Dynamic reconfiguration of the default mode network during narrative comprehension

Does the default mode network (DMN) reconfigure to encode information about the changing environment? This question has proven difficult, because patterns of functional connectivity reflect a mixture of stimulus-induced neural processes, intrinsic neural processes and non-neuronal noise. Here we introduce inter-subject functional correlation (ISFC), which isolates stimulus-dependent inter-regional correlations between brains exposed to the same stimulus. During fMRI, we had subjects listen to a real-life auditory narrative and to temporally scrambled versions of the narrative. We used ISFC to isolate correlation patterns within the DMN that were locked to the processing of each narrative segment and specific to its meaning within the narrative context. The momentary configurations of DMN ISFC were highly replicable across groups. Moreover, DMN coupling strength predicted memory of narrative segments. Thus, ISFC opens new avenues for linking brain network dynamics to stimulus features and behaviour.

the resting-state data (r=0.01), but they become much more similar in the intact story condition (r=0.88). (D) The number of subjects needed in order to isolate reliable ISFC patterns for the intact story (blue) and rest (gray) conditions.

Supplementary Figure 5 | Classification of intervals in a block-design theory-of-mind (TOM) task using DMN fingerprints.
To test ISFC classification performance in a block design paradigm we ran a theory of mind (ToM) localizer paradigm on 36 subjects. The ToM is a standard localizer 6 , developed to localize high-order areas which respond more strongly when subjects read a paragraph that requires an inference about beliefs held by different protagonists ("Belief" or "ToM" condition, 10 stories, each ~10sec, 5 repetitions) vs. stories describing photographs and maps with no belief content ("Photo" or "non-ToM" condition, 10 blocks, each ~10sec, 5 repetitions). First, using seed-based ISFC (seed in the precuneus), during the belief condition, we localized a set of brain areas including the temporal parietal junction, precuneus   t+90s] with a step-size of 1.5 s between windows). The ISFC across 12 subjects is shown for the intact movie (blue), and for the replication group of 12 subjects (green). (green). This division is compatible with prior publications that divide the DMN into two subnetworks: the core network and the medial temporal lobe (MTL) subsystem 8,9 . Finally, the two other networks resembled the division between the ventral and dorsal language streams proposed by Hickok and Poeppel 10,11 and were labeled, provisionally and tentatively, as ventral language network (vLANG , blue) and dorsal language network, respectively (dLANG, purple).

Supplementary Figure 10 | Voxel-Based ISFC correlation matrices reveal fine-grained
stimulus-dependent interaction within networks. We tested whether ISFC analysis can be extended to measure the stimulus-induced inter-regional correlation patterns between the DMN and other functional networks. Here we present the FC and ISFC correlation matrices for all voxels (8672x8672 voxels, 18 subjects) that responded reliably to the intact narrative (i.e., significant ISC along the diagonal of the matrix, see Methods). The correlation matrix was re-ordered by the output of a K-means clustering algorithm 12 performed on the FC matrix during rest. The algorithm found five consistent FC networks that could be replicated across two groups ( Supplementary Fig. 9B). The cluster surrounding Heschl's gyrus was labeled the "auditory network" (AUD, red). The DMN appeared to be split into two subnetworks, labeled DMN A (yellow), and DMN B (green). This division is compatible with prior publications that divide the DMN into two sub-networks: the core network and the medial temporal lobe (MTL) subsystem 8,9 . .Finally, because the remaining two networks resembled the division between the ventral and dorsal language streams proposed by Hickok and  Fig. 11). In addition, we computed the four-fold across-subject classification between the ROI-based correlation matrices (52x52) (Supplementary Table 2   K-means clustering and local clustering (see methods) were applied to each one of the ISFC voxel-wise covariance matrices (n=18) during the intact story. 52 ROIs across five networks were defined for each one of the groups.

Problem formulation
Suppose we have recorded neural data from k subjects. The neural signals i X , measured from subject i , are in the form of a p n  matrix that contains signals from p neural sources over n time points. We consider a model of the form: Our goal is to estimate the shared stimulus-induced covariance matrix, For simplicity, we assume that the measured signals have unit variance. Each i X has an intrinisc part i I , which is stimulus independent, and a joint hidden variable S , that can be transformed within each subject by a subject-specific factor i D . S is the stimulus-related joint set of p n 

Sample covariance
A first solution is to compute the sample covariances within a subject, as is done in standard functional connectivity (FC) analyses: Using the technical results below, for sufficiently large n and conditioned on i D , this sample covariance converges to ( )( The error in using this sample covariance as an estimate of C reduces to where || || fro is the Frobenius norm. This error does not decrease by increasing n or k . It

Sample cross covariance
A second approach is to compute the sample cross covariances between single subject responses and the average of the other subjects in the group. This approach eliminates the intrinsic components, and some of the stimulus-induced individual fluctuations. Specifically, we define the i th estimate as the subject-based Inter-subject functional correlation (ISFC) : For sufficiently large n and conditioned on the i D 's, this average cross covariance converges The main advantage is that the individual covariance Q disappears, because i I and j I are fro fro It is clear that the error in this case is much smaller than for the sample covariance computed in Section 2 above. Here, it no longer depends on Q , and the last two terms decrease with 1 k  .
Nonetheless, we still have a positive error floor, because the first term is independent of k . We used the subject-based ISFC matrices for classification in Figures 3,4,7. For simulation results see Supplemental Figure 3B.

Averaged sample cross covariances
In order to reduce the error floor to zero, we take another average with respect to i . This leads to the following estimate, which is called "group-based ISFC": , : As before, for sufficiently large n and conditioned on the i D 's, this average cross covariance converges to , : Thus, Classification accuracy was then computed as the proportion of times a subject was assigned to the correct condition.
FC classification of condition: we used the same ISFC procedure as described above. The only difference was that given a test subject, s, we calculated the correlation matrix of that condition (i.e., FC) within that subject. Hence, for a given test subject, we have one FC correlation matrix s C (in contrast to ISFC, where we have 4 matrices). Our predicted condition is the condition n that maximizes the correlation between s C and n C . The matrix C n was calculated in the training phase using within-subject FC and was then averaged across the M-1 subjects from that condition. Then the best matching condition was computed as: