Neuronal networks: Degeneracy unleashed

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.

Oscillatory network spontaneously recovers both activity and robustness after prolonged removal of neuromodulators

Robustness of neuronal activity is a property necessary for a neuronal network to withstand perturbations, which may otherwise disrupt or destroy the system. The robustness of complex systems has been shown to depend on a number of features of the system, including morphology and heterogeneity of the activity of the component neurons, size of the networks, synaptic connectivity, and neuromodulation. The activity of small networks, such as the pyloric network of the crustacean stomatogastric nervous system, appears to be robust despite some of the factors not being consistent with the expected properties of complex systems, e.g., small size and homogeneity of the synaptic connections. The activity of the pyloric network has been shown to be stable and robust in a neuromodulatory state-dependent manner. When neuromodulatory inputs are severed, activity is initially disrupted, losing both stability and robustness. Over the long term, however, stable activity homeostatically recovers without the restoration of neuromodulatory input. The question we address in this study is whether robustness can also be restored as the network reorganizes itself to compensate for the loss of neuromodulatory input and recovers the lost activity. Here, we use temperature changes as a perturbation to probe the robustness of the network's activity. We develop a simple metric of robustness, i.e., the variances of the network phase relationships, and show that robustness is indeed restored simultaneously along with its stable network activity, indicating that, whatever the reorganization of the network entails, it is deep enough also to restore this important property.

Diversity of neuropeptidergic modulation in decapod crustacean cardiac and feeding systems

All nervous systems are multiply modulated by polypeptides. However, a bulk of transmitter and modulation research has historically focused on small molecule transmitters released at synaptic sites. The stomatogastric nervous system (controls digestive movements of the foregut) and cardiac nervous system of decapod crustaceans have long been used to understand the processes that underlie neuromodulation. The circuits governing the rhythmic output from these nervous systems are comprised of a relatively small number of identified neurons, and the details of these nervous systems are well-defined. Here we discuss recent research highlighting advances in our understanding of peptidergic modulation in these systems. In particular, we focus on our ability to identify specific signaling peptide sequences and relate their expression patterns to their physiological effects, as well as on the multiple sites within a pattern generator-effector system at which modulation takes place. Recent efforts have enabled us to understand how co-modulation by two or more peptides can generate surprising effects on circuit physiology and that modulation at different receptor sites can produce supra-additive effects. Finally, we examine the protective role modulation plays in making circuits robust to perturbations, in this case, changes in temperature.

Persistent modulatory actions and task switching in the feeding network of Aplysia

The activity of multifunctional networks is configured by neuromodulators that exert persistent effects. This raises a question, does this impact the ability of a network to switch from one type of activity to another? We review studies that have addressed this question in the Aplysia feeding circuit. Task switching in this system occurs "asymmetrically." When there is a switch from egestion to ingestion neuromodulation impedes switching (creates a "negative bias"). When there is a switch from ingestion to egestion the biasing is "positive." Ingestion promotes subsequent egestion. We contrast mechanisms responsible for the two types of biasing and show that the observed asymmetry is a consequence of the fact that there is more than one set of egestive circuit parameters.

Computational and experimental modulation of a noisy chaotic neuronal system

In this work, we study the interplay between chaos and noise in neuronal state transitions involving period doubling cascades. Our approach involves the implementation of a neuronal mathematical model under the action of neuromodulatory input, with and without noise, as well as equivalent experimental work on a biological neuron in the stomatogastric ganglion of the crab Cancer borealis. Our simulations show typical transitions between tonic and bursting regimes that are mediated by chaos and period doubling cascades. While this transition is less evident when intrinsic noise is present in the model, the noisy computational output displays features akin to our experimental results. The differences and similarities observed in the computational and experimental approaches are discussed.

Extrasynaptic signaling enables an asymmetric juvenile motor circuit to produce symmetric undulation

In many animals, there is a direct correspondence between the motor patterns that drive locomotion and the motor neuron innervation. For example, the adult C. elegans moves with symmetric and alternating dorsal-ventral bending waves arising from symmetric motor neuron input onto the dorsal and ventral muscles. In contrast to the adult, the C. elegans motor circuit at the juvenile larval stage has asymmetric wiring between motor neurons and muscles but still generates adult-like bending waves with dorsal-ventral symmetry. We show that in the juvenile circuit, wiring between excitatory and inhibitory motor neurons coordinates the contraction of dorsal muscles with relaxation of ventral muscles, producing dorsal bends. However, ventral bending is not driven by analogous wiring. Instead, ventral muscles are excited uniformly by premotor interneurons through extrasynaptic signaling. Ventral bends occur in anti-phasic entrainment to activity of the same motor neurons that drive dorsal bends. During maturation, the juvenile motor circuit is replaced by two motor subcircuits that separately drive dorsal and ventral bending. Modeling reveals that the juvenile's immature motor circuit is an adequate solution to generate adult-like dorsal-ventral bending before the animal matures. Developmental rewiring between functionally degenerate circuit solutions, which both generate symmetric bending patterns, minimizes behavioral disruption across maturation.

Reciprocally inhibitory circuits operating with distinct mechanisms are differently robust to perturbation and modulation

Reciprocal inhibition is a building block in many sensory and motor circuits. We studied the features that underly robustness in reciprocally inhibitory two neuron circuits. We used the dynamic clamp to create reciprocally inhibitory circuits from pharmacologically isolated neurons of the crab stomatogastric ganglion by injecting artificial graded synaptic (I_Syn) and hyperpolarization-activated inward (I_H) currents. There is a continuum of mechanisms in circuits that generate antiphase oscillations, with ‘release’ and ‘escape’ mechanisms at the extremes, and mixed mode oscillations between these extremes. In release, the active neuron primarily controls the off/on transitions. In escape, the inhibited neuron controls the transitions. We characterized the robustness of escape and release circuits to alterations in circuit parameters, temperature, and neuromodulation. We found that escape circuits rely on tight correlations between synaptic and H conductances to generate bursting but are resilient to temperature increase. Release circuits are robust to variations in synaptic and H conductances but fragile to temperature increase. The modulatory current (I_MI) restores oscillations in release circuits but has little effect in escape circuits. Perturbations can alter the balance of escape and release mechanisms and can create mixed mode oscillations. We conclude that the same perturbation can have dramatically different effects depending on the circuits’ mechanism of operation that may not be observable from basal circuit activity.