Sensitivity and control analysis of periodically forced reaction networks using the Green's function method.

Area of Science:

• Systems Biology
• Biochemical Engineering
• Dynamical Systems Analysis

Background:

• Periodic processes in dynamical systems often exhibit unbounded sensitivity coefficients over time.
• Analyzing parameter sensitivities in periodically forced reaction networks is crucial for understanding complex biological and chemical systems.
• Existing methods face challenges in calculating meaningful sensitivity coefficients for long-term periodic behavior.

Purpose of the Study:

• To develop a general framework for sensitivity and control analysis of periodically forced reaction networks.
• To derive a control-matrix operator equation applicable to metabolic pathways and other reaction networks.
• To provide a method for calculating sensitivity coefficients that remain bounded over time.

Main Methods:

• Introduction of a relative time or phase variable to handle unbounded coefficients.
• Application of the Green's function method to define sensitivity coefficients via integral control operators.
• Derivation of a general control-matrix operator equation based on network connectivity and summation relationships.

Main Results:

• A general control-matrix operator equation for periodically forced reaction networks was derived.
• The method successfully defines bounded sensitivity coefficients using integral control operators.
• Analysis of high and low forcing frequency cases, as well as simultaneous modulation of enzyme activities and frequency, was performed.

Conclusions:

• The developed framework offers a robust method for sensitivity and control analysis in periodically forced reaction networks.
• The integral control operator approach effectively addresses the unboundedness issue of traditional sensitivity coefficients.
• This work provides valuable tools for understanding and manipulating complex reaction systems, including metabolic pathways.