Multistability of small zero-one reaction networks.

Area of Science:

• Biochemistry
• Systems Biology
• Chemical Kinetics

Background:

• Zero-one biochemical reaction networks are fundamental to cellular signaling pathways, particularly those involving protein phosphorylation.
• Multistability in these networks is a critical dynamic feature that underpins cellular decision-making processes.
• Understanding multistability in simplified network structures is key to deciphering complex biological functions.

Purpose of the Study:

• To explore and define the conditions for multistability in small zero-one biochemical reaction networks.
• To identify the minimal network size and complexity required for nondegenerate multistationarity.
• To develop systematic methods for detecting multistationarity in these systems.

Main Methods:

• Application of theorems derived from Brouwer degree theory.
• Utilizing principles from real algebraic geometry.
• Employing computational tools from real algebraic geometry for network analysis.

Main Results:

• One-dimensional zero-one networks admit at most one stable positive steady state.
• Two-dimensional zero-one networks with up to three species exhibit at most one stable positive steady state or only degenerate states.
• The smallest zero-one networks exhibiting nondegenerate multistationarity/multistability possess three species and five/six reactions, and are three-dimensional.

Conclusions:

• Characterization of steady-state behavior in low-dimensional zero-one networks provides foundational insights.
• The identification of minimal network structures for multistability advances the understanding of biological complexity.
• A systematic computational approach is established for detecting nondegenerate multistationarity in biochemical networks.