Figure 10.
Hierarchical self-similar structure in quiet times between consecutive θ-bursts indicates coupling between time of occurrence and burst duration. a, Schematic diagram of quiet times Δt between consecutive θ-bursts. A quiet time Δti is the time elapsed from the end of burst θi to the beginning of the following burst θi+1. b, Top, Time series of θ-burst durations for ∼600 min recording of a control rat. Middle, A 40 min segment from the sequence shown at the top. Bottom, Sequence comprised only of the θ-burst durations longer than D0 = 6 s that are present in the 600 min time series shown at the top. Selecting only bursts longer than D0 = 6 s, the temporal pattern at the scale of 600 min looks similar to the pattern at smaller scale of 60 min, indicating hierarchical self-similar structure in the quiet times. c, Distribution of quiet times for different thresholds D0 on θ-burst durations over a 24 h period in control rats (blue symbols). When rescaled by 〈Δt〉 (main panel), distributions obtained for different D0 collapse onto a unique function that is well described by a generalized Gamma distribution G(x; b, v, p) (solid green line), with b = 2.03, ν = 0.30, and p = 0.81. Applying the same procedure to a sequence of randomly reshuffled θ-burst durations leads to distributions that collapse onto an exponential function (dashed lines). Inset, Distributions of quiet times for different thresholds D0 before rescaling. d, Distributions of quiet times for different thresholds D0 on θ-burst durations over a 24 h period in VLPO-lesioned rats. Distributions collapse onto a unique function when rescaled by 〈Δt〉 (main panel). Similar to control rats, this function is well described by a generalized Gamma function G(x; b, v, p) (solid green line), with b = 1.55, ν = 0.28, and p = 0.70. Distribution of quiet times obtained from a sequence of randomly reshuffled θ-burst durations collapse onto an exponential distribution (dashed lines). Insets, Distributions of quiet times in VLPO-lesioned rats for different thresholds D0 before rescaling. Results are consistent when considering separately light and dark periods.