Multiplexed subspaces route neural activity across brain-wide networks

Abstract

Cognition is flexible, allowing behavior to change on a moment-by-moment basis. Such flexibility relies on the brain's ability to route information through different networks of brain regions to perform different cognitive computations. However, the mechanisms that determine which network of regions is active are not well understood. Here, we combined cortex-wide calcium imaging with high-density electrophysiological recordings in eight cortical and subcortical regions of mice to understand the interactions between regions. We found different dimensions within the population activity of each region were functionally connected with different cortex-wide 'subspace networks' of regions. These subspace networks were multiplexed; each region was functionally connected with multiple independent, yet overlapping, subspace networks. The subspace network that was active changed from moment-to-moment. These changes were associated with changes in the geometric relationship between the neural response within a region and the subspace dimensions: when neural responses were aligned with (i.e., projected along) a subspace dimension, neural activity was increased in the associated regions. Together, our results suggest that changing the geometry of neural representations within a brain region may allow the brain to flexibly engage different brain-wide networks, thereby supporting cognitive flexibility.

Fig. 1. Interactions between brain regions are organized into subspaces.

A Schematic of experiments combining recordings from four Neuropixels probes across cortical and subcortical regions and simultaneous widefield calcium imaging across dorsal cortex. Created in BioRender. Tafazoli, S. (2025) https://BioRender.com/y38t274. B Field-of-view of widefield imaging showing the dorsal cortex and four craniotomies with implanted electrodes (blue arrows). White lines outline cortical regions (see Fig. S1). R, L, A and P denote animal’s right, left, anterior and posterior. C Reconstructed probe locations from six recordings in three mice; colors indicate mice. D Correlogram showing correlation between pairs of cells for an example recording. Colored bars along axes indicate brain regions. E Schematic of reduced rank regression (RRR) to predict activity of each neural population. Spontaneous spiking activity was binned to 133 ms windows, and the average response was removed so that moment-to-moment spiking variability of one region was predicted using spiking variability of all other regions. F Cross-validated performance of all RRR models (n = 630 datasets, see Methods). G Schematic showing that a shared subspace is spanned by a set of dimensions within the neural activity of the predicted region that are correlated with neural activity in other regions. H, I A small subspace of neural activity within a region was shared with other regions. H Cumulative percent of the explainable variance captured by each dimension of the RRR model (see Methods). Red and gray lines show mean performance and cross-validated performance from n = 84 datasets, respectively. Dashed line shows 80% of explainable variance. I Bootstrapped distribution showing the number of ‘shared’ subspace dimensions and the number of ‘local’ dimensions within a region. Dimensionality was estimated as the number of dimensions of a RRR model that reliably predicted variance in neural activity in withheld data (using a subset of n = 25 neurons to balance across areas, decreasing the overall dimensionality estimate, see Methods). Dots show bootstrapped mean (n = 1000). Colors correspond to regions. Dotted lines show 1:1 and 2:1 ratio (red and grey, respectively). J Violin plots of estimated ratio of local-to-subspace dimensionality for each recorded region. Full distribution shown. See also Figs. S1-S4.

Fig. 2. Subspaces between areas reflect brain-wide networks.

A Schematic showing two hypotheses of how shared subspaces could integrate neural activity across brain regions. Subspaces may reflect pairwise interactions between regions (top) or may reflect networks of regions interacting through a single dimension (bottom). B Schematic of how beta weights of the regression model estimate the contribution of neurons in a source region to a target region. C Example distribution of beta weights (x-axis) across all neurons (y-axis) contributing to predicting activity along the first dimension of the shared subspace in visual cortex. Left plot shows distribution across all regions. Right plots show density histogram of weights within each region (normalized to account for different numbers of neurons: dotted lines added to aid visualization). D Cumulative distribution of the percent of neurons within a source area contributing to the beta weights along the first dimension of the visual subspace (as in C). X-axis shows the beta weights across all neurons, ordered from strongest to weakest. Lines show mean, shaded region shows bootstrapped 95% confidence interval from n = 84 datasets (see Methods). Inset shows the mean and confidence intervals of the area under the curve (AUC) for the contributions from each region. P values were p < 0.001; p = 0.026; p < 0.001 for RSP, SS, and HPC, respectively; one-sided bootstrap test versus an AUC of 0.5, n = 1000 permutations. E The relationship between subspace activity and motor activity was quantified by correlating the activity along each subspace dimension with the motion energy of animals’ nose (blue), whisker-pad (green), and shoulder (pink; see Methods). F Bootstrapped distribution showing the average correlation (y-axis, z-transformed) between motor activity and activity along each subspace dimension (x-axis) across datasets. Subspace dimension 1 was significantly more correlated with motor activity than all other dimensions (p < 0.001, one-sided bootstrap test, n = 1000 bootstraps from n = 630 datasets). See also Figs. S5-S6.

Fig. 3. Schematic of interactions between regions.

A Schematic showing the network of strongest (top) and second strongest (bottom) interactions between areas, across all datasets. Strength of contributions were taken as the AUC of beta weights (as in Fig. 2D, except averaged across all subspace dimensions). Colored lines indicate the subspace target region, e.g., the strongest contribution to FMR is from HPC (purple line). B Network graph showing the two strongest interactions between brain areas. Thicker/thinner lines show the first/second strongest interaction, respectively. See also Fig. S7.

Fig. 4. Subspaces engage independent but overlapping cortical networks.

A Electrophysiology was combined with widefield calcium imaging of population-level neural activity across cortex. Variance in neural activity projected along each subspace dimension was correlated with imaging signal to identify the subspace-associated cortical networks. To better match the time constants of imaging and electrophysiology, we used a feedforward neural network to estimate the neural activity underlying the imaged calcium signal (see Methods). Created in BioRender. Tafazoli, S. (2025) https://BioRender.com/y38t274. B Representative cortical maps for different subspace dimensions. Rows are different regions. Numbers indicate the subspace dimension corresponding to each map. Color intensity of map indicates the strength of correlation between fluorescence activity at that pixel and the spiking activity along a given subspace (see Methods). Transparency of the color in each image is thresholded at significance such that non-significant pixels are more transparent. For visualization, color is scaled independently for first network versus subsequent networks. Colored circles around numbers indicate cluster identity of subspace networks as determined through clustering analyses (Figs. 5 and S13). Note, presented data is from an example dataset and ordering may differ between recordings. C Similarity of cortical networks. Similarity (x-axis) was computed as the percentage of overlap in significant pixels between cortical maps across all subspace dimensions for a region (see Methods). Y-axis shows the fraction of all compared subspaces. Gray bars show all data (across regions, n = 630 dataset). Colored lines show mean distribution of each brain region (n = 8) across datasets. See also Figs. S8-S13.

Fig. 5. Canonical cortical subspace networks.

A Similarity matrix for all subspace networks, sorted by cluster identity shown in B. Cluster groupings are shown along the x and y axes. Colorbar shows correlation of subspace network across the entire spatial map. White boxes indicate the within-cluster pairs of subspace networks. B Median subspace network for each cluster. Color axis shows strength of correlation. Only pixels that were valid across all recordings were used (i.e., the map of vasculature is combined across all recordings). Clusters were labeled according to the number of subspace networks in each cluster (descending). See also Fig. S13.

Fig. 6. Cortex-wide subspace networks are multiplexed.

A Subspace networks uniformly involved regions across cortex. Map shows the average fraction of subspace networks that were significantly correlated with each pixel (out of 10 possible maps per subspace, averaged across datasets from all target regions, n = 630). B Honeycomb plots showing multiplexing of subspace networks across cortical areas. Each hexagon shows the dimensions of a subspace that significantly engaged over 25% of pixels within that hexagonal parcel of the cortical surface. For visualization, only a subset of dimensions (2-7) is shown. As in Fig. 4B, data is from an example dataset and so numbering and exact maps may vary across recordings. See also Figs. S11-S13.

Fig. 7. Neural responses are aligned to the shared subspace between two regions when those regions are engaged.

A Left plots show pattern of cortical fluorescent activity during motif A (top) and motif B (bottom). Right plots show the neural response in whisker (WHS), somatosensory (SS), and retrosplenial (RSP) cortex (from electrophysiological recordings) during each motif. Arrows reflect bidirectional interactions between brain regions since reduced rank regression cannot specify directionality. Dot and error bars indicate mean and standard error of baseline-normalized spiking activity across neurons during each motif for an example recording (SS, n = 29; WHS, n = 230; RSP, n = 190 neurons, see Methods; p-values estimated with two-sided paired signed-rank test). B Projection of neural activity in three-region neural space during motif A (red) and B (blue). Average neural activity in each region, during each motif, was projected along the first principal component (PC; see Methods). Arrows show evolution of neural activity over time following onset of each motif (motif A, n = 336 occurrences; B, n = 266; 133 ms timesteps). Top inset shows planes fit to this PC space projection. Bottom inset shows bootstrapped distribution of angle between projection of activity (n = 1000 bootstraps across motif occurrences). C Schematic of proposed mechanism wherein aligning a neural response to a subspace dimension propagates activity along the associated subspace network. Arrows reflect the predicted changes in the alignment during different motifs. See also Fig. S14.

Fig. 8. Neural responses were aligned to shared subspaces across regions, motifs, and recordings.

A Bootstrapped distribution of the average alignment between the neural response in SS, WHS, or RSP (denoted in bold) during motif A or B and the subspace between that region and another region (indicated by bidirectional arrows along top). Lower angles (y-axis) reflect stronger alignment. N = 1000 paired bootstraps. Panels reflect data from the same example recording as Fig. 7. B Distribution of average difference in alignment angle between motif A and B across recordings for SS, WHS, and RSP (n = 16 comparisons). Difference in angle was computed relative to the motif with greater engagement of a target brain region, i.e., motif A minus B for comparisons involving SS, but motif B minus A for comparisons involving RSP. Thus, negative values indicate that the motif with greater engagement exhibited better alignment between local neural activity and subspace activity. Vertical red lines show mean (solid) and 95% CI of mean (dashed). C Bootstrapped distribution of difference in alignment from multiple pairs of motifs and trios of brain regions across recordings (see Fig. S14). Orange violin shows the overall alignment across all comparisons (120 alignment comparisons, see Methods). Overall, the local neural representation and the associated subspace dimension were more aligned when the stronger motif was engaged (p < 0.001). Gray violins show alignment distribution for example pairs of motifs/trios of regions (n = 32–48 comparisons each, see Methods). Individually, neural activity during all compared motifs/regions exhibited significant alignment to the associated subspace (p < 0.001; p = 0.009; p < 0.001; p = 0.01; p = 0.035; p = 0.048, for plots top-to-bottom, respectively). # indicates the example motif pair/region trio used in A, B and Fig. 7. For all panels p-values estimated with one-sided bootstrap test, n = 1000 bootstraps. See also Fig. S14.

Fig. 9. Decreasing the angle between the neural response and subspace increases projection of neural response onto subspace.

A Projection of neural activity during Motif A and Motif B along both the first PC of activity in SS (x-axis) and the first SS-WHS subspace dimension (y-axis; as in Fig. 7). Greater alignment between the local neural response and subspace during Motif A was associated with a larger neural response along subspace. The domain and range of neural response during both motifs are shown by red and blue lines along axes. Points show timepoints of the neural activity during each motif (as in 7B). Line and shaded region show least squares fit and 95% confidence bounds, respectively. B Modest rotations in the neural representation can lead to large changes in the projection of the neural response along the subspace. Upper plot shows a relatively modest change in the alignment between the local representation of activity in SS (taken as the first PC) and the SS-WHS subspace dimension for Motif A (red) and Motif B (blue). Lower plot shows this translates into a large change in the response when projecting onto the SS-WHS subspace. The efficacy of the neural response is measured as the angle between the projection along the SS-WHS subspace and the first PC of the local response within SS. From example dataset shown in Fig. 7. Dotted line in B (lower) indicates 45 degrees (i.e., perfect alignment). See Fig. S15.

Fig. 10. Schematic modeling how changes in local representations can propagate activity to multiplexed subspace networks.

A Individual brain regions are connected to a network of independent but overlapping regions (i.e., multiplexed networks). Different style lines show the network of regions that are functionally connected through a shared subspace network. B Different aspects of the neural representation within a brain region can engage different subspace networks when aligned with different subspace dimensions. This is schematized as purple-to-pink and square-to-circle gradients being differentially aligned with different subspace dimensions, with gray arrows indicating the alignment of neural activity within a region. For example, aligning a region’s neural activity with subspace dimension 1 propagates ‘color’ information to the associated network. Conversely, alignment to subspace dimension 2 propagates ‘shape’ information to a different network.