Parallel One-Step Control of Parametrised Boolean Networks

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.

Robust Control of Partially Specified Boolean Networks

“…Instead of constructing a new graph for each perturbation, we model all perturbations in a single transition-labelled graph. We show that our approach scales well for highly unspecific models and outperforms the semi-symbolic approach from [46] primarily in terms of processable model size. On biologically relevant models, we also demonstrate that temporary and permanent perturbations are more robust compared to available one-step perturbations.…”

“…Otherwise, no fair run will visit it infinitely often, regardless of applied perturbations. It is therefore typically reasonable to only consider input valuations for which target is indeed an attractor state [46]. On the contrary, the permanent perturbation may induce the appearance of new attractors, including attractors containing the target state.…”

“…As such, most perturbations will correctly control the network only for some subset of input valuations. Depending on how large this subset is, we can then talk about robustness ρ of a one-step, permanent, or temporary perturbation q with respect to the network inputs [46]:…”

“…In [46], the control of partially specified BNs have been addressed for the first time. In particular, the paper introduced a method for one-step source-target control of BNs with logical parameters (encoding the partial specification of BNs).…”

Boolean Networks Models in Science and Engineering

“…In [5], Brim et al deal with the control problem for parametrized Boolean networks with asynchronous semantics. Parametrized Boolean networks represent Boolean models with partially unknown updating Boolean functions.…”