Locomotor Rhythm Generation Research Articles

Properties of rhythmogenic currents in spinal Shox2 interneurons across postnatal development.

Locomotor behaviors are performed by organisms throughout life, despite developmental changes in cellular properties, neural connectivity, and biomechanics. The basic rhythmic activity in the central nervous system that underlies locomotion is thought to be generated via a complex balance between network and intrinsic cellular properties. Within mature mammalian spinal locomotor circuitry, we have yet to determine which properties of spinal interneurons (INs) are critical to rhythmogenesis and how they change during development. Here, we combined whole cell patch clamp recordings, immunohistochemistry, and RNAscope targeting lumbar Shox2 INs in mice, which are known to be involved in locomotor rhythm generation. We focused on the properties of putatively rhythmogenic ionic currents and the expression of corresponding ion channels across postnatal time points in mice. We show that subsets of Shox2 INs display voltage-sensitive conductances, in addition to respective ion channels, which may contribute to or shape rhythmic bursting. Persistent inward currents, M-type potassium currents, slow afterhyperpolarization, and T-type calcium currents are enhanced with age. In contrast, the hyperpolarization-activated and A-type potassium currents were either found with low prevalence in subsets of neonatal, juvenile, and adult Shox2 INs or did not developmentally change. We show that Shox2 INs become more electrophysiologically diverse by juvenile and adult ages, when locomotor behavior is weight-bearing. These results suggest a developmental shift in the magnitude of rhythmogenic ionic currents and the expression of corresponding ion channels that may be important for mature, weight-bearing locomotor behavior.

The role of intraspinal sensory neurons in the control of quadrupedal locomotion

From swimming to walking and flying, animals have evolved specific locomotor strategies to thrive in different habitats. All types of locomotion depend on the integration of motor commands and sensory information to generate precisely coordinated movements. Cerebrospinal-fluid-contacting neurons (CSF-cN) constitute a vertebrate sensory system that monitors CSF composition and flow. In fish, CSF-cN modulate swimming activity in response to changes in pH and bending of the spinal cord; however, their role in mammals remains unknown. We used mouse genetics to study their function in quadrupedal locomotion. We found that CSF-cN are directly integrated into spinal motor circuits. The perturbation of CSF-cN function does not affect general motor activity nor the generation of locomotor rhythm and pattern but results in specific defects in skilled movements. These results identify a role for mouse CSF-cN in adaptive motor control and indicate that this sensory system evolved a novel function to accommodate the biomechanical requirements of limb-based locomotion.

Phase response analyses support a relaxation oscillator model of locomotor rhythm generation in Caenorhabditis elegans.

Neural circuits coordinate with muscles and sensory feedback to generate motor behaviors appropriate to an animal's environment. In C. elegans, the mechanisms by which the motor circuit generates undulations and modulates them based on the environment are largely unclear. We quantitatively analyzed C. elegans locomotion during free movement and during transient optogenetic muscle inhibition. Undulatory movements were highly asymmetrical with respect to the duration of bending and unbending during each cycle. Phase response curves induced by brief optogenetic inhibition of head muscles showed gradual increases and rapid decreases as a function of phase at which the perturbation was applied. A relaxation oscillator model based on proprioceptive thresholds that switch the active muscle moment was developed and is shown to quantitatively agree with data from free movement, phase responses, and previous results for gait adaptation to mechanical loadings. Our results suggest a neuromuscular mechanism underlying C. elegans motor pattern generation within a compact circuit.

Spinal Cord Injury Alters Spinal Shox2 Interneurons by Enhancing Excitatory Synaptic Input and Serotonergic Modulation While Maintaining Intrinsic Properties in Mouse.

Neural circuitry generating locomotor rhythm and pattern is located in the spinal cord. Most spinal cord injuries (SCIs) occur above the level of spinal locomotor neurons; therefore, these circuits are a target for improving motor function after SCI. Despite being relatively intact below the injury, locomotor circuitry undergoes substantial plasticity with the loss of descending control. Information regarding cell type-specific plasticity within locomotor circuits is limited. Shox2 interneurons (INs) have been linked to locomotor rhythm generation and patterning, making them a potential therapeutic target for the restoration of locomotion after SCI. The goal of the present study was to identify SCI-induced plasticity at the level of Shox2 INs in a complete thoracic transection model in adult male and female mice. Whole-cell patch-clamp recordings of Shox2 INs revealed minimal changes in intrinsic excitability properties after SCI. However, afferent stimulation resulted in mixed excitatory and inhibitory input to Shox2 INs in uninjured mice which became predominantly excitatory after SCI. Shox2 INs were differentially modulated by serotonin (5-HT) in a concentration-dependent manner in uninjured conditions but following SCI, 5-HT predominantly depolarized Shox2 INs. 5-HT7 receptors mediated excitatory effects on Shox2 INs from both uninjured and SCI mice, but activation of 5-HT2B/2C receptors enhanced excitability of Shox2 INs only after SCI. Overall, SCI alters sensory afferent input pathways to Shox2 INs and 5-HT modulation of Shox2 INs to enhance excitatory responses. Our findings provide relevant information regarding the locomotor circuitry response to SCI that could benefit strategies to improve locomotion after SCI.SIGNIFICANCE STATEMENT Current therapies to gain locomotor control after spinal cord injury (SCI) target spinal locomotor circuitry. Improvements in therapeutic strategies will require a better understanding of the SCI-induced plasticity within specific locomotor elements and their controllers, including sensory afferents and serotonergic modulation. Here, we demonstrate that excitability and intrinsic properties of Shox2 interneurons, which contribute to the generation of the locomotor rhythm and pattering, remain intact after SCI. However, SCI induces plasticity in both sensory afferent pathways and serotonergic modulation, enhancing the activation and excitation of Shox2 interneurons. Our findings will impact future strategies looking to harness these changes with the ultimate goal of restoring functional locomotion after SCI.

Neural Interactions in Developing Rhythmogenic Spinal Networks: Insights From Computational Modeling.

The mechanisms involved in generation of rhythmic locomotor activity in the mammalian spinal cord remain poorly understood. These mechanisms supposedly rely on both intrinsic properties of constituting neurons and interactions between them. A subset of Shox2 neurons was suggested to contribute to generation of spinal locomotor activity, but the possible cellular basis for rhythmic bursting in these neurons remains unknown. Ha and Dougherty (2018) recently revealed the presence of bidirectional electrical coupling between Shox2 neurons in neonatal spinal cords, which can be critically involved in neuronal synchronization and generation of populational bursting. Gap junctional connections found between functionally-related Shox2 interneurons decrease with age, possibly being replaced by increasing interactions through chemical synapses. Here, we developed a computational model of a heterogeneous population of neurons sparsely connected by electrical or/and chemical synapses and investigated the dependence of frequency of populational bursting on the type and strength of neuronal interconnections. The model proposes a mechanistic explanation that can account for the emergence of a synchronized rhythmic activity in the neuronal population and provides insights into the possible role of gap junctional coupling between Shox2 neurons in the spinal mechanisms for locomotor rhythm generation.

Spinal Shox2 interneuron interconnectivity related to function and development.

Neuronal networks generating hindlimb locomotion are located in the spinal cord. The mechanisms underlying spinal rhythmogenesis are unknown but network activity and interconnectivity of excitatory interneurons likely play prominent roles. Here, we investigate interconnectivity within the Shox2 interneuron population, a subset of which has been suggested to be involved in locomotor rhythm generation, using paired recordings in isolated spinal cords or slices from transgenic mice. Sparse unidirectional connections consistent with chemical synaptic transmission and prominent bidirectional connections mediated by electrical synapses were present within distinct subsets of Shox2 interneurons. Moreover, bidirectional electrical connections were preferentially found between functionally-related Shox2 interneurons. Though prevalent in neonatal mice, electrical coupling began to decline in incidence and strength in mice ~ 3 weeks of age. Overall, our data suggest that gap junctional coupling promotes synchronization of Shox2 interneurons, and may be implicated in locomotor rhythmicity in developing mice.

Control of Xenopus Tadpole Locomotion via Selective Expression of Ih in Excitatory Interneurons

SummaryLocomotion relies on the coordinated activity of rhythmic neurons in the hindbrain and spinal cord and depends critically on the intrinsic properties of excitatory interneurons. Therefore, understanding how ion channels sculpt the properties of these interneurons, and the consequences for circuit function and behavior, is an important task. The hyperpolarization-activated cation current, Ih, is known to play important roles in shaping neuronal properties and for rhythm generation in many neuronal networks. We show in stage 42 Xenopus laevis frog tadpoles that Ih is strongly expressed only in excitatory descending interneurons (dINs), an important ipsilaterally projecting population that drives swimming activity. The voltage-dependent HCN channel blocker ZD7288 completely abolished a prominent depolarizing sag potential in response to hyperpolarization, the hallmark of Ih, and hyperpolarized dINs. ZD7288 also affected dIN post-inhibitory rebound firing, upon which locomotor rhythm generation relies, and disrupted locomotor output. Block of Ih also unmasked an activity-dependent ultraslow afterhyperpolarization (usAHP) in dINs following swimming, mediated by a dynamic Na/K pump current. This usAHP, unmasked in dINs by ZD7288, resulted in suprathreshold stimuli failing to evoke swimming at short inter-swim intervals, indicating an important role for Ih in maintaining swim generation capacity and in setting the post-swim refractory period of the network. Collectively, our data suggest that the selective expression of Ih in dINs determines specific dIN properties that are important for rhythm generation and counteracts an activity-dependent usAHP to ensure that dINs can maintain coordinated swimming over a wide range of inter-swim intervals.

Swimming rhythm generation in the caudal hindbrain of the lamprey.

The spinal cord has been well established as the site of generation of the locomotor rhythm in vertebrates, but studies have suggested that the caudal hindbrain in larval fish and amphibians can also generate locomotor rhythms. Here, we investigated whether the caudal hindbrain of the adult lamprey ( Petromyzon marinus and Ichthyomyzon unicuspis) has the ability to generate the swimming rhythm. The hindbrain-spinal cord transition zone of the lamprey contains a bilateral column of somatic motoneurons that project via the spino-occipital (S-O) nerves to several muscles of the head. In the brainstem-spinal cord-muscle preparation, these muscles were found to burst and contract rhythmically with a left-right alternation when swimming activity was evoked with a brief electrical stimulation of the spinal cord. In the absence of muscles, the isolated brainstem-spinal cord preparation also produced alternating left-right bursts in S-O nerves (i.e., fictive swimming), and the S-O nerve bursts preceded the bursts occurring in the first ipsilateral spinal ventral root. After physical isolation of the S-O region using transverse cuts of the nervous system, the S-O nerves still exhibited rhythmic bursting with left-right alternation when glutamate was added to the bathing solution. We conclude that the S-O region of the lamprey contains a swimming rhythm generator that produces the leading motor nerve bursts of each swimming cycle, which then propagate down the spinal cord to produce forward swimming. The S-O region of the hindbrain-spinal cord transition zone may play a role in regulating speed, turning, and head orientation during swimming in lamprey. NEW & NOTEWORTHY Although it has been well established that locomotor rhythm generation occurs in the spinal cord of vertebrates, it was unknown whether the hindbrain of the adult vertebrate nervous system can also generate the locomotor rhythm. Here, we show that the isolated hindbrain-spinal cord transition zone of adult lamprey can generate the swimming rhythm. In addition, the swimming bursts of the hindbrain lead the bursts occurring in the first segment of the spinal cord.

Developmental changes in spinal neuronal properties, motor network configuration, and neuromodulation at free-swimming stages of Xenopus tadpoles.

We describe a novel preparation of the isolated brain stem and spinal cord from prometamorphic tadpole stages of the South African clawed frog ( Xenopus laevis) that permits whole cell patch-clamp recordings from neurons in the ventral spinal cord. Previous research on earlier stages of the same species has provided one of the most detailed understandings of the design and operation of a central pattern generator circuit. Here we have addressed how development sculpts complexity from this more basic circuit. The preparation generates bouts of fictive swimming activity either spontaneously or in response to electrical stimulation of the optic tectum, allowing an investigation into how the neuronal properties, activity patterns, and neuromodulation of locomotor rhythm generation change during development. We describe an increased repertoire of cellular responses compared with younger larval stages and investigate the cellular-level effects of nitrergic neuromodulation as well as the development of a sodium pump-mediated ultraslow afterhyperpolarization (usAHP) in these free-swimming larval animals. NEW & NOTEWORTHY A novel in vitro brain stem-spinal cord preparation is described that enables whole cell patch-clamp recordings from spinal neurons in prometamorphic Xenopus tadpoles. Compared with the well-characterized earlier stages of development, spinal neurons display a wider range of firing properties during swimming and have developed novel cellular properties. This preparation now makes it feasible to investigate in detail spinal central pattern generator maturation during the dramatic switch between undulatory and limb-based locomotion strategies during amphibian metamorphosis.

Delineating the Diversity of Spinal Interneurons in Locomotor Circuits.

Locomotion is common to all animals and is essential for survival. Neural circuits located in the spinal cord have been shown to be necessary and sufficient for the generation and control of the basic locomotor rhythm by activating muscles on either side of the body in a specific sequence. Activity in these neural circuits determines the speed, gait pattern, and direction of movement, so the specific locomotor pattern generated relies on the diversity of the neurons within spinal locomotor circuits. Here, we review findings demonstrating that developmental genetics can be used to identify populations of neurons that comprise these circuits and focus on recent work indicating that many of these populations can be further subdivided into distinct subtypes, with each likely to play complementary functions during locomotion. Finally, we discuss data describing the manner in which these populations interact with each other to produce efficient, task-dependent locomotion.

Diversity of molecularly defined spinal interneurons engaged in mammalian locomotor pattern generation.

Mapping the expression of transcription factors in the mouse spinal cord has identified ten progenitor domains, four of which are cardinal classes of molecularly defined, ventrally located interneurons that are integrated in the locomotor circuitry. This review focuses on the properties of these interneuronal populations and their contribution to hindlimb locomotor central pattern generation. Interneuronal populations are categorized based on their excitatory or inhibitory functions and their axonal projections as predictors of their role in locomotor rhythm generation and coordination. The synaptic connectivity and functions of these interneurons in the locomotor central pattern generators (CPGs) have been assessed by correlating their activity patterns with motor output responses to rhythmogenic neurochemicals and sensory and descending fibers stimulations as well as analyzing kinematic gait patterns in adult mice. The observed complex organization of interneurons in the locomotor CPG circuitry, some with seemingly similar physiological functions, reflects the intricate repertoire associated with mammalian motor control and is consistent with high transcriptional heterogeneity arising from cardinal interneuronal classes. This review discusses insights derived from recent studies to describe innovative approaches and limitations in experimental model systems and to identify missing links in current investigational enterprise.

Anatomical and electrophysiological characterization of a population of dI6 interneurons in the neonatal mouse spinal cord

The locomotor central pattern generator is a neural network located in the ventral aspect of the caudal spinal cord that underlies stepping in mammals. While many genetically defined interneurons that are thought to comprise this neural network have been identified and characterized, the dI6 cells- which express the transcription factors WT1 and/or DMRT3- are one population that settle in this region, are active during locomotion, whose function is poorly understood. These cells were originally hypothesized to be commissural premotor interneurons, however evidence in support of this is sparse. Here we characterize this population of cells using the TgDbx1Cre;R26EFP;Dbx1LacZ transgenic mouse line, which has been shown to be an effective marker of dI6 interneurons. We show dI6 cells to be abundant in laminae VII and VIII along the entire spinal cord and provide evidence that subtypes outside the WT1/DMRT3 expressing dI6 cells may exist. Retrograde tracing experiments indicate that the majority of dI6 cells project descending axons, and some make monosynaptic or disynaptic contacts onto motoneurons on either side of the spinal cord. Analysis of their activity during non-resetting deletions, which occur during bouts of fictive locomotion, suggests that these cells are involved in both locomotor rhythm generation and pattern formation. This study provides a thorough characterization of the dI6 cells labeled in the TgDbx1Cre;R26EFP;Dbx1LacZ transgenic mouse, and supports previous work suggesting that these cells play multiple roles during locomotor activity.

Neural Circuits Underlying Fly Larval Locomotion.

Locomotion is a complex motor behavior that may be expressed in different ways using a variety of strategies depending upon species and pathological or environmental conditions. Quadrupedal or bipedal walking, running, swimming, flying and gliding constitute some of the locomotor modes enabling the body, in all cases, to move from one place to another. Despite these apparent differences in modes of locomotion, both vertebrate and invertebrate species share, at least in part, comparable neural control mechanisms for locomotor rhythm and pattern generation and modulation. Significant advances have been made in recent years in studies of the genetic aspects of these control systems. Findings made specifically using Drosophila (fruit fly) models and preparations have contributed to further understanding of the key role of genes in locomotion. This review focuses on some of the main findings made in larval fruit flies while briefly summarizing the basic advantages of using this powerful animal model for studying the neural locomotor system.

Motor neurons control locomotor circuit function retrogradely via gap junctions.

Motor neurons are the final stage of neural processing for the execution of motor behaviours. Traditionally, motor neurons have been viewed as the 'final common pathway', serving as passive recipients merely conveying to the muscles the final motor program generated by upstream interneuron circuits. Here we reveal an unforeseen role of motor neurons in controlling the locomotor circuit function via gap junctions in zebrafish. These gap junctions mediate a retrograde analogue propagation of voltage fluctuations from motor neurons to control the synaptic release and recruitment of the upstream V2a interneurons that drive locomotion. Selective inhibition of motor neurons during ongoing locomotion de-recruits V2a interneurons and strongly influences locomotor circuit function. Rather than acting as separate units, gap junctions unite motor neurons and V2a interneurons into functional ensembles endowed with a retrograde analogue computation essential for locomotor rhythm generation. These results show that motor neurons are not a passive recipient of motor commands but an integral component of the neural circuits responsible for motor behaviour.

Preclinical evidence supporting the clinical development of central pattern generator-modulating therapies for chronic spinal cord-injured patients.

Ambulation or walking is one of the main gaits of locomotion. In terrestrial animals, it may be defined as a series of rhythmic and bilaterally coordinated movement of the limbs which creates a forward movement of the body. This applies regardless of the number of limbs—from arthropods with six or more limbs to bipedal primates. These fundamental similarities among species may explain why comparable neural systems and cellular properties have been found, thus far, to control in similar ways locomotor rhythm generation in most animal models. The aim of this article is to provide a comprehensive review of the known structural and functional features associated with central nervous system (CNS) networks that are involved in the control of ambulation and other stereotyped motor patterns—specifically Central Pattern Generators (CPGs) that produce basic rhythmic patterned outputs for locomotion, micturition, ejaculation, and defecation. Although there is compelling evidence of their existence in humans, CPGs have been most studied in reduced models including in vitro isolated preparations, genetically-engineered mice and spinal cord-transected animals. Compared with other structures of the CNS, the spinal cord is generally considered as being well-preserved phylogenetically. As such, most animal models of spinal cord-injured (SCI) should be considered as valuable tools for the development of novel pharmacological strategies aimed at modulating spinal activity and restoring corresponding functions in chronic SCI patients.

Activity-Dependent Changes in Extracellular Ca2+ and K+ Reveal Pacemakers in the Spinal Locomotor-Related Network

Changes in the extracellular ionic concentrations occur as a natural consequence of firing activity in large populations of neurons. The extent to which these changes alter the properties of individual neurons and the operation of neuronal networks remains unknown. Here, we show that the locomotor-like activity in the isolated neonatal rodent spinal cord reduces the extracellular calcium ([Ca(2+)]o) to 0.9mM and increases the extracellular potassium ([K(+)]o) to 6mM. Such changes in [Ca(2+)]o and [K(+)]o trigger pacemaker activities in interneurons considered to be part of the locomotor network. Experimental data and a modeling study show that the emergence of pacemaker properties critically involves a [Ca(2+)]o-dependent activation of the persistent sodium current (INaP). These results support a concept for locomotor rhythm generation in which INaP-dependent pacemaker properties in spinal interneurons are switched on and tuned by activity-dependent changes in [Ca(2+)]o and [K(+)]o.

Fast Silencing Reveals a Lost Role for Reciprocal Inhibition in Locomotion

SummaryAlternating contractions of antagonistic muscle groups during locomotion are generated by spinal “half-center” networks coupled in antiphase by reciprocal inhibition. It is widely thought that reciprocal inhibition only coordinates the activity of these muscles. We have devised two methods to rapidly and selectively silence neurons on just one side of Xenopus tadpole spinal cord and hindbrain, which generate swimming rhythms. Silencing activity on one side led to rapid cessation of activity on the other side. Analyses reveal that this resulted from the depression of reciprocal inhibition connecting the two sides. Although critical neurons in intact tadpoles are capable of pacemaker firing individually, an effect that could support motor rhythms without inhibition, the swimming network itself requires ∼23 min to regain rhythmic activity after blocking inhibition pharmacologically, implying some homeostatic changes. We conclude therefore that reciprocal inhibition is critical for the generation of normal locomotor rhythm.

Modeling [Ca2+]o- and [K+]o-dependent oscillations in spinal Hb9 interneurons

The spinal interneurons in newborn rodents, when synaptically isolated by removing the extracellular calcium ([Ca2+]o), demonstrate intrinsic rhythmic bursting activity that can be suppressed by riluzole, a blocker of the persistent sodium current (INaP) [2]. This finding led to the suggestion that lowering of [Ca2+]o may enhance INaP by shifting its activation threshold toward more negative voltages, and raised the question of functional relevance of this finding to generation of locomotor rhythm. To assess this issue, a series of experiments was performed in vitro using the isolated spinal cord preparation from the neonatal rat with measurements of [Ca2+]o and extracellular potassium concentration ([K+]o) during pharmacologically induced fictive locomotion. We demonstrated that with the onset of fictive locomotion, [Ca2+]o reduced from 1.2 up to 0.9 mM whereas [K+]o increased from 4 up to 6 mM. At the same time, a special study performed on the isolated genetically identified Hb9 excitatory interneurons showed that, at [Ca2+]o= 1 mM and [K+]o=5 mM, 12% of Hb9 cells expressed intrinsic INaP-dependent bursting, and at the concentrations typical for fictive locomotion ([Ca2+]o= 0.9 mM and [K+]o=6 mM), as many as 50% of identified Hb9 interneurons expressed INaP-dependent bursting. Importantly, the threshold of [Ca2+]o to generate bursting decreased as [K+]o increased. The analysis of Hb9 neuron behavior during slow ramp increase of voltage revealed that lowering [Ca2+]o from 1.2 to 0.9 mM induced a negative shift (~ -3 mV) in the INaP half-activation voltage (V1/2NaP). In contrast, V1/2NaP was not changed when [K+]o increased from 4 to 6 mM. To theoretically investigate the effect of changing [Ca2+]o and [K+]o on the Hb9’s pacemaker properties and firing behavior, we developed a single-compartment computational model of Hb9 neuron. In this model, we explicitly simulated a negative shift of V1/2NaP occurring with the reduction of [Ca2+]o.. At [K+]o=6 mM, our model exhibited tonic activity at V1/2NaP = –50 mV (Fig. ​(Fig.1A,1A, left). The rhythmic bursting emerged at V1/2NaP = –51 mV, and further shifting V1/2NaP to the left produced stable bursting (Fig. ​(Fig.1A,1A, right). In turn, an increase in [K+]o reduced the potassium reversal potential and hence all voltage-gated potassium currents (IK), which provided an additional augmentation of INaP-dependent bursting [1]. To study a synergistic effect of [Ca2+]o and [K+]oon the emergence of bursting activity, we modeled a population of 50 uncoupled neurons with randomly distributed parameters (see Fig. ​Fig.1B).1B). Our simulations have shown that shifting V1/2NaP towards more negative values induced by reducing [Ca2+]o may play a major role in emergence of bursting activity in the population of spinal interneurons. We have also demonstrated that accumulation of [K+]ocan facilitate the emergence of INaP-dependent bursting via the reduction of IK. Figure 1 A. Switching from tonic to bursting activity in the modeled neuron by shifting V1/2NaP to more negative value. B. The synergistic effect of [Ca2+]o and [K+]ochanges on emergence of bursting activity in the modeled population of 50 uncoupled cells. In summary we suggest that co-regulation of INaP and IK by the corresponding changes in [Ca2+]o and [K+]o may convert activity of spinal interneurons from asynchronous/tonic to the synchronized bursting. This activity-dependent switching in firing behavior may represent a fundamental mechanism for locomotor rhythm generation in the spinal cord.

Origin of excitation underlying locomotion in the spinal circuit of zebrafish

Neural circuits in the spinal cord transform instructive signals from the brain into well-coordinated locomotor movements by virtue of rhythm-generating components. Although evidence suggests that excitatory interneurons are the essence of locomotor rhythm generation, their molecular identity and the assessment of their necessity have remained unclear. Here we show, using larval zebrafish, that V2a interneurons represent an intrinsic source of excitation necessary for the normal expression of the locomotor rhythm. Acute and selective ablation of these interneurons increases the threshold of induction of swimming activity, decreases the burst frequency, and alters the coordination of the rostro-caudal propagation of activity. Thus, our results argue that V2a interneurons represent a source of excitation that endows the spinal circuit with the capacity to generate locomotion.

A dynamical systems analysis of afferent control in a neuromechanical model of locomotion: II. Phase asymmetry

In this paper we analyze a closed loop neuromechanical model of locomotor rhythm generation. The model is composed of a spinal central pattern generator (CPG) and a single-joint limb, with CPG outputs projecting via motoneurons to muscles that control the limb and afferent signals from the muscles feeding back to the CPG. In a preceding companion paper (Spardy et al 2011 J. Neural Eng. 8 065003), we analyzed how the model generates oscillations in the presence or absence of feedback, identified curves in a phase plane associated with the limb that signify where feedback levels induce phase transitions within the CPG, and explained how increasing feedback strength restores oscillations in a model representation of spinal cord injury; from these steps, we derived insights about features of locomotor rhythms in several scenarios and made predictions about rhythm responses to various perturbations. In this paper, we exploit our analytical observations to construct a reduced model that retains important characteristics from the original system. We prove the existence of an oscillatory solution to the reduced model using a novel version of a Melnikov function, adapted for discontinuous systems, and also comment on the uniqueness and stability of this solution. Our analysis yields a deeper understanding of how the model must be tuned to generate oscillations and how the details of the limb dynamics shape overall model behavior. In particular, we explain how, due to the feedback signals in the model, changes in the strength of a tonic supra-spinal drive to the CPG yield asymmetric alterations in the durations of different locomotor phases, despite symmetry within the CPG itself.