Fig 1.
Definition and schematic representation of intrinsic timescale estimation.
(A) Schematic illustration of an intrinsic timescale, defined as the decay time constant of the spike train ACF. (B) Schematic of the intrinsic timescale estimation pipeline for single-unit activity. (C) Representative examples of spike trains with known and increasing from top to bottom intrinsic timescales (left) and their corresponding estimated intrinsic timescales (right). In (C), blue dots represent the computed ACF, and the black line indicates the fitted exponential decay function.
Table 1.
Summary of used datasets.
Table 2.
Summary of used methods.
Fig 2.
Schematic representation of spike time tiling coefficient calculation (STTC) and its adaptation for intrinsic timescale estimation (iSTTC).
(A) Schematic representation of STTC calculation, modified from [35] and [37]. STTC quantifies the correlation between spike trains A and B at a time interval .
(
) denotes the proportion of the signal within
of any spike in A (B), and
(
) the proportion of spikes in A (B) that fall within
of a spike in B (A). (B) Schematic illustration of iSTTC. Spike trains A and B are created by truncating and realigning the original spike train, after which the standard STTC formula is applied as in (A). (C) Schematic illustration of iSTTC applied on epoched data. Each trial is zero-padded prior to computing iSTTC across lags. Bottom left, violin plot displaying the absolute difference in estimated intrinsic timescales relative to the reference condition in which the zero-padding length equals the trial length T.
Fig 3.
iSTTC is a better IT estimator than ACF on unsegmented data, particularly for low-firing rate and bursty units.
(A) Schematic illustration of the synthetic dataset generation (left), and the underlying parameters with corresponding representative spike train examples (right). (B) Definition of the relative estimation error (REE) metric. (C) Hexbin plot displaying the difference in REE between iSTTC and ACF method as a function of firing rate and excitation strength (left), and IT and excitation strength (right) (n = single units). Color codes for the median REE difference in each bin, with blue indicating better IT estimation for iSTTC. (D) Line plot displaying predicted REE values for iSTTC and ACF as a function of firing rate (left), excitation strength (middle), and IT (right) (n =
single units). Shaded areas represent 95% confidence intervals. Y-axes are plotted on a
scale. In (C) and (D), ACF parameters were: bin size = 50 ms, number of lags = 20; iSTTC parameters were: lag shift = 50 ms, dt = 25 ms, number of lags = 20. In (C), asterisks indicate a significant effect of the IT estimation method. In (D), asterisks indicate a significant effect of an interaction between method and firing rate (left), method and excitation strength (middle), and method and IT (right). *
, ***
Generalized linear model with interactions (C), (D).
Fig 4.
iSTTC provides better IT estimates from epoched spiking activity.
(A) Schematic illustration of the generation of epoched data based on randomly sampled unsegmented spike trains. Dice icon from svgrepo.com. (B) Hexbin plot displaying the difference in REE between iSTTC and PearsonR as a function of firing rate and excitation strength (left), and IT and excitation strength (right) (n = single units, 40 trials x 1000 ms each). Color codes for the median REE difference in each bin, with blue indicating lower error for iSTTC. (C) Line plot displaying predicted REE values for iSTTC and PearsonR as a function of firing rate (left), excitation strength (middle), and IT (right) (n =
single units, 40 trials x 1000 ms each). Shaded areas represent 95% confidence intervals. Y-axes are plotted on a
scale. In (B) and (C), PearsonR parameters were: bin size = 50 ms, number of lags = 20; iSTTC parameters were: lag shift = 50 ms, dt = 25 ms, number of lags = 20. In (B), asterisks indicate a significant effect of the method. In (C), asterisks indicate a significant effect of an interaction between method and firing rate (left), method and excitation strength (middle), and method and IT (right). *
, **
, ***
. Generalized linear model with interactions (B), (C).
Fig 5.
Relative estimation errors are higher for epoched than unsegmented spiking data.
(A) Comparison of IT estimation accuracy across four methods. Ridgeline plot displaying the distribution of REE. Only IT estimates with REE between 0% and 100% are shown. Percentages indicate the proportion of IT estimates within this interval for each method (left). Scatter plot displaying the percentage of IT estimates with REE falling within progressively narrower intervals (middle). Violin plot displaying the full distribution of REE values for each method. (right). (B) Line plot displaying predicted REE values for ACF and iSTTC as a function of signal length (n = single units per signal length). Shaded areas represent 95% confidence intervals. Y-axes are plotted on a
scale. (C) Heatmap displaying the percentage of spike trains with REE within specific intervals for ACF (left) and iSTTC (middle) across varying signal lengths. Color codes for the proportion of spike trains, with warmer colors indicating higher percentages of spike trains. (Right) Heatmap displaying the difference in performance between methods, computed as the difference between ACF and iSTTC. Negative values indicate better performance (lower REE) for iSTTC. Color codes for the magnitude of the difference in percentages. (D) Same as (B) for PearsonR and iSTTC. (E) Same as (C) for PearsonR and iSTTC. In (A)–(D), ACF/PearsonR parameters were: bin size = 50 ms, number of lags = 20; iSTTC parameters were: lag shift = 50 ms, dt = 25 ms, number of lags = 20. In (A) right, data is presented as median, 25th, 75th percentile, and interquartile range, with the shaded area representing the probability density distribution of the variable. In (B), asterisks indicate a significant effect of interaction between method and signal length. In (D), asterisks indicate a significant effect of an interaction between method and the number of trials. ***
. Generalized linear model with interactions (B), (D).
Fig 6.
iSTTC allows for the inclusion of more units than PearsonR.
(A) Bar plot displaying the percentage of excluded units across four methods. Color codes for the exclusion reason, with dark grey indicating failed exponential fits and light grey indicating negative R-squared values of the exponential fit (n = 23348 excluded fits across four methods, n = 248 excluded fits ACF, n = 238 excluded fits iSTTC, n = 16594 excluded fits PearsonR, n = 6268 excluded fits iSTTC (trials)). (B) Kernel density plot displaying the distribution of excluded units as a function of firing rate (left), excitation strength (middle), and IT (right) (n = 4469 units both methods failed, n = 12125 units only PearsonR, n = 1799 units only iSTTC). (C) Violin plot displaying REE values for exponential fits where the autocorrelation function declined (vs. not declined) in the 50–200 ms range (left), and for fits where the 95% confidence interval of the estimated IT included vs. excluded zero (middle) (n = 376652 fits across four methods). Line plot displaying predicted REE values as a function of R-squared (right) (n = 376652 fits across four methods). Shaded areas represent 95% confidence intervals. Y-axes are plotted on a scale. (D) Bar plots displaying the percentage of units with autocorrelation function decline in the 50–200 ms range (left, n = 291395 fits across four methods), and the percentage of units with 95% confidence intervals excluding zero (right, n = 253595 fits across four methods), across four methods. (E) Kernel density plot displaying the distribution of R-squared values (left), and bar plot displaying the percentage of units with R-squared
across four methods (right, n = 287967 fits across four methods). In (C), left and middle, data are presented as median, 25th, 75th percentile, and interquartile range, with the shaded area representing the probability density distribution of the variable. In (C), asterisks indicate a significant effect of the factor on REE. ***
. Generalized linear models (C).
Fig 7.
iSTTC provides more stable, robust and inclusive IT estimates than ACF and PearsonR also on experimental data.
(A) Schematic representation of Neuropixels recordings from the six visual cortical areas (V1, LM, RL, AL, PM, AM) and the two thalamic areas (LGN and LP), image source [2] (left), violin plots displaying the single units firing rate (top right) and local variation (bottom right). Mouse icon from scidraw.io (DOI https://zenodo.org/records/3925991). (B) Scatter plots displaying ITs at the brain area level. Black dots indicate area-level ITs used for the analyses in S12B–S12D Fig. Grey dots represent individual brain-area IT estimates for the trial-based methods across different sampling iterations (n = 50 samples). (C) Violin plots displaying the estimated ITs (n = 3053 single units, only units for which all methods produced an IT estimate are included) as a function of the estimation method (left). Violin plots displaying pseudo-REE as a function of the estimation method (middle). Scatter plot displaying the percentage of spike trains with pseudo-REE falling within progressively narrower bounds (right). (D) Line plot displaying predicted pseudo-REE values for iSTTC and ACF as a function of signal length (n = 5674 single units per signal length, only units for which both methods produced an IT estimate for all signal lengths are included). Shaded areas represent 95% confidence intervals. Y-axes are plotted on a scale. (E) Heatmap displaying the percentage of spike trains with pseudo-REE within specific intervals for ACF (left) and iSTTC (middle) across varying signal lengths. Color codes for the proportion of spike trains, with warmer colors indicating higher percentages of spike trains. (Right) Heatmap displaying the difference between ACF and iSTTC. Negative values indicate better performance (lower pseudo-REE) for iSTTC. Color codes for the magnitude of the difference. (F) Same as (D) for PearsonR and iSTTC (n = 4588 single units per number of trials, only units for which both methods produced an IT estimate for all numbers of trials are included). (G) Same as (E) for PearsonR and iSTTC. In (B)–(G), ACF/PearsonR parameters were: bin size = 50 ms, number of lags = 20; iSTTC parameters were: lag shift = 50 ms, dt = 25 ms, number of lags = 20. In (A) and (C) left and middle, data is presented as median, 25th, 75th percentile, and interquartile range, with the shaded area representing the probability density distribution of the variable.In (C), asterisks indicate a significant effect of the method. In (C) left, ACF is used as a reference. In (C) middle, PearsonR is used as a reference. In (D), asterisks indicate a significant effect of signal length. **
, ***
. Generalized linear models with interactions (C), (D), and (F).
Table 3.
Summary of synthetic datasets.