Supplementary Figure 4: Linearity is not dependent on stimulus frequency.

A linear model was fit using our standard 10 Hz stimuli and then cross validated on 10, 30 and 60 Hz stimuli. a, an example neuron. For each plot on the left the gray traces illustrate ten trials of frozen noise, along with the average response (blue) and predicted response (red). On the right, the voltage predicted by our model is plotted against the actual voltage of the neuron for each 1-ms time bin (gray). Blue dots are the binned meaned data. The red line is the least-squares regression of the data, which can be compared to the unity line (gray). Although model performance (R²) dropped as the frequency of stimulus increased from 10 to 30 to 60 Hz, the apparent linearity in fact increased (red line closer to unity, indicated by brackets). b, The R² for the model tested at 10, 30, and 60 Hz stimuli (N = 30 cells; not all three conditions were available for all neurons). There was a consistent drop in performance for almost all neurons as the frequency of whisker stimuli increased. However, c, the normalized signal-to-noise ratio (SNR) at 10, 30, and/or 60 Hz, as calculated in Sahani and Linden 2003, for the vast majority of cells dropped (both increased noise and decreased signal) as the frequency increases, explaining the drop in model performance seen in b. The neurons where the SNR increased in panel c were the same neurons where model performance also increased in panel b. d, To verify that the model was linearly dependent on the variability of the neuron and independent of stimulus frequency, we plotted the performance of the model against the trial-to-trial variability of the neurons (as in Fig. 2c). There was a similar relationship irrespective of whether models were tested on 10, 30, or 60 Hz stimuli. e. For a subset of neurons (N=5) we trained and tested the linear (black) and quadratic (gray) models at both 10 Hz and 30 Hz stimuli and compared the R² values. The linear model consistently outperformed the quadratic model, even at higher stimulus frequencies. The average of the linear model is shown in red and the average of the quadratic model is shown in cyan.