Controllability of Boolean networks via input controls under Harvey's update scheme

Area of Science:

• Systems Biology
• Control Theory
• Computational Neuroscience

Background:

• Boolean networks are widely used to model complex biological systems.
• Controlling these networks is crucial for understanding and manipulating system behavior.
• Harvey's update scheme offers a probabilistic approach to Boolean network dynamics.

Purpose of the Study:

• To propose a novel model for Boolean control networks under Harvey's stochastic update scheme.
• To develop a framework for analyzing the controllability of these networks.
• To establish conditions for achieving desired system states using different control strategies.

Main Methods:

• Utilizing the semi-tensor product approach to convert the Boolean control network into a discrete-time linear representation.
• Deriving a general formula for the control-dependent network transition matrix.
• Analytically discussing controllability based on discrete-time dynamics and reachable sets.

Main Results:

• A discrete-time linear model for Boolean control networks with Harvey's update scheme is presented.
• Necessary and sufficient conditions for controllability are derived for free Boolean control sequences, input control networks, and closed-loop control.
• The effectiveness and feasibility of the proposed control scheme are demonstrated through examples.

Conclusions:

• The proposed semi-tensor product approach effectively models and analyzes Boolean control networks under Harvey's update scheme.
• The derived controllability conditions provide a theoretical foundation for designing effective control strategies.
• This work contributes to the advancement of control methodologies for complex biological systems.