Concurrency in Boolean networks

Thomas Chatain (1, 2, 3) , Stefan Haar (2, 3) , Juraj Kolčák (2, 3) , Loïc Paulevé (4, 5) , Aalok Thakkar (6, 2)

1 ENS Paris Saclay - Ecole Normale Supérieure Paris-Saclay
2 MEXICO - Modeling and Exploitation of Interaction and Concurrency
3 LSV - Laboratoire Spécification et Vérification [Cachan]
4 BioInfo - LRI - Bioinformatique (LRI)
5 LaBRI - Laboratoire Bordelais de Recherche en Informatique
6 University of Pennsylvania

Boolean networks (BNs) are widely used to model the qualitative dynamics of biological systems. Besides the logical rules determining the evolution of each component with respect to the state of its regulators, the scheduling of component updates can have a dramatic impact on the predicted behaviours. In this paper, we explore the use of Read (contextual) Petri Nets (RPNs) to study dynamics of BNs from a concurrency theory perspective. After showing bi-directional translations between RPNs and BNs and analogies between results on synchronism sensitivity, we illustrate that usual updating modes for BNs can miss plausible behaviours, i.e., incorrectly conclude on the absence/impossibility of reaching specific configurations. We propose an encoding of BNs capitalizing on the RPN semantics enabling more behaviour than the generalized asynchronous updating mode. The proposed encoding ensures a correct abstraction of any multivalued refinement, as one may expect to achieve when modelling biological systems with no assumption on its time features.

Keywords: Models of concurrency; Systems Biology; Discrete dynamical systems; Reachability; Synchronism

Domains: Formal Languages and Automata Theory [cs.FL]; Logic in Computer Science [cs.LO]; Bioinformatics [q-bio.QM]

Thomas Chatain, Stefan Haar, Juraj Kolčák, Loïc Paulevé, Aalok Thakkar. Concurrency in Boolean networks. Natural Computing, 2019, ⟨10.1007/s11047-019-09748-4⟩. ⟨hal-01893106v1⟩