A central pattern generator producing alternative outputs: pattern, strength, and dynamics of premotor synaptic input to leech heart motor neurons

Degenerate neuronal and circuit mechanisms important for generating rhythmic motor patterns

In 1996, we published a review article (Marder E, Calabrese RL. Physiol Rev 76: 687-717, 1996) describing the state of knowledge about the structure and function of the central pattern-generating circuits important for producing rhythmic behaviors. Although many of the core questions persist, much has changed since 1996. Here, we focus on newer studies that reveal ambiguities that complicate understanding circuit dynamics, despite the enormous technical advances of the recent past. In particular, we highlight recent studies of animal-to-animal variability and our understanding that circuit rhythmicity may be supported by multiple state-dependent mechanisms within the same animal and that robustness and resilience in the face of perturbation may depend critically on the presence of modulators and degenerate circuit mechanisms. Additionally, we highlight the use of computational models to ask whether there are generalizable principles about circuit motifs that can be found across rhythmic motor systems in different animal species.

Network Degeneracy and the Dynamics of Task Switching in the Feeding Circuit in Aplysia

The characteristics of a network are determined by parameters that describe the intrinsic properties of the component neurons and their synapses. Degeneracy occurs when more than one set of parameters produces the same (or very similar) output. It is not clear whether network degeneracy impacts network function or is simply a reflection of the fact that, although it is important for a network to be able to generate a particular output, it is not important how this is achieved. We address this issue in the feeding network of the mollusc Aplysia In this system, there are two stimulation paradigms that generate egestive motor programs: repetition priming and positive biasing. We demonstrate that circuit parameters differ in the 2 cases (e.g., egestive repetition priming requires activity in an interneuron, B20, which is not essential for positive biasing). We show that degeneracy has consequences for task switching. If egestive repetition priming is immediately followed by stimulation of an ingestive input to the feeding central pattern generator, the first few cycles of activity are egestive (not ingestive). In this situation, there is a task switch cost. This "cost" is in part due to the potentiating effect of egestive repetition priming on B20. In contrast, there is no switch cost after positive biasing. Stimulation of the ingestive central pattern generator input immediately triggers ingestive activity. Our results indicate that the mechanisms used to pattern activity can impact network function in that they can determine how readily a network can switch from one configuration to another.SIGNIFICANCE STATEMENT A particular pattern of neural activity can be generated by more than one set of circuit parameters. How or whether this impacts network function is unclear. We address this issue in the feeding network of Aplysia and demonstrate that degeneracy in network function can have consequences for task switching. Namely, we show that, when egestive activity is generated via one set of circuit modifications, an immediate switch to ingestive activity is not possible. In contrast, rapid transitions to ingestive activity are possible if egestive activity is generated via a different set of circuit modifications.

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.

Na(+)/K(+) pump interacts with the h-current to control bursting activity in central pattern generator neurons of leeches

The dynamics of different ionic currents shape the bursting activity of neurons and networks that control motor output. Despite being ubiquitous in all animal cells, the contribution of the Na(+)/K(+) pump current to such bursting activity has not been well studied. We used monensin, a Na(+)/H(+) antiporter, to examine the role of the pump on the bursting activity of oscillator heart interneurons in leeches. When we stimulated the pump with monensin, the period of these neurons decreased significantly, an effect that was prevented or reversed when the h-current was blocked by Cs(+). The decreased period could also occur if the pump was inhibited with strophanthidin or K(+)-free saline. Our monensin results were reproduced in model, which explains the pump's contributions to bursting activity based on Na(+) dynamics. Our results indicate that a dynamically oscillating pump current that interacts with the h-current can regulate the bursting activity of neurons and networks.

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.

Consequences of degeneracy in network function

Often distinct elements serve similar functions within a network. However, it is unclear whether this network degeneracy is beneficial, or merely a reflection of tighter regulation of overall network performance relative to individual neuronal properties. We review circumstances where data strongly suggest that degeneracy is beneficial in that it makes network function more robust. Importantly, network degeneracy is likely to have functional consequences that are not widely appreciated. This is likely to be true when network activity is configured by modulators with persistent actions, and the history of network activity potentially impacts subsequent functioning. Data suggest that degeneracy in this context may be important for the creation of latent memories, and for state-dependent task switching.

Electrosensory Midbrain Neurons Display Feature Invariant Responses to Natural Communication Stimuli

Neurons that respond selectively but in an invariant manner to a given feature of natural stimuli have been observed across species and systems. Such responses emerge in higher brain areas, thereby suggesting that they occur by integrating afferent input. However, the mechanisms by which such integration occurs are poorly understood. Here we show that midbrain electrosensory neurons can respond selectively and in an invariant manner to heterogeneity in behaviorally relevant stimulus waveforms. Such invariant responses were not seen in hindbrain electrosensory neurons providing afferent input to these midbrain neurons, suggesting that response invariance results from nonlinear integration of such input. To test this hypothesis, we built a model based on the Hodgkin-Huxley formalism that received realistic afferent input. We found that multiple combinations of parameter values could give rise to invariant responses matching those seen experimentally. Our model thus shows that there are multiple solutions towards achieving invariant responses and reveals how subthreshold membrane conductances help promote robust and invariant firing in response to heterogeneous stimulus waveforms associated with behaviorally relevant stimuli. We discuss the implications of our findings for the electrosensory and other systems.

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.

High prevalence of multistability of rest states and bursting in a database of a model neuron

Flexibility in neuronal circuits has its roots in the dynamical richness of their neurons. Depending on their membrane properties single neurons can produce a plethora of activity regimes including silence, spiking and bursting. What is less appreciated is that these regimes can coexist with each other so that a transient stimulus can cause persistent change in the activity of a given neuron. Such multistability of the neuronal dynamics has been shown in a variety of neurons under different modulatory conditions. It can play either a functional role or present a substrate for dynamical diseases. We considered a database of an isolated leech heart interneuron model that can display silent, tonic spiking and bursting regimes. We analyzed only the cases of endogenous bursters producing functional half-center oscillators (HCOs). Using a one parameter (the leak conductance ()) bifurcation analysis, we extended the database to include silent regimes (stationary states) and systematically classified cases for the coexistence of silent and bursting regimes. We showed that different cases could exhibit two stable depolarized stationary states and two hyperpolarized stationary states in addition to various spiking and bursting regimes. We analyzed all cases of endogenous bursters and found that 18% of the cases were multistable, exhibiting coexistences of stationary states and bursting. Moreover, 91% of the cases exhibited multistability in some range of . We also explored HCOs built of multistable neuron cases with coexisting stationary states and a bursting regime. In 96% of cases analyzed, the HCOs resumed normal alternating bursting after one of the neurons was reset to a stationary state, proving themselves robust against this perturbation.

It is often not appreciated that different activity regimes can coexist with each other in a given neuron so that a transient stimulus can cause a persistent change of activity. Such multistability of the neuronal dynamics has in fact been shown in a variety of neurons and can play either a functional role or present a substrate for neurological diseases. We explored the propensity for multistability in a database of a leech heart interneuron model, testing each case (parameter set) in a database for multistability. We found a large proportion of multistable cases, especially the coexistence of silent and bursting regimes. This was a surprising result, since these cells pace the heartbeat of the leech, and the coexistence of silence and bursting could disrupt the functional pattern, threatening the viability of the leech. Analysis of networks of mutually inhibitory multistable neurons, however, showed robustness in maintaining functional activity, suggesting that the mutually inhibitory coupling can act as a protective mechanism against failures induced by multistability.

Robustness of a rhythmic circuit to short- and long-term temperature changes

Recent computational and experimental work has shown that similar network performance can result from variable sets of synaptic and intrinsic properties. Because temperature is a global perturbation that differentially influences every biological process within the nervous system, one might therefore expect that individual animals would respond differently to temperature. Nonetheless, the phase relationships of the pyloric rhythm of the stomatogastric ganglion (STG) of the crab, Cancer borealis, are remarkably invariant between 7 and 23°C (Tang et al., 2010). Here, we report that, when isolated STG preparations were exposed to more extreme temperature ranges, their networks became nonrhythmic, or "crashed", in a reversible fashion. Animals were acclimated for at least 3 weeks at 7, 11, or 19°C. When networks from the acclimated animals were perturbed by acute physiologically relevant temperature ramps (11-23°C), the network frequency and phase relationships were independent of the acclimation group. At high acute temperatures (>23°C), circuits from the cold-acclimated animals produced less-regular pyloric rhythms than those from warm-acclimated animals. At high acute temperatures, phase relationships between pyloric neurons were more variable from animal to animal than at moderate acute temperatures, suggesting that individual differences across animals in intrinsic circuit parameters are revealed at high temperatures. This shows that individual and variable neuronal circuits can behave similarly in normal conditions, but their behavior may diverge when confronted with extreme external perturbations.

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.

Neural networks: more about flexibility than synaptic strength

The leech heartbeat neural network is famous for its constancy in both architecture and functional output across animals. A recent study, however, has found that the synaptic strengths underlying this constancy are quite variable across animals.

Multiple models to capture the variability in biological neurons and networks

How tightly tuned are the synaptic and intrinsic properties that give rise to neuron and circuit function? Experimental work shows that these properties vary considerably across identified neurons in different animals. Given this variability in experimental data, this review describes some of the complications of building computational models to aid in understanding how system dynamics arise from the interaction of system components. We argue that instead of trying to build a single model that captures the generic behavior of a neuron or circuit, it is beneficial to construct a population of models that captures the behavior of the population that provided the experimental data. Studying a population of models with different underlying structure and similar behaviors provides opportunities to discover unsuspected compensatory mechanisms that contribute to neuron and network function.

Variability, compensation, and modulation in neurons and circuits

I summarize recent computational and experimental work that addresses the inherent variability in the synaptic and intrinsic conductances in normal healthy brains and shows that multiple solutions (sets of parameters) can produce similar circuit performance. I then discuss a number of issues raised by this observation, such as which parameter variations arise from compensatory mechanisms and which reflect insensitivity to those particular parameters. I ask whether networks with different sets of underlying parameters can nonetheless respond reliably to neuromodulation and other global perturbations. At the computational level, I describe a paradigm shift in which it is becoming increasingly common to develop families of models that reflect the variance in the biological data that the models are intended to illuminate rather than single, highly tuned models. On the experimental side, I discuss the inherent limitations of overreliance on mean data and suggest that it is important to look for compensations and correlations among as many system parameters as possible, and between each system parameter and circuit performance. This second paradigm shift will require moving away from measurements of each system component in isolation but should reveal important previously undescribed principles in the organization of complex systems such as brains.

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.