Combining co-expression and co-location for gene network inference in porcine muscle development in late gestation

Combining co-expression and
co-location for gene network inference
in porcine muscle development in late
gestation
Laurence Liaubet, Nathalie Vialaneix
October 14th, 2019 - NETBIO
Unités MIAT & GenPhySE, INRA Toulouse

General context, an interdisciplinary network
A fundamental molecular question, the regulation of gene expression
An ethical and economic breeding problem, survival at birth
A statistical question, modelization of gene co-expression with adding biological information

Interpretation of phenotypes not explained only by genetic approach.
The same genome sequence produce a wide range of differentiated cells.
Modulation of gene expression: Epigenetic marks and chromatin regulation, cis and trans
regulation  3D nuclear topography……
Response to physiological context: growth, health, reproduction, adaptation
Biological context: a fundamental molecular question

Fanucchi et al. Cell 2013
Hierarchical Transcription in a Multigene Complex
Biological context: a fundamental molecular question

Thèse de Maria Marti-Marimon, 2018
Biological context: an increased mortality at birth
14 % of newborns died between birth
and weaning
Peak of mortality in the first two days
after birth maturity
The selection for more prolificacy and
meat production has been
accompanied by a substantial increase
in mortality of piglets at birth

Wilson et al., 1998 ; Biensen et al., 1998 ; Leenhouwers et al., 2002 ; Canario, 2006 ; Thèse de Valentin Voillet, 2016
Specific mechanisms during late gestation in pigs
Maturity = plain development allowing survival at birth

Specific mechanisms during late gestation in pigs – muscle tissue
d114
d90 d110
Sampling of longissimus
(n=459)
ANR project PORCINET (2010)
Systems biology of piglet maturity
 Transcriptomic analysis (n = 64)

A dramatic switch of gene expression occurred in late gestation
5,167 genes differential between 90 and 110
dg in the fetal muscle (Bonferroni 1%)
With 1,131 DEGs for age x genotype (maturity)
found in Voillet et al. (2014)
PCA without variables selection

IGF2 (pat), insulin-like growth factor 2
Pig  QTL for adiposity muscle mass
Human  fetal growth and intrauterine growth restriction
Co-expression = co-regulation? = nuclear co-localization?
IGF2, a gene of fundamental importance in pig muscle development
IGF2
LWLW MSLW LWMS MSMS LWLW MSLW LWMS MSMS
90 110
Marti-Marimon et al., 2018.
RNA + DNA + Pig chr Gene 1 + Gene 2

1. Network inference with GGM
2. Coming back to our problem: gene expression and FISH
experiments
2

In short, what are we looking for?
Hypothetizing that co-expression is related to co-location:
• have an automated process to automatically find relevant
pairs of genes for which co-location can be tested (because
FISH experiments are time consumming and targeted experiments)
• improve network inference using co-location information
3

1. Network inference with GGM
4

Framework
Data: large scale gene expression data
individuals
n



X =




. . . . . .
. . Xj
i . . .
. . . . . .




variables (gene expressions), p
here: micro-array experiment, n = 61 (gestational age: 90
days) and p = 13, 855 uniquely annotated genes
5

Framework
Data: large scale gene expression data
individuals
n



X =




. . . . . .
. . Xj
i . . .
. . . . . .




variables (gene expressions), p
here: micro-array experiment, n = 61 (gestational age: 90
days) and p = 13, 855 uniquely annotated genes
What we want to obtain: a network with
• nodes: genes;
• edges: large and direct co-expression between two genes
(track transcription regulations)
5

Using correlations: relevance network
Butte and Kohane (1999, 2000)
First (naive) approach: calculate correlations between
expressions for all pairs of genes, threshold the smallest ones
and build the network.
“Correlations” Thresholding Graph
6

But correlation is not causality…
7

strong indirect correlation
y z
x
set.seed(2807); x <- runif(100)
y <- 2*x+1+rnorm(100,0,0.1); cor(x,y); [1] 0.9988261
z <- 2*x+1+rnorm(100,0,0.1); cor(x,z); [1] 0.998751
cor(y,z); [1] 0.9971105
7

y z
x
set.seed(2807); x <- runif(100)
y <- 2*x+1+rnorm(100,0,0.1); cor(x,y); [1] 0.9988261
z <- 2*x+1+rnorm(100,0,0.1); cor(x,z); [1] 0.998751
cor(y,z); [1] 0.9971105
♯ Partial correlation
cor(lm(y∼x)$residuals,lm(z∼x)$residuals) [1]
-0.1933699 7

y z
x
Networks are built using partial correlations, i.e., correlations
between gene expressions knowing the expression of all the
other genes (residual correlations).
7

Gaussian Graphical Model (GGM)
(Xi)i=1,...,n are i.i.d. Gaussian random variables N(0, Σ) (gene
expression); then
j ←→ j′
(genes j and j′
are linked) ⇔ Cor
(
Xj
, Xj′
|(Xk
)k̸=j,j′
)
̸= 0
8

expression); then
j ←→ j′
(genes j and j′
are linked) ⇔ Cor
(
Xj
, Xj′
|(Xk
)k̸=j,j′
)
̸= 0
Cor
(
Xj
, Xj′
|(Xk
)k̸=j,j′
)
≃
(
Σ−1
)
j,j′
⇒ find the partial
correlations by means of (Σn
)−1
.
8

expression); then
j ←→ j′
(genes j and j′
are linked) ⇔ Cor
(
Xj
, Xj′
|(Xk
)k̸=j,j′
)
̸= 0
Cor
(
Xj
, Xj′
|(Xk
)k̸=j,j′
)
≃
(
Σ−1
)
j,j′
⇒ find the partial
correlations by means of (Σn
)−1
.
Problem: Σ is a p-dimensional matrix (with p large) and n is
small compared to p ⇒ (Σn
)−1
is a poor estimate of Σ−1
!
8

Sparse approaches
Relation between partial correlation and LM: if S = Σ−1
and
writing
Xj
= β⊤
j X−j
+ ϵ
we have: βjj′ =
Sjj′
Sjj
. So edges (non zero partial correlations)
also correspond to coefficients different to zero in the p
regression models above (for j = 1, . . . , p).
9

Sparse approaches
Relation between partial correlation and LM: if S = Σ−1
and
writing
Xj
= β⊤
j X−j
+ ϵ
we have: βjj′ =
Sjj′
Sjj
. So edges (non zero partial correlations)
also correspond to coefficients different to zero in the p
regression models above (for j = 1, . . . , p).
To ensure sparsity of βj: Meinshausen and Bühlmann (2006)
argminβj
n∑
i=1
(
xj
i − β⊤
j x−j
i
)2
+ λ∥βj∥ℓ1
9

Including prior knowledge in this model
Suppose that we have some clues that:
• for some pairs (j, j′
), an edge is likely to occur between j
and j′
), it is likely that there is no edge
between j and j′
10

Including prior knowledge in this model
Suppose that we have some clues that:
), an edge is likely to occur between j
and j′
), it is likely that there is no edge
between j and j′
then, we want to drive βjj′
• toward ±a with a some positive value (the sign is that of
the correlation Cor(Xj
, Xj′
))
• toward 0
10

Including another penalty in the model
argminβj
n∑
i=1
(
xj
i − β⊤
j x−j
i
)2
+ λ∥βj∥ℓ1
+
µ


∑
j′ of type 1
(βjj′ ± a)2
+
∑
j′ of type 2
(βjj′ )2


smooth penalty for co-localized (or not) pairs
11

Including another penalty in the model
argminβj
n∑
i=1
(
xj
i − β⊤
j x−j
i
)2
+ λ∥βj∥ℓ1
+
µ


∑
j′ of type 1
(βjj′ ± a)2
+
∑
j′ of type 2
(βjj′ )2


smooth penalty for co-localized (or not) pairs
In practice:
• a = 1 (after scaling of gene expressions)
• λ chosen with stability selection based on bootstrap for a
fixed µ
• µ chosen as the minimum value recovering exactly prior
knowledge 11

2. Coming back to our problem:
gene expression and FISH
experiments
12

Starting point
• restricted to a list of genes likely involved in foetal
development (1,131 DEGs between 90 and 110 days of
gestation as found in Voillet et al. (2014))
13

Starting point
• restricted to a list of genes likely involved in foetal
development (1,131 DEGs between 90 and 110 days of
gestation as found in Voillet et al. (2014))
• started from an even more restricted list including genes
of interest (IGF2, DLK1 and MEG3) and the genes highly
correlated to these genes (p = 359 genes at the end)
13

Iterative process: from co-location to network and
conversely
14

What to do with these networks? Network mining…
1. Node importance
2. Clustering of nodes (and comparison of clustering with
NMI)
3. GO analysis
15

Node importance
For every node, computation of:
• degree (number of edges afferent to a given node)
• betweenness centrality measure
The orange node’s degree is equal to 2, its betweenness
to 4.
16

Node importance
For every node, computation of:
• degree (number of edges afferent to a given node)
• betweenness centrality measure
16

Find clusters by modularity optimization
The modularity Newman and Girvan (2004) of the partition
(C1, . . . , CK) is equal to:
Q(C1, . . . , CK) =
1
2m
K∑
k=1
∑
xi,xj∈Ck
(Wij − Pij)
with Pij: weight of a “null model” (graph with the same
degree distribution but no preferential attachment):
Pij =
didj
2m
with di = 1
2
∑
j̸=i Wij.
17

Interpretation of the modularity
A good clustering should maximize the modularity:
• Q ↗ when (xi, xj) are in the same cluster and Wij ≫ Pij
• Q ↘ when (xi, xj) are in two different clusters and
Wij ≫ Pij (m = 20)
Pij = 7.5
Wij = 5 ⇒ Wij − Pij = −2.5
di = 15 dj = 20
i and j in the same cluster decreases the modularity
18

Wij ≫ Pij (m = 20)
Pij = 0.05
Wij = 5 ⇒ Wij − Pij = 4.95
di = 1 dj = 2
i and j in the same cluster increases the modularity
18

Wij ≫ Pij
• Modularity
• helps separate hubs
• is not an increasing function of the number of clusters:
useful to choose the relevant number of clusters
Approximate optimization with the Louvain algorithm Blondel
et al. (2008) (among others)
18

Network inference iteration and 3D FISH validations
359 DEGs were selected for being highly correlated with IGF2, DLK1 and MEG3 (R² ≥ 0.84)
Network 0 to 3 with 359 nodes
Network 0 without a priori, 2,279 edges (density: 3.55%)
Sub-network extracted
around the three target
genes
Full network

Network 0 without a priori, 2,279 edges (density: 3.55%)
359 nodes, 2279 edges
Network0, no a priori
IGF2–DLK1
IGF2–MEG3
DLK1–MEG3A priori 1
Lahbib-Mansais et al, 2016

Network 0 without a priori, 2,279 edges (density 3.55%)
Network 1 with triple co-localization of IGF2, DLK1 and MEG3, 2,250 edges (density 3.50%)
Test FISH 3D
IGF2 and RPL32 were associated in 20%
of the analysed nuclei (threshold 10%)

Network 0 without a priori, 2,279 edges and density 3.55%
Network 1 with co-localization of IGF2, DLK1 and MEG3, 2,250 edges and density 3.50%
Network 2 with test of MEST and DCN associations, 2,091 edges and density 3.25%
Test FISH 3D
Network inference
34% (+)
10% (-)

Network 3 with test co-localization with MYH3 (ntw 0 and 1)
Network 0 Network 1

Network 3 with test co-localization with MYH3 (ntw 0 and 1)
MYH3 = Embryonic myosin, excellent biomarker of muscle maturity (Voillet et al., 2018)
No functional link known with IGF2!

Network 3 with test co-localization with MYH3 (ntw 0 and 1), 2,091 edges and density 3.25%
52% (+)
45% (+)
26% (+)
Test FISH 3D
Network inference

Network mining (network structure with key genes)
The degree of a node is the number of edges afferent to this gene. High degree genes are
connected to many other genes (hub).
The betweenness of the node is the number of shortest paths between pairs of genes in
the network that pass through that gene. High-betweenness genes are central and more
likely to disconnect the network if removed.

Network mining (network structure with key genes)
gene symbol degree betweeness degree betweeness degree betweeness degree betweeness Degree betweeness
ADIPOR2 15 646,65 14 487,32 15 628,78 14 660,97 -7 2
AKR7A2 19 492,63 17 436,71 15 474,10 14 291,90 -26 -41
CD81 17 551,17 18 616,7 15 478,76 17 600,58 0 9
CRAT 19 716,24 15 518,26 16 738,30 14 573,58 -26 -20
DCN 16 438,86 18 560,83 9 288,82 6 357,74 -63 -18
DLK1 10 103,52 6 81,7 5 74,22 5 24,13 -50 -77
DPP4 15 568,91 16 672,01 15 674,94 15 597,87 0 5
EGFR 16 624,92 12 375,87 12 385,35 11 354,78 -31 -43
GHITM 16 578,58 17 588,76 16 592,35 14 496,63 -13 -14
GLUD1 13 575,69 13 553,28 12 574,48 12 586,27 -8 2
IGF2 10 118,26 11 231,09 8 260,58 7 622,44 -30 426
LPAR4 14 464,31 17 644,76 18 812,81 16 798,82 14 72
MEG3 13 282,32 5 55,75 6 120,18 5 24,13 -62 -91
MESP1 12 228,49 14 320,34 14 483,27 14 775,31 17 239
MEST 13 148,2 12 121,44 10 345,69 7 385,27 -46 160
MRPS28 16 743 15 743,29 16 953,42 15 796,14 -6 7
MYH3 14 610,73 14 656,6 11 455,62 4 0,00 -71 -100
NMNAT3 17 562,63 18 664,84 16 473,55 17 573,15 0 2
RAVER1 16 613,84 16 665,73 16 696,35 16 745,66 0 21
RPL32 18 717,96 15 557,65 7 149,80 5 243,11 -72 -66
SELO 18 692,52 14 438,35 14 459,46 15 587,32 -17 -15
SYDE1 15 436,75 17 530,29 14 459,66 18 745,52 20 71
TFRC 15 595,1 15 534,83 13 437,38 17 846,81 13 42
TYRO3 20 785,95 18 659,9 16 603,94 17 700,03 -15 -11
YWHAB 20 670,22 17 470,35 17 538,41 17 547,17 -15 -18
Network 0 Network 1 Network 2 Network 3
Comparison between
Network 0 and Network 3
(% of variation)
↗
↘
↘
↘
↘
↘
↘

Network clustering
Network 0 Network 1 Network 2 Network 3
Network 0 1 0.3893 0.3381 0.3244
Network 1 0.3893 1 0.4007 0.3923
Network 2 0.3381 0.4007 1 0.4152
Network 3 0.3244 0.3923 0.4152 1
To analyse the evolution of the network structure from Network 0 to Network 3, clustering
of the genes was performed on each network.
Normalized mutual information (NMI) measure the similarity between two clusterings.
The value is comprised between 0 and 1 and is equal to 1 when the two clusterings are
identical.
clusterings become more consistent when introducing new biological information in
each network inference iteration

Network clustering: Networks 0 and 3 were analysed in depth to
search for any correspondence between clusters
Pairwise contingency tables between clusterings. Percentage of genes for each cluster in
Network 0 found in each cluster of Network 3. In bold and red, the most resembling values
between clusters.
1 2 3 4 5 6
1 64,10 7,69 7,69 2,56 7,69 10,26
2 8,77 68,42 0,00 1,75 19,30 1,75
3 14,89 0,00 65,96 19,15 0,00 0,00
4 3,92 1,96 11,76 82,35 0,00 0,00
5 34,09 6,82 4,55 11,36 43,18 0,00
6 3,57 17,86 14,29 32,14 0,00 32,14
7 11,11 38,89 0,00 11,11 38,89 0,00
8 0,00 48,72 33,33 10,26 5,13 2,56
9 5,56 11,11 16,67 27,78 38,89 0,00
Clusters in Network 3
Clusters in
Network 0

Functional enrichment analysis: Gene Ontology Biological Process
Network 0 - Cluster 1 Network 3 - Cluster 1
GOBP Terms FDR FDR Target
Extracellular structure 5,76E-05 1,14E-08 DCN
Cellular response to organonitrogen compound 6,80E-04 1,16E-02 IGF2
Reponse to transformaing growth factor beta 2,35E-03 1,24E-01
Multicellular organism metabolic process 2,35E-03 3,05E-03
Skin development 3,18E-03 1,44E-01
Neuron migration 2,82E-02 4,37E-01
Regulation of neuron projection development 3,07E-02 4,93E-01
Mesoderm development 1,24E-01 MEST
Muscle organ development 8,35E-01 MYH3
Notch signaling pathway 5,56E-01 DLK1
Collagen fibril organization 1,10E-04 1,02E-05
Network 0 - Cluster 8 Network 3 - Cluster 2
GOBP Terms FDR FDR
Generation of precursor metabolites and energy 1,64E-02 1,32E-07
Oxidation-reduction process 7,25E-03 5,63E-09
Energy derivation by oxidation of organic compounds 8,17E-03 1,88E-06
Cellular respiration 8,17E-03 2,65E-07
Functional enrichment analysis based on Gene Ontology was performed using the web tool
Webgestalt (WEB-based GEne SeT AnaLysis Toolkit)

Functional enrichment analysis: reconstructed network of genes in
cluster 1 of Network 3 with Ingenuity Pathway Analysis (IPA)
Villa-Vialaneix et al., 2013
IPA proposed to connecting 49 (82%) out of 60 genes in a network.
MYOD1 and CTNNB1 were identified by upstream regulator analysis as potential transcriptional
factors for a group of genes including IGF2 and MYH3.
“Cell Morphology”, 14 genes, p-value = 1.75e-08
“Quantity of cells”, 31 genes, p-value = 2.48e-09
“Morphology of connective tissue cells”, 8 genes, p-value = 1.27e-04
“Formation of muscle”, 10 genes, p-value = 2.98e-05, involved IGF2 and
MYH3 together with CTNNB1 and MYOD1.

• 82% of edges in Network 0 were conserved in Network 3
• The most important genes in Network 0 were among those showing the highest values of
betweenness and degree in Network 3.
Not major disturbances in the network structure
• In the local analysis, the NMI value revealed that the clusters resembled one another more with
each new network inferred.
• Four out of six clusters in the final network conserved more than 62% of genes in the corresponding
clusters of Network 0.
• IGF2-MEST, (DLK1/MEG3)-MEST, (DLK1/MEG3)-DCN, that were observed to be connected in co-
expression networks in other studies.
• DLK1, MEG3, RPL32, MEST, DCN and MYH3 were less connected with the rest of the other genes in
Network 3 but not IGF2.
• No previous association between IGF2 and MYH3, even though the two genes are known to be
involved in muscle development overexpression and accumulation of β-catenin in the nuclei of
differentiating murine myoblasts results in higher MyoD activation and Myhc induction (Ramazzotti et
al, 2016)
Conclusions

• What is published and what is not…
• Intermediate modelling is retained as valuable information on robust or non-robust
interactions currently, new interactions are being tested by FISH 3D
• Dramatic change in gene expression at the end of gestation Search of interaction
whole genome (Maria Marti-Marimon thesis)
Conclusions - Perspectives
Whole genome interaction Maps
3D Chromosome conformation capture
Hi-C in progress

Thank you for your attention!
19

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Butte, A. and Kohane, I. (2000). Mutual information
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Pacific Symposium on Biocomputing, pages 418–429.
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Meinshausen, N. and Bühlmann, P. (2006). High dimensional
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Newman, M. and Girvan, M. (2004). Finding and evaluating
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Voillet, V., SanCristobal, M., Lippi, Y., Martin, P. G.,
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21

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