1. Computational and Systems Biology
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Neuronal timescales are functionally dynamic and shaped by cortical microarchitecture

  1. Richard Gao  Is a corresponding author
  2. Ruud L van den Brink
  3. Thomas Pfeffer
  4. Bradley Voytek
  1. Department of Cognitive Science, University of California, San Diego, United States
  2. Section Computational Cognitive Neuroscience, Department of Neurophysiology and Pathophysiology, University Medical Center Hamburg-Eppendorf, Germany
  3. Center for Brain and Cognition, Computational Neuroscience Group, Universitat Pompeu Fabra, Spain
  4. Halıcıoğlu Data Science Institute, University of California, San Diego, United States
  5. Neurosciences Graduate Program, University of California, San Diego, United States
  6. Kavli Institute for Brain and Mind, University of California, San Diego, United States
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Cite this article as: eLife 2020;9:e61277 doi: 10.7554/eLife.61277

Abstract

Complex cognitive functions such as working memory and decision-making require information maintenance over seconds to years, from transient sensory stimuli to long-term contextual cues. While theoretical accounts predict the emergence of a corresponding hierarchy of neuronal timescales, direct electrophysiological evidence across the human cortex is lacking. Here, we infer neuronal timescales from invasive intracranial recordings. Timescales increase along the principal sensorimotor-to-association axis across the entire human cortex, and scale with single-unit timescales within macaques. Cortex-wide transcriptomic analysis shows direct alignment between timescales and expression of excitation- and inhibition-related genes, as well as genes specific to voltage-gated transmembrane ion transporters. Finally, neuronal timescales are functionally dynamic: prefrontal cortex timescales expand during working memory maintenance and predict individual performance, while cortex-wide timescales compress with aging. Thus, neuronal timescales follow cytoarchitectonic gradients across the human cortex and are relevant for cognition in both short and long terms, bridging microcircuit physiology with macroscale dynamics and behavior.

eLife digest

The human brain can both quickly react to a fleeting sight, like a changing traffic light, and slowly integrate complex information to form a long-term plan. To mirror these requirements, how long a neuron can be activated for – its ‘timescale’ – varies greatly between cells.

A range of timescales has been identified in animal brains, by measuring single neurons at a few different locations. However, a comprehensive study of this property in humans has been hindered by technical and ethical concerns. Without this knowledge, it is difficult to understand the factors that may shape different timescales, and how these can change in response to environmental demands.

To investigate this question, Gao et al. used a new computational method to analyse publicly available datasets and calculate neuronal timescales across the human brain. The data were produced using a technique called invasive electrocorticography, where electrodes placed directly on the brain record the total activity of many neurons. This allowed Gao et al. to examine the relationship between timescales and brain anatomy, gene expression, and cognition.

The analysis revealed a continuous gradient of neuronal timescales between areas that require neurons to react quickly and those relying on long-term activity. ‘Under the hood’, these timescales were associated with a number of biological processes, such as the activity of genes that shape the nature of the connections between neurons and the amount of proteins that let different charged particles in and out of cells. In addition, the timescales could be flexible: they could lengthen when areas specialised in working memory were actively maintaining information, or shorten with age across many areas of the brain. Ultimately, the technique and findings reported by Gao et al. could have useful applications in the clinic, using neuronal timescale to better understand brain disorders and pinpoint their underlying causes.

Introduction

Human brain regions are broadly specialized for different aspects of behavior and cognition, and the temporal dynamics of neuronal populations across the cortex are thought to be an intrinsic property (i.e., neuronal timescale) that enables the representation of information over multiple durations in a hierarchically embedded environment (Kiebel et al., 2008). For example, primary sensory neurons are tightly coupled to changes in the environment, firing rapidly to the onset and removal of a stimulus, and showing characteristically short intrinsic timescales (Ogawa and Komatsu, 2010; Runyan et al., 2017). In contrast, neurons in cortical association (or transmodal) regions, such as the prefrontal cortex (PFC), can sustain their activity for many seconds when a person is engaged in working memory (Zylberberg and Strowbridge, 2017), decision-making (Gold and Shadlen, 2007), and hierarchical reasoning (Sarafyazd and Jazayeri, 2019). This persistent activity in the absence of immediate sensory stimuli reflects longer neuronal timescales, which is thought to result from neural attractor states (Wang, 2002; Wimmer et al., 2014) shaped by N-methyl-D-aspartate receptor (NMDA)-mediated recurrent excitation and fast feedback inhibition (Wang, 2008; Wang, 1999), with contributions from other synaptic and cell-intrinsic properties (Duarte and Morrison, 2019; Gjorgjieva et al., 2016). How connectivity and various cellular properties combine to shape neuronal dynamics across the cortex remains an open question.

Anatomical connectivity measures based on tract tracing data, such as laminar feedforward vs. feedback projection patterns, have classically defined a hierarchical organization of the cortex (Felleman and Van Essen, 1991; Hilgetag and Goulas, 2020; Vezoli et al., 2020). Recent studies have also shown that variations in many microarchitectural features follow continuous and coinciding gradients along a sensory-to-association axis across the cortex, including cortical thickness, cell density, and distribution of excitatory and inhibitory neurons (Huntenburg et al., 2018; Wang, 2020). In particular, gray matter myelination (Glasser and Van Essen, 2011)—a noninvasive proxy of anatomical hierarchy consistent with laminar projection data—varies with the expression of genes related to microcircuit function in the human brain, such as NMDA receptor and inhibitory cell-type marker genes (Burt et al., 2018). Functionally, specialization of the human cortex, as well as structural and functional connectivity (Margulies et al., 2016), also follow similar macroscopic gradients. Moreover, in addition to the broad differentiation between sensory and association cortices, there is evidence for an even finer hierarchical organization within the frontal cortex (Sarafyazd and Jazayeri, 2019). For example, the anterior-most parts of the PFC are responsible for long timescale goal-planning behavior (Badre and D'Esposito, 2009; Voytek et al., 2015a), while healthy aging is associated with a shift in these gradients such that older adults become more reliant on higher-level association regions to compensate for altered lower-level cortical functioning (Davis et al., 2008).

Despite convergent observations of cortical gradients in structural features and cognitive specialization, there is no direct evidence for a similar gradient of neuronal timescales across the human cortex. Such a gradient of neuronal dynamics is predicted to be a natural consequence of macroscopic variations in synaptic connectivity and microarchitectural features (Chaudhuri et al., 2015; Duarte et al., 2017; Huang and Doiron, 2017; Huntenburg et al., 2018; Wang, 2020), and would be a primary candidate for how functional specialization emerges as a result of hierarchical temporal processing (Kiebel et al., 2008). Single-unit recordings in rodents and non-human primates demonstrated a hierarchy of timescales that increase, or lengthen, progressively along a posterior-to-anterior axis (Dotson et al., 2018; Murray et al., 2014; Runyan et al., 2017; Wasmuht et al., 2018), while intracranial recordings and functional neuroimaging data collected during perceptual and cognitive tasks suggest likewise in humans (Baldassano et al., 2017; Honey et al., 2012; Lerner et al., 2011; Watanabe et al., 2019). However, these data are either sparsely sampled across the cortex or do not measure neuronal activity at the cellular and synaptic level directly, prohibiting the full construction of an electrophysiological timescale gradient across the human cortex. As a result, while whole-cortex data of transcriptomic and anatomical variations exist, we cannot take advantage of them to dissect the contributions of synaptic, cellular, and circuit connectivity in shaping fast neuronal timescales, nor ask whether regional timescales are dynamic and relevant for human cognition.

Here we combine several publicly available datasets to infer neuronal timescales from invasive human electrocorticography (ECoG) recordings and relate them to whole-cortex transcriptomic and anatomical data, as well as probe their functional relevance during behavior (Figure 1A for schematic of study; Tables 1 and 2 for dataset information). Unless otherwise specified, (neuronal) timescale in the following sections refers to ECoG-derived timescales, which are more reflective of fast synaptic and transmembrane current timescales than single-unit or population spiking timescales (Figure 1A, left box), though we demonstrate in macaques a close correspondence between the two. In humans, neuronal timescales increase along the principal sensorimotor-to-association axis across the cortex and align with macroscopic gradients of gray matter myelination (T1w/T2w ratio) and synaptic receptor and ion channel gene expression. Finally, we find that human PFC timescales expand during working memory maintenance and predict individual performance, while cortex-wide timescales compress with aging. Thus, neuronal timescales follow cytoarchitectonic gradients across the human cortex and are relevant for cognition in both short and long terms, bridging microcircuit physiology with macroscale dynamics and behavior.

Table 1
Summary of open-access datasets used.
DataRef.Specific source/format usedParticipant infoRelevant figures
MNI Open iEEG AtlasFrauscher et al., 2018a; Frauscher et al., 2018bN = 105 (48 females)
Ages: 13–65, 33.4 ± 10.6
Figure 2A–D,
Figure 3,
Figure 4E and F
T1w/T2w and cortical thickness maps from
Human Connectome Project
Glasser et al., 2016; Glasser and Van Essen, 2011Release S1200, March 1, 2017N = 1096 (596 females)
Age: 22–36+ (details restricted due to identifiability)
Figure 2C and D,
Figure 3D–F
Neurotycho macaque ECoGNagasaka et al., 2011; Yanagawa et al., 2013Eyes-open state from anesthesia datasets (propofol and ketamine)Two animals (Chibi and George)
four sessions each
Figure 2E–G
Macaque single-unit timescalesMurray et al., 2014Figure 1 of referenceFigure 2E–G
Whole-cortex interpolated Allen Brain Atlas human gene expressionGryglewski et al., 2018; Hawrylycz et al., 2012Interpolated maps downloadable from http://www.meduniwien.ac.at/neuroimaging/mRNA.htmlN = 6 (one female)
Age: 24, 31, 39, 49, 55, 57 (42.5 ± 12.2)
Figure 3
Single-cell timescale-related genesBomkamp et al., 2019; Tripathy et al., 2017Table S3 from Tripathy et al., 2017, Online Table 1 from Bomkamp et al., 2019N = 170 (Tripathy et al., 2017) and 4168 (Bomkamp et al., 2019) genesFigure 3C and D
Human working memory ECoGJohnson, 2019; Johnson, 2018c; Johnson et al., 2018a, Johnson et al., 2018bCRCNS fcx-2 and fcx-3N = 14 (five females)
Age: 22–50, 30.9 ± 7.8
Figure 4A–D
Table 2
Reproducing figures from code repository.
All IPython notebooks (Gao, 2020): https://github.com/rdgao/field-echos/tree/master/notebooks
NotebookResults
1_sim_method_schematic.ipynbSimulations: Figure 1B–E
2_viz_NeuroTycho-SU.ipynbMacaque timescales: Figure 2E–G, Figure 2—figure supplement 4
3_viz_human_structural.ipynbHuman timescales vs. T1w/T2w and gene expression:

Figure 2A–D, Figure 2—figure supplements 1 and 3, Figure 3, Figure 3—figure supplements 1 and 2, Supplementary file 1–Supplementary file 2Supplementary file 3.
4b_viz_human_wm.ipynbHuman working memory: Figure 4A–D, Figure 4—figure supplement 1
4a_viz_human_aging.ipynbHuman aging: Figure 4E and F, Figure 4—figure supplement 2
 supp_spatialautocorr.ipynbSpatial autocorrelation-preserving nulls:
supp_spatialautocorr.ipynb

Spatial autocorrelation-preserving nulls: Figure 2—figure supplement 2
Schematic of study and timescale inference technique.

(A) In this study, we infer neuronal timescales from intracranial field potential recordings, which reflect integrated synaptic and transmembrane current fluctuations over large neural populations (Buzsáki et al., 2012). Combining multiple open-access datasets (Table 1), we link timescales to known human anatomical hierarchy, dissect its cellular and physiological basis via transcriptomic analysis, and demonstrate its functional modulation during behavior and through aging. (B) Simulated time series and their (C) autocorrelation functions (ACFs), with increasing (longer) decay time constant, τ (which neuronal timescale is defined to be). (D) Example human electrocorticography (ECoG) power spectral density (PSD) showing the aperiodic component fit (red dashed), and the ‘knee frequency’ at which power drops off (fk, red circle; insets: time series and ACF). (E) Estimation of timescale from PSDs of simulated time series in (B), where the knee frequency, fk, is converted to timescale, τ, via the embedded equation (inset: correlation between ground truth and estimated timescale values).

Results

Neuronal timescale can be inferred from the frequency domain

Neural time series often exhibit time-lagged correlation (i.e., autocorrelation), where future values are partially predictable from past values, and predictability decreases with increasing time lags. For demonstration, we simulate the aperiodic (non-rhythmic) component of ECoG recordings by convolving Poisson population spikes with exponentially decaying synaptic kernels with varying decay constant (Figure 1B). Empirically, the degree of self-similarity is characterized by the autocorrelation function (ACF), and ‘timescale’ is defined as the time constant (τ) of an exponential decay function (etτ) fit to the ACF, i.e., the time it takes for the autocorrelation to decrease by a factor of e (Figure 1C).

Equivalently, we can estimate timescale in the frequency domain from the power spectral density (PSD). PSDs of neural time series often follow a Lorentzian function of the form 1fk2+ f2, where power is approximately constant until the ‘knee frequency’ (fk, Figure 1D), then decays following a power law. This approach is similar to the one presented in Chaudhuri et al., 2017, but here we further allow the power law exponent (fixed at two in the equation above) to be a free parameter representing variable scale-free activity (He et al., 2010; Miller et al., 2009; Podvalny et al., 2015; Voytek et al., 2015c). We also simultaneously parameterize oscillatory components as Gaussians peaks, allowing us to remove their effect on the power spectrum, providing more accurate estimates of the knee frequency. From the knee frequency of the aperiodic component, neural timescale (decay constant) can then be computed exactly as τ= 12πfk.

Compared to fitting exponential decay functions in the time domain (e.g., Murray et al., 2014)—which can be biased even without the presence of additional components (Zeraati et al., 2020)—the frequency domain approach is advantageous when a variable power law exponent and strong oscillatory components are present, as is often the case for neural signals (example of real data in Figure 1D). While the oscillatory component can corrupt naive measurement of τ as time for the ACF to reach 1/e (Figure 1D, inset), it can be more easily accounted for and removed in the frequency domain as Gaussian-like peaks. This is especially important considering neural oscillations with non-stationary frequencies. For example, a broad peak in the power spectrum (e.g., ~10 Hz in bandwidth in Figure 1D) represents drifts in the oscillation frequency over time, which is easily accounted for with a single Gaussian, but requires multiple cosine terms to capture well in the autocorrelation. Therefore, in this study, we apply spectral parameterization to extract timescales from intracranial recordings (Donoghue et al., 2020). We validate this approach on PSDs computed from simulated neural time series and show that the extracted timescales closely match their ground-truth values (Figure 1E).

Timescales follow anatomical hierarchy and are ~10 times faster than spiking timescales

Applying this technique, we infer a continuous gradient of neuronal timescales across the human cortex by analyzing a large dataset of human intracranial (ECoG) recordings of task-free brain activity (Frauscher et al., 2018a). The MNI-iEEG dataset contains 1 min of resting state data across 1772 channels from 106 patients (13–62 years old, 48 females) with variable coverages, recorded using either surface strip/grid or stereoEEG electrodes, and cleaned of visible artifacts. Figure 2A shows example data traces along the cortical hierarchy with increasing timescales estimated from their PSDs (Figure 2B; circles denote fitted knee frequency). Timescales from individual channels were extracted and projected from MNI coordinates onto the left hemisphere of HCP-MMP1.0 surface parcellation (Glasser et al., 2016) for each patient using a Gaussian-weighted mask centered on each electrode. While coverage is sparse and idiosyncratic in individual patients, it does not vary as a function of age, and when pooling across the entire population, 178 of 180 parcels have at least one patient with an electrode within 4 mm (Figure 2—figure supplement 1A–F).

Figure 2 with 4 supplements see all
Timescale increases along the anatomical hierarchy in humans and macaques.

(A) Example time series from five electrodes along the human cortical hierarchy (M1: primary motor cortex; SMC: supplementary motor cortex; OFC: orbitofrontal cortex; ACC: anterior cingulate cortex; MTL: medial temporal lobe), and (B) their corresponding power spectral densities (PSDs) computed over 1 min. Circle and dashed line indicate the knee frequency for each PSD, derived from the aperiodic component fits (inset). Data: MNI-iEEG database, N = 106 participants. (C) Human cortical timescale gradient (left) falls predominantly along the rostrocaudal axis, similar to T1w/T2w ratio (right; z-scored, in units of standard deviation). Colored dots show electrode locations of example data. (D) Neuronal timescales are negatively correlated with cortical T1w/T2w, thus increasing along the anatomical hierarchy from sensory to association regions (Spearman correlation; p-value corrected for spatial autocorrelation, Figure 2—figure supplement 2A–C). (E) Example PSDs from macaque ECoG recordings, similar to (B) (LIP: lateral intraparietal cortex; LPFC: lateral prefrontal cortex; S1 and S2: primary and secondary somatosensory cortex). PSDs are averaged over electrodes within each region (inset of [F]). Data: Neurotycho, N = 8 sessions from two animals. (F) Macaque ECoG timescales track published single-unit spiking timescales (Murray et al., 2014) in corresponding regions (error bars represent mean ± s.e.m). Inset: ECoG electrode map of one animal and selected electrodes for comparison. (G) ECoG-derived timescales are consistently correlated with (left), and ~10 times faster than (right), single-unit timescales across individual sessions. Hollow markers: individual sessions; shapes: animals; solid circles: grand average from (F).

Across the human cortex, timescales of fast electrophysiological dynamics (~10–50 ms) predominantly follow a rostrocaudal gradient (Figure 2C, circles denote location of example data from 2A). Consistent with numerous accounts of a principal cortical axis spanning from primary sensory to association regions (Hilgetag and Goulas, 2020; Margulies et al., 2016; Wang, 2020), timescales are shorter in sensorimotor and early visual areas, and longer in association regions, especially cingulate, ventral/medial frontal, and medial temporal lobe (MTL) regions (Figure 2—figure supplement 1G shows further pooling into 21 labeled macro-regions). We then compare the timescale gradient to the average T1w/T2w map from the Human Connectome Project, which captures gray matter myelination and indexes the proportion of feedforward vs. feedback connections between cortical regions, thus acting as a noninvasive proxy of connectivity-based anatomical hierarchy (Burt et al., 2018; Glasser and Van Essen, 2011). We find that neuronal timescales are negatively correlated with T1w/T2w across the entire cortex (Figure 2D, ρ = −0.47, p<0.001; corrected for spatial autocorrelation [SA], see Materials and methods and Figure 2—figure supplement 2A–C for a comparison of correction methods), such that timescales are shorter in more heavily myelinated (i.e., lower-level, sensory) regions. Timescales are also positively correlated with cortical thickness (Figure 2—figure supplement 3, ρ = 0.37, p=0.035)—another index of cortical hierarchy that is itself anti-correlated with T1w/T2w. Thus, we observe that neuronal timescales lengthen along the human cortical hierarchy, from sensorimotor to association regions.

While surface ECoG recordings offer much broader spatial coverage than extracellular single-unit recordings, they are fundamentally different signals: ECoG and field potentials largely reflect integrated synaptic and other transmembrane currents across many neuronal and glial cells, rather than putative action potentials from single neurons (Buzsáki et al., 2012; Figure 1A, yellow box). Considering this, we ask whether timescales measured from ECoG in this study (τECoG) are related to single-unit spiking timescales along the cortical hierarchy (τspiking). To test this, we extract neuronal timescales from task-free ECoG recordings in macaques (Nagasaka et al., 2011) and compare them to a separate dataset of single-unit spiking timescales from a different group of macaques (Murray et al., 2014) (see Figure 2—figure supplement 4 for electrode locations). Consistent with τspiking estimates (Murray et al., 2014; Wasmuht et al., 2018), τECoG also increase along the macaque cortical hierarchy. While there is a strong correspondence between spiking and ECoG timescales (Figure 2F; ρ = 0.96, p<0.001)—measured from independent datasets—across the macaque cortex, τECoG are ~10 times faster than τspiking and are conserved across individual sessions (Figure 2G). This suggests that neuronal spiking and transmembrane currents have distinct but related timescales of fluctuations, and that both are hierarchically organized along the primate cortex.

Synaptic and ion channel genes shape timescales of neuronal dynamics

Next, we identify potential cellular and synaptic mechanisms underlying timescale variations across the human cortex. Theoretical accounts posit that NMDA-mediated recurrent excitation coupled with fast inhibition (Chaudhuri et al., 2015; Wang, 2008; Wang, 1999), as well as cell-intrinsic properties (Duarte and Morrison, 2019; Gjorgjieva et al., 2016; Koch et al., 1996), are crucial for shaping neuronal timescales. While in vitro and in vivo studies in model organisms (van Vugt et al., 2020; Wang et al., 2013) can test these hypotheses at the single-neuron level, causal manipulations and large-scale recordings of neuronal networks embedded in the human brain are severely limited. Here, we apply an approach analogous to multimodal single-cell profiling (Bomkamp et al., 2019) and examine the transcriptomic basis of neuronal dynamics at the macroscale.

Leveraging whole-cortex interpolation of the Allen Human Brain Atlas bulk mRNA expression (Gryglewski et al., 2018; Hawrylycz et al., 2012), we project voxel-wise expression maps onto the HCP-MMP1.0 surface parcellation, and find that the neuronal timescale gradient overlaps with the dominant axis of gene expression (i.e., first principal component of 2429 brain-related genes) across the human cortex (Figure 3A, ρ = −0.60, p<0.001; see Figure 3—figure supplement 1 for similar results with all 18,114 genes). Consistent with theoretical predictions (Figure 3B), timescales significantly correlate with the expression of genes encoding for NMDA (GRIN2B) and GABA-A (GABRA3) receptor subunits, voltage-gated sodium (SCN1A) and potassium (KCNA3) ion channel subunits, as well as inhibitory cell-type markers (parvalbumin, PVALB), and genes previously identified to be associated with single-neuron membrane time constants (PRR5) (Bomkamp et al., 2019) (all Spearman correlations corrected for SA in gradients).

Figure 3 with 2 supplements see all
Timescale gradient is linked to expression of genes related to synaptic receptors and transmembrane ion channels across the human cortex.

(A) Timescale gradient follows the dominant axis of gene expression variation across the cortex (z-scored PC1 of 2429 brain-specific genes, arbitrary direction). (B) Timescale gradient is significantly correlated with expression of genes known to alter synaptic and neuronal membrane time constants, as well as inhibitory cell-type markers, but (C) members within a gene family (e.g., NMDA receptor subunits) can be both positively and negatively associated with timescales, consistent with predictions from in vitro studies. (D) Macroscale timescale-transcriptomic correlation captures association between RNA-sequenced expression of the same genes and single-cell timescale properties fit to patch clamp data from two studies, and the correspondence improves for genes (separated by quintiles) that are more strongly correlated with timescale (solid: N = 170 [Tripathy et al., 2017], dashed: N = 4168 genes [Bomkamp et al., 2019]; horizontal lines: correlation across all genes from the two studies, ρ = 0.36 and 0.25, p<0.001 for both). (E) T1w/T2w gradient is regressed out from timescale and gene expression gradients, and a partial least squares (PLS) model is fit to the residual maps. Genes with significant PLS weights (filled blue boxes) compared to spatial autocorrelation (SA)-preserved null distributions are submitted for gene ontology enrichment analysis (GOEA), returning a set of significant GO terms that represent functional gene clusters (filled green boxes). (F) Enriched genes are primarily linked to potassium and chloride transmembrane transporters, and GABA-ergic synapses; genes specifically with strong negative associations further over-represent transmembrane ion exchange mechanisms, especially voltage-gated potassium and cation transporters. Branches indicate GO items that share higher-level (parent) items, e.g., voltage-gated cation channel activity is a child of cation channel activity in the molecular functions (MF) ontology, and both are significantly associated with timescale. Color of lines indicate curated ontology (BP—biological process, CC—cellular components, or MF). Dotted, dashed, and solid lines correspond to analysis performed using all genes or only those with positive or negative PLS weights. Spatial correlation p-values in (A–C) are corrected for SA (see Materials and methods; asterisks in (B,D) indicate p<0.05, 0.01, 0.005, and 0.001 respectively; filled markers in (C,D) indicate p<0.05).

More specifically, in vitro electrophysiological studies have shown that, for example, increased expression of receptor subunit 2B extends the NMDA current time course (Flint et al., 1997), while 2A expression shortens it (Monyer et al., 1994). Similarly, the GABA-A receptor time constant lengthens with increasing a3:a1 subunit ratio (Eyre et al., 2012). We show that these relationships are recapitulated at the macroscale, where neuronal timescales positively correlate with GRIN2B and GABRA3 expression and negatively correlate with GRIN2A and GABRA1 (Figure 3C). These results demonstrate that timescales of neural dynamics depend on specific receptor subunit combinations with different (de)activation timescales (Duarte et al., 2017; Gjorgjieva et al., 2016), in addition to broad excitation–inhibition interactions (Gao et al., 2017; Wang, 2020; Wang, 2002). Notably, almost all genes related to voltage-gated sodium and potassium ion channel alpha-subunits—the main functional subunits—are correlated with timescale, while all inhibitory cell-type markers except parvalbumin have strong positive associations with timescale (Figure 3C and Figure 3—figure supplement 2).

We further test whether single-cell timescale-transcriptomic associations are captured at the macroscale as follows: for a given gene, we can measure how strongly its expression correlates with membrane time constant parameters at the single-cell level using patch-clamp and RNA sequencing (scRNASeq) data (Bomkamp et al., 2019; Tripathy et al., 2017). Analogously, we can measure its macroscopic transcriptomic-timescale correlation using the cortical gradients above. If the association between the expression of this gene and neuronal timescale is preserved at both levels, then the correlation across cells at the microscale should be similar to the correlation across cortical regions at the macroscale. Comparing across these two scales for all previously identified timescale-related genes in two studies (N = 170 [Tripathy et al., 2017] and 4168 [Bomkamp et al., 2019] genes), we find a significant correlation between the strength of association at the single-cell and macroscale levels (Figure 3D, horizontal black lines; ρ = 0.36 and 0.25 for the two datasets, p<0.001 for both). Furthermore, genes with stronger associations to timescale tend to conserve this relationship across single-cell and macroscale levels (Figure 3D, separated by macroscale correlation magnitude). Thus, the association between cellular variations in gene expression and cell-intrinsic temporal dynamics is captured at the macroscale, even though scRNAseq and microarray data represent entirely different measurements of gene expression.

While we have shown associations between cortical timescales and genes suspected to influence neuronal dynamics, these data present an opportunity to discover additional novel genes that are functionally related to timescales through a data-driven approach. However, since transcriptomic variation and anatomical hierarchy overlap along a shared macroscopic gradient (Burt et al., 2018; Huntenburg et al., 2018; Margulies et al., 2016), we cannot specify the role certain genes play based on their level of association with timescale alone: gene expression differences across the cortex first result in cell-type and connectivity differences, sculpting the hierarchical organization of cortical anatomy. Consequently, anatomy and cell-intrinsic properties jointly shape neuronal dynamics through connectivity differences (Chaudhuri et al., 2015; Demirtaş et al., 2019) and expression of ion transport and receptor proteins with variable activation timescales, respectively. Therefore, we ask whether variation in gene expression still accounts for variation in timescale beyond the principal structural gradient, and if associated genes have known functional roles in biological processes (BP) (schematic in Figure 3E). To do this, we first remove the contribution of anatomical hierarchy by linearly regressing out the T1w/T2w gradient from both timescale and individual gene expression gradients. We then fit partial least squares (PLS) models to simultaneously estimate regression weights for all genes (Whitaker et al., 2016), submitting those with significant associations for gene ontology enrichment analysis (GOEA) (Klopfenstein et al., 2018).

We find that genes highly associated with neuronal timescales are preferentially related to transmembrane ion transporter complexes, as well as GABAergic synapses and chloride channels (see Figure 3F and Supplementary file 1 for GOEA results with brain genes only, and Supplementary file 2 for all genes). When restricted to positively associated genes only (expression increases with timescales), one functional group related to phosphatidate phosphatase activity is uncovered, including the gene PLPPR1, which has been linked to neuronal plasticity (Savaskan et al., 2004)—a much slower timescale physiological process. Conversely, genes that are negatively associated with timescale are related to numerous groups involved in the construction and functioning of transmembrane transporters and voltage-gated ion channels, especially potassium and other inorganic cation transporters. To further ensure that these genes specifically relate to neuronal timescale, we perform the same enrichment analysis with T1w/T2w vs. gene maps as a control. The control analysis yields no significant GO terms when restricted to brain-specific genes (in contrast to Figure 3F), while repeating the analysis with all genes does yield significant GO terms related to ion channels and synapses, but are much less specific to those (see Supplementary file 3), including a variety of other gene clusters associated with general metabolic processes, signaling pathways, and cellular components (CC). This further strengthens the point that removing the contribution of T1w/T2w aids in identifying genes that are more specifically associated with neurodynamics, suggesting that inhibition (Teleńczuk et al., 2017)—mediated by GABA and chloride channels—and voltage-gated potassium channels have prominent roles in shaping neuronal timescale dynamics at the macroscale level, beyond what is expected based on the anatomical hierarchy alone.

Timescales lengthen in working memory and shorten in aging

Finally, having shown that neuronal timescales are associated with stable anatomical and gene expression gradients across the human cortex, we turn to the final question of the study: are cortical timescales relatively static, or are they functionally dynamic and relevant for human cognition? While previous studies have shown hierarchical segregation of task-relevant information corresponding to intrinsic timescales of different cortical regions (Baldassano et al., 2017; Chien and Honey, 2020; Honey et al., 2012; Runyan et al., 2017; Sarafyazd and Jazayeri, 2019; Wasmuht et al., 2018), as well as optimal adaptation of behavioral timescales to match the environment (Ganupuru et al., 2019; Ossmy et al., 2013), evidence for functionally relevant changes in regional neuronal timescales is lacking. Here, we examine whether timescales undergo short- and long-term shifts during working memory maintenance and aging, respectively.

We first analyze human ECoG recordings from parietal, frontal (PFC and orbitofrontal cortex [OFC]), and medial temporal lobe (MTL) regions of patients (N = 14) performing a visuospatial working memory task that requires a delayed cued response (Figure 4A; Johnson et al., 2018a). Neuronal timescales were extracted for pre-stimulus baseline and memory maintenance delay periods (900 ms, both stimulus-free). Replicating our previous result in Figure 2—figure supplement 1G, we observe that baseline neuronal timescales follow a hierarchical progression across association regions, where parietal cortex (PC), PFC, OFC, and MTL have gradually longer timescales (pairwise Mann–Whitney U-test, Figure 4B). If neuronal timescales track the temporal persistence of information in a functional manner, then they should expand during delay periods. Consistent with our prediction, timescales in all regions are ~20% longer during delay periods (Figure 4C; Wilcoxon rank-sum test). Moreover, only timescale changes in the PFC are significantly correlated with behavior across participants, where longer delay-period timescales relative to baseline are associated with better working memory performance (Figure 4D, ρ = 0.75, p=0.003). No other spectral features in the recorded brain regions show consistent changes from baseline to delay periods while also significantly correlating with individual performance, including the 1/f-like spectral exponent, narrowband theta (3–8 Hz), and high-frequency (high gamma; 70–100 Hz) activity power (Figure 4—figure supplement 1).

Figure 4 with 2 supplements see all
Timescales expand during working memory maintenance while tracking performance, and task-free average timescales compress in older adults.

(A) Fourteen participants with overlapping intracranial coverage performed a visuospatial working memory task, with 900 ms of baseline (pre-stimulus) and delay period data analyzed (PC: parietal, PFC: prefrontal, OFC: orbitofrontal, MTL: medial temporal lobe; n denotes number of subjects with electrodes in that region). (B) Baseline timescales follow hierarchical organization within association regions (*: p<0.05, Mann–Whitney U-test; small dots represent individual participants, large dots and error bar for mean ± s.e.m. across participants). (C) All regions show significant timescale increase during delay period compared to baseline (asterisks represent p<0.05, 0.01, 0.005, 0.001, Wilcoxon signed-rank test). (D) PFC timescale expansion during delay periods predicts average working memory accuracy across participants (dot represents individual participants, mean ± s.e.m. across PFC electrodes within participant); inset: correlation between working memory accuracy and timescale change for all regions. (E) In the MNI-iEEG dataset, participant-average cortical timescales decrease (become faster) with age (n = 71 participants with at least 10 valid parcels, see Figure 4—figure supplement 2B). (F) Most cortical parcels show a negative relationship between timescales and age, with the exception being parts of the visual cortex and the temporal poles (one-sample t-test, t = −7.04, p<0.001; n = 114 parcels where at least six participants have data, see Figure 4—figure supplement 2C).

While timescales are consistent with the anatomical and gene expression hierarchy at a snapshot, brain structure itself is not static over time, undergoing many slower, neuroplastic changes during early development and throughout aging in older populations. In particular, aging is associated with a broad range of functional and structural changes, such as working memory impairments (Voytek et al., 2015c; Wang et al., 2011), as well as changes in neuronal dynamics (Voytek et al., 2015c; Voytek and Knight, 2015b; Wang et al., 2011) and cortical structure (de Villers-Sidani et al., 2010), such as the loss of slow-deactivating NMDA receptor subunits (Pegasiou et al., 2020). Since neuronal timescales may support working memory maintenance, we predict that timescales would shorten across the lifespan, in agreement with the observed cognitive and structural deteriorations. To this end, we leverage the wide age range in the MNI-iEEG dataset (13–62 years old) and probe average cortical timescales for each participant as a function of age. Since ECoG coverage is sparse and nonuniform across participants, simply averaging across parcels within individual participants confounds the effect of aging with the spatial effect of cortical hierarchy. Instead, we first normalize each parcel by its max value across all participants before averaging within participants, excluding those with fewer than 10 valid parcels (N = 71 of 106 subjects remaining; results hold for a large range of threshold values, Figure 4—figure supplement 2B). We observe that older adults have faster neuronal timescales (ρ = −0.31, p=0.010; Figure 4E), and that timescales shorten with age in most areas across the cortex (Figure 4F, t = −7.04, p<0.001; 114 out of 189 parcels where at least six participants have data, see Figure 4—figure supplement 2C). This timescale compression is especially prominent in sensorimotor, temporal, and medial frontal regions. These results support our hypothesis that neuronal timescales, estimated from transmembrane current fluctuations, can rapidly shift in a functionally relevant manner, as well as slowly—over decades—in healthy aging.

Discussion

Theoretical accounts and converging empirical evidence predict a graded variation of neuronal timescales across the human cortex (Chaudhuri et al., 2015; Huntenburg et al., 2018; Wang, 2020), which reflects functional specialization and implements hierarchical temporal processing crucial for complex cognition (Kiebel et al., 2008). This timescale gradient is thought to emerge as a consequence of cortical variations in cytoarchitecture, as well as both macroscale and microcircuit connectivity, thus serving as a bridge from brain structure to cognitive function (Kanai and Rees, 2011). In this work, we infer the timescale of non-rhythmic transmembrane current fluctuations from invasive human intracranial recordings and test those predictions explicitly. We discuss the implications and limitations of our findings below.

Multiple quantities for neuronal timescale and anatomical hierarchy

We first find that neuronal timescales vary continuously across the human cortex and coincide with the anatomical hierarchy, with timescales increasing from primary sensory and motor to association regions. While we use the continuous T1w/T2w gradient as a surrogate measure for anatomical hierarchy, there are multiple related but distinct perspectives on what ‘cortical hierarchy’ means, including, for example, laminar connectivity patterns from tract tracing data (Felleman and Van Essen, 1991; Vezoli et al., 2020), continuous (and latent-space) gradients of gene expression and microarchitectural features (Huntenburg et al., 2018), and network connectivity scales (see review of Hilgetag and Goulas, 2020)—with most of these following a graded sensorimotor-to-association area progression. Similarly, it is important to note that there exist many different quantities that can be considered as characteristic neuronal timescales across several spatial scales, including membrane potential and synaptic current timescales (Duarte et al., 2017), single-unit spike-train timescales (Murray et al., 2014), population code timescales (Runyan et al., 2017), and even large-scale circuit timescales measured from the fMRI BOLD signal (Watanabe et al., 2019). We show here that timescales inferred from ECoG are consistently approximately 10 times faster than single-unit spiking timescales in macaques, corroborating the fact that field potential signals mainly reflect fast transmembrane and synaptic currents (Buzsáki et al., 2012), whose timescales are related to, but distinct from, single-unit timescales measured in previous studies (Dotson et al., 2018; Ogawa and Komatsu, 2010; Wasmuht et al., 2018).

Because field potential fluctuations are driven by currents from both locally generated and distal inputs, our results raise questions on how and when these timescales interact to shape downstream spiking dynamics. Furthermore, while we specifically investigate here the aperiodic timescale, which corresponds to the exponential decay timescale measured in previous studies, recent work has shown a similar gradient of oscillatory timescales (i.e., frequency) along the anterior–posterior axis of the human cortex (Mahjoory et al., 2020). Based on the similarity of these gradients and known mechanisms of asynchronous and oscillatory population dynamics (e.g., balance of excitation and inhibition in generating gamma oscillations and the asynchronous irregular state in cortical circuits [Brunel, 2000; Brunel and Wang, 2003]), we speculate that timescales of oscillatory and aperiodic neural dynamics may share (at least partially) circuit mechanisms at different spatial scales, analogous to the relationship between characteristic frequency and decay constant in a damped harmonic oscillator model.

Collinearity and surrogate nature of postmortem gene expression gradients

Using postmortem gene expression data as a surrogate for protein density, transcriptomic analysis uncovers the potential roles that transmembrane ion transporters and synaptic receptors play in establishing the cortical gradient of neuronal timescales. The expression of voltage-gated potassium channel, chloride channel, and GABAergic receptor genes, in particular, are strongly associated with the spatial variation of neuronal timescale. Remarkably, we find that electrophysiology-transcriptomic relationships discovered at the single-cell level, through patch-clamp recordings and single-cell RNA sequencing, are recapitulated at the macroscale between bulk gene expression and timescales inferred from ECoG. That being said, it is impossible to make definitive causal claims with the data presented in this study, especially considering the fact that several microanatomical features, such as gray matter myelination and cortical thickness, follow similar gradients across the cortex (Burt et al., 2018). To discover genes specifically associated with timescale while accounting for the contribution of the overlapping anatomical hierarchy, we linearly regress out the T1w/T2w gradient from both timescale and gene expression gradients. Although this procedure does not account for any nonlinear contributions from anatomy, gene enrichment control analysis using T1w/T2w instead of timescales further demonstrates that the discovered genes—transmembrane ion transporters and inhibitory synaptic receptors—are more specifically associated with the timescale gradient, over and above the level predicted by anatomical hierarchy alone. From these results, we infer that potassium and chloride ion channels, as well as GABAergic receptors, may play a mechanistic role in altering the timescale of transmembrane currents at the macroscopic level.

However, this interpretation rests on the key assumption that mRNA expression level is a faithful representation of the amount of functional proteins in a given brain region. In general, gene expression levels are highly correlated with the percentage of cells expressing that gene within brain regions (Lein et al., 2007). Therefore, on a population level, the regional density of a particular ion channel or receptor protein is high if bulk mRNA expression is high. Furthermore, recent works have shown that neurotransmitter receptor density measured via autoradiography in postmortem brains follows similar cortical gradients (Goulas et al., 2020), and that gene expression levels of neurotransmitter receptors (e.g., 5HT) are strongly correlated with ligand binding potential measured via PET (Gryglewski et al., 2018). Thus, as a first order approximation, receptor gene expression is an adequate surrogate for receptor protein density in the brain at the macroscale, though the relationship between mRNA expression and their transport and translation into channel proteins, the process of incorporating those proteins into membranes and synapses, and how these gene expression maps can be related to other overlapping macroscopic gradients are complex issues (see e.g., Fornito et al., 2019; Liu et al., 2016). Thus, our analyses represent an initial data-mining process at the macroscopic level, which should motivate further studies in investigating the precise roles voltage-gated ion channels and synaptic inhibition play in shaping functional neuronal timescales through causal manipulations, complementary to existing lines of research focusing on NMDA activation and recurrent circuit motifs.

Structural constraints vs. behaviorally required flexibility in timescale

Finally, we show that neuronal timescales are not static, but can change both in the short and long terms. Transmembrane current timescales across multiple association regions, including parietal, frontal, and medial temporal cortices, increase during the delay period of a working memory task, consistent with the emergence of persistent spiking during working memory delay. Working memory performance across individuals, however, is predicted by the extent of timescale increase in the PFC only. This further suggests that behaviorally relevant neural activity may be localized despite widespread task-related modulation (Pinto et al., 2019), even at the level of neuronal membrane fluctuations. In the long term, we find that neuronal timescale shortens with age in most cortical regions, linking age-related synaptic, cellular, and connectivity changes—particularly those that influence neuronal integration timescale—to the compensatory posterior-to-anterior shift of functional specialization in healthy aging (Davis et al., 2008).

These results raise further questions regarding contrasting, and potentially complementary, aspects of neuronal timescale: on the one hand, task-free timescales across the cortex are shaped by relatively static macro- and microarchitectural properties (Figures 2 and 3); on the other hand, timescales are dynamic and shift with behavioral demand (Figure 4). While long-term structural changes in the brain can explain shifts in neuronal timescales throughout the aging process, properties such as ion channel protein density probably do not change within seconds during a working memory task. We speculate that structural properties may constrain dynamical properties (such as timescale) to a possible range within a particular brain region and at different spatial scales, while task requirements, input statistics, short-term synaptic plasticity, and neuromodulation can then shift timescale within this range. We posit, then, that only shifts in dynamics within the area of relevance (i.e., PFC for working memory) are indicative of task performance, consistent with recent ideas of computation-through-dynamics (Vyas et al., 2020). Nevertheless, which neuromodulatory and circuit mechanisms are involved in shifting local timescales, and how timescales at different spatial scales (e.g., synaptic, neuronal, population) interact to influence each other remain open questions for future investigation (Breakspear, 2017; Duarte et al., 2017; Freeman, 2000; Freeman and Erwin, 2008; Gjorgjieva et al., 2016; Shine et al., 2019).

Conclusion

In summary, we identify consistent and converging patterns between transcriptomics, anatomy, dynamics, and function across multiple datasets of different modalities from different individuals and multiple species. As a result, evidence for these relationships can be supplemented by more targeted approaches such as imaging of receptor metabolism. Furthermore, the introduction and validation of an open-source toolbox (Donoghue et al., 2020) for inferring timescales from macroscale electrophysiological recordings potentially allows for the noninvasive estimation of neuronal timescales, using widely accessible tools such as EEG and MEG. These results open up many avenues of research for discovering potential relationships between microscale gene expression and anatomy with the dynamics of neuronal population activity at the macroscale in humans.

Materials and methods

Inferring timescale from autocorrelation and PSD

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Consistent with previous studies, we define ‘neuronal timescale’ as the exponential decay time constant (τ) of the empirical ACF, or lagged correlation (Honey et al., 2012; Murray et al., 2014). τ can be naively estimated to be the time it takes for the ACF to decrease by a factor of e when there are no additional long-term, scale-free, or oscillatory processes, or by fitting a function of the form f(t) = etτ and extracting the parameter τ. Equivalently, the PSD is the Fourier Transform of the ACF via Wiener–Khinchin theorem (Khintchine, 1934) and follows a Lorentzian function of the form L(f) =Ak+fχ  for approximately exponential-decay processes, with χ=2 exactly when the ACF is solely composed of an exponential decay term, though it is often variable and in the range between 2 and 6 for neural time series (Donoghue et al., 2020Miller et al., 2009; Podvalny et al., 2015; Voytek et al., 2015c). Timescale can be computed from the parameter k as τ= 12πfk, where fk  k1/χ  is approximated to be the ‘knee frequency’, at which a bend or knee in the power spectrum occurs, and equality holds when χ=2.

Computing PSD

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PSDs are estimated using a modified Welch’s method, where short-time windowed Fourier transforms (STFT) are computed from the time series, but the median is taken across time instead of the mean (in conventional Welch’s method) to minimize the effect of high-amplitude transients and artifacts (Izhikevich et al., 2018). Custom functions for this can be found in NeuroDSP (Cole et al., 2019), a published and open-source digital signal processing toolbox for neural time series (neurodsp.spectral.compute_spectrum). For simulated data, Neurotycho macaque ECoG, and MNI-iEEG datasets, we use 1 s long Hamming windows with 0.5 s overlap. To estimate single-trial PSDs for the working memory ECoG dataset (CRCNS Johnson-ECoG Johnson et al., 2018a; Johnson et al., 2018b), we simply apply Hamming window to 900 ms long epoched time series and compute the squared magnitude of the windowed Fourier transform.

Spectral parametrization

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We apply spectral parameterization (Donoghue et al., 2020) to extract timescales from PSDs. Briefly, we decompose log-power spectra into a summation of narrowband periodic components—modeled as Gaussians—and an aperiodic component—modeled as a generalized Lorentzian function centered at 0 Hz (L(f) above). For inferring decay timescale, this formalism can be practically advantageous when a strong oscillatory or variable power-law (χ) component is present, as is often the case for neural signals. While oscillatory and power-law components can corrupt naive measurements of τ as time for the ACF to reach 1/e, they can be easily accounted for and ignored in the frequency domain as narrowband peaks and 1/f-exponent fit. We discard the periodic components and infer timescale from the aperiodic component of the PSD. For a complete mathematical description of the model, see Donoghue et al., 2020.

Simulation and validation

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We simulate the aperiodic background component of neural field potential recordings as autocorrelated stochastic processes by convolving Poisson population spikes with exponentially decaying synaptic kernels with predefined decay time constants (neurodsp.sim.sim_synaptic_current). PSDs of the simulated data are computed and parameterized as described above, and we compare the fitted timescales with their ground-truth values.

Macaque ECoG and single-unit timescales data

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Macaque single-unit timescales are taken directly from values reported in Figure 1c of Murray et al., 2014. Whole-brain surface ECoG data (1000 Hz sampling rate) is taken from the Neurotycho repository (Nagasaka et al., 2011; Yanagawa et al., 2013), with eight sessions of 128-channel recordings from two animals (George and Chibi, four sessions each). Results reported in Figure 2E–G are from ~10 min eyes-open resting periods to match the pre-stimulus baseline condition of single-unit experiments. Timescales for individual ECoG channels are extracted and averaged over regions corresponding to single-unit recording areas from Murray et al., 2014; Figure 2F inset and Figure 2—figure supplement 3, which are selected visually based on the overlapping cortical map and landmark sulci/gyri. Each region included between two and four electrodes (see Figure 2—figure supplement 3B for selected ECoG channel indices for each region).

Statistical analysis for macaque ECoG and spiking timescale

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For each individual recording session, as well as the grand average, Spearman rank correlation was computed between spiking and ECoG timescales. Linear regression models were fit using the python package scipy (Virtanen et al., 2020) (scipy.stats.linregress) and the linear slope was used to compute the scaling coefficient between spiking and ECoG timescales.

Variations in neuronal timescale, T1/T2 ratio, and mRNA expression across human cortex

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The following sections describe procedures for generating the average cortical gradient maps for neuronal timescale, MR-derived T1w/T2w ratio, and gene expression from the respective raw datasets. All maps were projected onto the 180 left hemisphere parcels of Human Connectome Project’s Multimodal Parcellation (Glasser et al., 2016) (HCP-MMP1.0) for comparison, described in the individual sections. Projection of T1w/T2w and gene expression maps from MNI volumetric coordinates to HCP-MMP1.0 can be found: https://github.com/rudyvdbrink/Surface_projection (van den Brink, 2020).

All spatial correlations are computed as Spearman rank correlations between maps. Procedure for computing statistical significance while accounting for SA is described in detail below under the sections 'Spatial statistics' and 'SA modeling'.

Neuronal timescale map

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The MNI Open iEEG dataset consists of 1 min of resting state data across 1772 channels from 106 epilepsy patients (13–62 years old, 58 males, and 48 females), recorded using either surface strip/grid or stereoEEG electrodes, and cleaned of visible artifacts (Frauscher et al., 2018a; Frauscher et al., 2018b). Neuronal timescales were extracted from PSDs of individual channels, and projected from MNI voxel coordinates onto HCP-MMP1.0 surface parcellation as follows.

For each patient, timescale estimated from each electrode was extrapolated to the rest of the cortex in MNI coordinates using a Gaussian weighting function (confidence mask), w(r) = e(r2/α2), where r is the Euclidean distance between the electrode and a voxel, and α is the distance scaling constant, chosen here such that a voxel 4 mm away has 50% weight (or confidence). Timescale at each voxel is computed as a weighted spatial average of timescales from all electrodes (i) of that patient:

i.e., τvoxel = iw(ri)τiiw(ri).

Similarly, each voxel is assigned a confidence rating that is the maximum of weights over all electrodes (wvoxel(rmin), of the closest electrode), i.e., a voxel right under an electrode has a confidence of 1, while a voxel 4 mm away from the closest electrode has a confidence of 0.5, etc.

Timescales for each HCP-MMP parcel were then computed as the confidence-weighted arithmetic mean across all voxels that fall within the boundaries of that parcel. HCP-MMP boundary map is loaded and used for projection using NiBabel (Brett et al., 2020). This results in a 180 parcels-by-106 patients timescale matrix. A per-parcel confidence matrix of the same dimensions was computed by taking the maximum confidence over all voxels for each parcel (Figure 2—figure supplement 1A). The average cortical timescale map (gradient) is computed by taking the confidence-weighted average at each parcel across all participants. Note that this procedure for locally thresholded and weighted average is different from projection procedures used for the mRNA and T1w/T2w data due to region-constrained and heterogeneous ECoG electrode sites across participants. While coverage is sparse and idiosyncratic in individual participants, it does not vary as a function of age, and when pooling across the entire population, 178 of 180 parcels have at least one patient with an electrode within 4 mm, with the best coverage in sensorimotor, temporal, and frontal regions (Figure 2—figure supplement 1).

T1w/T2w ratio and cortical thickness maps

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As a measure of structural cortical hierarchy, we used the ratio between T1- and T2-weighted structural MRI, referred to as T1w/T2w map in main text, or the myelin map (Burt et al., 2018; Glasser and Van Essen, 2011). Since there is little variation in the myelin map across individuals, we used the group average myelin map of the WU-Minn HCP S1200 release (N = 1096, March 1, 2017 release) provided in HCP-MMP1.0 surface space. For correlation with other variables, we computed the median value per parcel, identical to the procedure for mRNA expression below. Cortical thickness map was similarly generated.

mRNA expression maps

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We used the Allen Human Brain Atlas (AHBA) gene expression dataset (Hawrylycz et al., 2015; Hawrylycz et al., 2012) that comprised postmortem samples of six donors (one female and five males) that underwent microarray transcriptional profiling. Spatial maps of mRNA expression were available in volumetric 2 mm isotropic MNI space, following improved nonlinear registration and whole-brain prediction using variogram modeling as implemented by Gryglewski et al., 2018. We used whole-brain maps available from Gryglewski et al., 2018 rather than the native sample-wise values in the AHBA database to prevent bias that could occur due to spatial inhomogeneity of the sampled locations. In total, 18,114 genes were included for analyses that related to the dominant axis of expression across the genome.

We projected the volumetric mRNA expression data onto the HCP-MMP cortical surface using the HCP workbench software (v1.3.1 running on Windows OS 10) with the ‘enclosing’ method and custom MATLAB code (github.com/rudyvdbrink/surface_projection) (van den Brink, 2020). The enclosing method extracts for all vertices on the surface the value from enclosing voxels in the volumetric data. Alternative projection methods such as trilinear 3D linear interpolation of surrounding voxels, or ribbon mapping that constructs a polyhedron from each vertex's neighbors on the surface to compute a weighted mean for the respective vertices, yielded comparable values, but less complete cortical coverage. Moreover, the enclosing method ensured that no transformation of the data (nonlinear or otherwise) occurred during the projection process and thus the original values in the volumetric data were preserved.

Next, for each parcel of the left hemisphere in HCP-MMP, we extracted the median vertex-wise value. We used the median rather than the mean because it reduced the contribution of outliers in expression values within parcels. Vertices that were not enclosed by voxels that contained data in volumetric space were not included in the parcel-wise median. This was the case for 539 vertices (1.81% of total vertices). Linear interpolation across empty vertices prior to computing median parcel-wise values yielded near-identical results (r = 0.95 for reconstructed surfaces). Lastly, expression values were mean and variance normalized across parcels to facilitate visualization. Normalization had no effect on spatial correlation between gene expression and other variables since the spatial distribution of gene expression was left unaltered.

Selection of brain-specific genes

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Similar to Burt et al., 2018; Fagerberg et al., 2014; Genovese et al., 2016, N = 2429 brain-specific genes were selected based on the criteria that expression in brain tissues were four times higher than the median expression across all tissue types, using Supplementary Dataset 1 of Fagerberg et al., 2014. PC1 result shown in Figure 3A is computed from brain-specific genes, though findings are similar when using all genes (ρ = −0.56 with timescale map, Figure 3—figure supplement 1).

Spatial statistics

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All correlations between spatial maps (timescale, T1w/T2w, gene principal component [PC], and individual gene expressions) were computed using Spearman rank correlation. As noted in Burt et al., 2020; Burt et al., 2018; Vos de Wael et al., 2020, neural variables vary smoothly and continuously across the cortical surface, violating the assumption of independent samples. As a result, when correlating two variables, each with nontrivial SA, the naive p-value is artificially lowered since it is compared against an inappropriate null hypothesis, i.e., randomly distributed or shuffled values across space. Instead, a more appropriate null hypothesis introduces SA-preserving null maps, which destroys any potential correlation between two maps while respecting their SAs. For all spatial correlation analyses, we generated N = 1000 null maps of one variable (timescale map unless otherwise noted), and the test statistic, Spearman correlation (ρ), is computed against the other variable of interest to build the null distribution. Two-tailed significance is then computed as the proportion of the null distribution that is less extreme than the empirical correlation value. All regression lines were computed by fitting a linear regression to log-timescale and the structural feature maps.

SA modeling

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To generate SA-preserving null maps, we used Moran Spectral Randomization (MSR) (Wagner and Dray, 2015) from the python package BrainSpace (Vos de Wael et al., 2020). Details of the algorithm can be found in the above references. Briefly, MSR performs eigendecomposition on a spatial weight matrix of choice, which is taken here to be the inverse average geodesic distance matrix between all pairs of parcels in HCP-MMP1.0. The eigenvectors of the weight matrix are then used to generate randomized null feature maps that preserves the autocorrelation of the empirical map. We used the singleton procedure for null map generation. All significance values reported (Figures 2D and 3A–C) were adjusted using the above procedure.

We also compare two other methods of generating null maps: spatial variogram fitting (VF) (Burt et al., 2020) and spin permutation (Alexander-Bloch et al., 2018). Null maps were generated for timescale using spatial VF, while for spin permutation they were generated for vertex-wise T1w/T2w and gene PC1 maps before parcellation, so as to preserve surface locations of the parcellation itself. All methods perform similarly, producing comparable SA in the null maps, assessed using spatial variogram, as well as null distribution of spatial correlation coefficients between timescale and T1w/T2w (Figure 2—figure supplement 2).

Principal component analysis (PCA) of gene expression

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We used scikit-learn (Pedregosa, 2011) PCA (sklearn.decomposition.PCA) to identify the dominant axes of gene expression variation across the entire AHBA dataset, as well as for brain-specific genes. PCA was computed on the variance-normalized average gene expression maps, X, an N × P matrix where N = 18,114 (or N = 2429 brain-specific) genes, and P = 180 cortical parcels. Briefly, PCA factorizes X such that X = USVT, where U and V are unitary matrices of dimensionality N × N and P × P, respectively. S is the same dimensionality as X and contains non-negative descending eigenvalues on its main diagonal (Λ). Columns of V are defined as the PCs, and the dominant axis of gene expression is then defined as the first column of V, whose proportion of variance explained in the data is the first element of Λ divided by the sum over Λ. Results for PC1 and PC2-10 are shown in Figure 3A and Figure 3—figure supplement 1, respectively.

Comparison of timescale-transcriptomic association with single-cell timescale genes

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Single-cell timescale genes were selected based on data from Table S3 of Tripathy et al., 2017 and Online Table 1 of Bomkamp et al., 2019. Using single-cell RNA sequencing data and patch-clamp recordings from transgenic mice cortical neurons, these studies identified genes whose expression significantly correlated with electrophysiological features derived from generalized linear integrate and fire (GLIF) model fits. We selected genes that were significantly correlated with membrane time constant (tau), input resistance (Rin or ri), or capacitance (Cm or cap) in the referenced data tables, and extracted the level of association between gene expression and those electrophysiological feature (correlation ‘DiscCorr’ in Tripathy et al., 2017 and linear coefficient ‘beta_gene’ in Bomkamp et al., 2019).

To compare timescale-gene expression association at the single-cell and macroscale level, we correlated the single-cell associations extracted above with the spatial correlation coefficient (macroscale ρ) between ECoG timescale and AHBA microarray expression data for those same genes, restricting to genes with p<0.05 for macroscale correlation (results identical for non-restrictive gene set). Overall association for all genes, as well as split by quintiles of their absolute macroscale correlation coefficient, are shown in Figure 3D. Example ‘single-cell timescale’ genes shown in Figure 3B and C are genes showing the highest correlations with those electrophysiology features reported in Table 2 of Bomkamp et al., 2019.

T1w/T2w-removed timescale and gene expression residual maps

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To remove anatomical hierarchy as a potential mediating variable in timescale–gene expression relationships, we linearly regress out the T1w/T2w map from the (log) timescale map and individual gene expression maps. T1w/T2w was linearly fit to log-timescale, and the error between T1w/T2w-predicted timescale and empirical timescale was extracted (residual); this identical procedure was applied to every gene expression map to retrieve the gene residuals. SA-preserving null timescale residual maps were similarly created using MSR.

PLS regression model

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Due to multicollinearity in the high-dimensional gene expression dataset (many more genes than parcels), we fit a PLS model to the timescale map with one output dimension (sklearn.cross_decomposition.PLSRegression) to estimate regression coefficient for all genes simultaneously, resulting in N = 18,114 (or N = 2429 brain-specific) PLS weights (Vértes et al., 2016; Whitaker et al., 2016). To determine significantly associated (or ‘enriched’) genes, we repeated the above PLS-fitting procedure 1000 times but replaced the empirical timescale map (or residual map) with null timescale maps (or residual maps) that preserved its SA. Genes whose absolute empirical PLS weight was greater than 95% of its null weight distribution was deemed to be enriched, and submitted for GOEA.

Gene ontology enrichment analysis

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The Gene Ontology (GO) captures hierarchically structured relationships between GO items representing aspects of biological processes (BP), cellular components (CC), or molecular functions (MF). For example, ‘synaptic signaling’, ‘chemical synaptic transmission’, and ‘glutamatergic synaptic transmission’ are GO items with increasing specificity, with smaller subsets of genes associated with each function. Each GO item is annotated with a list of genes that have been linked to that particular process or function. GOEA examines the list of enriched genes from above to identify GO items that are more associated with those genes than expected by chance. We used GOATOOLS (Klopfenstein et al., 2018) to perform GOEA programmatically in python.

The list of unranked genes with significant empirical PLS weights was submitted for GOEA as the ‘study set’, while either the full ABHA list or brain-specific gene list was used as the ‘reference set’. The output of GOEA is a list of GO terms with annotated genes that are enriched or purified (i.e., preferentially appearing or missing in the study list, respectively) more often than by chance, determined by Fisher’s exact test.

Enrichment ratio is defined as follows: given a reference set with N total genes, and n were found to be significantly associated with timescale (in the study set), for a single GO item with B total genes annotated to it, where b of them overlap with the study set, then. Statistical significance is adjusted for multiple comparisons following Benjamini–Hochberg procedure (false discovery rate q-value reported in Figure 3F), and all significant GO items (q < 0.05) are reported in Figure 3F, in addition to some example items that did not pass significance threshold. For a detailed exposition, see Bauer, 2017. Figure 3F shows results using brain-specific genes. The GO items that are significantly associated are similar when using the full gene set, but typically with larger q-values (Supplementary file 1 and 2) due to a much larger set of (non-brain-specific) genes. Control analysis was conducted using T1w/T2w, with 1000 similarly generated null maps, instead of timescale.

Working memory ECoG data and analysis

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The CRCNS fcx-2 and fcx-3 datasets include 17 intracranial ECoG recordings in total from epilepsy patients (10 and 7, respectively) performing the same visuospatial working memory task (Johnson, 2019; Johnson, 2018c; Johnson et al., 2018a, Johnson et al., 2018b). Subject 3 (s3) from fcx-2 was discarded due to poor data quality upon examination of trial-averaged PSDs (high noise floor near 20 Hz), while s5 and s7 from fcx-3 correspond to s5 and s8 in fcx-2 and were thus combined. Together, data from 14 unique participants (22–50 years old, five females) were analyzed, with variable and overlapping coverage in PC (n = 14), PFC (n = 13), OFC (n = 8), and MTL (n = 9). Each channel was annotated as belonging to one of the above macro regions.

Experimental setup is described in Johnson, 2019; Johnson, 2018c; Johnson et al., 2018a, Johnson et al., 2018b in detail. Briefly, following a 1 s pre-trial fixation period (baseline), subjects were instructed to focus on one of two stimulus contexts (‘identity’ or ‘relation’ information). Then two shapes were presented in sequence for 200 ms each. After a 900 or 1150 ms jittered precue delay (delay1), the test cue appeared for 800 ms, followed by another post-cue delay period of the same length (delay2). Finally, the response period required participants to perform a 2-alternative forced choice test based on the test cue, which varied based on trial condition. For our analysis, we collapsed across the stimulus context conditions and compared neuronal timescales during the last 900 ms of baseline and delay periods from the epoched data, which were free of visual stimuli, in order to avoid stimulus-related event-related potential effects. Behavioral accuracy for each experimental condition was reported for each participant, and we average across both stimulus context conditions to produce a single working memory accuracy per participant.

Single-trial power spectra were computed for each channel as the squared magnitude of the Hamming-windowed Fourier Transform. We used 900 ms of data in all three periods (pre-trial, delay1, and delay2). Timescales were estimated by applying spectral parameterization as above, and the two delay-period estimates were averaged to produce a single delay period value. For comparison, we computed single-trial theta (3–8 Hz) and high-frequency activity (high gamma [Mukamel et al., 2005], 70–100 Hz) powers as the mean log-power within those frequency bins, as well as spectral exponent (χ). Single-trial timescale difference between delay and baseline was calculated as the difference of the log timescales due to the non-normal distribution of single-trial timescale estimates. All other neural features were computed by subtracting baseline from the delay period.

All neural features were then averaged across channels within the same regions, then trials, for each participant, to produce per-participant region-wise estimates, and finally averaged across all participants for the regional average in Figure 4B and C. Two-sided Mann–Whitney U-tests were used to test for significant differences in baseline timescale between pairs of regions (Figure 4B). Two-sided Wilcoxon rank-sum tests were used to determine the statistical significance of timescale change in each region (Figure 4C), where the null hypothesis was no change between baseline and delay periods (i.e., delay is 100% of baseline). Spearman rank correlation was used to determine the relationship between neural activity (timescale; theta; high-frequency; χ) change and working memory accuracy across participants (Figure 4D and Figure 4—figure supplement 1).

Per-subject average cortical timescale across age

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Since electrode coverage in the MNI-iEEG dataset is sparse and nonuniform across participants (Figure 2—figure supplement 1), simply averaging across parcels within individuals to estimate an average cortical timescale per participant confounds the effect of age with the spatial effect of cortical hierarchy. Therefore, we instead first normalize each parcel by its max value across all participants before averaging within participants, excluding those with fewer than 10 valid parcels (71 of 106 subjects remaining; results hold for a range of threshold values; Figure 4—figure supplement 2B). Spearman rank correlation was used to compute the association between age and average cortical timescale.

Age–timescale association for individual parcels

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Each cortical parcel had a variable number of participants with valid timescale estimates above the consistency threshold, so we compute Spearman correlation between age and timescale for each parcel, but including only those with at least five participants (114 of 180 parcels, result holds for a range of threshold values; Figure 4—figure supplement 2C). Spatial effect of age-timescale variation is plotted in Figure 4F, where parcels that did not meet the threshold criteria are grayed out. Mean age–timescale correlation from individual parcels was significantly negative under one-sample t-test.

Data and materials’ availability

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All data analyzed in this manuscript are from open data sources. All code used for all analyses and plots are publicly available on GitHub at https://github.com/rdgao/field-echos (Gao, 2020) and https://github.com/rudyvdbrink/surface_projection (van den Brink, 2020). See Tables 1 and 2 for details.

Data availability

All data analyzed in this manuscript are from open data sources:MNI Open iEEG (https://mni-open-ieegatlas.research.mcgill.ca/); Human Connectome Project S1200 Release (https://www.humanconnectome.org/study/hcp-young-adult/document/1200-subjects-data-release); Neurotycho Anesthesia and Sleep Task (http://neurotycho.org/anesthesia-and-sleep-task); and Whole brain gene expression (http://www.meduniwien.ac.at/neuroimaging/mRNA.html).All code used for all analyses and plots are publicly available on GitHub at https://github.com/rdgao/field-echos (archived at Zenodo http://doi.org/10.5281/zenodo.4362645) and https://github.com/rudyvdbrink/surface_projection (archived at Zenodo http://doi.org/10.5281/zenodo.4352385). See Tables 1 and 2 for details.

The following previously published data sets were used

References

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    1. Bauer S
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    In: Dessimoz C, Škunca N, editors. The Gene Ontology Handbook. Springer. pp. 175–188.
    https://doi.org/10.1007/978-1-4939-3743-1
    1. Hilgetag CC
    2. Goulas A
    (2020) ‘Hierarchy’ in the organization of brain networks
    Philosophical Transactions of the Royal Society B: Biological Sciences 375:20190319.
    https://doi.org/10.1098/rstb.2019.0319
    1. Pedregosa F
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    Scikit-learn: machine learning in Python
    Journal of Machine Learning Research : JMLR 12:2825–2830.

Decision letter

  1. Martin Vinck
    Reviewing Editor; Ernst Strüngmann Institute (ESI) for Neuroscience in Cooperation with Max Planck Society, Germany
  2. Laura L Colgin
    Senior Editor; University of Texas at Austin, United States
  3. Thilo Womelsdorf
    Reviewer

In the interests of transparency, eLife publishes the most substantive revision requests and the accompanying author responses.

Acceptance summary:

General value assessment: The brain is a hierarchically organized system. Is information in higher brain areas integrated over different time-scales than in lower brain areas? Gao et al. analyze intracranial recordings in humans across a large part of the neocortex using several new analytical techniques. They find that higher brain areas have longer neuronal time-scales. Neuronal time-scales are correlated with specific gene expression patterns, and are correlated with working memory performance.

Decision letter after peer review:

Thank you for submitting your article "Neuronal timescales are functionally dynamic and shaped by cortical microarchitecture" for consideration by eLife. Your article has been reviewed by four peer reviewers, one of whom is a member of our Board of Reviewing Editors, and the evaluation has been overseen by Laura Colgin as the Senior Editor. The following individual involved in review of your submission has agreed to reveal their identity: Thilo Womelsdorf (Reviewer #4).

The reviewers have discussed the reviews with one another and the Reviewing Editor has drafted this decision to help you prepare a revised submission.

We would like to draw your attention to changes in our revision policy that we have made in response to COVID-19 (https://elifesciences.org/articles/57162). Specifically, when editors judge that a submitted work as a whole belongs in eLife but that some conclusions require a modest amount of additional new data, as they do with your paper, we are asking that the manuscript be revised to either limit claims to those supported by data in hand, or to explicitly state that the relevant conclusions require additional supporting data.

Our expectation is that the authors will eventually carry out the additional experiments and report on how they affect the relevant conclusions either in a preprint on bioRxiv or medRxiv, or if appropriate, as a Research Advance in eLife, either of which would be linked to the original paper.

Summary:

Gao et al. analyze how brain-wide timescales of ECoG signals vary across the cortical hierarchy and relate these timescales to several other aspects of structure, behavior and function. They report the following main findings: 1) Timescales increase with the cortical hierarchy. 2) Time-scales, after regressing out the hierarchical T1w/T2w structure variable, correlate significantly with several genes related to synaptic receptors and ion channels. 3) Time-scales increase with working memory task vs. baseline, and predict working memory performance across subjects. 4) Time-scales decrease with aging, in a region-specific way. These findings are a significant advance in comparison to previous work by considering brain-wide hierarchy at a high spatial and temporal resolution and relating them to behaviour and genetics.

All four reviewers agreed the study is of substantial interest. The study was found of high quality.

Essential revisions:

1) Definition and comparison of timescales:

i) The comparison shown in Figure 2 between spiking time-scale and ECOG time-scale might be problematic, in the sense that the spiking time-scales were taken from the Murray et al., 2014 paper where they were quantified with a different technique. A possible solution would be to quantify time-scales in the same manner as Murray, or maybe there is a convincing argument why this is not a problem.

ii) For the non-specialist reader, the concept of neuronal timescales that is central to the paper should be defined more explicitly in the Introduction ('neuronal timescales' appear in paragraph three, while it gets defined in paragraphs one and two).

iii) Fast and slow responding to sensory versus cue related information may reflect a circular definition of timescales.

iv) The Results text says that the aperiodic components is interpreted as time scale but not how the inference is made, i.e. what quantity is interpreted as time scale.

v) It is difficult to keep track of which timescales are referred to when in the text, e.g. the authors start referring to neuronal timescales after having discussed ECOG based time scales and spike timescales. It seems important for cleanly separating the source of the timescale to denote them with a unique label depending on the source data that give rise to them. Why not using a subscript for spike, epiduralECoG, subduralECoG, intracranialLFP,.… ?

2) Timescales and hierarchy:

i) The correlations shown between transcriptomics and timescales need to be carefully considered. While the authors regress out T1w/T2w residuals, these might just be one structural factor that changes with cortical hierarchy and assumes that the underlying relationships are linear. Hence, it is possible that timescales and gene profiles are correlated with structure but that there is no causal relationship between these genes and timescales. In this sense, the correlation of genes with hierarchy might also yield similar genetic profiles. It would be important to show the correlation of hierarchy with genetic profiles, to see whether this looks different from the correlations that are obtained with timescale.

ii) The authors use T1W/T2W as the measure for cortical hierarchy. This is a gradient-based perspective on cortical hierarchy. However, there are other perspectives on hierarchy that are not gradient-based, but are based on anatomical connectivity, e.g. as pursued by Kennedy and Van Essen (Vezoli et al., 2020). This needs to be discussed.

iii) The manuscript addresses two distinct aspects of neuronal timescales: their relationship to local microarchitecture and their dynamics as a function of task or age. Although there is obviously a strong inter-relationship between these two aspects, this deserves a more extensive discussion. For example, in relation with the previous point, if local microstructural properties predict neuronal timescales, why is it that timescale changes during the delay seem to be ubiquitous (or are they)? And why should such changes (that are overall in the same range) correlate with subject performance in the PFC but not in the other areas? How does this relate to the aging observations? Although this discussion is bound to be speculative. It is important in order to strengthen the link between these two independent avenues of the paper, and to enrich the discussion about the functional role of these dynamic changes in neuronal timescales.

iv) The paper does not consider oscillations, which is fine, but the reader is left wondering how oscillations affect these time-scales. Discussion on this aspect would be useful.

4) Comments on figures, statistics and clarification:

i) Are the rho correlation values corrected for the expected value of the surrogate distribution? That is are they significantly overestimated due to the dependent samples issue? In this case it is recommended to report the corrected correlation values, rather than the raw correlation values.

ii) The correlation performed in Figure 4D is a bit unclear. Are the different dots+lines participants, or is this a binned correlation? If it is a binned correlation, does that represent a problem for the correlation analysis?

iii) It would be useful in Figure 1/2 to show some examples of ECOG time-scales related to the actual underlying signals and PSDs, rather than just illustrating the technique on simulated data, so that the validity of the technique can be judged.

iv) In general it would be useful to report carefully the N's and the dataset that is used for each analysis, because it is easy to get lost in what is what as the authors analyze a huge number of datasets.

v) The technique of removing spatial autocorrelations that influence the p-value appears to be sophisticated and well done. If the authors need another validation, one way of doing this would be to use a cross-validation prediction approach where a subset of subjects is used for training and the other subjects are used for testing.

vi) What are "these" limitations in the subsection “Neuronal timescale can be inferred from frequency domain”?

vii) Figure 1E: how is r2=1 when the dots do not fall on the line?

viii) The description of the methods needs be improved. For example, "we can estimate neuronal timescale from the 'characteristic frequency'" which implies a peak in the spectrum. Yet in the next sentence they write that they extract timescale from aperiodic components.

ix) Subsection “Synaptic and ion channel genes shape timescales of neuronal dynamics”: Are these markers also correlated with cell packing density? If so, it's possible that denser neural networks have longer timescales.

x) Relatedly, how strongly inter-correlated are these genetic markers across the cortex? The authors mostly take a mass-univariate approach except for showing gene-PC1 in Figure 3A. There isn't enough information shown to evaluate whether the top PC is suitable, or whether this PC comprises many/all gene contributions or is driven by a small number, etc.

xi) The modeling results seem to be missing. They appear as a schematic in Figure 1 and are mentioned in the Materials and methods section. Was this model actually used somewhere?

xii) In Figure 2B, some T1w/T2w values are above values of 2, which is not standard. Likewise, several outliers can be observed. This might have impacted the estimation of the regression slope. This slope currently matches the one from Burt et al., 2018, although the data point distribution is different.

xiii) Figure 4B is contradicting Figure 2C as the evidenced timescale hierarchy is different (comparing PC, PFC and OFC). Please explain.

xiv) Figure 4B and C, please show actual data points and justify parametric tests.

xv) Figure 4C: how consistent is the increase in delay period timescales across areas within each subject. In other words, is this a general property of the brain, task-related effects resulting in a non-specific adjustment in neuronal timescales or are there regional differences in the reported increase (you might want to exclude the PFC from the analysis to remove task related effects).

xvi) Given the described age-related effect, did the authors check that the different databases they used sampled from subjects with the same age distribution?

xvii) Legend of Figure 1 is not self-explanatory and a lot of the symbols and information plotted in the figures are not explained. Unfortunately, this information is also missing from the Results section.

5) General dense writing style and clarity:

The manuscript is written to be dense yet terse, which makes it harder to read, particularly given the complexity of the analyses. It feels like it was written for a journal with extreme word limitations. The manuscript would be overall improved if the authors would "loosen their belt" and explain the findings and methods in more detail. Figure legends should be more self-explanatory. Quite often, figure detail description and contextual information are missing both from the text and the figures. This also applies to the supplementary figures.

https://doi.org/10.7554/eLife.61277.sa1

Author response

Essential revisions:

1) Definition and comparison of timescales:

i) The comparison shown in Figure 2 between spiking time-scale and ECOG time-scale might be problematic, in the sense that the spiking time-scales were taken from the Murray et al., 2014 paper where they were quantified with a different technique. A possible solution would be to quantify time-scales in the same manner as Murray, or maybe there is a convincing argument why this is not a problem.

The spiking timescales taken from Murray et al., 2014, is estimated by fitting an exponential decay function to the spike count autocorrelogram (or autocorrelation function, ACF), and extracting the decay constant. To clarify, this approach measures a mathematically equivalent quantity (decay time constant) as our presented method (though from spiking data in the above case). However, it is problematic when the data has strong and non-stationary oscillatory and long-term variations, as is the case in most neural field potential data, because the oscillations result in ringing in the ACF, impairing precise fits of the decay function, requiring additional components like cosine terms (see Figure 1D inset). Furthermore, it was recently shown that the decay constant obtained via this approach is biased (underestimates) even when the ground-truth model has just a single exponential decay component, due to finite sample size and noise effects (Zeraati et al., 2020).

Alternatively, via the Wiener-Khinchin theorem (Khintchine, 1934), the decay time constant can be equivalently estimated in the frequency domain as the “knee frequency”, as Figure 1E demonstrates (also see, e.g., (Chaudhuri et al., 2017)). This is the approach we take, where oscillatory activity can be more easily accounted for and removed as Gaussian peaks using our spectral parameterization approach (Donogue et al., 2020), and long-term/scale-free components as the 1/f exponent. This is especially important given oscillations with non-stationary frequencies. For example, a broad oscillatory peak in the power spectrum (e.g., ~10Hz in bandwidth like in Figure 1D) represents drifts in the oscillation frequency over time, which is easily accounted for with a single Gaussian, but requires multiple cosine terms to capture well in the autocorrelation. In addition, neural data is dominated by low frequencies due to its power law nature, though we are often interested in capturing the low-power, high-frequency components accurately as well. Fitting the logged PSD (in frequency domain) de-emphasizes the low frequencies, while this is not achievable by fitting the ACF.

In short, the presented method is a more accurate way of estimating the exponential decay constant from data whose autocorrelation displays multiple mixed components. We now emphasize this distinction in the first part of the Results section to further highlight the advantages of the current method.

ii) For the non-specialist reader, the concept of neuronal timescales that is central to the paper should be defined more explicitly in the Introduction ('neuronal timescales' appear in paragraph three, while it gets defined in paragraphs one and two).

We agree, and thank you for this suggestion. In conjunction with another reviewer comment, we now explicitly consider several definitions of “neuronal timescale” and define them in the Introduction (“…and the temporal dynamics of neuronal populations across the cortex are thought to be an intrinsic property (i.e., neuronal timescale) that enables the representation of information over multiple durations in a hierarchically embedded environment”), as well as how our estimate from ECoG relates to previous definitions in the Discussion.

iii) Fast and slow responding to sensory versus cue related information may reflect a circular definition of timescales.

We apologize for the confusion here: the reference to sensory vs. cue-related information (in the first Introduction paragraph) is meant to convey differences in the timescale of stimuli in the natural environment, and an ongoing theory is that different populations in the brain should track these timescales to produce adaptive behavior. This was conflated with neural timescales in an unhelpful way. We have now expanded this section to be more precise:

“Human brain regions are broadly specialized for different aspects of behavior and cognition, and the temporal dynamics of neuronal populations across the cortex are thought to be an intrinsic property (i.e., neuronal timescale) that enables the representation of information over multiple durations in a hierarchically embedded environment (Kiebel et al., 2008)”.

iv) The Results text says that the aperiodic components is interpreted as time scale but not how the inference is made, i.e. what quantity is interpreted as time scale.

Indeed, this was glossed over. We now specify in the first paragraph of the Results section that neuronal timescale is computed from the knee frequency of the aperiodic component, along with mathematical details and reference to prior works, e.g., “From the knee frequency of the aperiodic component, neural timescale (decay constant) can then be computed exactly as τ=12πfk.”

v) It is difficult to keep track of which timescales are referred to when in the text, e.g. the authors start referring to neuronal timescales after having discussed ECOG based time scales and spike timescales. It seems important for cleanly separating the source of the timescale to denote them with a unique label depending on the source data that give rise to them. Why not using a subscript for spike, epiduralECoG, subduralECoG, intracranialLFP,.… ?

Thank you for this suggestion. We agree, there are multiple definitions of neuronal timescale, which is especially confusing when spiking timescales are compared with ECoG timescales. Since all main results pertain to timescale estimated from ECoG recordings (aside from the macaque results), we elected not to include a subscript for that quantity to preserve readability of the prose. To reduce confusion, this is now explicitly stated in the Introduction, and subscripts are now included in Figure 2 and the corresponding Results section when comparing spiking and ECoG timescales.

2) Timescales and hierarchy:

i) The correlations shown between transcriptomics and timescales need to be carefully considered. While the authors regress out T1w/T2w residuals, these might just be one structural factor that changes with cortical hierarchy and assumes that the underlying relationships are linear. Hence, it is possible that timescales and gene profiles are correlated with structure but that there is no causal relationship between these genes and timescales. In this sense, the correlation of genes with hierarchy might also yield similar genetic profiles. It would be important to show the correlation of hierarchy with genetic profiles, to see whether this looks different from the correlations that are obtained with timescale.

We agree with the reviewer here: in general, it is very difficult to make causal claims regarding the relationship between these co-occurring gradients. Importantly, It has been shown previously that cortical hierarchy (defined by the T1/T2 gradient) is correlated with the expression profile of many individual genes, as well as the overall patterning (top principal components of genes) (Burt et al., 2018). In that study, they perform a similar analysis (GOEA) and identify a number of gene ontologies items that are significantly overrepresented. In fact, as shown in that study, the T1/T2 gradient is more correlated with gene PC1 than timescale.

All this is to say that we acknowledge this limitation wholeheartedly, since there is clear data that the structural gradient is associated with the gene expression gradient, as is the timescale gradient, and the multiple macroscopic gradients are all likely to align to some capacity (e.g., Wang, 2020). This is exactly the motivation to regress out the contribution of T1/T2 from the timescale and gene gradients in the first place, but, as the reviewer points out, regressing out T1/T2 assumes a linear contribution, which does not account for possible nonlinear relationships.

To address this concern, we make three arguments here: first, as a baseline, if timescale provides no (linear) contribution on top of T1T2, then we should not see any significantly associated genes, but this is not the case, implying that timescales has some additional predictive power, which is the case we make in the paper.

Second, from a physiological point of view, gene expression shapes macro and micro-anatomical features, and subsequently, both gene expression and anatomy shape neural dynamics. So in some sense, neural dynamics (specifically, timescale) is downstream to macroanatomy (T1/T2), and we argue precisely that the other micro-anatomical features, such as synaptic receptor and ion channel density, should contribute to shaping neuronal timescale beyond T1/T2. In other words, neural dynamics have to be causally shaped by some structural property, and we show that macro-connectivity is not the sole mediating variable between gene expression and neural dynamics.

Third, we interpret that the reviewer would like to see a similar analysis performed for T1/T2 vs. gene maps, and to show that the gene clusters strongly associated with structural hierarchy are different from the ones associated with timescales, and we find this to be the case (Supplementary file 3). Specifically, PLS model fit to T1/T2 and gene expression data yields no significant GO terms when the analysis is restricted to brain-specific genes, compared to ones displayed in Figure 3F (and supplementary file 1) showing high specificity to ion channel and synaptic functions. Repeating the analysis with all genes against T1/T2 does yield GO terms that contain ion channel- and synapse-related genes. However, they are much less specific (compared to Supplementary file 2), including a variety of gene clusters associated with general metabolic processes, signalling pathways, and cellular components. This further strengthens the point that removing the contribution of macroanatomy would result in identifying genes that are more specifically associated with neurodynamics. These points are now raised in the Results and Discussion section, and we further stress the non-causal and linear nature of these analyses (Discussion section: “Collinearity and surrogate nature of post-mortem gene expression gradients”).

ii) The authors use T1W/T2W as the measure for cortical hierarchy. This is a gradient-based perspective on cortical hierarchy. However, there are other perspectives on hierarchy that are not gradient-based, but are based on anatomical connectivity, e.g. as pursued by Kennedy and Van Essen (Vezoli et al., 2020). This needs to be discussed.

Thank you for pointing us to this new paper. Our understanding is that (Burt et al., 2018) demonstrated that the T1/T2 gradient is a pragmatic proxy of anatomical hierarchy in human brains where tracing data is difficult to obtain, but closely follows the definition of hierarchy that Kennedy and colleagues have put forward, validating against macaque tracing data (i.e., laminar specificity of feedforward vs. feedback projections). However, it is true that several perspectives exist for the concept of “cortical hierarchy” – all closely related but qualitatively different – as recently reviewed in (Hilgetag and Goulas, 2020). We now specify this in the Introduction (e.g.: “Anatomical connectivity measures based on tract tracing data, such as laminar feedforward vs. feedback projection patterns, have classically defined a hierarchical organization of the cortex (Felleman and Van Essen, 1991; Hilgetag and Goulas, 2020; Vezoli et al., 2020)”) and provide a more detailed treatment of these perspectives in the Discussion section.

iii) The manuscript addresses two distinct aspects of neuronal timescales: their relationship to local microarchitecture and their dynamics as a function of task or age. Although there is obviously a strong inter-relationship between these two aspects, this deserves a more extensive discussion. For example, in relation with the previous point, if local microstructural properties predict neuronal timescales, why is it that timescale changes during the delay seem to be ubiquitous (or are they)? And why should such changes (that are overall in the same range) correlate with subject performance in the PFC but not in the other areas? How does this relate to the aging observations? Although this discussion is bound to be speculative. It is important in order to strengthen the link between these two independent avenues of the paper, and to enrich the discussion about the functional role of these dynamic changes in neuronal timescales.

We agree, and we believe that the integration of these two aspects is a fascinating avenue of future research. In brief, neuronal dynamics is first and foremost constrained by local and long-range structural properties, including connectivity and cell-type variations, and this has been previously shown in many different ways, both experimentally and through computational modeling. However, these structural properties only experience changes in the (relatively) longer term (e.g., development, long-term plasticity), and a brain where dynamical properties are fixed relative to its structural properties would not be very adaptive (or useful) in the short term.

In contrast, we observe relatively broad changes in timescales over both short and long terms, but area-specific correlation with behavior. The first point is one we intended to emphasize and provide initial evidence for in this manuscript, while providing suggestive interpretations for the second point. Our interpretation is that structural properties define a range for neural dynamic properties (specifically, timescale), while task requirements, input statistics, short term synaptic plasticity, and neuromodulation may broadly shift cortical timescale within this range, but only computations within the area of relevance (i.e., PFC) is indicative of task performance. Following the reviewer’s suggestion, we now provide a more detailed interpretation and some speculation in the Discussion section.

iv) The paper does not consider oscillations, which is fine, but the reader is left wondering how oscillations affect these time-scales. Discussion on this aspect would be useful.

Thank you for this suggestion. We agree – while oscillations are ignored on purpose here when estimating neuronal timescales, oscillatory parameters and aperiodic timescale likely co-evolve as a function of the underlying synaptic, neuronal, and network properties (e.g., time delay between interacting local excitatory and inhibitory populations), and deserve an extended discussion. In brief, we interpret timescale and oscillations to be related dynamical quantities, similar to the decay constant and characteristic (or resonant) frequency in a damped harmonic oscillator, which arise depending on the input and operating regime of the oscillator. Supporting this, a recent study reports an anterior-to-posterior gradient in oscillatory frequency across the human cortex using MEG data, and is also correlated with cortical hierarchy (Mahjoory et al., 2020). We now include these points in the Discussion section.

4) Comments on figures, statistics and clarification:

i) Are the rho correlation values corrected for the expected value of the surrogate distribution? That is are they significantly overestimated due to the dependent samples issue? In this case it is recommended to report the corrected correlation values, rather than the raw correlation values.

As the reviewer points out, these samples have non-trivial spatial autocorrelation, and must be accounted for when reporting statistical significance. To do this, all reported p-values are the “corrected p-values”, which are computed by comparing the raw correlation against a surrogate distribution of correlation values using permutation procedures that shuffle the data but preserve spatial autocorrelation (e.g., see Figure 2—figure supplement 2 for surrogate distributions). Consistent with existing literature (e.g., (Burt et al., 2020; Vos de Wael et al., 2020)), all reported rho values are “raw” in the sense that it is the direct Spearman correlation computed from a pair of vectors (e.g., timescale and T1/T2 over space), but the p-values are corrected.

ii) The correlation performed in Figure 4D is a bit unclear. Are the different dots+lines participants, or is this a binned correlation? If it is a binned correlation, does that represent a problem for the correlation analysis?

Each dot is a participant, and the error bars represent the SEM around that mean across all PFC electrodes for that participant. The figure legend for 4D is now updated to reflect this, and we apologize for being unclear here.

iii) It would be useful in Figure 1/2 to show some examples of ECOG time-scales related to the actual underlying signals and PSDs, rather than just illustrating the technique on simulated data, so that the validity of the technique can be judged.

Thank you for this suggestion, this would indeed improve the clarity of the manuscript. Figure 2 now includes example time-series and power spectra from representative electrodes along the cortical hierarchy from both the human and macaque datasets.

iv) In general it would be useful to report carefully the N's and the dataset that is used for each analysis, because it is easy to get lost in what is what as the authors analyze a huge number of datasets.

Agreed – the N’s and details of the dataset are now included in the figure legends, and summarized in Table 1.

v) The technique of removing spatial autocorrelations that influence the p-value appears to be sophisticated and well done. If the authors need another validation, one way of doing this would be to use a cross-validation prediction approach where a subset of subjects is used for training and the other subjects are used for testing.

Thank you for the kind words and the following suggestion. We agree that cross-validation with held-out participants would in general be a good approach. In this particular case, it is made more difficult by the fact that participants have heterogeneous electrode coverage, so a naive k-fold or leave-one-out approach would result in many empty cortical parcels, and thus require sophisticated grouping strategies to ensure complete coverage when averaging the training and validation sets.

vi) What are "these" limitations in the subsection “Neuronal timescale can be inferred from frequency domain”?

Original: “To overcome these limitations, we develop a novel computational method for inferring the timescale of neuronal transmembrane current fluctuations from human intracranial electrocorticography (ECoG) recordings (Figure 1A, box).”

New: “To relate whole-cortex transcriptomic and anatomical data with neuronal dynamic timescales in humans, we develop a novel computational method for inferring the timescale of neuronal transmembrane current fluctuations from intracranial electrocorticography (ECoG) recordings (Figure 1A, box).”

vii) Figure 1E: how is r2=1 when the dots do not fall on the line?

The correlation value is reported up to 3 decimal places, which was rounded up to 1. There is an error here, however, as we intended to report Pearson correlation (r), not r2. This is now reflected in the figure and legend.

viii) The description of the methods needs be improved. For example, "we can estimate neuronal timescale from the 'characteristic frequency'" which implies a peak in the spectrum. Yet in the next sentence they write that they extract timescale from aperiodic components.

We apologize for the confusion here. “Characteristic frequency” is terminology borrowed from the filter design literature that corresponds to the roll-off frequency of, for example, a low-pass filter. However, it introduces confusion in this context, so we have replaced it with “knee frequency” and expanded on the description of the timescale estimation procedure in the first paragraph of the Results section.

ix) Subsection “Synaptic and ion channel genes shape timescales of neuronal dynamics”: Are these markers also correlated with cell packing density? If so, it's possible that denser neural networks have longer timescales.

This is a very interesting question: previous theoretical works have demonstrated many network properties (including population size) to be important for creating long timescale dynamics around attractor states, especially in nonlinear and strongly recurrent networks, reviewed in, e.g., (Barak and Tsodyks, 2014; Huang and Doiron, 2017). However, this relationship is difficult to test directly, especially in the human cortex, due to the lack of detailed interareal neuronal count measurements. As such, it’s unclear whether there is a similarly graded variation in cell number from sensory to association cortices. A comprehensive review of mouse data suggests that sensory (especially visual) areas have the highest neuronal density (Keller et al., 2018), though the decreased count in higher order frontal regions may not apply to primate brains. It is possible to use non-invasive proxies to infer cell density in the human cortex. For example, gray matter volume has previously been used as a proxy for neuronal density, and correlates with fMRI timescales across individuals (Watanabe et al., 2019). However, it was shown to be unrelated to direct histological measurements of cell count within the temporal lobe when compared to resected tissue (Eriksson et al., 2009), and cell-type specific contributions inferred from gene expression analysis (using the same ABHA data) show a complex relationship between cell density and grey matter thickness (Shin et al., 2018).

Nevertheless, following this suggestion, we use cortical thickness from the HCP dataset as a surrogate for human cortical cell packing density. We see that thicker regions do have longer timescales (Figure 2—figure supplement 3, left), though this relationship is weaker than that of timescale vs. T1T2. Cortical thickness is also negatively correlated with T1T2 (Figure 2—figure supplement 3, right), furthering the point of multiple overlapping large-scale cortical gradients. As such, we cannot eliminate the possibility that denser networks directly contribute to having longer timescales (at least partially). However, we do not claim that cortical myelination (measured via T1T2) is the only contributor to neuronal timescale, but that timescale is a dynamic-readout of the abstract quantity of cortical hierarchy, which may be defined by gene expression and further shapes macroanatomical measures such as cortical thickness, cell density, and GM myelination. (Burt et al., 2018)(Figure 6) showed that T1T2 was a better predictor of gene expression gradients than cortical thickness, which we take to mean that T1T2 is a more representative measure of cortical hierarchy than cortical thickness. All these interpretations are consistent with each other, and we now address this in the Discussion.

x) Relatedly, how strongly inter-correlated are these genetic markers across the cortex? The authors mostly take a mass-univariate approach except for showing gene-PC1 in Figure 3A. There isn't enough information shown to evaluate whether the top PC is suitable, or whether this PC comprises many/all gene contributions or is driven by a small number, etc.

In general, these gene expression profiles are strongly correlated with each other and have topographies closely related to distinct cortical macroregions, as previous works have shown (e.g., (Burt et al., 2018; Hawrylycz et al., 2012)). As shown in Figure 2—figure supplement 2, the top principal component accounts for nearly 40% of the variance, while each of the first 5 PCs account for around 10% or more, and quickly approach 0 thereafter, implying a low-dimensional structure in the transcriptomic data. In the same figure, we note that only the 1st gene PC is significantly correlated with the timescale gradient after accounting for spatial autocorrelation. To address the reviewer’s question regarding whether many genes or a handful of outliers contribute to PC1, we also plot the distribution of weights for the first 5 PCs (Author response image 1), and observe that the extremes of the data (top and bottom ticks) are well within the main body of the distributions. This is especially true for PC1 where the weights are more uniformly distributed, hence receiving contributions from many genes.

Author response image 1

In addition, we note that the partial least squares (PLS) model we use for the gene ontology enrichment analysis is a multivariate approach, where weights for each gene are fit simultaneously and account for multicollinearity. Genes with large weights are then submitted to GOEA, where distinct functional gene clusters (i.e., gene ontology items) can be found. If it is the case that only a couple of genes are strongly associated with timescale, then we would not expect to see any significant gene clusters to be found. In contrast, Figure 3E and F show that many genes – and more importantly, genes belonging to the same functional groups (e.g., ion channel complex) – are associated with the cortical timescale gradient.

xi) The modeling results seem to be missing. They appear as a schematic in Figure 1 and are mentioned in the Materials and methods section. Was this model actually used somewhere?

We apologize for the confusion – ”model” is used to mean the spectral parameterization model with aperiodic and periodic components, like “model” in GLM or linear regression model. In other words, it’s a descriptive/statistical model, not a mechanistic one. The legend in Figure 1D thus refers to the fitted spectrum as the “full model fit” (but we’ve now removed “model” there to avoid confusion). There is no formal computational modeling of a circuit using, e.g., LIF networks, and all simulated time series data are referred to as simulations to avoid confusion.

xii) In Figure 2B, some T1w/T2w values are above values of 2, which is not standard. Likewise, several outliers can be observed. This might have impacted the estimation of the regression slope. This slope currently matches the one from Burt et al., 2018, although the data point distribution is different.

Figure 2B plots the standardized (z-scored) T1/T2 values on the x-axis, not their raw values (which range between ~1.07 and ~1.73), in order to be consistent with the topography in 2A and similar presentations of the gene expression data. We apologize for this confusion, and have emphasized this point accordingly in the figure and legend. Taking the reviewer’s suggestion, we also performed the correlation after removing all T1/T2 values outside of 2 standard deviations (Author response image 2), and we observed that the reported association is now even stronger (though we keep with the original data in Figure 2).

Author response image 2

xiii) Figure 4B is contradicting Figure 2C as the evidenced timescale hierarchy is different (comparing PC, PFC and OFC). Please explain.

In terms of cortical hierarchy, we expect timescales to increase from parietal regions (PC), to PFC, to OFC. This is observed in macaques in Murray et al., 2014 (which is plotted on the x-axis in Figure 2C), though PFC and OFC timescales are very similar. While we are hesitant to overinterpret, comparative anatomical studies across primates offer some insights regarding these differences. Compared to other primates, including macaques, the human OFC is larger and more specialized compared to surrounding frontal areas, and to other primates (Semendeferi et al., 2001). Since the evolutionary "distance" between PFC and OFC in humans is much greater than that in macaques, it could explain their relatively large difference in Figure 4B but not 2C (now 2F). In Figure 4C, we see that while this relationship is roughly preserved in humans, pairwise t-tests show that PC, PFC, and OFC are not statistically different from each other, and only MTL timescales are significantly longer than PC and PFC. Therefore, we cannot make a definite conclusion about the hierarchical ordering of these 3 regions from timescale alone, since numerical results appear to be statistical fluctuations. However, to further examine this in the larger MNI-iEEG human ECoG database, we grouped the 180 Glasser parcels into 21 macro-regions with broader regional labels (as discussed in Supplementary Materials of (Glasser et al., 2016)). Sorting by their average timescale (mean±sem), we see that the expected ranking is reproduced, where timescale increases from parietal regions, to dlPFC/mPFC, to OFC, and to MTL. We now include this as Figure 2—figure supplement 1G.

xiv) Figure 4B and C, please show actual data points and justify parametric tests.

Thank you for this suggestion – Figure 4B and C now show smaller dots for individual subjects, and we now use non-parametric tests (Mann-Whitney U test and Wilcoxon ranked signed rank test for 4B and C respectively), with nearly identical conclusions (with the exception that parietal cortex baseline timescale is now significantly faster than OFC in 4C). Figures and legends are updated accordingly.

xv) Figure 4C: how consistent is the increase in delay period timescales across areas within each subject. In other words, is this a general property of the brain, task-related effects resulting in a non-specific adjustment in neuronal timescales or are there regional differences in the reported increase (you might want to exclude the PFC from the analysis to remove task related effects).

Following an earlier comment (Point 4-ii), we now plot the per-area timescale change for each participant as individual dots in Figure 4C (each small dot is a participant, averaged over all electrodes in that region; large circle is mean across participants), and observe that the overall increase in timescale is very consistent across brain regions and subjects (even for non-task correlated regions).

Furthermore, pairwise Mann-Whitney U tests fail to detect significant differences in timescale change between any two regions, suggesting that the increase in timescale is general, at least within the association regions where electrode coverage exists in this dataset.

xvi) Given the described age-related effect, did the authors check that the different databases they used sampled from subjects with the same age distribution?

To clarify, we used two different human ECoG databases in the study, and the timescale-age analysis (Figure 4E and F) was done exclusively on the MNI-iEEG database due to the large participant pool with a wide age range (N = 106, ages 13-65, 33.40±10.63 years old, distribution – Author response image 3).

Author response image 3

Structural and gene expression data used for participant-average comparison were from cohorts with similar age distributions (HCP S1200: N = 1096, age: 22-36+ (details restricted due to identifiability); Allen Human Brain Atlas: N = 6, age: 42.5±12.2; now summarized in Table 1). We further ensure that the average timescale map is not biased by age-related implant locations (Figure 2—figure supplement 1).For the working memory analysis in Figure 4A-D, we used the fcx-2 and fcx-3 datasets from CRCNS (N = 14, age 30.9±7.8; one person age 50, everyone else between 22-42). This cohort has a much narrower age range and restricted electrode coverage, and is hence excluded from age-related analysis.

xvii) Legend of Figure 1 is not self-explanatory and a lot of the symbols and information plotted in the figures are not explained. Unfortunately, this information is also missing from the Results section.

Following this suggestion, a more detailed description, especially of Figure 1D, is now provided in the figure legend (“(D) example macaque ECoG power spectral density (PSD) showing the aperiodic component fit (red dashed), and the “knee frequency” at which power drops off (fk, red circle; insets: time series and ACF).”) and first section of the Results section.

5) General dense writing style and clarity:

The manuscript is written to be dense yet terse, which makes it harder to read, particularly given the complexity of the analyses. It feels like it was written for a journal with extreme word limitations. The manuscript would be overall improved if the authors would "loosen their belt" and explain the findings and methods in more detail. Figure legends should be more self-explanatory. Quite often, figure detail description and contextual information are missing both from the text and the figures. This also applies to the supplementary figures.

We agree with the reviewer here – we have now expanded on several of the places outlined here, including figure legends and all sections of the main text, especially pertaining to the method, as several other comments have suggested. Much more detailed discussions on results, assumptions, and limitations of the analyses are now included as well.

References:

Barak, O., and Tsodyks, M. (2014). Working models of working memory. Current Opinion in Neurobiology, 25, 20–24.

Eriksson, S. H., Free, S. L., Thom, M., Symms, M. R., Martinian, L., Duncan, J. S., and Sisodiya, S. M. (2009). Quantitative grey matter histological measures do not correlate with grey matter probability values from in vivo MRI in the temporal lobe. Journal of Neuroscience Methods, 181(1), 111–118.

Keller, D., Erö, C., and Markram, H. (2018). Cell Densities in the Mouse Brain: A Systematic Review. Frontiers in Neuroanatomy, 12, 83.

Semendeferi, K., Armstrong, E., Schleicher, A., Zilles, K., and Van Hoesen, G. W. (2001). Prefrontal cortex in humans and apes: a comparative study of area 10. American Journal of Physical Anthropology, 114(3), 224–241.

Shin, J., French, L., Xu, T., Leonard, G., Perron, M., Pike, G. B., Richer, L., Veillette, S., Pausova, Z., and Paus, T. (2018). Cell-Specific Gene-Expression Profiles and Cortical Thickness in the Human Brain. Cerebral Cortex , 28(9), 3267–3277.

https://doi.org/10.7554/eLife.61277.sa2

Article and author information

Author details

  1. Richard Gao

    Department of Cognitive Science, University of California, San Diego, La Jolla, United States
    Contribution
    Conceptualization, Data curation, Software, Formal analysis, Validation, Investigation, Visualization, Methodology, Writing - original draft, Writing - review and editing
    For correspondence
    r.dg.gao@gmail.com
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0001-5916-6433
  2. Ruud L van den Brink

    Section Computational Cognitive Neuroscience, Department of Neurophysiology and Pathophysiology, University Medical Center Hamburg-Eppendorf, Hamburg, Germany
    Contribution
    Conceptualization, Data curation, Software, Formal analysis, Validation, Visualization, Methodology, Writing - review and editing
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0002-3142-7248
  3. Thomas Pfeffer

    Center for Brain and Cognition, Computational Neuroscience Group, Universitat Pompeu Fabra, Barcelona, Spain
    Contribution
    Conceptualization, Resources, Data curation, Writing - review and editing
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0001-9561-3085
  4. Bradley Voytek

    1. Department of Cognitive Science, University of California, San Diego, La Jolla, United States
    2. Halıcıoğlu Data Science Institute, University of California, San Diego, La Jolla, United States
    3. Neurosciences Graduate Program, University of California, San Diego, La Jolla, United States
    4. Kavli Institute for Brain and Mind, University of California, San Diego, La Jolla, United States
    Contribution
    Conceptualization, Data curation, Software, Formal analysis, Supervision, Funding acquisition, Investigation, Methodology, Writing - original draft, Writing - review and editing
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0003-1640-2525

Funding

Natural Sciences and Engineering Research Council of Canada (CGSD3-488052-2016)

  • Richard Gao

Katzin Prize

  • Richard Gao

Alexander von Humboldt Foundation (Humboldt Fellowship)

  • Ruud L van den Brink

Alexander von Humboldt Foundation (Feodor Lynen Fellowship)

  • Thomas Pfeffer

Alfred P. Sloan Foundation (FG-2015-66057)

  • Bradley Voytek

Whitehall Foundation (2017-12-73)

  • Bradley Voytek

National Science Foundation (BCS-1736028)

  • Bradley Voytek

National Institutes of Health (R01GM134363-01)

  • Bradley Voytek

School of Medicine, UC San Diego (Shiley-Marcos Alzheimer's Disease Research Center)

  • Bradley Voytek

Halicioglu Data Science Institute Fellowship

  • Bradley Voytek

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

Acknowledgements

We would like to thank all the creators and curators of the publicly available datasets used in this study, as well as the developers of the open-source software packages, without whom none of this would be possible. We also thank Andrea Chiba, Eran Mukamel, and the Voytek Lab for their feedback and suggestions. We would like to additionally acknowledge the Deutsche Forschungsgemeinschaft (DFG) for their funding to Tobias H. Donner (SFB936/A7).

Senior Editor

  1. Laura L Colgin, University of Texas at Austin, United States

Reviewing Editor

  1. Martin Vinck, Ernst Strüngmann Institute (ESI) for Neuroscience in Cooperation with Max Planck Society, Germany

Reviewer

  1. Thilo Womelsdorf

Publication history

  1. Received: July 21, 2020
  2. Accepted: November 22, 2020
  3. Accepted Manuscript published: November 23, 2020 (version 1)
  4. Version of Record published: December 22, 2020 (version 2)

Copyright

© 2020, Gao et al.

This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.

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