A GRAPH PARTITIONING APPROACH TO PREDICTING PATTERNS IN LATERAL INHIBITION SYSTEMS.

Area of Science:

• Computational biology
• Mathematical modeling
• Systems biology

Background:

• Cells communicate via contact signaling, leading to spatial patterns.
• Understanding these patterns is crucial for developmental biology and disease.
• Previous models often simplify complex cell interactions.

Purpose of the Study:

• To develop a mathematical framework for predicting spatial patterns in cell networks with inhibitory signaling.
• To analyze the stability of these predicted patterns.
• To investigate the role of noise in pattern formation.

Main Methods:

• Representing cell networks as graphs with vertices for cell dynamics and edges for signaling.
• Utilizing equitable graph partitions to define cell classes with uniform fates.
• Applying monotone systems theory to prove pattern existence.
• Employing block decomposition and small-gain criteria for stability analysis.
• Using modal decomposition to study stochastic models.

Main Results:

• Demonstrated that equitable graph partitions predict cell fates.
• Proved the existence of stable patterns where cells in the same class share a fate.
• Established a stability criterion based on cell input-output properties.
• Showed that noise can increase the parameter range for pattern formation in stochastic models.

Conclusions:

• Equitable partitions provide a robust method for predicting cell fate patterns in inhibitory networks.
• The developed stability criterion ensures reliable pattern formation.
• Stochasticity, often considered disruptive, can be beneficial for pattern emergence.