Individual structural features 1 constrain the functional connectome 2 3

3 Francesca Melozzi*, Eyal Bergmann*, Julie A. Harris, Itamar Kahn**, 4 Viktor Jirsa**, Christophe Bernard** 5 6 *Equal contribution first authors 7 **Equal contribution last authors 8 9 1. Aix Marseille Univ, Inserm, INS, Institut de Neurosciences des Systèmes, Marseille, 10 France 11 2. Department of Neuroscience, Rappaport Faculty of Medicine, Technion – Israel 12 Institute of Technology, Haifa, Israel 13 3. Allen Institute for Brain Science, Seattle, United States 14 15 Corresponding authors: 16 Christophe Bernard and Viktor Jirsa 17 christophe.bernard@univ-amu.fr ; viktor.jirsa@univ-amu.fr 18 19


INTRODUCTION
Structural connectivity (SC) refers to set of physical links between brain areas (Connectome, 49 (1)) and constitutes an individual fingerprint in humans (2, 3). Since the connectome provides the 50 physical substrate for information flow in the brain, it should impose strong constraints on whole 51 brain dynamics. Functional connectivity (FC), in the context of resting-state functional MRI, refers 52 to coherent slow spontaneous fluctuations in the blood oxygenation level-dependent (BOLD) signals 53 measured in the passive awake individual. FC is commonly used to assess whole brain dynamics and 54 function (4). Similar to SC, FC constitutes an individual functional fingerprint (5-7), and shows 55 specific alterations during aging and in brain disorders (8). There is thus a strong correlation 56 between the structural and the functional connectome. However, the causal relation between SC 57 and FC remains unknown. Large scale brain modeling offers a way to explore causality between 58 structural and functional connectivity. Combining experimental and theoretical approaches, we 59 here unravel and quantify the degree to which the individual's SC explains the same individual's 60 variations in FC. 61 We use The Virtual Brain (TVB), which allows building individual brain network models based 62 on structural data (9). This brain network modeling approach operationalizes the functional 63 consequences of structural network variations (10, 11) and allows to systematically investigate SC-64 FC relations in individual human brains (12-15). If SC constrains FC, SC-based simulations of FC 65 should match empirical FC within the bounds of validity of the metric. In primates and rodents, 66 individual SCs are derived from diffusion MRI (dMRI). However, dMRI does not provide information 67 on fiber directionality and suffers from limitations, such as underestimation of fiber length and 68 misidentification of crossing fiber tracks (16,17). Given the imprecision of dMRI derived SC, it is 69 difficult to estimate the validity of the simulations. This would require the knowledge of the ground 70 truth connectome of an individual, which cannot be measured at present. However, the currently 71 best gold standard can be derived in mice from cellular-level tracing of axonal projections (18), here 72 named the Allen connectome. Although individuality is lost (the SC is a composite of many mice) 73 and despite other limitations (19, 20), the Allen connectome provides details not available 74 otherwise and in particular not available in humans. Focusing our attention on simulating mouse 75 brain dynamics, we can thus use this detailed connectome to explore which missing features in the 76 dMRI account for individual SC-FC relations. Specifically, we predict that fiber directionality and fine 77 grain connectivity patterns should be key determinants. 78 Using dMRI data of 19 mice, we constructed 19 virtual mouse brain models (21), and 79 compared predicted FC with empirical FC data acquired from the same mice during passive 80 wakefulness (22). We found that individual SC predicts individual FC better than the dMRI-based 81 averaged SC, and that predictions can be improved by considering fiber directionality, coupling 82 weights and specific fiber tracks derived from the Allen connectome. We also found that 83 hemispherical lateralization in the mouse connectome influences whole brain dynamics. 84 85 RESULTS 86 We collected both dMRI and awake resting-state fMRI data (7 sessions per animal) from 19 hybrid 87 B6/129P mice. We extracted SC from dMRI data to build individual virtual brains, which were 88 imported into The Virtual Mouse Brain (TVMB), the extension of the open source neuroinformatic 89 platform TVB (9) designed for accommodating large-scale simulations and analysis in the mouse, to 90 generate in silico BOLD activity (21) using the reduced Wong Wang model (14, 23). We then 91 compared simulated and empirical FC for each mouse in order to assess the power that an individual 92 SC has to predict individual empirical FC derived from resting-state fMRI data ( Figure 1). Further, SC 93 was also obtained from the Allen connectome (our gold standard) in TVMB (21) to determine the 94 contribution of information not available in dMRI-based SC. Experimental and simulated resting-95 state activity was characterized by a dynamical switching between stable functional configurations 96 as revealed by the typical checkerboard patterns of Functional Connectivity Dynamics (FCD, Figure  97 S1a and S1b), as observed previously (14, 24, 25). As expected, FCD varied across recording sessions 98 ( Figure S1b). In contrast, static Functional Connectivity (FC) was stable between experimental 99 recording sessions (Figure 2A and Figure S1c). To compare the goodness of in silico resting-state 100 dynamics against in vivo data, we needed a metric stable across experimental recording sessions in 101 individual subjects, and thus we used the static FC for evaluating the Predictive Power (PP) of a SC. 102 We first defined the upper bound of the PP. The correlation value calculated between any 103 pair of empirical FC for each mouse provides us with an upper boundary of the PP, taking into 104 account inter-session variability and other sources of noise that preclude 100% PP accuracy (7,26). 105 In keeping with human data (6, 27), we found a high inter-session correlation for each of the 19 106 mice, demonstrating stability across different recording sessions in a given mouse (Figure 2A). Inter-107 session correlations within the same animal were greater than inter-subject correlations, indicating 108 that there is an individual functional organization per mouse, which may act as a functional 109 fingerprint. Next, we sought to examine the extent to which individual functional connectomes 110 correspond to individual structural connectomes. 111

SC obtained with a deterministic algorithm is a better predictor of FC 113
Here we considered probabilistic ( Figure 2B) and deterministic ( Figure 2C) dMRI-based SCs, 114 using SD_Stream (28) and iFOD2 (29) within Mrtrix3 software (28) tractography algorithms, 115 respectively. SC obtained with the deterministic algorithm yielded a greater PP than the SC obtained 116 with the probabilistic one ( Welch's test: P < 0.001), by itself, is not enough to explain the observed discrepancy in the PP. 120 Connection density does not fully account for the predictive power of a connectome, but instead 121 the relation depends on the connectome derivation ( Figure S2). We argue that the observed 122 difference in PP between deterministic and probabilistic processed connectomes depends on the 123 proportion of false negative (FN) and false positive (FP) connections introduced by the two different 124 algorithms: Zalesky and colleagues (2016)(30) show that the typical brain small-world topology is 125 biased by the introduction of FP connections two times more than by the introduction of FN 126 connections. In line with this finding, we attribute the difference in PP of the two connectomes to 127 the detrimental role of FP connections, which are more likely introduced by probabilistic than 128 deterministic tractography. However, deterministic tractography more likely overlooks some 129  Figure  141 2D,E), suggesting that the tracer-based connectome has structural information that is not present 142 in dMRI, but which is central to explain the emergence of the functional connectome, even at the 143 individual level. As the Allen SC was built from C57BL/6 mice, we verified the generality of our results 144 in this strain ( Figure S3a). Global signal regression, which improves structure-function relations and 145 averaging recording sessions within each mouse (31), which reduces noise, increased the PP but did 146 not alter the results ( Figure S3b-c). Finally, splitting the recording sessions of each mouse, and 147 submitting the data to a test-retest analysis revealed a close agreement between datasets ( Figure  148 S3d). Thus, our conclusions are strain-and preprocessing-independent, and reproducible. 149 150

Importance of long-range connections and directionality 151
To identify the source of the systematic superior performance of the Allen SC, we focused 152 on the major limitations of dMRI: (1) difficulty to resolve long axonal tracts, (2) lack of information 153 on fiber directionality and (3) imprecise estimation of connection weights. We estimated the 154 contribution of fiber length by filtering the Allen SC to include only fibers present in the dMRI-based 155 SC ( Figure 3A); we characterized the role of fiber directionality by symmetrizing the Allen SC (Figure 156 3.57±0.03 mm, respectively (Welch's test, P<0.001). Figure 3C shows that the PP of the filtered Allen 167 SC is lower than the original Allen SC ( = 0.461 ± 0.005, = 0.488 ± 168 0.005, Welch's test: P < 0.001; Figure 3C), however it remains statistically greater than the PP of 169 individual SCs ( − = 0.415 ± 0.005, Welch's test: P < 0.001; Figure 3C). Thus, 170 although connections overlooked by the dMRI method, which are mainly long-range connections, 171 are important to explain FC, other important structural features present in the Allen SC are 172 necessary to explain the discrepancy in PP between the tracer-based and dMRI-based connectomes. 173 We next focused on fiber directionality, since imposing bidirectional communication between 174 regions connected with unidirectional links in vivo may affect FC. We used an approach based on 175 surrogate SCs to test the role of directionality. Since the Allen SC contains directionality between 176 regions, we removed this information by symmetrizing it ( Figure 3A). Figure 3C shows that 177 symmetrizing the Allen SC reduces its PP significantly ( = 0.418 ± 0.004, = 178 0.488 ± 0.005, Welch's test: P < 0.001; Figure 3C), making it comparable to the PP of the dMRI-179 based SCs (Welch's test, P < 0.001 ). This demonstrates that directionality is a key determinant of 180 FC. It is notable that symmetrizing the filtered Allen SC led to a more modest reduction of the PP 181 than the symmetrisation of the original Allen SC ( = 0.418 ± 0.004, 182 & = 0.446 ± 0.004, Welch's test: P < 0.001; Figure 3C). We argue that the PP 183 difference can be explained by considering the amount of false positive introduced in the surrogate 184 connectomes by the transformation: the filtering operation inserts FN connections, while the 185 symmetrisation operation inserts both FN and FP connections (34). It follows that the symmetrized 186 and filtered connectome contains less FP than just the symmetrized connectome. Thus, as 187 previously discussed for the tractography processing, introducing FP connections, as produced by 188 the symmetrisation but not by the filtering, is more detrimental than the introduction of FN 189 connections. To summarize when the tracer-based connectome is manipulated in order to remove 190 the information not detected by dMRI, which is the inability to detect (i) the directionality of brain 191 connections, as well as, (ii) some brain connections, especially the long-range ones, we found that 192 the removal of the directionality information biases the predictive power of the connectome more 193 than the removal of the connections not detected by the dMRI method.  Figure 3B,C). We argue that the 199 asymmetrization of the dMRI connectomes biased the PP because asymmetrizing a matrix is an ill-200 posed problem, since there is no unique solution (more details can be found in the Methods). In 201 addition, there is no 1:1 correspondence between the connection strengths obtained with dMRI 202 (axonal bundles) and Allen ones (axonal branches) since axons tend to branch more or less profusely 203 when reaching their target zone. 204 This result confirms that the specificity of connections in individuals is a key feature for brain 237

dynamics. 238
For each individual SC, we identified the region in which replacement of its dMRI-239 connections with the Allen ones generates a new connectome, hybrid best , which has the best PP 240 improvement as compared to the other hybrid connectomes ( Figure S5a). Figure 4C shows that the 241 PP achieved by hybrid best is statistically indistinguishable to the one achieved by the filtered Allen 242 SC (Welch's test: = 0.95). In other words, it is sufficient to replace in the dMRI SC the connections 243 of one particular region with the corresponding Allen ones, to get a similar prediction, which is 244 specific for each mouse. 245

246
The asymmetric mouse brain 247 Finally, we sought to estimate the potential contribution of asymmetric transhemispheric 248 connectivity. Figure 4D shows that there is a considerable improvement in the PP of hybrid SCs when 249 using connections from the right hemisphere, as compared to those from the left one. The Allen 250 connections have been estimated using unilateral injection in the right hemisphere (18). Since no 251 tracer injections were done in the left hemisphere, TVMB uses a mirror image of the right 252 hemisphere to build the left one (21). This suggests that the tracer-based intra-hemispheric 253 connectivity predicts better right intra-hemispheric functional behavior than the left one, as 254 demonstrated in Figure S6a. Figure 4E shows that there is a significant relation between hemispheric 255 lateralization in the functional connectomes and the improvement in PP when the right and left 256 homotopic tracer area's connections are introduced in the dMRI SC ( = 0.14, = 0.01). Namely, 257 the more functional connections are asymmetric, the more the PP decreases when using the right 258 hemisphere connections to build the left ones. These results suggest that connectivity asymmetry 259 impacts brain dynamics and that it is region-and mouse-specific. 260 261 Hemispherical lateralization of the mouse brain 262 Figure 4E shows that the region demonstrating the greatest lateralization in terms of 263 functional connectivity in individual mice is the supplemental somatosensory area (SSs). Figure 4B  264 shows that when we introduce the mirror image of the right SSs into the dMRI SC, the predictive 265 power is considerably decreased, which means that the mirror image of the right SSs poorly 266 represents the true left SSs. We thus focused on the SSs area. If SC drives FC, we predicted that 267 introducing in the tracer-based connectome the detailed left SSs connections, instead of using the 268 mirror image of the right SSs ones, would increase the PP of the connectome. We first performed 269 tracer injections in the left SSs and determined the projection pattern. As predicted, we found 270 evidence of an asymmetric distribution of fibers between the left and right SSs ( Figure 5A). To test 271 whether these structural differences were sufficient to explain the functional ones, we introduced 272 the connections of the left SSs into the tracer connectome and obtained a statistically greater PP as 273 compared to the ones of purely mirrored connectomes built from the injection experiments 274 performed in the right SSs ( Figure 5B). Next, we introduced the left connections of the SSs into the 275 dMRI-based SCs (hybrid connectome), and, as predicted, we found a greater PP as compared to 276 using the mirror image of the right connections of the SSs as shown in Figure 5C (between the 14 277 experiments performed in the right SSs we take into account the one whose injection location is 278 more similar to those used in the left SSs injection experiment). Finally, since our previous results 279 demonstrate that the lateralization is animal-dependent, we sought to examine whether lateralized 280 FC is supported by lateralized SC, and found that the improvement of the PP following hybridization 281 of left SSs dMRI connections is indeed proportional to the degree of functional lateralization ( = 282 0.42, = 0.01; Figure 5D). Together, these results show that the mouse brain is structurally 283 lateralized, and that this lateralization impacts whole brain dynamics at the individual subject-level. 284 285 286

287
Our results provide direct evidence of a type of causality between SC and FC, in the sense 288 that individual structural connectomes predict their functional counterparts better than the dMRI-289 based averaged connectomes. Previous studies utilized the Allen Mouse Connectivity Atlas to study 290 structure-function relations at the group level using voltage-sensitive dyes (37) and FC (22,25,38). 291 In addition, a recent work in rats (39) used TVB to simulate FC based on SC and found strong 292 correlation at the group level; a similar finding has been reported in humans (40). Here we compared 293 structure-function relations in individual brains and we used the detailed Allen connectome as a 294 gold standard to identify regions and connections that play a preeminent role in the emergence of 295 individual brain dynamics. We showed that, similar to humans (6), intra-mice FCs are more stable 296 than inter-mice FCs (Figure 2A). We propose that the emergence of the personal features in the 297 functional data is, at least partially, driven by the emergence of underlying individual-specific 298 structural organization with individual stable features ( Figure 2E). Notwithstanding, we cannot 299 exclude that the variations in hemodynamic response functions (HRF) across animals and brain 300 location affect SC-FC relations, as it has been shown in humans (41). However, the fact that we 301 analyzed awake animals reduces the impact of this confounding factor (42, 43). 302 The detrimental role of false positive (FP) connections in the connectome topology has been 303 explored by (30) and (34) analyzing, respectively, the effect of FP as introduced by probabilistic 304 tractography and overlooking connections' directionality. In line with these findings, we showed 305 that the introduction of FP connections biases the connectome predictions. We found the dMRI-306 based connectomes processed with the deterministic tractography have a statistically greater PP 307 than those processed with probabilistic algorithms. Since the observed difference in PP is not 308 directly related with the difference in connections density ( Figure S2), we argue that the difference 309 in PP is driven by the different characteristics of the connections overlooked by both types of 310 tractography processing: more FP and less FN in the case of probabilistic processed connectivity, 311 and conversely in the case of deterministic processed connectivity. This highlights that brain 312 dynamics predictions are more accurate if connectome specificity is preserved, even at the cost of 313 sensitivity, as it is the case of deterministic processed connectome. 314 When processing the tracer-based data, the probabilistic computational model used to 315 construct the original Allen connectome (18) may introduce several false negative connections, 316 resulting in a low connection density reconstruction (35-73%), whilst others reported a 97% density 317 (19, 20). Here, we have used the Allen connectome builder interface, which implements a 318 deterministic approach to reconstruct whole brain connectivity (21), leading to a 98% density of 319 connections. Still, as shown in Figure 3B, the introduction of FN connections (filtered tracer-based 320 connectome) does not dramatically influence the PP of the connectome. 321 The main drawback of the Allen connectome is that it has been obtained from hundreds of 322 different mice, thus blurring individual variability. In keeping with this, we found that replacing most 323 individual dMRI connections with Allen connections reduces the PP. However, in some regions such 324 as the anterior cingulate and the caudoputamen, group-level Allen connections outperform 325 individual dMRI connections. This finding can be explained by the fact that connections from the 326 anterior cingulate are difficult to resolve as this area is located in the midline brain region, where 327 the cortex folds, resulting in an abrupt change in fiber directionality. Moreover, the axons make 328 sharp turns around the corpus callosum while the extraction algorithm assumes a logical 329 continuation of the vector direction. The connections of the striatum are often short and, due to its 330 multipolar organization without a clear gradient orientation limiting fiber reconstruction. To sum 331 up, including the tracer information of these complex fiber pathways in the dMRI-based 332 connectome significantly increases the predictive power of individual connectomes. It would be 333 interesting to test the same procedure when using whole brain modeling of human individuals by 334 including tracer information from non-human primates experiments. 335 Although the Allen connectome was obtained from C57BL/6 mice, brain dynamics of hybrid 336 F1 mice could be predicted by the Allen connectome, suggesting that the structural organization of 337 the mouse brain was not impacted by out-breeding. Findings from hybrid mice are considered more 338 generalizable to other strains (44), thus suggesting that the pattern observed here is not strain-339 specific. Nonetheless, since the genetic background affects the behavioral phenotype (45), it will be 340 important to systematically assess these findings in mouse strains where this aspect is directly 341 manipulated. 342 The Allen SC includes directionality and long-range connections, which are not well (or at all) 343 resolved by dMRI. However, the removal of the connections not resolved by dMRI-based 344 connectomes, mostly those characterized by long-range length, is not sufficient to explain the 345 discrepancy between the tracer-based and dMRI-based predictive power. In addition, we showed 346 that removing the directionality information from the tracer-based connectome, that it is 347 symmetrizing the connectome, thus introducing FP and FN connections, worsens the predictive 348 power more than the filtering operation, that consist in introducing just FN connections (34). This 349 shows the key role of connections directionality in predicting brain dynamics; and it confirms our 350 results on tractography algorithm processing: FP connections biases the predictive power ability of 351 the connectome more than FN. Finally, analyzing the connections strength differences between the 352 dMRI and tracer-based connectome, we have showed that connection strengths are the main 353 determinant of these dynamics, and consequently of individuality ( Figure 3D). Progress in connectomics enabled the development of large-scale brain models to study brain 362 function in health and disease (12, 47). Although individual whole brain modelling has a potentially 363 high translational value for the benefit of patients (15, 48, 49), the entire approach relies on the 364 extent to which individual differences in structural connectomes determine the emergent network 365 dynamics and consequent neuroimaging signals. Although SC does not provide enough 366 information to predict an epileptogenic zone in humans (50), our work shows that using more 367 precise information (e.g. obtained from tracer injections in non-human primates) to take into 368 account directionality, synaptic weights and poorly-resolved dMRI connections, will increase the 369 predictive power. Our here demonstrated link of individual SC and FC variability and brain network 370 modeling bears the promise to build a systematic approach to individual diagnosis and clinical 371 decision making (15, 47). 372

374
All procedures were conducted in accordance with the ethical guidelines of the National Institutes 375 of Health and were approved by the institutional animal care and use committee (IACUC) at 376 Technion. 19 male first generation hybrid mice (B6129PF/J1, 9-12 weeks old) were implanted with 377 MRI compatible head-posts using dental cement as previously described (22). After 3 days of 378 recovery, the animals were acclimatized to extended head fixation. This training included 5 handling 379 sessions performed over 3-5 days, and 4 daily acclimatization sessions inside the MRI scanner. In 380 each acclimatization session, mice were briefly anesthetized with isoflurane (5%), and then head-381 fixed to a custom-made cradle for gradually longer periods (2, 5, 10, 25 min). Subsequently, mice 382 underwent seven 45 min long awake imaging sessions, and one diffusion tensor imaging (DTI) 383 session under continuous isoflurane anesthesia (0.5-1%). A second group that included 7 male 384 inbred C57BL/6 mice (11-16 weeks old) was operated and scanned according to the same protocol. 385 Experiments involving mice were approved by the Institutional Animal Care and Use Committees of 386 the Allen Institute for Brain Science in accordance with NIH guidelines. For left side injections into 387 SSs, surgical procedures were followed as described in (18). In brief, a pan-neuronal AAV expressing 388 EGFP (rAAV2/1.hSynapsin.EGFP.WPRE.bGH, Penn Vector Core, AV-1-PV1696, Addgene ID 105539) 389 was used for injections into wildtype C57BL/6J mice at postnatal day 56 (stock no. 00064, The 390 Jackson Laboratory). SSs was targeted using stereotaxic coordinates from Bregma (AP: -0.7, ML, -391 3.4 and -3.9) and from brain surface (DV: 1.66). rAAV was delivered by iontophoresis with current 392 settings of 3 µA at 7 s 'on' and 7 s 'off' cycles for 5 min total, using glass pipettes (inner tip diameters 393 of 10-20 µm). Mice were perfused transcardially and brains collected 3 weeks post-injection for 394 imaging using serial two-photon tomography, using methods as previously described for the Allen 395 Mouse Connectivity Atlas (18). 396 397 To estimate functional connectomes, we build a parceled volume with a resolution compatible with 437 the fMRI technical constraints by manipulating the Allen Mouse Brain Connectivity Atlas (18) 438 downloaded through The Virtual Brain (9, 21). The volume was registered to the space of the 439 functional data ('target.nii.gz') using the nearest neighbor interpolation (FLIRT software, (51)). The 440 parcellation was reduced only to the areas where the SNR was higher than 12, and that had a volume 441 greater than 10 voxels (>0.1mm 3 ). Finally, very anterior and posterior areas, such as the main 442 olfactory bulb and cerebellum, were excluded from the parcellation due to registration problems 443 and susceptibility artifacts associated with the head-post implantation. Once the parcellation 444 volume was built, mean BOLD signals were extracted from the voxels composing each parcel, and 445 correlations were calculated from included frames only (based on motion scrubbing). 446 447

Diffusion-MRI data: 448
We processed diffusion-MRI data using MRtrix3 software (28). 449 The fiber orientation distribution of each voxel was estimated using the Constrained Spherical 450 Deconvolution (CSD, (52)). To obtain the tract streamlines we integrated the field of orientation 451 probability density using both deterministic (SD_Stream, (28)) and probabilistic (iFOD2, (29)) 452 algorithms; in both cases, the tracts number was set to 100 million. The streamlines were then 453 filtered using the SIFT algorithm (53) which selectively reduces the number of tracts exploiting the 454 fiber orientation density information obtained through the CSD in the previous step. The filtered 455 tracts of the right SSp-bfd obtained with probabilistic and deterministic algorithm, for an illustrative 456 mouse, are shown in Figure 2B and 2C respectively. We defined seed regions using the Allen Mouse 457 Brain Connectivity Atlas (18) obtained through the The Virtual Brain (9, 21); after registering the 458 volume in the individual mouse diffusion space, we reduced the parcellation only to those areas 459 whose volume was greater than 250 voxels (>1.125mm 3 ). 460 Using the deterministic and probabilistic streamlines and the node parcellation image, we 461 generated a connectome. The connection strength between each pair of nodes was defined as the 462 streamline count between the two nodes scaled by the inverse of the volumes of the two areas. A 463 radial research was performed to assign each streamline end point to a given node. If no node was 464 found inside a sphere of 1 mm radius, the streamline was not assigned to any node. We excluded 465  In order to assess the role of individual variability in dMRI data, we built an averaged connectome, 501 both for deterministic and probabilistic tractography. We defined the averaged connectome as a 502 matrix whose entry ´, i.e. the connection strength between area i and area j, is the arithmetic 503 mean of the values of the connection strength of the N individual dMRI connectomes containing 504 both area i and area j: 505 where n is the connectome index. 508 509

Filtered connectome: the role of long range connections 510
Comparing the connectomes in Figure 2B-D it is possible to notice that the number of long range 511 connections detected with probabilistic, and more dramatically with deterministic, tractography is 512 drastically lower than the one retrieved with the tracer method. It is well known that the accuracy 513 of fiber reconstruction with diffusion-MRI data decreases with fiber distance; however, it is still 514 unclear how to address this methodological limitation. 515 In order to quantify the impact of long-range connections presence in the simulated system, we 516 filtered down the tracer connectome by removing all the connection not present in the deterministic 517 diffusion-MRI connectomes. The filtered tracer connectome is shown in Figure 3A. 518 519 Symmetrized and asymmetrized connectome: the role of fiber directionality 520 The incapacity to detect fiber directionality is one of the main drawbacks of dMRI method. 521 In order to understand the influence of this property in the simulated system, we symmetrized the 522 tracer connectome and we asymmetrized the diffusion-MRI connectome. 523

Symmetrized tracer connectome: 524
For each asymmetric matrix exists one, and only one, decomposition that enables us to find the 525 corresponding symmetric matrix: each generic matrix A can be decomposed in its symmetric and 526 asymmetric part as: 527 = sym + asym = 1 2 ( + ) ⏟ symmetric part + 1 2 ( − ) ⏟ asymmetric part 528 thus, symmetrizing a matrix means neglecting its asymmetric part. 529 Following this consideration, the tracer symmetric connectome was defined as the matrix whose 530 entries ^ are defined as: 531 532 ^= + 2 533 ( 2 ) 534 where represents the original tracer connection strength between area i and area j. 535 The symmetric tracer structural connectivity is shown in Figure 3A. 536 537 Asymmetrized dMRI connectome: 538 As opposed to symmetrizing a matrix which is a straightforward procedure, a-symmetrizing a matrix 539 is an ill-posed problem, since it means introducing a new degree of freedom in the system, and not 540 a unique solution exists. Thus, to find the asymmetric version of the dMRI connectome we assumed 541 some constraints: we injected in each connection the same degree of asymmetry contained in the 542 respective tracer connection, while preserving the dMRI weight balancing. In other words, our 543 asymmetrization method assumes that the degree of asymmetry is independent on the connection 544 strength value. 545 We defined the asymmetry degree between connection i and connection j as: Specifically, we defined ˇ= − and ˇ= + , where is defined as: 559 It is important to notice that the asymmetrization of the connectome does not imply the 562 introduction of new connections: if the original diffusion-MRI connection is absent it follows, 563 from the last equation, that also the increment will be zero. 564 The asymmetrized deterministic connectome is shown in Figure 3C. The test involves the calculation of a statistic, usually called U. 596 For sample size above 20, which is our case, the distribution of the U variable under the null 597 hypothesis can be approximated using the normal distribution. The U variable ranges between 0 598 and 1 2 , where 1 and 2 are the dimensionalities of the two connectomes. For ≤ * = 1 2 2 ⁄ 599 the test states that the 0 can be rejected. 600 It follows that it is possible to normalize the U value between 0 and 1, by dividing it by the product 601 of the dimensionality of the two connectomes; in this case the discriminator value * is 0.5. 602 603

Graph theory measures 604
We characterized anatomical mouse brain structures using graph theory tools; in particular, we 605 characterized each connectome by calculating its degree distribution and its topological properties. 606 607 Degree distribution 608 For each connectome, we calculated the directed degree distribution as: 609 We quantified the probability that the degree distribution comes from a given theoretical 611 distribution through the Kolmogorov Smirnov test. is the local excitatory recurrence and is the 647 external input current.
is the coupling strength i.e. a scalar parameter which scales all the 648 connection strengths without altering the global topology of the network. We set the noise 649 amplitude σ of the normally distributed stochastic variable to 0.015 since this level of noise is 650 able to sustain brain states oscillations. 651 The local excitatory recurrence, , and of the local excitatory recurrence and are set to 0.3 nA 652 and 1, respectively, in order to enrich the non-linearity of the dynamics of each brain region. In this 653 case, studying the dynamics of isolated brain areas ( = 0 in equation ( 7 ), it is possible to notice 654 that each brain area is in a bistable state and it oscillates between high and low activity fixed points 655 (14). It has been noticed in (14) that enriching the non-linearity of each brain areas introduces global 656 network's attractors that are not in trivial relation with the anatomical connectivity; this model 657 offers the chance to reproduce the non-stationary features of the functional connectivity patterns, 658 as shown by the checkboard pattern of the simulated FCD in Figure S1b. 659 For each connectome, we identified the coupling strength values for which the system is 660 experiencing multistability. The optimal coupling strength range is defined as the values for which 661 the system low and high states coexist, and it is identified by building the system's bifurcation 662 diagram as described in (13). The FC matrix is defined as the matrix whose ij-th element is the Pearson correlation between the 685 BOLD signal of the brain region i and of the brain region j. An example of empirical and simulated 686 FC is shown in figure 1. An example of empirical and simulated FCD is shown in Figure 1. 702 The typical FCD matrix during resting-state has a checkboard appearance (see experimental FCD in 703 Figure 1) indicating that the system is switching between stable networks configuration (14, 24). We 704 quantified the switching degree of the simulated and experimental system as the variance of the 705 triangular part of the FCD once excluded the overlapping entries (i.e. the entries of the FCD matrix 706 that quantify the correlation of FCs calculated over the sliding window of overlapping time interval). 707 We called this quantity clue of switching (cs). 708

Functional Meta-Connectivity (FMC) 710
To compare the dynamical evolution of the functional connections between different systems we 711 calculate, for each system, the FMC. The FMC, of a BOLD signals of N areas, is a 2 x 2 matrix that 712 quantifies the inter-region functional correlation of the system. The ij-th element of the FMC 713 represents the Pearson correlation between the temporal evolution of the i-th functional link and 714 the j-th functional link. 715 716 1.8. Comparing experimental and simulated BOLD signals 717 We quantified the ability of a given connectome to be used as a skeleton of the virtual system by 718 comparing the accordance between the simulated functional connections, generated using that 719 connectome, and the functional connections arranged during the experimental resting state 720 recordings. 721 As discussed in the article we used the FC as the metric for quantifying the experimental and 722 simulated functional connections. Indeed, although the FC metric is not able to capture the non-723 stationary nature of the resting state signals, the static functional connections are stable across 724 resting state recordings in the same animal; on the other hand, FMC, that is able to quantify the 725 dynamical evolution of the functional connections, is not stable across resting state recordings (see 726 Figure S1), and thus cannot be used for quantifying the goodness of the simulated activity. 727

728
The simulated functional network is generally composed of more areas than the experimental one 729 since the simulation is based on the anatomical information that has a greater spatial resolution 730 than the functional ones. Thus, in order to correlate the eFC and the sFC we reduced them to the 731 same number of areas. For each virtual mouse brain we simulated for different values of the 732 coupling strength G and then select the value of G for which the simulated neuronal network is able 733 to obtain the more realistic outcome, i.e. the maximum correlation between the empirical and 734 simulated FC (12, 14, 58).     Table S1.   We quantify the presence of the switching, i.e. the checkboard pattern in the FCD matrix, as the variance of the triangular part of the FCD, once excluded the overlapping entries. We call this quantity: clue of switching (cs). The cs value is indicated below each FCD. FCDs are ordered for increasing cs values. The checkboard pattern appears more clearly as cs increases.

Supplementary information
(c) The height of the bar represents the Pearson correlation between inter-sessions for experimental FC (magenta bar) and FMC (blue bar). The result shows that the FMC matrix can not be considered as a metric since FMC is poorly reproducible across sessions in the same animal.      green labels are for tracer-based connectomes.
(b) Topological measures calculated for all the connectomes used in this study (x-axis); blue, magenta and green labels are for connectomes obtained with, respectively, probabilistic dMRI, deterministic dMRI and tracer method. Bullet and diamond labels are the fractional deviations of the clustering coefficient and shortest path length, respectively, from their respective null mode (lattice and random, respectively). These values are used to define the Small World Propensity (SWP, star marker), for each graph. All connectomes have a SWP index above the threshold for small world topological structure (φ > 0.6, Muldoon et al., 2016). Importantly, the tracer connectomes have a SWP index always smaller than that of the deterministic dMRI connectomes, which in turn have a SWP index always smaller than that of the probabilistic dMRI connectomes. Note that the relation between the SWP index of the different connectomes' families is exactly the inverse of the relation between the predictive power (PP) of the different connectomes' families: SW P prob > SW P det > SW P tracer and P P prob < P P det < P P tracer .
(c) and (d) show the relation between the SWP and the predictive power of dMRI connectomes processed with probabilistic and deterministic tractography, respectively. Note the significant inverse linear relation between the SWP of a given deterministic dMRI connectome and its corresponding predictive power. In line with the previous observation (b), we can conclude that the more a connectome has a topological structure similar to the tracer one, the more reliable is the prediction of resting state dynamics.  hemisphere. The difference in the predictive power shows that intra-hemispheric tracer-based connections, obtained after injecting the compound in the right hemisphere, are able to predict better right than left intra-hemispheric functional connections. The result suggests that the mouse brain is lateralized.