<figure><img src="image_1.png" /></figure>

HAL
open science

# Chemogenetic Interrogation of a Brain-wide Fear Memory Network in Mice

Gisella Vetere, Justin Kenney, Lina Tran, Frances Xia, Patrick Steadman,

John Parkinson, Sheena Josselyn, Paul Frankland

► To cite this version:

Gisella Vetere, Justin Kenney, Lina Tran, Frances Xia, Patrick Steadman, et al. Chemogenetic Interrogation of a Brain-wide Fear Memory Network in Mice. Neuron, 2017, 94 (2), pp.363-374.e4. 10.1016/j.neuron.2017.03.037. hal-04065754

HAL Id: hal-04065754

https://hal.science/hal-04065754

Submitted on 12 Apr 2023

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

Public Domain
1 **Chemogenetic interrogation of a brain-wide fear memory network in mice**

2

3 Gisella Vetere¹,², Justin W. Kenney¹,², Lina M. Tran¹,³, Frances Xia¹,³, Patrick E. Steadman¹,⁴,

4 John Parkinson⁵,⁶, Sheena A Josselyn¹,³⁻⁴,⁷, Paul W Frankland¹,³⁻⁴,⁷⁻⁸

5

6 ¹ Program in Neurosciences and Mental Health, The Hospital for Sick Children, Toronto,

7 Canada, M5G 1X8.

8 ² Co-first authors

9 ³ Department of Physiology, University of Toronto, Toronto, Canada, Ontario, M5S 1A8.

10 ⁴ Institute of Medical Science, University of Toronto, Toronto, Canada, Ontario, M5S 1A8.

11 ⁵ Program in Molecular Structure and Function, The Hospital for Sick Children, Toronto,

12 Canada, M5G 1X8.

13 ⁶ Departments of Biochemistry, Computer Science and Molecular Genetics, University of

14 Toronto, Toronto, Canada, Ontario, M5S 1A8.

15 ⁷ Department of Psychology, University of Toronto, Toronto, Canada, Ontario, M5S 3GM.

16 ⁸ Correspondence: paul.frankland@sickkids.ca

17

18

19

20

21

22

23

24 **Keywords:** Graph theory, hippocampus, neocortex, contextual fear conditioning,

25 chemogenetics, functional connectivity, network, CA1, reuniens thalamic nucleus, lateral septal

26 nucleus, laterodorsal thalamic nucleus

Lead author: Paul Frankland
27 SUMMARY

28
29 Behavior depends on coordinated activity across multiple brain regions. Within such networks,
30 highly-connected hub regions are assumed to disproportionately influence behavioral output,
31 although this hypothesis has not been systematically evaluated. By mapping brain-wide
32 expression of the activity-regulated gene, *c-fos*, previously we identified a network of brain
33 regions co-activated by fear memory. To test the hypothesis that hub regions are more
34 important for network function, here we simulated node deletion *in silico* in this behaviorally-
35 defined functional network. Removal of high degree nodes produced greatest network disruption
36 (e.g., reduction in global efficiency). To test these predictions *in vivo*, we examined the impact of
37 post-training chemogenetic silencing of different network nodes on fear memory consolidation.

38 In a series of independent experiments encompassing 25% of network nodes (i.e., 21/84 brain
39 regions), we found that node degree accurately predicted observed deficits in memory
40 consolidation, with silencing of highly-connected hubs producing the largest impairments.

41 Correspondence between *in silico* predictions and observed deficits following silencing *in vivo*
42 demonstrates the utility of this network-based approach in guiding behavioral studies.

43
44
45
46 INTRODUCTION

47
48 A predominant view in the nineteenth century was that specific cognitive functions were
49 localized to discrete brain regions. This view has since evolved to one where specific cognitive
50 functions are thought to be supported by the coordinated activity of a distributed network of
51 brain regions, rather than isolated brain regions alone (McIntosh, 1999; Park and Friston, 2013;
52 Sporns, 2012). Graph theory is a branch of mathematics that has been used to analyse such
53 complex networks. Any network consists of nodes (or vertices) connected through links (or
54 edges), with degree centrality describing the number of links per node. Analysis of many real
55 world networks (including social, ecological, protein interaction, gene, finance and
56 communication networks) reveals that probability distributions for node degree are typically
57 heavy-tailed (e.g., scale-free), with low degree nodes being common and high degree nodes
58 being more scarce (Barabasi, 2009). However, despite their scarcity, high degree nodes (or
59 'hubs') are thought to exert greater influence on network function by virtue of greater
60 connectivity, and targeting hubs disproportionately impacts the function of real-world networks.
61 For example, in protein interaction networks, experimental deletion of genes coding for high-
62 degree proteins is associated with greater lethality than similar deletion of genes coding for low-
63 degree proteins (Babu et al., 2014; Babu et al., 2012; Jeong et al., 2001).
64
65 Network-based approaches have been used to describe large-scale structural (i.e., anatomical)
66 and functional (i.e., co-activation) connections in the brain (Bargmann and Marder, 2013;
67 Bullmore and Sporns, 2012; Chiang et al., 2011; Jarrell et al., 2012; Markov et al., 2014; Oh et
68 al., 2014; Varshney et al., 2011; White et al., 1986). Similar to other networks, probability
69 distributions for node degree are heavy-tailed (Bullmore and Bassett, 2011; Rubinov and
70 Sporns, 2010; van den Heuvel et al., 2016). This 'small-world' organization is thought to
71 facilitate rapid brain-wide synchronization and information transfer and, at the same time, this
72 architecture minimizes wiring costs and provides a balance between local processing and global integration (Sporns, 2013). Although brain diseases, including Alzheimer's disease and schizophrenia, are more likely to impact brain regions identified as hubs in human anatomical connectomic analyses (Crossley et al., 2014), systematic manipulation of nodes within a task-relevant network has not been possible to date.

77
78 By mapping activity-regulated gene expression induced by memory recall, we recently described a network engaged by contextual fear memory in mice (Wheeler et al., 2013). In this study, we quantified expression of the activity-regulated gene, c-fos, in 84 brain regions after fear memory recall in mice. By computing inter-regional correlations, we identified collections of brain regions that were co-activated by memory recall (i.e., a memory network, with nodes representing individual brain regions and edges representing super-threshold functional connections). As expected, the probability distribution for node degree was heavy-tailed, and the network contained several high degree hubs including, for example, the CA1 region of the hippocampus and the reuniens thalamic nucleus (Re). To directly test the hypothesis that higher degree nodes exert greater influence on network function, here simulated the impact of node deletion on network function using a novel disruption propagation model. We found that deletion of high degree nodes caused greatest network disruption. We then tested these *in silico* predictions *in vivo* by examining the impact of post-training chemogenetic silencing on consolidation of a fear memory. In a series of experiments, we independently probed 25% of network nodes (i.e., 21/84 brain regions). We found that *in silico* simulation of node deletion accurately predicted observed *in vivo* data, with silencing of highly-connected hubs producing the largest consolidation impairments. This systematic interrogation of an identified, task-relevant network supports the hypothesis that high degree nodes are more crucial for brain function and confirms the predictive value of this network-based approach.

97
98

RESULTS

99

100

Generation of a fear memory network

101

102

Two brain regions are functionally connected when activity in these regions co-varies (Park and Friston, 2013). To measure activity following recall of a fear memory in mice, we previously quantified expression of the activity-regulated gene *c-fos* in 84 brain regions, including regions in the cortex, hippocampus, thalamus, midbrain, cerebral and hypothalamic nuclei (Table S1).

103

104

105

106

To estimate patterns of functional connectivity, we computed a complete set of inter-regional correlations. By considering only the strongest correlations, we identified a network of brain regions that were co-activated by memory recall (Figure 1A). In this fear memory functional network, nodes represent individual brain regions and edges represent super-threshold functional connections (Figure 1B) (Wheeler et al., 2013).

107

108

109

110

111

112

This fear memory network displayed several features that were consistent with both theoretical predictions and experimental observations. First, similar to other brain networks (van den Heuvel et al., 2016), the probability distribution for node degree was heavy-tailed (Figure S1A).

113

114

115

Second, the network was highly-clustered such that a small-world network model approximated the clustering distribution (Figure S1B). Third, several high degree nodes within the network corresponded to regions with established roles in fear memory (e.g., CA1, Re) (Tanaka et al., 2014; Xu and Sudhof, 2013) (Figure S1C). Importantly, these features were observed when we used alternate correlation coefficients to generate the network, as well as more or less conservative thresholds for functional connections (Wheeler et al., 2013). Furthermore, equivalent patterns of functional connections were observed when another activity-related gene, *zif268*, was quantified in the same brains (Wheeler et al., 2013).

116

117

118

119

120

121

122

123
We additionally generated two types of comparison network. For the first network, we quantified Fos expression in the same 84 brain regions in a control condition, run in parallel with the fear conditioned mice. In this control condition, mice were treated identically to the fear conditioned group except that they did not receive a shock during training (Wheeler et al., 2013) (Figure 1C-D). Similar to the fear memory network, the probability distribution for node degree was non-Gaussian, with the nucleus accumbens shell (AcbSh), ventromedial thalamic nucleus (VM) and anteroventral thalamic nucleus (AV) having the most connections (Figure S1D). However, compared to the memory network, this control network was less dense, reflecting reduced interactions between brain regions in the absence of fear memory expression.

The second type of network was generated to evaluate corresponding anatomical connections (using structural data from the Allen Brain Atlas connectomic dataset (Oh et al., 2014)). Because the functional (i.e., fear memory and control) and anatomical networks were generated in fundamentally different ways, we used two methods to generate corresponding anatomical networks: 1) an anatomical network thresholded at the same p-value as the functional network, and, 2) an anatomical network with the same density (i.e., number of edges) as the functional network (see Supplemental Experimental Procedures for details) (Figure S1E-F). As expected, these networks contained a subset of hub-like regions, with the caudate putamen (CPu), claustrum (Cl) and agranular insular cortex, ventral part (AIV) having the most connections (Figure S1G-H).

The fear memory network appeared to differ qualitatively from both the control and anatomical networks. Consistent with this, degree centrality was not correlated between the fear memory network and either the control or anatomical networks, indicating that hubs in the fear memory network differed from hubs in these other networks. Comparing the fear memory and the control networks, this was the case whether we used equivalent thresholds to generate the networks (r
150 = 0.045, *p* = 0.68) or we matched networks in terms of density (*r* = -0.072, *p* = 0.51) (Figure S1I-J). Comparing the fear memory and the anatomical networks, this was the case whether we used equivalent thresholds to generate the networks (*r* = 0.078, *p* = 0.52) or we matched networks in terms of density (*r* = -0.024, *p* = 0.84) (Figure S1K-L). The lack of correspondence between the fear memory and control networks suggests that interactions between regions vary across conditions (i.e., fear memory vs. control). The lack of correspondence between the fear memory and anatomical networks suggests that patterns of behaviorally-determined functional connections provide important information beyond underlying structural connections (Misic et al., 2016).

159
160 **In silico node deletion**
161
162 Within these types of networks, high degree nodes (or 'hubs') are thought to exert greater
163 influence on network function by virtue of their greater connectivity. We first developed an *in
164 silico* approach to model the effects of node removal on global network properties. The brain is
165 highly interconnected and inactivation of any single node is likely to exert effects beyond its
166 immediate neighborhood (Goshen et al., 2011; Grayson et al., 2016; Liu et al., 2012; Lohani et
167 al., 2016; Otchy et al., 2015). Therefore, in contrast to network analyses in which a node is
168 simply removed from a network while global network measures are recalculated, we modeled
169 the effects of inhibiting individual brain regions (nodes) in the fear memory network by
170 propagating the effect of inactivation beyond a given node along the contours of the
171 connectome. This disruption propagation model (DPM) directly exploits the functional
172 connectome associated with a specific behavior. Related approaches have been used to model
173 cascading failures in electric grid networks (Crucitti et al., 2004).
174
In the DPM, an individual node and its associated edges are deleted from the network. In order to propagate this disruption beyond the deleted node's neighborhood, the weights of all adjacent edges are adjusted (1) proportionally to the weight of the deleted edge, and, (2) inversely proportional to their own neighboring edges. These steps are iterated through the network until edge weights no longer change (Figure S2). The resulting network is then thresholded after propagation to produce the disrupted network. The model has two tunable parameters: (1) the number of times any edge can be updated, and (2) the threshold applied following edge updating to generate the disrupted network. Exploration of these parameters indicated that combining one edge update with a threshold matching that used for initial network generation yielded high information content (i.e., Shannon's Entropy; Figure S3A-D) and therefore we used these parameters in all our subsequent analyses.

We applied our disruption propagation model to each node to simulate the effect of inactivation on overall network function. To measure the impact of inactivating individual nodes, we compared the network before and after disruption and calculated the change in global efficiency ($\Delta GE$) (Figure 2A-B, example for Re shown) and giant component size ($\Delta GC$) for each node. For the fear memory network, we found that changes in global efficiency were correlated with node degree ($r = 0.92, p < 0.001$; Figure 2C), with inactivation of high degree nodes associated with greater reductions in global efficiency than similar inactivation of low degree nodes. An equivalent pattern of results was observed for changes in giant component size ($r = 0.65, p < 0.01$; Figure S3E-F). As expected, reductions in global efficiency and giant component using the DPM were greater in magnitude than reductions in these measures following simple node deletion (Figure S4A-B). Furthermore, $\Delta GE$ and $\Delta GC$ were more strongly correlated with degree centrality using the DPM compared to simple node deletion (for simple deletion: $\Delta GE, r = 0.66, p < 0.001$; $\Delta GC, r = 0.20, p = 0.067$; Fig. S4C-D).
201 **In vivo node silencing**

202
203 We next tested whether the predicted *in silico* deficits would be observed *in vivo*. To do this, we
204 chronically silenced brain regions identified in our network analysis and examined the impact on
205 memory consolidation. To chronically suppress neural activity in targeted brain regions we
206 virally expressed the inhibitory DREADD (designer receptor exclusively activated by designer
207 drugs), hM4Di (Armbruster et al., 2007), using long-term expressing replication-defective herpes
208 simplex viruses (HSVs). This strategy offers two key advantages. First, HSVs are neurotropic,
209 infecting predominantly excitatory neurons and not glia (Cole et al., 2012; Rashid et al., 2016;
210 Yiu et al., 2014). Second, unlike optogenetic manipulations, DREADDs allow chronic silencing
211 of neuronal activity (i.e., days to weeks (Jain et al., 2013)) by administering the hM4Di ligand
212 clozapine-N-oxide (CNO) in drinking water.

213
214 We previously showed that bath application of the hM4Di ligand, CNO, hyperpolarized infected
215 neurons and suppressed spiking in ex vivo whole cell patch clamp recording experiments
216 (Richards et al., 2014). In order to further verify that hM4Di expression decreases neuronal
217 activity in vivo, we microinjected HSV-hM4Di into the anterior cingulate cortex. Three days later
218 (when expression of hM4Di began), mice were given continuous home cage access to CNO (or
219 its vehicle (VEH)) in their drinking water to silence infected neurons. Three days later, we
220 trained mice in contextual fear conditioning at different Zeitgeber (ZT) times, with ZT0
221 corresponding to lights on and ZT12 corresponding to lights off. Ninety minutes following
222 training, mice were perfused and expression of the activity-dependent immediate early gene, c-
223 fos, in neurons expressing hM4Di was examined (Figure 3A). The proportion of hM4Di-
224 expressing neurons expressing Fos was reduced following CNO treatment (main Treatment
225 effect: F₁,₃₉ = 20.76, *p* < 0.0001), indicating that the combination of hM4Di and CNO
226 administered in drinking water reduced neuronal activity in vivo (Figure 3B). Importantly, the
degree of Fos reduction was similar at all ZT times (Treatment × ZT interaction: $F_{1,39} = 0.15, p = 0.93$), consistent with previous studies showing that a) drinking is reduced, but not absent, during the inactive phase of the light-dark cycle in mice (Gordon et al., 1986), and, b) systemically administered CNO suppresses neuronal firing in hM4Di-expressing neurons for up to 9 h (Armbruster et al., 2007).

Using the same procedures, we additionally assessed whether similar CNO treatment (i.e., 3 d) decreases neuronal activity in hM4Di-infected neurons in other brain regions (CA1, laterodorsal thalamic nucleus [LD] and medial geniculate nucleus, medial part [MGM]). Ninety minutes following training (at ZT6), the proportion of hM4Di-expressing neurons expressing Fos was reduced in CNO-treated mice in all brain regions (Treatment effect: $F_{1,18} = 17.78, p < 0.0005$) (Figure 3C). The magnitude of this reduction was similar in all regions (Treatment × Region interaction: $F_{2,18} = 0.06, p = 0.94$), suggesting that there are no obvious regional variations in the efficiency of CNO-induced neural suppression. Furthermore, in a separate experiment, Fos expression was similarly reduced in infected neurons in CA1 following extended CNO treatment (i.e., 10 d, matching the time course of the main experiments, below) ($t_6 = 2.64, p < 0.05$) (Figure 3D).

Targeting 21 different regions in independent experiments

To systematically examine the relationship between a region's node degree and necessity in memory consolidation, we targeted 21 different regions from our network in a series of independent experiments (i.e., these experiments encompassed 25% of network nodes) (Figure 4A; Table S2). Targeted regions included low, medium and high degree nodes (node degree range 0-17), and encompassed the anterior-posterior extent of the network (including regions in association and sensory cortices, thalamus, hippocampus, cerebral and hypothalamic
nuclei). For each region, mice were bilaterally microinjected with HSV-hM4Di into the target region and trained in contextual fear conditioning 3 d later. Immediately following training, mice were given continuous home cage access to CNO or VEH in their drinking water, and tested 10 d later (for each region, Ns ranged 6-10 for CNO and VEH) (Figure 4B). Across all experiments, a total of 344 mice were tested (VEH, N = 174; CNO, N = 170). Within each region, ~2000 neurons were infected (range 900-3000) (Figure 5A). To assess differences in freezing between CNO- and VEH-treated mice, we conducted permutation tests, and then to control for multiple tests (across 21 experiments) we adjusted p values using false discovery rate (FDR) of 5% (Benjamini et al., 2001). Using this criterion, chronic suppression of neuronal activity in 4/21 brain regions targeted impaired consolidation (Figure 5B). These regions were the CA1 region of the hippocampus, lateral septal nucleus (LSI), laterodorsal thalamic nucleus (LD) and reuniens thalamic nucleus (Re). Importantly, the combination of hM4Di and CNO administration appears to be necessary for the observed behavioral effects. Compared to VEH, CNO treatment did not impair consolidation in mice infected with control virus in CA1 ($t_{14} = 0.51, p = 0.62$) (Figure S5A).

## Correspondence between *in silico* and *in vivo* node silencing

We next examined the extent to which our *in silico* predictions of the effects of node silencing corresponded to the observed *in vivo* consolidation deficits. Reductions in freezing (consolidation deficits) following *in vivo* chemogenetic silencing correlated with reductions in global efficiency following *in silico* node deletion ($r = 0.61, p < 0.01$) (Figure 6A; see also Table S3). Similarly, reductions in freezing following regional *in vivo* chemogenetic silencing correlated with reductions in giant component following *in silico* node deletion ($r = 0.56, p < 0.01$) (Figure S5B). This correspondence between DPM-based predictions and *in vivo* observations was insensitive to variations in network generation. Applying the DPM to either higher confidence
(thresholded at *p* < 0.005) or lower confidence (thresholded at *p* < 0.05) networks, produced similar correspondence between *in silico* reductions in global efficiency and *in vivo* data (high, *r* = 0.58, *p* < 0.01; low, *r* = 0.46, *p* < 0.05), indicating that the predictive power of DPM is insensitive to network thresholding. These results suggest that inactivation of higher degree nodes is associated with greater consolidation deficits. Consistent with this conclusion, we found that a region's 'hubness' predicted the observed consolidation deficits following silencing.

This was the case for degree centrality (*r* = 0.57, *p* < 0.01; **Figure S5C**), as well as alternate measures of centrality including node strength (*r* = 0.57, *p* < 0.01), closeness (*r* = 0.56, *p* < 0.01), communicability (*r* = 0.45, *p* < 0.05), eigenvector (*r* = 0.53, *p* < 0.05) and Katz centrality (*r* = 0.52, *p* < 0.05).

We next contrasted our DPM-based predictions to predictions produced by either simple node removal or the cascading failure model, a related approach that has been used to model electrical grid failure (Crucitti et al., 2004). The DPM was superior to both simple node removal (correlation between ΔGE and Δfreezing: *r* = 0.45, *p* < 0.05) and the cascading failure model (correlation between α<sub>critical</sub> and Δfreezing: *r* = 0.41, *p* = 0.064) (**Figure S5D-E**), suggesting that features of DPM more faithfully mimic the impact of localized inactivation on brain network function.

In our experiments we microinjected a fixed volume of HSV-hM4Di into the different regions of interest. As the volume of targeted regions varied across brain regions, it is possible that observed consolidation deficits are related to the proportion of the target region infected by our viral vector. However, the volume of targeted regions did not correlate with observed deficits (*r* = 0.09, *p* = 0.70) (**Figure S5F**).

303

304 **Control and anatomical networks do not predict consolidation deficits**
The present results indicate that our fear memory network model successfully predicted the effectiveness of chemogenetic silencing, and are consistent with the idea that inactivation of higher degree nodes is associated with greater consolidation deficits. However, there are alternate possibilities. For example, it is possible that basal network interactions between these same brain regions during other behavioral states predict the observed consolidation deficits.

Alternatively, the underlying anatomical connections between the same brain regions might predict the observed consolidation deficits. A third possibility is that differences in regional activation levels (relative to the control condition) account for the observed *in vivo* results.

In order to test the first possibility we asked whether the topological organization observed in control network predicted the effectiveness of chemogenetic silencing. As in the fear memory network, we applied the DPM to the control network and calculated changes in global efficiency.

We found that changes in global efficiency did not predict consolidation deficits. This was the case regardless of whether we used an equivalent thresholding criteria compared to the fear memory network (*r* = 0.21, *p* = 0.36; **Figure 6B**), or matched control network density with the fear memory network (*r* = 0.36, *p* = 0.11; **Figure S6A**).

To test the second possibility, we asked whether the topological organization observed in anatomical networks predicted the effectiveness of chemogenetic silencing. As in the fear memory network, we applied the DPM to the anatomical networks and calculated changes in global efficiency. We found that changes in global efficiency did not predict consolidation deficits. This was the case regardless of whether we used an equivalent thresholding criteria compared to the fear memory network (*r* = 0.25, *p* = 0.28; **Figure 6B**), or matched anatomical network density with the fear memory network (*r* = 0.048, *p* = 0.84; **Figure S6B**).

330
331 Finally, we found that relative activation levels (i.e., Fos counts normalized to a control group)
332 did not predict consolidation deficits ($r = 0.027$, $p = 0.91$; **Figure 6D**).

333
334 **DISCUSSION**
335
336 By quantifying expression of the activity-regulated gene *c-fos*, we previously identified a network
337 of brain regions that were co-activated by recall of a fear memory in mice (Wheeler et al., 2013).

338 Graph theoretical analysis identified several highly-connected hub regions within this functional
339 network, and here we tested the hypothesis that these hubs would play more influential roles in
340 memory consolidation compared to non-hub regions. First, we developed the DPM to simulate
341 removal of individual brain regions *in silico*. As expected, removal of high degree nodes
342 produced greater network disruption (reductions in global efficiency and giant component size)
343 than removal of low degree nodes. Second, we examined the impact of silencing individual
344 brain regions on fear memory consolidation *in vivo*. We found that inactivation of higher degree
345 nodes was associated with greater consolidation deficits than similar inactivation of low degree
346 nodes. Network-based approaches have previously been used to analyse large-scale structural
347 (i.e., anatomical) and functional (i.e., co-activation) connections in the brain. However, formal
348 interrogation of these networks using invasive interventions has not been conducted. The
349 current study indicates that network-based approaches may provide a predictive framework that
350 may be useful in identifying novel brain-behavior relationships.

351
352 In our network generation (Wheeler et al., 2013), two regions were determined to be functionally
353 connected when activity in one region was statistically dependent upon activity in another region
354 (McIntosh, 1999; Park and Friston, 2013). In previous studies, hemodynamic (fMRI) or
355 electrophysiological estimates of regional and/or neuronal activity have been used to estimate
356 patterns of functional connectivity, and resulting functional networks, in humans and
experimental animals (Sporns and Betzel, 2016). The use of an activity-regulated gene marker, such as Fos, to measure regional patterns of activation in mice necessarily means that the present network generation differs in two important ways. First, Fos expression was measured 90 min following memory testing (in order to match the time-course of elevated Fos protein following sustained neuronal activation). While functional connections may be defined across a range of timescales (McIntosh, 1999), this timescale is longer than that used in fMRI or electrophysiological studies. Correlations in Fos expression therefore likely incompletely capture the richness of all inter-regional interactions (e.g., although the amygdala is known to be important for fear learning, it was not identified as an important node in our network). They are useful in detecting co-activation of brain regions when it is sustained over minutes, but are insensitive to coupling that may occur over shorter timescales (e.g., inter-regional coupling of oscillations). It is additionally worth noting that relatively small populations of neurons may robustly influence network activity (e.g., (Witten et al., 2010)), and such contributions may also be underestimated using the current approach. Second, post-mortem assessment of Fos provides a single indication of activation (rather than a time series) per region per mouse, and therefore functional connections are estimated by computing co-variance across, rather than within, mice. While both within and between subject co-variance can be used to estimate functional connections (Grady et al., 2003; McIntosh, 1999), within subject co-variance is more typically used in fMRI or electrophysiological studies.

Despite these differences, we were able to use our fear memory network in an unbiased manner to predict which brain regions within this network are important for consolidation of a fear memory. Consistent with the *in silico* analyses, the most pronounced deficits in fear memory consolidation occurred when activity in higher degree nodes was suppressed post-training. Importantly, neither the corresponding control nor anatomical networks accurately predicted the observed consolidation deficits. With respect to the control network, this suggests
that network interactions among these same brain regions vary according to behavioral state (in this case, fear memory vs. control). With respect to the anatomical network, this emphasizes that analyses of patterns of behaviorally-determined functional connections provide important information beyond underlying structural connections. Indeed, while anatomical networks constrain and influence resulting functional networks, there is often considerable topographical divergence (e.g., (Misic and Sporns, 2016)).

The importance of hubs for network function has previously been assessed in a wide range of biological (Babu et al., 2014; Babu et al., 2012; Jeong et al., 2001) and non-biological complex networks including the internet (Albert et al., 2000), electricity grid (Buldyrev et al., 2010) and financial networks (Haldane and May, 2011). However, systematic, node-by-node interrogation of brain networks has not previously been conducted, even in model organisms with well-defined and tractable connectomes such as *c. elegans*. The current study confirms that hubs play disproportionately important roles, at least in a network engaged by contextual fear memory in mice. Our findings are broadly consistent with a previous meta-analysis finding that highly connected brain regions are more likely to be impacted in a range of brain disorders (Crossley et al., 2014). In the future, two developments may further refine this general approach in rodents, and allow broader application. First, the development of improved methods for brain-wide quantification of activity-regulated gene expression will allow for the generation of more accurate activity maps (Renier et al., 2016; Ye et al., 2016). Further refinements will allow phenotyping of cells expressing activity-regulated genes, and therefore segregation of signals by cell type and/or neurotransmitter content (Romanov et al., 2016). Second, the development of imaging approaches that allow neuronal activity to be tracked in real time across large expanses of tissue (e.g., based on voltage, $Ca^{2+}$ or hemodynamic signals) will improve temporal resolution (Ahrens et al., 2013; Ferenczi et al., 2016; Gong et al., 2015; Mohajerani et al., 2013).
408 This will permit use of time series data for network generation and analysis and, additionally,
409 make it possible to track inter-regional coupling over shorter timescales.

410
411 We found that post-training chemogenetic inhibition of four (out of 21) regions impaired memory
412 consolidation. These regions were CA1, Re, LSI and LD. Of these, two were unsurprising.
413 Previous studies have established roles for both the CA1 region of the hippocampus and the Re
414 in the consolidation and expression of contextual fear memories. For example, fear conditioning
415 activates CA1 neurons (Beck and Fibiger, 1995), and inhibition of CA1 neurons during training,
416 following training or during retrieval impairs contextual fear memories (Fanselow, 2000). The Re
417 has been shown to influence fear memory expression. Inhibition of prefrontal inputs to Re or Re
418 projections increases generalized freezing in non-trained contexts. Conversely, activation of Re
419 neurons reduced generalized freezing in non-trained contexts (Xu and Sudhof, 2013).

420 Nonetheless, previous studies did not evaluate whether neural activity in the Re is important for
421 fear memory consolidation, as we showed here.

422
423 The observations that post-training inhibition of either LSI or LD impaired consolidation of
424 contextual fear conditioning are novel. However, there is anatomical and functional data that
425 plausibly implicate these regions in circuits supporting fear-related behaviors and/or mnemonic
426 processing. The LD has dense reciprocal connectivity with the hippocampus and retrosplenial
427 cortex (Aggleton et al., 2016). This region has been implicated in cortical-hippocampal-thalamic
428 circuits involved in recognition memory (Aggleton et al., 2016), and LD inactivation disrupts
429 hippocampal place representations and spatial learning (Mizumori et al., 1994; van Groen et al.,
430 2002). The LSI receives strong inputs from the hippocampus and amygdala, and sends
431 projections to midbrain and brainstem regions implicated in behavioral and autonomic reactions
432 to threatening stimuli (Swanson and Cowan, 1979). The LSI is activated by threatening stimuli
433 (Beck and Fibiger, 1995), and mediates, for example, anxiogenic responses and enhanced fear
434 induced by social defeat (Guzman et al., 2013). Furthermore, inactivation of hippocampal-LSI
435 projections impairs expression of context-reward associations (Luo et al., 2011). Consistent with
436 the present study, this suggests that hippocampal-LSI interactions play a broader role in
437 processing contextual memories.

438
439 We developed a new model to simulate the impact of node removal, and generate predictions
440 for the *in vivo* experiments. Most crucially, in this model, the impact of node deletion (and loss of
441 associated edges) was propagated through the network, beyond the node's immediate
442 neighborhood. This particular feature of the DPM was based on many recent observations that
443 localized brain perturbations alter activity in remote brain regions (e.g., (Goshen et al., 2011;
444 Grayson et al., 2016; Liu et al., 2012; Lohani et al., 2016; Otchy et al., 2015)). For example,
445 prolonged optogenetic inhibition of the CA1 region of the hippocampus during fear memory
446 recall induces hyper-activation of the anterior cingulate cortex (Goshen et al., 2011). Similarly,
447 optogenetic stimulation of VTA dopaminergic neurons in rats alters brain-wide activation of both
448 non-dopaminergic and dopaminergic circuits, as measured by fMRI (Lohani et al., 2016).

449 Finally, and perhaps most relevant to the approach outlined here, chemogenetic inhibition of the
450 amygdala alters cortex-wide patterns of resting state functional connectivity in the monkey
451 (Grayson et al., 2016).

452
453 Compared to simple node deletion, the DPM provided better predictions of the observed
454 consolidation deficits following localized regional neuronal suppression. This suggests that
455 features of DPM (e.g., mutual dependence of activity in connected brain regions) more faithfully
456 mimic the impact of localized inactivation on brain network function. The DPM also
457 outperformed a conceptually related cascading failure model that has been used to model
458 failures in electricity grids and the internet (Crucitti et al., 2004). In the cascading failure model,
459 the effects of node deletion extend beyond adjacent edges by redistributing loads network-wide.
460 Critically, in the cascading failure model there is a tolerance parameter that defines the change
461 in load that any individual node can sustain before adjacent edges are impacted. Since DPM
462 performed better than the cascading failure model, this suggests that the concept of node
463 overload may not be as relevant to brain networks.

464
465 EXPERIMENTAL PROCEDURES

466
467 Network analysis

468 Networks were derived from previously published Fos quantifications from 84 brain regions in
469 two conditions: 1) contextual fear conditioned mice, tested 36 days following training (5 × 0.75
470 mA shocks); 2) control mice, treated identically but not shocked during training (Wheeler et al.,
471 2013). We computed inter-regional Pearson correlations and applied a threshold of *p* < 0.01
472 (two-sided) to generate a matrix used for creating an undirected network.

473
474 Disruption Propagation model

475 We developed a model of brain region inactivation that propagates the effects of inhibiting a
476 brain region along the contours of the functional connectome. After propagation, the network
477 was re-thresholded at the same value used for network generation and changes in the global
478 efficiency and size of the largest connected component were calculated.

479
480 Mice

481 Mice were derived from a cross between 129Svev [129] and C57BL/6N [C57] mice (Taconic).
482 Cages of 8-9 week-old mice were randomly assigned to 21 different experimental groups
483 (corresponding to 21 target brain regions). Each target brain region group was further divided
484 into 2 treatment groups that received CNO or vehicle (VEH) with all mice in the same cage
485 treated with either CNO or VEH.
486

487 **Surgery**

488 HSV-hM4Di-mCherry was bilaterally microinjected in the target brain region (see **Table S2** for
489 corresponding coordinates of targeted regions).

490

491 **Contextual fear training and test**

492 Seven days following surgery, mice were trained in contextual fear conditioning. During training,
493 mice were placed in the conditioning context, and 2 min later, presented with 3 footshocks (2 s
494 duration, 0.7 mA, 1 min apart). Mice were removed from the conditioning context, injected with
495 CNO (5 mg/kg, i.p.) or VEH (i.p.) and returned to their home cage. In the home cage, mice were
496 continuously treated with CNO or VEH (via drinking water) for 10 days. Contextual fear memory
497 was tested by placing mice back in the conditioning context and assessing the time mice spent
498 freezing. Only mice with robust, bilateral expression of HSV-hM4Di were included in subsequent
499 data analyses.

500

501 **In vivo assessment of chemogenetic inhibition**

502 To assess the efficiency of chemogenetic suppression of neural activity by CNO delivered in
503 drinking water, we microinjected HSV-hM4Di-mCherry into the anterior cingulate cortex of mice
504 and treated mice with either CNO or VEH (delivered via drinking water in home cage) for 3
505 days. Mice were fear conditioned at ZT0, 6, 12 or 18. Ninety min after training, mice were
506 perfused and Fos expression in mCherry⁺ neurons was assessed using immunohistochemical
507 methods. Using these same methods, we additionally evaluated the efficiency of chemogenetic
508 suppression in three other brain regions (CA1, LD and MGM) and over more a prolonged time
509 course (CA1, 10 days CNO treatment). Following the completion of CNO treatment, training
510 occurred at ZT6 in these experiments.

511
512 **Anatomical network analysis**

513 Graph theoretical measures from the mouse anatomical connectome (Oh et al., 2014) were
514 derived for comparison to the behavioral data. Because the anatomical connectome and the
515 memory network were built differently we took two different approaches for generating
516 equivalent networks: 1) an anatomical network thresholded at the same *p* value as the
517 functional network, and 2) an anatomical network with the same number of nodes and edges as
518 the functional network.

519

520 **Permutation testing**

521 Permutation testing was performed by resampling the freezing data from all experiments without
522 replacement while shuffling the assignment of both brain region and drug (CNO vs. VEH) 1000
523 times. Resulting *p* values were adjusted using an FDR of 5%.

524

525 **Cascading failure model**

526 The cascading failure model was implemented as described by (Crucitti et al., 2004) and
527 resulting α<sub>critical</sub> values were calculated for each node.

528

529 **AUTHOR CONTRIBUTIONS**

530

531 PWF, GV and JWK designed the experiments. GV, LMT and FX conducted the behavioural
532 experiments; JWK, PES and JP developed the disruption propagation model and conducted
533 graph theoretical analyses; GV and FX conducted the immunohistochemical analyses. PWF
534 supervised the project and PWF, GV, JWK, SAJ and JP wrote the paper.

535

536 **ACKNOWLEDGMENTS**

537
538 We thank Leonardo Restivo and Anne Wheeler for their technical input at various stages of this
539 project. This work was supported by Canadian Institutes of Health Research (CIHR) grants to
540 PWF (FDN143227), SAJ (MOP74650), and a Natural Sciences and Engineering Research
541 Council (NSERC) grant to JP (RGPIN-2014-06664). JWK was supported by a long-term
542 fellowship from Human Frontiers Science Program (LT000759/2014).

543

544

545

546

547
549

**Figure 1. Identification and characterization of a fear memory network.** **A.** Matrix showing inter-regional correlations for Fos expression following fear memory recall. Axes correspond to 550 84 brain regions (listed in **Table S1**) organized by major brain division (red = association cortex; 551 purple = hypothalamus; orange = sensory cortex; teal = hippocampus; blue = thalamus; 552 turquoise = midbrain; green = cerebral nuclei). Colors reflect strength of correlation (scale, 553 right). **B.** Resulting network graph with nodes grouped by major brain divisions. Node size is 554 proportional to its degree (i.e., number of connections). Connections correspond to above 555 threshold correlations (Pearson's *r* > 0.83, *p* < 0.01). **C.** Matrix showing inter-regional 556 correlations for Fos expression for mice in the control condition. Axes correspond to 84 brain 557 regions (listed in **Table S1**) organized by major brain division (red = association cortex; purple = 558 hypothalamus; orange = sensory cortex; teal = hippocampus; blue = thalamus; turquoise = 559 midbrain; green = cerebral nuclei). Colors reflect strength of correlation (scale, right). **D.** 560 Resulting network graph with nodes grouped by major brain divisions. Node size is proportional 561 to its degree (i.e., number of connections). Connections correspond to above threshold 562 correlations (Pearson's *r* > 0.83, *p* < 0.01). 563

565

**Figure 2.** *In silico* silencing of individual network nodes. **A.** Fear memory network before 566 (left) and after (right) application of the disruption propagation model (DPM) targeting reuniens 567 thalamic nucleus (Re; light blue). **B.** Network global efficiency decreases after application of 568 DPM targeting the Re. **C.** Positive correlation between degree and change in global efficiency 569 (ΔGE) following DPM application. 570

571

**Figure 3.** Chemogenetic inhibition suppresses neuronal activation. **A.** Anterior cingulate 572 cortex neurons expressing hM4Di-mCherry (red) show lower levels of Fos (green) following 573
contextual fear conditioning in mice treated with CNO (lower) versus VEH (upper) in drinking water. Note overlap of hM4Di with Fos (yellow) in VEH-treated mice but not CNO-treated mice.

Scale bar = 20 µm. B. Probability of Fos expression in neurons expressing hM4Di-mCherry following fear conditioning was reduced in mice treated with CNO (versus VEH) in drinking water, regardless of Zeitgeber time (ZT) of training. C. Probability of Fos expression in neurons expressing hM4Di-mCherry following fear conditioning was reduced in mice treated with CNO (versus VEH) in drinking water, regardless of site of infection. D. Prolonged CNO treatment (10 d) reduces probability of Fos expression in neurons expressing hM4Di-mCherry in CA1 following fear conditioning. All data represent mean ± s.e.m.

583

**Figure 4.** *In vivo* silencing of individual network nodes. A. Twenty-one brain regions were chemogenetically silenced in independent experiments. B. HSV-hM4Di was bilaterally microinjected into 21 different brain regions. Mice were trained in contextual fear conditioning and tested 10 d later. After training, mice received CNO or VEH in drinking water.

588

**Figure 5.** Effects of chemogenetic silencing of 21 different brain regions. A. Bilateral microinjection of HSV-hM4Di produced localized transgene expression (white) in the targeted 21 brain regions. Targeted regions outlined (white dotted lines). Scale bar (green) = 1 mm. Insets show high magnification of infected regions. Inset scale bar (white) = 50 µm. B. Contextual fear memory (percent freezing) varied across silenced target brain region in mice treated with VEH (dark green) or CNO (light green). Dots represent freezing scores for individual mice. Statistically reliable differences (after false discovery rate (FDR) correction) highlighted by darker green bar (LSI, Re, LD, CA1).

597

**Figure 6.** *In silico* analysis predicts *in vivo* observations. A. Reductions in global efficiency (ΔGE) following application of the DPM *in silico* (applied to the fear memory network) predict
600 reductions in freezing (Δfreezing) following chemogenetic silencing observed *in vivo*. **B.**

601 Changes in global efficiency (ΔGE) following application of the DPM *in silico* (applied to the

602 control network) do not predict reductions in freezing (Δfreezing) following chemogenetic

603 silencing observed *in vivo*. **C.** Changes in global efficiency (ΔGE) following application of the

604 DPM *in silico* (applied to the anatomical network) do not predict reductions in freezing

605 (Δfreezing) following chemogenetic silencing observed *in vivo*. **D.** Differences in regional Fos

606 expression (normalized to untrained control group) did not predict reductions in freezing

607 (Δfreezing) observed *in vivo*.

608

609

610

611
614 Aggleton, J.P., Pralus, A., Nelson, A.J., and Hornberger, M. (2016). Thalamic pathology and
615 memory loss in early Alzheimer's disease: moving the focus from the medial temporal lobe to
616 Papez circuit. Brain : a journal of neurology 139, 1877-1890.

617 Ahrens, M.B., Orger, M.B., Robson, D.N., Li, J.M., and Keller, P.J. (2013). Whole-brain
618 functional imaging at cellular resolution using light-sheet microscopy. Nature methods 10, 413-
619 420.

620 Albert, R., Jeong, H., and Barabasi, A.L. (2000). Error and attack tolerance of complex
621 networks. Nature 406, 378-382.

622 Armbruster, B.N., Li, X., Pausch, M.H., Herlitze, S., and Roth, B.L. (2007). Evolving the lock to
623 fit the key to create a family of G protein-coupled receptors potently activated by an inert ligand.

624 Proceedings of the National Academy of Sciences of the United States of America 104, 5163-5168.

625 Babu, M., Arnold, R., Bundalovic-Torma, C., Gagarinova, A., Wong, K.S., Kumar, A., Stewart,
626 G., Samanfar, B., Aoki, H., Wagih, O., et al. (2014). Quantitative genome-wide genetic
627 interaction screens reveal global epistatic relationships of protein complexes in Escherichia coli.

628 PLoS genetics 10, e1004120.

630 Babu, M., Vlasblom, J., Pu, S., Guo, X., Graham, C., Bean, B.D., Burston, H.E., Vizeacoumar,
631 F.J., Snider, J., Phanse, S., et al. (2012). Interaction landscape of membrane-protein complexes
632 in Saccharomyces cerevisiae. Nature 489, 585-589.

633 Barabasi, A.L. (2009). Scale-free networks: a decade and beyond. Science 325, 412-413.

634 Bargmann, C.I., and Marder, E. (2013). From the connectome to brain function. Nature methods
635 10, 483-490.

636 Beck, C.H., and Fibiger, H.C. (1995). Conditioned fear-induced changes in behavior and in the
637 expression of the immediate early gene c-fos: with and without diazepam pretreatment. The
638 Journal of neuroscience : the official journal of the Society for Neuroscience 15, 709-720.

639 Benjamini, Y., Drai, D., Elmer, G., Kafkafi, N., and Golani, I. (2001). Controlling the false discovery rate in behavior genetics research. Behavioural brain research 125, 279-284.

640 Buldyrev, S.V., Parshani, R., Paul, G., Stanley, H.E., and Havlin, S. (2010). Catastrophic
cascade of failures in interdependent networks. Nature 464, 1025-1028.

641 Bullmore, E., and Sporns, O. (2012). The economy of brain network organization. Nature
reviews Neuroscience 13, 336-349.

642 Bullmore, E.T., and Bassett, D.S. (2011). Brain graphs: graphical models of the human brain
connectome. Annual review of clinical psychology 7, 113-140.

643 Chiang, A.S., Lin, C.Y., Chuang, C.C., Chang, H.M., Hsieh, C.H., Yeh, C.W., Shih, C.T., Wu,
644 J.J., Wang, G.T., Chen, Y.C., et al. (2011). Three-dimensional reconstruction of brain-wide
645 wiring networks in Drosophila at single-cell resolution. Current biology : CB 21, 1-11.

646 Cole, C.J., Mercaldo, V., Restivo, L., Yiu, A.P., Sekeres, M.J., Han, J.H., Vetere, G., Pekar, T.,
647 Ross, P.J., Neve, R.L., et al. (2012). MEF2 negatively regulates learning-induced structural
648 plasticity and memory formation. Nature neuroscience 15, 1255-1264.

649 Crossley, N.A., Mechelli, A., Scott, J., Carletti, F., Fox, P.T., McGuire, P., and Bullmore, E.T.
650 (2014). The hubs of the human connectome are generally implicated in the anatomy of brain
disorders. Brain : a journal of neurology 137, 2382-2395.

651 Crucitti, P., Latora, V., and Marchiori, M. (2004). Model for cascading failures in complex
networks. Physical review E, Statistical, nonlinear, and soft matter physics 69, 045104.

652 Fanselow, M.S. (2000). Contextual fear, gestalt memories, and the hippocampus. Behavioural
brain research 110, 73-81.
660 Ferenczi, E.A., Zalocusky, K.A., Liston, C., Grosenick, L., Warden, M.R., Amatya, D., Katovich, K., Mehta, H., Patenaude, B., Ramakrishnan, C., et al. (2016). Prefrontal cortical regulation of brainwide circuit dynamics and reward-related behavior. *Science* **351**, aac9698.
661
662
663 Gong, Y., Huang, C., Li, J.Z., Grewe, B.F., Zhang, Y., Eismann, S., and Schnitzer, M.J. (2015). High-speed recording of neural spikes in awake mice and flies with a fluorescent voltage sensor. *Science* **350**, 1361-1366.
664
665
666 Gordon, M.N., Osterburg, H.H., May, P.C., and Finch, C.E. (1986). Effective oral administration of 17 beta-estradiol to female C57BL/6J mice through the drinking water. *Biology of reproduction* **35**, 1088-1095.
667
668
669 Goshen, I., Brodsky, M., Prakash, R., Wallace, J., Gradinaru, V., Ramakrishnan, C., and Deisseroth, K. (2011). Dynamics of retrieval strategies for remote memories. *Cell* **147**, 678-689.
670
671 Grady, C.L., McIntosh, A.R., and Craik, F.I. (2003). Age-related differences in the functional connectivity of the hippocampus during memory encoding. *Hippocampus* **13**, 572-586.
672
673
674 Grayson, D.S., Bliss-Moreau, E., Machado, C.J., Bennett, J., Shen, K., Grant, K.A., Fair, D.A., and Amaral, D.G. (2016). The Rhesus Monkey Connectome Predicts Disrupted Functional Networks Resulting from Pharmacogenetic Inactivation of the Amygdala. *Neuron* **91**, 453-466.
675
676
677 Guzman, Y.F., Tronson, N.C., Jovasevic, V., Sato, K., Guedea, A.L., Mizukami, H., Nishimori, K., and Radulovic, J. (2013). Fear-enhancing effects of septal oxytocin receptors. *Nature neuroscience* **16**, 1185-1187.
678
679
680 Haldane, A.G., and May, R.M. (2011). Systemic risk in banking ecosystems. *Nature* **469**, 351-355.
681
682
683 Jain, S., Ruiz de Azua, I., Lu, H., White, M.F., Guettier, J.M., and Wess, J. (2013). Chronic activation of a designer G(q)-coupled receptor improves beta cell function. *The Journal of clinical investigation* **123**, 1750-1762.
684
685 Jarrell, T.A., Wang, Y., Bloniarz, A.E., Brittin, C.A., Xu, M., Thomson, J.N., Albertson, D.G., Hall, D.H., and Emmons, S.W. (2012). The connectome of a decision-making neural network. *Science* **337**, 437-444.
686
687
688 Jeong, H., Mason, S.P., Barabasi, A.L., and Oltvai, Z.N. (2001). Lethality and centrality in protein networks. *Nature* **411**, 41-42.
689
690 Liu, X., Ramirez, S., Pang, P.T., Puryear, C.B., Govindarajan, A., Deisseroth, K., and Tonegawa, S. (2012). Optogenetic stimulation of a hippocampal engram activates fear memory recall. *Nature* **484**, 381-385.
691
692
693 Lohani, S., Poplawsky, A.J., Kim, S.G., and Moghaddam, B. (2016). Unexpected global impact of VTA dopamine neuron activation as measured by opto-fMRI. *Molecular psychiatry*.
694
695 Luo, A.H., Tahsili-Fahadan, P., Wise, R.A., Lupica, C.R., and Aston-Jones, G. (2011). Linking context with reward: a functional circuit from hippocampal CA3 to ventral tegmental area. *Science* **333**, 353-357.
696
697
698 Markov, N.T., Ercsey-Ravasz, M.M., Ribeiro Gomes, A.R., Lamy, C., Magrou, L., Vezoli, J., Misery, P., Falchier, A., Quilodran, R., Gariel, M.A., et al. (2014). A weighted and directed interareal connectivity matrix for macaque cerebral cortex. *Cerebral cortex* **24**, 17-36.
699
700 McIntosh, A.R. (1999). Mapping cognition to the brain through neural interactions. *Memory* **7**, 523-548.
701
702
703 Misic, B., Betzel, R.F., de Reus, M.A., van den Heuvel, M.P., Berman, M.G., McIntosh, A.R., and Sporns, O. (2016). Network-Level Structure-Function Relationships in Human Neocortex. *Cerebral cortex* **26**, 3285-3296.
704
705
706 Misic, B., and Sporns, O. (2016). From regions to connections and networks: new bridges between brain and behavior. *Current opinion in neurobiology* **40**, 1-7.
707
708 Mizumori, S.J., Miya, D.Y., and Ward, K.E. (1994). Reversible inactivation of the lateral dorsal thalamus disrupts hippocampal place representation and impairs spatial learning. *Brain research* **644**, 168-174.
709
710 Mohajerani, M.H., Chan, A.W., Mohsenvand, M., LeDue, J., Liu, R., McVea, D.A., Boyd, J.D.,
711 Wang, Y.T., Reimers, M., and Murphy, T.H. (2013). Spontaneous cortical activity alternates
712 between motifs defined by regional axonal projections. Nature neuroscience 16, 1426-1435.
713 Oh, S.W., Harris, J.A., Ng, L., Winslow, B., Cain, N., Mihalas, S., Wang, Q., Lau, C., Kuan, L.,
714 Henry, A.M., et al. (2014). A mesoscale connectome of the mouse brain. Nature 508, 207-214.
715 Otchy, T.M., Wolff, S.B., Rhee, J.Y., Pehlevan, C., Kawai, R., Kempf, A., Gobes, S.M., and
716 Olveczky, B.P. (2015). Acute off-target effects of neural circuit manipulations. Nature 528, 358-
717 363.
718 Park, H.J., and Friston, K. (2013). Structural and functional brain networks: from connections to
719 cognition. Science 342, 1238411.
720 Rashid, A.J., Yan, C., Mercaldo, V., Hsiang, H.L., Park, S., Cole, C.J., De Cristofaro, A., Yu, J.,
721 Ramakrishnan, C., Lee, S.Y., et al. (2016). Competition between engrams influences fear
722 memory formation and recall. Science 353, 383-387.
723 Renier, N., Adams, E.L., Kirst, C., Wu, Z., Azevedo, R., Kohl, J., Autry, A.E., Kadiri, L., Umadevi
724 Venkataraju, K., Zhou, Y., et al. (2016). Mapping of Brain Activity by Automated Volume
725 Analysis of Immediate Early Genes. Cell 165, 1789-1802.
726 Richards, B.A., Xia, F., Santoro, A., Husse, J., Woodin, M.A., Josselyn, S.A., and Frankland,
727 P.W. (2014). Patterns across multiple memories are identified over time. Nature neuroscience
728 17, 981-986.
729 Romanov, R.A., Zeisel, A., Bakker, J., Girach, F., Hellysaz, A., Tomer, R., Alpar, A., Mulder, J.,
730 Clotman, F., Keimpema, E., et al. (2016). Molecular interrogation of hypothalamic organization
731 reveals distinct dopamine neuronal subtypes. Nature neuroscience.
732 Rubinov, M., and Sporns, O. (2010). Complex network measures of brain connectivity: uses and
733 interpretations. NeuroImage 52, 1059-1069.
734 Sporns, O. (2012). From simple graphs to the connectome: networks in neuroimaging.
735 NeuroImage 62, 881-886.
736 Sporns, O. (2013). Network attributes for segregation and integration in the human brain.
737 Current opinion in neurobiology 23, 162-171.
738 Sporns, O., and Betzel, R.F. (2016). Modular Brain Networks. Annual review of psychology 67,
739 613-640.
740 Swanson, L.W., and Cowan, W.M. (1979). The connections of the septal region in the rat. The
741 Journal of comparative neurology 186, 621-655.
742 Tanaka, K.Z., Pevzner, A., Hamidi, A.B., Nakazawa, Y., Graham, J., and Wiltgen, B.J. (2014).
743 Cortical representations are reinstated by the hippocampus during memory retrieval. Neuron 84,
744 347-354.
745 van den Heuvel, M.P., Bullmore, E.T., and Sporns, O. (2016). Comparative Connectomics.
746 Trends in cognitive sciences 20, 345-361.
747 van Groen, T., Kadish, I., and Wyss, J.M. (2002). The role of the laterodorsal nucleus of the
748 thalamus in spatial learning and memory in the rat. Behavioural brain research 136, 329-337.
749 Varshney, L.R., Chen, B.L., Paniagua, E., Hall, D.H., and Chklovskii, D.B. (2011). Structural
750 properties of the Caenorhabditis elegans neuronal network. PLoS computational biology 7,
751 e1001066.
752 Wheeler, A.L., Teixeira, C.M., Wang, A.H., Xiong, X., Kovacevic, N., Lerch, J.P., McIntosh, A.R.,
753 Parkinson, J., and Frankland, P.W. (2013). Identification of a functional connectome for long-
754 term fear memory in mice. PLoS computational biology 9, e1002853.
755 White, J.G., Southgate, E., Thomson, J.N., and Brenner, S. (1986). The structure of the nervous
756 system of the nematode Caenorhabditis elegans. Philosophical transactions of the Royal
757 Society of London Series B, Biological sciences 314, 1-340.
758 Witten, I.B., Lin, S.C., Brodsky, M., Prakash, R., Diester, I., Anikeeva, P., Gradinaru, V.,
759 Ramakrishnan, C., and Deisseroth, K. (2010). Cholinergic interneurons control local circuit
760 activity and cocaine conditioning. Science 330, 1677-1681.
761 Xu, W., and Sudhof, T.C. (2013). A neural circuit for memory specificity and generalization.

762 Science 339, 1290-1295.

763 Ye, L., Allen, W.E., Thompson, K.R., Tian, Q., Hsueh, B., Ramakrishnan, C., Wang, A.C.,

764 Jennings, J.H., Adhikari, A., Halpern, C.H., et al. (2016). Wiring and Molecular Features of
765 Prefrontal Ensembles Representing Distinct Experiences. Cell 165, 1776-1788.

766 Yiu, A.P., Mercaldo, V., Yan, C., Richards, B., Rashid, A.J., Hsiang, H.L., Pressey, J.,

767 Mahadevan, V., Tran, M.M., Kushner, S.A., et al. (2014). Neurons are recruited to a memory
768 trace based on relative neuronal excitability immediately before training. Neuron 83, 722-735.

769

770
A

<figure><img src="image_2.png" /></figure>

B

<figure><img src="image_3.png" /></figure>

C

<figure><img src="image_4.png" /></figure>

D

<figure><img src="image_5.png" /></figure>
<figure><img src="image_6.png" /><figcaption>A</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>B</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>C</figcaption></figure>

<figure><img src="image_9.png" /></figure>
A

<figure><img src="image_10.png" /></figure>

B

<figure><img src="image_11.png" /></figure>

C

<figure><img src="image_12.png" /></figure>

D

<figure><img src="image_13.png" /></figure>
A

<figure><img src="image_14.png" /></figure>

B

<figure><img src="image_15.png" /></figure>
A

LO

<figure><img src="image_16.png" /></figure>

VO

<figure><img src="image_17.png" /></figure>

PrL

<figure><img src="image_18.png" /></figure>

AcbC

<figure><img src="image_19.png" /></figure>

Cpu

<figure><img src="image_20.png" /></figure>

Cga

<figure><img src="image_21.png" /></figure>

MS

<figure><img src="image_22.png" /></figure>

LSI

<figure><img src="image_23.png" /></figure>

S1

<figure><img src="image_24.png" /></figure>

LPO

<figure><img src="image_25.png" /></figure>

RE

<figure><img src="image_26.png" /></figure>

MD

<figure><img src="image_27.png" /></figure>

S2

<figure><img src="image_28.png" /></figure>

LD

<figure><img src="image_29.png" /></figure>

Sub

<figure><img src="image_30.png" /></figure>

PO

<figure><img src="image_31.png" /></figure>

DM

<figure><img src="image_32.png" /></figure>

CA1

<figure><img src="image_33.png" /></figure>

RSG

<figure><img src="image_34.png" /></figure>

ECT

<figure><img src="image_35.png" /></figure>

MGM

<figure><img src="image_36.png" /></figure>

B

<figure><img src="image_37.png" /></figure>

LO

AcbC

<figure><img src="image_38.png" /></figure>

MS

<figure><img src="image_39.png" /></figure>

LPO

<figure><img src="image_40.png" /></figure>

S2

<figure><img src="image_41.png" /></figure>

Po

<figure><img src="image_42.png" /></figure>

RSG

<figure><img src="image_43.png" /></figure>

<figure><img src="image_44.png" /></figure>

VO

Cpu

<figure><img src="image_45.png" /></figure>

LSI

<figure><img src="image_46.png" /></figure>

Re

<figure><img src="image_47.png" /></figure>

LD

<figure><img src="image_48.png" /></figure>

DM

<figure><img src="image_49.png" /></figure>

Ect

<figure><img src="image_50.png" /></figure>

<figure><img src="image_51.png" /></figure>

PrL

Cga

<figure><img src="image_52.png" /></figure>

S1FL

<figure><img src="image_53.png" /></figure>

MD

<figure><img src="image_54.png" /></figure>

Sub

<figure><img src="image_55.png" /></figure>

CA1

<figure><img src="image_56.png" /></figure>

MGM

<figure><img src="image_57.png" /></figure>

hM4D/DAPI
A

<figure><img src="image_58.png" /></figure>

B

<figure><img src="image_59.png" /></figure>

C

<figure><img src="image_60.png" /></figure>

D

<figure><img src="image_61.png" /></figure>
SUPPLEMENTAL INFORMATION

<figure><img src="image_62.png" /><figcaption>Figure S1 Characterization of the fear memory, control, and anatomical networks. Related to Figure 1.</figcaption></figure>
<figure><img src="image_63.png" /><figcaption>Figure S2. The disruption propagation model (DPM). Related to Figure 2.</figcaption></figure>
A

<figure><img src="image_64.png" /></figure>

B

<figure><img src="image_65.png" /></figure>

C

<figure><img src="image_66.png" /></figure>

D

<figure><img src="image_67.png" /></figure>

E

<figure><img src="image_68.png" /></figure>

F

<figure><img src="image_69.png" /><figcaption>Figure S3. DPM characterization. Related to Figure 2.</figcaption></figure>
<figure><img src="image_70.png" /><figcaption>Figure S4. Comparing network effects of simple node removal versus DPM. Related to Figure 2.</figcaption></figure>
<figure><img src="image_71.png" /></figure>

<figure><img src="image_72.png" /></figure>

<figure><img src="image_73.png" /></figure>

<figure><img src="image_74.png" /></figure>

<figure><img src="image_75.png" /></figure>

<figure><img src="image_76.png" /><figcaption>Figure S5. In silico DPM-based predictions provide best estimates of observed in vivo data. Related to Figures 5 and 6.</figcaption></figure>
<figure><img src="image_77.png" /><figcaption>Figure S6. Control and anatomical networks do not predict consolidation deficits. Related to Figure 6.</figcaption></figure>
SUPPLEMENTAL FIGURE LEGENDS

**Figure S1. Characterization of the fear memory, control, and anatomical networks.** A-B. Degree (A) and clustering (B) distributions of fear memory network contrasted with distributions generated using 1000 iterations of the Barabasi-Alberts preferential attachment scale-free model (light blue) or Watts-Strogatz small-world model (light green). C-D. Brain regions sorted by degree value (colors correspond to major brain division) for the fear memory network (C) and the control network built using the same p-value threshold (D). E-F. The anatomical network built using the same p-value threshold (E) or density (F) as the fear memory network. G-H. Brain regions sorted by degree value for the anatomical network built using the same p-value threshold (G) or density (H) as the fear memory network. I-J. Correlations between degree in the fear memory and control networks, with control networks generated using either the same p-value threshold (I) or density (J) as the fear memory network. K-L. Correlations between degree in the fear memory and anatomical networks, with anatomical networks generated using either the same p-value threshold (K) or density (L) as the fear memory network. *Related to Figure 1.*

**Figure S2. The disruption propagation model (DPM).** To illustrate the DPM, we implemented it in an exemplar network. At $t = 1$, the edges of the target node (green) are removed. Subsequent edge weights are altered according to the update rule described in the methods ($t = 2-4$). Once all edges have the opportunity to be updated once, all edges falling below a threshold are removed from the network ($t = 5$). *Related to Figure 2.*

**Figure S3. DPM characterization.** A-D. Plots showing how Shannon's entropy (H) varies with two model parameters (edge changes and threshold). A. How entropy for ΔGE changes with number of edge updates (holding the threshold at the value used for generating the network) B. How entropy for ΔGE changes with threshold (holding the number of edge updates at 1). C. How entropy for ΔGC changes with number of edge updates (holding the threshold at the value used for generating the network) D. How entropy for ΔGC changes with threshold (holding the number of edge updates at 1). In each plot, red circles indicate parameters used for modelling (i.e., 1 edge change allowed and using the same threshold as used for network generation). E. Example of change in size of giant component following DPM targeting the Re. F. Correlation between DPM-derived ΔGC and degree centrality for each individual node in the fear memory network. *Related to Figure 2.*

**Figure S4. Comparing network effects of simple node removal versus DPM.** A-B. Change in ΔGE (A) and ΔGC (B) for each brain region (node) calculated using either simple node deletion or DPM. Application of DPM to the network produced greater magnitude changes in global efficiency and giant component than the simple node deletion. Correlations between node degree and (C) ΔGE or (D) ΔGC following simple node deletion. *Related to Figure 2.*

**Figure S5. In silico DPM-based predictions provide best estimates of observed in vivo data.** A. Contextual fear memory (percent freezing) in mice infected with a control virus in the CA1 and treated with VEH (dark green) or CNO (light green). B-F. Correlation between behavioral data (Δfreezing) and DPM derived ΔGC (B), degree from the fear memory network (C), ΔGE from simple node removal (D), the $\alpha_{critical}$ values from the cascading failure model (E), and volume of individual brain regions (F). *Related to Figures 5 and 6.*

**Figure S6. Control and anatomical networks do not predict consolidation deficits.** A-B. Correlation between behavioral data (Δfreezing) and DPM-derived ΔGE from the control (A) or anatomical (B) networks built to match the density of the fear memory network. *Related to Figure 6.*
<table><caption>Table S1. List of abbreviations of nodes in fear memory network</caption><thead><tr><th>Subregion</th><th>Acronym</th><th>Name</th></tr></thead><tbody><tr><td>Association cortex</td><td>DLO</td><td>dorsolateral orbital cortex</td></tr><tr><td>Association cortex</td><td>LO</td><td>lateral orbital</td></tr><tr><td>Association cortex</td><td>VO</td><td>ventral orbital cortex</td></tr><tr><td>Association cortex</td><td>MO</td><td>medial orbital cortex</td></tr><tr><td>Association cortex</td><td>FrA</td><td>frontal association cortex</td></tr><tr><td>Association cortex</td><td>RSG</td><td>retrosplenial granular cortex</td></tr><tr><td>Association cortex</td><td>Ect</td><td>ectorhinal cortex</td></tr><tr><td>Association cortex</td><td>LEnt</td><td>lateral entorhinal cortex</td></tr><tr><td>Association cortex</td><td>PRh</td><td>perirhinal cortex</td></tr><tr><td>Association cortex</td><td>LPtA</td><td>lateral parietal association cortex</td></tr><tr><td>Association cortex</td><td>MPtA</td><td>medial parietal association cortex</td></tr><tr><td>Association cortex</td><td>TeA</td><td>temporal association cortex</td></tr><tr><td>Association cortex</td><td>IL</td><td>infralimbic cortex</td></tr><tr><td>Association cortex</td><td>PrL</td><td>prelimbic</td></tr><tr><td>Association cortex</td><td>Cg - a</td><td>anterio cingulate cortex - anterior</td></tr><tr><td>Association cortex</td><td>Cg - p</td><td>anterio cingulate cortex - posterior</td></tr><tr><td>Association cortex</td><td>AID</td><td>agranular insular cortex, dorsal part</td></tr><tr><td>Association cortex</td><td>AIP</td><td>agranular insular cortex, posterior part</td></tr><tr><td>Association cortex</td><td>AIV</td><td>agranular insular cortex, ventral part</td></tr><tr><td>Sensory cortex</td><td>AuV</td><td>secondary auditory cortex, ventral area</td></tr><tr><td>Sensory cortex</td><td>V1</td><td>primary visual cortex</td></tr><tr><td>Sensory cortex</td><td>S1ULp</td><td>primary somatosensory cortex, upper lip region</td></tr><tr><td>Sensory cortex</td><td>S1BF</td><td>primary somatosensory cortex, barrel field</td></tr><tr><td>Sensory cortex</td><td>S1FL</td><td>primary somatosensory cortex, forelimb region</td></tr><tr><td>Sensory cortex</td><td>S1J</td><td>primary somatosensory cortex, jaw region</td></tr><tr><td>Sensory cortex</td><td>S1HL</td><td>primary somatosensory cortex, hindlimb region</td></tr><tr><td>Sensory cortex</td><td>S1DZ</td><td>primary somatosensory cortex, dysgranular region</td></tr><tr><td>Sensory cortex</td><td>S1Sh</td><td>primary somatosensory cortex, shoulder region</td></tr><tr><td>Sensory cortex</td><td>S1Tr</td><td>primary somatosensory cortex, trunk region</td></tr><tr><td>Sensory cortex</td><td>S2</td><td>secondary somatosensory cortex</td></tr><tr><td>Hypothalamus</td><td>LH</td><td>lateral hypothalamic area</td></tr><tr><td>Hypothalamus</td><td>AH</td><td>anterior hypothalamic area</td></tr><tr><td>Hypothalamus</td><td>PH</td><td>posterior hypothalamic area</td></tr><tr><td>Hypothalamus</td><td>DM</td><td>dorsomedial hypothalamic nucleus</td></tr><tr><td>Hypothalamus</td><td>VMH</td><td>ventromedial hypothalamic nucleus</td></tr><tr><td>Hypothalamus</td><td>SHy</td><td>septohypothalamic nucleus</td></tr><tr><td>Hypothalamus</td><td>LM</td><td>lateral mammillary nucleus</td></tr><tr><td>Hypothalamus</td><td>RM</td><td>retromammillary nucleus</td></tr><tr><td>Hypothalamus</td><td>MM</td><td>medial mammillary nucleus</td></tr><tr><td>Hypothalamus</td><td>MPA</td><td>medial preoptic area</td></tr><tr><td>Hypothalamus</td><td>LPO</td><td>lateral preoptic area</td></tr><tr><td>Hippocampus</td><td>CA1 - a</td><td>field CA1 of hippocampus - anterior</td></tr><tr><td>Hippocampus</td><td>CA1 - m</td><td>field CA1 of hippocampus - medial</td></tr><tr><td>Hippocampus</td><td>CA1 - d</td><td>field CA1 of hippocampus - distal</td></tr><tr><td>Hippocampus</td><td>CA1 - p</td><td>field CA1 of hippocampus - posterior</td></tr><tr><td>Hippocampus</td><td>CA3</td><td>field CA3 of hippocampus</td></tr><tr><td>Hippocampus</td><td>DG - up</td><td>dentate gyrus - upper blade</td></tr><tr><td>Hippocampus</td><td>DG - low</td><td>dentate gyrus - lower blade</td></tr><tr><td>Cerebral nuclei</td><td>MS</td><td>medial septal nucleus</td></tr><tr><td>Cerebral nuclei</td><td>LSV</td><td>lateral septal nucleus, ventral part</td></tr><tr><td>Cerebral nuclei</td><td>LSD</td><td>lateral septal nucleus, dorsal part</td></tr><tr><td>Cerebral nuclei</td><td>LSI</td><td>lateral septal nucleus, intermediate part</td></tr><tr><td>Cerebral nuclei</td><td>BST</td><td>bed nucleus of the stria terminalis</td></tr><tr><td>Cerebral nuclei</td><td>VDB</td><td>nucleus of the vertical limb of the diagonal band</td></tr><tr><td>Cerebral nuclei</td><td>VP</td><td>ventral pallidum</td></tr><tr><td>Cerebral nuclei</td><td>CI</td><td>claustrum</td></tr><tr><td>Cerebral nuclei</td><td>La</td><td>lateral amygdaloid nucleus</td></tr><tr><td>Cerebral nuclei</td><td>BL</td><td>basolateral amygdaloid nucleus</td></tr><tr><td>Cerebral nuclei</td><td>Ce</td><td>central amygdaloid nucleus</td></tr><tr><td>Cerebral nuclei</td><td>AcbC</td><td>accumbens nucleus, core</td></tr><tr><td>Cerebral nuclei</td><td>AcbSh</td><td>accumbens nucleus, shell</td></tr><tr><td>Cerebral nuclei</td><td>Cpu - dl</td><td>caudate putamen (striatum) - dorsal lateral</td></tr><tr><td>Cerebral nuclei</td><td>Cpu - dm</td><td>caudate putamen (striatum) - dorsal medial</td></tr><tr><td>Midbrain</td><td>PAG</td><td>periaqueductal gray</td></tr><tr><td>Midbrain</td><td>VTA</td><td>ventral tegmental area</td></tr><tr><td>Midbrain</td><td>SN</td><td>substantia nigra</td></tr><tr><td>Thalamus</td><td>C</td><td>central thalamic nucleus</td></tr><tr><td>Thalamus</td><td>Hb</td><td>habenular nucleus</td></tr><tr><td>Thalamus</td><td>LP</td><td>lateral posterior thalamic nucleus</td></tr><tr><td>Thalamus</td><td>Rt</td><td>reticular thalamic nucleus</td></tr><tr><td>Thalamus</td><td>MGM</td><td>medial geniculate nucleus, medial part</td></tr><tr><td>Thalamus</td><td>MD</td><td>mediodorsal thalamic nucleus</td></tr><tr><td>Thalamus</td><td>Po</td><td>posterior thalamic nuclear group</td></tr><tr><td>Thalamus</td><td>PV</td><td>paraventricular thalamic nucleus</td></tr><tr><td>Thalamus</td><td>Sub</td><td>submedius thalamic nucleus</td></tr><tr><td>Thalamus</td><td>Re</td><td>reuniens thalamic nucleus</td></tr><tr><td>Thalamus</td><td>LD</td><td>laterodorsal thalamic nucleus</td></tr><tr><td>Thalamus</td><td>VPM</td><td>ventral posteromedial thalamic nucleus</td></tr><tr><td>Thalamus</td><td>VM</td><td>ventromedial thalamic nucleus</td></tr><tr><td>Thalamus</td><td>VL</td><td>ventrolateral thalamic nucleus</td></tr><tr><td>Thalamus</td><td>ZI</td><td>zona inserta</td></tr><tr><td>Thalamus</td><td>AM</td><td>anteromedial thalamic nucleus</td></tr><tr><td>Thalamus</td><td>AV</td><td>anteroventral thalamic nucleus</td></tr><tr><td>Thalamus</td><td>AD</td><td>anterodorsal thalamic nucleus</td></tr></tbody></table>
<table><caption>**Table S2.** Anatomical coordinates for targeted regions (from Paxinos and Franklin [2004])</caption><thead><tr><th rowspan="2">Region</th><th colspan="3">Coordinates</th></tr><tr><th>Antero_posterior</th><th>Dorso_ventral</th><th>Medio_lateral</th></tr></thead><tbody><tr><td>LO</td><td>2.34</td><td>2.9</td><td>1.5</td></tr><tr><td>VO</td><td>2.1</td><td>2.8</td><td>0.8</td></tr><tr><td>PrL</td><td>2.3</td><td>2</td><td>0.3</td></tr><tr><td>Cga</td><td>0.8</td><td>1.75</td><td>0.3</td></tr><tr><td>RSG</td><td>-2</td><td>1</td><td>0.2</td></tr><tr><td>Ect</td><td>-2</td><td>3.4</td><td>4</td></tr><tr><td>S1FL</td><td>0.38</td><td>1.5</td><td>2.2</td></tr><tr><td>S2</td><td>-0.82</td><td>2.8</td><td>3.7</td></tr><tr><td>LD</td><td>-1.2</td><td>3.2</td><td>1.2</td></tr><tr><td>MD</td><td>-0.82</td><td>3</td><td>0.25</td></tr><tr><td>Po</td><td>-1.7</td><td>3.2</td><td>1.3</td></tr><tr><td>Re</td><td>-0.58</td><td>4.2</td><td>0.2</td></tr><tr><td>Sub</td><td>-1.4</td><td>4.1</td><td>0.4</td></tr><tr><td>MGM</td><td>-2.92</td><td>3.2</td><td>1.75</td></tr><tr><td>Cpudm</td><td>0.85</td><td>3.5</td><td>1.7</td></tr><tr><td>AcbC</td><td>1.2</td><td>4.4</td><td>1.2</td></tr><tr><td>LSI</td><td>0.5</td><td>3.6</td><td>0.35</td></tr><tr><td>MS</td><td>0.6</td><td>4</td><td>0</td></tr><tr><td>DM</td><td>-1.7</td><td>5.1</td><td>0.5</td></tr><tr><td>LPO</td><td>0.15</td><td>5.4</td><td>0.8</td></tr><tr><td>CA1m</td><td>-1.8</td><td>1.5</td><td>1.5</td></tr></tbody></table>
<table><caption>**Table S3.** List of brain regions and their associated degree, DPM-derived ΔGE, and behavioral (ΔFreezing) values</caption><thead><tr><th>Subregion</th><th>Acronym</th><th>Degree</th><th>Δ GE</th><th>Δ Freezing (CNO-VEH)</th></tr></thead><tbody><tr><td>Association cortex</td><td>DLO</td><td>8</td><td>0.048</td><td></td></tr><tr><td>Association cortex</td><td>LO</td><td>10</td><td>0.070</td><td>-10.41</td></tr><tr><td>Association cortex</td><td>VO</td><td>5</td><td>0.052</td><td>-15.91</td></tr><tr><td>Association cortex</td><td>MO</td><td>4</td><td>0.034</td><td></td></tr><tr><td>Association cortex</td><td>FrA</td><td>2</td><td>0.012</td><td></td></tr><tr><td>Association cortex</td><td>RSG</td><td>3</td><td>0.028</td><td>-1.18</td></tr><tr><td>Association cortex</td><td>Ect</td><td>2</td><td>0.027</td><td>9.69</td></tr><tr><td>Association cortex</td><td>LEnt</td><td>1</td><td>0.020</td><td></td></tr><tr><td>Association cortex</td><td>PRh</td><td>2</td><td>0.026</td><td></td></tr><tr><td>Association cortex</td><td>LPtA</td><td>6</td><td>0.029</td><td></td></tr><tr><td>Association cortex</td><td>MPtA</td><td>3</td><td>0.027</td><td></td></tr><tr><td>Association cortex</td><td>TeA</td><td>4</td><td>0.062</td><td></td></tr><tr><td>Association cortex</td><td>IL</td><td>6</td><td>0.044</td><td></td></tr><tr><td>Association cortex</td><td>PrL</td><td>12</td><td>0.068</td><td>0.48</td></tr><tr><td>Association cortex</td><td>Cg - a</td><td>13</td><td>0.092</td><td>-5.74</td></tr><tr><td>Association cortex</td><td>Cg - p</td><td>11</td><td>0.068</td><td></td></tr><tr><td>Association cortex</td><td>AID</td><td>7</td><td>0.029</td><td></td></tr><tr><td>Association cortex</td><td>AIP</td><td>0</td><td>0</td><td></td></tr><tr><td>Association cortex</td><td>AIV</td><td>0</td><td>0</td><td></td></tr><tr><td>Sensory cortex</td><td>AuV</td><td>3</td><td>0.023</td><td></td></tr><tr><td>Sensory cortex</td><td>V1</td><td>4</td><td>0.066</td><td></td></tr><tr><td>Sensory cortex</td><td>S1ULp</td><td>2</td><td>0.015</td><td></td></tr><tr><td>Sensory cortex</td><td>S1BF</td><td>11</td><td>0.053</td><td></td></tr><tr><td>Sensory cortex</td><td>S1FL</td><td>12</td><td>0.052</td><td>-5.76</td></tr><tr><td>Sensory cortex</td><td>S1J</td><td>11</td><td>0.053</td><td></td></tr><tr><td>Sensory cortex</td><td>S1HL</td><td>11</td><td>0.061</td><td></td></tr><tr><td>Sensory cortex</td><td>S1DZ</td><td>17</td><td>0.118</td><td></td></tr><tr><td>Sensory cortex</td><td>S1Sh</td><td>8</td><td>0.054</td><td></td></tr><tr><td>Sensory cortex</td><td>S1Tr</td><td>12</td><td>0.078</td><td></td></tr><tr><td>Sensory cortex</td><td>S2</td><td>14</td><td>0.078</td><td>-5.60</td></tr><tr><td>Hypothalamus</td><td>LH</td><td>3</td><td>0.048</td><td></td></tr><tr><td>Hypothalamus</td><td>AH</td><td>0</td><td>0</td><td></td></tr><tr><td>Hypothalamus</td><td>PH</td><td>0</td><td>0</td><td></td></tr><tr><td>Hypothalamus</td><td>DM</td><td>0</td><td>0</td><td>-5.49</td></tr><tr><td>Hypothalamus</td><td>VMH</td><td>0</td><td>0</td><td></td></tr><tr><td>Hypothalamus</td><td>SHy</td><td>0</td><td>0</td><td></td></tr><tr><td>Hypothalamus</td><td>LM</td><td>2</td><td>0.020</td><td></td></tr><tr><td>Hypothalamus</td><td>RM</td><td>0</td><td>0</td><td></td></tr><tr><td>Hypothalamus</td><td>MM</td><td>0</td><td>0</td><td></td></tr><tr><td>Hypothalamus</td><td>MPA</td><td>3</td><td>0.015</td><td></td></tr><tr><td>Hypothalamus</td><td>LPO</td><td>7</td><td>0.048</td><td>-17.34</td></tr><tr><td>Hippocampus</td><td>CA1 - a</td><td>3</td><td>0.025</td><td></td></tr><tr><td>Hippocampus</td><td>CA1 - m</td><td>14</td><td>0.072</td><td>-22.02</td></tr><tr><td>Hippocampus</td><td>CA1 - d</td><td>11</td><td>0.063</td><td></td></tr><tr><td>Hippocampus</td><td>CA1 - p</td><td>6</td><td>0.045</td><td></td></tr><tr><td>Hippocampus</td><td>CA3</td><td>3</td><td>0.034</td><td></td></tr><tr><td>Hippocampus</td><td>DG - up</td><td>0</td><td>0</td><td></td></tr><tr><td>Hippocampus</td><td>DG - low</td><td>0</td><td>0</td><td></td></tr><tr><td>Cerebral nuclei</td><td>MS</td><td>0</td><td>0</td><td>4.15</td></tr><tr><td>Cerebral nuclei</td><td>LSV</td><td>0</td><td>0</td><td></td></tr><tr><td>Cerebral nuclei</td><td>LSD</td><td>5</td><td>0.034</td><td></td></tr><tr><td>Cerebral nuclei</td><td>LSI</td><td>15</td><td>0.089</td><td>-22.34</td></tr><tr><td>Cerebral nuclei</td><td>BST</td><td>4</td><td>0.063</td><td></td></tr><tr><td>Cerebral nuclei</td><td>VDB</td><td>4</td><td>0.037</td><td></td></tr><tr><td>Cerebral nuclei</td><td>VP</td><td>1</td><td>0.017</td><td></td></tr><tr><td>Cerebral nuclei</td><td>CI</td><td>0</td><td>0</td><td></td></tr><tr><td>Cerebral nuclei</td><td>La</td><td>0</td><td>0</td><td></td></tr><tr><td>Cerebral nuclei</td><td>BL</td><td>3</td><td>0.029</td><td></td></tr><tr><td>Cerebral nuclei</td><td>Ce</td><td>0</td><td>0</td><td></td></tr><tr><td>Cerebral nuclei</td><td>AcbC</td><td>13</td><td>0.082</td><td>-15.02</td></tr><tr><td>Cerebral nuclei</td><td>AcbSh</td><td>6</td><td>0.036</td><td></td></tr><tr><td>Cerebral nuclei</td><td>Cpu - dl</td><td>2</td><td>0.015</td><td></td></tr><tr><td>Cerebral nuclei</td><td>Cpu - dm</td><td>5</td><td>0.020</td><td>-7.59</td></tr><tr><td>Midbrain</td><td>VTA</td><td>2</td><td>0.011</td><td></td></tr><tr><td>Midbrain</td><td>PAG</td><td>5</td><td>0.044</td><td></td></tr><tr><td>Midbrain</td><td>SN</td><td>8</td><td>0.045</td><td></td></tr><tr><td>Thalamus</td><td>C</td><td>1</td><td>0.008</td><td></td></tr><tr><td>Thalamus</td><td>Hb</td><td>3</td><td>0.028</td><td></td></tr><tr><td>Thalamus</td><td>LP</td><td>2</td><td>0.011</td><td></td></tr><tr><td>Thalamus</td><td>Rt</td><td>1</td><td>0.011</td><td></td></tr><tr><td>Thalamus</td><td>MGM</td><td>0</td><td>0</td><td>10.68</td></tr><tr><td>Thalamus</td><td>MD</td><td>7</td><td>0.039</td><td>-2.89</td></tr><tr><td>Thalamus</td><td>Po</td><td>11</td><td>0.061</td><td>-8.81</td></tr><tr><td>Thalamus</td><td>PV</td><td>4</td><td>0.054</td><td></td></tr><tr><td>Thalamus</td><td>Sub</td><td>17</td><td>0.089</td><td>-0.35</td></tr><tr><td>Thalamus</td><td>Re</td><td>16</td><td>0.137</td><td>-23.68</td></tr><tr><td>Thalamus</td><td>LD</td><td>13</td><td>0.063</td><td>-21.6</td></tr><tr><td>Thalamus</td><td>VPM</td><td>12</td><td>0.067</td><td></td></tr><tr><td>Thalamus</td><td>VM</td><td>5</td><td>0.029</td><td></td></tr><tr><td>Thalamus</td><td>VL</td><td>1</td><td>0.015</td><td></td></tr><tr><td>Thalamus</td><td>ZI</td><td>4</td><td>0.023</td><td></td></tr><tr><td>Thalamus</td><td>AM</td><td>2</td><td>0.013</td><td></td></tr><tr><td>Thalamus</td><td>AV</td><td>4</td><td>0.029</td><td></td></tr><tr><td>Thalamus</td><td>AD</td><td>0</td><td>0</td><td></td></tr></tbody></table>
# SUPPLEMENTAL EXPERIMENTAL PROCEDURES

## Network analysis

The fear network was derived from previously published Fos count data from 84 brain regions following recall of contextual fear memory, tested 36 days following training (Wheeler et al., 2013). Inter-regional Pearson correlations were computed and a threshold of $p < 0.01$ (two-sided) was applied. We also examined lower and higher confidence networks with thresholds of $p < 0.05$, and $p < 0.005$, respectively. Positive correlations with $p$ values below the threshold were included as edges in the resulting networks. A control network was also generated from mice that were treated identically, but did not receive shock during training (Wheeler et al., 2013). This control network was thresholded using either the same p-value ($p < 0.01$, two-sided) or to yield approximately the same number of edges (i.e., equal density) as the fear memory network. Graph theoretical analysis and unweighted centrality measures were calculated using the NetworkX toolbox (version 1.11) in Python 2.7.11 (Hagberg et al., 2008).

## Disruption propagation model

To examine the effects of network node inactivation we developed a model to simulate the effect of node inactivation in a functional connectome. Typically, the effect of removing a node on the global efficiency or size of the largest connected component (giant component) on network function is performed by removing all edges associated with a node followed by recalculating global efficiency and giant component size. However, brain region inactivation is likely to have effects beyond its immediate neighborhood to other brain regions, so we developed a model to approximate this spreading disruption.

We applied an update rule to edge weights associated with a network that is iterated until the weights in the network no longer change. In the first step, all the edges associated with a specific node are set to zero. The node strength is then calculated for each node, defined as:

$$n_i(t) = \sum_j e_{ij}(t)$$

Where $e_{ij}$ is the edge weight between nodes i and j. Next, the change in node strength is calculated as:

$$\Delta n_i(t) = n_i(t - 1) - n_i(t)$$

Edge weights are then updated according to the following rule:

$$e_{ij}(t + 1) = e_{ij}(t) \left( 1 - \frac{\Delta n_i(t) + \Delta n_j(t)}{n_i(t) + n_j(t) - 2e_{ij}(t)} \right)$$

The adjacency matrix is updated until the edge weights no longer change, with the limitation that edge weights are permitted only one alteration. After the model is implemented, any weights which fall below the threshold that was used to originally generate the network are set to zero and the resulting change in global efficiency ($\Delta$GE) and size of the giant component ($\Delta$GC) are calculated. We applied the disruption propagation model individually to each node of the fear and control functional connectomes to obtain $\Delta$GE and $\Delta$GC values for each brain region. The model was implemented in R (version 3.2.2) using igraph (version 1.0.1) (Csardi and Nepusz, 2006).

To explore the parameter space of the model, we varied the number of edge weight changes and thresholds for removing edges following propagation in the fear memory network. We used the Shannon's entropy (H) for both $\Delta$GE and $\Delta$GC to determine the information content of the model output. H was calculated using the Entropy package [version 1.2.1] (Hausser and Strimmer, 2009) by discretizing the data into 50 bins ranging from 0 to the maximum value for each measure.

## Anatomical network analysis

The mouse anatomical connectome was obtained from Oh et al (2014), which uses the Allen Brain Atlas (ABA) to define brain regions. Our fear memory network was based on the brain atlas from Paxinos and Franklin (2004). To reconcile these two databases we combined regions to yield a common set of 70 nodes. We used two approaches to generate anatomical networks that were equivalent to the fear memory functional connectome.
In the first approach, we generated networks that were thresholded using the same *p* value (p ≤ 0.01). After thresholding, the ipsilateral and contralateral anatomical networks were combined. Next, nodes in both networks were combined such that the same brain regions were represented resulting in 70 nodes. Edges from combined nodes were averaged to generate the final edge weights.

The above approach to analyze the anatomical networks resulted in very different network densities (functional: 0.08, anatomical: 0.21). Therefore, in the second approach, we generated functional and anatomical networks of approximately equal densities. We generated the anatomical network by first combining ipsilateral and contralateral regions, then thresholded the network by retaining edges with the highest weights such that the network had the same density as the functional network (0.08). In both approaches, unweighted centrality metrics were then calculated as described above.

In order to apply the disruption propagation model to the anatomical network, we set all edge weights in the network to one. Next, we applied the model limiting the edge updates to one and using final cut-off thresholds ranging from 0 to 0.99 at intervals of 0.01. For each threshold, w calculated the Shannon's entropy (H) as described above and chose the threshold value that resulted in maximal entropy for each network.

## Mice

All procedures were conducted in accordance with policies of the Hospital for Sick Children Animal Care and Use Committee and conformed to both Canadian Council on Animal Care (CCAC) and National Institutes of Health (NIH) Guidelines on Care and Use of Laboratory. Male (8-9-week old) wild-type mice were used in all experiments. Mice were the F1 generation derived from crossing 129Svev [129] and C57BL/6N [C57] parents. Mice were weaned at 21 d, then housed 4-5 mice per cage. The housing room was maintained on a 12 h-12 h light-dark cycle, with lights on during the day.

Cages of mice were randomly assigned to 21 different experimental groups (target brain regions). Each target region group was further divided into 2 treatment groups (6-12 mice per group) that received either CNO or VEH. All mice in one cage were assigned to the same treatment group (as all mice in the same cage consumed drinking water containing either CNO or VEH).

## Virus

To silence neurons, we used a replication-defective herpes simplex viral vector (HSV) expressing the inhibitory DREADD receptor, hM4Di (kindly provided by Bryan Roth, UNC), along with a fluorescent marker (mCherry). Expression of hM4Di was driven by an EF1α (Human elongation factor-1 alpha) such that long-term (> 4 weeks) expression of the transgene is achieved. HSV virus was packaged using a replication-defective helper virus, purified on a sucrose gradient, pelleted and resuspended in 10% sucrose, as previously described (Richards et al., 2014, Rashid et al., 2016). The average titer of the virus stocks was 4.0 x 10⁷ infectious units/ml. We observed high transgene expression 3 d following microinjection of this virus.

## Surgery

Mice were pre-treated with atropine sulfate (0.1 mg/kg, ip), anesthetized (chloral hydrate, 400 mg/kg, ip) and placed in a stereotaxic frame. Viral vectors were bilaterally microinjected (1.5-2.0 µl/side, 0.1 µl/min) into the target region (see Table S2 for region coordinates) via glass micropipettes connected via polyethelene tubing to a microsyringe (Hamilton, Reno, NV). Micropipettes remained in place for 5 min after microinjection to ensure vector diffusion. Mice were treated with analgesia (ketoprofen, 5 mg/kg, sc) following surgery. Behavioral training began 7 d after surgery.

## Contextual fear training and testing

Context fear conditioning was conducted in stainless steel chambers (31 cm X 24 cm X 21 cm; Med Associates, St. Albans, VT). The floor consisted of stainless steel bars (diameter 3.2 mm) spaced 7.9 mm apart, through which a mild footshock could be delivered. The front, top and back of the chamber were made of clear acrylic and the two sides made of modular aluminum. Behavior was monitored via overhead cameras. An automated scoring system (Freezeframe software; Actimetrics) digitized the video signal at 4 Hz and compared frame by frame movement to determine the amount of time spent freezing. Mice were handled for 5 min/day for 3 days before training. During training, mice were placed in the conditioning chamber for a total of 5 min. After two min, 3 unsignalled footshocks were presented (2 s duration, 0.6 mA, 1 min apart). Following the last footshock, mice remained in the chamber for an additional min, and then returned to their home cage. Memory was tested 10 days after training by placing mice back in the chamber for 5 min while freezing was assessed.
## CNO treatment

Immediately after training, mice were systemically administered CNO (5 mg/kg, i.p., Toronto Research Chemicals) or VEH, depending on treatment group. CNO was first dissolved in 20 µl DMSO (Dimethyl sulfoxide, Sigma), then mixed into 380 µl 1× PBS. Mice assigned to the VEH condition received an injection of 20 µl DMSO mixed with 380 µl 1× PBS. After CNO or VEH injection, mice were returned to their home cage. According to treatment group assignment, CNO (5 mg/kg) or VEH was delivered via drinking water for 10 days. The CNO dose in drinking water was determined based on the amount of water consumed by mice in one day. No other water was available during this time. To assess whether CNO alone impacts fear conditioning, we infused a control virus (HSV-EF1α-GFP) into the CA1 region, administered VEH or CNO, and subjected mice to fear conditioning as described above (N = 8 mice/group).

## Verifying location of vector microinjection and extent of viral infection

Following testing in contextual fear conditioning, mice were deeply anesthetized and perfused transcardially with PBS followed by 4% paraformaldehyde (PFA). Brains were removed, fixed overnight in PFA, then transferred to 30% sucrose solution and stored at 4°C. Coronal brain slices (50 µm) were collected across the anterior-posterior extent of the injected region. Mice were included in subsequent data analysis only if robust bilateral mCherry expression in the target region was observed in at least 5 consecutive brain sections (across anterior-posterior axis). To determine the percent infected (mCherry+) cells within a given target region, we traced the target region across 15 serial sections in a set of randomly-selected brains (at least *N* = 2 per region) then counted the number of mCherry+ neurons within this specific region of interest (ImageJ software, NIH).

## In vivo assessment of chemogenetic inhibition

In the present series of experiments, we delivered CNO to mice via drinking water. Drinking is reduced, but not absent, in the inactive phase of the light-dark cycle in mice (Gordon et al., 1986). To test whether CNO administered in drinking water inhibits the activity of neurons expressing hM4Di at different times throughout the light-dark cycle, we microinjected HSV-hM4Di-mCherry bilaterally into the anterior cingulate cortex of mice. Three days later, mice received CNO or VEH in drinking water for 3 consecutive days. Mice were trained in context fear conditioning (as above, 3 footshocks, 0.6 mA, 2 sec, 1 min apart) at Zeitgeber time 0, 6, 12 or 18 (N = 3-8 mice/group), and were perfused 90 min after training. Brains were collected and processed for Fos immunohistochemistry. We observed that, despite being trained at different points in the light-dark cycle, CNO always reduced neuronal activation in neurons expressing hM4Di.

Using the same protocol, we tested whether 3 days of CNO treatment decreased neuronal activity in neurons infected with HSV-hM4Di in other brain regions (CA1, LD and MGM, N = 3-5 mice/group). For this experiment, mice were trained at ZT 6 and perfused 90 minutes later to assess the levels of Fos in infected neurons. In an additional experiment, we tested the effect of 10 days of CNO administered in drinking water (matching the time course of the main experiments) in CA1 infected neurons (N = 4 mice/group). We observed a similar reduction of neuronal activation in all brain regions analyzed irrespective of the number of days CNO was administered.

## Immunohistochemistry

To examine Fos protein levels across brain regions, coronal brain slices were incubated with blocking solution (0.1% BSA, 2% NGS, 0.3% Triton X-100) for 2 h at room temperature, then with anti-c-Fos primary rabbit antibody (1:1000, SC-52; Santa Cruz Biotechnology, Santa Cruz, CA) for 24 h. Sections were washed, incubated with anti-mouse Alexa 488 secondary antibody (1:500, Invitrogen) for 2 h at room temperature. Sections were washed, mounted on slides and coverslipped using PermaFluor mounting medium. Nuclei were counterstained with DAPI (Vectashield, Vector Labs Burlingame, CA). Images were obtained using a confocal laser scanning microscope (LSM 710; Zeiss).

## Permutation testing

We conducted permutation testing to determine the level of significance of the difference in freezing in CNO- versus VEH-treated mice. Permutation testing was performed by resampling the freezing data from all 21 experiments without replacement and shuffling drug (CNO vs. VEH) and brain region 1000 times. After each resampling, Δfreezing was recalculated for each brain region, resulting in a distribution of Δfreezing values that was used to calculate a *p* value for each of the 21 experiments. To correct for the inclusion of 21 individual experiments, we adjusted the resulting *p* values using an FDR of 5% using the Benjamani and Hochberg (1995) procedure as implemented in R (version 3.2.2) (Benjamini and Hochberg, 1995).
Cascading failure model

The cascading failure model described in (Crucitti et al., 2004) was implemented in R (version 3.2.2) using both the igraph (version 1.0.1) and sna (version 2.3.2) packages (Carter T. Butts (2014). sna: Tools for Social Network Analysis. R package version 2.3-2. http://CRAN.R-project.org/package=sna). Critical tolerance values (αcritical) were defined as tolerance values that resulted in the largest increase in global efficiency as the tolerance was increased.

SUPPLEMENTAL REFERENCES

Benjamini Y, Hochberg Y (1995) Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing. Journal of the Royal Statistical Society 57:289-300.

Crucitti P, Latora V, Marchiori M (2004) Model for cascading failures in complex networks. Physical review E, Statistical, nonlinear, and soft matter physics 69:045104.

Csardi G, Nepusz T (2006) The igraph software package for complex network research. InterJournal, Complex Systems 1696.5:1-9.

Gordon MN, Osterburg HH, May PC, Finch CE (1986) Effective oral administration of 17 beta-estradiol to female C57BL/6J mice through the drinking water. Biology of reproduction 35:1088-1095.

Hagberg AA, Schult DA, Swart PJ (2008) Exploring network structure, dynamics, and function using NetworkX. In: Proceedings of the 7th Python in Science Conference (Varoquaux, G. et al., eds), pp 11-15.

Hausser J, Strimmer K (2009) Entropy inference and the James-Stein estimator, with application to nonlinear gene association networks. Journal of Machine Learning Research 1669-1484.

Rashid AJ, Yan C, Mercaldo V, Hsiang HL, Park S, Cole CJ, De Cristofaro A, Yu J, Ramakrishnan C, Lee SY, Deisseroth K, Frankland PW, Josselyn SA (2016) Competition between engrams influences fear memory formation and recall. Science 353:383-387.

Richards BA, Xia F, Santoro A, Husse J, Woodin MA, Josselyn SA, Frankland PW (2014) Patterns across multiple memories are identified over time. Nature neuroscience 17:981-986.

Wheeler AL, Teixeira CM, Wang AH, Xiong X, Kovacevic N, Lerch JP, McIntosh AR, Parkinson J, Frankland PW (2013) Identification of a functional connectome for long-term fear memory in mice. PLoS computational biology 9:e1002853.