Robust Output Tracking of Boolean Control Networks Subject to Stochastic Function Perturbations

Area of Science:

• Systems Biology
• Control Theory
• Computational Biology

Background:

• Boolean control networks (BCNs) are used to model complex biological systems.
• Stochastic function perturbations (SFPs) can introduce uncertainty into BCN models.
• Understanding the impact of SFPs is crucial for reliable BCN analysis.

Purpose of the Study:

• To investigate the influence of SFPs on the output tracking of BCNs.
• To develop criteria for assessing SFP impact on BCN state transitions.
• To establish conditions for robust output tracking in the presence of SFPs.

Main Methods:

• Establishing the transition probability matrix for BCNs with SFPs.
• Developing a criterion to detect SFP influence on state transitions.
• Constructing a perturbed parameterized set based on original BCNs and SFPs.
• Deriving necessary and sufficient conditions for robust output tracking.

Main Results:

• A criterion is presented to determine if SFPs affect BCN state transitions.
• Necessary and sufficient conditions for finite-time and asymptotic output tracking under SFPs are derived.
• The theoretical results are validated using a Boolean model of the lac operon in E. coli.

Conclusions:

• SFPs can significantly influence BCN behavior and output tracking.
• The developed methods provide a framework for analyzing and ensuring robust control in perturbed BCNs.
• This research offers insights into the resilience of biological regulatory networks to stochastic noise.