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

1 Department of Physiology and Pharmacology, State University of New York Health Science Center, Brooklyn, New York 11203; and 2 School of Biomedical Sciences, University of Leeds, Leeds LS2 9NL, United Kingdom Bibbig, Andrea, Roger D. Traub, and Miles A. Whittington. Long-Range Synchronization of and Oscillations and the Plasticity of Excitatory and Inhibitory Synapses: A Network Model. J. Neurophysiol. 88: 1634-1654, 2002. The ability of oscillating networks to synchronize despite significant separation in space, and thus time, is of biological significance, given that human 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 frequency (with i-cells firing at 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 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 period (delays from 8 to 17 ms in our simulations) and that are firing at frequency. 4 ) Two assemblies