Robust Stabilizing Control of Perturbed Biological Networks via Coordinate Transformation and Algebraic Analysis

Area of Science:

• Systems Biology
• Control Theory
• Computational Biology

Background:

• Biological systems can be modeled using Boolean networks (BNs).
• Mutations can disrupt BN dynamics, preventing stabilization to desired attractors.
• Robust control is essential for maintaining biological system stability.

Purpose of the Study:

• To develop a robust stabilizing control strategy for populations of Boolean networks with perturbed dynamics.
• To ensure nominal BNs converge to a desired attractor and perturbed BNs to their closest possible attractors.

Main Methods:

• A two-step control strategy is proposed.
• Step 1: Transform and reduce the nominal BN to a sub-BN, applying feedback vertex set (FVS) control.
• Step 2: Apply derived control inputs and account for mutated nodes to identify residual dynamics, using canalization effects for additional control.

Main Results:

• The proposed control scheme successfully stabilizes nominal BNs to the desired attractor.
• Perturbed BNs are guided to their closest possible attractors, demonstrating robustness.
• Numerical experiments on random and complex biological networks validate the control scheme's performance.

Conclusions:

• The developed robust control strategy effectively manages perturbations in Boolean network models of biological systems.
• This method offers a way to achieve stable system dynamics even in the presence of mutations.
• The findings have implications for understanding and controlling complex biological processes.