Parallel One-Step Control of Parametrised Boolean Networks

Luboš Brim, Samuel Pastva, David Šafránek and Eva Šmijáková
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Luboš Brim: Faculty of Informatics, Masaryk University, 60200 Brno, Czech Republic
Samuel Pastva: Faculty of Informatics, Masaryk University, 60200 Brno, Czech Republic
David Šafránek: Faculty of Informatics, Masaryk University, 60200 Brno, Czech Republic
Eva Šmijáková: Faculty of Informatics, Masaryk University, 60200 Brno, Czech Republic

Mathematics, 2021, vol. 9, issue 5, 1-16

Abstract: Boolean network (BN) is a simple model widely used to study complex dynamic behaviour of biological systems. Nonetheless, it might be difficult to gather enough data to precisely capture the behavior of a biological system into a set of Boolean functions. These issues can be dealt with to some extent using parametrised Boolean networks (ParBNs), as this model allows leaving some update functions unspecified. In our work, we attack the control problem for ParBNs with asynchronous semantics. While there is an extensive work on controlling BNs without parameters, the problem of control for ParBNs has not been in fact addressed yet. The goal of control is to ensure the stabilisation of a system in a given state using as few interventions as possible. There are many ways to control BN dynamics. Here, we consider the one-step approach in which the system is instantaneously perturbed out of its actual state. A naïve approach to handle control of ParBNs is using parameter scan and solve the control problem for each parameter valuation separately using known techniques for non-parametrised BNs. This approach is however highly inefficient as the parameter space of ParBNs grows doubly exponentially in the worst case. We propose a novel semi-symbolic algorithm for the one-step control problem of ParBNs, that builds on symbolic data structures to avoid scanning individual parameters. We evaluate the performance of our approach on real biological models.

Keywords: boolean networks; parameters; control; reprogramming; attractors; perturbations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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