Different approaches for the identification of perturbations in Boolean networks

Different approaches for the identification of
perturbations in Boolean networks and their application
to precision medicine
Célia Biane-Fourati
IRISA, Univ. Rennes, Inria, CNRS
celia.biane-fourati@inria.fr
July 1, 2019
Célia Biane-Fourati (Inria Rennes) Identification of perturbations in BNs July 1, 2019 1 / 22

Boolean networks - deﬁnition
m1
m2 m3
m4
∧ ∨
{m1, m2, m3, m4} are Boolean variables
fm1 = m1
fm2 = m1 ∧ m3
fm3 = m1 ∨ ¬m2
fm4 = m3
0100 0000 0010 0011

Boolean networks - deﬁnition
m1
m2 m3
m4
∧ ∨
{m1, m2, m3, m4} are Boolean variables
fm1 = m1
fm2 = m1 ∧ m3
fm3 = m1 ∨ ¬m2
fm4 = m3
0100 0000 0010 0011
0011 is a stable attractor.

Biological networks
Gene regulatory networks : Genes/Transcriptional regulations ; Cell
fate decision
Signalling pathways : Proteins/RNA/Metabolites/Biochemical
regulations ; Information propagation
these networks are intertwined
Model Reference
Mammalian cell cycle [Faur´e, 2006]
Cellular diﬀerentiation of Th cells [Naldi, 2010]
Cancerous transformation in bladder [Remy, 2015]
Prediction of drug synergies [Flobak, 2015]
Table: Examples of cellular processes modeled by Boolean networks
Interpretation : Phenotypes are attractors of the Boolean model.

Simulation versus identification
Node perturbation
A node perturbation sets a molecule mi to a constant Boolean value.
Once you have a network you can :
Compute the effects of node perturbations (simulation)
Compute sets of node perturbations from a desired effect
(identification)
Comparison of approaches computing perturbations :
Stable Motifs [Zanudo, 2015]
Caspo-control [Videla, 2017]
ActoNet [Biane, 2018]

Stable Motifs
Input : a Boolean network
Output : a set of sets of node perturbations driving any initial state
to each of the network attractors
Example
m1
m2 m3
m4
∧ ∨
Attractor Perturbations
1111 m1 = 1
0011 m1 = 0

Stable Motifs
Example
m1
m2 m3
m4
∧ ∨
1111 m1 = 1
0011 m1 = 0
The perturbation m1 = 1 drives the system
to the stable attractor 1111

Stable Motifs
Example
m1
m2 m3
m4
∧ ∨
1111 m1 = 1
0011 m1 = 0
The perturbation m1 = 0 drives the system
to the stable attractor 0011

Caspo-control
Input : a Boolean network + a desired I/O behavior.
Output : a set of sets of node perturbations forcing the reachability,
from the input, of an attractor verifying the output.

Caspo-control
Example I/O : m1 = 0/m4 = 0
m1
m2 m3
m4
∧ ∨

Caspo-control
Example I/O : m1 = 0/m4 = 0
m1
m2 m3
m4
∧ ∨
# Perturbations
1 m2 = 1
2 m3 = 0

Comparison of Stable Motifs and Caspo-control approaches
Stable Motifs identiﬁes transient node perturbations forcing the
reachability of an attractor of the global system.
Caspo-control identiﬁes permanent node perturbations forcing the
reachability of a new attractor.
Example
m1 = 1
m1
m2 m3
m4
∧ ∨
Once the system is stabilized, the
perturbation can be relaxed.
m2 = 1
m1
m2 m3
m4
∧ ∨
If the perturbations are relaxed,
the system leaves the attractor.

Regulation perturbations of Boolean networks
Regulation perturbation
A regulation perturbation sets a molecule mi to a constant Boolean value
in the activation function of an other molecule mj .
Example
Set m1 to 1 in fm2
fm1 = m1
fm2 = m1∧ m3,
fm3 = m1 ∨ ¬m2
fm4 = m3
Deletion of m1 → m2, m1 → m3 conserved.
m1
m2 m3
m4
∧ ∨

ActoNet
Input : a Boolean network + a desired output + a modal operator
(possible ♦, impossible ¬Diamond).
Output : a set of sets of node/regulation perturbations forcing the
stability of the output.
Example ♦(m4 = 0)
m2 = 1
m1
m2 m3
m4
∧ ∨
m3 = 0
m1
m2 m3
m4
∧ ∨

ActoNet
Input : a Boolean network + a desired output + a modal operator
(possible ♦, impossible ¬♦).
Output : a set of sets of node/regulation perturbations forcing the
stability of the output.
Example ♦(m4 = 0)
m2 → m3 = 1
m1
m2 m3
m4
m1 → m3 = 0, m3 → m2 = 1
m1
m2 m3
m4
∧ ∨

Comparison of the three approaches
Stable Motifs: Control the global (from any initial state) reachability
of an attractor of the model with transient node perturbations.
Caspo-control: Control the partial (from a subset of initial states)
reachability of a new attractor including a desired output with
permanent node perturbations.
ActoNet : Control the stabilization (♦) or the de-stabilization (¬♦) of
an output with permanent node and regulation perturbations.

Application - Bladder cancer
Heterogeneous disease : different histological and molecular subtypes.
Precision medicine : definition of diseases at the molecular level
Problem : Propose a mechanistic definition of molecular subtypes
signatures.

Bladder model
From [Remy, 2015]

Wild-type behavior of the model
Wild-type model :
Multistability : Proliferation/growth arrest
Unique phenotype (one stable state) : Apoptosis, proliferation,
growth arrest
Oscillations : Proliferation/growth arrest

Different definitions of molecular signatures
In an environmental condition inducing multistability, find the
perturbations forcing the reachability of the proliferative stable attractor.
In an environmental condition inducing a unique phenotype apoptosis or
growth arrest, find the node perturbations forcing the reachability of a
proliferative stable attractor.
In an environmental condition inducing a unique phenotype apoptosis or
growth arrest, find the node perturbations forcing the possibility to reach a
proliferative stable attractor.
In an environmental condition inducing a phenotype apoptosis, find the
perturbations such that apoptosis is no longer stable.

Computation of signatures - Stable Motifs
In an environmental condition inducing multistability, ﬁnd the
perturbations forcing the reachability of the proliferative stable attractor.

Preliminary analysis of results

On going work
Development of algorithms for the computation of node and
regulation perturbations (modal operators)
Performance comparison ASP versus ILP for the computation of
solutions in ActoNet
Application of diﬀerent approaches to the Bladder cancer model
Building of a protocol for classifying computed signatures and
patients proﬁles based on epistasis

References - Boolean models
Fauré, A., Naldi, A., Chaouiya, C. & Thieffry, D. (2006).
Dynamical analysis of a generic Boolean model for the control of the mammalian
cell cycle.
Bioinformatics
Naldi, A., Carneiro, J., Chaouiya, C., & Thieffry, D. (2010).
Diversity and plasticity of Th cell types predicted from regulatory network
modelling.
PLoS computational biology
Flobak, ˚A., Baudot, A., Remy, E., Thommesen, L., Thieffry, D., Kuiper, M., &
Lægreid, A. (2015).
Discovery of drug synergies in gastric cancer cells predicted by logical modeling.
PLoS Computational Biology
Remy, E., Rebouissou, S., Chaouiya, C., Zinovyev, A., Radvanyi, F., & Calzone, L.
(2015).
A modeling approach to explain mutually exclusive and co-occurring genetic
alterations in bladder tumorigenesis.
Cancer research

References - Approaches
Zanudo, J. G., & Albert, R. (2015)
Cell fate reprogramming by control of intracellular network dynamics.
PLoS Computational Biology
Videla, S., Saez-Rodriguez, J., Guziolowski, C., & Siegel, A. (2017)
Caspo: a toolbox for automated reasoning on the response of logical signaling
networks families.
Bioinformatics
Biane, C. & Delaplace, F. (2018)
Causal reasoning on Boolean control networks based on abduction: theory and
application to Cancer drug discovery.
IEEE/ACM Transactions on Computational Biology and Bioinformatics

Acknowledgments

Thank you for your attention
Questions ?

Different approaches for the identification of perturbations in Boolean networks

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Different approaches for the identification of perturbations in Boolean networks