A central pattern generator producing alternative outputs: phase relations of leech heart motor neurons with respect to premotor synaptic input

A CPG-Based Versatile Control Framework for Metameric Earthworm-Like Robotic Locomotion

Annelids such as earthworms are considered to have central pattern generators (CPGs) that generate rhythms in neural circuits to coordinate the deformation of body segments for effective locomotion. At present, the states of earthworm-like robot segments are often assigned holistically and artificially by mimicking the earthworms' retrograde peristalsis wave, which is unable to adapt their gaits for variable environments and tasks. This motivates the authors to extend the bioinspired research from morphology to neurobiology by mimicking the CPG to build a versatile framework for spontaneous motion control. Here, the spatiotemporal dynamics is exploited from the coupled Hopf oscillators to not only unify the two existing gait generators for restoring temporal-symmetric phase-coordinated gaits and discrete gaits but also generate novel temporal-asymmetric phase-coordinated gaits. Theoretical and experimental tests consistently confirm that the introduction of temporal asymmetry improves the robot's locomotion performance. The CPG-based controller also enables seamless online switching of locomotion gaits to avoid abrupt changes, sharp stops, and starts, thus improving the robot's adaptability in variable working scenarios.

The neuromuscular transform in a single segment of a segmented heart tube

Leech hearts are hybrids; they are myogenic but need entrainment by a heartbeat central pattern generator (CPG) to execute functional constriction patterns. Leech hearts are modular: two lateral segmented heart tubes running the length of the animal. Moving blood through the segmented heart tubes of leeches requires sequential constrictions, timed by a heartbeat CPG and relayed to each heart segment by likewise segmental motor neurons. The heartbeat CPG produces bilaterally asymmetric coordinations: rear-to-front peristaltic on one side and nearly synchronous on the other, periodically switching sides. We examined the neuromuscular transform of isolated heart segments in response to electrical nerve stimulation to identify the range of parameters (burst duration, intraburst pulse frequency, period) allowing the heart to constrict continuously and reliably. Constriction amplitudes increased with increasing intraburst frequencies and decreased with decreasing burst durations. Similar amplitudes were achieved with longer burst durations combined with lower frequencies or with shorter burst durations combined with higher frequencies. Long burst durations delayed relaxation, leading to summation and tetanus. The time, and its variability, between stimulus onset and time to constriction onset or to peak decreased with increasing frequency. Data previously obtained in vivo showed that the heart excitatory motor neurons fired longer bursts at lower frequencies at long periods moving to shorter bursts with higher intraburst frequencies as the period shortened. In this scenario, active constriction started earlier and the time to reach full systole shortened, allowing more time for relaxation. Relaxation time before the next motor neuron burst appears critical for maintaining constriction amplitude.NEW & NOTEWORTHY Moving blood through the segmented heart tubes of leeches requires sequential constrictions driven by motor neurons controlled by a central pattern generator. In a single heart segment, we varied stimuli to explore the neuromuscular transform. Decreasing the cycle period, e.g., to increase volume pumped over time, without altering motor burst duration and intraburst spike frequency shortens relaxation time and decreases amplitude. The likely strategy to preserve constriction amplitude is to shorten burst duration while increasing spike frequency.

Synaptic Strengths Dominate Phasing of Motor Circuit: Intrinsic Conductances of Neuron Types Need Not Vary across Animals

Identified neurons and the networks they compose produce stereotypical, albeit individually unique, activity across members of a species. We propose, for a motor circuit driven by a central pattern generator (CPG), that the uniqueness derives mainly from differences in synaptic strength rather than from differences in intrinsic membrane conductances. We studied a dataset of recordings from six leech (Hirudo sp.) heartbeat control networks, containing complete spiking activity patterns from inhibitory premotor interneurons, motor output spike patterns, and synaptic strength patterns to investigate the source of uniqueness. We used a conductance-based multicompartmental motor neuron model to construct a bilateral motor circuit model, and controlled it by playing recorded input spike trains from premotor interneurons to generate output inhibitory synaptic patterns similar to experimental measurements. By generating different synaptic conductance parameter sets of this circuit model, we found that relative premotor synaptic strengths impinging onto motor neurons must be different across individuals to produce animal-specific output burst phasing. Obtaining unique outputs from each individual’s circuit model did not require different intrinsic ionic conductance parameters. Furthermore, changing intrinsic conductances failed to compensate for modified synaptic strength patterns. Thus, the pattern of synaptic strengths of motor neuron inputs is critical for the phasing of this motor circuit and can explain individual differences. When intrinsic conductances were allowed to vary, they exhibited the same conductance correlations across individuals, suggesting a motor neuron “type” required for proper network function. Our results are general and may translate to other systems and neuronal networks that control output phasing.

Output variability across animals and levels in a motor system

Rhythmic behaviors vary across individuals. We investigated the sources of this output variability across a motor system, from the central pattern generator (CPG) to the motor plant. In the bilaterally symmetric leech heartbeat system, the CPG orchestrates two coordinations in the bilateral hearts with different intersegmental phase relations (Δϕ) and periodic side-to-side switches. Population variability is large. We show that the system is precise within a coordination, that differences in repetitions of a coordination contribute little to population output variability, but that differences between bilaterally homologous cells may contribute to some of this variability. Nevertheless, much output variability is likely associated with genetic and life history differences among individuals. Variability of Δϕ were coordination-specific: similar at all levels in one, but significantly lower for the motor pattern than the CPG pattern in the other. Mechanisms that transform CPG output to motor neurons may limit output variability in the motor pattern.

A classic model animal in the 21st century: recent lessons from the leech nervous system

The medicinal leech (genus Hirudo) is a classic model animal in systems neuroscience. The leech has been central to many integrative studies that establish how properties of neurons and their interconnections give rise to the functioning of the animal at the behavioral level. Leeches exhibit several discrete behaviors (such as crawling, swimming and feeding) that are each relatively simple. Importantly, these behaviors can all be studied - at least at a basal level - in the isolated nervous system. The leech nervous system is particularly amenable to such studies because of its distributed nature; sensory processing and generation of behavior occur to a large degree in iterated segmental ganglia that each contain only ∼400 neurons. Furthermore, the neurons are relatively large and are arranged with stereotyped topography on the surface of the ganglion, which greatly facilitates their identification and accessibility. This Commentary provides an overview of recent work on the leech nervous system, with particular focus on circuits that underlie leech behavior. Studies that combine the unique features of the leech with modern optical and genetic techniques are also discussed. Thus, this Commentary aims to explain the continued appeal of the leech as an experimental animal in the 21st century.

The neural control of heartbeat in invertebrates

The neurogenic heartbeat of certain invertebrates has long been studied both as a way of understanding how automatic functions are regulated and for how neuronal networks generate the inherent rhythmic activity that controls and coordinates this vital function. This review focuses on the heartbeat of decapod crustaceans and hirudinid leeches, which remain important experimental systems for the exploration of central pattern generator networks, their properties, network and cellular mechanisms, modulation, and how animal-to-animal variation in neuronal and network properties are managed to produce functional output.

Variation in motor output and motor performance in a centrally generated motor pattern

Central pattern generators (CPGs) produce motor patterns that ultimately drive motor outputs. We studied how functional motor performance is achieved, specifically, whether the variation seen in motor patterns is reflected in motor performance and whether fictive motor patterns differ from those in vivo. We used the leech heartbeat system in which a bilaterally symmetrical CPG coordinates segmental heart motor neurons and two segmented heart tubes into two mutually exclusive coordination modes: rear-to-front peristaltic on one side and nearly synchronous on the other, with regular side-to-side switches. We assessed individual variability of the motor pattern and the beat pattern in vivo. To quantify the beat pattern we imaged intact adults. To quantify the phase relations between motor neurons and heart constrictions we recorded extracellularly from two heart motor neurons and movement from the corresponding heart segments in minimally dissected leeches. Variation in the motor pattern was reflected in motor performance only in the peristaltic mode, where larger intersegmental phase differences in the motor neurons resulted in larger phase differences between heart constrictions. Fictive motor patterns differed from those in vivo only in the synchronous mode, where intersegmental phase differences in vivo had a larger front-to-rear bias and were more constrained. Additionally, load-influenced constriction timing might explain the amplification of the phase differences between heart segments in the peristaltic mode and the higher variability in motor output due to body shape assumed in this soft-bodied animal. The motor pattern determines the beat pattern, peristaltic or synchronous, but heart mechanics influence the phase relations achieved.

A codimension-2 bifurcation controlling endogenous bursting activity and pulse-triggered responses of a neuron model

The dynamics of individual neurons are crucial for producing functional activity in neuronal networks. An open question is how temporal characteristics can be controlled in bursting activity and in transient neuronal responses to synaptic input. Bifurcation theory provides a framework to discover generic mechanisms addressing this question. We present a family of mechanisms organized around a global codimension-2 bifurcation. The cornerstone bifurcation is located at the intersection of the border between bursting and spiking and the border between bursting and silence. These borders correspond to the blue sky catastrophe bifurcation and the saddle-node bifurcation on an invariant circle (SNIC) curves, respectively. The cornerstone bifurcation satisfies the conditions for both the blue sky catastrophe and SNIC. The burst duration and interburst interval increase as the inverse of the square root of the difference between the corresponding bifurcation parameter and its bifurcation value. For a given set of burst duration and interburst interval, one can find the parameter values supporting these temporal characteristics. The cornerstone bifurcation also determines the responses of silent and spiking neurons. In a silent neuron with parameters close to the SNIC, a pulse of current triggers a single burst. In a spiking neuron with parameters close to the blue sky catastrophe, a pulse of current temporarily silences the neuron. These responses are stereotypical: the durations of the transient intervals-the duration of the burst and the duration of latency to spiking-are governed by the inverse-square-root laws. The mechanisms described here could be used to coordinate neuromuscular control in central pattern generators. As proof of principle, we construct small networks that control metachronal-wave motor pattern exhibited in locomotion. This pattern is determined by the phase relations of bursting neurons in a simple central pattern generator modeled by a chain of oscillators.

Real-time biomimetic Central Pattern Generators in an FPGA for hybrid experiments

This investigation of the leech heartbeat neural network system led to the development of a low resources, real-time, biomimetic digital hardware for use in hybrid experiments. The leech heartbeat neural network is one of the simplest central pattern generators (CPG). In biology, CPG provide the rhythmic bursts of spikes that form the basis for all muscle contraction orders (heartbeat) and locomotion (walking, running, etc.). The leech neural network system was previously investigated and this CPG formalized in the Hodgkin–Huxley neural model (HH), the most complex devised to date. However, the resources required for a neural model are proportional to its complexity. In response to this issue, this article describes a biomimetic implementation of a network of 240 CPGs in an FPGA (Field Programmable Gate Array), using a simple model (Izhikevich) and proposes a new synapse model: activity-dependent depression synapse. The network implementation architecture operates on a single computation core. This digital system works in real-time, requires few resources, and has the same bursting activity behavior as the complex model. The implementation of this CPG was initially validated by comparing it with a simulation of the complex model. Its activity was then matched with pharmacological data from the rat spinal cord activity. This digital system opens the way for future hybrid experiments and represents an important step toward hybridization of biological tissue and artificial neural networks. This CPG network is also likely to be useful for mimicking the locomotion activity of various animals and developing hybrid experiments for neuroprosthesis development.

Correlated conductance parameters in leech heart motor neurons contribute to motor pattern formation

Neurons can have widely differing intrinsic membrane properties, in particular the density of specific conductances, but how these contribute to characteristic neuronal activity or pattern formation is not well understood. To explore the relationship between conductances, and in particular how they influence the activity of motor neurons in the well characterized leech heartbeat system, we developed a new multi-compartmental Hodgkin-Huxley style leech heart motor neuron model. To do so, we evolved a population of model instances, which differed in the density of specific conductances, capable of achieving specific output activity targets given an associated input pattern. We then examined the sensitivity of measures of output activity to conductances and how the model instances responded to hyperpolarizing current injections. We found that the strengths of many conductances, including those with differing dynamics, had strong partial correlations and that these relationships appeared to be linked by their influence on heart motor neuron activity. Conductances that had positive correlations opposed one another and had the opposite effects on activity metrics when perturbed whereas conductances that had negative correlations could compensate for one another and had similar effects on activity metrics.

Centrally patterned rhythmic activity integrated by a peripheral circuit linking multiple oscillators

The central pattern generator for heartbeat in the medicinal leech, Hirudo generates rhythmic activity conveyed by heart excitor motor neurons in segments 3-18 to coordinate the bilateral tubular hearts and side vessels. We focus on behavior and the influence of previously un-described peripheral nerve circuitry. Extracellular recordings from the valve junction (VJ) where afferent vessels join the heart tube were combined with optical recording of contractions. Action potential bursts at VJs occurred in advance of heart tube and afferent vessel contractions. Transections of nerves were performed to reduce the output of the central pattern generator reaching the heart tube. Muscle contractions persisted but with a less regular rhythm despite normal central pattern generator rhythmicity. With no connections between the central pattern generator and heart tube, a much slower rhythm became manifest. Heart excitor neuron recordings showed that peripheral activity might contribute to the disruption of centrally entrained contractions. In the model presented, peripheral activity would normally modify the activity actually reaching the muscle. We also propose that the fundamental efferent unit is not a single heart excitor neuron, but rather is a functionally defined unit of about three adjacent motor neurons and the peripheral assembly of coupled peripheral oscillators.

Animal-to-animal variability of connection strength in the leech heartbeat central pattern generator

The heartbeat central pattern generator (CPG) in medicinal leeches controls blood flow within a closed circulatory by programming the constrictions of two parallel heart tubes. This circuit reliably produces a stereotyped fictive pattern of activity and has been extensively characterized. Here we determined, as quantitatively as possible, the strength of each inhibitory synapse and electrical junction within the core circuit of the heartbeat CPG. We also examined the animal-to-animal variability in strengths of these connections and, for some, determined the correlations between connections to the same postsynaptic target. The core CPG is composed of seven bilateral pairs of heart interneurons connected via both inhibitory chemical synapses and electrical junctions. Fifteen different connections within the core CPG were measured for strength using extracellular presynaptic recordings and postsynaptic voltage-clamp recordings across a minimum of seven individuals each, and the animal-to-animal variability was characterized. Connection strengths within the core network varied three to more than sevenfold among individuals (depending on the specific connection). The balance between two inputs onto various postsynaptic targets was explored by within-individual comparisons and correlation across individuals. Of the seven comparisons made within the core CPG, three showed a clear correlation of connection strengths, while the other four did not. We conclude that the leech heartbeat CPG can withstand wide variability in connection strengths and still produce stereotyped output. The network appears to preserve the relative strengths of some pairs of inputs, despite the animal-to-animal variability.

Bringing up the rear: new premotor interneurons add regional complexity to a segmentally distributed motor pattern

Central pattern generators (CPGs) pace and pattern many rhythmic activities. We have uncovered a new module in the heartbeat CPG of leeches that creates a regional difference in this segmentally distributed motor pattern. The core CPG consists of seven identified pairs and one unidentified pair of heart interneurons of which 5 pairs are premotor and inhibit 16 pairs of heart motor neurons. The heartbeat CPG produces a side-to-side asymmetric pattern of activity of the premotor heart interneurons corresponding to an asymmetric fictive motor pattern and an asymmetric constriction pattern of the hearts with regular switches between the two sides. The premotor pattern progresses from rear to front on one side and nearly synchronously on the other; the motor pattern shows corresponding intersegmental coordination, but only from segment 15 forward. In the rearmost segments the fictive motor pattern and the constriction pattern progress from front to rear on both sides and converge in phase. Modeling studies suggested that the known inhibitory inputs to the rearmost heart motor neurons were insufficient to account for this activity. We therefore reexamined the constriction pattern of intact leeches. We also identified electrophysiologically two additional pairs of heart interneurons in the rear. These new heart interneurons make inhibitory connections with the rear heart motor neurons, are coordinated with the core heartbeat CPG, and are dye-coupled to their contralateral homologs. Their strong inhibitory connections with the rearmost heart motor neurons and the small side-to-side phase difference of their bursting contribute to the different motor and beating pattern observed in the animal's rear.

Coping with variability in small neuronal networks

Experimental and corresponding modeling studies indicate that there is a 2- to 5-fold variation of intrinsic and synaptic parameters across animals while functional output is maintained. Here, we review experiments, using the heartbeat central pattern generator (CPG) in medicinal leeches, which explore the consequences of animal-to-animal variation in synaptic strength for coordinated motor output. We focus on a set of segmental heart motor neurons that all receive inhibitory synaptic input from the same four premotor interneurons. These four premotor inputs fire in a phase progression and the motor neurons also fire in a phase progression because of differences in synaptic strength profiles of the four inputs among segments. Our work tested the hypothesis that functional output is maintained in the face of animal-to-animal variation in the absolute strength of connections because relative strengths of the four inputs onto particular motor neurons is maintained across animals. Our experiments showed that relative strength is not strictly maintained across animals even as functional output is maintained, and animal-to-animal variations in strength of particular inputs do not correlate strongly with output phase. Further experiments measured the precise temporal pattern of the premotor inputs, the segmental synaptic strength profiles of their connections onto motor neurons, and the temporal pattern (phase progression) of those motor neurons all in the same animal for a series of 12 animals. The analysis of input and output in this sample of 12 individuals suggests that the number (four) of inputs to each motor neuron and the variability of the temporal pattern of input from the CPG across individuals weaken the influence of the strength of individual inputs. Moreover, the temporal pattern of the output varies as much across individuals as that of the input. Essentially, each animal arrives at a unique solution for how the network produces functional output.

Constancy and variability in the output of a central pattern generator

Experimental and corresponding modeling studies have demonstrated a twofold to fivefold variation of intrinsic and synaptic parameters across animals, whereas functional output is maintained. These studies have led to the hypothesis that correlated, compensatory changes in particular parameters can at least partially explain the biological variability in parameters. Using the leech heartbeat central pattern generator (CPG), we selected three different segmental motor neurons that fire in a functional phase progression but receive input from the same four premotor interneurons. Previous work suggested that the phase progression arises because the pattern of relative strength of the four inputs varies systematically across the segmental motor neurons. Nevertheless, there was considerable animal-to-animal variation in the absolute strengths of these connections. We tested the hypothesis that functional output is maintained in the face of variation in the absolute strength of connections because relative strengths onto particular motor neurons are maintained. We found that relative strength is not strictly maintained across animals even as functional output is maintained, and animal-to-animal variations in relative strength of particular inputs do not correlate strongly with output phase. In parallel with this variation in synaptic strength, the firing phase of the premotor inputs to these motor neurons varies considerably across individuals. We conclude that the number (four) of inputs to each motor neuron, which each vary in strength, and the phase diversity of the temporal pattern of input from the CPG diminish the influence of individual inputs. We hypothesize that each animal arrives at a unique solution for how the network produces functional output.

Contribution of motoneuron intrinsic properties to fictive motor pattern generation

Previously, we reported a canonical ensemble model of the heart motoneurons that underlie heartbeat in the medicinal leech. The model motoneurons contained a minimal set of electrical intrinsic properties and received a synaptic input pattern based on measurements performed in the living system. Although the model captured the synchronous and peristaltic motor patterns observed in the living system, it did not match quantitatively the motor output observed. Because the model motoneurons had minimal intrinsic electrical properties, the mismatch between model and living system suggests a role for additional intrinsic properties in generating the motor pattern. We used the dynamic clamp to test this hypothesis. We introduced the same segmental input pattern used in the model to motoneurons isolated pharmacologically from their endogenous input in the living system. We show that, although the segmental input pattern determines the segmental phasing differences observed in motoneurons, the intrinsic properties of the motoneurons play an important role in determining their phasing, particularly when receiving the synchronous input pattern. We then used trapezoidal input waveforms to show that the intrinsic properties present in the living system promote phase advances compared with our model motoneurons. Electrical coupling between heart motoneurons also plays a role in shaping motoneuron output by synchronizing the activity of the motoneurons within a segment. These experiments provide a direct assessment of how motoneuron intrinsic properties interact with their premotor pattern of synaptic drive to produce rhythmic output.

Functional consequences of animal-to-animal variation in circuit parameters

How different are the neuronal circuits for a given behavior across individual animals? To address this question, we measured multiple cellular and synaptic parameters in individual preparations to see how they correlated with circuit function, using neurons and synapses in the pyloric circuit of the stomatogastric ganglion of the crab Cancer borealis. There was considerable preparation-to-preparation variability in the strength of two identified synapses, in the amplitude of a modulator-evoked current and in the expression of six ion channel genes. Nonetheless, we found strong correlations across preparations among these parameters and attributes of circuit performance. These data illustrate the importance of making multidimensional measurements from single preparations for understanding how variability in circuit output is related to the variability of multiple circuit parameters.

Using a model to assess the role of the spatiotemporal pattern of inhibitory input and intrasegmental electrical coupling in the intersegmental and side-to-side coordination of motor neurons by the leech heartbeat central pattern generator

Previously we presented a quantitative description of the spatiotemporal pattern of inhibitory synaptic input from the heartbeat central pattern generator (CPG) to segmental motor neurons that drive heartbeat in the medicinal leech and the resultant coordination of CPG interneurons and motor neurons. To begin elucidating the mechanisms of coordination, we explore intersegmental and side-to-side coordination in an ensemble model of all heart motor neurons and their known synaptic inputs and electrical coupling. Model motor neuron intrinsic properties were kept simple, enabling us to determine the extent to which input and electrical coupling acting together can account for observed coordination in the living system in the absence of a substantive contribution from the motor neurons themselves. The living system produces an asymmetric motor pattern: motor neurons on one side fire nearly in synchrony (synchronous), whereas on the other they fire in a rear-to-front progression (peristaltic). The model reproduces the general trends of intersegmental and side-to-side phase relations among motor neurons, but the match with the living system is not quantitatively accurate. Thus realistic (experimentally determined) inputs do not produce similarly realistic output in our model, suggesting that motor neuron intrinsic properties may contribute to their coordination. By varying parameters that determine electrical coupling, conduction delays, intraburst synaptic plasticity, and motor neuron excitability, we show that the most important determinant of intersegmental and side-to-side phase relations in the model was the spatiotemporal pattern of synaptic inputs, although phasing was influenced significantly by electrical coupling.