This article presents attractor-transition control of complex biological networks represented by Boolean networks (BNs) wherein the BN is steered from a prescribed initial attractor toward a desired one. The proposed approach leverages the similarity between attractors and Boolean algebraic properties embedded in the underlying state transition equations. To enhance the clarity of expression regarding stabilization toward the desired attractor, a simple coordinate transformation is performed on the considered BN. Based on the characteristics of transformed state equations, self-stabilizing state variables requiring no control efforts are derived in the first. Next, by applying the feedback vertex set (FVS) control scheme, control inputs stabilizing the remaining state variables are determined. The proposed control scheme exhibits versatility by accommodating both fixed-point and cyclic attractors. We validate the effectiveness of the proposed strategy through extensive numerical experiments conducted on random BNs as well as complex biological systems. In adherence to the reproducible research initiative, detailed results of numerical experiments and all the implementation codes are provided on the authors' website: https://github.com/choonlog/AttractorTransition.

Output stabilizing control of biological systems is of utmost importance in systems biology since key phenotypes of biological networks are often encoded by a small subset of their phenotypic marker nodes. This study addresses the challenge of output stabilizing control for complex biological systems modeled by Boolean networks (BNs). The objective is to identify a set of constant control inputs capable of driving the BN toward a desirable long-term behavior with respect to specified output nodes. Leveraging the algebraic properties of Boolean logic, we develop a novel control algorithm that reformulates the output stabilizing control problem into a simple graph theoretic problem involving auxiliary BNs, the scale of which significantly decreases compared to the original BN. The proposed method ensures superiority over previous results in terms of both the number of control inputs and computational loads, since it searches for the solution within the reduced BNs while retaining essential structures needed for output stabilization. The efficacy of the proposed control scheme is demonstrated through extensive numerical experiments with complex random BNs and real biological networks. To support the reproducible research initiative, detailed results of numerical experiments are provided in the supplementary material, and all the implementation codes are made accessible at https://github.com/choonlog/OutputStabilization.

This article investigates robust stabilizing control of biological systems modeled by Boolean networks (BNs). A population of BNs is considered where a majority of BNs have the same BN dynamics, but some BNs are inflicted by mutations damaging particular nodes, leading to perturbed dynamics that prohibit global stabilization to the desired attractor. The proposed control strategy consists of two steps. First, the nominal BN is transformed and curtailed into a sub-BN via a simple coordinate transformation and network reduction associated with the desired attractor. The feedback vertex set (FVS) control is then applied to the reduced BN to determine the control inputs for the nominal BN. Next, the control inputs derived in the first step and mutated nodes are applied to the nominal BN so as to identify residual dynamics of perturbed BNs, and additional control inputs are selected according to the canalization effect of each node. The overall control inputs are applied to the BN population, so that the nominal BN converges to the desired attractor and perturbed BNs to their own attractors that are the closest possible to the desired attractor. The performance of the proposed robust control scheme is validated through numerical experiments on random BNs and a complex biological network.

MOTIVATION: Cellular behavior is determined by complex non-linear interactions between numerous intracellular molecules that are often represented by Boolean network models. To achieve a desired cellular behavior with minimal intervention, we need to identify optimal control targets that can drive heterogeneous cellular states to the desired phenotypic cellular state with minimal node intervention. Previous attempts to realize such global stabilization were based solely on either network structure information or simple linear dynamics. Other attempts based on non-linear dynamics are not scalable. RESULTS: Here, we investigate the underlying relationship between structurally identified control targets and optimal global stabilizing control targets based on non-linear dynamics. We discovered that optimal global stabilizing control targets can be identified by analyzing the dynamics between structurally identified control targets. Utilizing these findings, we developed a scalable global stabilizing control framework using both structural and dynamic information. Our framework narrows down the search space based on strongly connected components and feedback vertex sets then identifies global stabilizing control targets based on the canalization of Boolean network dynamics. We find that the proposed global stabilizing control is superior with respect to the number of control target nodes, scalability, and computational complexity. AVAILABILITY AND IMPLEMENTATION: We provide a GitHub repository that contains the DCGS framework written in Python as well as biological random Boolean network datasets (https://github.com/sugyun/DCGS). SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.