Use of implicit methods from general sensitivity theory to develop a systematic approach to metabolic control. II....

Area of Science:

• Biochemistry
• Systems Biology
• Metabolic Control Theory

Background:

• General sensitivity theory provides a matrix algebra to link global and local properties in sequential reactions.
• Complex biochemical systems exhibit linear dependencies, hindering direct property relationships.
• Existing metabolic control theory (MCT) and biochemical systems theory (BST) have limitations in analyzing these dependencies.

Purpose of the Study:

• To adapt matrix algebra for analyzing conserved cycles and branched pathways.
• To demonstrate how modified algebra relates global system properties to local enzyme properties.
• To generalize existing metabolic control theory theorems for complex pathways.

Main Methods:

• Application of a generalized matrix algebra to conserved cycles and branched pathways.
• Modification of the algebra to account for linear dependencies in metabolite concentrations and fluxes.
• Development of rules for constructing matrices applicable to arbitrary systems of cycles and branches.

Main Results:

• The modified matrix algebra successfully relates global properties to local enzyme properties in conserved cycles and branched pathways.
• Elasticities in conserved cycles are modified by linear dependencies.
• Branched pathways introduce new matrix elements involving flux ratios, unifying MCT theorems as special cases.

Conclusions:

• The generalized implicit approach offers a more direct comparison with explicit methods like BST.
• The developed matrix algebra provides a unified framework for analyzing complex metabolic pathways.
• This work advances the understanding of metabolic regulation in intricate biological systems.