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.