Neuronal Network Mechanisms of Gamma Oscillations

Neuronal oscillations at various frequency bands play an important role in neuronal information processing. In this thesis, we mathematically and computationally investigated the properties of the gamma band (30-80 Hz) with different networks: a simplified network with two neurons, a large network with thousands of neurons, and interactions between distant brain areas. Our mathematical description of the neurons ranges from a very simple one (one state variable) to a very complex one (more than ten state variables). The gamma-band rhythmogenesis at a microscopic scale involves two major classes of neurons; pyramidal cells and interneurons. Experimental studies suggest that two major mechanisms, namely ING and PING, underlie their generation. For ING, the gamma rhythm is generated by coupled interneurons, while for PING, it stems from interactions between interneurons and pyramidal cells. Chapter 2 illustrates how ING and PING interact using computer simulations of the large network. Chapter 3 addresses the same question analytically for the simplified network. Both approaches demonstrate that ING and PING compete: The mechanism generating the higher oscillation frequency "wins". The winning mechanism determines the frequency of the network oscillation and suppresses the other mechanism. Experimental studies report that neuronal activity between distant brain areas synchronizes with zero phase lag. This is a remarkable result because of relatively significant time delays between the interacting brain areas. Chapter 4 analytically shows under what conditions zero-lag synchrony between distant brain areas is possible supported by computer simulations. In Chapter 5, we extended the model of the oscillators by including additional features of the neurons. From the results in both chapters, we conclude that zero-lag synchrony is possible, but not likely for the actual conditions in the brain. This suggests a cautious re-evaluation of the existence and proposed role of zero-lag synchrony in neuronal communication