Extended Data Fig. 5: Visualizing directions of hippocampal graph transformations in the network co-firing space.

a, Computing the topological distances that separate co-firing graphs across the six task sessions. The co-firing graph of each task session was used to define a 6-dimensional vector of topological Riemannian Log-Euclidean distances to the other co-firing graphs obtained that day (for example here illustrated re-exposure versus exposure), including itself (see Methods). For each 6-session task day, this procedure thus gives a 6 x 6 matrix of topological distances. All distance matrices were then stacked together to form a 6 x N matrix (with N the number of total graphs, that is N = 17 days x 6 sessions = 102) onto which we apply a dimensionality reduction technique (PCA, ICA or MDS). b,c, Segregation of co-firing graphs using Independent Components Analysis (ICA; b) or Multidimensional Scaling (MDS; c). (b) ICA applied to the same matrices of topological distances used with PCA in the CPP dataset (Fig. 2) as another dimensionality reduction method to visualize axes explaining across-session variance in co-firing motifs. Note that co-firing graphs computed for the exposure and the re-exposure overlap on the first two independent components (IC) as they do along the first principal component (Fig. 2c–e); co-firing graphs are separated across the 4 CPP task events, as they are along the second principal component (Fig. 2c–e). (c) MDS also applied to the same matrices of topological distances used with PCA in the CPP dataset (Fig. 2); this method preserves the six-dimensional distances between co-firing graphs and maps them onto a 2D plane. Note that the co-firing graphs computed for each task session of each CPP day are well separated, indicating the existence of multiple axes along which co-firing patterns change across CPP task events. d,e, Here the Pearson correlation coefficient is used instead of the Riemannian Log-Euclidean distance to compute the topological distance between co-firing graphs across the six CPP task sessions. In (d) the average topological distance matrix (left) and its first three PCs (right) are shown. In (e) the segregation of the six CPP task sessions is shown using the PCs shown in (d). Note that for both the Riemannian Log-Euclidean distance (Fig. 2c–e) and the Pearson correlation coefficient (d,e) approaches, the PCA of the CPP dataset reveals that the variance in hippocampal co-firing segregated the familiar enclosure from the whole CPP test apparatus along PC1. Surprisingly, PC1 did not segregate the two compartments (Nov1 and Nov2) that formed the CPP apparatus on each day. This suggests that these compartments were treated together as one spatial continuum along PC1 because when the animal first encountered the CPP apparatus, these two compartments were equally novel and physically connected by the bridge during the pre-test. Therefore, a refined interpretation why along PC1 the two CPP compartments are clustered together (and different from the familiar enclosure) is that neuronal co-firing along this axis also accounts for spatial familiarity versus novelty. f,g, PCA with the two compartments of the CPP apparatus considered separately during both pre-test (f) and CPP test (g) sessions. Here, we computed a co-firing graph using the spike trains associated with the visits of each CPP compartment during both test sessions, thus obtaining one co-firing graph per individual compartment (Nov1 versus Nov2) during each test session. Projecting the resulting four co-firing graphs (two for pre-test and two for CPP test) onto the PCA axes obtained when considering the CPP apparatus as a whole entity (Fig. 2e) shows that PC2 segregates co-firing patterns related to each CPP compartment during test compared to pre-test. Likewise, PC2 segregated the two CPP compartments when explored separately during the conditioning sessions where we removed the bridge (Fig. 2e). h-j, The topological distance projections of the co-firing graphs from the other 6-session tasks. As for the CPP dataset, multiple PCs accounted for the variance in co-firing across the 6 sessions of each task. Note, however, that co-firing variance relates to the specifics of each task, and so is each set of PCs and their interpretation. For each task, we used the PCs explaining at least 80% of the total variance to project the co-firing graphs topological distance. The variance explained by these PCs is: “Novel context only” PC1=57%, PC2=19% and PC3=8%; “Spontaneous Place Preference” PC1=52%, PC2=18% and PC3=16%; “Familiar context with reward experience” PC1=69%, PC2=15%; and “CPP” PC1=48%, PC2=19% and PC3=14% (Fig. 2e).