Instantaneous rates at onset and offset intervals

To compare the population rates at the U-onset and U-offset (Figures 3 and ​and6),6), we computed for each neuron the mean of rDUi(τ) over the window τ = (50,200) s (U-onset) and the mean of rUDi(τ) over the window τ = (−200,–50) s (U-offset). We positioned the windows 50 ms away of the DU and UD transitions in order to preclude the possibility of contamination in the mean rate estimations due to possible misalignments from the U and D period detections. In the averaging we used U and D periods longer than 0.5 s, so that onset and offset windows were always non-overlapping. Equivalent D-onset and D-offset windows were defined in order to compare individual rates during D periods. To make the distribution of mean rates across the cell population Gaussian, we normalized each of the rates rDUi(τ) and rUDi(τ) by the overall time-averaged rate of the neuron ri=<ri(t)>t finally obtaining onset and offset-aligned normalized averaged rates (e.g. rDUi(τ)/ri). Despite this normalization, the distribution of the normalized rates in the D-onset and D-offset was non-Gaussian (most neurons fired no spikes). Thus we used the non-parametric two-sided Wilcoxon signed rank test to compare onset and offset rates (Figure 3E). To test the rates changes during U periods in E and I neurons we used a four-way mixed-effects ANOVA with fixed factors onset/offset, E/I and random factors neuron index and animal. We compared the distribution of normalized averaged rate difference at the U-onset minus the U -offset (Figure 3E right, dark gray histogram) with a distribution obtained from the same neurons but randomly shuffling the onset and offset labels of the spike counts but preserving trial and neuron indices (Figure 3E right, light gray bands show 95% C.I. of the mean histograms across 1000 shuffles). This surrogate data set represents the hypothesis in which none of the neurons shows any onset vs offset modulation. The comparison shows that there are significant fractions of neurons showing a rate decrease and increase that compensate to yield no significant difference on the population averaged rate. The same procedure was followed with the normalized rates in the D-onset and D-offset but the limited number of non-zero spike counts limited the analysis yielding inconclusive results (Figure 3E left).