Rhythm generation, robustness, and control in stick insect locomotion: modeling and analysis

The effective production of many motor behaviors requires the strict coordination of discrete motor pattern generating circuits ([Hill et al. 2003][1]). Locomotor behaviors usually require this coordination at several levels of the nervous system, within single limbs (interjoint coordination),

V3 Spinal Neurons Establish a Robust and Balanced Locomotor Rhythm during Walking

Modeling the mammalian locomotor CPG: insights from mistakes and perturbations

Rhythmic limb movements during locomotion are controlled by central pattern generator (CPG) circuits located in the spinal cord. It is considered that these circuits are composed of individual rhythm generators (RGs) for each limb interacting with each other through multiple commissural and long propriospinal circuits. The organization and operation of each RG are not fully understood, and different competing theories exist about interactions between its flexor and extensor components, as well as about left–right commissural interactions between the RGs. The central idea of circuit organization proposed in this study is that with an increase of excitatory input to each RG (or an increase in locomotor speed) the rhythmogenic mechanism of the RGs changes from “flexor-driven” rhythmicity to a “classical half-center” mechanism. We test this hypothesis using our experimental data on changes in duration of stance and swing phases in the intact and spinal cats walking on the ground or tied-belt treadmills (symmetric conditions) or split-belt treadmills with different left and right belt speeds (asymmetric conditions). We compare these experimental data with the results of mathematical modeling, in which simulated CPG circuits operate in similar symmetric and asymmetric conditions with matching or differing control drives to the left and right RGs. The obtained results support the proposed concept of state-dependent changes in RG operation and specific commissural interactions between the RGs. The performed simulations and mathematical analysis of model operation under different conditions provide new insights into CPG network organization and limb coordination during locomotion.

Plasticity properties of CPG circuits in humans: Impact on gait recovery

Organization of mammalian locomotor rhythm and pattern generation

What are the mechanisms that generate the motor patterns for rhythmic movements in animals? Until recently it has widely been accepted that the relative timing of motor activity is determined by central neuronal circuits termed central pattern generators (CPGs). The validity of this view is examined for four motor systems in which there is a high degree of sensory regulation: the walking systems of the cat, cockroach and stick insect, and the flight system of the locust. In none of these systems is the evidence sufficient to conclude that a CPG is primarily responsible for establishing the timing of motor activity. In the stick insect there is no evidence for the existence of a CPG for walking at all, while in the cockroach the deafferented motor pattern differs from the normal walking pattern to such an extent that phasic afferent input must play an important part in establishing the timing of motor activity. Reflex pathways have been identified which appear to function to produce some aspects of the normal motor pattern for walking in insects. No firm conclusion can be reached regarding the role of central pattern generators in establishing the timing of motor activity in the walking system of the cat because the motor patterns in completely deafferented preparations have not been analysed in sufficient detail to allow an adequate comparison with the intact motor pattern. Finally, in the flight system of the locust it has recently been found that one entire phase of the normal flight cycle depends on phasic afferent input from wing receptors, and that sensory feedback is involved in the generation of rhythmicity. It is now clear that CPGs as defined in deafferented preparations do not form the basis for establishing the timing of activity in all rhythmic motor systems. Thus central pattern generation cannot be regarded as universal functional principle for rhythmic motor systems.

Presently, the internal organization of the mammalian locomotor central pattern generator (CPG) is unknown due to the difficulty in identifying and localizing interneurones involved in the network. The CPG was initially thought to be composed of half-centres, which set the basic locomotor rhythm by generating alternating excitation of antagonist motoneurone (MN) pools (e.g. flexors and extensors) via reciprocal inhibition (see Rybak et al. 2006 for a discussion). While this reproduced alternating activity of antagonists it failed to account for various recruitment patterns possible during locomotion. This led to a suggestion that the CPG consisted of multiple, coupled, unit burst generators allowing for flexible recruitment of MNs (Grillner, 1981). However, others stated that half-centres could likewise produce multiple recruitment patterns if additional interneuronal circuits were interposed between networks responsible for rhythm generation and MN activation (Perret, 1983). As a result, which theory better approximates the locomotor CPG has remained contentious. To circumvent the problem of identifying ensembles of neurones involved in locomotor rhythm generation, a method clearly more amenable to conceptualize the functional organization of the mammalian locomotor CPG is to employ ‘in silico’ simulations, using available experimental data, as recently done in an issue of The Journal of Physiology (Rybak et al. 2006). Whether the model by Rybak and colleagues provides an accurate description of the locomotor CPG is unknown but it offers a theoretical framework to refine and test hypotheses regarding the functional organization of the CPG. The purpose of this short review is to briefly describe and discuss some of the model's underlying assumptions, to highlight some key findings, and make a few recommendations. Rybak et al. designed a two-level CPG, which activated antagonist motor pools for a single hindlimb, with one level consisting of half-centre rhythm generators (RG) and a second level comprising pattern formation (PF) networks. Each RG (one for flexors, one for extensors) set the basic locomotor rhythm, defined durations of flexor and extensor phases, and controlled the PF networks that distributed and coordinated the activity of MN pools. Reciprocal inhibition at both levels and between antagonist MNs ensured that a given MN population was active only during a specific phase(s) of the step cycle. The two-layered CPG enabled the locomotor rhythm and pattern of MN activity to be separately controlled. The model was composed of interneurones and MNs and several ionic conductances were implemented using Hodgkin–Huxley equations. Interestingly, the model included persistent (slowly inactivating) sodium currents, which endowed excitatory populations of the RGs with rhythmogenic properties. The model reproduced several aspects of fictive locomotion including alternating rhythmic activity of flexors and extensors evoked by tonic drive to the CPG, appropriate locomotor step cycle periods, increasing speed with increased mesencephalic locomotor region (MLR) drive, slow locomotor-like activity without MLR drive, and synchronized oscillations of flexors and extensors if synaptic inhibition was blocked. As mentioned, the model added persistent sodium currents (INaP) to RG neurones allowing them to generate endogenous oscillations (bursts). The bursting properties of the model were realized through dynamics of INaP within RGs and reciprocal inhibition between antagonistic RGs. During MLR-induced locomotion the membrane potential of rhythm-generating neurones enters a depolarized state highlighted by repetitive action potential discharges. This state, or plateau potential, is sustained by persistent (slowly inactivating) inward currents (PICs). Although the model included a persistent sodium current, at least one other channel, the L-type calcium channel, can produce PICs (Brownstone, 2006). Several investigations report that the L-type calcium channel is largely responsible for PICs in cat, turtle, mouse and rat MNs (Brownstone, 2006). A future step in the model could be to evaluate contributions of L-type calcium channels of RG and PF neurones but also of MNs, since it is believed that MN properties, such as PICs, are standard components of normal motor behaviours, including locomotion. The model incorporated various inhibitory and excitatory connections, with a different weighting value afforded to each. Interestingly, both mutual excitation and reciprocal inhibition were included within and between extensor and flexor RGs. Whereas reciprocal inhibition is a widely accepted property of CPGs, the purpose of mutual excitation between antagonists is less obvious. However, if the weights of all inhibitory connections in the model were set to zero slow spontaneous synchronized bursting of flexor and extensor MNs occurred similar to blockade of inhibitory synaptic transmission during experimental conditions (Rybak et al. 2006). Mutual excitation in the model between RGs ensures that flexors and extensors discharge in-phase and not at an independent rhythm from each other in the absence of synaptic inhibition. Another explanation for synchronized activity of flexors and extensors in the absence of synaptic inhibition could be the presence of only one rhythm generator that equally excites the flexor and extensor PF networks and under normal circumstances the alternating activity of antagonists is mediated by inhibitory circuits at PF and MN levels. The model also provided a clear framework for grouping different types of neurones according to their functional contribution in locomotor pattern generation. One contentious issue is separating MNs from the PF layer. In the model, MNs are simple output nodes omitted from pattern formation. However, MNs are modified directly by sensory feedback, recurrent feedback, neuromodulatory systems, and have intrinsic patterning properties, such as plateau-potentials, that are not included in the current model. As such, the model could test the inclusion of MNs in the PF network thus making some PF neurones redundant for evoking different recruitment patterns during locomotion. The two-layered CPG architecture separating rhythm generation and MN activation was largely based on experimental observations of brief spontaneous failures in the alternating activity of flexors and extensors during fictive locomotion called deletions (Rybak et al. 2006). Deletions are periods of silenced activity in some MN populations accompanied by sustained or rhythmic activity in antagonists. In most cases, the post-deletion rhythm is maintained, meaning that the burst of activity reappears at a time when it would have normally been present if a deletion had not occurred. According to the model, the disruption in excitability occurs within the PF network preventing MNs from discharging while the RG maintains its normal ‘clock function’. Once the disturbance in the PF network is removed, MN activity reappears in line with descending drive from the RG. There are also instances where the post-deletion rhythm is altered (i.e. resetting). For these resetting deletions, the normal rhythm is modified because excitability in the RG is directly altered. Although the two-layered model accounts well for deletions of both types, there are alternative explanations for non-resetting deletions other than separating rhythm generation and MN activation. For instance, if locomotor rhythm is the product of multiple rhythmogenic neural oscillators distributed bilaterally along the spinal cord (Deliagina et al. 1983), it is possible that failure of one of these subunits (e.g. a deletion) could be rectified by compound influences from remaining elements in the network. Indeed, even the ‘non-deleted’ half of the half-centre (RG) could maintain the post-deletion rhythm. For example, in oscillations with a ‘dominant’ phase (e.g. flexor-dominant during MLR locomotion) one may predict that self-inhibitory properties of the dominant oscillator determine the rhythm even when activity of the non-dominant oscillator is suppressed. Thus, although non-resetting deletions result from failure of the non-dominant oscillator, the CPG rhythm remains constant because the dominant oscillator maintained its own endogenous rhythmic bursting. This explanation is supported by observations of non-resetting deletions occurring predominantly in the non-dominant phase. The post-deletion rhythm could also be maintained at the level of interacting CPG networks (e.g. one CPG for each limb). In intact cats, the four limbs normally operate together during locomotion and although each limb can have its own rhythm, as demonstrated when each limb steps at a different speed on a split-belt treadmill, there is no evidence that such rhythmic dissociation occurs during fictive locomotion. Failure at one level could alter the fictive locomotor pattern of all four limbs and not simply represent a local failure. Rybak et al. proposed that forelimb CPGs do not maintain the rhythm since deletions in motor pools of one hindlimb have been reported in a chronic spinal cat. They also indicated that deletions were observed in one hindlimb despite no rhythmic activity in the contralateral hindlimb. However, the model specifies that absence of rhythmic activity in the contralateral hindlimb could simply reflect failure at the PF or MN level. It is possible that RG centres are still active and via their connections with the contralateral side maintain the rhythm during deletions. To eliminate possible influences from other CPGs, deletions would have to be recorded in one hindlimb in complete isolation from the forelimbs (e.g. spinalization) and from the contralateral hindlimb (e.g. spinal hemisection or longitudinal section along the midline of the spinal cord). In conclusion, although some of the CPG properties included in the model could be explored in greater detail, the model faithfully reproduced several features of fictive locomotion and therefore constitutes a remarkable conceptualization of the internal organization of the mammalian locomotor CPG.

Genetic Ablation of V2a Ipsilateral Interneurons Disrupts Left-Right Locomotor Coordination in Mammalian Spinal Cord

It has been established in experiments that, in the stick insect, antagonistic muscle pairs of each leg joint are associated with their own central pattern generator (CPG) which is, in essence, responsible for driving the motoneurones (MNs) that innervate the muscles of the antagonistic muscle pair [1]. This arrangement ensures large flexibility of the leg movements in these animals. It is therefore of paramount interest to study the function of the CPG-MN-muscle systems at the different joints of the leg. Modelling can be a useful integrative tool in this study and in understanding the interactions between the elements (CPG, MN and muscles) of the neuro-mechanical system in question. In this paper, we report on the results of our modelling work of the levator-depressor neuro-mechanical system. The model includes all three elements of the system: the CPG, the MNs and the levator and depressor muscles. The CPG consists of two mutually inhibitory neurones which form a relaxation oscillator [2], and which control the MN activity via inhibitory interneurones like in [3]. However, additional interneurones convey the afferent information from the campaniform sensilla (CS) to the CPG. The core of the mechanical model is the mechanical equation of motion of the femur. The muscles are modelled as nonlinear springs with variable elasticity moduli and with viscous damping parallel to the springs. Finally, the coupling between the neuronal and the muscle system is done by using a simple, linear, 1st order synapse model [4]. The synaptic activity, as it varied in time, depending on the activity of the MNs, set the actual value of the elasticity moduli of the muscles (springs). The model successfully reproduced the electrical activity of the CPG neurones and MNs, as well as the angular movement of the femur as seen during normal straightforward locomotion. In this case, the activity of the MNs was fully controlled by that of the CPG. However, additional modulation of the synaptic input to the MNs changed this picture and the angular motion of the femur could be modified to have either the depression or the levation as the dominating state, e.g. mimicking backward or curve walking. We could also simulate the experimental conditions after partial removal of the femoral CS. In this case, the original dominance of the depression was overturned, and the levator MN was continuously active because the corresponding CPG neurone showed tonic activity. However, the depressor MN and muscle could be activated in the model by stimulation of the CS. The balance between contraction of the levator and depressor muscle could again be shifted by separately modulating the synaptic input to the MNs. In conclusion, we showed that the model could successfully mimic the behaviour of its biological counterpart. The above simulations provided strong evidence for a high behavioural flexibility of the model under various peripheral (CS stimuli) or central (modulatory signals) influences. Some of these behavioural modes also hint at corresponding processes that might take place in the stick insect during locomotion in a changing environment.

Understanding central pattern generator (CPG) circuits requires a detailed knowledge of the intrinsic cellular properties of the constituent neurons. These properties are poorly understood in most CPGs because of the complexity resulting from interactions with other neurons of the circuit. This is also the case in the feeding network of the snail, Lymnaea, one of the best-characterized CPG networks. We addressed this problem by isolating the interneurons comprising the feeding CPG in cell culture, which enabled us to study their basic intrinsic electrical and pharmacological cellular properties without interference from other network components. These results were then related to the activity patterns of the neurons in the intact feeding network. The most striking finding was the intrinsic generation of plateau potentials by medial N1 (N1M) interneurons. This property is probably critical for rhythm generation in the whole feeding circuit because the N1M interneurons are known to play a pivotal role in the initiation of feeding cycles in response to food. Plateau potential generation in another cell type, the ventral N2 (N2v), appeared to be conditional on the presence of acetylcholine. Examination of the other isolated feeding CPG interneurons [lateral N1 (N1L), dorsal N2 (N2d), phasic N3 (N3p)] and the modulatory slow oscillator (SO) revealed no significant intrinsic properties in relation to pattern generation. Instead, their firing patterns in the circuit appear to be determined largely by cholinergic and glutamatergic synaptic inputs from other CPG interneurons, which were mimicked in culture by application of these transmitters. This is an example of a CPG system where the initiation of each cycle appears to be determined by the intrinsic properties of a key interneuron, N1M, but most other features of the rhythm are probably determined by network interactions.

New findings in the nervous system of invertebrates have shown how a number of features of central pattern generator (CPG) circuits contribute to the generation of robust flexible rhythms. In this paper we consider recently revealed strategies that living CPGs follow to design CPG control paradigms for modular robots. To illustrate them, we divide the task of designing an example CPG for a modular robot into independent problems. We formulate each problem in a general way and provide a bio-inspired solution for each of them: locomotion information coding, individual module control and inter-module coordination. We analyse the stability of the CPG numerically, and then test it on a real robot. We analyse steady state locomotion and recovery after perturbations. In both cases, the robot is able to autonomously find a stable effective locomotion state. Finally, we discuss how these strategies can result in a more general design approach for CPG-based locomotion.

Animals like stick insects can adaptively walk on the complex terrain with different gait patterns. The change of gait patterns involves the adaptation of moving frequency and duty cycle of swing-stance period of individual legs. Inspired by the coupled Matsuoka and resonate-and-fire neuron models, we present a nonlinear oscillation model as the central pattern generator (CPG) for rhythmic gait pattern generation. This dynamic model can be used, as a building block, to actuate the motoneurons on a leg joint with adjustable driving frequencies and duty cycles by changing a few of model parameters. Three identical CPG models being used to drive three joints can make an arthropod leg of three degrees-of-freedom (DOFs). With appropriate model parameter settings, and thus suitable phase lags among joints, the leg is expected to walk on a complex terrain with adaptive steps.

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.

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