In this talk, I will describe several recently developed methods to study disease perturbations through the lens of network science. First I will present evidence that one can accurately predict perturbation patterns from the topology of biological networks, even when lacking measurements on the kinetic parameters governing the dynamics of these interactions. Using 87 biochemical networks with experimentally measured kinetic parameters, we show that a knowledge of the network topology offers 65% to 80% accuracy in predicting the impact of perturbations. In other words, we can use the increasingly accurate topological models to approximate perturbation patterns, bypassing expensive kinetic constant measurement. These results open new avenues in modeling drug action, and in identifying drug targets relying on the human interactome only.
Then, I will present a novel approach to identify the collective impact of miRNAs in disease. Instead of focusing on the magnitude of miRNA differential expression, here we address the secondary consequences for the interactome. We developed the Impact of Differential Expression Across Layers (IDEAL), a network-based algorithm to prioritize disease-relevant miRNAs based on the central role of their targets in the molecular interactome. This method was used in the context of asthmatic Th2 inflammation and identified five Th2-related miRNAs (mir27b, mir206, mir106b, mir203, and mir23b) whose antagonization led to a sharp reduction of the Th2 phenotype. This result offers novel approaches for therapeutic interventions.
Finally, I will present an investigation of the personalized gene expression responses when inducing hypertrophy and heart failure in 100+ strains of genetically distinct mice from the Hybrid Mouse Diversity Panel (HMDP). I will show that genes whose expression change significantly correlates with the severity of the disease are either up- or down-regulated across strains, and therefore missed by traditional population-wide analyses of differential gene expression. These uncovered personalised genes are enriched in human cardiac disease genes and form a dense co-regulated module strongly interacting with the cardiac hypertrophic signaling network in the human interactome, the set of molecular interactions in the cell. We validate our approach by showing that the knockdown of Hes1, predicted as a strong candidate, induces a dramatic reduction of hypertrophy by 80-90% in neonatal rat ventricular myocytes, demonstrating that individualized approaches are crucial to identify genes underlying complex diseases as well as to develop personalized therapies.
5. PART I
TOPOLOGY VS DYNAMICS IN PERTURBATION
SPREADING
Marc Santolini, Albert-László Barabási, “Predicting Perturbation Patterns From The Topology Of
Biological Networks”
33. ACCURACIES ACROSS 87 MODELS
‣ 65% recovery rate without kinetics
(80% when just looking at sign recovery)
(dashed line: Z=2 random
expectation)
Topology
Direction
Sign
Kinetics
+
+
+
+
+
+
+
-
+
+
-
-
+
-
-
-
Accuracyofperturbationpatterns
Biochemical
Diffusion(d+s)
Distance(d)
Firstneighbors(d+s)
Influencestrengthrecovery
0.00.20.40.60.81.0
Accuracy of
perturbation patterns
Biochemical
Perturbed node
Effect
Network
Perturbed nodePerturbed node
Effect
Biochemical
Network
kinetics
34. OTHER FEATURES
Best models are modular, sparse and have fewer hubs
Number of structural holes
Edge density
Mean degree
Mean Jacobian value
Mean eigenvector centrality
Number of reversible equations
Model size
Mean betweenness centrality
Number of strong connected components
Correlation with network model accuracy
−1.0 −0.5 0.0 0.5 1.0
●
●
●
●
●
●
●
●
●
35. MODULARITY BUFFERS PERTURBATIONS
INSIGHTS | PERSPECTIVES
:A.KITTERMAN/SCIENCE
By Marta Sales-Pardo
I
n the 1970s, ecologists began to specu-
late that modular systems—which are
organized into blocks or modules—can
better contain perturbations and are
therefore more resilient against exter-
nal damage (1). This simple concept can
be applied to any networked system, be it
an ecosystem, cellular metabolism, traffic
flows, human disease contagion, a power
grid, or an economy (2, 3). However, experi-
mental evidence has been lacking (4). On
page 199 of this issue, Gilarranz et al. (5)
provide empirical evidence showing that
modular networked systems do indeed have
an advantage over nonmodular systems
when faced with external perturbations.
The authors designed an elegant meta-
population experiment with the arthro-
pod Folsomia candida. In the experiment,
habitat patches (nodes) were connected in
a modular fashion; specimens could freely
move between patches. Initially, the au-
thors inoculated all patches with the same
number of specimens. Once the whole sys-
tem had reached a stable population, they
continuously removed specimens from one
of the nodes for a sustained period of time.
The results show that modular systems can
contain the spread of such a perturbation
more effectively than a nonmodular system
would, so that only the populations of nodes
within the same module as the perturbed
node is affected (see the figure).
Gilarranz et al. also show that the capac-
ity to contain perturbations comes with a
cost. The more modular the system, the
larger the overall population in the presence
of even strong perturbations, but that is not
the case in the absence of a perturbation. In
the latter case, the overall population levels
are higher in nonmodular systems. These
results not only align with theoretical ex-
pectations, they also help explain the large-
scale organization of complex systems.
To further put this result in historical con-
text, we should cast our minds back more
than 10 years. At that time, the definition
of module in a networked system was still a
loose concept, especially for large systems (6).
Based on commonalities in the systems-level
organization of large networked systems, net-
work scientists proposed to define a module
as a set of nodes that are densely connected
among themselves but loosely connected
to other parts of the network (7, 8). This is
the definition that Gilarranz et al. use. The
modularity of a network then quantifies how
well-defined these densely connected groups
of nodes are within the network.
Using this definition of modules, scien-
tists soon found that the vast majority of
large-scale networked systems in any con-
text—including social, biological, ecologi-
cal, and engineering systems—have a strong
modular component (9, 10). The question
arose why this was the case. In engineered
systems, modularity is arguably a useful
design principle because modular systems
are easy to fix and update (11). However, the
justification for the modularity of natural
networked systems mostly hinged on the
aforementioned theoretical stability consid-
erations. The results reported by Gilarranz
et al. show that the need to contain pertur-
bations can plausibly explain the modular-
ity of at least some natural systems.
NETWORKS
The importance of being modular
An experiment proves the value of modularity in complex systems under perturbation
Department of Chemical Engineering, Universitat Rovira i
Virgili, 43007 Tarragona, Spain. Email: marta.sales@urv.cat
System state
RealityRandomModular
Perturbation starts Perturbation spreads
Contained
in a module
Perturbed
node
Node
Module
Spread?
Spread?
Uncontained
spread
Interconnected
network
How to contain perturbations
In modular systems,perturbations can be contained in one module,whereas they spread throughout randomly connected systems.Real systems could be
represented as a combination of the two types,making it difficult to predict the effects of perturbations.
onSeptember14,2017http://science.sciencemag.org/Downloadedfrom
128 14 JULY 2017 • VOL 357 ISSUE 6347 sciencemag.org SCIENCE
GRAPHIC:A.KITTERMAN/SCIENCE
be applied to any networked system, be it
an ecosystem, cellular metabolism, traffic
flows, human disease contagion, a power
grid, or an economy (2, 3). However, experi-
mental evidence has been lacking (4). On
page 199 of this issue, Gilarranz et al. (5)
provide empirical evidence showing that
modular networked systems do indeed have
an advantage over nonmodular systems
when faced with external perturbations.
The authors designed an elegant meta-
population experiment with the arthro-
pod Folsomia candida. In the experiment,
habitat patches (nodes) were connected in
a modular fashion; specimens could freely
move between patches. Initially, the au-
would, so that only the populations of nodes
within the same module as the perturbed
node is affected (see the figure).
Gilarranz et al. also show that the capac-
ity to contain perturbations comes with a
cost. The more modular the system, the
larger the overall population in the presence
of even strong perturbations, but that is not
the case in the absence of a perturbation. In
the latter case, the overall population levels
are higher in nonmodular systems. These
results not only align with theoretical ex-
pectations, they also help explain the large-
scale organization of complex systems.
To further put this result in historical con-
text, we should cast our minds back more
than 10 years. At that time, the definition
of module in a networked system was still a
loose concept, especially for large systems (6).
well-defined these densely connected groups
of nodes are within the network.
Using this definition of modules, scien-
tists soon found that the vast majority of
large-scale networked systems in any con-
text—including social, biological, ecologi-
cal, and engineering systems—have a strong
modular component (9, 10). The question
arose why this was the case. In engineered
systems, modularity is arguably a useful
design principle because modular systems
are easy to fix and update (11). However, the
justification for the modularity of natural
networked systems mostly hinged on the
aforementioned theoretical stability consid-
erations. The results reported by Gilarranz
et al. show that the need to contain pertur-
bations can plausibly explain the modular-
ity of at least some natural systems.
Department of Chemical Engineering, Universitat Rovira i
Virgili, 43007 Tarragona, Spain. Email: marta.sales@urv.cat
System state
RealityRandomModular
Perturbation starts Perturbation spreads
Contained
in a module
Perturbed
node
Node
Module
Spread?
Spread?
Uncontained
spread
Unperturbed nodes in modular systems Unperturbed nodes in randomly connected systems Perturbed nodes
Interconnected
network
How to contain perturbations
In modular systems,perturbations can be contained in one module,whereas they spread throughout randomly connected systems.Real systems could be
represented as a combination of the two types,making it difficult to predict the effects of perturbations.
Published by AAAS
onSeptember14,2017http://science.sciencemag.org/Downloadedfrom
Science, 2017
38. EXPERIMENTAL EVIDENCE
Phenotype
Gene
expression
A
-
,Yp
Y
-
,Yp
Z
-
,Yp
A
-
Z
-
,Yp
Y
-
Z
-
,Yp
B
-
Y
-
Z
-
,Yp
A2+
,Yp
T2+
,A
T2+
,TA
B2+
,Ap
B2+
,Yp
W2+
,A
W2+
,WA
Z2+
,Yp
Y2+
,Yp
Biochemical
Network
A
-
Y
-
Z
-
A
-
Z
-
Y
-
Z
-
B
-
Y
-
Z
-
A2+
T2+
B2+
W2+
Z2+
Y2+
Biochemical
Network
Sign
-1 0 1
Comparing predictions with experimental assays in bacterial chemotaxis
Perturbation of
gene X
Expression of gene Y
random
walk
biased
walk
a Wild-type
Phenotype
Observed
change
b c
86%
correct
75%
correct
Bacterial Chemotaxis Simulation
[Ro] and [Lo] are the total concentrations of receptor and ligand,
ively, [RL] is the concentration of the protein-ligand complex,
d is the dissociation constant of the complex.
ther binding steps in the simulation involve the association of
asmic proteins at comparable, and usually low, concentrations
r this we use the relationship:
0.5{[Ro] + [Lo] + Kd - V([Ro] + [Lo] + Kd)2 - 4[Ro] X [Lo]}
[Ro] and [Lo] are arbitrarily assigned to the two proteins (see
1975).
tion steps are not assumed to run to completion within At and
egrated by successive steps of the simulation. For protein au-
phorylations we use the simple Michaelis-Menten relationship
V J=[lkcat X [ATP]l
] [ATP] + Km
J
v is the rate of formation of the phosphorylated species in
per second, [E] is the free enzyme concentration, [ATP] is the
tration of ATP, k_cat is the catalytic rate constant and Km is
haelis constant (Michaelis and Menten, 1913; Fersht, 1984).
other reactions we assume that the concentrations of reacting
are small, so that the reactions are simply described by
v = (k.cat/Km) [E] X [S]
autodephosphorylations
v = klcat [E]
llar Motor
all other components of the simulation, the flagellar motor is
ingle molecular species. It is a complex structure, built from
imately 40 distinct proteins that rotates either clockwise or
rclockwise at speeds of .300 cycles/s (significantly less when
terium is tethered to a surface) (Jones and Aizawa, 1991). The
on of rotation is controlled by the phosphorylated form of CheY
h an interaction with the switch components (FliG, FliM, and
oteins) of the motor Uones and Aizawa, 1991). The interaction
s to be a simple binding of CheYp rather than a phosphotransfer
n (Bourret et al., 1990).
s shown previously by Block et al. (1982, 1983) that a simple
te model in which run and tumble states differ in the binding
ngle ligand has similar stochastic properties to the runs and
Different states ofthe flagellar motor (M) are
determined by the binding of CheYp (Yp):
State 'T M
State '3' MYp
State '5' MYpYp
State '7' MYpYpYp
State '9' MYpYpYpYp
ccw rotation
ccw rotation
zero rotation
cw rotation
cw rotation
(run)
(run)
(pause)
(tumble)
(tumble)
Occupation of the different states is governed by
reversible equilibria:
M + Yp q-b MYp
MYp + Yp W MYpYp
MYpYp + Yp W MYpYpYp
Ki = kil/klr
K2 = k2l/k2r
K3 = k3d/k3r
1.0
0.6 -
0
0
*~0.4-
coLo 10 20 30
CheYp (nM)
Figure 3. Proportion of time spent in run (l), tumble (0), and pause
(A) modes predicted for the flagellar motor model, with the resting
concentration of CheYp in a wild-type bacterium set to 9 nM.
tumbles of the flagellar motor. In the present simulation, this model
has been extended to incorporate two additional features. One is the
cooperativity between CheY levels and flagellar motor response seen
in mutant strains in which CheY is over-expressed to different levels
(Kuo and Koshland, 1989). The effective species is now thought to
be CheYp. The other feature added to the motor model is the capacity
for pausing, which has been reported by Eisenbach and colleagues
to be an inherent part of the behavioral repertoire of coliform bacteria
(Lapidus et al., 1988; Eisenbach et al., 1990).
These observations are incorporated into a model in which the motor
complex, denoted M, binds sequentially up to four CheYp molecules
thereby producing five distinct molecular species. Two of these (M
and MYp) rotate counterclockwise, another two (MYpYpYp and
MYpYpYpYp) rotate clockwise, and one species (MYpYp) is stationary,
corresponding to the pausing of the motor (Figure 2). In a population
of bacteria, the rotational bias (defined as the fraction of time spent
in the counterclockwise mode) is therefore given by the following:
bias = M + MYp
M + MYp + MYpYp + MYpYpYp + MYpYpYpYp
As in the earlier model of Block et al. (1982, 1983), transitions between
each pair of states are governed by paired first-order rate constants,
such as kl, and k2rYp (which is pseudo first-order at a given concen-
tration of Yp). For an individual motor, these rate constants represent
the probabilities per unit time of terminating the current state.
The Adair-Pauling model of a multisite allosteric enzyme allows
dissociation constants for each binding step to be calculated from two
parameters-the dissociation constant of binding of the first binding
site (K) and the factor (a) by which the affinity of successive binding
sites change (Segel, 1975). We have assumed that the flagellar motor
is similarly well-behaved and calculated K and a from an arbitrarily
39. I. TAKE HOME MESSAGE
1/3
kinetics
Marc Santolini - CCNR
Topology
Direction
Sign
Kinetics
+
+
+
+
+
+
+
-
+
+
-
-
+
-
-
-
Accuracyofperturbationpatterns
Biochemical
Diffusion(d+s)
Distance(d)
Firstneighbors(d+s)
Influencestrengthrecovery
0.00.20.40.60.81.0
2/3
interactome
40. PART II
NETWORK PERTURBATION BY MIRNAS
Ayşe Kılıç, Marc Santolini, Taiji Nakano, Matthias Schiller, Mizue Teranishi, Pascal Gellert, Yuliya
Ponomareva, Thomas Braun, Shizuka Uchida, Scott T. Weiss, Amitabh Sharma And Harald Renz, “A
Novel Systems Immunology Approach Identifies The Collective Impact Of Five Mirnas In Th2
Inflammation"
45. EXPRESSION DATA FROM ASTHMA MODEL
Naive
Th1-
acute
Th1-
chronic
Th2-
acute
Th2-
chronic
miRNA matrix mRNA matrix Protein matrix
Meta-dimensional analysis using human Interactome
Model: female BALB/c mice aged 6–8 weeks
Mice were sensitized by injections of 10 µg OVA grade VI
47. BUILDING THE TH2 DISEASE MODULE
Maximize Largest Connected Component (LCC)
size compare to random (Z-score)
● ●
●
●
●
●
●
●
● ● ●
●
●
●
●
● ●
●
● ●
1.0 1.5 2.0 2.5
012345
Choosing a FC cutoff for mRNAs
Fold−change cutoff
LCCZscore
Optimal FC=1.3
stable
● ●
●
●
●
●
●
1.0 1.5
01234
Choosing a
Fold
LCCZscore
O
F
48. MIRNAS IMPACT
• LCC Z score after removal of miRNA targets
• Compare to random targets
Th2 stableTh2 early
123456
e(r)
cute
c(r)
onic
Assessing the collective attack of miRNA
LCCZscore
miRNAs impact on
Th2 disease module
random
observed
56. PART III
PERSONALIZED RESPONSE TO A
PERTURBATION
Marc Santolini, Milagros C. Romay, Clara L. Yukhtman, Christoph D. Rau, Shuxun Ren, Jeffrey J.
Saucerman, Jessica J. Wang, James N. Weiss, Yibin Wang, Aldons J. Lusis, Alain Karma, “A
Personalized, Multi-Omics Approach Identifies Genes Involved In Cardiac Hypertrophy And
Heart Failure”
57. Hybrid Mouse Diversity Panel
100+ strains of mice
DNA variants (500k+ SNPs)
Heart Failure HMDP: Overview of the Study
Isoproterenol
Induced
Phenotypic
Spectrum
Compensated
Heart
Decompensated
Heart
Hybrid Mouse Diversity Panel
Treat with 20 mg/kg body
weight/day ISO for 3
weeks
Collected phenotypes
Weights
Heart (total and
each chamber)
Liver Lung
Adrenal Body
Echocardiography
Ejection Fraction
& Fractional
Shortening
LV chamber
diameter
(diastolic and
systolic)
Posterior Wall
Thickness (diastolic
and systolic)
E/A Ratio LV mass Ejection Time
Other
Plasma Lipids Fibrosis
% Death in
Response to
Isoproternol
Mitochondrial
DNA content
RNA Transcriptomes
THE HYBRID MOUSE DIVERSITY PANEL (HMDP)
Ghazalpour et al, Mamm Genome (2012)
Combines genetic and phenotypic diversity
Spectrum of phenotypes
42 traits pre/post ISO
mRNAs microarrays
+ISO
Isoproterenol-induced
heart failure (3 weeks)
List of collected phenotypes
Weights
Heart (total and each chamber) Body%
Adrenal Liver Lung
Echocardiography
Ejection
Fraction
& Fractional
Shortening
LV chamber
diameter
(diastolic and
systolic)
Posterior Wall
Thickness
(diastolic and
systolic)
E/A Ratio LV mass Ejection Time
Other
Myocyte Cross-
section Area
Fibrosis Apoptosis
Mitochondrial
DNA content
RNA Transcriptomes
64. PATHWAY ENRICHMENT OF NEIGHBORS IN THE INTERACTOME
8,693 pathways from mSigDb & wikipathways
d
INTERACTION WITH THE CARDIAC HYPERTROPHIC SIGNALING NETWORK (CHSN)
e
Proportion of PPI neighbors in CHSN
Expectedfrequency
0.00 0.05 0.10 0.15
050100150200
FC
Z = 4
SAM
Z = 1.2
FC gene
65. HES1 AS A CANDIDATE
−1.00.00.51.0
Fold-Change
BXD−14/TyJ
BXA16/PgnJ
DBA/2J
BXA24/PgnJ
BXD32/TyJ
BXD−32/TyJ
BXHB2
KK/HlJ
AXB19/PgnJ
CXB−3/ByJ
AXB−20/PgnJ
BXD75
BUB/BnJ
LG/J
NOD/LtJ
BXD−11/TyJ
FVB/NJ
PL/J
CXB−12/HiAJ
BXA−4/PgnJ
BXD66
BXD62
SJL/J
CXBH
BXD50
BXH−19/TyJ
BXD87
RIIIS/J
SEA/GnJ
129X1/SvJ
BXD56
SM/J
BXH−9/TyJ
BXD48
BALB/cByJ
BXA−2/PgnJ
C3H/HeJ
CBA/J
BXD45
BXD−38/TyJ
CXB−7/ByJ
AXB−6/PgnJ
BXD49
BALB/cJ
BXD73
BXD40/TyJ
BXD−40/TyJ
BXD43
AKR/J
CXB−6/ByJ
BXA14/PgnJ
C57BLKS/J
BXD64
BXD61
AXB10/PgnJ
BXA−8/PgnJ
BXD21/TyJ
BXA−1/PgnJ
NZB/BlNJ
BXD68
NON/LtJ
SWR/J
BXD84
BXD74
BXD71
BXD79
BXD−5/TyJ
BXA−7/PgnJ
BXA−11/PgnJ
BXD55
BXD−12/TyJ
BXD85
AXB18
BXD44
CE/J
AXB8/PgnJ
NZW/LacJ
BXD−24/TyJ
BXD70
BXD39/TyJ
LP/J
CXB−11/HiAJ
BXH−6/TyJ
CXB−13/HiAJ
1.01.31.6
Fold-Change(log2)
Hes1
Heart mass
Hes1 downregulation
Mild hypertrophy
Hes1 upregulation
Strong hypertrophy
a
b
Hes1 expression FC in the HMDP
Hes1 is a FC gene, a predicted TF and interacts with cardiac hypertrophy pathway
66. HES1 VALIDATION
a
VALIDATION OF HES1 AS A NEW CARDIAC HYPERTROPHY REGULATOR
b Effect on known hypertrophic markersHes1 expression 48h after
siRNA transfection
c Effect on cardiac
cell size
0
0.2
0.4
0.6
0.8
1
1.2
TransfectionControl
Hes1siRNA-1
Hes1siRNA-2
TransfectionControl
Hes1siRNA-1
Hes1siRNA-2
TransfectionControl
Hes1siRNA-1
Hes1siRNA-2
Control Isoproterenol Phenylepherine
FoldChangeRelativetoControl
0
0.5
1
1.5
2
2.5
Control
Isoproterenol
Phenylepherine
Control
Isoproterenol
Phenylepherine
Control
Isoproterenol
Phenylepherine
Transfection
Control
Hes1 siRNA 1 Hes1 siRNA 2
Fold Change Relative To Control
***
***
***
***
0
2
4
6
8
10
12
14
Control
Isoproterenol
Phenylepherine
Control
Isoproterenol
Phenylepherine
Control
Isoproterenol
Phenylepherine
Transfection
Control
Hes1 siRNA - 1 Hes1 siRNA - 2
Fold Change Relative To Control
***
***
***
***
Nppa
0
2
4
6
8
10
12
14
16
Control
Isoproterenol
Phenylepherine
Control
Isoproterenol
Phenylepherine
Control
Isoproterenol
Phenylepherine
Transfection
Control
Hes1 siRNA - 1 Hes1 siRNA - 2FoldChangeRelativetoControl
*
***
***
***
Nppb
67. III. TAKE HOME MESSAGE
−1012345
−1.5−0.50.51.5
a
b
INTERACTION WITH THE CARDIAC HYPERTROPHIC SIGNALING NETWORK (CHSN)
FC gene
predicted TF
Proportion of PPI neighbors in cardiac hypertrophic pathway
Expectedfrequency
0.00 0.05 0.10 0.15
050100150
FC
Z = 4.8
SAM
Z = −0.21
Proportion of PPI neighbors in CHSN
BXD−14/TyJ
BXA16/PgnJ
DBA/2J
BXA24/PgnJ
BXD32/TyJ
BXD−32/TyJ
BXHB2
KK/HlJ
AXB19/PgnJ
CXB−3/ByJ
AXB−20/PgnJ
BXD75
BUB/BnJ
LG/J
NOD/LtJ
BXD−11/TyJ
FVB/NJ
PL/J
CXB−12/HiAJ
BXA−4/PgnJ
BXD66
BXD62
SJL/J
CXBH
BXD50
BXH−19/TyJ
BXD87
RIIIS/J
SEA/GnJ
129X1/SvJ
BXD56
SM/J
BXH−9/TyJ
BXD48
BALB/cByJ
BXA−2/PgnJ
C3H/HeJ
CBA/J
BXD45
BXD−38/TyJ
CXB−7/ByJ
AXB−6/PgnJ
BXD49
BALB/cJ
BXD73
BXD40/TyJ
BXD−40/TyJ
BXD43
AKR/J
CXB−6/ByJ
BXA14/PgnJ
C57BLKS/J
BXD64
BXD61
AXB10/PgnJ
BXA−8/PgnJ
BXD21/TyJ
BXA−1/PgnJ
NZB/BlNJ
BXD68
NON/LtJ
SWR/J
BXD84
BXD74
BXD71
BXD79
BXD−5/TyJ
BXA−7/PgnJ
BXA−11/PgnJ
BXD55
BXD−12/TyJ
BXD85
AXB18
BXD44
CE/J
AXB8/PgnJ
NZW/LacJ
BXD−24/TyJ
BXD70
BXD39/TyJ
LP/J
CXB−11/HiAJ
BXH−6/TyJ
CXB−13/HiAJ
1.01.31.6
FC SAM
hypertrophy spectrum
Ttc13
Kcnip2
Ankrd1
Cab39l
Prnpip1
Rffl
AW549877
Fgf16
Ehd2
2310022B05Rik
Bclaf1
Ptrf
Wdr1
Gss
Nipsnap3b
Kremen
Polydom
Acot1
Pacrg
Col14a1
Scara5
BC020188
Tnc
Timp1
Arpc3 Ms4a7
Clec4n Lox
DctTnc Arhgdig
Catnal1
Mfap5 Clecsf8
2610028H24Rik
Slc1a2Ces3
Fhl1
Fhl1
Panx1
Adamts2
Snai3
Adamts2
Nppb
Klhl23
Tnni2
9430041O17Rik
Dtr
Pcdhgc4
Eif4a1
Akap9
Ppp1r9a
Zfp523
Nfatc1
Hes1
4930504E06Rik
Atp6v0a1
Dedd
BC020188
Timp1
AI593442
Serpina3n
Cysltr1
Lgals3
Retnla
Rpp25Gp38
Corin
Lrrc1
BC025833
Mkrn3
Tspan17
Global response
68. Method also used to find genes associated to drug
response and classify responders vs non-responders
71. PERTURBATION PATTERNS
Perturbation patterns can be exactly computed from the Jacobian matrix
(Barzel, Barabasi, Nat Biotech 2013)
S = (1 J) 1
D(
1
(1 J) 1
)
Perturbation patterns
(long distance correlations)
Jacobian
(direct influence)
Sij =
dxi/xi
dxj/xj
Jij =
@xi/xi
@xj/xj
(Vanunu et al, PLoS Comp Biol 2009)
The requirements on F can be expressed in linea
follows:
F~aW’Fz(1{a)YuF~(I{aW’){1
(1{a)Y
where W’ is a jVj|jVj matrix whose values are given b
F and Y are viewed here as vectors of size jVj. We re
eigenvalues of W’ to be in ½{1,1Š. Since a[(0,1), the ei
of (I{aW’) are positive and, hence, (I{aW’){1
exist
While the above linear system can be solved exactly
networks an iterative propagation-based algorithm works
is guaranteed to converge to the system’s solution. Speci
use the algorithm of Zhou et al. [21] which at iteration t
Ft
: ~aW’Ft{1
z(1{a)Y
where F1
: ~Y. This iterative algorithm can be best und
simulating a process where nodes for which prior informa
PLoS Computational Biology | www.ploscompbiol.or
weighted adjacency
matrix (normalized by
degrees of end-points)
prioritization
function
origin of impact
PRINCE algorithm
Network model
Biochemical model