The principles governing the functional organization and development of long-range network interactions in the neocortex remain poorly understood. Using in vivo widefield and two-photon calcium imaging of spontaneous activity patterns in mature ferret visual cortex, we find widespread modular correlation patterns that accurately predict the local structure of visually evoked orientation columns several millimeters away. Longitudinal imaging demonstrates that long-range spontaneous correlations are present early in cortical development before the elaboration of horizontal connections and predict mature network structure. Silencing feedforward drive through retinal or thalamic blockade does not eliminate early long-range correlated activity, suggesting a cortical origin. Circuit models containing only local, but heterogeneous, connections are sufficient to generate long-range correlated activity by confining activity patterns to a low-dimensional subspace via multisynaptic short-range interactions. These results suggest that local connections in early cortical circuits can generate structured long-range network correlations that guide the formation of visually evoked distributed functional networks.
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The data that support the findings of this study are available from the corresponding author upon reasonable request.
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We thank D. Ouimet and V. Hoke for technical and surgical assistance, P. Hülsdunk for assistance registering and motion-correcting imaging data, and members of the Fitzpatrick and Kaschube laboratories for helpful discussions. This research was supported by US National Institutes of Health grants EY011488 and EY026273 (D.F.), Bernstein Focus Neurotechnology grant 01GQ0840 (M.K.), BMBF project D-USA-Verbund: SpontVision, FKZ 01GQ1507 (M.K.), the International Max Planck Research School for Neural Circuits in Frankfurt, and the Max Planck Florida Institute for Neuroscience.
The authors declare no competing interests.
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Integrated supplementary information
(a). Time-course of spontaneous activity (mean frame ΔF/F) measured during wide-field imaging. Green bars above trace indicate event epochs. Scale bars: 5 sec, 100% ΔF/F. (b). Distribution of event durations across ages (n = 10 animals). Inset: Median and IQR of event duration across age. (c). Time-course of spontaneous activity measured at the single cell level with 2-photon imaging, plotted as mean ΔF/F across all cells. Green bars above trace indicate event epochs. Scale bars: 5 s, 100% ΔF/F. (d). Event durations measured at the cellular level are similar to those observed at a columnar scale with wide-field imaging.
Supplementary Figure 2 Within events, the spatial pattern of spontaneous activity is fairly stable, particularly in young animals.
(a) Spread of activity during an event differs broadly across events. Activated cortical area (threshold=80% of total size of ROI) as a function of time from event onset for sets of representative events (gray lines). Left: from an animal 7 days prior to EO; Right: at EO. A sigmoidal function a/(1+exp(r(t-t0)) was used to fit the traces. (b), Distributions of time of half peak (t0) and rate of activity spread (r*a/4). Rates > 100 mm2/s can hardly be distinguished from instantaneous/uniform rise of activity in our field of view. Events were pooled across all animals and all days. (c). Left: Representative example of spontaneous activity during an event one day after eye-opening (EO). The spatial pattern changes moderately during the first 1.5 s (left and middle). Right: Contour lines delineating active regions across time (represented by color), superimposed on the frame at 1.5s. While there is moderate change, the basic layout is fairly stable. (d). Pattern stability within individual events. Correlations of frames to frame at peak activity, for all awake animals post eye-opening (n = 3). (e). A representative example seven days prior to EO (as in a), showing a similar degree of stability across time. (f). The mean correlation to peak, averaged across events for each animal, remains high and changes relatively little with age (12 individual animals). (g). The average correlation coefficient 1.5s after the peak activity is decreasing during development being highest in the youngest animals. Age groups (markers with errorbars) in (f and g) where EO-10 to EO-6, EO-5 to EO-1, EO, and > EO. Errorbars indicate SD across individuals. Only frames with activity above threshold (threshold=80% of total size of ROI) were considered. Scale bar is 1mm (c,e).
a. The spontaneous activity events contain a moderate number of relevant principal components as shown by the cumulative explained variance. Black lines show 10 individual animals. Gray dashed line indicates 75% variance. b. The number of components needed to explain 75% variance is shown for 10 individual animals (solid black) and the group mean ± SD (13±3, n=10 animals) is shown.
(a). Time course of spontaneous activity for awake animal (mean activity across ROI). (b). Three representative events at times indicated. c. Time-course of spontaneous activity in same animal under anesthesia (0.5–1% isoflurane). (d). Representative events. (e). Three spontaneous activity correlation patterns (Pearson’s correlation) for awake activity (top) and under anesthesia (bottom). (f). Similarity of awake vs. anesthetized correlation patters evaluated at each pixel in ROI. (g). Similarity for shuffled patterns. (h). Similarity of awake patterns calculated from 50% of spontaneous events to patterns calculated from remaining 50% of events.
Supplementary Figure 5 The correlation structure of spontaneous activity more closely resembles the functional layout of iso-orientation domains than ocular dominance domains.
(a). An orientation preference map (OPM). The black-dotted line represents 0°−90° zero contours. (b). An ocular dominance map (ODM). The dark green line represents zero-contours separating contralateral and ipsilateral domains. (c,d). The contours from the OPM in (c) better match the correlation structure (Pearson’s correlation) of spontaneous activity than the contours from the ODM in (d). The seed point in (c) and (d) corresponds to a region preferentially driven by a contralaterally presented horizontal grating. (e,f). For the example animal shown in (a-d), most spontaneous correlation patterns show higher similarity to the layout of the OPM (e) than to the ODM (f). (g). On average, spontaneous correlation patterns show significantly higher pairwise similarity to the OPM than the ODM (p = 0.02, Mann-Whitney U test, two-sided, n = 8 for orientation map and n = 3 for ocular dominance map), but the mean pairwise similarity to both the orientation preference and ocular dominance maps is significantly higher than to control shuffled maps (p < 0.0001, bootstrap test). Dashed lines and shaded bars indicate mean and 5th-95th percentile for control shuffled maps.
(a). Registration across days was achieved by matching radial (descending) blood vessels and computing an affine transform. (b). Correlation patterns (Pearson’s correlation) for same reference point over 8 days prior to eye opening. (c). Spontaneous fractures. (d). Similarity of correlation patterns to the next imaging session (top) or to final day (middle and bottom). (e). Similarity of correlation patterns to reference day (eye opening; EO=0; n=11 animals; error bars: mean ± SEM). Blue region indicates within-day similarity for subsampled reference day correlations. (f). Similarity of spontaneous fracture patterns as a function of relative age (n=11 animals; error bars: mean ± SEM).
Supplementary Figure 7 Long-range correlations in spontaneous activity persist in the absence of retinal activity.
(a). Cortical spontaneous activity was measured before and following retinal inactivation via intraocular injection of TTX. (b). Cortical responses (averaged across all pixels in ROI) to full-field luminance changes before (left) and after (right) retinal inactivation. Scale bars: 5 sec, 0.5 ΔF/F. (c). Time-course of spontaneous activity for mean of all pixels before (top) and after (bottom) inactivation. Scale bars: 30 sec, 0.15 ΔF/F. (d). Representative spontaneous events (left) and correlation patterns (Pearson’s correlation) (right) before (top) and after (bottom) inactivation. (e). Similarity of correlation structure in representative experiment before and after inactivation for all cortical locations. (top) and versus shuffled data (bottom). Scale bar 1mm (d,e). (f). The spatial structure of spontaneous events following LGN inactivation shows significantly more similarity across events than shuffled controls (p < 0.001 vs. shuffle, bootstrap test, n = 3 animals; error bars: mean ± SEM).
Supplementary Figure 8 Networks with homogeneous and isotropic connections generate modular and regular activity patterns, but do not account for the long-range correlations observed in early visual cortex.
(a). Model (i): The spatial profile of lateral connections follows an isotropic Mexican hat in all neurons. (b). With constant input drive, the activity converges to a regular hexagonal patterns (two representative solutions are shown; simulations performed on a 100×100 grid, see Methods). (c). Correlations (Methods equation (1)) between remote sites are only moderate, owing to the fact that all translated and rotated hexagonal patterns are solutions as well (computed over 100 solutions). (d). Model (ii): An excitatory (E) and inhibitory (I) population. Connections within E and from E to I both follow the same isotropic Gaussian profile. Connections from I also follow Gaussian profiles, but have a shorter spatial range. (e), Representative solution of excitatory (left) and inhibitory (right) population (parameter setting: aee = 22.2, aei = aie = 21.6, aii = 20.8, σe = 1.9 σei = 1.4, σii = 0.6); simulations performed on a 80×80 grid, see Methods). (f). Correlation pattern (as in c) for the excitatory population. (g). Representative example of a correlation pattern observed in ferret visual cortex 7 days prior to eye-opening. (h). For the correlation patterns in the early cortex the peak values decay significantly slower with spatial distance from the seed points (fits, dashed red; n = 5) than in model (i) (a) (104 patterns, p < 0.0097, one-sided bootstrap), model (ii) (d) (109 patterns, p < 0.009, one-sided bootstrap) and in an ensemble of randomly shifted and rotated ideal hexagonal patterns (100 patterns, p < 0.01, one-sided bootstrap). To assess significance we used bootstrap tests for all three comparisons, see Methods. All correlations were baseline corrected, see Methods. Scale bars: domain spacing 1Λ (b, c, f, g); 1 mm (h).
(a, c, e, g): Model analysis; (b, d, f, h): Comparison model vs. experiment. (a). Long-range organization of correlation patterns (left) is quantified by fitting an exponential decay to the peaks (local maxima) in the correlation pattern as a function of their distance to the seed point, using all correlation patterns. (b). Left: Shaded region in the diagram with systematically varied heterogeneity and input modulation indicates the parameter settings in which the model values for spatial scale correlation lie within the interval (mean ± SD) given by the experimental data (n=4 animals, 5 experiments). The parameter setting of the example shown in Fig. 7c (red triangle in 7d) is highlighted. Right: Comparison of dimensionality (Methods equation (16)) for indicated model parameters and experimental data. (c). The geometrical layout of correlation patterns (left) can change drastically over only a short distance (middle). Rate of change reveals organization of fractures (right). Region of fractures shown is highlighted by black box in correlation patterns (left). (d). Comparison of fracture magnitude with experimental data (n = 4 animals, 5 experiments). (e). Covariance matrix (middle) over 100 spontaneous activity events (left) shows that different locations co-vary. A moderate number of components (right) is needed to explain 75% of the variance indicating low dimensional activity patterns. (f). Comparison of dimensionality for model with experimental data (n = 4 animals, 5 experiments). (g). Left: The anisotropic structure of local correlation (that is the peak around the seed point) is quantified by fitting an ellipse to the 0.7 contour line (least-square fit) and computing its eccentricity. Right: The eccentricity of local correlation shows a similar distribution in data and model. (h). Comparison of eccentricity of local correlation with experimental data (n = 4 animals, 5 experiments).
Supplementary Figure 10 Constraining activity patterns to low dimensionality can generate strong correlations over large distances, pronounced fractures, and anisotropic local correlations.
(a). Spontaneous activity patterns are significantly lower-dimensional than shuffled controls (n = 27 experiments of 10 animals, p = 0.01 one-sided test). (b). A statistical model generates pattern ensembles with dimensionality k by superposition of k orthonormal basis patterns with random weights. (c). The strength of long-range correlations, fractures, and the eccentricity of the local correlations all increase with decreasing dimensionality. Blue lines (mean ± SD) indicate the range of dimensionality in the data (a). (d,e,f). The correlation pattern computed over an ensemble of n = 10000 patterns and dimensionality d = 11 expresses long-range correlations (d, left) and pronounced fractures (d, right). Example spontaneous correlation pattern (left) and fractures (right) for dimensionality d = 3 (e), and d = 41 (f). Scale bar is 1Λ.
Supplementary Figure 11 Systematic overview over different variants of the two types of circuit models studied, showing the correlation structure they produce.
(a), Columns (left to right): schematic diagram of model, a typical activity pattern, a representative correlation pattern (Pearson’s correlation), correlation fractures, and the spatial scale of correlations for the value of heterogeneity of connections, H, used (open symbol) and for varying H (closed symbols). The yellow circle on top of the activity patterns indicates the size of the average local connectivity. Rows (top to bottom): (1) The model shown in Fig. 7 (Mexican hat connectivity, H = 0.8, η = 0.016). (2) As in (1), but here the properties of the Mexican hat vary smoothly across space, on a spatial scale Λ marked by the scale bar on the activity pattern. Results are similar to the discontinuous version (1). (3) The model with two separate populations for inhibitory and excitatory neurons in the discontinuous, heterogeneous regime, analogue to (1) (H = 0.7, η = 0.01). In the heterogeneous regime, all three models (1–3) agree quantitatively with experiment. (4) Ideal hexagonal patterns, sampled from the distribution known to be the solution set for isotropic, homogeneous Mexican hat connectivity. Rows (5) and (6): Numerical solutions of the isotropic homogeneous versions of models (1) and (3) respectively. For (4)-(6) the correlation structure is inconsistent with experiment. The yellow circle on top of the activity patterns indicates the size of the average local connectivity (MH models only). All scalebars are 1Λ. (b), Quantitative comparison of models (1) to (6) with experiment. Shown are (from left to right; mean (solid line) ± SD (shaded region)): the fracture strength, the spatial scale, the average at correlation peaks at 2Λ subtracted by the shuffle average correlation, the dimensionality, and the mean eccentricity (see Methods). The heterogeneous network models (n = 10 simulations) all lie within the experimentally observed range of values (n = 5 experiments from 4 animals) for all five quantities, while this is not the case for models with homogenous, isotropic connectivity (n = 10 simulations).
(a). Coronal section showing widespread GCAMP6 expression in layer 2/3 neurons of primary visual cortex (Green - GCAMP6s / Red - NeuN). (b). Expanded view of region indicated in (a). Scale bars are 1 mm (a) and 0.5 mm (b). Similar expression patterns were observed in 5 of 5 animals processed for histology.
Supplementary Figure 13 Correlation patterns from all events are highly similar to those computed from large events only.
(a). Example correlation pattern (Pearson’s correlation) calculated over only the maximally active frames of large events (left) is highly similar to correlation pattern from same seed point calculated over all frames of all events (right). (b). The average similarity between all correlation patterns within the ROI are shown for n = 12 animals, n = 33 experiments throughout development.
(a). Correlation pattern (Pearson’s correlation) from all events (393 events) for a seed point indicated in green. (b). Two example correlation patterns produced by randomly subsampling 10 of 393 events. (c). Similarity (second order correlation) of subsampled correlation patterns to the pattern computed from all events (n = 6 experiments with > 100 spontaneous events; error bars: mean ± SEM). Correlation similarity of 0.5 is reached with approximately 10 events. Gray markers indicate individual animals; black marker indicate mean. (d). Similarity of subsampled correlation patterns to complete pattern as a function of the fraction of events sampled for 5, 10, 20, 30, or 50 events (blue, orange, yellow, purple, and green curves respectively). Subsamples of 10 events asymptote at a similarity of approximately 0.5, even for cases with a large number of events (in which the fraction of events sampled is very low), indicating that 10 events is sufficient to capture major features of correlation structure.
Representative spontaneous events shown as ∆F/F (top) and after high-pass filtering (bottom). Modular nature of spontaneous events is clearly evident already prior to filtering.
Supplementary Figures 1–15
List of experiments used in analysis
Spontaneous activity in the awake visual cortex is highly dynamic and modular. Ongoing spontaneous activity visualized through wide-field calcium imaging shows highly dynamic distributed sets of active domains spanning millimeters. This approach affords high signal-to-noise measurements of large-scale spontaneous activity, with active domains clearly visible. Spontaneous activity was recorded in a dark room, while viewing a black screen. Trace shows activity (ΔF/F) for a single pixel located at center of blue box. Green bars above trace indicate event epochs, with red dots indicating the maximally-active frame for each event used to compute correlations. Movie frames are raw fluorescence images. Movie is shown in real time, scale bar: 1mm. Similar activity patterns were observed in 5 of 5 experiments
Spontaneous correlation patterns are highly diverse and show both fine- and large-scale organization across the cortical surface. Moving the correlation seed point across the cortical surface reveals a broad range of correlation patterns, indicating the presence of multiple distributed functional networks within the visual cortex. Across most of the cortical surface, large-scale correlation patterns change smoothly, however this progression is occasionally punctuated by abrupt shifts in correlation structure between nearby seed points, revealing the fine-scale precision of distributed functional networks. Scale bar: 1mm. Similar results were observed in 39 of 39 experiments
Spontaneous activity in the anesthetized visual cortex shows large-scale modular activity patterns. Raw fluorescence images showing spontaneous activity in the same ferret as Supplementary Movie 1 under isoflurane anesthesia (0.5–1%), during viewing of a black screen. Movie is shown in real time, scale bar: 1mm. Trace shows activity (ΔF/F) for a single pixel located at center of blue box. Green bars above trace indicate event epochs, with red dots indicating the maximally-active frame for each event used to compute correlations. Similar results were observed in 39 of 39 experiments
Spontaneous activity at the cellular level is modular and locally coherent. 2-photon imaging of spontaneous activity in the awake ferret cortex during viewing of black screen shows adjacent regions of co-active neurons. Images are shown as raw fluorescence, temporally smoothed with a 167 ms median filter. Movie is shown in real time, scale bar: 200 µm. Trace shows mean population activity (ΔF/F) for all cells in FOV. Green bars above trace indicate event epochs used to compute correlations. Similar results were observed in 5 of 5 experiments
Spontaneous activity in the early visual cortex shows widespread modular activity patterns. Spontaneous activity in ferret visual cortex imaged at P23 under isoflurane anesthesia (0.5–1%) during viewing of black screen. Images are shown as ∆F/F0, clipped to 0–150%. Movie is shown in real time, scale bar: 1mm. Similar results were observed in 8 of 8 animals imaged at P26 or earlier
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Smith, G.B., Hein, B., Whitney, D.E. et al. Distributed network interactions and their emergence in developing neocortex. Nat Neurosci 21, 1600–1608 (2018). https://doi.org/10.1038/s41593-018-0247-5
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