Stochastic gene expression: density of defects frozen into permanent Turing patterns

Area of Science:

• Developmental biology
• Systems biology
• Biophysics

Background:

• Biological Turing patterns are fundamental to morphogenesis.
• Pattern formation can be disrupted by defects, impacting development.
• The rate of pattern initiation influences defect density.

Purpose of the Study:

• To estimate the density of defects in biological Turing patterns initiated at a finite rate.
• To understand the relationship between transition rate and defect formation.
• To identify methods for achieving defect-free Turing patterns.

Main Methods:

• Analysis of defect density in biological Turing patterns.
• Modeling the effect of gene expression self-locking on pattern stability.
• Investigating the scaling of defect density with transition rate.
• Exploring strategies for defect-free pattern formation through controlled gene activation.

Main Results:

• Defect density scales with the fourth root of the transition rate, indicating a weak dependence.
• Self-locking of gene expression stabilizes patterns and their defects.
• Slow activator spread velocity below a threshold can yield defect-free patterns.
• Defects act as permanent records of the pattern transition, influencing lifelong characteristics.

Conclusions:

• Defect formation is an intrinsic aspect of finite-rate biological Turing pattern initiation.
• Slowing the transition rate alone is insufficient to eliminate defects during morphogenesis.
• Spatially inhomogeneous gene activation, specifically controlling activator spread velocity, offers a viable strategy for generating defect-free patterns.