Response experiments for nonlinear systems with application to reaction kinetics and genetics

Area of Science:

• Complex Systems Analysis
• Physical Chemistry
• Biochemistry
• Genetics

Background:

• Existing methods for analyzing complex systems often rely on linearization techniques.
• Linearization can lead to unpredictable results due to error amplification when combined with measurement errors.
• A unified approach is needed to analyze diverse systems, including physical, chemical, and biological ones.

Purpose of the Study:

• To propose a unified response experiment for complex systems.
• To develop a method that avoids linearization of evolution equations.
• To provide a more consistent approach for analyzing system dynamics and rate coefficients.

Main Methods:

• The proposed method utilizes labeled and unlabeled species with identical kinetic and transport properties (neutrality assumption).
• The experiment preserves total fluxes, varying only the fractions of labeled compounds in input and output.
• A linear integral superposition law is derived, connecting input and output fractions, valid for various system types.

Main Results:

• A linear superposition law is established, applicable to homogeneous, inhomogeneous, and systems with hidden variables, even under nonlinear dynamics.
• The proposed method demonstrates more consistent results compared to linearization techniques, particularly concerning experimental and linearization errors.
• Error amplification or compensation effects observed with linearization are avoided across a broad range of input fractions.

Conclusions:

• The developed response experiment and superposition law offer a robust framework for analyzing complex systems without linearization.
• This approach mitigates issues associated with error interference, leading to more reliable estimations of rate coefficients.
• The method holds significant potential for advancing the study of intricate physical, chemical, and biological processes.