Modular subgraphs in large-scale connectomes underpin spontaneous co-fluctuation events in mouse and human brains

Abstract

Previous studies have adopted an edge-centric framework to study fine-scale network dynamics in human fMRI. To date, however, no studies have applied this framework to data collected from model organisms. Here, we analyze structural and functional imaging data from lightly anesthetized mice through an edge-centric lens. We find evidence of "bursty" dynamics and events - brief periods of high-amplitude network connectivity. Further, we show that on a per-frame basis events best explain static FC and can be divided into a series of hierarchically-related clusters. The co-fluctuation patterns associated with each cluster centroid link distinct anatomical areas and largely adhere to the boundaries of algorithmically detected functional brain systems. We then investigate the anatomical connectivity undergirding high-amplitude co-fluctuation patterns. We find that events induce modular bipartitions of the anatomical network of inter-areal axonal projections. Finally, we replicate these same findings in a human imaging dataset. In summary, this report recapitulates in a model organism many of the same phenomena observed in previously edge-centric analyses of human imaging data. However, unlike human subjects, the murine nervous system is amenable to invasive experimental perturbations. Thus, this study sets the stage for future investigation into the causal origins of fine-scale brain dynamics and high-amplitude co-fluctuations. Moreover, the cross-species consistency of the reported findings enhances the likelihood of future translation.

Fig. 1. Schematic illustrating edge time series construction and clustering.

a Array of parcel time series. Rows and columns correspond to parcels (ordered by anatomical division) and frames, respectively. b Whole-brain functional connectivity is typically estimated as the correlation matrix of parcel time series. That is, the weight of the functional connection between nodes i and j is specified as the product-moment correlation coefficient, r_ij. c The procedure for estimating r_ij entails z-scoring each parcel time series, calculating their elementwise product—i.e., z_i(1) × z_j(1), …, z_i(T) × z_j(T)—and taking the mean of those products (sum divided by the number of samples divided by one). Omitting the averaging step yields the co-fluctuation (or edge) time series r_ij(t) = [z_i(1) × z_j(1), …, z_i(T) × z_j(T)], whose elements encode time-varying changes in the weight of the connection between nodes i and j. In this panel, we show time series for regions i and j (green and blue curves) and their corresponding edge time series (gray). d We can calculate edge time series for all node pairs (edges) in the network and arrange them as rows in an edge-by-frame matrix. e Previous studies identified infrequent and short-lived high-amplitude bursts. These bursts or events can be detected by calculating the root mean square (RMS) across all edges at each frame and identifying peaks whose amplitude exceeds that of a null distribution (estimated using the same procedures as empirical RMS but starting with circularly shifted parcel time series). f The co-fluctuation patterns expressed during events are very different than those expressed during low-amplitude frames. Here, we highlight approximately 175 frames and show whole-brain co-fluctuation matrices for three local maxima (events; red border) and three local minima (troughs; gray border). g Although no two events are identical in terms of co-fluctuation patterns, events can be grouped (broadly) into clusters—i.e., groups of co-fluctuation patterns whose mutual similarity to one another exceeds what would be expected by chance. We detect them by computing the similarity (concordance) between all pairs of events and directly clustering the resulting matrix using a hierarchical algorithm. Here, we highlight two large clusters and their respective centroids (the mean co-fluctuation pattern across all events assigned to each cluster).

Fig. 2. Differential correlation between frame categories and static FC.

Previous studies have documented a strong correspondence between static FC and high-amplitude frames (events). Here, we compare four categories of frames: high-amplitude peaks (Events), peaks that are not considered high-amplitude (Peaks), low-amplitude frames (Troughs), and random selections of frames (Random). a The diagonal shows example co-fluctuation matrices from each of the four categories as well as static FC. The off-diagonal blocks show example scatterplots between each pair of categories. Matrices and scatterplots depicted here come from a single mouse and for the sub-sampled categories, a single sub-sample. b Example correlations from a single subject over 100 random sub-samples from within each category. Each sub-sample contained the same number of frames as the number of detected events. c Median correlations aggregated across all 18 mice. Lines connect data points from the same mouse. Vertical lines represent ±1 standard deviation. Error bars in panels b and c correspond to one standard deviation.

Fig. 3. Hierarchical clustering of high-amplitude co-fluctuations.

a Concordance matrix. Rows and columns represent events co-fluctuation matrices aggregated across subjects. b Hierarchical clustering of co-fluctuations patterns. Gray circles represent clusters—groups of co-fluctuation patterns derived using a variant of modularity maximization—and lines indicate parent–child relationships. c Co-assignment matrix (counts) from hierarchical clustering. Panels d–f represent centroids for the three large clusters detected at hierarchical level 2. Here, centroids refer to the mean across all co-fluctuation patterns assigned to a given cluster. Panels g–i depict the largest eigenvector of each matrix projected back into anatomical space.

Fig. 4. Linking high-amplitude events to structural connectivity.

Panels a, d, and g represent bipartition communities for each of the three largest event cluster centroids in hierarchical level 2. Panels b, e, and h force-directed layouts of the induced sub-graph containing only nodes in either of the bipartition communities. The size of nodes is proportional to their weighted degree (strength). Panels c, f, and i show the induced modularity of each sub-graph.

Fig. 5. Replication of mouse findings using human MRI data.

a Hierarchical clustering of 12854 event co-fluctuation patterns from 95 participants in the Human Connectome Project. Panels b, c, and d show cluster centroids for the three largest event clusters in hierarchical level 2, their projection onto the cortical surface, and the structural modularity induced by a bipartition derived from the co-fluctuation matrix. Here, we include a spatially constrained permutation as a null model—i.e., a spin test^,. Panels e–j show analogous plots for cluster centroids 2 and 3.