A half-center oscillator (HCO) is a common circuit building block of central pattern generator networks that produce rhythmic motor patterns in animals. Here we constructed an efficient relational database table with the resulting characteristics of the Hill et al.'s (J Comput Neurosci 10:281-302, 2001) HCO simple conductance-based model. The model consists of two reciprocally inhibitory neurons and replicates the electrical activity of the oscillator interneurons of the leech heartbeat central pattern generator under a variety of experimental conditions. Our long-range goal is to understand how this basic circuit building block produces functional activity under a variety of parameter regimes and how different parameter regimes influence stability and modulatability. By using the latest developments in computer technology, we simulated and stored large amounts of data (on the order of terabytes). We systematically explored the parameter space of the HCO and corresponding isolated neuron models using a brute-force approach. We varied a set of selected parameters (maximal conductance of intrinsic and synaptic currents) in all combinations, resulting in about 10 million simulations. We classified these HCO and isolated neuron model simulations by their activity characteristics into identifiable groups and quantified their prevalence. By querying the database, we compared the activity characteristics of the identified groups of our simulated HCO models with those of our simulated isolated neuron models and found that regularly bursting neurons compose only a small minority of functional HCO models; the vast majority was composed of spiking neurons.

Wenning A, Norris BJ, Doloc-Mihu A, Calabrese RL. Variation in motor output and motor performance in a centrally generated motor pattern.

Recent experimental and computational studies suggest that linearly correlated sets of parameters (intrinsic and synaptic properties of neurons) allow central pattern-generating networks to produce and maintain their rhythmic activity regardless of changing internal and external conditions. To determine the role of correlated conductances in the robust maintenance of functional bursting activity, we used our existing database of half-center oscillator (HCO) model instances of the leech heartbeat CPG. From the database, we identified functional activity groups of burster (isolated neuron) and half-center oscillator model instances and realistic subgroups of each that showed burst characteristics (principally period and spike frequency) similar to the animal. To find linear correlations among the conductance parameters maintaining functional leech bursting activity, we applied Principal Component Analysis (PCA) to each of these four groups. PCA identified a set of three maximal conductances (leak current, Leak; a persistent K current, K2; and of a persistent Na+ current, P) that correlate linearly for the two groups of burster instances but not for the HCO groups. Visualizations of HCO instances in a reduced space suggested that there might be non-linear relationships between these parameters for these instances. Experimental studies have shown that period is a key attribute influenced by modulatory inputs and temperature variations in heart interneurons. Thus, we explored the sensitivity of period to changes in maximal conductances of Leak, K2, and P, and we found that for our realistic bursters the effect of these parameters on period could not be assessed because when varied individually bursting activity was not maintained.

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.

Wenning A, Norris BJ, Doloc-Mihu A, Calabrese RL. Bringing up the rear: new premotor interneurons add regional complexity to a segmentally distributed motor pattern.