A Deficiency-Based Approach to Parametrizing Positive Equilibria of Biochemical Reaction Systems

Area of Science:

• Systems Biology
• Biochemical Reaction Networks
• Chemical Kinetics

Background:

• Generalized mass-action systems are fundamental in modeling biochemical processes.
• Understanding the set of positive equilibria is crucial for analyzing system dynamics.
• Parametrization of equilibria aids in studying multistationarity and robustness.

Purpose of the Study:

• To establish conditions guaranteeing a parametrization of positive equilibria in generalized mass-action systems.
• To connect network properties (deficiency, reversibility) to equilibrium set characteristics.
• To apply these findings to specific biochemical pathways.

Main Methods:

• Analysis of generalized chemical reaction networks.
• Utilizing concepts of effective and kinetic deficiency.
• Application of network translation for classical mass-action systems.

Main Results:

• For networks with effective deficiency zero, positive equilibria equal complex-balanced equilibria.
• For weakly reversible networks with kinetic deficiency zero, equilibria are non-empty and positively parametrized.
• Demonstrated application to EnvZ-OmpR and WNT signaling pathways.

Conclusions:

• The derived conditions provide a powerful tool for analyzing generalized mass-action systems.
• Parametrization facilitates the study of multistationarity and absolute concentration robustness.
• The findings offer insights into the behavior of complex biological signaling networks.