Synchronized neural activity, in which the firing of neurons is coordinated in time, is an observed phenomenon in many neural functions. The conditions that promote synchrony and the dynamics of synchronized activity are active areas of investigation because they are incompletely understood. In addition, variability is intrinsic to biological systems, but the effect of neuron spike time variability on synchronization dynamics is a question that merits more attention. Previous experiments using a hybrid circuit of one biological neuron coupled to one computational neuron revealed that irregularity in biological neuron spike timing could change synchronization in the circuit, transitioning the activity between phase-locked and phase slipping. Simulations of this circuit could not replicate the transitions in network activity if neuron period was represented as a Gaussian process, but could if a process with history and a stochastic component were used. The phase resetting curve (PRC), which describes how neuron cycles change in response to input, can be used to construct a map that predicts if synchronization will occur in hybrid circuits. Without modification, these maps did not always capture observed network activity. I conducted long-term recordings of invertebrate neurons and show that interspike interval (ISI) can be represented as an autoregressive integrated moving average process, where ISI is dependent on past history and a stochastic component with history. Using integrate and fire model simulations, I suggest that stochastic activity in adaptation channels could be responsible for the history dependence and correlational structure observed in these neurons. This evidence for stochastic, history-dependent noise in neural systems indicates that our understanding of network dynamics could be enhanced by including more complex, but relevant, forms of noise. I show that cycle-by-cycle dynamics of the coupled system can be used to infer features of the dynamic map, even if it cannot be measured or is changing over time. Using this method, stable fixed points can be distinguished from ghost attractors in the presence of noise, networks with similar phase but different underlying dynamics can be resolved, and the movement of stable fixed points can be observed. The time-series vector method is a valuable tool for distinguishing dynamics and describing robustness. It can be adapted for use in larger populations and non-reciprocal circuits. Finally, some larger implications of neuroscience research, specifically the use of neural interfaces for national security, are discussed. Neural interfaces for human enhancement in a national security context raise a number of unique ethical and policy concerns not common to dual use research of concern or traditional human subjects research. Guidelines about which technologies should be developed are lacking. We discuss a two-step framework with 1) an initial screen to prioritize technologies that should be reviewed immediately, and 2) a comprehensive ethical review regarding concerns for the enhanced individual, operational norms, and multi-use applications in the case of transfer to civilian contexts.

Neuronal networks produce reliable functional output throughout the lifespan of an animal despite ceaseless molecular turnover and a constantly changing environment. The cellular and molecular mechanisms underlying the ability of these networks to maintain functional stability remain poorly understood. Central pattern generating circuits produce a stable, predictable rhythm, making them ideal candidates for studying mechanisms of activity maintenance. By identifying and characterizing the regulators of activity in small neuronal circuits, we not only obtain a clearer understanding of how neural activity is generated, but also arm ourselves with knowledge that may eventually be used to improve medical care for patients whose normal nervous system activity has been disrupted through trauma or disease. We utilize the pattern-generating pyloric circuit in the crustacean stomatogastric nervous system to investigate the general scientific question: How are specific aspects of rhythmic activity regulated in a small neuronal network? The first aim of this thesis poses this question in the context of a single neuron. We used a single-compartment model neuron database to investigate whether co-regulation of ionic conductances supports the maintenance of spike phase in rhythmically bursting “pacemaker” neurons. The second aim of the project extends the question to a network context. Through a combination of computational and electrophysiology studies, we investigated how the intrinsic membrane conductances of the pacemaker neuron influence its response to synaptic input within the framework of the Phase Resetting Curve (PRC). The third aim of the project further extends the question to a systems-level context. We examined how ambient temperatures affect the stability of the pyloric rhythm in the intact, behaving animal. The results of this work have furthered our understanding of the principles underlying the long-term stability of neuronal network function.