design, optimization, and implementation of the CPG-based control as well as possible alternatives are further discussed, with an attempt to shed more light on locomotion control-oriented theories and applications. The design challenges and trends associated with the further advancement of this area are also summarized.

Insects use two distinct classes of steps during unrestrained locomotion

Background

Adaptive, context-dependent control of locomotion requires modulation of centrally generated rhythmic motor patterns through peripheral control loops and postural reflexes. Thus assuming that the modulation of rhythmic motor patterns accounts for much of the behavioural variability observed in legged locomotion, investigating behavioural variability is a key to the understanding of context-dependent control mechanisms in locomotion. To date, the variability of unrestrained locomotion is poorly understood, and virtually nothing is known about the features that characterise the natural statistics of legged locomotion. In this study, we quantify the natural variability of hexapedal walking and climbing in insects, drawing from a database of several thousand steps recorded over two hours of walking time.

Results

We show that the range of step length used by unrestrained climbing stick insects is large, showing that step length can be changed substantially for adaptive locomotion. Step length distributions were always bimodal, irrespective of leg type and walking condition, suggesting the presence of two distinct classes of steps: short and long steps. Probability density of step length was well-described by a gamma distribution for short steps, and a logistic distribution for long steps. Major coefficients of these distributions remained largely unaffected by walking conditions. Short and long steps differed concerning their spatial occurrence on the walking substrate, their timing within the step sequence, and their prevalent swing direction. Finally, ablation of structures that serve to improve foothold increased the ratio of short to long steps, indicating a corrective function of short steps.

Conclusions

Statistical and functional differences suggest that short and long steps are physiologically distinct classes of leg movements that likely reflect distinct control mechanisms at work.

Instantaneous kinematic phase reflects neuromechanical response to lateral perturbations of running cockroaches

Instantaneous kinematic phase calculation allows the development of reduced-order oscillator models useful in generating hypotheses of neuromechanical control. When perturbed, changes in instantaneous kinematic phase and frequency of rhythmic movements can provide details of movement and evidence for neural feedback to a system-level neural oscillator with a time resolution not possible with traditional approaches. We elicited an escape response in cockroaches (Blaberus discoidalis) that ran onto a movable cart accelerated laterally with respect to the animals' motion causing a perturbation. The specific impulse imposed on animals (0.50 [Formula: see text] 0.04 m s[Formula: see text]; mean, SD) was nearly twice their forward speed (0.25 [Formula: see text] 0.06 m s[Formula: see text]. Instantaneous residual phase computed from kinematic phase remained constant for 110 ms after the onset of perturbation, but then decreased representing a decrease in stride frequency. Results from direct muscle action potential recordings supported kinematic phase results in showing that recovery begins with self-stabilizing mechanical feedback followed by neural feedback to an abstracted neural oscillator or central pattern generator. Trials fell into two classes of forward velocity changes, while exhibiting statistically indistinguishable frequency changes. Animals pulled away from the side with front and hind legs of the tripod in stance recovered heading within 300 ms, whereas animals that only had a middle leg of the tripod resisting the pull did not recover within this period. Animals with eight or more legs might be more robust to lateral perturbations than hexapods.