Stability of pattern formation in systems with dynamic source regions

TL;DR

This paper investigates how gene expression patterns stabilize in systems with dynamic source regions using a reaction-diffusion model, revealing phase transitions and stability conditions for various gene regulatory motifs.

Contribution

It introduces an analytical model explaining pattern stabilization and phase transitions in gene expression systems with dynamic source regions.

Findings

Identifies phase transition between indeterminate and stable patterning.

Provides analytical conditions for pattern stability across gene network motifs.

Explains domain dynamics in single- and two-gene systems.

Abstract

We explain the principles of gene expression pattern stabilization in systems of interacting, diffusible morphogens, with dynamically established source regions. Using a reaction-diffusion model with step-function production term, we identify the phase transition between low-precision indeterminate patterning and the phase in which a traveling, well-defined contact zone between two domains is formed. Our model analytically explains single- and two-gene domain dynamics and provides pattern stability conditions for all possible two-gene regulatory network motifs.