Bias-free estimation of information content in temporally sparse neuronal activity
Fig 9
A bias-free estimation of spatial information uncovers hippocampal neuronal tuning properties that may be masked by the bias in the naïve estimation.
(A) The estimated SI (mean ± SEM) as a function of the within-field peak firing rates for the naïve calculation (blue), SSR (magenta), and BAE (green). SI was not found to increase with peak rate based on the naïve estimation (linear regression(10), R2 = 0.001, slope = -0.001 ± 0.015, p = 0.92), but did increase with peak rate based on SSR (linear regression(10), R2 = 0.95, slope = 0.07 ± 0.01, p = 1.8·10−6) and BAE (linear regression(10), R2 = 0.90, slope = 0.08 ± 0.02, p = 2.8·10−5). (B) Average number of track traversals (in each running direction; mean ± SEM) as a function of time in the experiment. Day one is the first exposure to the environment. (C) The estimated SI (mean ± SEM) as a function of time in the experiment for the naïve calculation (blue), SSR (magenta), and BAE (green). SI changed throughout learning for both the naïve estimation (repeated-measures ANOVA(7), F = 7.42, p = 2.7·10−6), and the bias-corrected estimations (repeated-measures ANOVA(7), F = 10.32, p = 3.1·10−8, and F = 10.10, p = 4.2·10−8 for SSR and BAE, respectively). Post hoc pairwise comparison tests revealed that the bias-corrected estimation, but not the naïve, significantly increased with learning. (D-F) Estimated SI (mean) as a function of the sample duration in both hippocampal subfields CA1 and CA3 (D), CA1 only (E), and CA3 only (F) during different learning sessions (colors) for the naïve calculation (dashed curves), and SSR (solid curves). Insets, the SI (mean ± SEM) as a function of time in the experiment was estimated from short subsamples of the data (3 minutes in D and 5 minutes in E-F) using the naïve calculation (left) and SSR (right). Note that even for short sample durations, the bias-corrected estimation clearly reveals an increase in information over time, while the naïve estimation fails to uncover this trend. Data were averaged across N = 9 mice. Data in B-F for each familiarity level (day in the experiment) were averaged across the two environments. For the analyses presented in panels C-F, only place cells with ≥ 10 active time bins in a given session were used. *p < 0.05; ***p < 0.001.