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Three Interdependent Architectural Gradients
Intrinsic Functional Connectivity is Organized as Three Interdependent Gradients
Jiahe Zhanga1, Olamide Abioseb1, Yuta Katsumia, Alexandra Touroutoglouc,d,e, Bradford C.
Dickersonc,d,e & Lisa Feldman Barretta,c,d*
aDepartment of Psychology, Northeastern University, Boston, MA 02115
bCenter for Law, Brain and Behavior, Massachusetts General Hospital, Boston, MA 02114
cAthinoula A. Martinos Center for Biomedical Imaging, Massachusetts General Hospital and
Harvard Medical School, 149 13th St., Charlestown, MA 02129
dDepartment of Neurology, Massachusetts General Hospital and Harvard Medical School, 149
13th St., Charlestown, MA 02129
eFrontotemporal Disorders Unit, Department of Neurology, Massachusetts General Hospital and
Harvard Medical School, 149 13th St., Charlestown, MA 02129
1J.Z. and O.A. contributed equally to this work.
Supplementary Information
Figure S1. We sampled 109 seeds based on previous literature. These seeds span 5 major motifs:
attention (red), default (yellow), executive (green), exteroceptive (light blue), and salience (dark
blue). Note seeds belonging to different motifs sometimes occupy the same anatomical region,
e.g. attention (red) and salience (dark blue) in superior parietal lobule. We visualized the seeds
on inflated brain surfaces using the BrainNet Viewer1.
Attention Default Executive Exteroceptive Salience
Three Interdependent Architectural Gradients
Figure S2. Flowchart for functional connectivity and similarity matrix calculation. We relied on
replication instead of arbitrary threshold to find meaningful connectivity.
Joint
mask
Orbitofrontal
insula seed
Discovery group map Replication group map
Calculate connectivity
Binarize at 0
Conjoin
Calculate connectivity
Binarize at 0
Conjoin
Mask
Mask
Apply mask
Apply mask
Discovery group mask Replication group mask
Masked discovery
group map
Discovery group
other masked maps
Masked replication
group map
Replication group
other masked maps
Discovery group similarity matrix Replication group similarity matrix
DISCOVERY GROUP REPLICATION GROUP
Calculate
h
2
Calculate
h
2
Calculate
h
2
Calculate
h
2
Calculate
h
2
Calculate
h
2
Three Interdependent Architectural Gradients
Figure S3. Illustration of possible MDS results. A) Circumplex. B) Discrete simple structure. C)
Non-discrete simple structure.
Dimension 2
Dimension 1
Dimension 2
Dimension 1
Dimension 2
Dimension 1
ABC
Three Interdependent Architectural Gradients
Figure S4. MDS results of the replication sample also revealed a circumplex structure of
similarity. Each point in the scatterplot represents a connectivity map. We plotted A) Dimension
1 vs. Dimension 2, B) Dimension 1 vs. Dimension 3, and C) Dimension 2 vs. Dimension 3 to
facilitate interpretation. N = 109.
Attention Defaul t Executive Exteroceptive Salience
A B C
Three Interdependent Architectural Gradients
Figure S5. Gradient maps of the replication sample visualized on the brain surfaces. For each
dimension, we created a gradient map by weighting every connectivity map by its dimension
loading and summing across all weighted maps to create a composite (i.e., a weighted sum akin
to factor scores). We visualized the gradient maps on inflated brain surfaces using Caret2.
Gradient 1 Gradient 2 Gradient 3
External
Internal
Representation
Modulation
Peripheral
Central
Three Interdependent Architectural Gradients
Figure S6. Gradient 3 loadings of the replication sample also correlated positively with
anatomical centrality (r = 0.681, p < 0.001).
Three Interdependent Architectural Gradients
Figure S7. We tested robustness of the three-dimensional solution of MDS. The original analysis
was based on 109 seeds and retained global signal regression (GSR+) (boxed, middle row). We
varied these parameters by removing global signal regression from preprocessing (GSR-; top
row) and by sampling 264 seeds across the cortex per3 (bottom row). Across all three sets of
parameters, a three-dimensional solution consistently led to substantial reduction in stress and
gain in explained variance. A) Stress was plotted as a function of the number of estimated
dimensions. Lower stress indicates better fit. The scree plot of normalized stress had an “elbow”
when dimensionality was at 3, since further addition of dimensions did not substantially reduce
normalized stress. Dashed line indicates normalized stress of 0.05. B) DAF was plotted as a
function of the number of estimated dimensions. Higher DAF indicates better fit. Dashed line
indicates DAF of 0.98.
2 4 6 8 10
Dimensionality
0.8
0.85
0.9
0.95
1
Dispersion accounted for (DAF)
109 seeds, GSR-
2 4 6 8 10
Dimensionality
0
0.05
0.1
0.15
0.2
Normalized raw stress
109 seeds, GSR-
2 4 6 8 10
Dimensionality
0
0.05
0.1
0.15
0.2
Normalized raw stress
109 seeds, GSR+
2 4 6 8 10
Dimensionality
0.8
0.85
0.9
0.95
1
Dispersion accounted for (DAF)
109 seeds, GSR+
2 4 6 8 10
Dimensionality
0.8
0.85
0.9
0.95
1
Dispersion accounted for (DAF)
264 Seeds, GSR+
2 4 6 8 10
Dimensionality
0
0.05
0.1
0.15
0.2
Normalized raw stress
264 Seeds, GSR+
109 seeds
GSR-
109 seeds
GSR+
264 seeds
GSR+
Stress Explained variance
Three Interdependent Architectural Gradients
Figure S8. We tested robustness of the circumplex structure of MDS output. The original
analysis was based on 109 seeds and retained global signal regression (GSR+) (boxed, middle
row). We varied these parameters by removing global signal regression from preprocessing
(GSR-; top row) and by sampling 264 seeds across the cortex per3 (bottom row). Across both
sets of GSR+ solutions (bottom two rows), scatterplots in coordinate space consistently revealed
a circumplex-like shape. The GSR- condition (top row) showed decreased power in detecting
circumplexity. Each point in the scatterplot represents a connectivity map. Dimensions 1-3 are
plotted pairwise in two-dimensional coordinate space to facilitate interpretation.
-1 -0.5 0 0.5 1
Dimension 1 loadings
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Dimension 2 loadings
-1 -0.5 0 0.5 1
Dimension 1 loadings
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Dimension 3 loadings
-1 -0.5 0 0.5 1
Dimension 2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Dimension 3
-1 -0.5 0 0.5 1
Dimension 1 loadings
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Dimension 3 loadings
-1 -0.5 0 0.5 1
Dimension 2 loadings
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Dimension 3 loadings
-1 -0.5 0 0.5 1
Dimension 1 loadings
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Dimension 3 loadings
-1 -0.5 0 0.5 1
Dimension 2 loadings
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Dimension 3 loadings
109 seeds
GSR-
109 seeds
GSR+
264 seeds
GSR+
-1 -0.5 0 0.5 1
Dimension 1 loadings
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Dimension 2 loadings
-1 -0.5 0 0.5 1
Dimension 1 loadings
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Dimension 2 loadings
Three Interdependent Architectural Gradients
Figure S9. The anterior commissure (red dot), with MNI coordinates (0, 0, 0), was used as a
proxy for the center point of the brain since it is approximately equidistant from the most distal
points of the cerebrum, and approximately occupies the middle point along the anterior-posterior
axis of the medial limbic ring consisting of the cingulate cortex and medial orbitofrontal cortex.
x=0 y=0
Three Interdependent Architectural Gradients
Figure S10. When functional connectivity maps were thresholded at z > 0.2, both goodness-of-fit
estimates were still highly replicable.
Stress Explained variance
Discovery
group
Replication
group
2 4 6 8 10
Dimensionality
0
0.05
0.1
0.15
0.2
0.25
0.3
Normalized raw stress
2 4 6 8 10
Dimensionality
0
0.05
0.1
0.15
0.2
0.25
0.3
Normalized raw stress
2 4 6 8 10
Dimensionality
0.7
0.75
0.8
0.85
0.9
0.95
1
Dispersion accounted for (DAF)
2 4 6 8 10
Dimensionality
0.7
0.75
0.8
0.85
0.9
0.95
1
Dispersion accounted for (DAF)
Three Interdependent Architectural Gradients
Figure S11. When functional connectivity maps were thresholded at z > 0.2, the circumplex-like
structure was retained.
Attention Defaul t Executive Exteroceptive Salience
Discovery group
Replication group
Three Interdependent Architectural Gradients
Figure S12. When functional connectivity maps were thresholded at z > 0.2 and z < -0.2, both
goodness-of-fit estimates were still highly replicable.
Stress Explained variance
Discovery
group
Replication
group
2 4 6 8 10
Dimensionality
0.75
0.8
0.85
0.9
0.95
1
Dispersion accounted for (DAF)
2 4 6 8 10
Dimensionality
0.75
0.8
0.85
0.9
0.95
1
Dispersion accounted for (DAF)
2 4 6 8 10
Dimensionality
0
0.05
0.1
0.15
0.2
0.25
Normalized raw stress
2 4 6 8 10
Dimensionality
0
0.05
0.1
0.15
0.2
0.25
Normalized raw stress
Three Interdependent Architectural Gradients
Figure S13. When functional connectivity maps were thresholded at z > 0.2 and z < -0.2, the
circumplex-like structure was retained.
Attention Defaul t Executive Exteroceptive Salience
Discovery group
Replication group
Three Interdependent Architectural Gradients
Table S1. Literature-based seeds.
Major
Domain
Network
Name
Seed
Hemisphere
Region
Reference
MNI Coordinates
x
y
z
Attention
Dorsal
Attention
L
frontal eye field
Fox et al. (2006)
-24
-21
49
L
frontal eye field
Vincent et al. (2008)
-26
-8
50
L
frontal eye field
Yeo et al. (2011)
-24
2
58
L
intraparietal sulcus
Fox et al. (2006)
-28
-66
56
L
middle temporal motion area
Vincent et al. (2008)
-46
-70
-2
L
premotor cortex
Yeo et al. (2011)
-50
10
28
L
superior parietal lobule
Vincent et al. (2008)
-28
-52
58
L
superior parietal lobule
Yeo et al. (2011)
-24
-60
64
R
frontal eye field
Fox et al. (2006)
25
-20
49
R
frontal eye field
Vincent et al. (2008)
28
-8
50
R
frontal eye field
Yeo et al. (2011)
24
2
58
R
intraparietal sulcus
Fox et al. (2006)
27
-67
57
R
middle temporal motion area
Vincent et al. (2008)
46
-70
-4
R
premotor cortex
Yeo et al. (2011)
50
10
28
R
superior parietal lobule
Vincent et al. (2008)
24
-56
56
R
superior parietal lobule
Yeo et al. (2011)
24
-60
64
Default
Amygdala
affiliation
L
medial amygdala
Bickart et al. (2012)
-14
-4
-20
R
medial amygdala
Bickart et al. (2012)
14
-4
-20
Default
L
anterior medial prefrontal
cortex
Andrews-Hanna et al.
(2010)
-6
52
-2
L
hippocampus
Andrews-Hanna et al.
(2010)
-22
-20
-26
L
posterior cingulate cortex
Andrews-Hanna et al.
(2010)
-8
-56
26
Three Interdependent Architectural Gradients
L
retrosplenial cortex
Andrews-Hanna et al.
(2010)
-14
-52
8
L
temporo-parietal junction
Andrews-Hanna et al.
(2010)
-54
-54
28
R
hippocampus
Andrews-Hanna et al.
(2010)
22
-20
-26
R
retrosplenial cortex
Andrews-Hanna et al.
(2010)
14
-52
8
R
temporo-parietal junction
Andrews-Hanna et al.
(2010)
54
-54
28
M
dorsomedial prefrontal cortex
Andrews-Hanna et al.
(2010)
0
52
26
M
dorsomedial prefrontal cortex
Yeo et al. (2011)
0
50
24
M
posterior cingulate cortex
Yeo et al. (2011)
0
-64
40
M
ventromedial prefrontal cortex
Andrews-Hanna et al.
(2010)
0
26
18
Language
L
middle temporal gyrus
Turken & Dronkers
(2011)
-64
-32
-6
L
pars triangularis
Turken & Dronkers
(2011)
-55
34
3
L
pars triangularis
Tomasi & Volkow (2012)
-51
27
18
L
superior temporal gyrus
Tomasi & Volkow (2012)
-51
-51
30
Mentalizing
L
dorsomedial prefrontal cortex
Baetens et al. (2014)
-10
58
24
L
precuneus
Baetens et al. (2014)
-4
-52
30
L
ventromedial prefrontal cortex
Baetens et al. (2014)
-2
44
-12
Executive
Executive
L
anterior intraparietal lobule
Vincent et al. (2008)
-52
-50
46
L
anterior intraparietal lobule
Yeo et al. (2011)
-50
-40
48
L
anterior prefrontal cortex
Vincent et al. (2008)
-36
58
10
L
dorsolateral prefrontal cortex
Seeley et al. (2007)
-42
34
20
L
dorsolateral prefrontal cortex
Vincent et al. (2008)
-50
20
34
L
dorsolateral prefrontal cortex
Yeo et al. (2011)
-50
28
24
Three Interdependent Architectural Gradients
L
lateral parietal lobe
Seeley et al. (2007)
-42
-50
48
R
anterior intraparietal lobule
Vincent et al. (2008)
52
-46
46
R
anterior intraparietal lobule
Yeo et al. (2011)
50
-40
48
R
anterior prefrontal cortex
Vincent et al. (2008)
34
52
10
R
dorsolateral prefrontal cortex
Seeley et al. (2007)
46
36
18
R
dorsolateral prefrontal cortex
Vincent et al. (2008)
46
14
44
R
dorsolateral prefrontal cortex
Yeo et al. (2011)
50
28
24
R
lateral parietal lobe
Seeley et al. (2007)
46
-54
42
M
medial superior frontal gyrus
Yeo et al. (2011)
0
28
44
Multiple-
demand
L
anterior insula
Fedorenko et al. (2013)
-35
18
3
L
inferior frontal sulcus
Fedorenko et al. (2013)
-41
23
29
L
intraparietal sulcus
Fedorenko et al. (2013)
-37
-56
41
L
rostral prefrontal cortex
Fedorenko et al. (2013)
-21
43
-10
R
anterior insula
Fedorenko et al. (2013)
35
18
3
R
inferior frontal sulcus
Fedorenko et al. (2013)
41
23
29
R
intraparietal sulcus
Fedorenko et al. (2013)
37
-56
41
R
rostral prefrontal cortex
Fedorenko et al. (2013)
21
43
10
M
anterior cingulate cortex
Fedorenko et al. (2013)
0
31
24
M
presupplementary motor area
Fedorenko et al. (2013)
0
18
50
Exteroceptive
Amygdala
perception
L
ventrolateral amygdala
Bickart et al. (2012)
-28
-4
-22
R
ventrolateral amygdala
Bickart et al. (2012)
28
-4
-22
Auditory
L
superior temporal gyrus
De Luca et al. (2006)
-56
-19
8
R
Heschl's gryus
Krienen & Buckner
(2009)
46
-18
8
R
primary auditory cortex
Andoh et al. (2015)
58
-18
8
R
superior temporal gyrus
Andoh et al. (2015)
57
-11
-3
Sensorimotor
L
postcentral gyrus
Vahdat et al. (2011)
-36
-38
58
Three Interdependent Architectural Gradients
L
precentral gyrus
Krienen & Buckner
(2009)
-42
-24
60
L
premotor cortex
Vahdat et al. (2011)
-26
-22
66
R
postcentral gyrus
Andoh et al. (2015)
49
-25
56
R
precentral gyrus
Andoh et al. (2015)
1
-25
53
R
precentral gyrus
Krienen & Buckner
(2009)
42
-24
6
M
precentral gyrus
Yeo et al. (2011)
0
-26
58
Visual
L
middle occipital gyrus
De Luca et al. (2006)
-30
-93
17
L
occipital fusiform gyrus
Yeo et al. (2011)
-28
-76
-14
L
primary visual cortex
Krienen & Buckner
(2009)
-4
-88
2
R
lingual gyrus
De Luca et al. (2006)
6
-80
-8
R
occipital fusiform gyrus
De Luca et al. (2006)
24
-80
-17
R
occipital fusiform gyrus
Yeo et al. (2011)
28
-76
-14
R
primary visual cortex
Krienen & Buckner
(2009)
4
-88
2
Salience
Amygdala
aversion
L
dorsal amygdala
Bickart et al. (2012)
-22
-4
-12
R
dorsal amygdala
Bickart et al. (2012)
22
-4
-12
Cingulo-
opercular
L
anterior insula
Dosenbach et al. (2007)
-36
17
3
L
anterior prefrontal cortex
Dosenbach et al. (2007)
-28
53
16
L
dorsal anterior cingulate
cortex
Dosenbach et al. (2007)
-2
7
50
R
anterior insula
Dosenbach et al. (2007)
38
19
0
R
anterior prefrontal cortex
Dosenbach et al. (2007)
28
51
25
Multimodal
L
anterior insula
Sepulcre et al. (2012)
-50
3
-7
L
dorsal anterior cingulate
cortex
Sepulcre et al. (2012)
-6
2
48
L
dorsolateral prefrontal cortex
Sepulcre et al. (2012)
-34
43
25
L
lateral occipitotemporal
Sepulcre et al. (2012)
-50
-61
1
Three Interdependent Architectural Gradients
L
pars operculum
Sepulcre et al. (2012)
-58
-21
25
L
superior parietal lobule
Sepulcre et al. (2012)
-18
-45
57
Salience
R
caudal anterior cingulate
cortex
Seeley et al. (2007)
8
18
34
R
dorsal anterior insula
Touroutoglou et al. (2012)
36
21
1
R
orbital frontal insula
Seeley et al. (2007)
38
26
-10
R
ventral anterior insula
Touroutoglou et al. (2012)
28
17
-5
Ventral
Attention
L
anterior insula
Yeo et al. (2011)
-40
12
-4
L
anterior intraparietal sulcus
Corbetta et al. (2000)
-25
-61
50
L
posterior intraparietal sulcus
Corbetta et al. (2000)
-25
-71
53
L
supramarginal gyrus
Yeo et al. (2011)
-60
-30
28
L
ventral intraparietal sulcus
Corbetta et al. (2000)
-23
-71
34
R
anterior insula
Yeo et al. (2011)
40
12
-4
R
anterior intraparietal sulcus
Corbetta et al. (2000)
26
-64
58
R
posterior intraparietal sulcus
Corbetta et al. (2000)
20
-70
58
R
supramarginal gyrus
Yeo et al. (2011)
60
-30
28
R
ventral intraparietal sulcus
Corbetta et al. (2000)
28
-74
21
Note: Hemisphere can be left (L), right (R) or medial (M). Medial seeds have an x-coordinate of 0.
Three Interdependent Architectural Gradients
References
1 Xia, M., Wang, J. & He, Y. BrainNet Viewer: a network visualization tool for human
brain connectomics. PLoS One 8, e68910, doi:10.1371/journal.pone.0068910 (2013).
2 Van Essen, D. C. et al. An integrated software suite for surface-based analyses of
cerebral cortex. J Am Med Inform Assoc 8, 443-459 (2001).
3 Power, J. D. et al. Functional network organization of the human brain. Neuron 72, 665-
678, doi:10.1016/j.neuron.2011.09.006 (2011).

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