Research Article: Identification of bifurcation transitions in biological regulatory networks using Answer-Set Programming

Date Published: July 20, 2017

Publisher: BioMed Central

Author(s): Louis Fippo Fitime, Olivier Roux, Carito Guziolowski, Loïc Paulevé.


Numerous cellular differentiation processes can be captured using discrete qualitative models of biological regulatory networks. These models describe the temporal evolution of the state of the network subject to different competing transitions, potentially leading the system to different attractors. This paper focusses on the formal identification of states and transitions that are crucial for preserving or pre-empting the reachability of a given behaviour.

In the context of non-deterministic automata networks, we propose a static identification of so-called bifurcations, i.e., transitions after which a given goal is no longer reachable. Such transitions are naturally good candidates for controlling the occurrence of the goal, notably by modulating their propensity. Our method combines Answer-Set Programming with static analysis of reachability properties to provide an under-approximation of all the existing bifurcations.

We illustrate our discrete bifurcation analysis on several models of biological systems, for which we identify transitions which impact the reachability of given long-term behaviour. In particular, we apply our implementation on a regulatory network among hundreds of biological species, supporting the scalability of our approach.

Our method allows a formal and scalable identification of transitions which are responsible for the lost of capability to reach a given state. It can be applied to any asynchronous automata networks, which encompass Boolean and multi-valued models. An implementation is provided as part of the Pint software, available at

The online version of this article (doi:10.1186/s13015-017-0110-3) contains supplementary material, which is available to authorized users.

Partial Text

The emerging complexity of dynamics of biological networks, and in particular of signalling and gene regulatory networks, is mainly driven by the interactions between the species, and the numerous feedback circuits they generate [1–4]. One of the prominent and fascinating features of cells is their capability to differentiate: starting from a multi-potent state (for instance, a stem cell), cellular processes progressively confine the cell dynamics in a narrow state space, an attractor. Deciphering those decision processes is a tremendous challenge, with important applications in cell reprogramming and regenerative medicine.

We evaluated our method in three real biological networks case studies that show differentiation capabilities. We selected networks that show at least two attractors reachable from the same initial state. For each network, we supplied a goal state representing one attractor. Thus, the goal state is a state reachable from the selected initial state. Because at least one attractor is reachable from the same selected initial state, transitions that lead to the other attractors are by definition bifurcation transitions. We aimed at identifying transitions that cause a bifurcation for the reachability of the goal state. The three case studies used are briefly described in the following paragraphs.

This paper presents an original combination of computational techniques to identify transitions of a dynamical system that can remove its capability to reach a (set of) states of interest. Our methodology combines static analysis of ANs dynamics, partial order representations of the state space, and constraint programming to efficiently enumerate those bifurcations. To our knowledge, this is the first integrated approach for deriving bifurcation transitions from concurrent models, and ANs in particular.




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