The dynamical underpinnings of complex computation and information transmission within the brain, while of great interest to the neuroscience community at large, remain poorly understood. One of the striking manifestations of neuronal population activity is that of rhythmic oscillations in the local field potential. It is thought that distinct patterns of these oscillations such as cross-frequency coupling within a given spatial location and coherence between disparate brain regions may represent neuronal computation and communication, respectively. Here we show such dynamics within a human temporal neocortical in vitro model. In specific, we show theta-gamma cross frequency coupling in deep and superficial layers, phase coherence between layers at theta frequencies, and a measure of communication (phase dependent power correlations) between layers at theta frequency. Additionally, we show a novel correlation between communication across layers and cross frequency coupling within layers, demonstrating a dynamic link between local computation and intralaminar communication.

The dynamical underpinnings of complex computation and information transmission within the brain, while of great interest to the neuroscience community at large, remain poorly understood. One of the striking manifestations of neuronal population activity is that of rhythmic oscillations in the local field potential. It is thought that distinct patterns of these oscillations such as cross-frequency coupling within a given spatial location and coherence between disparate brain regions may represent neuronal computation and communication, respectively. Here we show such dynamics within a human temporal neocortical in vitro model. In specific, we show theta-gamma cross frequency coupling in deep and superficial layers, phase coherence between layers at theta frequencies, and a measure of communication (phase dependent power correlations) between layers at theta frequency. Additionally, we show a novel correlation between communication across layers and cross frequency coupling within layers, demonstrating a dynamic link between local computation and intralaminar communication.

Local gamma-band (~30-100Hz) oscillations in the brain, produced by feedback inhibition on a characteristic timescale, appear in multiple areas of the brain and are associated with a wide range of cognitive functions. Some regions producing gamma also receive gamma-rhythmic input, and the interaction and coordination of these rhythms has been hypothesized to serve various functional roles. This thesis consists of three stand-alone chapters, each of which considers the response of a gamma-rhythmic neuronal circuit to input in an analytical framework. In the first, we demonstrate that several related models of a gamma-generating circuit under periodic forcing are asymptotically drawn onto an attracting invariant torus due to the convergence of inhibition trajectories at spikes and the convergence of voltage trajectories during sustained inhibition, and therefore display a restricted range of dynamics. In the second, we show that a model of a gamma-generating circuit under forcing by square pulses cannot maintain multiple stably phase-locked solutions. In the third, we show that a separation of time scales of membrane potential dynamics and synaptic decay causes the gamma model to phase align its spiking such that periodic forcing pulses arrive under minimal inhibition. When two of these models are mutually coupled, the same effect causes excitatory pulses from the faster oscillator to arrive at the slower under minimal inhibition, while pulses from the slower to the faster arrive under maximal inhibition. We also show that such a time scale separation allows the model to respond sensitively to input pulse coherence to an extent that is not possible for a simple one-dimensional oscillator. We draw on a wide range of mathematical tools and structures including return maps, saltation matrices, contraction methods, phase response formalism, and singular perturbation theory in order to show that the neuronal mechanism of gamma oscillations is uniquely suited to reliably phase lock across brain regions and facilitate the selective transmission of information.

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