Mayer-Type Optimal Control of Probabilistic Boolean Control Network With Uncertain Selection Probabilities.

Area of Science:

• Control Theory
• Computational Biology
• Network Science

Background:

• Probabilistic Boolean control networks (PBCNs) are increasingly used to model complex biological systems.
• Uncertainty in selection probabilities poses a significant challenge for controlling these networks.
• Existing control methods often struggle to account for probabilistic transitions and state variable dynamics.

Purpose of the Study:

• To develop an optimal control framework for PBCNs with Beta-distributed selection probabilities.
• To address uncertainty in both selection probabilities and state variable transitions.
• To formulate the problem as a solvable multistage decision problem.

Main Methods:

• Formulation of a Mayer-type optimal control problem for PBCNs.
• Definition of a cost function based on expectation over probabilities and transitions.
• Application of dynamic programming and a novel semitensor product-based optimization algorithm.

Main Results:

• An equivalent formulation of the optimal control problem as a multistage decision problem.
• A novel optimization algorithm for solving the identified problem.
• Demonstration of the framework's effectiveness using a biological model of apoptosis protein.

Conclusions:

• The proposed framework and algorithms are effective and feasible for optimal control of PBCNs with probabilistic uncertainty.
• The study provides a robust method for analyzing and controlling complex biological networks.
• This work advances the application of optimal control theory in computational biology.