Controlling large Boolean networks with single-step perturbations

Abstract

Motivation The control of Boolean networks has traditionally focussed on strategies where the perturbations are applied to the nodes of the network for an extended period of time. In this work, we study if and how a Boolean network can be controlled by perturbing a minimal set of nodes for a single-step and letting the system evolve afterwards according to its original dynamics. More precisely, given a Boolean network (BN), we compute a minimal subset Cmin of the nodes such that BN can be driven from any initial state in an attractor to another ‘desired’ attractor by perturbing some or all of the nodes of Cmin for a single-step. Such kind of control is attractive for biological systems because they are less time consuming than the traditional strategies for control while also being financially more viable. However, due to the phenomenon of state-space explosion, computing such a minimal subset is computationally inefficient and an approach that deals with the entire network in one-go, does not scale well for large networks. Results We develop a ‘divide-and-conquer’ approach by decomposing the network into smaller partitions, computing the minimal control on the projection of the attractors to these partitions and then composing the results to obtain Cmin for the whole network. We implement our method and test it on various real-life biological networks to demonstrate its applicability and efficiency. Supplementary information Supplementary data are available at Bioinformatics online.

Scalable Control of Asynchronous Boolean Networks

“…To cope with this problem, we employ the 'divide and conquer' strategy to explore both the structural and dynamical properties of a BN. As shown in Table 1, we have developed efficient methods to solve the minimal one-step source-target control with instantaneous, temporary and permanent perturbations [8,9,11], the minimal sequential source-target control with instantaneous perturbations [4,5], as well as the target control with instantaneous perturbations [1]. Among these methods, sequential source-target control identifies a sequence of intermediate states and the associated perturbations.…”

Data Integration in Logic-based Models of Biological Mechanisms

“…Researchers compute a minimal subset of nodes (Cmin) in recent work that allows a BN to be driven from any initial state in an attractor to an attractor of interest by a single step perturbation of Cmin. In their method, they decompose the network into modules, compute the minimal control on the projection of the attractors to these modules, and then compose the results to obtain the global Cmin [52].…”

AEON: Attractor Bifurcation Analysis of Parametrised Boolean Networks

“…The third case is what we call a disordered attractor (or chaotic oscillation [ 32 ]), an attractor that is neither stable not periodically oscillating and in which the system may behave unpredictably, due to the nondeterminism of the asynchronous semantics of BNs. Attractors are particularly relevant in the context of biological modelling as they are used to represent differentiated cellular types or tissues (in the case of fixed points) [ 2 ] and biological rhythms or oscillations (in the case of cycles) [ 17 ].…”