Output Stabilizing Control of Complex Biological Networks Based on Boolean Algebra Analysis

Abstract

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.