A neuromechanical model explaining forward and backward stepping in the stick insect

Mechanosensory bristles mediate avoidance behavior by triggering sustained local motor activity in Drosophila melanogaster

During locomotion, most vertebrates-and invertebrates such as Drosophila melanogaster-are able to quickly adapt to terrain irregularities or avoid physical threats by integrating sensory information along with motor commands. Key to this adaptability are leg mechanosensory structures, which assist in motor coordination by transmitting external cues and proprioceptive information to motor centers in the central nervous system. Nevertheless, how different mechanosensory structures engage these locomotor centers remains poorly understood. Here, we tested the role of mechanosensory structures in movement initiation by optogenetically stimulating specific classes of leg sensory structures. We found that stimulation of leg mechanosensory bristles (MsBs) and the femoral chordotonal organ (ChO) is sufficient to initiate forward movement in immobile animals. While the stimulation of the ChO required brain centers to induce forward movement, unexpectedly, brief stimulation of leg MsBs triggered a fast response and sustained motor activity dependent only on the ventral nerve cord (VNC). Moreover, this leg-MsB-mediated movement lacked inter- and intra-leg coordination but preserved antagonistic muscle activity within joints. Finally, we show that leg-MsB activation mediates strong avoidance behavior away from the stimulus source, which is preserved even in the absence of a central brain. Overall, our data show that mechanosensory stimulation can elicit a fast motor response, independently of central brain commands, to evade potentially harmful stimuli. In addition, it sheds light on how specific sensory circuits modulate motor control, including initiation of movement, allowing a better understanding of how different levels of coordination are controlled by the VNC and central brain locomotor circuits.

Distributed control of motor circuits for backward walking in Drosophila

How do descending inputs from the brain control leg motor circuits to change how an animal walks? Conceptually, descending neurons are thought to function either as command-type neurons, in which a single type of descending neuron exerts a high-level control to elicit a coordinated change in motor output, or through a population coding mechanism, whereby a group of neurons, each with local effects, act in combination to elicit a global motor response. The Drosophila Moonwalker Descending Neurons (MDNs), which alter leg motor circuit dynamics so that the fly walks backwards, exemplify the command-type mechanism. Here, we identify several dozen MDN target neurons within the leg motor circuits, and show that two of them mediate distinct and highly-specific changes in leg muscle activity during backward walking: LBL40 neurons provide the hindleg power stroke during stance phase; LUL130 neurons lift the legs at the end of stance to initiate swing. Through these two effector neurons, MDN directly controls both the stance and swing phases of the backward stepping cycle. These findings suggest that command-type descending neurons can also operate through the distributed control of local motor circuits.

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.

Two Brain Pathways Initiate Distinct Forward Walking Programs in Drosophila

An animal at rest or engaged in stationary behaviors can instantaneously initiate goal-directed walking. How descending brain inputs trigger rapid transitions from a non-walking state to an appropriate walking state is unclear. Here, we identify two neuronal types, P9 and BPN, in the Drosophila brain that, upon activation, initiate and maintain two distinct coordinated walking patterns. P9 drives forward walking with ipsilateral turning, receives inputs from central courtship-promoting neurons and visual projection neurons, and is necessary for a male to pursue a female during courtship. In contrast, BPN drives straight, forward walking and is not required during courtship. BPN is instead recruited during and required for fast, straight, forward walking bouts. Thus, this study reveals separate brain pathways for object-directed walking and fast, straight, forward walking, providing insight into how the brain initiates context-appropriate walking programs.

A multilayer circuit architecture for the generation of distinct locomotor behaviors in Drosophila

Animals generate diverse motor behaviors, yet how the same motor neurons (MNs) generate two distinct or antagonistic behaviors remains an open question. Here, we characterize Drosophila larval muscle activity patterns and premotor/motor circuits to understand how they generate forward and backward locomotion. We show that all body wall MNs are activated during both behaviors, but a subset of MNs change recruitment timing for each behavior. We used TEM to reconstruct a full segment of all 60 MNs and 236 premotor neurons (PMNs), including differentially-recruited MNs. Analysis of this comprehensive connectome identified PMN-MN 'labeled line' connectivity; PMN-MN combinatorial connectivity; asymmetric neuronal morphology; and PMN-MN circuit motifs that could all contribute to generating distinct behaviors. We generated a recurrent network model that reproduced the observed behaviors, and used functional optogenetics to validate selected model predictions. This PMN-MN connectome will provide a foundation for analyzing the full suite of larval behaviors.

A kinematic model of stick-insect walking

Animal, and insect walking (locomotion) in particular, have attracted much attention from scientists over many years up to now. The investigations included behavioral, electrophysiological experiments, as well as modeling studies. Despite the large amount of material collected, there are left many unanswered questions as to how walking and related activities are generated, maintained, and controlled. It is obvious that for them to take place, precise coordination within muscle groups of one leg and between the legs is required: intra- and interleg coordination. The nature, the details, and the interactions of these coordination mechanisms are not entirely clear. To help uncover them, we made use of modeling techniques, and succeeded in developing a six-leg model of stick-insect walking. Our main goal was to prove that the same model can mimic a variety of walking-related behavioral modes, as well as the most common coordination patterns of walking just by changing the values of a few input or internal variables. As a result, the model can reproduce the basic coordination patterns of walking: tetrapod and tripod and the transition between them. It can also mimic stop and restart, change from forward-to-backward walking and back. Finally, it can exhibit so-called search movements of the front legs both while walking or standing still. The mechanisms of the model that enable it to produce the aforementioned behavioral modes can hint at and prove helpful in uncovering further details of the biological mechanisms underlying walking.

A load-based mechanism for inter-leg coordination in insects

Animals rely on an adaptive coordination of legs during walking. However, which specific mechanisms underlie coordination during natural locomotion remains largely unknown. One hypothesis is that legs can be coordinated mechanically based on a transfer of body load from one leg to another. To test this hypothesis, we simultaneously recorded leg kinematics, ground reaction forces and muscle activity in freely walking stick insects (Carausius morosus). Based on torque calculations, we show that load sensors (campaniform sensilla) at the proximal leg joints are well suited to encode the unloading of the leg in individual steps. The unloading coincides with a switch from stance to swing muscle activity, consistent with a load reflex promoting the stance-to-swing transition. Moreover, a mechanical simulation reveals that the unloading can be ascribed to the loading of a specific neighbouring leg, making it exploitable for inter-leg coordination. We propose that mechanically mediated load-based coordination is used across insects analogously to mammals.

Nitric oxide-mediated intersegmental modulation of cycle frequency in the crayfish swimmeret system

Crayfish swimmerets are paired appendages located on the ventral side of each abdominal segment that show rhythmic beating during forward swimming produced by central pattern generators in most abdominal segments. For animals with multiple body segments and limbs, intersegmental coordination of central pattern generators in each segment is crucial for the production of effective movements. Here we develop a novel pharmacological approach to analyse intersegmental modulation of swimmeret rhythm by selectively elevating nitric oxide levels and reducing them with pharmacological agents, in specific ganglia. Bath application of L-arginine, the substrate NO synthesis, increased the cyclical spike responses of the power-stroke motor neurons. By contrast the NOS inhibitor, L-NAME decreased them. To determine the role of the different local centres in producing and controlling the swimmeret rhythm, these two drugs were applied locally to two separate ganglia following bath application of carbachol. Results revealed that there was both ascending and descending intersegmental modulation of cycle frequency of the swimmeret rhythm in the abdominal ganglia and that synchrony of cyclical activity between segments of segments was maintained. We also found that there were gradients in the strength effectiveness in modulation, that ascending modulation of the swimmeret rhythm was stronger than descending modulation.

Summary: We develop a novel pharmacological approach using a nitric oxide donor and a nitric oxide synthase inhibitor to analyse modulation and segmental synchrony in the swimmeret rhythm of the crayfish.

Leg-local neural mechanisms for searching and learning enhance robotic locomotion

Adapting motor output based on environmental forces is critical for successful locomotion in the real world. Arthropods use at least two neural mechanisms to adjust muscle activation while walking based on detected forces. Mechanism 1 uses negative feedback of leg depressor force to ensure that each stance leg supports an appropriate amount of the body's weight. Mechanism 2 encourages searching for ground contact if the leg supports no body weight. We expand the neural controller for MantisBot, a robot based upon a praying mantis, to include these mechanisms by incorporating leg-local memory and command neurons, as observed in arthropods. We present results from MantisBot transitioning between searching and stepping, mimicking data from animals as reported in the literature.

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.

Mantisbot is a robotic model of visually guided motion in the praying mantis

Insects use highly distributed nervous systems to process exteroception from head sensors, compare that information with state-based goals, and direct posture or locomotion toward those goals. To study how descending commands from brain centers produce coordinated, goal-directed motion in distributed nervous systems, we have constructed a conductance-based neural system for our robot MantisBot, a 29 degree-of-freedom, 13.3:1 scale praying mantis robot. Using the literature on mantis prey tracking and insect locomotion, we designed a hierarchical, distributed neural controller that establishes the goal, coordinates different joints, and executes prey-tracking motion. In our controller, brain networks perceive the location of prey and predict its future location, store this location in memory, and formulate descending commands for ballistic saccades like those seen in the animal. The descending commands are simple, indicating only 1) whether the robot should walk or stand still, and 2) the intended direction of motion. Each joint's controller uses the descending commands differently to alter sensory-motor interactions, changing the sensory pathways that coordinate the joints' central pattern generators into one cohesive motion. Experiments with one leg of MantisBot show that visual input produces simple descending commands that alter walking kinematics, change the walking direction in a predictable manner, enact reflex reversals when necessary, and can control both static posture and locomotion with the same network.

Effects of functional decoupling of a leg in a model of stick insect walking incorporating three ipsilateral legs

Legged locomotion is a fundamental form of activity of insects during which the legs perform coordinated movements. Sensory signals conveying position, velocity and load of a leg are sent between the thoracic ganglia where the local control networks of the leg muscles are situated. They affect the actual state of the local control networks, hence the stepping of the legs. Sensory coordination in stepping has been intensively studied but important details of its neuronal mechanisms are still unclear. One possibility to tackle this problem is to study what happens to the coordination if a leg is, reversibly or irreversibly, deprived of its normal function. There are numerous behavioral studies on this topic but they could not fully uncover the underlying neuronal mechanisms. Another promising approach to make further progress here can be the use of appropriate models that help elucidate those coordinating mechanisms. We constructed a model of three ipsilateral legs of a stick insect that can mimic coordinated stepping of these legs. We used this model to investigate the possible effects of decoupling a leg. We found that decoupling of the front or the hind leg did not disrupt the coordinated walking of the two remaining legs. However, decoupling of the middle leg yielded mixed results. Both disruption and continuation of coordinated stepping of the front and hind leg occurred. These results agree with the majority of corresponding experimental findings. The model suggests a number of possible mechanisms of decoupling that might bring about the changes.

Robustness, flexibility, and sensitivity in a multifunctional motor control model

Motor systems must adapt to perturbations and changing conditions both within and outside the body. We refer to the ability of a system to maintain performance despite perturbations as "robustness," and the ability of a system to deploy alternative strategies that improve fitness as "flexibility." Different classes of pattern-generating circuits yield dynamics with differential sensitivities to perturbations and parameter variation. Depending on the task and the type of perturbation, high sensitivity can either facilitate or hinder robustness and flexibility. Here we explore the role of multiple coexisting oscillatory modes and sensory feedback in allowing multiphasic motor pattern generation to be both robust and flexible. As a concrete example, we focus on a nominal neuromechanical model of triphasic motor patterns in the feeding apparatus of the marine mollusk Aplysia californica. We find that the model can operate within two distinct oscillatory modes and that the system exhibits bistability between the two. In the "heteroclinic mode," higher sensitivity makes the system more robust to changing mechanical loads, but less robust to internal parameter variations. In the "limit cycle mode," lower sensitivity makes the system more robust to changes in internal parameter values, but less robust to changes in mechanical load. Finally, we show that overall performance on a variable feeding task is improved when the system can flexibly transition between oscillatory modes in response to the changing demands of the task. Thus, our results suggest that the interplay of sensory feedback and multiple oscillatory modes can allow motor systems to be both robust and flexible in a variable environment.

Body side-specific control of motor activity during turning in a walking animal

Animals and humans need to move deftly and flexibly to adapt to environmental demands. Despite a large body of work on the neural control of walking in invertebrates and vertebrates alike, the mechanisms underlying the motor flexibility that is needed to adjust the motor behavior remain largely unknown. Here, we investigated optomotor-induced turning and the neuronal mechanisms underlying the differences between the leg movements of the two body sides in the stick insect Carausius morosus. We present data to show that the generation of turning kinematics in an insect are the combined result of descending unilateral commands that change the leg motor output via task-specific modifications in the processing of local sensory feedback as well as modification of the activity of local central pattern generating networks in a body-side-specific way. To our knowledge, this is the first study to demonstrate the specificity of such modifications in a defined motor task.

DOI:http://dx.doi.org/10.7554/eLife.13799.001

Walking along a curve or turning is a complex manoeuvre for the nervous system, as it must coordinate different leg movements on each side of the body. Rhythmic processes such as walking are controlled by networks of neurons called central pattern generators. The resulting movements can be adjusted by feedback from sense organs in response to environmental conditions. For example, sensory feedback that provides information about the load placed on each leg, allows the animal to control the duration of a stance. How the nerve cells, or neurons, involved in these processes work together to produce complex, flexible movements such as turning is largely unknown.

Previous work on how the brain negotiates turning movements has been carried out mostly in animals that swim or fly. To understand what happens during walking, Gruhn et al. monitored stick insects that walked in a curve on a slippery surface, and recorded the electrical activity within the animals' nervous system as they turned.

By comparing the activity of the nervous system on each side of the body while the insects walked a curve, Gruhn et al. found that the nervous system uses at least three different mechanisms to produce the different movements on the inside and outside. Firstly, the sensory feedback signals that communicate the load on the leg are processed in the legs on the outside of the curve to support forward steps, while they are processed on the inside legs to support forward, sideward, and backward steps. Secondly, the motor activity produced by the central pattern generator is modulated to be stronger for the muscle that moves the leg backward on the outside of the curve. At the same time, this activity is stronger for the muscle that moves the leg forward on the inside of the curve. Thirdly, signals from a front leg influence the movement of the other legs on the same side of the body. This influence is strong on the inside and weak on the outside of the curve.

Together or separately, these three mechanisms could provide the animal with the means to perform turns in all their different curvatures. Future work will need to work out exactly which local neurons process the signals sent from the brain to control movement.

DOI:http://dx.doi.org/10.7554/eLife.13799.002

A three-leg model producing tetrapod and tripod coordination patterns of ipsilateral legs in the stick insect

Insect locomotion requires the precise coordination of the movement of all six legs. Detailed investigations have revealed that the movement of the legs is controlled by local dedicated neuronal networks, which interact to produce walking of the animal. The stick insect is well suited to experimental investigations aimed at understanding the mechanisms of insect locomotion. Beside the experimental approach, models have also been constructed to elucidate those mechanisms. Here, we describe a model that replicates both the tetrapod and tripod coordination pattern of three ipsilateral legs. The model is based on an earlier insect leg model, which includes the three main leg joints, three antagonistic muscle pairs, and their local neuronal control networks. These networks are coupled via angular signals to establish intraleg coordination of the three neuromuscular systems during locomotion. In the present three-leg model, we coupled three such leg models, representing front, middle, and hind leg, in this way. The coupling was between the levator-depressor local control networks of the three legs. The model could successfully simulate tetrapod and tripod coordination patterns, as well as the transition between them. The simulations showed that for the interleg coordination during tripod, the position signals of the levator-depressor neuromuscular systems sent between the legs were sufficient, while in tetrapod, additional information on the angular velocities in the same system was necessary, and together with the position information also sufficient. We therefore suggest that, during stepping, the connections between the levator-depressor neuromuscular systems of the different legs are of primary importance.

Fluctuation-Driven Neural Dynamics Reproduce Drosophila Locomotor Patterns

The neural mechanisms determining the timing of even simple actions, such as when to walk or rest, are largely mysterious. One intriguing, but untested, hypothesis posits a role for ongoing activity fluctuations in neurons of central action selection circuits that drive animal behavior from moment to moment. To examine how fluctuating activity can contribute to action timing, we paired high-resolution measurements of freely walking Drosophila melanogaster with data-driven neural network modeling and dynamical systems analysis. We generated fluctuation-driven network models whose outputs-locomotor bouts-matched those measured from sensory-deprived Drosophila. From these models, we identified those that could also reproduce a second, unrelated dataset: the complex time-course of odor-evoked walking for genetically diverse Drosophila strains. Dynamical models that best reproduced both Drosophila basal and odor-evoked locomotor patterns exhibited specific characteristics. First, ongoing fluctuations were required. In a stochastic resonance-like manner, these fluctuations allowed neural activity to escape stable equilibria and to exceed a threshold for locomotion. Second, odor-induced shifts of equilibria in these models caused a depression in locomotor frequency following olfactory stimulation. Our models predict that activity fluctuations in action selection circuits cause behavioral output to more closely match sensory drive and may therefore enhance navigation in complex sensory environments. Together these data reveal how simple neural dynamics, when coupled with activity fluctuations, can give rise to complex patterns of animal behavior.

Controlling legs for locomotion-insights from robotics and neurobiology

Walking is the most common terrestrial form of locomotion in animals. Its great versatility and flexibility has led to many attempts at building walking machines with similar capabilities. The control of walking is an active research area both in neurobiology and robotics, with a large and growing body of work. This paper gives an overview of the current knowledge on the control of legged locomotion in animals and machines and attempts to give walking control researchers from biology and robotics an overview of the current knowledge in both fields. We try to summarize the knowledge on the neurobiological basis of walking control in animals, emphasizing common principles seen in different species. In a section on walking robots, we review common approaches to walking controller design with a slight emphasis on biped walking control. We show where parallels between robotic and neurobiological walking controllers exist and how robotics and biology may benefit from each other. Finally, we discuss where research in the two fields diverges and suggest ways to bridge these gaps.

Investigating inter-segmental connections between thoracic ganglia in the stick insect by means of experimental and simulated phase response curves

The neuronal networks that control the motion of the individual legs in insects, in particular in the stick insect, are located in the pro-, meso- and meta-thoracic ganglia. They ensure high flexibility of movement control. Thus, the legs can move in an apparently independent way, e.g., during search movements, but also in tight coordination during locomotion. The latter is evidently a very important behavioural mode. It has, therefore, inspired a large number of studies, all aiming at uncovering the nature of the inter-leg coordination. One of the basic questions has been as to how the individual control networks in the three thoracic ganglia are connected to each other. One way to study this problem is to use phase response curves. They can reveal properties of the coupling between oscillatory systems, such as the central pattern generators in the control networks in the thoracic ganglia. In this paper, we report results that we have achieved by means of a combined experimental and modelling approach. We have calculated phase response curves from data obtained in as yet unpublished experiments as well as from those in previously published ones. By using models of the connected pro- and meso-thoracic control networks of the protractor and retractor neuromuscular systems, we have also produced simulated phase response curves and compared them with the experimental ones. In this way, we could gain important information of the nature of the connections between the aforementioned control networks. Specifically, we have found that connections from both the protractor and the retractor "sides" of the pro-thoracic network to the meso-thoracic one are necessary for producing phase response curves that show close similarity to the experimental ones. Furthermore, the strength of the excitatory connections has been proven to be crucial, while the inhibitory connections have essentially been irrelevant. We, thus, suggest that this type of connection might also be present in the stick insect, and possibly in other insect species.

Neuronal Control of Drosophila Walking Direction

Most land animals normally walk forward but switch to backward walking upon sensing an obstacle or danger in the path ahead. A change in walking direction is likely to be triggered by descending “command” neurons from the brain that act upon local motor circuits to alter the timing of leg muscle activation. Here we identify descending neurons for backward walking in Drosophila—the MDN neurons. MDN activity is required for flies to walk backward when they encounter an impassable barrier and is sufficient to trigger backward walking under conditions in which flies would otherwise walk forward. We also identify ascending neurons, MAN, that promote persistent backward walking, possibly by inhibiting forward walking. These findings provide an initial glimpse into the circuits and logic that control walking direction in Drosophila.

A neuromechanical simulation of insect walking and transition to turning of the cockroach Blaberus discoidalis

A neuromechanical simulation of the cockroach Blaberus discoidalis was developed to explore changes in locomotion when the animal transitions from walking straight to turning. The simulation was based upon the biological data taken from three sources. Neural circuitry was adapted from the extensive literature primarily obtained from the studies of neural connections within thoracic ganglia of stick insect and adapted to cockroach. The 3D joint kinematic data on straight, forward walking for cockroach were taken from a paper that describes these movements in all joints simultaneously as the cockroach walked on an oiled-plate tether (Bender et al. in PloS one 5(10):1-15, 2010b). Joint kinematics for turning were only available for some leg joints (Mu and Ritzmann in J Comp Physiol A Neuroethol Sens Neural Behav Physiol 191(11):1037-54, 2005) and thus had to be obtained using the methods that were applied for straight walking by Bender et al. (PloS one 5(10):1-15, 2010b). Once walking, inside turning, and outside turning were characterized, phase and amplitude changes for each joint of each leg were quantified. Apparent reflex reversals and joint activity changes were used to modify sensory coupling pathways between the CPG at each joint of the simulation. Oiled-plate experiments in simulation produced tarsus trajectories in stance similar to those seen in the animal. Simulations including forces that would be experienced if the insect was walking freely (i.e., weight support and friction) again produced similar results. These data were not considered during the design of the simulation, suggesting that the simulation captures some key underlying the principles of walking, turning, and transitioning in the cockroach. In addition, since the nervous system was modeled with realistic neuron models, biologically plausible reflex reversals are simulated, motivating future neurobiological research.

A neuro-mechanical model explaining the physiological role of fast and slow muscle fibres at stop and start of stepping of an insect leg

Stop and start of stepping are two basic actions of the musculo-skeletal system of a leg. Although they are basic phenomena, they require the coordinated activities of the leg muscles. However, little is known of the details of how these activities are generated by the interactions between the local neuronal networks controlling the fast and slow muscle fibres at the individual leg joints. In the present work, we aim at uncovering some of those details using a suitable neuro-mechanical model. It is an extension of the model in the accompanying paper and now includes all three antagonistic muscle pairs of the main joints of an insect leg, together with their dedicated neuronal control, as well as common inhibitory motoneurons and the residual stiffness of the slow muscles. This model enabled us to study putative processes of intra-leg coordination during stop and start of stepping. We also made use of the effects of sensory signals encoding the position and velocity of the leg joints. Where experimental observations are available, the corresponding simulation results are in good agreement with them. Our model makes detailed predictions as to the coordination processes of the individual muscle systems both at stop and start of stepping. In particular, it reveals a possible role of the slow muscle fibres at stop in accelerating the convergence of the leg to its steady-state position. These findings lend our model physiological relevance and can therefore be used to elucidate details of the stop and start of stepping in insects, and perhaps in other animals, too.

A neuro-mechanical model of a single leg joint highlighting the basic physiological role of fast and slow muscle fibres of an insect muscle system

In legged animals, the muscle system has a dual function: to produce forces and torques necessary to move the limbs in a systematic way, and to maintain the body in a static position. These two functions are performed by the contribution of specialized motor units, i.e. motoneurons driving sets of specialized muscle fibres. With reference to their overall contraction and metabolic properties they are called fast and slow muscle fibres and can be found ubiquitously in skeletal muscles. Both fibre types are active during stepping, but only the slow ones maintain the posture of the body. From these findings, the general hypothesis on a functional segregation between both fibre types and their neuronal control has arisen. Earlier muscle models did not fully take this aspect into account. They either focused on certain aspects of muscular function or were developed to describe specific behaviours only. By contrast, our neuro-mechanical model is more general as it allows functionally to differentiate between static and dynamic aspects of movement control. It does so by including both muscle fibre types and separate motoneuron drives. Our model helps to gain a deeper insight into how the nervous system might combine neuronal control of locomotion and posture. It predicts that (1) positioning the leg at a specific retraction angle in steady state is most likely due to the extent of recruitment of slow muscle fibres and not to the force developed in the individual fibres of the antagonistic muscles; (2) the fast muscle fibres of antagonistic muscles contract alternately during stepping, while co-contraction of the slow muscle fibres takes place during steady state; (3) there are several possible ways of transition between movement and steady state of the leg achieved by varying the time course of recruitment of the fibres in the participating muscles.

A hexapod walker using a heterarchical architecture for action selection

Moving in a cluttered environment with a six-legged walking machine that has additional body actuators, therefore controlling 22 DoFs, is not a trivial task. Already simple forward walking on a flat plane requires the system to select between different internal states. The orchestration of these states depends on walking velocity and on external disturbances. Such disturbances occur continuously, for example due to irregular up-and-down movements of the body or slipping of the legs, even on flat surfaces, in particular when negotiating tight curves. The number of possible states is further increased when the system is allowed to walk backward or when front legs are used as grippers and cannot contribute to walking. Further states are necessary for expansion that allow for navigation. Here we demonstrate a solution for the selection and sequencing of different (attractor) states required to control different behaviors as are forward walking at different speeds, backward walking, as well as negotiation of tight curves. This selection is made by a recurrent neural network (RNN) of motivation units, controlling a bank of decentralized memory elements in combination with the feedback through the environment. The underlying heterarchical architecture of the network allows to select various combinations of these elements. This modular approach representing an example of neural reuse of a limited number of procedures allows for adaptation to different internal and external conditions. A way is sketched as to how this approach may be expanded to form a cognitive system being able to plan ahead. This architecture is characterized by different types of modules being arranged in layers and columns, but the complete network can also be considered as a holistic system showing emergent properties which cannot be attributed to a specific module.

Walknet, a bio-inspired controller for hexapod walking

Walknet comprises an artificial neural network that allows for the simulation of a considerable amount of behavioral data obtained from walking and standing stick insects. It has been tested by kinematic and dynamic simulations as well as on a number of six-legged robots. Over the years, various different expansions of this network have been provided leading to different versions of Walknet. This review summarizes the most important biological findings described by Walknet and how they can be simulated. Walknet shows how a number of properties observed in insects may emerge from a decentralized architecture. Examples are the continuum of so-called "gaits," coordination of up to 18 leg joints during stance when walking forward or backward over uneven surfaces and negotiation of curves, dealing with leg loss, as well as being able following motion trajectories without explicit precalculation. The different Walknet versions are compared to other approaches describing insect-inspired hexapod walking. Finally, we briefly address the ability of this decentralized reactive controller to form the basis for the simulation of higher-level cognitive faculties exceeding the capabilities of insects.

Hysteresis in the metachronal-tripod gait transition of insects: a modeling study

Locomotion in biological systems involves various gaits, and hysteresis appears when the gaits change in accordance with the locomotion speed. That is, the gaits vary at different locomotion speeds depending on the direction of speed change. Although hysteresis is a typical characteristic of nonlinear dynamic systems, the underlying mechanism for the hysteresis in gait transitions remains largely unclear. In this study, we construct a neuromechanical model of an insect and investigate the dynamic characteristics of its gait and gait transition. The simulation results show that our insect model produces metachronal and tripod gaits depending on the locomotion speed through dynamic interactions among the body mechanical system, the nervous system, and the environment in a self-organized manner. They also show that it undergoes the metachronal-tripod gait transition with hysteresis by changing the locomotion speed. We examined the hysteresis mechanism in the metachronal-tripod gait transition of insects from a dynamic viewpoint.

A neuromechanical model for the neuronal basis of curve walking in the stick insect

The coordination of the movement of single and multiple limbs is essential for the generation of locomotion. Movement about single joints and the resulting stepping patterns are usually generated by the activity of antagonistic muscle pairs. In the stick insect, the three major muscle pairs of a leg are the protractor and retractor coxae, the levator and depressor trochanteris, and the flexor and extensor tibiae. The protractor and retractor move the coxa, and thereby the leg, forward and backward. The levator and depressor move the femur up and down. The flexor flexes, and the extensor extends the tibia about the femur-tibia joint. The underlying neuronal mechanisms for a forward stepping middle leg have been thoroughly investigated in experimental and theoretical studies. However, the details of the neuronal and mechanical mechanisms driving a stepping single leg in situations other than forward walking remain largely unknown. Here, we present a neuromechanical model of the coupled three joint control system of the stick insect's middle leg. The model can generate forward, backward, or sideward stepping. Switching between them is achieved by changing only a few central signals controlling the neuromechanical model. In kinematic simulations, we are able to generate curve walking with two different mechanisms. In the first, the inner middle leg is switched from forward to sideward and in the second to backward stepping. Both are observed in the behaving animal, and in the model and animal alike, backward stepping of the inner middle leg produces tighter turns than sideward stepping.

Force encoding in stick insect legs delineates a reference frame for motor control

The regulation of forces is integral to motor control. However, it is unclear how information from sense organs that detect forces at individual muscles or joints is incorporated into a frame of reference for motor control. Campaniform sensilla are receptors that monitor forces by cuticular strains. We studied how loads and muscle forces are encoded by trochanteral campaniform sensilla in stick insects. Forces were applied to the middle leg to emulate loading and/or muscle contractions. Selective sensory ablations limited activities recorded in the main leg nerve to specific receptor groups. The trochanteral campaniform sensilla consist of four discrete groups. We found that the dorsal groups (Groups 3 and 4) encoded force increases and decreases in the plane of movement of the coxo-trochanteral joint. Group 3 receptors discharged to increases in dorsal loading and decreases in ventral load. Group 4 showed the reverse directional sensitivities. Vigorous, directional responses also occurred to contractions of the trochanteral depressor muscle and to forces applied at the muscle insertion. All sensory discharges encoded the amplitude and rate of loading or muscle force. Stimulation of the receptors produced reflex effects in the depressor motoneurons that could reverse in sign during active movements. These data, in conjunction with findings of previous studies, support a model in which the trochanteral receptors function as an array that can detect forces in all directions relative to the intrinsic plane of leg movement. The array could provide requisite information about forces and simplify the control and adaptation of posture and walking.