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.

Analysis of Family Structures Reveals Robustness or Sensitivity of Bursting Activity to Parameter Variations in a Half-Center Oscillator (HCO) Model.

The underlying mechanisms that support robustness in neuronal networks are as yet unknown. However, recent studies provide evidence that neuronal networks are robust to natural variations, modulation, and environmental perturbations of parameters, such as maximal conductances of intrinsic membrane and synaptic currents. Here we sought a method for assessing robustness, which might easily be applied to large brute-force databases of model instances. Starting with groups of instances with appropriate activity (e.g., tonic spiking), our method classifies instances into much smaller subgroups, called families, in which all members vary only by the one parameter that defines the family. By analyzing the structures of families, we developed measures of robustness for activity type. Then, we applied these measures to our previously developed model database, HCO-db, of a two-neuron half-center oscillator (HCO), a neuronal microcircuit from the leech heartbeat central pattern generator where the appropriate activity type is alternating bursting. In HCO-db, the maximal conductances of five intrinsic and two synaptic currents were varied over eight values (leak reversal potential also varied, five values). We focused on how variations of particular conductance parameters maintain normal alternating bursting activity while still allowing for functional modulation of period and spike frequency. We explored the trade-off between robustness of activity type and desirable change in activity characteristics when intrinsic conductances are altered and identified the hyperpolarization-activated (h) current as an ideal target for modulation. We also identified ensembles of model instances that closely approximate physiological activity and can be used in future modeling studies.

Identifying crucial parameter correlations maintaining bursting activity.

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, [Formula: see text]Leak; a persistent K current, [Formula: see text]K2; and of a persistent Na+ current, [Formula: see text]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 [Formula: see text]Leak, [Formula: see text]K2, and [Formula: see text]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.

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.

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 (g(leak)) 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 g(leak). 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.

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.

A database of computational models of a half-center oscillator for analyzing how neuronal parameters influence network activity.

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.