Long-Range Synchronization of γ and β Oscillations and the Plasticity of Excitatory and Inhibitory Synapses: A Network Model

Abstract

The ability of oscillating networks to synchronize despite significant separation in space, and thus time, is of biological significance, given that human γ activity can synchronize over distances of several millimeters to centimeters during perceptual and learning tasks. We use computer simulations of networks consisting of excitatory pyramidal cells (e-cells) and inhibitory interneurons (i-cells), modeling two tonically driven assemblies separated by large (≥8 ms) conduction delays. The results are as follows. 1) Two assemblies separated by large conduction delays can fire synchronously at β frequency (with i-cells firing at γ frequency) under two timing conditions: e-cells of (say) assembly 2 are still inhibited “delay + spike generation milliseconds” after the e-cell beat of assembly 1; this means that the e-cell inhibitory postsynaptic potential (IPSP) cannot be significantly shorter than the delay (2-site effect). This implies for a given decay time constant that the interneuron → pyramidal cell conductances must be large enough. The e-cell IPSP must last longer than the i-cell IPSP, i.e., the interneuron → pyramidal cell conductance must be sufficiently large and the interneuron → interneuron conductance sufficiently small (local effect). 2) We define a “ long-interval doublet” as a pair of interneuron action potentials—separated by approximately “delay milliseconds”—in which a) the first spike is induced by tonic inputs and/or excitation from nearby e-cells, while b) the second spike is induced by (delayed) excitation from distant e-cells. “Long-interval population doublets” (long-interval doublets of the i-cell population) are necessary for synchronized firing in our networks. Failure to produce them leads to almost anti-phase activity at γ frequency. 3) An (almost) anti-phase oscillation is the most stable oscillation pattern of two assemblies that are separated by axonal conduction delays of approximately one-half a γ period (delays from 8 to 17 ms in our simulations) and that are firing at γ frequency. 4) Two assemblies separated by large conduction delays can synchronize their activity with the help of interneuron plasticity. They can also synchronize without pyramidal cell → pyramidal cell connections being present. The presence of pyramidal cell → pyramidal cell connections allows, however, for synchronization if other parameters are at inappropriate values for synchronization to occur. 5) Synchronization of two assemblies separated by large conduction delays with the help of interneuron plasticity is not simply due to slowing down of the oscillation frequency. It is reached with the help of a “ synchronizing-weak-beat,” which induces sudden changes in the oscillation period length of the two assemblies.

Beta oscillations in a large-scale sensorimotor cortical network: Directional influences revealed by Granger causality

“…This result is consistent with previous findings of widespread, high-amplitude LFP oscillations transiently synchronized in sensorimotor areas during sensorimotor tasks (4,11), and with models indicating that beta oscillations are particularly well suited to support interactions between widespread cortical areas (20,21). By distinguishing between large-scale network synchrony due to driving and that due to mutual interactions, Granger causality analysis provided a deeper understanding of cortical interaction patterns than could be obtained from correlation or coherence measures.…”

“…It has long been proposed that behavior of this type depends on a corticoperipheral cortical sensorimotor loop (17,18), and more recently that this loop is supported by oscillatory neuronal activity (19). Reports of beta oscillations in both somatosensory and motor cortices during premovement maintenance behavior (3,5,6,9), taken together with recent studies proposing that beta rhythms are uniquely suited for synchronization over long conduction delays (20,21), thus suggest the hypothesis that beta oscillations provide a mechanism that binds sensory and motor cortical areas into a functioning loop.…”

Role of tau protein on neocortical and hippocampal oscillatory patterns

“…Electrical communication between interneurons has been demonstrated to be essential for the generation of gamma waves (Katsumaru et al, 1988;Gibson et al, 1999;Tamas et al, 2000), thereby supporting a role for interneuronal gap junctions at producing fast rhythmic synchronization in small patches of nervous tissue . Gamma oscillations are relevant in neuronal communication and synaptic plasticity (Bibbig et al, 2002), providing cues for understanding neuronal processing in both local and distributed cortical networks involved in cognitive functions (Jensen et al, 2007). Hypothetically, the lack of tau in neocortical regions and hippocampus might affect the maturation of parvalbumin interneurons involved in gamma synchronization within local neocortical circuits and/or the proper functioning of gap-junction channels in hippocampal networks.…”

Beta- and gamma-frequency coupling between olfactory and motor brain regions prior to skilled, olfactory-driven reaching

“…More recently, hippocampal theta oscillations have been found to drive processing in the prefrontal cortex (Jensen 2005), and several studies have suggested that gamma oscillations nested within theta (4-12 Hz) oscillations play a role in working memory functions (Jensen and Lisman 2005). Also, substantial recent data suggest that corticothalamic (Llinas et al 1998;Llinas and Ribary 2001;Neuenschwander et al 2002;Ribary 2005) and hippocampal networks (Buzsaki 1997;Harris et al 2003) make use of beta band (12-30 Hz) and gamma band (30-100 Hz) activity for long-distance transmission of information among task-related brain sites, although a number of those studies were carried out in brain slices or models (Kopell et al 2000;Bibbig et al 2002;Klausberger et al 2003;Olufsen et al 2003). These results suggest that task-related brain regions with differing network and cellular architectures may nonetheless display enhanced beta and gamma oscillations during attention to, and recognition of a rewarded stimulus, but to our knowledge this hypothesis had never been explicitly tested.…”