Simultaneous, cortex-wide dynamics of up to 1 million neurons reveal unbounded scaling of dimensionality with neuron number

Abstract

The brain's remarkable properties arise from the collective activity of millions of neurons. Widespread application of dimensionality reduction to multi-neuron recordings implies that neural dynamics can be approximated by low-dimensional "latent" signals reflecting neural computations. However, can such low-dimensional representations truly explain the vast range of brain activity, and if not, what is the appropriate resolution and scale of recording to capture them? Imaging neural activity at cellular resolution and near-simultaneously across the mouse cortex, we demonstrate an unbounded scaling of dimensionality with neuron number in populations up to 1 million neurons. Although half of the neural variance is contained within sixteen dimensions correlated with behavior, our discovered scaling of dimensionality corresponds to an ever-increasing number of neuronal ensembles without immediate behavioral or sensory correlates. The activity patterns underlying these higher dimensions are fine grained and cortex wide, highlighting that large-scale, cellular-resolution recording is required to uncover the full substrates of neuronal computations.

Keywords: dimensionality reduction; large-scale imaging; light beads microscopy; neural decoding; neural manifolds; neural population dynamics; spontaneous behavior; spontaneous cortical dynamics; two-photon microscopy; volumetric calcium imaging.

Figure 1.. Light Beads Microscopy (LBM) enables large-scale, volumetric recording of neuronal activity across cortex at cellular resolution.

A. A schematic representation of two possible scenarios: bounded versus unbounded scaling of the measured neuronal dimensionality as a function of number of recorded neurons. B. A schematic of the LBM imaging setup. A 0.5 mm column of light beads is scanned across a lateral FOV with a maximum size of 6 mm (represented by the dashed area on the mouse brain rendering), enabling volumetric recording of neuronal activity at multi-Hertz rate. C. The number of recorded neurons is proportional to the size of the imaged volume, ranging from 6,519 to 970,546 neurons. D. An example single hemisphere recording of 204,798 neurons. Top: the approximate imaging location denoted by a black box. Middle: The standard deviation projection of a plane 183 μm below the cortical surface. Scale bar: 1 mm. Bottom, red inset: zoom in. Scale bar: 100 μm. E. Z-scored heatmap of neural activity from a 3-minute portion of the single hemisphere recording in panel D. The neurons are sorted utilizing Rastermap. F. 30 representative examples of individual neuronal traces from the red highlighted region in E. G and H. Behavior activity corresponding to panels E and F, respectively. The behavior is quantified with total motion energy, defined as the sum of the absolute difference in pixel values between frames.

Figure 2.. Shared variance component analysis (SVCA) reveals unbounded scaling of reliable neural dimensionality.

A. Schematics of SVCA: (i): SVCA splits the neurons into two sets (green and purple). (ii): SVCs are the maximally covarying projections of each neural set. (iii): The reliability of each neural SVC is quantified using the covariance of the two sets’ projections on held-out testing timepoints. B. The normalized variance spectra across neural SVC dimensions decays smoothly. Data from a 3×5×0.5 mm³ single hemisphere containing 146,741 total neurons. C. The percentage of reliable variance quantifies the robustness of each SVC, which eventually decreases at higher SVCs. The data for the same population as in panel B is shown in black. The shuffled data is shown in red, where the neural sets were drawn from distinct recordings. D. Visualization of the reliability of SVCs as a function of neuronal population size. SVC signals for both neural sets from a random sampling of (i): 1,024 and (ii): 970,546 total neurons from a 5.4×6.0×0.5 mm³ bi-hemispheric recording. The percentage of reliable variance in each SVC is shown on the left. E. The reliable dimensionality grows with neuron number. Colored traces show different size neural populations randomly sampled from the population in panel D, with each trace indicating the mean percentage of reliable variance in each SVC over n=10 samplings. F and G. The reliable dimensionality exhibits unbounded scaling with neuron number across different neuronal sampling strategies. The reliable dimensionality represents the number of SVCs a reliability greater than four standard deviations above the mean of shuffled data. Each line indicates the mean over n=10 samplings in a single recording. In F, neurons are sampled randomly from the entire volume, while in G, neurons are sampled in order of their distance from the center of the volume.

Figure 3.. Behavior-related activity is encoded in a low-dimensional subspace of reliable neuronal dynamics.

A. Example behavior videography image, with a box denoting the area in which facial motion energy was monitored. B. The top three behavior PCs for an example mouse. C. Schematics of the prediction of neural SVCs from the behavior PCs. SVCs are predicted from behavior PCs using either a linear or nonlinear (multilayer perceptron, MLP) regressor. While all models predict a single timepoint of neural SVC activity, the behavior PC inputs are either: instantaneous or multi-timepoint. D. Example z-scored SVC timeseries (green) and their linear, instantaneous predictions from behavior PCs (purple) using held-out testing timepoints. While the initial SVCs appear highly predictable from behavior, the higher SVCs (e.g., SVC 64) do not. Scalebars at the right visualize the relative scale of each SVC. E. Only the lowest neural SVCs are predictable from instantaneous behavior. Using the linear, instantaneous reduced-rank regression model, the percentage of each SVC’s reliable variance that is explained by behavior decays rapidly with SVC dimension, such that only 16 ± 8 SVCs (mean ± 95% CI, n=6 recordings with at least 131,072 neurons) show significantly more variance explained by behavior than shuffled data (indicated in red, p<0.05, two-sided t-test). Each line indicates one recording. F. Saturation of predictability of neural SVCs from behavior with increasing neuron number. Using the linear, instantaneous model, the reliable variance explained by behavior saturates around 10,000 neurons in the first 32 SVCs (individual recordings in gray). The remaining SVCs above 32 (orange) are not predictable from behavior at any neuron number. G. The lowest, behavior-related SVCs represent a much greater fraction of the neural variance during epochs of motor behavior. Timepoints were separated into idle and motor epochs (see STAR Methods). The ratio of the fraction of variance explained by each SVC during behaving versus idle epochs is shown. Shown in panels G-I is the mean ± SEM of n=6 recordings with at least 131,072 neurons. H. A comparison of the three different model types: linear, instantaneous; nonlinear (MLP), instantaneous; and linear, multi-timepoint. Including nonlinearities and history both slightly improve the prediction of the first neural 32 SVCs. I. Each neural SVC’s percent reliable variance explained by behavior for the three models. The SVCs for each recording are sorted by the percent of their reliable variance that is explained by behavior. Multi-timepoint models (gray line) predict many more SVCs than the instantaneous models (black and blue lines). The shuffled data for the linear, multi-timepoint models are shown in red. The lines of corresponding color at the top of the plot indicate the number of SVCs that exhibit significantly higher predictability than shuffled data (p<0.05, two-sided t-test). J. Volumetric neural activity patterns and corresponding predictions from behavior. (i) Instantaneous facial motion energy. (ii-iv) Example coarse-grained volumetric neural activity maps (ii), predictions from behavior using a linear, multi-timepoint model (iii), and their difference (iv). Timepoint t₁ occurs during grooming, whereas t₂ is idle. Shown is an example 5×6×0.5 mm³ bi-hemispheric recording. The scale bars in (ii) correspond to 1 mm laterally and 250 μm axially.

Figure 4.. Lack of correlation of high-dimensional neural SVCs with comprehensive behavioral monitoring and sensory-related activity.

A. Example images from simultaneous, all-around behavior monitoring. (i) The left side of mouse. (ii) Left: the right side of the face and pupil. Right: an inset depicting the pupil. (iii) The body of the mouse from underneath, which can freely move on a transparent wheel. Shown as red dots are tracked keypoints. B. Interpretable behavior features and comprehensive behavioral monitoring explained little additional neural variance. Shown is the percentage of reliable neural variance explained by behavior within the first 32 SVCs (black) compared to the higher SVCs (>32, orange) as a function of the complexity of the behavioral tracking (mean ± 95% CI across n=6 recordings). Treadmill: the mouse’s running speed measured via the treadmill; pupil: pupil diameter; DLC: speeds of all tracked keypoints; cameras: corresponding to labels in A. C. Additional behavior features did not explain significantly more neural SVCs. Shown is the percentage of reliable variance within each neural SVC that is explained by behavior utilizing a single camera (black) as in Figure 3, compared to all three cameras (blue, mean ± SEM of n=6 recordings). The lines of corresponding color at the top of the plot indicate the number of SVCs that exhibit significantly higher predictability than the shuffled data (p<0.05, two-sided t-test). D. Schematic of the visual stimulation experiments (see STAR Methods). Three example natural images are shown. E. Timeseries of example SVCs identified from spontaneous (black) or trial-averaged visual (blue) neural activity. The timing of visual stimulus presentations is highlighted in blue. While visual components were highly synchronized to the visual stimulation, spontaneous SVCs did not show stimulus-locked activity patterns. F. Visually-related SVCs are nearly orthogonal to spontaneous SVCs. Shown for a single recording is the distribution of maximum cosine similarity between the spontaneous SVCs and those identified during either another spontaneous epoch (Spont./Spont., black), the visual stimulation epoch (Spont./Vis., blue), or shuffled data (Spont./Shuff., red). Values of 1 indicate identical neural representations, whereas 0 indicates orthogonal and independent representations. G. Orthogonality of spontaneous and visual SVCs across mice. As in panel F, except across n=4 recordings. The Spont./Spont. cosine similarities (black) are significantly higher (p<10⁻⁶, two-sided Wilcoxon rank-sum test) than Spont./Visual (blue). The Spont./Visual cosine similarities are significantly higher (p<10⁻⁶, two-sided Wilcoxon rank-sum test) than the Spont./Shuff. (red).

Figure 5.. Latent neural SVC dynamics represent a continuum of timescales.

A. Example autocorrelation curves for four neural SVCs from the same recording as Figure 2B-C. B. Characteristic dominant timescales within each SVC. The dominant autocorrelation timescale τ, computed by fitting an exponential decay to the autocorrelation, decays with neural SVC dimension. Gray lines show n=6 recordings with at least 131,072 neurons, black indicates their mean. Shown are SVCs with at least 25% reliable variance on average. C. Characteristic dominant timescales increase as a function of the number of recorded neurons. As in B, but with a varying number of randomly sampled neurons. Shown is the mean dominant timescales across recordings, with each neuron number randomly sampled four times per recording. D - G. Example heatmaps of reconstructed neural activity from various SVCs for the recording in Figure 1E. D. Reconstructed activity from SVCs 1–15. E. Reconstructed neural activity from SVCs 16–256, which visually exhibits shorter timescale dynamics and a greater diversity of neuronal coactivation patterns. F and G display the red highlighted insets in D and E, respectively. H and I. Corresponding timeseries for example SVCs used in D and E, respectively.

Figure 6.. Lower and higher neural SVCs form distinct, spatially organized neuronal assemblies.

A. Lower and higher SVCs exhibit distinct cortex-wide neuronal distribution profiles. The lateral spatial distribution of the neurons participating in four example SVCs in a single hemisphere recording containing 315,363 neurons. Scale bar, 1 mm. B. The local homogeneity, which quantities local spatial clustering of participating neurons, decreases with SVC number. The local homogeneity index, computed as the average percent of neighbors within a given distance that are also contributing to that same neural SVC, as a function of the radial distance for the four example SVCs in A. C. The spatial distribution of the participating neurons contributing to four example SVCs in a bi-hemispheric recording with 970,546 neurons. The neurons contributing to each SVC are generally not restricted to single cortical regions or hemispheres. Scale bar, 1 mm. See also Video 6. D. The local homogeneity index as a function of distance shown for the SVCs in panel C. E. The local homogeneity index profiles are consistent across mice. The local homogeneity computed at a radial distance of 30 μm for n=6 recordings. Each recording is shown in gray and their mean is showed in black. The mean of n=6 shuffled recordings is shown in red. F. Hundreds of neurons participate in each neural SVC. Shown is the mean ± 95% CI of the number of participating neurons for each SVC dimension across n=6 recordings (black), compared with shuffled datasets (red).