Control involving metabolism and gene expression: the square-matrix method for modular decomposition

Area of Science:

• Biochemistry
• Molecular Biology
• Systems Biology

Background:

• DNA supercoiling is crucial for gene expression and is regulated by topoisomerases.
• The free-energy of ATP hydrolysis plays a role in this regulatory process.
• Metabolic control analysis provides a framework for understanding complex biological systems.

Purpose of the Study:

• To analyze the control of DNA supercoiling by ATP hydrolysis within a hierarchical gene expression system.
• To extend the square-matrix method for analyzing interconnected metabolic pathways to this hierarchical control system.
• To investigate the relationship between control coefficients and elasticity coefficients in this system.

Main Methods:

• Analysis of DNA supercoiling control through three levels: mRNA synthesis/breakdown, protein synthesis/breakdown, and DNA supercoiling/relaxation.
• Application and extension of the square-matrix method for metabolic control analysis.
• Derivation of control coefficients and elasticity coefficients for the hierarchical system.

Main Results:

• The matrix of control coefficients was found to be the inverse of the elasticity matrix.
• This inverse relationship holds true for the hierarchical control system of DNA supercoiling.
• An implicit method for matrix inversion was demonstrated for a two-level hierarchy, simplifying analysis.

Conclusions:

• The square-matrix method effectively describes the hierarchical control of DNA supercoiling.
• The inverse relationship between control and elasticity matrices provides insights into system regulation.
• The implicit method offers a more tractable approach for analyzing complex, multi-level biological systems.