Identifying the structure and dynamics of synaptic interactions between neurons is the first step to understanding neural network dynamics. The presence of synaptic connections is traditionally inferred through the use of targeted stimulation and paired recordings or by post-hoc histology. More recently, causal network inference algorithms have been proposed to deduce connectivity directly from electrophysiological signals, such as extracellularly recorded spiking activity. Usually, these algorithms have not been validated on a neurophysiological data set for which the actual circuitry is known. Recent work has shown that traditional network inference algorithms based on linear models typically fail to identify the correct coupling of a small central pattern generating circuit in the stomatogastric ganglion of the crab Cancer borealis. In this work, we show that point process models of observed spike trains can guide inference of relative connectivity estimates that match the known physiological connectivity of the central pattern generator up to a choice of threshold. We elucidate the necessary steps to derive faithful connectivity estimates from a model that incorporates the spike train nature of the data. We then apply the model to measure changes in the effective connectivity pattern in response to two pharmacological interventions, which affect both intrinsic neural dynamics and synaptic transmission. Our results provide the first successful application of a network inference algorithm to a circuit for which the actual physiological synapses between neurons are known. The point process methodology presented here generalizes well to larger networks and can describe the statistics of neural populations. In general we show that advanced statistical models allow for the characterization of effective network structure, deciphering underlying network dynamics and estimating information-processing capabilities.

The crab Cancer borealis undergoes large daily fluctuations in environmental temperature (8-24°C) and must maintain appropriate neural function in the face of this perturbation. In the pyloric circuit of the crab stomatogastric ganglion, we pharmacologically isolated the pacemaker kernel (the AB and PD neurons) and characterized its behavior in response to temperature ramps from 7°C to 31°C. For moderate temperatures, the pacemaker displayed a frequency-temperature curve statistically indistinguishable from that of the intact circuit, and like the intact circuit maintained a constant duty cycle. At high temperatures (above 23°C), a variety of different behaviors were seen: in some preparations the pacemaker increased in frequency, in some it slowed, and in many preparations the pacemaker stopped oscillating ("crashed"). Furthermore, these crashes seemed to fall into two qualitatively different classes. Additionally, the animal-to-animal variability in frequency increased at high temperatures. We used a series of Morris-Lecar mathematical models to gain insight into these phenomena. The biophysical components of the final model have temperature sensitivities similar to those found in nature, and can crash via two qualitatively different mechanisms that resemble those observed experimentally. The crash type is determined by the precise parameters of the model at the reference temperature, 11°C, which could explain why some preparations seem to crash in one way and some in another. Furthermore, even models with very similar behavior at the reference temperature diverge greatly at high temperatures, resembling the experimental observations.

Activity-dependent plasticity appears to play an important role in the modification of neurons and neural circuits that occurs during development and learning. Plasticity is also essential for the maintenance of stable patterns of activity in the face of variable environmental and internal conditions. Previous theoretical and experimental results suggest that neurons stabilize their activity by altering the number or characteristics of ion channels to regulate their intrinsic electrical properties. We present both experimental and modeling evidence to show that activity-dependent regulation of conductances, operating at the level of individual neurons, can also stabilize network activity. These results indicate that the stomatogastric ganglion of the crab can generate a characteristic rhythmic pattern of activity in two fundamentally different modes of operation. In one mode, the rhythm is strictly conditional on the presence of neuromodulatory afferents from adjacent ganglia. In the other, it is independent of neuromodulatory input but relies on newly developed intrinsic properties of the component neurons.

We study the properties of a network consisting of two model neurons that are coupled by reciprocal inhibition. The study was motivated by data from a pair of cells in the crustacean stomatogastric ganglion. One of the model neurons is an endogenous burster; the other is excitable but not bursting in the absence of phasic input. We show that the presence of a hyperpolarization activated inward current (i h ) in the excitable neuron allows these neurons to fire in integer subharmonics, with the excitable cell firing once for every N ≥ 1 bursts of the oscillator. The value of N depends on the amount of hyperpolarizing current injected into the excitable cell as well as the voltage activation curve of i h . For a fast synapse, these parameter changes do not affect the characteristic point in the oscillator cycle at which the excitable cell bursts; for slower synapses, such a relationship is maintained within small windows for each N. The network behavior in the current work contrasts with the activity of a pair of coupled oscillators for which the interaction is through phase differences; in the latter case, subharmonics exist if the uncoupled oscillators have near integral frequency relationships, but the phase relationships of the oscillators in general change significantly with parameters. The mechanism of this paper provides a potential means of coordinating subnetworks acting on different time scales but maintaining fixed relationships between characteristic points of the cycles.

The pyloric network of the stomatogastric ganglion in crustacea is a central pattern generator that can produce the same basic rhythm over a wide frequency range. Three electrically coupled neurons, the anterior burster (AB) neuron and two pyloric dilator (PD) neurons, act as a pacemaker unit for the pyloric network. The functional characteristics of the pacemaker network are the result of electrical coupling between neurons with quite different intrinsic properties, each contributing a basic feature to the complete circuit. The AB neuron, a conditional oscillator, plays a dominant role in rhythm generation. In the work described here, we manipulate the frequency of the AB neuron both isolated and electrically coupled to the PD neurons. Physiological and modeling studies indicate that the PD neurons play an important role in regulating the duration of the bursts produced by the pacemaker unit.

A preliminary report is presented on modeling studies of the pyloric circuit of the crustacean stomatogastric ganglion. The goal of this research is to understand how this small network is able to perform the dynamic adjustments needed to maintain a stable rhythmic pattern over a wide range of frequencies and conditions. A discussion is presented of models of individual cell behaviors and the procedure by which they may be reduced to a manageable form. Some indications of how these intrinsic characteristics may interact to produce the full network behavior are presented