Intra-ripple frequency accommodation in an inhibitory network model for hippocampal ripple oscillations
Fig 2
Transient dynamics of the spiking network and IFA.
(A) Example simulation showing a transient ripple with IFA. From bottom to top: SPW-like drive (Eq (17)); histogram of membrane potentials (normalized), horizontal dotted lines: threshold and reset potential; raster plot showing spike times of 10 example units; population rate exhibiting transient ripple oscillation; wavelet spectrogram indicating instantaneous power (blue-yellow colorbar) for a frequency range of 0–400 Hz. Solid curve: continuous estimate of instantaneous frequency based on wavelet spectrogram with gray scale indicating maximal instantaneous power. Dotted line: cutoff frequency for peak detection fmin = 70Hz. Red lines in scalebars: power threshold (see Methods). White dots: discrete estimate of instantaneous frequency based on peak-to-peak distance in population rate. Network size N = 10, 000. (B) Quantification of IFA. Top: Grey dots: discrete instantaneous frequency estimates from 50 repetitions of the simulation shown in (A) with different noise realizations. Grey line: linear regression line with negative slope (χIFA = −3.04 Hz/ms) indicating IFA (see Methods, Eq (18)). Black line: asymptotic frequencies (cf. Fig 1B, top). Bottom: The same SPW-like drive was applied in all 50 simulations. Network size N = 10, 000. (C) Dependency of IFA slope χIFA on the slope of the external drive for different network sizes (color coded). (D) Instantaneous (dots) vs asymptotic (black lines) network frequencies (top) for piecewise linear drives (bottom) of decreasing slopes (left to right). Color/linestyle indicates network size N. Thin, colored linear regression lines illustrate decreasing strength of IFA for shallower drive (regression slopes summarized in C). Asymptotic network frequencies are derived via interpolation of the constant-drive results shown in Fig 1B, top. The asymptotic frequencies for N = 103 and N = 104 are nearly identical (dash-dotted and solid lines). Note that the drive is identical in panels A, B, and in the left panel of D.