An Efficient Approach Towards the Source-Target Control of Boolean Networks

Abstract

We study the problem of computing a minimal subset of nodes of a given asynchronous Boolean network that need to be perturbed in a single-step to drive its dynamics from an initial state to a target steady state (or attractor), which we call the source-target control of Boolean networks. Due to the phenomenon of state-space explosion, a simple global approach that performs computations on the entire network, may not scale well for large networks. We believe that efficient algorithms for such networks must exploit the structure of the networks together with their dynamics. Taking this view, we derive a decomposition-based solution to the minimal source-target control problem which can be significantly faster than the existing approaches on large networks. We then show that the solution can be further optimised if we take into account appropriate information about the source state. We apply our solutions to both real-life biological networks and randomly generated networks, demonstrating the efficiency and efficacy of our approach.

Controlling Large Boolean Networks with Temporary and Permanent Perturbations

“…Otherwise, one can simply choose a control C such that C(s) ∈ A in each case. In [19,25], we developed a method for the efficient minimal simultaneous control of Boolean networks, where given a source state s and an attractor of TS BN of BN the control C is applied simultaneously and instantaneously to s so that the dynamics of BN eventually reaches A and C is minimal. Such a control is a special case of the temporary control defined above with t = 0.…”

“…Such a control is a special case of the temporary control defined above with t = 0. Since the minimal simultaneous control problem of [19,25] is computationally difficult (PSPACE-hard), the control problems that we study here, defined above, are also computationally difficult (at least PSPACE-hard). Thus, efficient algorithms to solve these problems are highly unlikely.…”

“…Thus, efficient algorithms to solve these problems are highly unlikely. However, we showed in [19,25], that if the BNs are structurally well-behaved (e.g., the graph of the BN has small strongly connected components (SCCs), with a small number of interdependencies between the SCCs etc. ), we can have relatively efficient methods to compute the attractors and basins of such BNs.…”

“…Since it is known that real-life BNs corresponding to GRNs are reasonably well-behaved, this led us to develop efficient algorithms for computing the weak and strong basins of desired target attractors of such BNs by decomposing the BNs based on the SCCs of their graphs. The algorithms we develop here will crucially use the procedures developed in [19,25] for the computation of the weak and strong basins of the target attractors, denoted as Comp WB(A) and Comp SB(A) [19,25], respectively. These then applied to real-life networks can result in a significant level of efficiency as will be demonstrated later.…”

Sequential Temporary and Permanent Control of Boolean Networks

“…Instantaneous perturbations are applied instantaneously; temporary perturbations are applied for sufficient time steps and then released; permanent perturbations are applied for all the following steps. So far, we have developed methods for the minimal one-step instantaneous, temporary and permanent control (OI, OT and OP) [21,22,26] and the attractor-based sequential instantaneous control (ASI) [11]. In this work, we focus on the attractor-based sequential temporary and permanent control (AST and ASP).…”