Introduction to 'Recent progress and open frontiers in Turing's theory of morphogenesis'

Area of Science:

• Physical Sciences
• Chemical Sciences
• Biological Sciences

Background:

• Turing's theory, focusing on reaction-diffusion systems, explains pattern formation from initially homogeneous mixtures.
• Despite extensive research for over 50 years, fundamental questions in Turing's theory of morphogenesis remain unresolved.
• This theme issue addresses the current state and future directions of pattern formation research.

Purpose of the Study:

• To place Turing's theory of pattern formation in a modern context.
• To discuss current frontiers in reaction-diffusion systems and related pattern formation theories.
• To highlight the relevance and limitations of Turing's mechanism in real morphogenesis.

Main Methods:

• Reviewing foundational aspects of pattern formation in reaction-diffusion systems.
• Highlighting ongoing work in chemical, synthetic, and developmental biology settings.
• Surveying recent mathematical research extending Turing's original theory.

Main Results:

• Discussion of current frontiers in pattern formation theory.
• Identification of gaps in matching theoretical models to biological reality.
• Exploration of advanced mathematical models for complex settings.

Conclusions:

• Consolidating current research frontiers in Turing's theory of morphogenesis.
• Highlighting promising future research directions.
• Emphasizing the need to bridge theoretical advancements with experimental observations.