Macroscopic Fluctuation-Response Theory and Its Use for Gene Regulatory Networks.

Area of Science:

• Theoretical physics
• Statistical mechanics
• Systems biology

Background:

• Gaussian macroscopic fluctuation theory is crucial for understanding noise in nonequilibrium systems.
• Stationary fluctuations and linear response are key characteristics of these systems.

Purpose of the Study:

• To derive exact fluctuation-response relations for nonequilibrium systems.
• To enable experimental determination of system dynamics and noise properties.
• To apply the theory to gene regulatory networks.

Main Methods:

• Derivation of exact fluctuation-response relations.
• Linking power spectral density of fluctuations to linear response.
• Reconstruction of linearized dynamics kernel and diffusion matrix.
• Application to gene regulatory networks with negative feedback.

Main Results:

• Established exact fluctuation-response relations for stable nonequilibrium steady states.
• Demonstrated experimental determination of dynamics and diffusion matrix.
• Derived an explicit internal-external noise decomposition for power spectral density.
• Included cross-correlations in the analysis for general networks.

Conclusions:

• The developed theory provides a comprehensive framework for analyzing noise in a wide range of nonequilibrium systems.
• The method allows for detailed characterization of system dynamics and noise sources.
• Applicable to complex biological systems like gene regulatory networks.