Figure 2. Innovations clarify the effect of movement and pupil size on cortical state fluctuations.

(A) Linear mixed model regression (Methods) of firing rate (FR; top) and Synch (bottom) on movement and pupil size. Graphs show values of regression coefficients. Box plots here and elsewhere represent median, interquartile range and 95% confidence interval (CI) on the bootstrap distribution of the corresponding parameter (Methods). Offset can be read from the right y-axis. (B) Example of the process of calculating innovations for the baseline FR of one recording session. Top, raw data and prediction of the raw data (Figure 2—figure supplement 2; Methods). The innovation FR_I (bottom) is the difference (prediction residual) between the two traces in the top. (C) Correlation between OpticF, PupilS, FR, and Synch innovations. Diagonal and above, cross-correlations between each of the four signals (black, median across recordings; gray, median absolute deviation [MAD]). Below diagonal. For each pair of innovations, histogram across recordings of their instantaneous correlation. Triangles mark the median across recordings. (D) Identical analysis as panel (A) but using innovations instead of the raw signals.

Figure 2—figure supplement 1. Slow trends of baseline signals during the session.

(A) Median (black) and median absolute deviation (MAD; gray shading) across sessions of each of the four baseline signals. All the signals display slow trends and in some cases monotonic increases or decreases through the recording session. (B) Diagonal and above shows the auto- and cross-correlations of each of the four baseline signals (median ± MAD). Below diagonal shows the histogram of the instantaneous correlation between each pair of signals across sessions. Triangle is the median across sessions (same format as Figure 2C). Non-zero values of auto- and cross-correlations far from zero lag reflect existence of slow timescales, which are eliminated by our cross-whitening procedure (Methods, Figure 2—figure supplement 2) and are thus absent from the equivalent analysis performed on innovations (Figure 2 in the main text.).

Figure 2—figure supplement 2. Constructing innovations by cross-whitening.

(A) Schematic description of the linear fit and associated residuals used to generate the firing rate (FR) innovations. The same procedure was used for Synch, PupilS, and OpticF. (B) Example traces for obtaining the PupilS innovations in one recording. Left, raw and linear fit of the PupilS. Right, residuals. (C) Histogram across sessions of the fraction of variance ($R^2$) explained by the linear fits of each of the four signals. Triangle is the median of each histogram.