Employing Sparse Optimal Linear Feedback Control to Identify Key Bacterial Species for Gut Microbiome Stabilization

Background: By understanding which bacteria play an important role in enhancing gut microbiome stability, more targeted therapeutic designs can be developed. Objective: This study aims to identify the most influential bacterial species for gut microbiome stabilization and design frugal optimal feedback control strategies using a data-driven framework that combines the Sparsity-Promoting Linear Quadratic Regulator (LQRSP), Controllability Gramian analysis, and Network Theory (graph analysis). Methods: Accordingly, this study employs the Sparsity-Promoting Linear Quadratic Regulator (LQRSP) across a diverse range of γ values (γ = 0.05, γ = 44.58, and γ = 49.84), alongside the Linear Quadratic Regulator (LQR) (γ = 0) and additional supporting methodologies, including Controllability Gramian analysis and Network Theory (graph analysis). Results: The findings indicate that six bacterial species may contribute to the prevention and management of gut-related diseases. Controllability Gramian analysis identified five species with high controllability, while Network Theory supported the selection of Bacteroides uniformis despite its lower index. Step and impulse disturbance simulations further confirmed the effectiveness of the proposed controllers. Conclusion: The results indicate a significant difference in disturbance robustness between the controlled and uncontrolled systems, with a critical sparsity threshold identified at γ ≈ 40. These findings provide a quantitative foundation for targeted and systematic intervention strategies in gut microbiome modulation, with promising implications for precision medicine and the prevention of gut-related diseases.