Fine structure of neural spiking and synchronization in the presence of conduction delays

Abstract

Hippocampal networks of excitatory and inhibitory neurons that produce gamma-frequency rhythms display behavior in which the inhibitory cells produce spike doublets when there is strong stimulation at separated sites. It has been suggested that the doublets play a key role in the ability to synchronize over a distance. Here we analyze the mechanisms by which timing in the spike doublet can affect the synchronization process. The analysis describes two independent effects: one comes from the timing of excitation from separated local circuits to an inhibitory cell, and the other comes from the timing of inhibition from separated local circuits to an excitatory cell. We show that a network with both of these effects has different synchronization properties than a network with either excitatory or inhibitory type of coupling alone, and we give a rationale for the shorter space scales associated with inhibitory interactions.

Figure 1

Network of two coupled local circuits, each with one E and one I cell.

Figure 2

Latency to firing of I-cell after last received E-pulse. (A) Dependence on maximal excitatory conductance c_ei between circuits; g_ii = 0.15, g_ei = 0.2. (B) Dependence on inputs g_ei and g_ii to I cell within a circuit; c_ei = 0.1.

Figure 3

Latency to firing of E-cell after last received I-pulse. Discrete data points are computed from equations in Appendix. The three graphs correspond (top to bottom) to c_ei/g_ei = 1.0, 0.5, 0.25. Dashed lines for the top two are computed from formula 1 with τ = 20, t_p = 25, t_ei = 1.5.